Aspen polymersunitopsv8 2-usr

Aspen Polymers
Unit Operations and Reaction Models

Version Number: V8.2
May 2013
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Contents
Introducing Aspen Polymers ...................................................................................1
About This Documentation Set ...........................................................................1
Related Documentation.....................................................................................2
Technical Support ............................................................................................3
1 Polymer Manufacturing Process Overview...........................................................5
About Aspen Polymers ......................................................................................5
Overview of Polymerization Processes.................................................................6
Polymer Manufacturing Process Steps .......................................................6
Issues of Concern in Polymer Process Modeling....................................................7
Monomer Synthesis and Purification .........................................................8
Polymerization .......................................................................................8
Recovery / Separation ............................................................................9
Polymer Processing ................................................................................9
Summary ..............................................................................................9
Aspen Polymers Tools .......................................................................................9
Component Characterization.................................................................. 10
Polymer Physical Properties ................................................................... 10
Polymerization Kinetics ......................................................................... 10
Modeling Data...................................................................................... 11
Process Flowsheeting............................................................................ 11
Defining a Model in Aspen Polymers ................................................................. 12
References .................................................................................................... 14
2 Polymer Structural Characterization .................................................................15
Polymer Structure .......................................................................................... 15
Polymer Structural Properties .......................................................................... 19
Characterization Approach............................................................................... 19
Component Attributes........................................................................... 20
References .................................................................................................... 20
3 Component Classification ..................................................................................21
Component Categories.................................................................................... 21
Conventional Components ..................................................................... 22
Polymers............................................................................................. 22
Oligomers ........................................................................................... 23
Segments............................................................................................ 24
Site-Based .......................................................................................... 24
Component Databanks.................................................................................... 25
Pure Component Databank.................................................................... 25
PC-SAFT Databank ............................................................................... 26
POLYPCSF Databank ............................................................................. 26
Contents iii

INITIATO Databank .............................................................................. 26
Segment Databank............................................................................... 26
Polymer Databank................................................................................ 27
Segment Methodology .................................................................................... 27
Specifying Components................................................................................... 28
Selecting Databanks ............................................................................. 28
Defining Component Names and Types ................................................... 28
Specifying Segments ............................................................................ 29
Specifying Polymers ............................................................................. 29
Specifying Oligomers ............................................................................ 30
Specifying Site-Based Components......................................................... 30
References .................................................................................................... 31
4 Polymer Structural Properties ...........................................................................33
Structural Properties as Component Attributes................................................... 33
Component Attribute Classes ........................................................................... 34
Component Attribute Categories ...................................................................... 35
Polymer Component Attributes............................................................... 35
Site-Based Species Attributes ................................................................ 44
User Attributes .................................................................................... 45
Component Attribute Initialization .................................................................... 46
Attribute Initialization Scheme ............................................................... 47
Component Attribute Scale Factors................................................................... 50
Specifying Component Attributes ..................................................................... 51
Specifying Polymer Component Attributes ............................................... 51
Specifying Site-Based Component Attributes ........................................... 51
Specifying Conventional Component Attributes ........................................ 52
Initializing Component Attributes in Streams or Blocks.............................. 52
Specifying Component Attribute Scaling Factors....................................... 53
References .................................................................................................... 53
5 Structural Property Distributions ......................................................................55
Property Distribution Types ............................................................................. 55
Distribution Functions ..................................................................................... 56
Schulz-Flory Most Probable Distribution................................................... 56
Stockmayer Bivariate Distribution .......................................................... 58
Distributions in Process Models ........................................................................ 58
Average Properties and Moments ........................................................... 58
Method of Instantaneous Properties........................................................ 60
Copolymerization ................................................................................. 64
Mechanism for Tracking Distributions................................................................ 65
Distributions in Kinetic Reactors ............................................................. 65
Distributions in Process Streams ............................................................ 67
Verifying the Accuracy of Distribution Calculations.................................... 68
Requesting Distribution Calculations ................................................................. 69
Selecting Distribution Characteristics ...................................................... 69
Displaying Distribution Data for a Reactor ............................................... 70
Displaying Distribution Data for Streams ................................................. 70
References .................................................................................................... 71
iv Contents

6 End-Use Properties............................................................................................73
Polymer Properties ......................................................................................... 73
Prop-Set Properties ........................................................................................ 73
End-Use Properties......................................................................................... 74
Relationship to Molecular Structure ........................................................ 75
Method for Calculating End-Use Properties ........................................................ 76
Intrinsic Viscosity ................................................................................. 77
Zero-Shear Viscosity ............................................................................ 77
Density of Copolymer ........................................................................... 78
Melt Index........................................................................................... 78
Melt Index Ratio................................................................................... 79
Calculating End-Use Properties ........................................................................ 79
Selecting an End-Use Property............................................................... 79
Adding an End-Use Property Prop-Set ..................................................... 79
References .................................................................................................... 79
7 Polymerization Reactions ..................................................................................81
Polymerization Reaction Categories .................................................................. 81
Step-Growth Polymerization .................................................................. 83
Chain-Growth Polymerization................................................................. 83
Polymerization Process Types .......................................................................... 84
Aspen Polymers Reaction Models...................................................................... 85
Built-in Models..................................................................................... 85
User Models......................................................................................... 86
References .................................................................................................... 86
8 Step-Growth Polymerization Model ...................................................................89
Summary of Applications................................................................................. 89
Step-Growth Processes ................................................................................... 90
Polyesters ........................................................................................... 90
Nylon-6............................................................................................... 96
Nylon-6,6............................................................................................ 98
Polycarbonate.................................................................................... 100
Reaction Kinetic Scheme ............................................................................... 101
Nucleophilic Reactions ........................................................................ 101
Polyester Reaction Kinetics.................................................................. 105
Nylon-6 Reaction Kinetics.................................................................... 111
Nylon-6,6 Reaction Kinetics ................................................................. 115
Melt Polycarbonate Reaction Kinetics .................................................... 122
Model Features and Assumptions ................................................................... 124
Model Predictions ............................................................................... 124
Phase Equilibria ................................................................................. 126
Reaction Mechanism........................................................................... 126
Model Structure ........................................................................................... 127
Reacting Groups and Species............................................................... 127
Reaction Stoichiometry Generation....................................................... 132
Model-Generated Reactions ................................................................. 133
User Reactions................................................................................... 138
User Subroutines ............................................................................... 140
Specifying Step-Growth Polymerization Kinetics ............................................... 155
Accessing the Step-Growth Model......................................................... 155
Contents v

Specifying the Step-Growth Model........................................................ 156
Specifying Reacting Components.......................................................... 156
Listing Built-In Reactions..................................................................... 157
Specifying Built-In Reaction Rate Constants........................................... 157
Assigning Rate Constants to Reactions.................................................. 158
Including User Reactions ..................................................................... 158
Adding or Editing User Reactions.......................................................... 159
Specifying Rate Constants for User Reactions ........................................ 159
Assigning Rate Constants to User Reactions........................................... 159
Selecting Report Options..................................................................... 160
Selecting the Reacting Phase ............................................................... 160
Specifying Units of Measurement for Pre-Exponential Factors................... 160
Including a User Kinetic Subroutine ...................................................... 161
Including a User Rate Constant Subroutine............................................ 161
Including a User Basis Subroutine ........................................................ 161
References .................................................................................................. 161
9 Free-Radical Bulk Polymerization Model..........................................................163
Summary of Applications............................................................................... 163
Free-Radical Bulk/Solution Processes.............................................................. 164
Initiation ........................................................................................... 171
Propagation....................................................................................... 176
Chain Transfer to Small Molecules ........................................................ 178
Termination....................................................................................... 179
Long Chain Branching ......................................................................... 181
Short Chain Branching ........................................................................ 182
Beta-Scission..................................................................................... 183
Reactions Involving Diene Monomers.................................................... 183
Calculation Method ............................................................................. 185
Quasi-Steady-State Approximation (QSSA) ........................................... 188
Phase Equilibrium............................................................................... 188
Gel Effect .......................................................................................... 188
Polymer Properties Calculated........................................................................ 190
Specifying Free-Radical Polymerization Kinetics................................................ 193
Accessing the Free-Radical Model ......................................................... 193
Specifying the Free-Radical Model ........................................................ 193
Specifying Reacting Species................................................................. 194
Listing Reactions ................................................................................ 194
Adding Reactions ............................................................................... 194
Editing Reactions ............................................................................... 195
Adding Gel-Effect ............................................................................... 196
Selecting Calculation Options............................................................... 196
Specifying User Profiles....................................................................... 197
References .................................................................................................. 197
10 Emulsion Polymerization Model .....................................................................199
Emulsion Polymerization Processes................................................................. 200
vi Contents

Micellar Nucleation ............................................................................. 201
Homogeneous Nucleation .................................................................... 204
Particle Growth .................................................................................. 206
Radical Balance.................................................................................. 207
Kinetics of Emulsion Polymerization...................................................... 211
Model Assumptions............................................................................. 215
Thermodynamics of Monomer Partitioning ............................................. 215
Polymer Particle Size Distribution ......................................................... 216
Polymer Particle Properties Calculated ............................................................ 218
User Profiles ...................................................................................... 218
Specifying Emulsion Polymerization Kinetics .................................................... 219
Accessing the Emulsion Model.............................................................. 219
Specifying the Emulsion Model ............................................................. 219
Selecting Calculation Options............................................................... 222
Adding Gel-Effect ............................................................................... 222
Specifying Phase Partitioning ............................................................... 222
Specifying Particle Growth Parameters .................................................. 223
References .................................................................................................. 223
11 Ziegler-Natta Polymerization Model ..............................................................225
Ziegler-Natta Processes ................................................................................ 226
Catalyst Types ................................................................................... 226
Ethylene Process Types....................................................................... 227
Propylene Process Types ..................................................................... 228
Catalyst Pre-Activation........................................................................ 237
Catalyst Site Activation ....................................................................... 237
Chain Initiation .................................................................................. 237
Propagation....................................................................................... 238
Chain Transfer to Small Molecules ........................................................ 239
Site Deactivation................................................................................ 239
Site Inhibition.................................................................................... 240
Cocatalyst Poisoning........................................................................... 240
Terminal Double Bond Polymerization ................................................... 240
Rate Calculations ............................................................................... 243
Specifying Ziegler-Natta Polymerization Kinetics .............................................. 244
Accessing the Ziegler-Natta Model ........................................................ 244
Specifying the Ziegler-Natta Model ....................................................... 244
Contents vii

References .................................................................................................. 247
12 Ionic Polymerization Model ...........................................................................249
Ionic Processes ............................................................................................ 250
Formation of Active Species................................................................. 254
Chain Initiation .................................................................................. 255
Propagation....................................................................................... 255
Association or Aggregation .................................................................. 256
Exchange .......................................................................................... 256
Equilibrium with Counter-Ion ............................................................... 256
Chain Transfer ................................................................................... 257
Chain Termination.............................................................................. 257
Coupling ........................................................................................... 258
Rate Calculations ............................................................................... 258
Specifying Ionic Polymerization Kinetics .......................................................... 260
Accessing the Ionic Model ................................................................... 260
Specifying the Ionic Model................................................................... 260
References .................................................................................................. 262
13 Segment-Based Reaction Model ....................................................................265
Step-Growth Addition Processes........................................................... 266
Polymer Modification Processes ............................................................ 266
Segment-Based Model Allowed Reactions ........................................................ 267
Conventional Species.......................................................................... 268
Side Group or Backbone Modifications................................................... 269
Chain Scission ................................................................................... 269
Depolymerization ............................................................................... 269
Propagation....................................................................................... 270
Combination ...................................................................................... 270
Branch Formation............................................................................... 270
Cross Linking..................................................................................... 270
Kinetic Rate Expression....................................................................... 270
User Subroutines ............................................................................... 274
Specifying Segment-Based Kinetics ................................................................ 285
Accessing the Segment-Based Model .................................................... 285
Specifying the Segment-Based Model ................................................... 285
Specifying Reaction Settings................................................................ 285
Building A Reaction Scheme ................................................................ 287
viii Contents

Adding or Editing Reactions ................................................................. 287
Specifying Reaction Rate Constants ...................................................... 288
Including a User Rate Constant Subroutine............................................ 289
Including a User Basis Subroutine ........................................................ 289
References .................................................................................................. 289
14 Steady-State Flowsheeting............................................................................291
Polymer Manufacturing Flowsheets ................................................................. 291
Monomer Synthesis ............................................................................ 292
Polymerization ................................................................................... 293
Recovery / Separations ....................................................................... 293
Polymer Processing ............................................................................ 293
Modeling Polymer Process Flowsheets ............................................................. 293
Steady-State Modeling Features..................................................................... 294
Unit Operations Modeling Features ....................................................... 294
Plant Data Fitting Features .................................................................. 294
Process Model Application Tools ........................................................... 294
References .................................................................................................. 294
15 Steady-State Unit Operation Models..............................................................295
Summary of Aspen Plus Unit Operation Models ................................................ 295
Dupl ................................................................................................. 296
Flash2............................................................................................... 298
Flash3............................................................................................... 298
FSplit................................................................................................ 299
Heater .............................................................................................. 299
Mixer ................................................................................................ 299
Mult.................................................................................................. 299
Pump................................................................................................ 300
Pipe.................................................................................................. 300
Sep .................................................................................................. 301
Sep2 ................................................................................................ 301
Distillation Models ........................................................................................ 301
RadFrac ............................................................................................ 301
Reactor Models ............................................................................................ 302
Mass-Balance Reactor Models ........................................................................ 302
RStoic............................................................................................... 302
RYield............................................................................................... 303
Equilibrium Reactor Models............................................................................ 304
REquil ............................................................................................... 304
RGibbs.............................................................................................. 304
Kinetic Reactor Models.................................................................................. 304
RCSTR .............................................................................................. 304
RPlug................................................................................................ 317
RBatch.............................................................................................. 327
Treatment of Component Attributes in Unit Operation Models ............................ 335
References .................................................................................................. 338
16 Plant Data Fitting ..........................................................................................339
Data Fitting Applications ............................................................................... 339
Contents ix

Data Fitting For Polymer Models..................................................................... 340
Data Collection and Verification............................................................ 341
Literature Review............................................................................... 341
Preliminary Parameter Fitting............................................................... 342
Preliminary Model Development ........................................................... 343
Trend Analysis ................................................................................... 343
Model Refinement .............................................................................. 344
Steps for Using the Data Regression Tool ........................................................ 345
Identifying Flowsheet Variables............................................................ 346
Manipulating Variables Indirectly.......................................................... 347
Entering Point Data ............................................................................ 349
Entering Profile Data........................................................................... 350
Entering Standard Deviations .............................................................. 351
Defining Data Regression Cases ........................................................... 352
Sequencing Data Regression Cases ...................................................... 352
Interpreting Data Regression Results.................................................... 352
Troubleshooting Convergence Problems ................................................ 353
17 User Models...................................................................................................359
User Unit Operation Models ........................................................................... 359
User Unit Operation Models Structure ................................................... 359
User Unit Operation Model Calculations ................................................. 360
User Unit Operation Report Writing....................................................... 365
User Kinetic Models ...................................................................................... 365
User Physical Property Models........................................................................ 370
References .................................................................................................. 373
18 Application Tools...........................................................................................375
Example Applications for a Simulation Model ................................................... 375
Application Tools Available in Aspen Polymers.................................................. 376
CALCULATOR..................................................................................... 376
DESIGN-SPEC.................................................................................... 377
SENSITIVITY ..................................................................................... 377
OPTIMIZATION .................................................................................. 377
Model Variable Accessing .............................................................................. 378
References .................................................................................................. 380
19 Run-Time Environment..................................................................................381
Aspen Polymers Architecture ......................................................................... 381
Installation Issues ........................................................................................ 382
Hardware Requirements...................................................................... 382
Installation Procedure ......................................................................... 382
Configuration Tips ........................................................................................ 382
Startup Files...................................................................................... 382
Simulation Templates ......................................................................... 382
User Fortran ................................................................................................ 383
User Fortran Templates....................................................................... 383
User Fortran Linking ........................................................................... 383
Troubleshooting Guide .................................................................................. 383
User Interface Problems...................................................................... 383
Simulation Engine Run-Time Problems ................................................. 385
x Contents

References .................................................................................................. 386
A Component Databanks ....................................................................................387
Pure Component Databank............................................................................ 387
POLYMER Databank ...................................................................................... 387
POLYMER Property Parameters............................................................. 387
POLYMER Databank Components.......................................................... 388
SEGMENT Databank ..................................................................................... 391
SEGMENT Property Parameters ............................................................ 391
SEGMENT Databank Components ......................................................... 392
B Kinetic Rate Constant Parameters...................................................................431
Initiator Decomposition Rate Parameters......................................................... 431
Solvent Dependency........................................................................... 431
Concentration Dependency.................................................................. 432
Temperature Dependency ................................................................... 432
Pressure Dependency ......................................................................... 433
References .................................................................................................. 444
C Fortran Utilities ...............................................................................................445
D Input Language Reference..............................................................................447
Specifying Components................................................................................. 447
Naming Components .......................................................................... 447
Specifying Component Characterization Inputs........................................ 448
Specifying Component Attributes ................................................................... 451
Specifying Characterization Attributes................................................... 451
Specifying Conventional Component Attributes ...................................... 451
Initializing Attributes in Streams .......................................................... 451
Specifying Attribute Scaling Factors................................................................ 453
Specifying Component Attribute Scale Factors ....................................... 453
Requesting Distribution Calculations ............................................................... 454
Calculating End Use Properties....................................................................... 454
Specifying Physical Property Inputs ................................................................ 456
Specifying Property Methods................................................................ 456
Specifying Property Data..................................................................... 458
Estimating Property Parameters ........................................................... 459
Specifying Step-Growth Polymerization Kinetics ............................................... 460
Specifying Free-Radical Polymerization Kinetics................................................ 467
Specifying Emulsion Polymerization Kinetics .................................................... 477
Specifying Ziegler-Natta Polymerization Kinetics .............................................. 484
Specifying Ionic Polymerization Kinetics .......................................................... 494
Specifying Segment-Based Polymer Modification Reactions................................ 501
References .................................................................................................. 505
Index ..................................................................................................................507
Contents xi

Introducing Aspen Polymers
Aspen Polymers (formerly known as Aspen Polymers Plus) is a general-purpose
process modeling system for the simulation of polymer
manufacturing processes. The modeling system includes modules for the
estimation of thermophysical properties, and for performing polymerization
kinetic calculations and associated mass and energy balances.
Also included in Aspen Polymers are modules for:
 Characterizing polymer molecular structure
 Calculating rheological and mechanical properties
 Tracking these properties throughout a flowsheet
There are also many additional features that permit the simulation of the
entire manufacturing processes.
About This Documentation Set
The Aspen Polymers User Guide is divided into two volumes. Each volume
documents features unique to Aspen Polymers. This User Guide assumes prior
knowledge of basic Aspen Plus capabilities or user access to the Aspen Plus
documentation set. If you are using Aspen Polymers with Aspen Dynamics,
please refer to the Aspen Dynamics documentation set.
Volume 1 provides an introduction to the use of modeling for polymer
processes and discusses specific Aspen Polymers capabilities. Topics include:
 Polymer manufacturing process overview - describes the basics of
polymer process modeling and the steps involved in defining a model in
Aspen Polymers.
 Polymer structural characterization - describes the methods used for
characterizing components. Included are the methodologies for calculating
distributions and features for tracking end-use properties.
 Polymerization reactions - describes the polymerization kinetic models,
including: step-growth, free-radical, emulsion, Ziegler-Natta, ionic, and
segment based. An overview of the various categories of polymerization
kinetic schemes is given.
 Steady-state flowsheeting - provides an overview of capabilities used
in constructing a polymer process flowsheet model. For example, the unit
Introducing Aspen Polymers 1

operation models, data fitting tools, and analysis tools, such as sensitivity
studies.
 Run-time environment - covers issues concerning the run-time
environment including configuration and troubleshooting tips.
Volume 2 describes methodologies for tracking chemical component
properties, physical properties, and phase equilibria. It covers the physical
property methods and models available in Aspen Polymers. Topics include:
 Thermodynamic properties of polymer systems – describes polymer
thermodynamic properties, their importance to process modeling, and
available property methods and models.
 Equation-of-state (EOS) models – provides an overview of the
properties calculated from EOS models and describes available models,
including: Sanchez-Lacombe, polymer SRK, SAFT, and PC-SAFT.
 Activity coefficient models – provides an overview of the properties
calculated from activity coefficient models and describes available models,
including: Flory-Huggins, polymer NRTL, electrolyte-polymer NRTL,
polymer UNIFAC.
 Thermophysical properties of polymers – provides and overview of
the thermophysical properties exhibited by polymers and describes
available models, including: Aspen ideal gas, Tait liquid molar volume,
pure component liquid enthalpy, and Van Krevelen liquid and solid, melt
and glass transition temperature correlations, and group contribution
methods.
 Polymer viscosity models – describes polymer viscosity model
implementation and available models, including: modified Mark-
Houwink/van Krevelen, Aspen polymer mixture, and van Krevelen polymer
solution.
 Polymer thermal conductivity models - describes thermal conductivity
model implementation and available models, including: modified van
Krevelen and Aspen polymer mixture.
Related Documentation
A volume devoted to simulation and application examples for Aspen Polymers
is provided as a complement to this User Guide. These examples are designed
to give you an overall understanding of the steps involved in using Aspen
Polymers to model specific systems. In addition to this document, a number
of other documents are provided to help you learn and use Aspen Polymers,
Aspen Plus, and Aspen Dynamics applications. The documentation set consists
of the following:
Installation Guides
Aspen Engineering Suite Installation Guide
Aspen Polymers Guides
Aspen Polymers User Guide, Volume 1
2 Introducing Aspen Polymers

Aspen Polymers User Guide, Volume 2
(Physical Property Methods & Models)
Aspen Polymers Examples & Applications Case Book
Aspen Plus Guides
Aspen Plus User Guide
Aspen Plus Getting Started Guides
Aspen Physical Property System Guides
Aspen Physical Property System Physical Property Methods and Models
Aspen Physical Property System Physical Property Data
Aspen Dynamics Guides
Aspen Dynamics Examples
Aspen Dynamics User Guide
Aspen Dynamics Reference Guide
Help
Aspen Polymers has a complete system of online help and context-sensitive
prompts. The help system contains both context-sensitive help and reference
information. For more information about using Aspen Polymers help, see the
Aspen Plus User Guide.
Third-Party
More detailed examples are available in Step-Growth Polymerization Process
Modeling and Product Design by Kevin Seavey and Y. A. Liu, ISBN: 978-0-
470-23823-3, Wiley, 2008.
Technical Support
AspenTech customers with a valid license and software maintenance
agreement can register to access the online AspenTech Support Center at:
http://support.aspentech.com
This Web support site allows you to:
 Access current product documentation
 Search for tech tips, solutions and frequently asked questions (FAQs)
 Search for and download application examples
 Search for and download service packs and product updates
 Submit and track technical issues
 Send suggestions
 Report product defects
Introducing Aspen Polymers 3

 Review lists of known deficiencies and defects
Registered users can also subscribe to our Technical Support e-Bulletins.
These e-Bulletins are used to alert users to important technical support
information such as:
 Technical advisories
 Product updates and releases
Customer support is also available by phone, fax, and email. The most up-to-date
contact information is available at the AspenTech Support Center at
http://support.aspentech.com.
4 Introducing Aspen Polymers

1 Polymer Manufacturing
Process Overview
This chapter provides an overview of the issues related to polymer
manufacturing process modeling and their handling in Aspen Polymers
(formerly known as Aspen Polymers Plus).
Topics covered include:
 About Aspen Polymers, 5
 Overview of Polymerization Processes, 6
 Issues of Concern in Polymer Process Modeling, 7
 Aspen Polymers Tools, 9
 Defining a Model in Aspen Polymers, 12
About Aspen Polymers
Aspen Polymers is a general-purpose process modeling system for the
simulation of polymer manufacturing processes. The modeling system
includes modules for the estimation of thermophysical properties, and for
performing polymerization kinetic calculations and associated mass and
energy balances.
Also included in Aspen Polymers are modules for:
 Characterizing polymer molecular structure
 Calculating rheological and mechanical properties
 Tracking these properties throughout a flowsheet
There are also many additional features that permit the simulation of the
entire manufacturing processes.
1 Polymer Manufacturing Process Overview 5

Overview of Polymerization
Processes
Polymer Definition
A polymer is a macromolecule made up of many smaller repeating units
providing linear and branched chain structures. Although a wide variety of
polymers are produced naturally, synthetic or man-made polymers can be
tailored to satisfy specific needs in the market place, and affect our daily lives
at an ever-increasing rate. The worldwide production of synthetic polymers,
estimated at approximately 100 million tons annually, provides products such
as plastics, rubber, fibers, paints, and adhesives used in the manufacture of
construction and packaging materials, tires, clothing, and decorative and
protective products.
Polymer Molecular
Bonds
Polymer molecules involve the same chemical bonds and intermolecular
forces as other smaller chemical species. However, the interactions are
magnified due to the molecular size of the polymers. Also important in
polymer production are production rate optimization, waste minimization and
compliance to environmental constraints, yield increases and product quality.
In addition to these considerations, end-product processing characteristics
and properties must be taken into account in the production of polymers
(Dotson, 1996).
Polymer Manufacturing Process Steps
Polymer manufacturing processes are usually divided into the following major
steps:
1 Monomer Synthesis and Purification
2 Polymerization
3 Recovery / Separation
4 Polymer Processing
The four steps may be carried out by the same manufacturer within a single
integrated plant, or specific companies may focus on one or more of these
steps (Grulke, 1994).
The four steps may be carried out by the same manufacturer within a single
integrated plant, or specific companies may focus on one or more of these
steps (Grulke, 1994).
The following figure illustrates the important stages for each of the four
polymer production steps. The main issues of concern for each of these steps
are described next.
6 1 Polymer Manufacturing Process Overview

Issues of Concern in Polymer
Process Modeling
There are modeling issues associated with each step in the production of
polymers. The following table summarizes these issues along with the
required tools:
1 Polymer Manufacturing Process Overview
7

Step Modeling Issues/Concerns Tools Required
Monomer synthesis
and purification
Feedstock purity
Monomer degradation
Emissions
Waste disposal
Unit operations: separators
Reaction kinetics
Phase equilibria
Polymerization Temperature control
Molecular weight control, polymer
specifications
Conversion yield
Reaction medium viscosity
Residence time
Reactor stability
Waste minimization
Characterization
Reaction kinetics
Phase equilibria
Heat transfer
Unit operations: reactors
Transport phenomena
Process dynamics
Process control
Recovery / Separation Solvent removal
Monomer recovery
Phase equilibria
Heat and mass transfer
Polymer processing Solvent removal
Solids handling
Heat and mass transfer
Monomer Synthesis and Purification
During monomer synthesis and purification, the engineer is concerned with
purity. This is because the presence of contaminants, such as water or
dissolved gases for example, may adversely affect the subsequent
polymerization stage by:
 Poisoning catalysts
 Depleting initiators
 Causing undesirable chain transfer or branching reactions
Another concern of this step is the prevention of monomer degradation
through proper handling or the addition of stabilizers. Control of emissions,
and waste disposal are also important factors in this step.
Polymerization
The polymerization step is usually the most important step in terms of the
economic viability of the manufacturing process. The desired outcome for this
step is a polymer product with specified properties such as:
 Molecular weight distribution
 Melt index
 Composition
 Crystallinity/density
 Viscosity

The obstacles that must be overcome to reach this goal depend on both the
mechanism of polymer synthesis (chain growth or step growth), and on the
polymerization process used.
Polymerization processes may be batch, semi-batch or continuous. In
addition, they may be carried out in bulk, solution, slurry, gas-phase,
suspension or emulsion. Batch and semi-batch processes are preferred for
specialty grade polymers. Continuous processes are usually used to
manufacture large volume commodity polymers. Productivity depends on heat
removal rates and monomer conversion levels achieved. Viscosity of polymer
solutions, and polymer particle suspensions and mixing are important
considerations. These factors influence the choice of, for example, bulk versus
solution versus slurry polymerization. Another example is the choice of
emulsion polymerization that is often dictated by the form of the end-use
product, water-based coating or adhesive. Other important considerations
may include health, safety and environmental impact.
Most polymerizations are highly exothermic, some involve monomers that are
known carcinogens and others may have to deal with contaminated water.
In summary, for the polymerization step, the reactions which occur usually
cause dramatic changes in the reaction medium (e.g. significant viscosity
increases may occur), which in turn make high conversion kinetics, residence-time
distribution, agitation and heat transfer the most important issues for
the majority of process types.
Recovery / Separation
The recovery/separation step can be considered the step where the desired
polymer produced is further purified or isolated from by-products or residual
reactants. In this step, monomers and solvents are separated and purified for
recycle or resale. The important concerns for this step are heat and mass
transfer.
Polymer Processing
The last step, polymer processing, can also be considered a recovery step. In
this step, the polymer slurry is turned into solid pellets or chips. Heat of
vaporization is an important factor in this step (Grulke, 1994).
Summary
In summary, production rate optimization, waste minimization and
compliance to environmental constraints, yield increase, and product quality
are also important issues in the production of polymers. In addition, process
dynamics and stability constitute important factors primarily for reactors.
Aspen Polymers Tools
Aspen Polymers provides the tools that allow polymer manufacturers to
capture the benefits of process modeling.

Aspen Polymers can be used to build models for representing processes in
two modes: with Aspen Plus for steady-state models, and with Aspen
Dynamics or Aspen Custom Modeler™ for dynamic models. In both cases, the
tools used specifically for representing polymer systems fall into four
categories:
 Polymer characterization
 Physical properties
 Reaction kinetics
 Data
Through Aspen Plus, Aspen Dynamics and Aspen Custom Modeler, Aspen
Polymers provides robust and efficient algorithms for handling:
 Flowsheet convergence and optimization
 Complex separation and reaction problems
 User customization through an open architecture
Component Characterization
Characterization of a polymer component poses some unique challenges. For
example, the polymer component is not a single species but a mixture of
many species. Properties such as molecular weight and copolymer
composition are not necessarily constant and may vary throughout the
flowsheet and with time. Aspen Polymers provides a flexible methodology for
characterizing polymer components (U.S. Patent No. 5,687,090).
Each polymer is considered to be made up of a series of segments. Segments
have a fixed structure. The changing nature of the polymer is accounted for
by the specification of the number and type of segments it contains at a given
processing step.
Each polymer component has associated attributes used to store information
on molecular structure and distributions, product properties, and particle size
when necessary. The polymer attributes are solved/integrated together with
the material and energy balances in the unit operation models.
Polymer Physical Properties
Correlative and predictive models are available in Aspen Polymers for
representing the thermophysical properties of a polymer system, the phase
equilibrium, and the transport phenomena. Several physical property methods
combining these models are available. In addition to the built-in
thermodynamic models, the open architecture design allows users to override
the existing models with their own in-house models.
Polymerization Kinetics
The polymerization step represents the most important stage in polymer
processes. In this step, kinetics play a crucial role. Aspen Polymers provides
built-in kinetic mechanisms for several chain-growth and step-growth type
polymerization processes. The mechanisms are based on well-established
sources from the open literature, and have been extensively used and

validated against data during modeling projects of industrial polymerization
reactors.
There are also models for representing polymer modification reactions, and
for modeling standard chemical kinetics. In addition to the built-in kinetic
mechanisms, the open-architecture design allows users to specify additional
reactions, or to override the built-in mechanisms.
Modeling Data
A key factor in the development of a successful simulation model is the use of
accurate thermodynamic data for representing the physical properties of the
system, and of kinetic rate constant data which provide a good match against
observed trends.
In order to provide the physical property models with the parameters
necessary for property calculations, Aspen Polymers has property parameter
databanks available. These include:
 Polymer databank containing parameters independent of chain length
 Segment databank containing parameters to which composition and chain
length are applied for polymer property calculations
 Functional group databank containing parameters for models using a
group contribution approach is also included
This User Guide contains several tabulated parameters which may be used as
starting values for specific property models. Property data packages are also
being compiled for some polymerization processes and will be made available
in future versions.
In addition to physical property data, Aspen Polymers provides users with
ways of estimating missing reaction rate constant data. For example, the data
regression tool can be used to fit rate constants against molecular weight
data.
Process Flowsheeting
Aspen Polymers provides unit operation models, flowsheeting options, and
analysis tools for a complete representation of a process.
Models for batch, semi-batch and continuous reactors with mixing extremes
of plug flow to backmix are available. In addition, other unit operation models
essential for flowsheet modeling are available such as:
 Mixers
 Flow splitters
 Flash tanks
 Devolatilization units
Flowsheet connectivity and sequencing is handled in a straightforward
manner.
Several analysis tools are available for applying the simulation models
developed. These include tools for:
 Process optimization

 Examining process alternatives
 Analyzing the sensitivities of key process variables on polymer product
properties
 Fitting process variables to meet design specifications
Defining a Model in Aspen
Polymers
In order to build a model of a polymer process you must already be familiar
with Aspen Plus. Therefore, only the steps specific to polymer systems will be
described in detail later in this User Guide. The steps for defining a model in
Aspen Polymers are as follows:
Step 1. Specifying Global Simulation Options
The first step in defining the model is the specification of:
 Global simulation options, i.e. simulation type
 Units to be used for simulation inputs and results
 Basis for flowrates
 Maximum simulation times
 Diagnostic options
Step 2. Defining the Flowsheet
For a full flowsheet model, the next step is the flowsheet definition. Here you
would specify the unit operation models contained in the flowsheet and define
their connectivity.
Chapter 4 describes the unit operation models available for building a
flowsheet.
Step 3. Defining Components
Most simulation types require a definition of the component system. You must
correctly identify polymers, polymer segments, and oligomers as such. All
other components are considered conventional by default.
Chapter 2 provides information on defining components.
Step 4. Characterizing Components
Conventional components in the system are categorized by type. Additional
characterization information is required for other than conventional
components. You must specify the:
 Component attributes to be tracked for polymers
 Type of segments present
 Structure of oligomers
 Type and activity of catalysts
In addition, you may wish to request tracking of molecular weight
distribution.
Component characterization is discussed in Chapter 2.

Step 5. Specifying Property Models
You must select the models to be used to represent the physical properties of
your system.
The Aspen Polymers User Guide, Volume 2, Aspen Polymers Physical Property
Methods and Models, describes the options available for specifying physical
property models.
Step 6. Defining Polymerization Kinetics
Once you have made selections out of the built-in polymerization kinetic
models to represent your reaction system, you need to choose specific
reactions from the sets available and enter rate constant parameters for these
reactions.
Chapter 3 describes the models available and provides descriptions of the
input options.
Step 7. Defining Feed Streams
For flowsheet simulations, you must enter the conditions of the process feed
streams. If the feed streams contain polymers, you must initialize the
polymer attributes.
Polymer attribute definition in streams is discussed in a separate section of
Chapter 2.
Step 8. Specifying UOS Model Operating Conditions
You must specify the configuration and operating condition for unit operation
models contained in the flowsheet. In the case of reactors, you have the
option of assigning kinetic models defined in step 6 to specific reactors.
Chapter 4 provides some general information regarding the use of unit
operation models.
Step 9. Specifying Additional Simulation Options
For a basic simulation the input information you are required to enter in steps
1-8 is sufficient. However, there are many more advanced simulation options
you may wish to add in order to refine or apply your model. These include
setting up the model for plant data fitting, sensitivity analyses, etc.
Many of these options are described in a separate section of Chapter 4.
Information for building dynamic models is given in the Aspen Dynamics and
Aspen Custom Modeler documentation sets. Note that for building dynamic
models, users must first build a steady-state model containing:
 Definition of the polymer system in terms of components present
 Physical property models
 Polymerization kinetic models
Note: Aspen Polymers setup and configuration instructions are given in
Chapter 5.

References
Dotson, N. A., Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization
Process Modeling. New York: VCH Publishers.
Grulke, E. A. (1994). Polymer Process Engineering. Englewood Cliffs, NJ:
Prentice Hall.
Odian, George. (1991). Principles of Polymerization (3rd Ed.). New York: John
Wiley and Sons.

2 Polymer Structural
Characterization
One of the fundamental aspects of modeling polymer systems is the handling
of the molecular structure information of polymers. This chapter discusses the
approaches used to address this issue in Aspen Polymers (formerly known as
Aspen Polymers Plus).
 Polymer Structure, 15
 Polymer Structural Properties, 19
 Characterization Approach, 19
Included in this manual are several sections devoted to the specification of
polymer structural characterization information.
 3 Component Classification, 21
 Polymer Structural Properties, 33
 Structural Property Distributions, 55
 End-Use Properties, 73
Polymer Structure
Polymers can be defined as large molecules or macromolecules where a
smaller constituting structure repeats itself along a chain. For this reason,
polymers tend to exhibit different physical behavior than small molecules also
called monomers. Synthetic polymers are produced when monomers bond
together through polymerization and become the repeating structure or
segment within a chain. When two or more monomers bond together, a
polymer is formed. Small polymer chains containing 20 or less repeating units
are usually called oligomers.
The fact that identifiable segments are found repeatedly along a polymer
chain, provides convenient ways to categorize polymers. Polymers can be
classified based on segment composition or sequence:
 Homopolymers - containing one type of repeating unit which can be
mapped into one segment
2 Polymer Structural Characterization 15

 Copolymers - which have two or more repeating units. Copolymers can be
in a random, alternating, block, or graft configuration
If we consider the arrangement of a given chain, another classification arises.
Polymers may be:
 Linear
 Branched (with short or long chains)
 Star
 Ladder
 Network
Another classification that results from polymer structure has to do with
physical state. A solid polymer may be:
 Amorphous - when the chains are not arranged in a particular pattern
 Crystalline - when the chains are arranged in a regular pattern
A related classification divides polymers by thermal and mechanical properties
into:
 Thermoplastics (may go from solid to melt and vice versa)
 Thermosets (remain solid through heating)
 Elastomers (which have elastic properties)
Finally, polymers can be categorized based on the form they are
manufactured into: plastics, fibers, film, coatings, adhesives, foams, and
composites.
Polymer Types by Physical Structure
The following figure illustrates the various polymer types based on chain
structure:
16 2 Polymer Structural Characterization

Polymer Types by Property
The following table illustrates the various polymer types based on properties:
Classification Type Physical Property
Thermal /
Mechanical
properties
Thermoplastics
Thermosets
Elastomers
Can melt and solidify again
Remain solid through heating
Have elastic properties
Fabrication Plastics
Fibers
Coatings
Adhesives
Foams
Composites
Elastomers
Very versatile in terms of application
Most commonly used as textiles
Used for both decorative and protective
purposes
Used for their bonding properties
Used as packaging, upholstery, insulation,
etc.
Can be tailored to many applications
Used for their elastic properties
In addition to these classifications, polymers can be categorized based on the
type of constituting atoms on the chains.
Homochains produced through chain-growth polymerization have only carbon
atoms on the polymer backbone.
Heterochains produced through step-growth polymerization have other types
of atom incorporated into the polymer backbone.
Polymer Categories by Chemical Structure
The following table lists various homochain and heterochain polymers based
on the type of atoms on the polymer backbone or the substituted side
groups:
Polymer
Category Description Examples
Polymers with carbon-carbon backbone
Polyacrylics Ethylene backbone with one acrylic
acid (or derivative) as side group
per ethylene
Polyacrylic acid, polymethyl
methacrylate, polyacrylonitrile,
polyacrylamide
Polydienes One double bond per repeat unit Polybutadiene
Polyhalogen
Fluorine or chlorine side group per
hydrocarbons
ethylene
Polyvinyl fluoride, polyvinylidene
fluoride, polyvinylchloride,
Polyolefins Alphatic or aromatic substituents Polyethylene, polypropylene,
polyisobutylene, polystyrene
Polyvinyls From vinyl monomers Polyvinyl acetate, polyvinyl alcohol
Polymers with carbon-nitrogen backbone
Polyamides Amide group on backbone Nylon 6, nylon 6,6
Polyurethanes Urethane group on backbone Polyurethane foams
Polyureas Urea group on backbone Polyurea resins

Polymer
Category Description Examples
Polymers with carbon-oxygen backbone
Polyacetals Acetal group on backbone Polyacetate
Polyethers Ether group on backbone Polyethylene oxide, polyphenylene
oxide
Polyesters Ester group on backbone Polycarbonate polyethylene
therephthalate, polybutylene
therephthalate polylactide
Polymers with carbon-sulfur backbone
Polysulfides Sulfide group on backbone Polysulfide fibers
Polymer Structural Properties
All the methods of categorizing polymers point to certain key characteristics
that must be taken into account in order to fully define polymer molecules.
Typical information needed to capture the structure and behavior of polymers
includes:
 Chemical structure of segments: segment type, and configuration
 Chain size for the mixture of polymer chains
 Crystallinity
 Additional structural, thermal, and mechanical characteristics
Characterization Approach
Aspen Polymers allows for the different types of chemical species that may be
found in a polymer system:
 Monomers
 Solvents
 Catalysts
 Oligomers
 Polymers
Polymer segments are introduced to identify the chemical structure of the
polymer or oligomer repeat unit. In addition, they are used as building blocks
within polymerization reactions, and in the determination of thermodynamic
properties.
More than the chemical structure of the segments is needed in order to define
a polymer. Also needed is the segment composition of the chains. In addition,
properties related to size are needed: degree of polymerization or number of
segments.

Component Attributes
Within Aspen Polymers, component attributes are used to define these
structural characteristics. Component attributes are available to track
segment composition, degree of polymerization, molecular weight, etc.
Because the polymer is a mixture of chains, there is normally a distribution of
these structural characteristics. The component attributes are used to track
the averages.
There are additional attributes used to track information about the
distribution of chain sizes. These are the moments of chain length
distribution. For detailed information about component attributes, see
Polymer Structural Properties on page 33.
In addition to the component attributes, users have the option within Aspen
Polymers to examine polymer molecular weight distribution. This feature is
based on a method of instantaneous properties. For more information, see
Method of Instantaneous Properties on page 60.
References
Prentice Hall.
Munk, P. (1989). Introduction to Macromolecular Science. New York: John
Wiley and Sons.
Odian, G. (1991). Principles of Polymerization (3rd Ed.). New York: John
Wiley and Sons.
Rudin, A. (1982). The Elements of Polymer Science and Engineering. Orlando:
Academic Press.

3 Component Classification
This section discusses the specification of components in a simulation model.
 Component Categories, 21
 Component Databanks, 25
 Segment Methodology, 27
 Specifying Components, 28
Component Categories
When developing a simulation model in Aspen Polymers (formerly known as
Aspen Polymers Plus), users must assign components present in process flow
streams to one of the following categories:
 Conventional
 Polymer
 Oligomer
 Segment
 Site-based
The following figure illustrates the different categories of components and
their input requirements:
3 Component Classification 21

22
Conventional Components
Standard conventional components are molecular components such as water.
These components have a fixed molecular structure and participate in phase
equilibrium. Components falling into this category include:
 Monomers
 Initiators
 Chain transfer agents
 Solvents
 Catalysts
In order to fully specify conventional c
component data required for the phase equilibrium calculations. This data
may be entered or retrieved from component databanks.
Note: Ziegler-Natta catalysts and ionic initiators require additional
characterization inf
Polymers
In Aspen Polymers, polymer components represent a distribution of polymeric
species. The average size and composition of the molecules in this distribution
3 Component Classification
quilibrium. components, you need only specify pure
information.
omponents,

can change throughout the simulation. Each polymer molecule is considered
to be made up of repeating units or segments. Typically, the segments
correspond to the monomers that are used to grow the polymer.
The structure of polymers depends on the number and type of segments they
contain and the arrangement of segments in linear, branched, or cross-linked
forms.
Component attributes are used to track polymer structural properties (U.S.
Patent No. 5,687,090) such as:
 Segment composition
 Copolymer composition and average sequence length
 Degree of polymerization
 Molecular weight
 Branching
 Moments of molecular weight distribution
 Molecular architecture (physical arrangement of segments within the
polymer molecule)
Segments are specified independently from polymers. For each polymer, you
must select the types of component attributes to be included in the simulation
model. If the polymer is present in the process feed streams, you must
provide its properties by initializing the component attributes while specifying
input data for these feed streams.
For more information on component attribute specification, see Polymer
Structural Properties on page 33.
Oligomers
By convention, oligomers are defined as components with two or more
segments and a fixed molecular structure. They can be defined as volatile or
non-volatile. Typically, the oligomer feature is used to allow users to track the
loss of volatile short-chain polymers.
In order to specify oligomers, you must specify their composition in terms of
the number and type of segments they contain. Oligomers do not require
component attributes. For this reason, you may treat a polymer as an
oligomer in cases where you want to process the polymer within a unit
operation model which cannot handle polymer component attribute data.
When using oligomer components, you may specify addition properties
through the following unary property parameters:
Parameter Definition Default
POLDP Number-average chain
length
Calculated *
POLPDI Polydispersity index 1 **
POLCRY Mass fraction crystallinity
* Calculated from the number of segments in the oligomer as specified in the
Polymers form Oligomers subform.
** Used to calculate DPW and MWW.

Note: Not all kinetic models track oligomers as separate components. If a
model does not provide fields for specifying oligomers on its input forms, then
these components are not tracked.
Segments
Segments are the structural units of a polymer or oligomer and are specified
independently from these components. Their structure is fixed throughout a
simulation. Segments typically correspond to the monomers used to grow the
polymer. They are divided into types depending on their location on the
polymer chain:
 Repeat units
 End groups
 Branch point (attached to three or four branches)
Site-Based
Site-based components pertain to multisite reaction kinetic models (Ziegler-
Natta and Ionic). Site-based components include Ziegler-Natta catalysts and
ionic initiators.
Ziegler-Natta Catalysts
Ziegler-Natta catalysts are often used to initiate polymer chain formation in
chain-growth polymerization reactions. Catalysts can be treated as standard
conventional components. Ziegler-Natta catalysts or metallocene catalysts
involve one or more polymerization site types which may be in an activated or
deactivated state.
In order to use Ziegler-Natta catalysts, you must specify the number of site
types and the catalyst properties to be tracked, that is, the site activity.
Catalyst properties are defined as component attributes. You must initialize
the catalyst properties while specifying input data for the streams containing
the catalysts.
For more information on component attribute specification, see Polymer
Structural Properties on page 33.
Ionic Initiators
Ionic initiators are used in anionic and cationic polymerization. The ionic
initiators can be treated as standard conventional components. The
propagating species in ionic polymerization can be:
 Free-ions
 Ion-pairs
 Dormant esters
24 3 Component Classification

In Aspen Polymers, these different species are modeled as different sites of
an ionic initiator. Three different site-based attributes are tracked for an ionic
initiator. For more information, see Ionic Initiator Attributes on page 45.
Component Databanks
The thermodynamic and transport property models needed to perform the
physical property and phase equilibrium calculations during a simulation
require pure component property data. These include:
 Molecular weight
 Heat capacity
 Heat of formation
 Heat of vaporization
 Vapor pressure
 Density
Enter that information while selecting and specifying physical property
models. Normally, you would make use of the pure component databanks and
retrieve data from them for each of the components present in the simulation
model:
 Data for conventional components are retrieved from the Pure Component
databank
 Data for free-radical initiators are retrieved from the INITIATOR databank
 Data for polymers are retrieved from the POLYMER databank
 Data for oligomers are retrieved either from the pure component databank
or from the POLYMER databank
 Data for segments are retrieved from the SEGMENT databank
 Data for PC-SAFT are retrieved from the PC-SAFT databank
 Data for POLYPCSF are retrieved from the POLYPCSF databank
Descriptions of the databanks, and the parameters they contain are given in
Appendix A.
Pure Component Databank
In the Pure Component databank, components are named using a
nomenclature developed for Aspen Plus. Each component is given an alias
summarizing the number of each type of atom: C, H, O, N, P, S, CL, F, etc.
(e.g. C2H4 for ethylene). For cases where the same alias matches several
components, a counter is added to make the distinction (e.g. C2H4O2-1 for
acetic acid).
Note: Catalysts are often solid components and may not be found in the
PURE11 databank. Normally, you do not need a rigorous representation of
these components.

An acceptable approach is to assign a monomer alias to the catalyst and then
provide the correct molecular weight and certain parameters which will
prevent the catalyst from vaporizing. If an activity coefficient model is being
used for phase equilibrium representation, the catalysts can be assumed to be
non-volatile by specifying -40 as the first Antoine parameter (PLXANT(1) = -
40).
PC-SAFT Databank
The PC-SAFT databank contains pure and binary parameters used with the
PC-SAFT property method. The parameters are taken from the literature,
including many normal compounds, polar compounds and associating
compounds.
POLYPCSF Databank
The POLYPCSF databank contains pure and binary parameters used with the
POLYPCSF property method. The parameters are taken from the literature,
including many normal compounds, but excluding polar compounds and
associating compounds.
INITIATO Databank
The INITIATO databank contains data for initiator components. Rate
constants in this databank are derived from half-life data in vendor
datasheets published on public web sites. These datasheets generally contain
data at several temperatures, allowing the activation energy and prefactor to
be determined. These rate constants depend on the reaction environment,
and may vary between polar and non-polar solvents. Where multiple sets of
data were available, the data from monomer or organic solvents were used in
preference to data from aqueous solutions.
Molecular weight and other parameters are calculated from structure using
estimation methods from Aspen Plus, except in those few cases where vapor
pressure data was provided in the datasheets.
In the INITIATO databank, components are named using industry-standard
acronyms. Each component is given an alias summarizing the number of each
type of atom: C, H, O, N, P, S, CL, F, etc. For cases where the same alias
matches several components, a counter is added to make the distinction (e.g.
–1,-2, etc).
Segment Databank
In the Segment Databank, a segment name comes from the name of the
monomer from which it originates. Therefore, in this databank component
names and aliases follow the same conventions as those for the Pure
Component Databank.
A label is added to the monomer name to identify the segment as either a
repeat unit,-R, an end group,-E, or a branch point, -B (e.g. for butadiene
segments: C4H6R1or BUTADIENER1 corresponding to the repeat unit –

CH2–CH=CH–CH2, C4H5E1 or BUTADIENEE1 corresponding to the end
group –CH=CH–CH=CH2 and C4H5B or BUTADIENEB corresponding to the
branch segment CH2 CH CH CH ).
Polymer Databank
The Polymer Databank does not follow the conventional nomenclature. The
polymer aliases are the typical acronyms used in industry or academia, and
the polymer names consist of the repeat unit name enclosed in parentheses
and preceded by the prefix Poly (e.g. PS or POLY(STYRENE) for polystyrene).
Note: The MW property parameter used to store molecular weights in the
component databanks is the true molecular weight for all component types
except polymers. For polymers, the true polymer molecular weight is normally
tracked as a component attribute only. The molecular weight stored in the
databank is the apparent molecular weight calculated as the average segment
molecular weight (See Appendix A).
Segment Methodology
The segment approach to characterizing components is a fundamental
methodology which affects almost every functionality within Aspen Polymers.
Segments are used as the building blocks for polymers. Once you have
specified the types of segments in the polymer, the segment composition and
degree of polymerization defined as component attributes may be used to
define the size and composition of the polymer.
For oligomers, although component attributes are not used, the number of
each segment must be specified directly.
Most of the Aspen Polymers physical property models calculate polymer and
oligomer properties from segment properties. This is done by taking into
account the degree of polymerization and the segment composition. The
calculated properties should be the same for both oligomers and polymers,
assuming that the oligomer structure and molecular weight were specified
correctly. Note that this is true for mass-based properties only. Mole-based
properties will be different between polymer and oligomer if their apparent
molecular weights are different.
Within the polymerization reaction models, segments also play a key role. As
polymerization progresses, the models map the reacting monomers into the
corresponding segments and return rates of change for the segment
composition.

Specifying Components
To specify components within your model you need to know the following:
Item For
Component types All the species in your system
Property parameter databank
The species in the system
selections
IUPAC names All conventional components or you need their
physical properties (molecular weight, boiling point,
Antoine constants, etc.)
Segment structure All polymers and oligomers (define whether you want
to include any end groups or branch points)
Polymer properties to be
tracked
All polymers, that is, degree of polymerization,
segment composition
Additional characteristics All additional characteristics for catalysts, or ionic
initiators
Selecting Databanks
For an Aspen Polymers simulation, you generally retrieve physical property
data from the following databanks:
 Pure component databank (PURE12)
 Polymer databank (POLYMER)
 Polymer segment databank (SEGMENT)
 Initiator databank (INITIATOR)
You can also use other Aspen Plus databanks, user databanks, or in-house
databanks. Appendix A provides descriptions of the polymer and segment
databanks and the parameters they contain.
If you selected a polymer template to start your simulation, the correct
databanks are already specified.
If you did not select a polymer template, or if you want to modify the
databank selection:
1 From the Data Browser, click Components.
2 From the Components folder, click Specifications.
3 On the Selection sheet, click the Databanks tab to open the databank
selection form.
Defining Component Names and Types
You must specify a:
 Name and a type for each component in the simulation
 Component name or identifier
 Databank name or alias that sets the pure component properties for the
component

 Component type that sets the category to which the component belongs
and determines the treatment of that component
To access the components specifications input sheet:
2 From the Components folder, click Specifications.
3 On the Selection sheet, click the Databanks tab to set the databanks to
be searched for pure component properties.
To define component names and types:
1 On the Selection sheet, in the Component ID field, specify an ID for
each component.
This ID is used to refer to the component in all subsequent input, and is
also used to identify the component in the simulation report.
2 For polymers, oligomers, and segments, specify the component type in
the Type field.
By default, all components are assumed to be standard conventional
components. For Aspen Polymers simulation you must correctly identify
the component types:
Use For
Conventional Standard conventional components
Polymer Homo and copolymers
Oligomer Short chain polymer molecules
Segment Polymer or oligomer repeat units
3 If component property data is being retrieved from databanks, you must
also supply either the databank alias in the Alias field, or the databank
name in the Component name field.
Specifying Segments
The Type of each polymer or oligomer segment must be specified on the
Polymer Characterization Segments sheet. Segments can be repeat units,
end groups or branch points attached to three or four branches.
To access the segments definition input form:
2 From the Components folder, click Polymers.
3 From the Polymers folder, click Characterization.
To define segments:
 On the Segments sheet, assign a type to the segments from the Type
field.
Specifying Polymers
For each polymer you must define the component attributes to be tracked. All
components specified Polymer in the Components Specifications folder
require component attributes.

To access the polymer input specifications:
4 From the Characterization form, click the Polymers tab.
To specify component attributes for the polymers in your simulation:
1 In the Polymer ID field, select the polymer.
2 If you want to retrieve a predefined set of component attributes, in Built-in
attribute group select a grouping. The attribute summary table is
filled in.
For a complete discussion of Aspen Polymers component attributes, see
Polymer Structural Properties on page 33.
 or 
If you do not want to use a predefined set of attributes, or if you want to
change the attribute selection for a given group, click the attribute table
or click Edit to open the attribute list.
3 Click specific attributes to add or remove them from the list.
Repeat these steps for each polymer.
Specifying Oligomers
For each oligomer you must specify an ID and a structure in terms of number
and name of contained segments.
To access the oligomers definition input form:
4 From the Characterization form, click the Oligomers tab.
To define oligomers:
1 In the Oligomer field, select the oligomer.
2 In the Segment field, enter the name of a segment contained in the
oligomer.
3 Repeat these steps for each oligomer.
You can define as many segments as needed for an oligomer.
Specifying Site-Based Components
Specify the structure and activity of site-based catalytic species such as
Ziegler-Natta catalysts and ionic initiators.
To access the site-based species definition form:
4 From the Characterization form, click the Site-Based Species tab.

To specify site-based species characteristics:
1 Select the component type: Ziegler-Natta catalyst, ionic initiator, etc.
2 In the Comp ID field, specify the component name.
3 Specify the number of site types in Number of sites for the component.
For Ziegler-Natta catalysts, you must also specify the moles of sites per
gram of catalyst.
4 Select the list of properties or component attributes to be tracked for that
component. Click the attribute list table or Edit to open the attribute list.
5 Click specific attributes to add or remove them from the list for the
component.
References
Bailey, J., & Ollis, D. F. (1986) Biochemical Engineering Fundamentals (2nd
Ed.). New York: McGraw-Hill.
Brandrup, J., & Immergut, E. H. (Eds.). (1989). Polymer Handbook (3rd Ed.).
New York: John Wiley & Sons.
Danner R. P., & High, M. S. (1992). Handbook of Polymer Solution
Thermodynamics. New York: American Institute of Chemical Engineers.
Kroschwitz, J. (Ed.). (1990). Concise Encyclopedia of Polymer Science and
Engineering. New York: John Wiley and Sons.

4 Polymer Structural
Properties
This section discusses the use of component attributes for tracking polymer
structural properties in a simulation model.
 Structural Properties as Component Attributes, 33
 Component Attribute Classes, 34
 Component Attribute Categories, 35
 Component Attribute Initialization, 46
 Component Attribute Scale Factors, 50
 Specifying Component Attributes, 51
Structural Properties as
Component Attributes
Component attributes provide a convenient framework to associate structural
characterization data to components in a flow stream. They are carried
throughout the flowsheet along with state and composition information, and
effectively extend the stream structure.
Aspen Polymers (formerly known as Aspen Polymers Plus) uses component
attributes as a vehicle for tracking important modeling information for
polymers, ionic initiators and Ziegler-Natta catalysts (U.S. Patent No.
5,687,090). For example, there are component attributes to store:
 Segment composition (segment fraction or segment flow)
 Copolymer composition and average sequence length
 Degree of polymerization (number, weight, and z-average)
 Molecular weight (number, weight, and z-average)
 Degree of branching (long and short)
 Degree of cross-linking (cross-link density)
 Molecular architecture (physical arrangement of segments within the
polymer molecule)
4 Polymer Structural Properties 33

 Live polymer properties
 Aggregate polymer properties
In the case of multi-site-type Ziegler-Natta catalyst polymerization, the
attributes provide the structure to store the properties by site. Examples of
catalyst attributes include the fraction of dead and potential sites. The
catalyst attributes are used to track catalyst activity. There are also
component attributes available to track user defined data.
The complete list of available attributes is given in the Polymer Component
Attributes, Site-Based Species Attributes, and User Attributes sections of this
chapter (pages 35 through 45).
Component Attribute Classes
Component attributes are divided into classes to reflect the nature of various
structural properties carried in process streams:
 Class 0 component attributes are derived quantities from other attributes.
They are therefore recalculated from these attributes after they are
updated. For example, number average degree of polymerization is a
Class 0 component attribute. It is computed from the zeroth and the first
moments of chain length distribution.
 Class 1 component attributes are structural properties per unit mass. They
are not used for polymers.
 Class 2 component attributes are structural properties per unit time.
Examples are zeroth and first moments of chain length distribution
The following table lists the differences between the Aspen Polymers
component attribute classes:
Class Conserved
Quantity
Convergence
Treatment
Unit of Measurement Examples
0 N/A Recalculated Varies Degree of
polymerization
1 Attribute 
component mass
Direct substitution Attribute / component
mass
None for polymers
2 Attribute Accelerated
convergence
Attribute / time Segment flows,
moments of chain
length distribution
For a typical polymer process simulation, Class 0 and Class 2 component
attributes are used. Since Class 0 component attributes are calculated from
Class 2 attributes, users have the option of entering either of the two types
for simulation models where polymer is present in the process feed streams.
For this reason, an attribute initialization scheme has been designed. For
more information, see Component Attribute Initialization on page 46.
34 4 Polymer Structural Properties

Component Attribute
Categories
The main categories of component attributes available are:
 Polymer attributes
 Ziegler-Natta catalyst attributes
 Ionic initiator attributes
 User attributes
Polymer Component Attributes
The polymer properties tracked as component attributes include:
 Segment fraction
 Segment flow
 Flow and fraction of segment dyads (pairs)
 Number-average degree of polymerization and molecular weight
 Weight-average degree of polymerization and molecular weight
 Z-average degree of polymerization and molecular weight
 Zeroth through third moment of chain length distribution
 Number of long and short chain branches
 Long and short chain branching frequency
 Number and frequency of cross-links
 Number-average block length (sequence length)
 Several aspects of molecular architecture, including tacticity, head-to-head
insertions (orienticity)
 Flow and fraction of terminal double bonds
 Flow and fraction of cis-, trans-, and vinyl- isomers associated with diene
segments (internal and pendent double bonds)
There are component attributes available to track most of these properties for
dead polymer, live polymer, and aggregate polymer. You may want to track
information for live polymers for cases of free-radical polymerization where
the quasi-steady-state approximation (QSSA) is not used. Site based
component attributes are also available to accommodate multi-site type
Ziegler-Natta catalyst polymerization. Composite attributes are summed over
all site types. They represent the average properties of the polymer.
Polymer Attribute Sets
In summary, there are six sets of polymer component attributes.
 Composite Polymer Set contains the basic attributes that may be used for
any type of polymerization, including the minimum required set for all
simulation models.
 Composite Live Polymer Set contains the attributes required to track the
characteristics of live polymer chains in chain growth polymerization.

 Composite Aggregate Polymer Set contains the attributes required to track
the characteristics of aggregate polymer chain in ionic polymerization.
 Site-Based Polymer Set contains attributes corresponding to the
composite set, but structured to track information for each catalyst site
type.
 Site-Based Live Polymer Set contains attributes corresponding to the
composite live polymer set, structured to track information by catalyst site
type.
 Site-Based Aggregate Polymer Set contains attributes corresponding to
the composite aggregate polymer set, structured to track information by
ionic site type.
The tables that follow list the component attributes available in each set.
Attributes must be associated from these sets to each of your polymer
components when building a simulation model. To simplify this, the attributes
in the tables were grouped by model usage, or polymerization reaction type
(for example, physical property simulation model, free-radical polymerization
model). Select a grouping and all the attributes needed are retrieved
automatically. A table of the minimum required attributes by model usage is
also provided.
Attribute Definitions – Composite Polymer Attribute Set
Name Symbol† Description Equation‡ Class Dimension Units
DPN D Pn Number-average
degree of
polymerization
DPn    1 0 / 0 1 Unitless
DPW DPw
Weight-average degree
of polymerization
DPw    2 1 / 0 1 Unitless
DPZ DPz
Z-average degree of
polymerization
DPz    3 2 / 0 1 Unitless
PDI PDI Polydispersity index PDI = DPw /D Pn 0 1 Unitless
MWN Mn
Number-average
molecular weight M DP M n  n seg 0 1 Unitless
MWW Mw
Weight-average
molecular weight M DP M w  w seg 0 1 Unitless
MWZ Mz
Z-average molecular
weight M DP M z  z seg 0 1 Unitless
MWSEG Mseg
Average segment
molecular weight
Mseg Fp (i)Mi 0 1 Unitless
ZMOM 0 Zeroth moment of chain
length distribution
---- 2 1 Mole
flow
length distribution 1 1   (i) 0 1 Mole
flow
FMOM 1 First moment of chain
SMOM 2 Second moment of
chain length distribution
---- 2 1 Mole
flow
TMOM 3 Third moment of chain
length distribution
---- 2 1 Mole
flow
SFLOW 1(i) Mole flow of segments
of type i
---- 2 NSEG Mole
flow

Attribute Definitions - Composite Polymer Attribute Set (continued)
SFRAC Fp (i) Mole fraction of
segments of type i
F i i p ( )   ( ) /  1 1
0 NSEG Unitless
EFRAC F i e ( ) Fraction of chain end
( )   ( ) / ( ) 1 1
segments of type i F i i i e
ends
0 NEND Unitless
DYADFLOW
i, j  Molar flow rate of
dyads composed of
type I and j segments
---- 2  
2
seg seg N  N Mole
2
flow
DYADFRAC
i, j  Fraction of dyads
composed of type I
and j segments
, , 1  / i j i j   0  
2
seg seg N  N Unitless
2
BLOCKN
i Bn Number-average block
length for segment i
 0 NSEG Unitless
ii
i
i
Bni
1
 


1
Attributes Related to Branching and Terminal Double Bonds
LCB LCB Number of long chain
branches
---- 2 1 Mole
flow
SCB SCB Number of short chain
branches
---- 2 1 Mole
flow
FLCB FLCB Long chain branching
frequency FLCB
LCB

103
1 
0 1 Unitless
FSCB FSCB Short chain branching
frequency FSLB
SCB

103
1 
0 1 Unitless
TBDFLOW   i 0
 Mole flow of terminal
double bond segments
of type i
---- 2 NSEG Mole
flow
TBDFRAC Mole fraction of
terminal double bond
segments of type i
0 NSEG Unitless

F (i) p
  
0 1 F (i)  (i) / p
Attributes Related to Molecular Architecture (Tacticity and Orienticity)
ATACFLOW atactic
1 
Apparent mole flow of
atactic polymer
---- 2 1 Mole
flow
ATACFRAC Fatactic Mass fraction of
atactic polymer 1 1 Fatactic  atactic / 0 1 Unitless
HTHFLOW HTH
ii  Mole flow rate of i-I
dyads with head-to-head
orientation
---- 2 NSEG Mole
flow
HTHFRAC HTH
ii  Fraction of i-I dyads
with head-to-head
orientation
 HTH
  HTH
/ 0 NSEG Unitless
ii ii
ii

Attribute Definitions - Composite Polymer Attribute Set (continued)
Attributes Related to Reactions with Diene Monomers
XFLOW XFLOW Number of cross links ---- 2 NSEG* Mole
flow
XDENSITY
XL  Cross-linking density
 XLFLOW 0 NSEG* Kmol/kg
0 

n
XL M
CIS-FLOW i,cis
1 
Flow rate of diene
segment i in cis
configuration
---- 2 NSEG* Mole
flow
TRANSFLO i,trans
1 
Flow rate of diene
segment i in trans
configuration
---- 2 NSEG* Mole
flow
VINYLFLO i,vinyl
1 
Flow rate of diene
segment i in vinyl
configuration
---- 2 NSEG* Mole
flow
CIS-FRAC cis
i f Fraction of diene
segment i in cis
configuration
,
1   / 0 NSEG* Unitless
cis i cis i
i f 1
TRANSFRA Fraction of diene
trans
i f trans i trans i
i f 1
segment i in trans
configuration
0 NSEG* Unitless
VINYLFRA Fraction of diene
vinyl
i f vinyl i vinyl i
i f 1
segment i in vinyl
configuration
0 NSEG* Unitless
,
1   /
,
1   /
Attributes Related to Particle Size (Emulsion Polymerization)
PDV PDv
Polydispersity for PSD
(volume) PD V
 0 1 Unitless
n
v
v V
PSDZMOM 0
Zeroth moment of the
particle size
distribution (volume)
---- 2 1 # /s
PSDFMOM 1
First moment of the
PSD (volume)
  1  Mass / 0 1 m3/s
PSDSMOM 2
Second moment of the
PSD (volume)
---- 2 1 m6 /s
PSDTMOM 3
Third moment of the
PSD (volume)
---- 2 1 m9 /s
VOLN Vn
Number average
volume of the
particles
Vn 


1
0
0 1 m3
VOLV Vv
Volume average
volume of the
particles
Vv 


2
1
0 1 m3
VOLZ Vz
Z-average volume of
the particles Vz 


3
2
0 1 m3
DIAV Dv
Volume average
diameter Dv  3 6 1


0 
0 1 m

† i = Segment index
Moments of the chain length distribution are defined as   n m
Q
m n
Where:
m = 0-3
n = Chain length
Qn
= Number of moles of polymer of length n.
‡ Equation for recalculating class 0 attributes only. Class 2 attributes are integrated.
* Although the dimension is NSEG, these attributes only apply to diene segments, other elements
will be set to zero.
Attribute Definitions – Composite Live Polymer Attribute Set
LDPN DPL Number average DP
n
L    1 0 / 0 1 Unitless
of live polymer DPn
LDPW DPw
L Weight average DP of
L    2 1 / 0 1 Unitless
live polymer DPw
LPDI PDI L Polydispersity index
 / L 0 1 Unitless
PDI L DP L
DP
of live polymer w
n
LMWN Mn
L Number average MW
L
 L
L 0 1 Unitless
M DP M of live polymer n
n
seg
LMWW Mw
L Weight average MW
L
 L
L 0 1 Unitless
M DP M of live polymer w
w
seg
LMWSEG Mseg
L Average segment
molecular weight of
live polymer
L
p i   ( ) 0 1 Unitless
M LF i M seg
LZMOM 0
Zeroth moment of
live polymer
  0 0  (i) 0 1 Mole flow
LFMOM 1
First moment of live
polymer
  1 1  (i) 0 1 Mole flow
LSMOM 2
Second moment of
live polymer
---- 2 1 Mole flow
LSFLOW 1(i) Segment flow rates in
live polymer
---- 2 NSEG Mole flow
LSFRAC LF i p ( ) Segment mole
fraction in live
polymer
LFp (i)   (i) /  1 1
0 NSEG Unitless
LEFLOW 0 (i) End segment flow
rates in live polymer
---- 2 NSEG Mole flow
LEFRAC LF i e ( ) End segment mole
fractions in live
polymer
LFe (i)   (i) /  0 0
0 NSEG Unitless
LPFRAC Flp
Fraction of polymer
that is live Flp 


0
0
0 1 Mole
fraction

Attribute Definitions – Composite Aggregate Polymer Attribute Set
ADPN DPA Number average DP of
n
A    1 0 / 0 1 Unitless
aggregate polymer DPn
ADPW DPw
A Weight average DP of
A    2 1 / 0 1 Unitless
aggregate polymer DPw
APDI PDI A Polydispersity index of
 / A 0 1 Unitless
PDI A DP A
DP
aggregate polymer w
n
AMWN Mn
A Number average MW of
A
 A
A 0 1 Unitless
M DP M aggregate polymer n
n
seg
AMWW Mw
A Weight average MW of
A
 A
A 0 1 Unitless
M DP M aggregate polymer w
w
seg
AMWSEG Mseg
A Average segment
molecular weight of
aggregate polymer
A
p i   ( ) 0 1 Unitless
M AF i M seg
AZMOM 0
Zeroth moment of
aggregate polymer   0 0  (i) 0 1 Mole
flow
AFMOM 1
First moment of
flow
ASMOM 2
Second moment of
flow
aggregate polymer   1 1 (i)  (i, j) 0 NSEG Mole
flow
ASFLOW 1(i) Segment flow rates in
ASFRAC AF i p ( ) Segment mole fraction in
aggregate polymer
AF i i p ( )   ( ) /  1 1
0 NSEG Unitless
in aggregate polymer   0 0 (i)  (i, j) 0 NSEG Mole
flow
AEFLOW 0(i) End segment flow rates
AF i e ( )
AEFRAC End segment mole
fractions in aggregate
polymer
AF i i e( )   ( ) /  0 0
0 NSEG Unitless
Fap
APFRAC Fraction of polymer that
is aggregate Fap 


0
0
0 1 Mole
fraction
Attribute Definitions – Site-Based Polymer Attribute Set
SDPN DP j n ( ) Number average degree
of polymerization at site
j
DP j j j n ( )   ( ) /  ( ) 1 0
0 NSITE Unitless
SDPW DP j w ( ) Weight average degree
of polymerization at site
j
DP j j j w( )   ( ) /  ( ) 2 1
0 NSITE Unitless
SDPZ DP j z ( ) Z-average degree of
polymerization at site j
DP j j j z ( )   ( ) /  ( ) 3 2
0 NSITE Unitless

SPDI PDI( j) Polydispersity index at
site j
PDI j DP j DP j w n ( )  ( ) / ( )0 NSITE Unitless
SMWN M j n ( ) Number-average
molecular weight at site
j
M j DP j M j n n seg ( )  ( ) ( ) 0 NSITE Unitless
SMWW M j w ( ) Weight-average
j
M j DP j M j w w seg ( )  ( ) ( ) 0 NSITE Unitless
SMWZ M j z ( ) Z-average molecular
weight at site j M j DP j M j z z seg ( )  ( ) ( ) 0 NSITE Unitless
SMWSEG M j seg ( ) Average segment
j
Mseg ( j) Fp (i, j)Mi 0 NSITE Unitless
SZMOM 0( j) Zeroth moment of chain
length distribution at
site j
---- 2 NSITE Mole
flow
SFMOM 1( j) First moment of chain
site j
  1( j)  1(i, j) 0 NSITE Mole
flow
SSMOM 2( j) Second moment of chain
site j
---- 2 NSITE Mole
flow
STMOM 3( j) Third moment of chain
site j
---- 2 NSITE Mole
flow
SSFLOW 1(i, j) Mole flow of segments
of type I at site j
---- 2 NSEG,
NSITE
Mole
flow
SSFRAC F i j p ( , ) Mole fraction of
segments of type I at
site j
Fp (i, j)   (i, j) /  ( j) 1 1
0 NSEG;
NSITE
Unitless
SEFRAC F i j e ( , ) Fraction of chain end
segments of type i at
site j
( , )   ( , ) / ( , 1 1
F i j i j i j e
ends
0 NEND,
NSITE
Unitless
SLCB LCB( j) Number of long chain
branches at site j
---- 2 NSITE Mole
flow
SCB( j)
FLCB( j)
SSCB Number of short chain
branches at site j
---- 2 NSITE Mole
flow
SFLCB Long chain branching
frequency at site j
0 NSITE Unitless
FSCB( j)
SFSCB Short chain branching
frequency at site j
0 NSITE Unitless
FSP( j)
SPFRAC Mass fraction of
composite polymers at
that site
0 NSITE Unitless
j = Site number
 103
FLCB j LCB j
( ) ( )
j
( )
1
 103
FSLB j SCB j
( ) ( )
j
( )
1

Attribute Definitions – Site-Based Live Polymer Attribute Set
LSDPN DP L ( j ) Number average
n
DP of live
polymer
L ( )   ( ) /  1 0( ) 0 NSITE Unitless
DP j j j n
LSDPW DP j w
L ( ) Weight average
DP of live
polymer
L ( )   ( ) /  2 1( ) 0 NSITE Unitless
DP j j j w
LSPDI PDI L( j) Polydispersity
index of live
polymer
( )  ( ) / L( ) 0 NSITE Unitless
PDI L j DP L
j DP j
w
n
LSMWN M j n
L ( ) Number average
MW of live
polymer
L
( )  L
( ) L ( ) 0 NSITE Unitless
M j DP j M j n
n
seg
LSMWW M j w
L ( ) Weight average
MW of live
polymer
L
( )  L
( ) L ( ) 0 NSITE Unitless
M j DP j M j w
w
seg
LSMWSEG M j seg
L ( ) Average segment
molecular weight
of live polymer
L
p i ( )  ( , ) 0 NSITE Unitless
M j LF i j M seg
LSZMOM 0 ( j) Zeroth moment
of live polymer
  0 ( j)  0 (i, j) 0 NSITE Mole
flow
LSFMOM 1( j) First moment of
live polymer
  1( j)  1(i, j) 0 NSITE Mole
flow
LSSMOM 2 ( j) Second moment
of live polymer
---- 2 NSITE Mole
flow
LSSFLOW 1(i, j) Segment flow
rates in live
polymer
---- 2 NSEG,
NSITE
Mole
flow
LSSFRAC LF i p ( ) Segment mole
fraction in live
polymer
LFp (i, j)   (i, j) /  ( j) 1 1
0 NSEG,
NSITE
Unitless
LSEFLOW 0 (i, j) End segment flow
rates in live
polymer
---- 2 NSEG,
NSITE
Mole
flow
LSEFRAC LF i j e ( , ) End segment
mole fractions in
live polymer
LFe (i, j)   (i, j) /  ( j) 0 0
0 NSEG,
NSITE
Unitless
LSPFRAC F j lp ( ) Fraction of
polymer that is
live
F j 
( ) 
( j
)
lp 
( j )
0
0
0 NSITE Mole
fraction
j = Site number

Attribute Definitions – Site-Based Aggregate Polymer Attribute Set
ASDPN DP A( j ) Number average DP
n
A( )   ( ) /  1 0( ) 0 NSITE Unitless
of aggregate polymer DP j j j n
ASDPW DP j w
A( ) Weight average DP of
A( )   ( ) /  2 1( ) 0 NSITE Unitless
aggregate polymer DP j j j w
ASPDI PDI A( j) Polydispersity index
( )  ( ) / A( ) 0 NSITE Unitless
PDI A j DP A
j DP j
of aggregate polymer w
n
ASMWN M j n
A( ) Number average MW
A
( )  A
( ) A ( ) 0 NSITE Unitless
M j DP j M j of aggregate polymer n
n
seg
ASMWW M j w
A( ) Weight average MW
A
( )  A
( ) A ( ) 0 NSITE Unitless
M j DP j M j of aggregate polymer w
w
seg
ASMWSEG M j seg
A ( ) Average segment
molecular weight of
aggregate polymer
A
p i ( )  ( , ) 0 NSITE Unitless
M j AF i j M seg
aggregate polymer   0 0 ( j)  (i, j) 0 NSITE Mole
flow
ASZMOM 0( j) Zeroth moment of
aggregate polymer   1 1 ( j)  (i, j) 0 NSITE Mole
flow
ASFMOM 1( j) First moment of
ASSMOM 2( j) Second moment of
aggregate polymer
---- 2 NSITE Mole
flow
ASSFLOW 1(i, j) Segment flow rates
in aggregate polymer
---- 2 NSEG,
NSITE
Mole
flow
ASSFRAC AF i p ( ) Segment mole
fraction in aggregate
polymer
AF i j i j j p ( , )   ( , ) /  ( ) 1 1
0 NSEG,
NSITE
Unitless
ASEFLOW 0(i, j) End segment flow
rates in aggregate
polymer
---- 2 NSEG,
NSITE
Mole
flow
ASEFRAC AF i j e ( , ) End segment mole
fractions in aggregate
polymer
AF i j i j j e( , )   ( , ) /  ( ) 0 0
0 NSEG,
NSITE
Unitless
ASPFRAC F j ap ( ) Fraction of polymer
that is aggregate F j
j
( )
( )


0
0
( )

ap j 0 NSITE Mole
fraction
DSEFLOW 0 (i, j) End segment flow
rates in dissociated
(from aggregate)
polymer
---- 2 NSEG,
NSITE
---
DSSFLOW 1(i, j) Segment polymer
flow rates in
dissociated (from
aggregate) polymer
---- 2 NSEG,
NSITE
---
DSSMOM 2 ( j) Second moment of
dissociated (from
aggregate) polymer
---- 2 NSITE ---
j = Site number

The following table lists the minimum required component attributes by
model:
Model Attributes
Property
Models
MWN, DPN or both ZMOM and FMOM
SFRAC or SFLOW
Emulsion MWN, DPN or both ZMOM and FMOM
SFRAC or SFLOW
DIAV or both PSDZMOM and PSDFMOM
Other polymer particle attributes (optional)
Free-Radical MWN, DPN or both ZMOM and FMOM
SFRAC or SFLOW
Other composite attributes (optional)
Composite live attributes (optional)
Step-Growth MWN, DPN or both ZMOM and FMOM
SFRAC or SFLOW
Ziegler-Natta MWN, DPN or both ZMOM and FMOM
SFRAC or SFLOW
Other composite attributes (optional)
Composite live attributes (optional)
Site based component attributes (optional)
Site based live component attributes (optional)
Ionic SZMOM, LSEFLOW
ASEFLOW, DSEFLOW (if association reaction
present)
LSSFLOW, SSFLOW
ASSFLOW, DSSFLOW (if association reaction
present)
Site-Based Species Attributes
There are two types of site-based species attributes:
 Zielger-Natta catalyst attributes
 Ionic initiator attributes
Zielger-Natta Catalyst attributes
Component attributes are used to track multi-site Ziegler-Natta catalyst site
activity, in terms of mole flow and fraction of potential, inhibited, vacant, and
dead sites. The occupied sites are not tracked since that information may be
obtained from the live polymer zeroth moment of chain length distribution.
The site types are defined as follows:
 Potential Sites - these are sites not yet activated.
 Vacant Site - these are activated sites without a growing polymer
attached.

 Inhibited Sites - these are activated sites temporarily in an inactive state.
 Dead Sites - these are sites having permanently lost their catalytic
activity.
 Occupied Sites - these are activated sites with a growing polymer
attached.
The following table lists the catalyst component attributes:
Attribute Description Class Dimension
CPSFLOW Mole flow of potential sites 2 NSITE
CPSFRAC Mole fraction of potential sites 0 NSITE
CVSFLOW Mole flow of vacant sites of type k 2 NSITE
CVSFRAC Mole fraction of vacant sites of type
k
0 NSITE
CISFLOW Mole flow of inhibited sites of type k 2 NSITE
CISFRAC Mole fraction of inhibited sites of
type k
0 NSITE
CDSFLOW Mole flow of dead sites 2 NSITE
CDSFRAC Mole fraction of dead sites 0 NSITE
CMSFLOW Mole flow of metal hydride 2 NSITE
CMSFRAC Mole fraction of metal hydride 0 NSITE
Ionic Initiator Attributes
The component attributes are used to track various states of ionic initiator
(free ions, ion pairs, dormant esters) using a multi-site model.
The following table lists the three ionic component attributes:
Attribute Description Class Dimension
P0FLOW Mole flow of P2 NSITE
0
PT0FLOW Mole flow of PT 0
2 NSITE
CIONFLOW Mole flow of counter-ion
CI
2 NSITE
For more information on ionic attributes, see Ionic Polymerization Model in
Chapter 3.
User Attributes
Generic component attributes are available for tracking user-specified data.
These may be used to track additional properties not available through the
pre-defined attributes.
User component attributes are available as Class 0 through Class 2 attributes.
You must supply a Fortran subroutine to return rates of change for Class 2
attributes and recalculate Class 0 attributes. This would typically be a user
kinetic routine.

User attributes DPSDN and DPSDW are designed to hold data related to
particle size distributions of solid polymers or monomers. The number flow
rates (DPSDN) have units of inverse time. Since particle flow rates are often
very high the user may wish to apply appropriate scaling to define this
attribute on a relative basis (for example use this attribute to track flow rates
in trillions of particles/sec). The DPSDW attribute tracks the mass flow rate of
each element of the distribution. User subroutines are required to use this
advanced feature.
The following table lists the available user component attributes:
Attribute Description Unit Type Dimension
CACLASS0 Class 0 user attribute Unitless 10
CAUSR1…5 Class 1 user attributes Unitless 10
CAUSRA…E Class 2 user attributes Mole flow 10
DPSDN Discrete particle size
distribution, particle number
flow rates. Class 2.
Inverse time 50
DPSDW Discrete particle size
distribution, particle mass flow
rates. Class 2.
Mass flow 50
Component Attribute
Initialization
In cases where polymer is present in the process feed streams, values for the
polymer component attributes must be specified. Enter this information while
specifying the feed stream conditions.
Within Aspen Polymers, material streams are made up of substreams that
carry the flow of material of different types:
 Conventional vapor/liquid flow goes into the “Mixed” substream type
 Solid polymer and other solid components which do not participate in
phase equilibrium go into the “Cisolid” substream type
Most simulations only make use of the “Mixed” substream. In this substream,
you would enter the conditions, such as temperature and pressure, the
number of phases (2 if both vapor and liquid are present), and the
composition in terms of component flows or fractions (along with the total
stream flow).
If one of the components for which you enter composition data is a polymer
or a catalyst, you must specify its component attributes. Because users are
allowed to specify either Class 0 or Class 2 component attributes, an
initialization mechanism had to be defined to calculate the corresponding
Class 2. Remember that the Class 2 attributes are the ones which are
converged upon during simulation.

Attribute Initialization Scheme
The attribute initialization scheme performs several important functions. In
addition to calculating the needed Class 2 attributes, it automatically
calculates an expanded component attribute set from the minimum required
and specified by the user. The minimum required attributes are:
 Segment flow rates (SFLOW), or segment fractions (SFRAC)
 Number average degree of polymerization (DPN), or both
 Zeroth and first moment of chain length distribution (ZMOM and FMOM)
From this set, several other attributes can be calculated using the definitions
given in the attribute definition tables provided earlier in this chapter. The
scheme uses priority rules to decide how to calculate each attribute.
The following table describes the calculation methods and order of priority.
The initialization scheme is also used for recalculating Class 0 attributes
during flowsheet convergence. Finally, it can be considered as a method of
ensuring consistency between interrelated attributes.
The Aspen Polymers component attribute initialization methodology is:
Attribute Calculated from† Priority
Composite Bulk Polymer Attribute Set
SFRAC SFRAC
SFLOW / SUM (SFLOW)
1 / NSEG
1
2
3
ZMOM ZMOM
FMOM / DPN
FMOM*MWSEG / MWN
PDI*FMOM*FMOM / SMOM
1
2
3
4
FMOM SUM (SFLOW)
PMASS / MWSEG
1
2
SMOM SMOM
FMOM*DPW
FMOM*MWW / MWSEG
FMOM*FMOM*PDI / ZMOM
ZMOM
1
2
3
4
5
TMOM TMOM
SMOM*DPZ
SMOM*MWZ / MWSEG
1
2
3
LCB LCB
FMOM*FLCB / 1.E3
1
2
SCB SCB
FMOM*FSCB / 1.E3
1
2
PSDZMOM PSDZMOM 1
PSDFMOM PSDFMOM
PMASS / PDENS
1
2
PSDSMOM PSDSMOM 1
PSDTMOM PSDTMOM 1

VOLN VOLN
PSDFMOM / PSDZMOM
0.0
1
2
3
VOLV VOLV
PSDSMOM / PSDSMOM / PSDFMOM
0.0
1
2
3
VOLZ VOLZ
PSDTMOM / PSDSMOM
0.0
1
2
3
DIAV DIAV
(6.0*PSDFMOM /  / PSDZMOM)
0.0
1
2
3
PDV PDV
(PSDZMOM*PSDSMOM) / (PSDFMOM)
0.0
1
2
3
Composite Live Polymer Attribute Set
LSFRAC LSFRAC
LSFLOW / SUM (LSFLOW)
1 / NSEG
1
2
3
LZMOM LZMOM
LPFRA*ZMOM
LFMOM / LDPN
LFMOM*LMWSEG / LMWN
LPDI*LFMOM*LFMOM / LSMOM
1
2
3
4
5
LFMOM SUM (LSFLOW)
LZMOM*LDPN
LZMOM*LMWN / LMWSEG
LZMOM*LSMOM / LPDI
1
2
3
4
LSMOM LSMOM
LFMOM*LDPW
LFMOM*LMWW / LMWSEG
LFMOM*LFMOM*LPDI / LZMOM
1
2
3
4
Composite Aggregate Polymer Attribute Set
ASFRAC ASFRAC
ASFLOW / SUM (ASFLOW)
1 / NSEG
1
2
3

AZMOM AZMOM
APFRA*ZMOM
AFMOM / ADPN
AFMOM*AMWSEG / AMWN
APDI*AFMOM*AFMOM / ASMOM
1
2
3
4
5
AFMOM SUM (ASFLOW)
AZMOM*ADPN
AZMOM*AMWN / AMWSEG
AZMOM*ASMOM / APDI
1
2
3
4
ASMOM ASMOM
AFMOM*ADPW
AFMOM*AMWW / AMWSEG
AFMOM*AFMOM*APDI / AZMOM
1
2
3
4
Site Based Bulk Polymer Attribute Set
SSFRAC SSFRAC
SSFLOW / SUM (SSFLOW)
1 / NSEG
1
2
3
SZMOM SZMOM
SFMOM / SDPN
SFMOM*SMWSEG / SMWN
SPDI*SFMOM*SFMOM / SSMOM
1
2
3
4
SFMOM SUM(SSFLOW)
SPFRAC*PMASS / SMWSEG
1
2
SSMOM SSMOM
SFMOM*SDPW
SFMOM*SMWW / SMWSEG
SFMOM*SFMOM*SPDI / SZMOM
SZMOM
1
2
3
4
5
STMOM STMOM
SSMOM*SDPZ
SSMOM*SMWZ / SMWSEG
1
2
3
SLCB SLCB
SFMOM*SFLCB / 1.E3
1
2
SSCB SSCB
SFMOM*SFLCB / 1.E3
1
2
Site Based Live Polymer Attribute Set
LSSFRAC LSSFRAC
LSSFLOW / SUM (LSSFLOW)
1 / NSEG
1
2
3

LSZMOM LSZMOM
LSPFRA*SZMOM
LFSMOM / SLDPN
LSFMOM*LSMWSEG / SLMWN
LSPDI*LSFMOM*LSFMOM / LSSMOM
1
2
3
4
5
LSFMOM SUM (LSSFLOW)
LSZMOM*LSDPN
LSZMOM*LSMWN / LSMWSEG
DSQRT (LSZMOM*LSSMOM / LSPDI)
1
2
3
4
LSSMOM LSSMOM
LSFMOM*LSDPW
LSFMOM*LSMWW / LSMWSEG
LSFMOM*LSFMOM*LSPDI / LSZMOM
1
2
3
4
Site Based Aggregate Polymer Attribute Set
ASSFRAC ASSFRAC
ASSFLOW / SUM (ASSFLOW)
1 / NSEG
1
2
3
ASZMOM ASZMOM
ASPFRA*SZMOM
AFSMOM / SADPN
ASFMOM*ASMWSEG / SAMWN
ASPDI*ASFMOM*ASFMOM / ASSMOM
1
2
3
4
5
ASFMOM SUM (ASSFLOW)
ASZMOM*ASDPN
ASZMOM*ASMWN / ASMWSEG
DSQRT (ASZMOM*ASSMOM / ASPDI)
1
2
3
4
ASSMOM ASSMOM
ASFMOM*ASDPW
ASFMOM*ASMWW / ASMWSEG
ASFMOM*ASFMOM*ASPDI / ASZMOM
1
2
3
4
† PMASS is polymer mass, PDENS is polymer density
Component Attribute Scale
Factors
Aspen Plus uses numerical solvers to resolve flowsheet recycle streams and to
solve the conservation equations in each of the kinetic reactor models
(RCSTR, RPLUG, and RBATCH). The solver algorithms use scaled variables.
Typically, the ideal scale factors for each type of variable should be on the
same order of magnitude as the variable itself. In other words, the solvers
work best when the scaled variables are all close to unity.

In Aspen Polymers, default scaling factors are defined for each type of
component attribute variable. These defaults are designed to address a wide
range of problems, however they may not be ideal for any particular problem.
The Scaling form lets you view and change the default scaling factors for each
type of component attribute.
Under some circumstances, you may be able to improve the reactor and/or
flowsheet recycle stream convergence by optimizing the attribute scaling
factors. For example, in a Ziegler-Natta polymerization process the live end
flow rate (LEFLOW) and the related attributes LZMOM and LSZMOM are
sensitive to the catalyst activity. Highly active catalysts result in very low live
end flow rates. Further, the number of vacant and potential sites (CVSFLOW
and CPSFLOW) may be very low for the catalyst.
The Scaling form can be used to specify more accurate scaling factors for the
component attributes for polymers, catalysts, and other types of attributed
components.
Reducing the scaling factors on this form tightens the tolerance on the
selected variables. If the scaling factors are set too low, the tolerance will be
unreasonably tight, leading to convergence problems or excessive CPU time.
If the scaling factors are set too high, the problem may be loosely converged
and the simulation accuracy may suffer.
The reactor models and flowsheet recycle convergence algorithms currently
ignore the attribute upper bound limits that appear on this form.
Specifying Component
Attributes
There are several categories of components for which you can specify
component attributes:
 Polymers
 Site-based components
 Conventional components
Specifying Polymer Component Attributes
See Specifying Polymers on page 29.
Specifying Site-Based Component
Attributes
See Specifying Site-Based Components on page 30.

Specifying Conventional Component
Attributes
You can associate attributes to conventional components by selecting user
attributes. Typically, you do this if you have a user subroutine to return
values for these attributes.
To access the user component attribute selection form:
2 From the Components folder, click Component Attributes.
To associate user attributes to conventional components:
1 On the Selection sheet, specify the component name in the Component
field.
2 In the Attribute field, specify the attribute name.
3 Continue adding as many attributes as needed.
Initializing Component Attributes in
Streams or Blocks
If you have an attributed component present in a feed stream, you must
specify component attribute values for that component.
To access the component attribute input form for a stream:
1 From the Process Flowsheet window, use the right mouse button to click
the feed stream.
2 Click Input.
3 From the stream input specifications sheet, click the Component Attr.
tab.
4 On the Component Attr. sheet, select the Component ID.
5 For each attribute, select the Attribute ID and enter the values for the
attributes.
If you have an attributed component produced within a reactor, you can
specify attribute values (product values or product value estimates) for that
component. This is not available for all reactors.
For a description of the treatment of component attributes in reactors, see
Steady-State Unit Operation Models in Chapter 4.
To access the component attribute input form for a reactor:
the reactor.
2 Click Input.
3 From the reactor input specifications sheet, click the Component Attr.
tab.
4 On the Component Attr. sheet, select the Component ID.
5 For each attribute, select the Attribute ID and enter the values for the
attributes.

Specifying Component Attribute Scaling
Factors
You can override default component attribute convergence parameters for
polymer or catalyst components. Adjusting the scaling factor helps you
improve flowsheet convergence and internal convergence in reactor models.
Typically, the scaling factor should be the same order as the expected value
of the variable.
To access the component attribute scaling form:
2 From the Components folder, click Scaling.
To adjust the default scaling factor and upper bound of defined attributes:
1 On the Input tab, specify the component name in the Component ID
field.
2 In the Attribute field, specify the attribute name.
3 Continue adding as many attributes as needed.
4 Adjust the Scaling factor and/or Upper bound as needed.
References
Aspen Plus User Guide. Burlington, MA: Aspen Technology, Inc.

5 Structural Property
Distributions
This section discusses the mechanism available in Aspen Polymers (formerly
known as Aspen Polymers Plus) for tracking structural property distributions,
in particular chain size distribution, for chain-growth polymerization processes
(U.S. Patent No. 6,093,211).
 Property Distribution Types, 55
 Distribution Functions, 56
 Distributions in Process Models, 58
 Mechanism for Tracking Distributions, 65
 Requesting Distribution Calculations, 69
Property Distribution Types
The common polymer structural properties for which distributions are typically
considered include:
 Chain size - molecular weight or chain length
 Copolymer composition
 Degree of branching
 Polymer particle size
In order to accurately characterize a polymer component, and maintain
control of polymer product properties, engineers must concern themselves
with these distributions.
From a modeling standpoint, many theoretical and empirical functions have
been developed to represent distributions. These functions tend to fall into
categories derived from their formulation, or from their graphical
representation.
For example, distributions that consider two dependent parameters
simultaneously (for example, chain size and copolymer composition) are
termed bivariate distributions.
5 Structural Property Distributions 55

Distributions that mimic the normal bell-shaped graphical representation are
called unimodal distributions.
This is in contrast with distributions that reveal several peaks and are called
bimodal or multimodal distributions. The following figure shows examples of
unimodal and bimodal distributions:
Distribution Functions
In the majority of cases, the distribution functions proposed in the literature
are based on a statistical approach and use one of three types of
mathematical functions: binomial, Poisson or Gaussian.
The parameters in these distribution functions can easily be calculated from
the polymer average properties (degree of polymerization, polydispersity
index, etc.). The following are the common distribution functions that have
been applied to the calculation of polymer property distributions:
 Schulz-Flory Most Probable (Flory, 1936, 1953; Schulz, 1935, 1939)
 Schulz (Schulz, 1935, 1939)
 Weibull-Tung Generalized Exponential (Tung, 1956; Weibull, 1951)
 Normal (Biesenberger & Sebastian, 1983)
 Wesslau Logarithmic Normal (Wesslau, 1956)
 Lansing Logarithmic Normal (Lansing, 1935)
 Poisson (Biesenberger & Sebastian, 1983)
 Zimm (Zimm, 1948)
 Stockmayer Bivariate (Stockmayer, 1945)
In addition to these distribution functions, a method using the moments of
distributions is also available (Tompa, 1976). Of these functions, two have
greater importance for Aspen Polymers.
Schulz-Flory Most Probable Distribution
Schulz and Flory developed a one-parameter equation to represent the
distribution of polymers falling into one of the following categories:
56 5 Structural Property Distributions

 Addition polymers - formed by a constant rate of initiation, with invariant
monomer concentration, with termination by disproportionation only, and
with no chain transfer to monomer
 Linear condensation polymers - obeying the assumption of equal
reactivities of chain ends or linear condensation polymers formed by
random interchange of units
 Low molecular weight polymer - formed from a high molecular weight
polymer by random scission
The Schulz-Flory distribution is also known as the Most-Probable distribution
since it is dictated by the probability of random events, such as the location of
a scission reaction on a long-chain molecule. The number or mole-fraction
distribution and the weight fraction distribution are given by:
Mole-Fraction Distribution
F(r)  pr1(1 p) (number distribution)
Weight-Fraction Distribution
W(r)  rpr1(1 p)2 (weight distribution)
Where:
p = Extent of reaction
r = Size of the molecule or number of segments
For addition polymerizations p is the probability that a growing live polymer
molecule will propagate. For step-growth reactions, p is the fractional
conversion of monomer end groups.
From these distributions, the number, weight, and z-average degree of
polymerization are:
DP
1
(1 )
n 

p DP p
( 1

)
( 1

)
w p 
F(r)  pr1(1 p)
PDI  1 p
To generate the distribution, p can be calculated from degree of
polymerization as:
p
 1 1
DPn
Note that the polydispersity approaches two as p  unity.

Stockmayer Bivariate Distribution
There are cases where two polymer property distributions must be considered
simultaneously, which are called bivariate. Stockmayer developed a
distribution function to consider both chain size and composition distribution
for example (Stockmayer, 1945).
This model may be extended to other combinations of polymer properties
such as chain size and long chain branching distribution for the case of
copolymers.
Distributions in Process Models
There is a great demand to know the full molecular weight distribution,
particularly for complex distributions that may have a shoulder, or are even
bimodal. This information is needed for optimization of rheological and
mechanical properties of the final polymer product.
Within Aspen Polymers a dual approach for determining polymer properties is
used:
 Method of moments continues to be the preferred approach for calculating
average properties.
 Method of instantaneous properties is used to calculate distributions. This
method addresses the issue of data storage and computational complexity
in tracking distributions.
Under special circumstances, the most general form of the instantaneous
distribution function reduces to Flory’s most probable distribution. The
instantaneous distribution functions are unimodal. However, the distribution
functions for polymer accumulated in a multi-reactor system may be
multimodal.
Average Properties and Moments
It is convenient to examine polymer molecular properties in terms of
averages instead of considering the complete distribution. Average properties
must be determined from the actual distributions either through distribution
moments or through instantaneous properties.
The average properties tracked for polymers were described in the Polymer
Component Attributes section on page 35. These properties are calculated
using the method of moments within kinetic models.
For a given property s, the property distribution may be described by a
frequency function f when the property is a discrete variable, and by a
s density function f (s)
when the property s is continuous.
Therefore, f and f (s) represent the portion (for example, number, weight,
s volume, fraction) of the population whose property is exactly s (discrete) or
whose property lies between s and s + ds.
The frequency and density distribution functions are respectively:

Frequency Function
F f S s
S
 
s
0
and
Density Function
F S S
f s ds
( )   ( ) s
0
Where:
s= Initial value of s
0 S = Arbitrary higher value (Biesenberger & Sebastian,
1983)
Distribution moments may be defined from the origin of the average property,
i.e. property is equal to 0, or from the mean value of that property. The
moments employed in Aspen Polymers use the first approach.
In this case, the generalized form of the relationship between distribution
moment and distribution function is shown below:


s f
s
s f  s 
ds
k
k
all s
k
all s


 
 
for the frequency function
for the density function
Where:
 = Moment
k = Moment order (e.g. 0-3 for zeroth through third
moment)
s = Property value (e.g. chain length, molecular weight,
particle size, etc.)
f s = Frequency function
f (s) = Density function
Average Properties
The average properties can be calculated as ratios of the moments. Number
average is the ratio of first to zeroth moment,   1 0 / . Weight or Volume
average is the ratio of second to first moment,   2 1 / . Z-average is the ratio
of third to second moment,   3 2 / .
For the case of chain length distribution the moment frequency distribution is
given by:
m
n m
Q
n 5 Structural Property Distributions 59

Where:
 = Moment
m = Moment order
n = Chain length or degree of polymerization
Q= Number of moles of polymer of length n
n The average chain length properties are then:
DPn   /
 1 0 DPw   /
 2 1 DPz   /
 3 2 PDI    /  2
2 0 1
A similar definition of moments for the frequency distribution can be applied
to molecular weight. Typically, in Aspen Polymers it is applied to chain length.
Then the average molecular weight values are determined using the average
degree of polymerization and average segment molecular weight.
Method of Instantaneous Properties
Applying the method of moments for the calculation of property distributions
has several drawbacks. In addition to CPU requirements and computational
complexity, a larger number of moments than currently calculated would be
required. Knowledge of leading moments of a distribution does not permit one
to unambiguously construct a complex distribution. One must therefore look
beyond the method of moments for a more powerful method to predict these
complex distributions.
A better approach for generating molecular weight distributions consists of
storing reaction rate data throughout the kinetic calculations, and later using
them to construct the full distribution of polymer accumulated in the reactor
system. Such an approach was developed by Hamielec (Hamielec, 1992).
Note: The method of instantaneous properties assumes that polymer
molecules grow and deactivate quickly as the growing center terminates or
moves to another molecule of monomer, solvent, or chain transfer agent. The
method assumes that the polymer molecules are conserved once they are
formed. These assumptions limit the method of instantaneous properties to
addition polymerization (ionic polymerization and step-growth condensation
reactions are specifically excluded because these reaction schemes are
reversible).

Further, the assumption that polymer molecules are conserved once they are
formed can be invalid in the presence of certain side reactions, including
random (thermal) scission, which destroys polymer molecules, and chain
transfer to polymer, which causes inactive polymer molecules to become
active again, leading to long-chain branch formation and significantly
increasing the weight-average molecular weight and PDI. The molecular
weight distribution charts display the MWW and PDI calculated by the method
of moments and the method of instantaneous properties. If the predicted
values for the PDI are not in reasonable agreement with each other, it is most
likely due to these types of side reactions.
In the simplest case, linear polymerization in a single CSTR reactor, the ratios
of termination and chain transfer reaction rates to propagation reaction rates
are stored. The instantaneous chain length distribution is expressed as a
function of these ratios and chain length.
For the case of two CSTRs in series, at steady-state, the outlet polymer
distribution function is the weighted average of the distribution function in
each CSTR taken separately. The case of a plug flow reactor can be
approximated using multiple CSTRs, and similarly for a batch reactor.
By looking at the treatment of such reactor configurations, it can be deduced
that the final polymer distribution is a result of the entire system of reactors.
For this reason, the MWD implementation in Aspen Polymers needs to
consider the proper data structure to track distribution parameters at every
point in the flowsheet. Users should be able to request MWD from any point in
the flowsheet, and from this point the Aspen Plus flowsheet connectivity
information can be used to track polymerization history.
The calculation of chain length distribution for a batch reactor from reaction
rate parameters for linear addition polymerization was described by Hamielec
(Hamielec, 1992).
Consider the equations for the generation and consumption of free radicals. A
similar approach may be used for other active centers (Ziegler-Natta,
metallocene, etc.):
Radical Generation and Consumption Rates
  R  K [ M ][ R o
] 
K [ T ][ R
o
]
I fm
fT
K [ M ]  K [ M ]  K [ T ]   K 
K [ R
o
]
p fm fT tc td
l
o
R

o
K M R
[ ][ 1]
   p
r

K [ M ]  K [ M ]  K [ T ]   K 
K [ R
o
]
p fm fT tc td
r
o
R
Where:
R  K f I I d  2 [ ] = Initiation rate
Instantaneous Distribution Parameters
Introducing two dimensionless parameters  and .

 
o
R 
R  

R
K R K M K T
[ ] [ ] [ ]
fm fT
p
K M
td f
p
td
[ ]
R
R
tc
p
  
o
K R
tc
K M
p
[ ]
[ ]
Where:
R K R M p p
 [ o ][ ] = Propagation rate
R K R td td
 [ o ]2 = Rate of termination by disproportionation
R  K [ R o ]2 = Rate of termination by combination
tc tc
R K R M K R T f fm
 [ o
][ ] [ o ][ ] = Total rate of chain transfer to
fT
small molecules (not
polymers)
If we assume that the stationary-state hypothesis holds, then the initiation
rate is equal to the sum of the termination rates, RI  Rtd  Rtc .
The equations for the rate of generation and consumption of radicals can be
written as follows:
Ro  R 
l
 

1   

 o
1
Ro   R o

r
r
1    

1 Therefore:
Ro r
 R  
 o    r
Where:
 
1
1   

The rate of production of polymer molecules of chain length r , RFp (r) is
given by:
1      1
r

1
R ( r )  r
 K  M   K  T   K R o  R o
  K   R o
 s
R 
FP
r  s
V
d V P
dt
fm fT td
r tc
2 s
1
o

Substituting [ ] Rf o
gives:


 
2
R r K R M   r  FP p

( )  o    
   1 
r

Instantaneous Weight Chain Length Distribution
Therefore, the instantaneous weight chain length distribution can be
calculated from production rate of polymer molecules as follows:
 
 

 
    
    
rR r
rR r

r r
r
1

 

2 1

  
W r     

( )   r
FP r r
FP

1
r
  
1  
2
    


1
 

In other words, W(r) is the weight chain length distribution of dead polymer
chains produced in a small time interval t to t+dt, in a batch reactor. W(r) is
also the weight chain length distribution of dead polymer chains produced in a
CSTR operating at steady-state.
If    , which is the case when the polymer chains are formed by chain
transfer or by termination by disproportionation, this equation reduces to:
W r r r r
r
2 
1
( )  
1
1 2 1 
1
 
 



 
 




Where:
1/ (1 ) = Probability of growth for a polymer radical
 /1  = Probability that a polymer radical stops growing
Chain Length distribution equation
Since r is usually large, W(r) in the original equation on page 63 can be
approximated as a continuous function with small error:
W(r)        r   r.exp  r


   
2

1
    
For most free-radical polymerizations    1 and is of the order
106 102 .
The weight-average chain length for polymer produced instantaneously is
given by:
   
 2       3   
 2 3
 

 

P  rW ( r )

w
r
    2 2
  



1
The instantaneous number-average chain length distribution is given by:
 
1 1
Pn W r

( )
r r

 
  
 
   
 

1
2
  
 
1

2
The polydispersity index for polymer produced instantaneously is given by:

   
   
 
P
P
w
n
2 3 2
PDI
 
   
 

2
Copolymerization
The chain length distribution equation on page 63 applies to both homo- and
co-polymerization with two or more monomer types. When chain growth
polymerizations are done with active center types other than radicals
(Ziegler-Natta, metallocene, etc.)  = 0 in the equation, and the
instantaneous chain length distribution becomes a single parameter 
distribution, which is Flory’s most probable distribution with a polydispersity
index of 2.0.
This equation is the main expression used in Aspen Polymers to generate
chain length distribution. Within the context of a polymerization reactor, this
expression is valid for the case of linear chains of a homopolymer produced in
a single CSTR at steady-state.
CSTR in Series
For the case of two CSTRs in series, the end product polymer distribution is a
composite that is a weighted average of the distributions of polymer produced
in the first and the second reactor:
W r
m
m
( )  1 * W ( r
)  * W ( r )
out 1
m
m
2
2
Where:
m  m  m 1 2 = Total mass of polymer produced in the first and second reactor
per unit time
The distribution function in each reactor is given by the chain length
distribution equation on page 63 with the  and , varying from reactor 1 to
reactor 2, and independent of time under steady-state operation.
Plug Flow & Batch Reactors
A plug flow reactor can be divided into several volume elements and treated
as a series of CSTRs. The , , and polymer mass values are stored for each
volume element and later used for the calculation of the composite chain
length distribution function. A batch reactor is handled using a similar
approach. In this case, the , , and polymer mass values are stored for each
time element.
For linear chains of a copolymer, the difference from the homopolymer case
can be factored into the calculation of the reaction rates for propagation,
termination, and transfer reactions, Rp , Rtc , Rtd , and Rfm .

Mechanism for Tracking
Distributions
The method of instantaneous properties is used to generate chain length
distributions in Aspen Polymers. This method is applied at two levels:
 Reactor level for determining the distribution of polymer newly produced
within the vessel (local distribution), and
 Flowstream level for determining the distribution of polymer produced up
to that point in the flowsheet (cumulative distribution)
Distributions in Kinetic Reactors
Within kinetic reactors, the method of instantaneous properties is used to
determine the distribution of newly produced polymer. The reaction models
calculate the instantaneous properties  and  using the respective equations
on page 62. In addition, the polymer mass corresponding to these values is
saved.
Calculating Distribution Increments
The distribution increments are spaced in logarithmic steps between unity and
the specified upper limit (Upper) using the following formula:
 

 


r max i ,alog i log10
upper i
 


 

 
 


point
N
Where i varies between one and the specified number of points Npoint, and
upper is the user-specified upper bound of the distribution. This spacing
provides good resolution over the entire spectrum of molecular weights, with
emphasis on the low molecular weight species that are more likely to be lost
in fractionation steps. To ensure accuracy, the upper bound should be set at
least five times higher than the observed weight-average degree of
polymerization.
Calculating Local Distributions
For CSTR reactors, the values of  and  are stored during simulation. For
multi-site kinetics (such as Ziegler-Natta kinetics), values of  and  and
polymer mass generation are stored for each site j. These parameters are
used to calculate the local distribution for the CSTR reactor.
For single-site kinetics (free radical and emulsion):

Wlocal  r      r  
r
         
r 1 exp
      

2
For multi-site kinetics (Ziegler-Natta):




  j
      j j j j
W local
 r       r 1 exp
r  
r j       

j j j
, 2
 

m W
local j r j
r m
W ,

j j
j
local
For plug-flow reactors, the values of  and  are calculated at each axial step
during the numerical integration. The local distribution for the reactor is
calculated by summing the instantaneous distributions (from either equations
for local
r W given previously) at each step over all the steps from the reactor
inlet (z = 0) to the reactor outlet (z = L).
For single-site kinetics:

      1 
exp
        z z z z
r z z z z W r   r r  

   z
   
2 ,
L
m W
 L
z r z





z
z
z
local
r
m
W
0
0
,
For multi-site kinetics:



  j ,
z
      j z j z j z j z
W  r     r 
1 exp
r r , j , z j , z j , z j , z , , , ,

     2
    

L
m W
j z r j z
 L
, , ,





z
j z
z
local
r j
m
W
0
,
0
,
The local composite distribution is calculated using the equation given
previously for local
r W for multi-site kinetics.
The local site-based and composite distributions are stored in the reactor
results form and can be viewed from the Reactor folder Results subfolder,
Distributions sheet and plotted using the Aspen Plot Wizard.
Calculating Cumulative Distributions
For a reactor with multiple feeds, the feed distribution is calculated as shown
below:
m W
k r k
feeds
feeds
1
N

N

1




k
m
k
k
feed
r
W
,

The cumulative composite distribution is calculated by adding the feed
distribution to the local composite distribution:
feed local
r
m  W  m 
W
composite
r m m
feed local
local
r
feed
W


The composite cumulative distribution is stored in the outlet stream of the
reactor and can be viewed through the stream results form.
GPC Distributions
If the user selects the GPC Distribution format, the distribution is calculated
as r rW .
Distributions in Process Streams
The polymer distribution calculated within kinetic reactors is transferred into
the outlet stream. This allows flowsheeting of the cumulative distribution
data, i.e. the data follows the polymer component throughout the flowsheet.
The cumulative distribution is stored within the stream.
Aspen Plus provides several different vehicles for associating data with
process streams. These include:
 Basic stream vector, which contains composition and state information
 Component attributes, which are a fundamental tool in Aspen Polymers
 Prop-Sets, which allow users to request additional properties for streams
 Other non-accessible storage space
The first two categories are processed during convergence calculations while
the last two are not.
The information used for calculating the distributions is derived from
converged quantities. There is no need for applying convergence calculations
to the distribution data itself. Therefore, the polymer distribution data is
carried in non-accessible storage space.
The following figure illustrates the procedure followed to generate the
distribution:

68
Verifying the Accuracy of Distribution
Calculations
The molecular weight distributions calculations involve round
associated with the discretization into a finite number of elements and
truncation error due to the upper bound imposed on the distribution. distribution
The
following expressions can be used to verify the accuracy of the distribution.
These expressions calculate the area under the distribution curve and the
number- and weight
weight-average molecular weight of the polymer in the
distribution.
For non-GPC curve
w r r W
   
 1

i
i i i
  2
For GPC curves (distribution stores
 
 
w r 1 r W
 

i i i


i r
i
2
Where:

W
i
r
1
i W = Y-axis value of distribution element
i r = X-axis value of distribution element
round-off error
i w = Mass-fraction of polymer in the size range between
i1 r
The total mass fraction of all elements in the distribution should sum to unity:
1.0
Npoints

w
 i i
1
5 Structural Property Distributions
curves:

1 i W
i rW ):
 


i
1
i
i
i r and

If the calculated area is below unity, the specified upper bound of the
distribution may be too low. If the calculated area is greater than one, the
number of points in the distribution may need to be increased to improve the
accuracy of the distribution calculations.
For chain-length distributions, the value r refers to the molecular size. The
number average and weight average degree of polymerization can be
calculated as:
N 1
Npoints

points
P w i
 
  n 1
r r
 i
1 2 1

 

 


 


i i
P  1
w r 
r
w i i  i 2 1
1
i
For molecular-weight distributions, the term r refers to the molecular weight
of each increment. The number and weight average molecular weights of the
distributions are calculated as:
N 1
Npoints

points
M w i
 
  n 1
r r
 i
1 2 1

 

 


 


i i
M  1
w r 
r
w i i  i 2 1
1
i
The area under the distribution curve and the number- and weight-average
properties of the distribution can be generated by the plot wizard and
displayed on the distribution plots.
For unit operation blocks, the number- and weight-average properties of the
distribution may be verified against the local polymer results, displayed on
the Polymer Results sheet for each reactor.
For streams, the number- and weight-average properties of the distribution
may be verified against the polymer component attributes shown in the
stream table.
Requesting Distribution
Calculations
In order to track distributions in your simulation, you must select the
distribution characteristics. After the simulation is complete you must retrieve
the distribution data for plotting. You can display and plot the distribution
data for the polymerization reactor, or you can display a distribution table for
a stream or for the entire flowsheet.
Selecting Distribution Characteristics
To access the polymer distribution specifications:
3 From the Polymers folder, click Distributions.
The Selection sheet appears.
To request tracking of distributions, from the Selection sheet:

1 In the Polymer ID field, select the polymer for which you would like
distributions tracked.
2 In the Distribution type frame, select the type of distribution.
3 Select the distribution plot characteristics: number of points for plot
resolution, maximum for x-axis.
4 For a GPC distribution, select Perform GPC Distribution Calculations.
The distribution is calculated as rW(r) vs. r where r is number-average
degree of polymerization.
Displaying Distribution Data for a Reactor
Once simulation calculations are complete, you can display and plot the
distribution data for the polymerization reactor (RCSTR, RPLUG, or RBATCH) .
To display the distribution data for a polymerization reactor:
the reactor.
2 Click Results.
3 From the reactor Results form, click the Distributions tab.
4 On the Distributions sheet, select the distribution to view.
To plot the distribution data:
1 From the Plot menu, select Plot Wizard.
2 Click Next.
3 Click a distribution plot sample, then click Next.
4 Change the plot settings as needed, then click Next or Finish to display
the plot.
5 Click the plot graphics to change the plot configuration: reconfigure axes,
legends, or change titles. If you requested the GPC distribution format,
you must set the x-axis to a log scale for the plot to display properly.
Displaying Distribution Data for Streams
To display a distribution data table for a stream:
the feed stream.
2 Click Results.
3 From the Results form, click the Poly. Curves tab.
4 On the Poly. Curves sheet, select the distribution to view.
To display a distribution data table for the flowsheet:
1 From the Data Browser, click Results Summary.
2 From the Results Summary folder, click Streams.
3 From the Streams form, click the Poly. Curves tab.
4 On the Poly. Curves sheet, select the distribution to view.
To plot the distribution data:
1 From the Plot menu, select Plot Wizard.

2 Click Next.
3 Click a distribution plot sample, then click Next.
4 Change the plot settings as needed, then click Next or Finish to display
the plot.
5 Click the plot graphics to change the plot configuration: reconfigure axes,
legends, or change titles.
References
Biesenberger, J. A., & Sebastian, D. H. (1983). Principles of Polymerization
Engineering. New York: Wiley-Interscience.
Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley-
Interscience.
Flory, P. J. (1936). Molecular Size Distribution in Linear Condensation
Polymers. J. Am. Chem. Soc., 58, 1877.
Flory, P. J. (1953). Principles of Polymer Chemistry. Ithaca, NY: Cornell
University Press.
Hamielec, A. E. (1992). Polymerization Processes. In B. Elvers, S. Hawkins, &
G. Schulz (Eds.), Ullmann’s Encyclopedia of Industrial Chemistry (5th Ed.)
A21, (pp. 324-330). New York: VCH.
Lansing, W. D., & Kramer, E.O. (1935). Molecular Weight Analysis of Mixtures
by Sedimentation Equilibrium in the Svedberg Ultracentrifuge. J. Am. Chem.
Soc., 57, 1369.
Peebles, L. H., Jr. (1971). Molecular Weight Distribution in Polymers. New
York: Wiley-Interscience.
Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere
Publishing.
Schulz, G. V. (1935). Uber die Beziehung zwischen Reaktionsgeschwindigkeit
und Zusammensetzung des Reaktionsproduktes bei
Makropolymerisationsvorgängen., Z. Physik. Chem., B30, 379.
Schulz, G. V. (1939). Uber die Kinetik der kettenpolymerisationen. V. Der
Einfluss verschiedener Reaktionsarten auf die Polymolekularität. Z. Physik.
Chem., B43, 25.
Stockmayer, W. H. (1945). J. Chem. Phys., 13, 199.
Tompa, H. (1976). The Calculation of Mole-Weight Distributions from Kinetic
Schemes. In C.H. Bamford & C.F.H. Tipper (Eds.), Comprehensive Chemical
Kinetics, 14A. New York: American Elsevier.
Tung, L. H. (1956). Fractionation of Polyethylene. J. Polymer Sci., 20, 495.
Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. J.
Appl. Mech., 18, 293.
Wesslau, H. (1956). Die Molekulargewichtsverteilung einiger
Niederdruckpolyäthelene. Makromol. Chem., 20, 111.

Zimm, B. H. (1948). Apparatus and Methods for Measurement and
Interpretation of the Angular Variation of Light Scattering; Preliminary Results
on Polystyrene Solutions. J. Chem. Phys., 16, 1099.

6 End-Use Properties
This section describes polymer end-use properties. First, an overview of the
properties of interest for polymers is given, followed by methods available in
Aspen Polymers (formerly known as Aspen Polymers Plus) for calculating
these properties.
 Polymer Properties, 73
 Prop-Set Properties, 73
 End-Use Properties, 74
 Method for Calculating End-Use Properties, 76
 Calculating End-Use Properties, 79
Polymer Properties
Polymer properties fall into many categories:
 Structural properties
 Thermophysical properties - which provide an indication of the
thermodynamic behavior of polymers
 Thermochemical properties - which provide information on thermal
stability
 Transport properties
 Processing and end-use properties - which provide information about
processability and performance during end-use
Polymer structural properties do not provide a direct measure of the
performance of the polymer product during processing or during its end use.
However, there is a relationship between polymer structural properties and
the end use properties. For this reason, it is important to account for such
properties within polymer process simulation models.
Prop-Set Properties
A property set is a collection of thermodynamic, transport, and other
properties that you can use in:
6 End-Use Properties 73

 Stream reports
 Physical property tables and Analysis
 Unit operation model heating/cooling curve reports
 Distillation column stage property reports and performance specifications
 Reactor profiles
 Design specifications and constraints
 Calculator and sensitivity blocks
 Optimization and Data-Fit blocks
Aspen Plus has several built-in property sets that are sufficient for many
applications. The list of built-in property sets is determined by the Template
you choose when creating a new run.
You can use a built-in property set and modify it to fit your needs, or you can
create your own property sets. To see the built-in sets available or to select
one, use the drop-down list on any property set list box. The list prompts
describe the contents of each built-in property set.
For information on defining a property set, see the Aspen Plus User Guide.
The following table summarizes key property sets for the major
thermophysical and transport properties of interest in polymer process
simulations:
Property
Set Name Description
Valid Qualifiers
Phase Comps. Temp. Pres.
CP Pure component heat capacity X X X X
CPMX Mixture heat capacity X X X
K Pure component thermal
conductivity
X X X X
KMX Mixture thermal conductivity X X X
KINVISC Mixture kinematic viscosity X X X
MU Pure component viscosity (zero
shear)
X X X X
MUMX Mixture viscosity (at zero shear) X X X
RHO Pure component density X X X X
RHOMX Mixture density X X X
TG Component glass transition
temp.
X X
TM Component melt transition temp. X X
TRUEFLOW Component true mole flow rate X X
TRUEFRAC Component true mole fraction X X
TRUEMW Component true molecular
weight
X
End-Use Properties
The end-use or processing properties of interest for polymers include
properties that describe their performance in the last stage of the polymer
74 6 End-Use Properties

manufacturing process. Also of interest are properties relating to their
performance when they reach the consumer.
The following table summarizes some end-use properties:
Category Property Availability in
Aspen Polymers
Processing Melt index
Melt index ratio (I10/I2)
Moldability index
Zero-shear viscosity
Density of copolymer
Yes
No
No
Yes
Yes
Polymer
product
Deformation
Toughness/hardness
Flammability
No
No
No
Relationship to Molecular Structure
The end-use properties such as rheological and mechanical properties are
functions of the polymer structural properties and processing history. For
example, long chain branching raises low shear viscosity, increases shear
thinning, delays melt fracture, and increases extrudate swell.
For example, one could relate end-use properties of polyethylene to density,
molecular weight, or melt index (Foster, 1993). See the following table:
Properties Molecular
Weight 
Melt
Index 
Density 
Molecular weight   ---
Melt Index   ---
Impact strength   
Stress crack resistance   
Elongation   ---
Tensile strength   
Melt strength   ---
Orientation   ---
Elasticity   ---
Parision sag resistance   ---
Distortion resistance   ---
Weatherability   
Stiffness --- --- 
Heat Resistance --- --- 
Hardness --- --- 
Permeation resistance --- -- 
Shrinkage --- --- 
Creep resistance --- --- 
Transparency --- --- 

Properties Molecular
Weight 
Melt
Index 
Density 
Flexibility --- --- 
The basic structure-property relationship has attracted much research activity
as the relationship is critical for product performance control. We
recommended you follow the recent developments in structure-property
relationship (Bicerano, 1996; Foster, 1993).
Method for Calculating End-Use
Properties
Few end-use properties of interest for polymers are currently available in
Aspen Polymers. However, the method used for implementing the ones
available is a good mechanism for users to incorporate additional ones if they
have the necessary correlations to molecular structure and/or thermophysical
properties.
Within Aspen Polymers, end-use properties are available as property sets
(Prop-Set). A Prop-Set provides a method for calculating properties for
components within process flowstreams or vessel contents.
A number of built-in Prop-Sets are available (See your Aspen Plus User Guide
documentation). In addition, Prop-Sets allow the specification of a property
set with add-on user correlations. When doing this, a Fortran subroutine is
required to perform the calculations.
End-use polymer properties are available as user property sets. This is
because the correlations available to calculate these properties are highly
empirical and are often dependent on the type of polymer for which they are
used.
User property sets can easily be modified. Users can directly change the
property correlation in the associated Fortran subroutine.
User Property Sets
The following table summarizes the Prop-Set name and Fortran subroutine
name for the built-in user property sets:
Property Prop-Set Name Fortran Subroutine
Melt index MI-KAR, MI-SIN USRPRP
Intrinsic viscosity IV USRPRP
Zero-shear viscosity ZVIS USRPRP
Density of copolymer DENS USRPRP

Intrinsic Viscosity
The intrinsic viscosity is given as:
  K M  JM w w
Where:
 = Intrinsic viscosity
Mw = Weight-average molecular weight
J and K = Correlation constants
Zero-Shear Viscosity
For some ethyl branched paraffinic monodisperse polymers, Arnett and
Thomas reported an empirical correlation for zero-shear viscosity as a
function of molecular weight, number of branched sites per 1000 carbon
atoms, and temperature (Arnett & Thomas, 1980):
 
d 1 
cn
3  
bn
a M 
e B n w
ln  ln ( ) 0
T
Where:
0 =Zero shear viscosity in Poise
Mw =Molecular weight
n =Number of branched sites per 1000 carbon
atoms
a =3.41
d =3523
c =0.832
b =2.368
B(n) =Function of number of branches with:
B(0) =-35.78
B(0.02) =-37.04
B(0.069) =-38.11
B(0.13) =-40.88
B(0.183) =-43.54

Density of Copolymer
Randall and Ruff presented an empirical correlation for semicrystalline
copolymer density (Randall & Ruff, 1988):
   
 
n
 
a b 1 i 2
 


  
a
c a
i
i
1
Where:
 = Actual density
c = Crystalline density
a = Amorphous density
a and b = Correlation constants
n = Minimum crystallization run length of monomer
 = Reaction probability that monomer is followed by
similar monomer
Melt Index
Karol and colleagues suggested a Quackenbos equation for high density
polyethylene prepared with chromocene-based catalysts (Karol et al., 1973;
Quackenbos, 1969):
MI  abM 
cM  d w n
Where:
MI = Melt index
a = 1.0 1018
b = 0.2
c = 0.8
d = -3.9
Mw = Weight-average molecular weight
Mn = Number-average molecular weight
Sinclair suggested a simpler correlation (Sinclair, 1983):
MI
a
Mw
1
b


 

 
Where:
a = 111,525
b = 0.288

Melt Index Ratio
The Quackenbos equation can also be used to correlate melt index ratio.
Calculating End-Use Properties
End-use properties are calculated as Prop-Sets. You must first select which
end-use property to include in the simulation, then you must define this
property as a Prop-Set.
Selecting an End-Use Property
To access end-use property Prop-Sets:
1 From the Data Browser, click Properties.
2 From the Properties folder, click Advanced.
3 From the Advanced folder, click User Properties.
4 From the User Properties object manager, click New.
5 If necessary, change the default ID for the user-property and click OK.
6 From the User Properties Specifications sheet, choose the standard
property as the type (default), then provide the subroutine name.
Create one User-Property for each end-use property.
Adding an End-Use Property Prop-Set
To access Prop-Sets:
1 From the Data Browser, click Properties.
2 From the Properties folder, click Prop-Sets.
3 From the Prop-Sets object manager, click New.
4 If necessary, change the default ID for the Prop-set and click OK.
5 From the Prop-Set Properties sheet, in the Physical Properties field,
select the ID for the end-use property User-Property.
You can have as many User-Properties as needed.
References
Arnett, R. L. & Thomas, C. P. (1980). Zero-Shear Viscosity of Some Ethyl
Branched Paraffinic Model Polymers. J. Phys. Chem., 84, 649-652.
Bicerano, J. (1996). Prediction of Polymer Properties. New York: Marcel
Dekker.
Foster, G.N. (1993). Short Course: Polymer Reaction Engineering. Ontario,
Canada: McMaster Institute for Polymer Production Technology.

Prentice Hall.
Hamielec, A. E. (1996), Polymer Reactor Modeling Technology (Course
Notes). Cambridge, MA: Aspen Technology, Inc.
Karol, F. J., Brown, G. L., & Davison, J. M. (1973) Chromocene-Based
Catalysts for Ethylene Polymerization: Kinetic Parameters. J. of Polymer
Science: Polymer Chemistry Edition, 11, 413-424.
Quackenbos, H. M. (1969). Practical Use of Intrinsic Viscosity for
Polyethylenes. J. of Applied Polymer Science, 13, 341-351.
Randall, J. C. & Ruff, C. J. (1988). A New Look at the 'Run Number' Concept
in Copolymer Characterization. Macromolecules, 21, 3446-3454.
Rudin, A. (1982). The Elements of Polymer Science and Engineering. New
York: Academic Press Inc., Harcourt Brace Jovanovich.
Sinclair, K. B. (1983). Characteristics of Linear LPPE and Description of UCC
Gas Phase Process, Process Economics Report. Menlo Park, CA: SRI
International.

7 Polymerization Reactions
This chapter discusses polymerization mechanisms and kinetics. Topics
discussed in the introductory section include:
 Polymerization Reaction Categories, 81
 Polymerization Process Types, 84
 Aspen Polymers Reaction Models, 85
Following an introduction that provides background information of the
subject, a separate section is devoted to each of the polymerization kinetic
models available in Aspen Polymers (formerly known as Aspen Polymers
Plus).
 Step-Growth Polymerization Model, 89
 Free-Radical Bulk Polymerization Model,
 Emulsion Polymerization Model,
 Ziegler-Natta Polymerization Model,
 Ionic Polymerization Model,
 Segment-Based Reaction Model,
Polymerization Reaction
Categories
Over the years, many classifications have been developed for polymerization
reactions. One classification divides them into condensation and addition
polymerization.
Condensation Polymerization
Condensation polymerization results in the elimination of a smaller molecule,
water for example, through the reaction of bi- or polyfunctional monomers.
Addition Polymerization
Addition polymerization, on the other hand, does not produce small molecule
byproducts. The repeating units within the polymer have the same structure
as the monomers from which they originated.
7 Polymerization Reactions 81

The problem with this classification is that while it describes differences in the
molecular structure of the resulting polymer, it does not fully capture the
differences in the reaction mechanism. Furthermore, a given polymer can be
made by more then one pathway, one which would result in an addition
polymer, and one which would result in a condensation polymer, by this
classification.
For example, Nylon-6 can be made through a caprolactam, and therefore be
labeled an addition polymer, or through an -aminohexanoic acid, and in this
case be labeled a condensation polymer.
Step Growth and Chain Growth Polymerization
A classification that is more useful for capturing the difference in the
mechanisms through which polymers are produced divides polymerization
reactions into step-growth and chain-growth polymerization. The differences
between step-growth and chain-growth polymerization are summarized in the
following tables:
Step Growth
Polymerization
Chain Growth
Polymerization
Monomer type Bi-, polyfunctional No functionality
Reaction
Single intermolecular
categories
reaction
Several consecutive reactions
for initiation, growth, and
termination
Reacting species Any combination of
monomers, oligomers,
polymer chains
Monomers and active centers
(free-radical, ion, polymer,
catalyst end)
Elimination
product
Small molecule elimination
product for condensation
polymerization only
None
Polymer growth
rate
Slow, chain lifetime of the
order of hours
Rapid, chain lifetime of the
order of seconds
Polymer size High molecular weight at
high conversion
High molecular weight at all
conversion levels
Reaction Type Active Center Initiation Growth Reaction
Step Growth
Condensation Bi-, polyfunctional
end groups
None Nucleophilic substitution
Pseudo
condensation
Bi-, polyfunctional
end groups
None Nucleophilic addition
Ring Scission Bi-, polyfunctional
end groups
Yes for ring
opening
Nucleophilic addition or
substitution
Chain Growth
Free-radical Free radical Chemical,
thermal, radiative
Monomers add on to radical
Coordination Metal complex Catalyst activation Monomers insert into metal
complex carbon bond
Ionic Anion or cation Dissociation Monomers add on at ion pair
82 7 Polymerization Reactions

Step-Growth Polymerization
Step-growth polymerization retains the definition given for condensation
polymers for the majority of cases. That is, monomers react with each other
to eliminate small molecules. Step-growth polymers are formed through the
same reaction type occurring between functional groups located on any
combination of monomers, oligomers, or polymer chains. The polymer chains
continue to grow from both ends as polymerization progresses. The reactions
occur at a relatively slow rate and chains grow slowly.
Some examples of step-growth polymers include polyamides, polyesters,
polycarbonates, and polyurethanes (See Polymer Structure in Chapter 2 for a
discussion of polymer types based on molecular structure).
Step Growth Polymer Categories
Step-growth polymerization can be sub-categorized as condensation,
pseudocondensation, and ring-opening or ring-scission depending on the
chemical pathways through which the reactions occur. The following table lists
typical commercial step-growth polymers:
Polymer
(Trade
Name)
Monomers Repeat Unit Reaction
Type
Applications
(Similar
Polymers)
Polyamide
(Nylon 6,6)
Adipic acid
Hexamethylene
diamine NH (CH2)6NHC(CH2)4C
O O Dicarboxylic
acid +
diamines
Fiber, plastics
(Lycra, Nylon
6)
Polyester
(PET)
Terephthalic acid
Ethylene glycol C
O
O Dicarboxylic
C O CH2 CH2 O
onhydride +
glycols
Fiber (PBT,
Dacron, Nylon)
Polycarbonate
(Lexan)
Bisphenol-A
Phosgene O C
CH3
CH3
O Dihydroxy
O C
reactant +
Phosgene
Lenses,
packaging
(Merlon)
Polyurethane Toluene
diisoyamate
polyether diol
R NH CO O R1
Diisocyanate
+ dialcohol
Foam,
packaging
Chain-Growth Polymerization
Chain growth polymers are formed through the addition of monomers to an
active center (free-radical, ion, or polymer-catalyst bond), in a “chain”
reaction, at a very fast rate. Furthermore, several different types of reaction
occur to initiate, propagate, and terminate polymer growth. Examples of
chain growth polymers include various polyolefins, polyvinyls, and several
copolymers (styrenic copolymers, for example).

Chain Growth Polymer Categories
Chain-growth polymerization can be categorized as free-radical, coordination
complex, or ionic, depending on the type and method of formation of the
active center. The following table lists typical commercial chain-growth
polymers:
Polymer Monomers Repeat Unit Reaction Types Applications
Polyethylene Ethylene Bulk/solution (free-radical)
Coordination complex
(Ziegler-Natta)
Film,
packaging
CH2 CH2
Polystyrene Styrene Bulk/solution/
suspension (free-radical)
Containers,
packaging,
insulation
CH2 CH
Polypropylene Propylene Coordination complex
(Ziegler-Natta)
Films,
packaging,
autoparts,
sealants
CH CH2
CH3
Polyisobutylene Isobutylene Ionic Films, plastic
tubing
Polyvinyl chloride Vinyl
chloride
Bulk/solution/
suspension (free-radical)
Floor
coverings,
pipes
Polymethalmethacryl
ate
Methyl
Methacrylat
e
Bulk/solution (free-radical)
Lenses,
plastics
Styrene butadiene
rubber
Styrene
Butadiene
Emulsion (free-radical) Tires, belting,
shoe soles
CH3
C CH2
CH3
CH2 CH
Cl
CH3
CH2 C
COOCH3
CH2 CH CH2 CH CH CH2
Polymerization Process Types
Step Growth Reaction Sub-classes
In addition to chemical pathways, the environment or process conditions in
which the polymerization reactions occur introduce more sub-classes of
polymers. For example, step-growth reactions may take place as melt phase,
solid-state, solution, or interfacial polymerization:
 Melt-phase processes are carried out above the melting point of the
polymer
 Solid-state processes are carried out below the melting point of the
polymer
 Solution processes are carried out in the presence of an inert solvent
 Interfacial processes are carried out in the interface between an organic
phase and an aqueous phase

Chain Growth Reaction Sub-classes
Chain-growth polymerization may take place in bulk phase, solution,
precipitation, suspension, or emulsion:
 Bulk polymerization is carried out in the bulk monomer phase without a
solvent
 Solution polymerization is carried out in the presence of an inert solvent in
which monomers and polymer are dissolved
 Precipitation polymerization is carried out using a solvent to precipitate
out the polymer
 Suspension polymerization involves monomers suspended as droplets in a
continuous phase (usually water) to which an oil-soluble initiator is added
 Emulsion polymerization involves monomers and micelles dispersed in a
continuous water phase using surfactants. Initiator is added to the
emulsion of partially water soluble monomers in the surfactant solution
There are additional process related classifications that have to do with
reactor geometry. These are discussed in sections covering unit operation
modeling later in this User Guide.
Aspen Polymers Reaction
Models
There are two types of reaction models available in Aspen Polymers:
 Built-in models
 User models
Built-in Models
The polymerization reaction models available in Aspen Polymers are
summarized in the following table:
Model Name Chemistry Processes Polymers
Step-growth
STEP-GROWTH Step-growth condensation Melt phase,
solution,
interfacial
PC, PBT, PET, Nylons
SEGMENT-BAS Step-growth addition Melt phase,
solution,
interfacial
Polyurethanes,
polyimides, PPO,
engineering plastics
Chain-growth
FREE-RAD Free-radical Bulk, solution PS, PVAC, SAN, PMMA
EMULSION Free-radical Emulsion SBR, SBA
ZIEGLER-NAT Ziegler-Natta / metallocene
coordination complex
Bulk, solution HDPE, PP, LLDPE
IONIC Anionic/Cationic group
transfer
Solution PIB, SBR, PEO

Model Name Chemistry Processes Polymers
Generic
SEGMENT-BAS Segment-based power-law
reaction model
N/A PVA from PVAC
In addition to models for the chemistries and process types listed, there is
one model available for generic polymer modification reactions. This model
follows a standard power-law scheme and is used to represent reactions
involving modifications to segments of polymers made through one of the
conventional reaction schemes. One of the standard Aspen Plus reaction
models can also be used in conjunction with the polymerization reaction
models. The standard Aspen Plus reaction models are:
Model Name Description
LHHW Langmuir-Hinshelwood-Hougen-Watson reaction rate expressions
POWERLAW Power-law reaction rate expressions
USER Kinetic rate expressions supplied by user, kinetic rate computed in
user supplied subroutine
For more information about these models, consult the Aspen Plus User Guide
and Aspen Plus User Models.
User Models
There are cases where the built-in models do not provide the features
necessary to model specific polymerization kinetics. Some of the
polymerization reaction models provide capabilities to incorporate user
reactions. In addition, the USER reaction model provides the capabilities for
defining user kinetic schemes.
The USER reaction model is structured to allow the specification of the
reaction stoichiometry. In addition, there are vectors for entering user real
and integer parameters. This input information along with the reaction vessel
contents, in the form of the stream structure, is made available to a user
supplied Fortran subroutine during calculations.
Note that component attributes are part of the stream structure. There is an
update and initialization scheme to automatically process these attributes.
The user supplied Fortran subroutine can return rates for components and
component attributes.
From the subroutine, Aspen Plus utilities including physical property routines,
math utilities, and stream handling utilities can be accessed. Some of these
utilities are documented in Chapter 4 of Aspen Plus User Models.
References
Aspen Plus User Models. Burlington, MA: Aspen Technology, Inc.

Dotson, N. A, Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization
Prentice Hall.
Hamielec, A. E. (1992). Polymerization Processes. In B. Elvers, S. Hawkins, &
G. Schulz (Eds.), Ullmann’s Encyclopedia of Industrial Chemistry (5th Ed.)
A21, (pp. 324-330). New York: VCH.
Odian, G. (1991). Principles of Polymerization, 3rd Ed. New York: John Wiley
& Sons.
Rudin, A. P. (1982). The Elements of Polymer Science and Engineering.
Orlando, FL: Academic Press.
Sun, S. F. (1994). Physical Chemistry of Macromolecules. New York: John
Wiley & Sons.

8 Step-Growth
Polymerization Model
This section covers the step-growth polymerization model available in Aspen
Polymers (formerly known as Aspen Polymers Plus). It begins with general
background information on step-growth polymerization and covers some of
the terms associated with these kinetics. Several industrial polymerization
processes are examined in detail. A discussion of the model features and
usage is also included.
 Summary of Applications, 89
 Step-Growth Processes, 90
 Reaction Kinetic Scheme, 101
 Model Features and Assumptions, 124
 Model Structure, 127
 Specifying Step-Growth Polymerization Kinetics, 155
The Aspen Polymers Examples & Applications Case Book illustrates how to use
the step-growth model to simulate nylon-6 polymerization from caprolactam.
More detailed examples are available in Step-Growth Polymerization Process
Modeling and Product Design by Kevin Seavey and Y. A. Liu, ISBN: 978-0-
470-23823-3, Wiley, 2008.
Summary of Applications
Step-growth polymerization can be used to model various polycondensation
and specialty plastic processes. Some of the applicable polymers are
described below:
 Aliphatic polycarbonates - Transesterification of diols with lower dialkyl
carbonates, dioxolanones, or diphenyl carbonate in the presence of
catalysts such as alkali metal, tin, and titanium compounds.
 Aromatic polycarbonates - Reaction product of bisphenols with carbonic
acid derivatives. May be prepared by transesterification, solution
polymerization, and, most often by interfacial polymerization.
8 Step-Growth Polymerization Model 89

 Polyesters - Produced commercially in two steps: monomer formation by
ester interchange of diesters with diols or esterification of diacids with
diols, followed by polycondensation by removing excess diols to promote
chain extension. This is accomplished commercially on a simple two-vessel
batch process or on large-scale multi-vessel continuous-polymerization
process.
 Polyamides - Produced via direct amidation, reaction of acid chlorides with
amines, ring-opening polymerization, reaction of diacids and
diisocyanates, etc. Commercially prepared by melt polycondensation, ring-opening
polymerization, and low temperature solution polymerization.
 Polyurethanes - Polyurethane isocyanates are usually produced
commercially by the phosgenation of amines. Polyester polyols are
prepared by step-growth polymerization.
Step-Growth Processes
Several commodity polymers, including polyesters, nylons, and
polycarbonate, are manufactured through step-growth polymerization
processes. This section examines some of the major processes that can be
represented using the step-growth polymerization kinetics model.
Polyesters
Continuous Polyethylene-Terephthalate Processes
Polyethylene-terephthalate (PET) is produced by the step-growth
polymerization of ethylene glycol, a diol, and either terephthalic acid, a diacid,
or dimethyl terephthalate, a diester. Most processes are continuous although
many older process lines operate in batch or semi-batch mode.
Direct Esterification
The direct esterification process involves the reaction of ethylene glycol with
terephthalic acid. The terephthalic acid is mixed with excess ethylene glycol to
form a solid-liquid paste. In the continuous process, the monomer paste is
typically fed to a well-mixed reactor, the primary esterifier, which operates at
temperatures of 250-290 C and pressures ranging from one to several
atmospheres. Typical residence times range from one to four hours in this
stage of the process.
A solid at room temperature, terephthalic acid has limited solubility in the
polymer solution, even at the relatively high process temperatures. Further,
the dissolution rate of TPA may be limited by the solid-liquid mass transfer
rate, especially if the average particle size is large, or when the reactor
operates at high temperatures and pressures.
The following figure illustrates a continuous direct esterification process for
PET:
90 8 Step-Growth Polymerization Model

Secondary Esterification
In most continuous plants, the primary esterifier is followed by secondary
and, occasionally, a tertiary esterifier. These reactors range from single-tank
CSTRs to a variety of multiple-stage CSTRs composed of vertical or horizontal
vessels divided into two or more chambers by partitions. Secondary
esterification reactors typically have residence times on the order of an hour,
with temperatures similar to or slightly higher than the primary esterifier. The
secondary esterification reactor is often run under atmospheric conditions,
although slight positive pressure or vacuum pressures are also used in some
processes.
Vapor from the esterification reactors flows to one or more distillation
columns which separate ethylene glycol from the reaction by-products which
include water and acetaldehyde. In some processes, spray-condenser loops
are used to “wash” entrained TPA and vaporized low-molecular weight
oligomers from the vapor stream to prevent oligomer build-up in the
distillation columns.
Glycol Recovery
The ethylene glycol from the esterification distillation columns can be recycled
directly to the esterification reactors, to the paste mixing tank, or, in the case
of high-quality products, it can be collected for further processing to remove
contaminants. The companies which license PET technology use a wide
variety of glycol recovery and recycling schemes. All of these recycling
schemes can be simulated using conventional distillation, flash, and heat
exchanger models available in Aspen Plus.
Esterification Results
The product of the esterification reactors is composed of short-chain
oligomers with some residual monomers. The main oligomer in the product is

bis-hydroxyethyl-terephthalate (BHET), which is slightly volatile under typical
operating conditions. The step-growth model includes an “oligomer” feature
which can be used to account for evaporative loss of linear oligomers such as
BHET.
Transesterification Process
In the transesterification process, dimethyl terephthalate (DMT) is used
instead of terephthalic acid (TPA). One advantage of this process is the
relatively high solubility of DMT, which eliminates the solid-liquid mass
transfer problem in the first stage of the process. A second advantage is the
low acidity of DMT, which reduces several of the side reaction rates and
results in a higher quality polymer. The limitations of the transesterification
process include increased monomer cost, production of methanol as a by-product
(instead of water), and reduced reactivity in the finishing stages.
The transesterification process produces methanol as a reaction by-product.
The methanol is distilled from ethylene glycol through distillation columns.
Recovered glycol may be recycled to the reactor, the paste mixing tank, or
accumulated for additional processing.
It is desirable to minimize the concentration of methylester ends in the feed
to the polymerization section. Obtaining high conversions is very important in
the DMT process because the reverse reaction of methanol with PET is more
highly favored than the reaction of water and PET. A wide variety of
proprietary reactors are used to effect high end-group conversion during the
transesterification process.
Continuous Polymerization
The continuous polymerization process is the same for the direct esterification
and transesterification processes. Typically, the polymerization section
consists of one or more CSTR reactors (pre-polymerization reactors) followed
by one or more horizontal “finishing reactors” (polymerization reactors).
These reactors consist of a series of rotating blades or disks which lift polymer
from a pool at the bottom of the reactor into a vapor space over the pool. The
design criteria of these reactors are to maximize surface area generation
while minimizing back-mixing. In polyester processes, the finishing reactors
are almost always limited by the liquid-vapor mass transfer rates. In some
cases, the pre-polymerization reactors are also limited by mass transfer.
The reactors in the polymerization section operate at increasingly higher
temperatures and lower pressures to enhance the devolatilization of excess
glycol and reaction byproducts such as water, methanol, and acetaldehyde.
Reactor residence times range from thirty minutes to four hours depending on
the number and type of reactors in the polymerization section.
Vapor from the polymerization section is scrubbed by spray-condenser loops
composed of a contacting vessel, accumulation tank, pump, and heat
exchanger. In most plants, vacuum is generated through venturi jets
operated by steam or vaporized glycol. In some process configurations, the
condensed glycol and water mixture is recycled to the esterification columns.
Otherwise, the condensate is accumulated and processed to recover glycol.

Operating Conditions
The esterification and transesterification sections of PET processes frequently
operate below the melting point of the polymer. Under these operating
conditions, the process can be considered solution polymerization. The
polymerization reactors operate above the melting point of the polymer in a
true melt-phase polymerization. The step-growth reaction model may be used
for both modes of operation. In most cases, the same reaction kinetics apply
to both solution- and melt-phase reaction processes.
Final Products
The continuous melt-phase PET processes generally produce polymer with an
average intrinsic viscosity of approximately 0.6 dl/g, which corresponds to a
number-average degree of polymerization near 100 units. This product may
be directly spun as clothing fiber, partially oriented yarn (POY), film, or it may
be cooled and chipped for on- or off-site use.
Recent increases in consumer recycling programs and consumer preference
for unbreakable bottles has created a very large market for polyester bottles.
These bottles are molded from a higher molecular weight polyester chip which
is produced by a solid state process. Fundamentally, the step-growth model
can apply to solid-state polymerization. However, at this time, Aspen
Polymers does not include a solid-state polymerization (SSP) reactor model.
Semi-rigorous SSP models can be developed using a series of CSTR reactors.
Solid phase polymer solutions can be treated as a liquid phase in Aspen
Polymers. The property system switches between liquid-phase property
models and solid-phase property models when the temperature drops below
the melting point of the polymer component.
Batch Polyethylene-Terephthalate Processes
Polyethylene Terephthalate is also produced in batch and semi-batch
processes, as shown in the following figure. Usually, the process consists of
two batch reactors in series. The role of the first reactor is to reach high
conversions of the terephthalate monomer while minimizing undesirable side
reactions. The role of the second reactor is to raise the molecular weight of
the polymer to appropriate levels.

The first reactor is coupled to a column which separates the volatile reaction
by-products from excess ethylene glycol and evaporated oligomers. The
heavy components are continuously returned to the reactor during most of
the batch cycle. Towards the end of the cycle, the evaporated ethylene glycol
and residual monomers are removed and accumulated for re-use in the next
batch.
The batch esterification process commonly uses a semi-continuous feeding
system for the solid TPA. In most batch esterification processes, the reaction
rate is limited by the rate of dissolution of TPA. This is complicated by the
relationship between the mass transfer rates and particle size.
To enhance TPA solubility, a portion of the polymer product is retained in the
reactor at the end of the cycle. The recycled product is used to start the next
batch. This design allows the cycle to start at a higher temperature, reducing
the cycle time for each batch. The trade off between the batch cycle time and
the quantity of recycle polymer is one of the most interesting problems to
examine using simulation technology.
The batch transesterification process is typically operated in true-batch mode,
without recycling polymer. In this process, the monomers, ethylene glycol
and DMT, are charged to the reactor at the beginning of the cycle. The
continuous removal of methanol from the batch reactor makes very high end-group
concentrations possible.
This version of Aspen Plus does not include an appropriate reactor model to
simulate batch polymerization reactors with overhead distillation columns.
AspenTech’s Polyester Technology Package includes several modeling
solutions for representing these types of batch processes in the Aspen Plus
and Aspen Custom Modeler environments.

Second Batch Stage
The liquid product from the batch esterification or transesterification is
charged to a second batch stage. In this stage, the reactor is evacuated as
the temperature is increased. These operating profiles enhance the removal
of excess ethylene glycol from the reaction mixture, allowing these highly
reversible reactions to proceed.
As the polymer viscosity increases, the reactions become limited by the rate
of mass transfer from the liquid phase to the vapor phase due to decreased
surface renewal rates and reduced agitator speeds.
Other Polyester Processes
Polybutylene-terephthalate (PBT) is an engineering plastic frequently used for
machine parts, car body panels, and other applications. Polybutylene
terephthalate is analogous to PET, except butylene glycol is used in place of
ethylene glycol. Most PBT is manufactured from DMT through continuous
transesterification processes, although batch processes and direct
esterification processes are also found in industry.
In the PBT process, tetrahydrofurane, THF, is formed from butylene glycol
end groups as an undesirable reaction by-product. The transesterification
process is favored over direct esterification because the acid end groups in
TPA catalyze the formation of THF.
Polypropylene-terephthalate (PPT) is used for carpet fiber and other
applications. Like PET and PBT, PPT can be manufactured from terephthalic
acid or dimethyl terephthalate. In the PPT process, propylene glycol is used as
the diol monomer.
Polyethylene-naphthalate (PEN) manufacturing processes are under
development by several polyester producers. This new product has a higher
melting point than PET, and is aimed at specific demands, such as hot-fill
bottles, which are not well satisfied by other polyesters. The dimethyl ester
naphthalate monomer is much more expensive than TPA or DMT, so PEN is
frequently produced as a copolymer with PET.
At this time, most PEN is produced in batch processes which are analogous to
the batch PET process. Copolymers of PEN and PET are being used for some
bottling applications already. The similarities in the chemical mechanism for
PET and PEN make them relatively easy to copolymerize in various ratios,
resulting in several product grades with properties intermediate between pure
PET and pure PEN.
Polyester Technology Package
Aspen Technology offers several solutions for polyester processes. The
AspenTech Polyester Technology Package provides steady-state simulation of
melt-phase continuous processes and also includes process models for batch
polyester processes. The Polyester Technology Package is designed for PET
and PBT, but can be easily modified for analogous polyesters such as PEN,
PTT, etc.

Aspen PolyQuestSM, jointly developed with Hosokawa Bepex corporation, is a
simulation package covering all varieties of solid-state PET processes. Aspen
PolyQuest includes detailed and rigorous models for reaction kinetics,
diffusion, heat transfer, and crystallization, as well as a library of detailed unit
operation models for solid-state processing equipment. Aspen PolyQuest runs
on the Aspen Custom Modeler platform. The underlying equation-based
models can be used for dynamic or steady-state process simulation.
The models in these packages account for all the major side reactions in the
process, such as thermal scission, aldehyde formation, DEG formation, and
cyclic trimer formation. The reaction kinetic models consider the influence of
several common catalysts and additives as well as acid catalysis and
uncatalyzed side reactions. The package includes reactor models which
consider solid-liquid mass transfer for the direct esterification process, and
liquid-vapor mass transfer limited kinetics for the polymerization reactors.
The Polyester Technology Package includes models of several common
process configurations, including both batch and continuous processes. The
models predict various quality parameters such as the acid end group
concentration (acid value), intrinsic viscosity, vinyl end content, DEG content,
conversion, etc.
Contact your Aspen Technology sales representative for more information
about the Polyester Technology Package, Aspen PolyQuest, and advanced
consulting services.
Nylon-6
Nylon-6 is produced by ring-opening polymerization of -caprolactam. Water
and caprolactam are fed to a primary reactor where the ring-opening reaction
takes place. The primary reactor may be a single (liquid) phase tubular
reactor, CSTR, or one of a variety of proprietary reactors.
The following figure illustrates a continuous melt-phase nylon-6 process:

VK Column
One of the most well known of these proprietary designs is the Vereinfacht
Kontinuierliches (or VK) column. The VK column is a reactor with a high
aspect ratio which is filled to relatively high liquid levels. The reacting mixture
boils vigorously near the top of the VK column, resulting in considerable radial
and axial mixing. Below this well-mixed zone is a plug-flow zone in which the
hydrostatic pressure is sufficient to suppress boiling. Reactors of this type can
be simulated using one or more two-phase CSTR reactors (model RCSTR) in
series with a single liquid-phase plug flow reactor (model RPlug).
The top of the VK column typically operates near atmospheric pressure. Heat
exchangers inside the upper section of the reactor bring the reactants to
temperatures of 220-270C. Typical residence times are in the order of three
to five hours. A reflux condenser or distillation column over the reactor
returns the monomer and most of the water back to the VK column.
Although the initial stages of Nylon-6,6 polymerization are catalyzed by
water, the water must be removed in later stages to allow the condensation
reactions to proceed to high conversion. Water removal is accomplished by
carrying out the reaction in a series of stages at successively lower pressures.
Secondary stages typically involve one or more CSTR reactors followed by
vertical wiped-film evaporators. Inert gas may be used to strip water from the
polymer melt.
For some products, chain terminators are used to control the molecular
weight of the product. Acetic acid is commonly used, but any monofunctional
acid or alcohol can be used to control molecular weight build-up.
Horizontal finishing reactors may be used to increase the polymer molecular
weight and reduce the residual monomer and cyclic oligomer concentrations.
In these devolatilization stages, the evaporation of water, excess

caprolactam, aminocaproic acid, and cyclic oligomers is limited by the rate of
mass transfer from the liquid phase to the vapor phase.
Nylon-6,6
Nylon-6,6 is manufactured by two types of processes. In the most common
process, dyadic nylon salt is first produced by mixing adipic acid (ADA) in an
aqueous solution of hexamethylene diamine (HMDA). A newer process
involves the direct melt polymerization of the two monomers.
Salt Preparation
In the traditional salting process, the formation of nylon salt ensures
stoichiometric ratios of the two monomers, allowing the production of high
molecular weight polymers. In the salt solution process, solid adipic acid is
dissolved in an aqueous solution of HMDA. The resulting aqueous salt solution
is concentrated by further addition of the monomers and/or by partial
evaporation.
An alternative salting process uses methanol as the primary solvent. Solutions
of adipic acid and HMDA in methanol are prepared separately in continuously
stirred heated tanks. These solutions are mixed in a reactor where the nylon
salt is generated. Most of the nylon salt precipitates out of solution due to the
low solubility of the nylon salt in methanol. A small amount of the salt,
however, remains dissolved in the reactor, resulting in the generation of some
short-chain oligomers. The salt slurry is centrifuged to remove the solid salt.
Methanol is used as a washing solution in the centrifuge to further purify the
salt. The methanol is purified in a distillation column and recycled. The solid
nylon salt is dried and collected for use on- or off-site.
Polymerization from Aqueous Salt Solutions
Most nylon-6,6 is produced in continuous processes made up of several
stages. The primary stage operates at high pressures and temperatures to
control the loss of volatile monomers and to accelerate the reactions. In the
intermediate reactors, the operating pressure is reduced substantially and
much of the excess water is evaporated. The finishing stages of the process
are made up of one or more wiped-film evaporators which help to remove the
remaining residuals.
A typical nylon-6,6 continuous process is shown here:

First Stage
In the first stage, aqueous salt solutions are fed to a reactor which operates
at high temperatures (230-290C) and pressures (> 250 psig). High
temperatures are required to dissolve the salt and to accelerate the reaction
rates. The high pressure is required to avoid excess loss of HMDA, which is
generated by polymerization reactions. In the first reactor, the nylon salt
dissolves and condensation reactions take place between molecules of the
dissolved salt and between the dissolved salt and polymer end groups. Much
of the water which enters with the salt and is generated by the condensation
reactions is boiled off in the first stage due to the high operating temperature.
In some processes, the salt solution is fed to a column over the first reactor.
As the solution flows down the column, excess water is driven off.
Condensation reactions take place in the reactor at the bottom of the column
as well as in the trays of the column. The column also condenses evaporated
HMDA, returning it to the reactor vessel. Additives, such as titanium dioxide,
are fed to the primary reactor vessel.
The reactor vessel is made up of two parts: a separation vessel and a heat
exchanger tube-bank. The separator vessel is located at the bottom of the
column, where it receives the reflux from the column. The liquid at the
bottom of the separator is pumped through the tube-bank heat exchanger,
which acts as the reboiler for the column. The high circulation rates through
the heat exchanger section of the reactor keep the reactor contents well
mixed.

Intermediate Stage
Liquid from the primary reactor must be throttled to lower pressures to
remove water, which allows the reversible condensation reaction to proceed
to higher conversions. The depressurization and devolatilization of the
intermediate are carried out by several different techniques involving a series
of degassing vessels connected by throttle valves. In some processes, a loop-type
reactor is used to reduce the pressure.
Excess HMDA or adipic acid or monofunctional chain stoppers, such as acetic
acid, may be added in the intermediate stages of the process to control the
molecular weight build-up. Catalysts and thermal stabilizers are also added to
the oligomer.
Final Stage
In the final stages of polymerization, wiped-wall evaporators are used to
finish the reaction at high temperatures (up to 300C) and medium vacuum
pressures (760-200 torr). Typical finishing reactor residence times range from
20-60 minutes. The removal of water and excess monomers from the liquid
phase may be limited by the mass transfer rate.
Melt-Phase Polymerization
Recent developments in nylon-6,6 polymerization have led to the
development of continuous melt-phase polymerization processes. Adipic acid
and hexamethylene diamine solutions are fed to a tubular primary reactor,
which operates at very high pressures (approximately 1000 psig),
temperatures around 275C, and residence times of 15-30 minutes. Under
these conditions, boiling does not occur in the reactor.
The pressure is throttled down to 250-350 psig through a series of valves or
tubes of successively larger diameter. The pressure profile must be adjusted
to minimize cooling caused by the rapid evaporation of steam, which can
cause the polymer solution to freeze.
In the final stage, the polymer is brought close to chemical equilibrium (with
dissolved water and excess monomers) in a wiped film evaporator.
Polycarbonate
Polycarbonate is a relatively strong polymer with good optical and mechanical
properties. It is used in several applications including car body parts
(frequently blended with PBT), specialty films, and laser disc media.
Historically, most polycarbonate was produced by interfacial polymerization of
bisphenol-A (BPA) with phosgene. In the interfacial process, the reactions are
relatively fast, but the reaction rate is limited by the mass transfer rates of
the reactants from the bulk liquid phases into the swollen polymer phase.
A limited amount of polycarbonate is produced from BPA and phosgene in a
solution polymerization process. The reaction is carried out by solution
polymerization in pyridine. The pyridine solvent captures chlorine from the
phosgene groups, resulting in pyridine chloride as a reaction by-product.

Recently, the melt-phase polymerization of bisphenol-A with diphenyl
carbonate (DPC) has become an important industrial process. The melt
polymerization process has a significant safety advantage over the interfacial
process because phosgene is highly volatile and extremely toxic. A typical
melt-phase polycarbonate process is shown here:
The monomers, BPA and DPC, are fed in a carefully controlled ratio to a series
of CSTRs. Phenol, which is generated as a reaction by-product, is vaporized in
the reactors and must be condensed and recycled. Distillation columns are
used to recover residual monomers from phenol.
The CSTRs are followed by a series of wiped film evaporators and horizontal
finishing reactors which operate at successively lower pressures to enhance
the removal of residual monomers and phenol. These reactors are limited by
the mass transfer rate of phenol from the melt.
Reaction Kinetic Scheme
This section gives a general overview of nucleophilic reactions and reaction
nomenclature, as well as specific information on polyester, nylon-6, nylon-
6,6, and melt polycarbonate reaction kinetics.
Nucleophilic Reactions
Step-growth polymerization involves reactions between monomers containing
nucleophilic and electrophilic functional groups. Nucleophilic groups are
electron-strong groups, typically alcohols (~OH), amines (~NH2 ), or water.

Electrophilic groups are electron-weak groups such as acids (~COOH), esters
(~COO~), amides (~CONH~), and isocyanates (~NCO). When two chemical
species react, the species with the strongest nucleophilic group is called the
nucleophile; the other reactant bearing the strongest electrophilic group is
called the electrophile.
Nucleophiles and electrophiles participate in bimolecular reactions. Depending
on the types of functional groups in each reactant, the reaction mechanism
may be nucleophilic substitution or nucleophilic addition.
Nucleophilic Substitution
In nucleophilic substitution reactions, a nucleophilic group from one reactant
(the nucleophile) displace a nucleophilic group in the other reactant (the
electrophile), resulting in two new products. (Note: Electrophilic groups are
highlighted in each of the following figures.) Nucleophilic substitution
reactions tend to be highly reversible.
O
CH3OH + HO C
O
HOH + CH C 3O
Nucleophilic
Species
Electrophilic
Species
Electrophilic
Species
Nucleophilic
Species
Forward Reaction Reverse Reaction
Nucleophilic Addition
In nucleophilic addition reactions, the electrophile and nucleophile combine to
form a new functional group. These reactions are typically irreversible.
O
CH3OH + CH3O C NH
O C N
Electrophilic
Species
Nucleophilic
Species
Currently, the step-growth reaction generation algorithm is limited to
condensation reactions. Pseudocondensation reactions must be defined
through the user reaction feature or through the segment-based power-law
reaction model.
In some reverse reactions and re-arrangement reactions, the electrophile
may be a polymer or oligomer. These reactions occur at the bonds which link
two segments together. To fully describe these reactions, the two segments in
the electrophile must be identified. In this case, we refer to the electrophile as
the “victim” reactant and the nucleophile as the “attacking” reactant. The
victim reactant includes a nucleophilic segment and an electrophilic segment.
Attacking
Nucleophilic
Species
Victim
Nucleophilic
Species
Victim
Electrophilic
Species
CH3OH + C O
O
O(CH2)2O C
O O
O(CH2)2OH + CH3O
C C
The following table lists the role of electrophiles and nucleophiles in several
step-growth polymerization processes, as well as the typical reacting

functional groups, the characteristic repeat unit, and the by-product related to
each polymerization process:
Polymer Class Nucleophile Electrophile Repeat Unit Condensate
By-product
Polyester ~OH
~OH
~COOH
~COOCH3
~COOH
~(C=O)O~
~(C=O)O~
~(C=O)O~
~O(C=O)CH3
Polyamide ~COOH ~(C=O)NH~
Polyacetal
(Polycarbonate)
~NH2 H2O
~OH
~OH
~O(C=O)Cl
~O(C=O)Oph
~O(C=O)O~
~O(C=O)O~
H2O
CH3OH
CH3COOH
HCl
PhOH
Polyurethanes
~NH2
~OH
~(C=O)Cl
~N=C=O
~NH(C=O)O~
~NH(C=O)O~
HCl
none
Polyurea ~N=C=O ~NH(C=O)NH
~
none
~NH2
Polyether ~OH none
O
CH CH2
~OCH2C(OH)H~
Reaction Nomenclature
Polymerization reactions are classified by chemical mechanism, by the
number of reacting components, and by the influence a reaction has on the
chain length distribution. This section describes the basic types of reactions
found in step-growth polymerization and serves as a glossary of reaction
nomenclature.
Intermolecular reactions involve two or more molecules.
Intramolecular reactions involve two sites on the same molecule.
Condensation reactions are polymerization reactions which produce a small
molecule as a by-product. Typically, the condensate is a volatile compound
such as water, methanol, acetic acid, or phenol. Step-growth reactions
involving chlorine end groups result in hydrochloric acid or chlorinated
hydrocarbon condensate products.
Reverse condensation reactions are where condensate molecules cleave an
existing polymer chain, producing two smaller chains. Reverse condensation
reactions near the end of a polymer molecule can generate free monomers.
Pseudocondensation reactions are nucleophilic addition reactions. These
reactions involve rearrangement of atoms in two different functional groups,
resulting in a new functional group. No by-products are produced by
pseudocondensation reactions. Pseudocondensation reactions can involve two
monomers, a monomer and a polymer end group, or two polymer end
groups.
Addition reactions are reactions in which small molecules, including free
monomers, dyadic salts, and cyclic monomers and dimers react with the end

of a growing polymer molecule. These reactions are responsible for the
conversion of the monomers and most of the conversion of functional end
groups.
Combination reactions involve reactions between the end groups of two
polymer molecules. In most systems, combination reactions play an
important role in molecular weight growth.
Rearrangement reactions occur between two polymer molecules, resulting in
two new polymer molecules with different molecular weights. These reactions
may involve the end group of one molecule and an internal site on another
molecule, or they may involve internal sites on both molecules.
Ring opening reactions are intermolecular reactions between condensate or
monomer molecules and cyclic monomers or oligomers. Condensate
molecules or monomers react with cyclic compounds, opening the ring
structure to produce linear oligomers or cyclic monomers.
Ring closing reactions are intramolecular reactions which occur between the
two end groups of a linear molecule. Ring-closing reactions which occur
between two end groups of a branched or network molecule are referred to
here as intramolecular cyclization to differentiate them from reactions which
form ring-shaped molecules.
Ring addition reactions are intermolecular reactions between polymer end
groups and cyclic monomers or oligomers. The end group of the polymer links
to the cyclic compound, opening the ring and lengthening the chain of the
linear molecule.
Cyclodepolymerization reactions are intramolecular reactions in which a
polymer end group reacts with a segment in the same molecule, forming a
ring. The ring-shaped molecule is lost from the linear parent molecule,
reducing the molecular weight of the parent.
Terminal monomer loss involves the loss of a monomer unit at the end of a
polymer chain due to thermal degradation mechanisms.
Random scission involves the spontaneous cleavage of a polymer chain due to
thermal degradation.
End group reformation reactions are those reactions which convert one type
of end group into another without influencing the chain length.
The following table summarizes the reactions for step-growth polymerization:

Reaction
Class Reaction Mechanism Reaction Type Reaction Scheme Included
Inter-molecular
Nucleophilic
Substitution
Condensation -
Monomer Addition
M  M  P W 2
P M P W n n    1
Yes
Yes
Condensation - Polymer
Addition
P P P W n m n m    
Yes
Reverse Condensation -
Terminal Monomer Loss
W  P  M  M 2
W P P M n n    1
Yes
Yes
Reverse Condensation -
Scission
W P P P n n m m    
Yes
Forward
Polycondensation
P P P M n m n m     1
Yes
Reverse
Polycondensation
M P P P n n m m     1
Yes
Re-arrangement P P P P n m n m q q     
Yes
Ring Opening W  C  P No
n n Ring Addition P  C  P No
n m n 
m Nucleophilic Addition
(Pseudo-condensation)
Monomer Addition M  M  P2
P M P n n   1
No
No
Polymer Addition P P P n m n m   
No
Intra-molecular
Pseudo-condensation
or Thermal
mechanisms
Terminal Monomer Loss P M M 2  
P P M n n   1
No
No
Scission P P P n n m m   
No
Nucleophilic
Substitution
Ring-Closing P  C  W No
n n Cyclodepolymerization P  P  C No
n n 
m m Nucleophilic Addition Ring-Closing P C n n  No
Pn = Linear polymer with n segments
Cn = Cyclic polymer with n segments (C1 = cyclic monomer, such as caprolactam)
M = Monomer
W = Condensate
Polyester Reaction Kinetics
In the direct esterification process, polyesters are produced by the reaction of
diols, such as ethylene glycol, with diacids, such as terephthalic acid. The
esterification reactions generate one mole of water for each mole of ester
groups formed. The reactions are catalyzed by acid end groups in the polymer
and diacid monomer.

Side Reactions
Several of the key side reactions are also acid-catalyzed. In the PET process,
these reactions include the formation of diethylene glycol, or DEG, from
ethylene glycol. The transesterification process does not involve acids, and
substantially less DEG is produced.
An analogous reaction generates tetrahydrofurane (THF) in the PBT process.
Like DEG formation, THF formation is accelerated by acid end groups. Since
THF poses environmental concerns, the generation of THF should be
minimized. For this reason, PBT is usually produced by the transesterification
route.
Metal acetate catalysts are used to accelerate the reaction rates in the later
stages of the direct esterification process and throughout the
transesterification process. These catalysts accelerate the main reactions and
several side reactions including thermal scission and aldehyde formation.
In the transesterification process, acid end groups may be formed by thermal
degradation reactions or by exchange reactions with water, which may be
formed as a reaction by-product. These acid end groups participate in the
reaction scheme, making transesterification kinetics a superset of
esterification kinetics.
Polymerization Stage
The polymerization stage involves chain building reactions. There are two
main growth mechanisms. Condensation reactions occur between two
polymer end groups, releasing water or methanol. Polymerization reactions
occur between diol end groups in different polymer molecules, generating a
molecule of free glycol.
The polymer end group distribution and molecular weight distribution are
randomized by redistribution reactions.
Polyester Production Final Stages
In the final stages of polyester production, high temperatures lead to thermal
degradation reactions. In the PET process, these reactions degrade glycol end
groups, producing acid ends and free acetaldehyde. Thermal scission
reactions generate acid end groups and oxyvinyl end groups. Analogous
reactions in the PBT process yield butenol and 1,4-butadiene. Additional side
reactions involving these vinyl groups are the main source of color bodies in
polyesters.
Cyclic compounds are formed by ring-closing and cyclodepolymerization
reactions. Cyclic monomers, and some cyclic dimers do not form in
terephthalic polyesters because of steric limitations. Trace amounts of larger
cyclic oligomers, including trimers, tetramers, and pentamers, are commonly
observed in terephthalate polyesters. These cyclic compounds reduce the
quality of the polyester. Cyclic oligomers evaporate from the finishing reactors
and condense in vapor vent lines, causing maintenance problems.
The reaction kinetics of terephthalate polyesters are summarized in the tables
that follow.
The components involved in the reactions are:

Component
ID
Databank
ID
Component
Structure Component Name
TPA C8H6O4-D3 Terephthalic acid
O O
HO C C
OH
T-TPA C8H5O3-E Terephthalic acid end group
O O
C C
OH
B-TPA C8H4O2-R Terephthalate repeat unit
DMT C10H10O4-
D2
Dimethyl terephthalate
O O
C C
O O
CH3O C C
OCH3
T-DMT C9H7O3-E Dimethyl terephthalate end
group
O O
C C
OCH3
MMT none Monomethyl terephthalate
O O
HO C C
OCH3
H2O
CH3OH
H2O H2O Water
MEOH CH4O Methanol
Components In Polyethylene Terephthalate Processes
EG C2H6O2 Ethylene glycol
HO(CH2)2OH
~O(CH2)2OH
~O(CH2)2O~
HO(CH2)2O(CH2)2OH
~O(CH2)2O(CH2)2OH
~O(CH2)2O(CH2)2O~
~OCH=CH2
T-EG C2H5O2-E Ethylene glycol end group
B-EG C2H4O2-R Ethylene glycol repeat unit
DEG C4H10O3 Diethylene glycol
T-DEG C4H9O3-E Diethylene glycol end group
B-DEG C4H8O3-R Diethylene glycol repeat
unit
T-VINYL C2H3O-E Oxyvinyl end group
C3 none Cyclic trimer
G T
T
G T
G
O O
T = C C
G = O(CH2)2O
Components In Polybutylene Terephthalate Processes
BD C4H10O2 1,4 Butane diol
HO(CH2)4OH
~O(CH2)4OH
~O(CH2)4O~
~O(CH2)2CH=CH2
o
T-BD C4H9O2-E 1,4 Butane diol end group
B-BD C4H8O2-R 1,4 Butane diol repeat unit
T-BUTENOL C4H11O2-E Butenol end group
THF C4H8O-4 Tetrahydrofurane

The following table summarizes the step-growth reactions associated with
terephthalate polyesters. For brevity, the table shows a subset of the
reactions which actually occur - an analogous set of reactions involving DEG
are also generated by the step-growth model.
Reaction Type Stoichiometric Reactions - Direct Esterification Route†
Condensation
Polymerization
Rearrangement
O O
O O
1
2
3
4
5
6
HO(CH2)xOH + HO C C
OH C C
HO(CH2)xO OH + H2O
O O
O O
HO OH + H2O
O(CH2)xOH + C C O(CH2)xO C C
OH
O O
O O
HO(CH2)xO + H2O
HO(CH2)xOH + HO C C
C C
O O
O O
O(CH2)xO + H2O
78
O(CH2)xOH + HO C C
C C
O O
O O
9
10
11
12
OH + HO(CH2)xOH
HO(CH2)xO OH
O O
O O
+ HO(CH2)xOH
HO(CH2)xO
O O
O O
13
14
+ HO(CH2)xO
O(CH2)xO
Reaction Type Additional Reactions - Transesterification Route
Condensation
Polymerization
End-group
Exchange
O O
O O
HO(CH2)xOH + CH3O C C
OCH3 C C
O O
CH3O OCH3 + CH3OH
O(CH2)xOH + C C O(CH2)xO OCH3
O O
O O
HO(CH2)xO + CH3OH
HO(CH2)xOH + CH3O C C
C C
O O
O O
O(CH2)xOH + CH3O C C
C C
O O
O(CH2)xOH + C C O(CH2)xO OCH3 + HO(CH2)xOH
HO(CH2)xO OCH3
O O
O O
CH3O C C + CH3OH
H2O HO
+ C C 26
† x = 2 for polyethylene-terephthalate
x = 3 for polypropylene-terephthalate
x = 4 for polybutylene-terephthalate
15
16
17
18
19
20
21
22
HO(CH2)xO OCH3 + CH3OH
O O
C C
O(CH2)xO + CH3OH
23
24
O O
C C
25

The following table describes how to assign rate constants to each of the
reactions listed in the previous table:
Reaction
No.
Attacking
Nucleophilic
Species
Victim
Electrophilic
Species
Victim
Nucleophilic
Species
1 EG TPA none
2 H2O T-TPA T-EG
3 T-EG TPA none
4 H2O T-TPA B-EG
5 EG T-TPA none
6 H2O B-TPA T-EG
7 T-EG T-TPA none
8 H2O B-TPA B-EG
9 T-EG T-TPA T-EG
10 EG T-TPA B-EG
11 T-EG B-TPA T-EG
12 EG B-TPA B-EG
13 T-EG B-TPA B-EG
14 T-EG B-TPA B-EG
15 EG DMT none
16 MEOH T-DMT T-EG
17 T-EG DMT none
18 MEOH T-DMT B-EG
19 EG T-DMT none
20 MEOH B-TPA T-EG
21 T-EG T-DMT none
22 MEOH B-TPA B-EG
23 T-EG T-DMT T-EG
24 EG T-DMT B-EG
25 H2O T-DMT none
26 MEOH T-TPA none
Many of the side reactions in the polyester process are not included in the
reaction generation scheme, and must be added to the model as “user
reactions”. These reactions are:
Reaction
Type Reaction Stoichiometry
DEG Formation
Thermal
Scission
HO(CH U1 2)2OH + HO(CH2)2OH HO(CH2)2O(CH2)2OH + H2O
HO(CH2)2OH + HO(CH2)2O U2 HO(CH2)2O(CH2)2O + H2O
O(CH U3 2)2OH + HO(CH2)2O O(CH2)2O(CH2)2O + H2O
O O
C C
O O
U4
O(CH2)2O C C
OH +
H2C CHO

Reaction
Type Reaction Stoichiometry
Acetaldehyde
Formation
Cyclic Trimer
Formation
O O
C C
O O
U5
O(CH2)2OH C C
O
OH + HCCH3
O
HCCH3
O O
O O
U6
O(CH2)2OH + OCH CH2 C C
C C +
O(CH2)2O
U7
U8
G T
HOT G T G T GH + H2O
T
G T
G
U9
U10
G T
HG T G T G T GH + HO(CH2)2OH
T
G T
G
U11
U12
G T
T
G T
G
G T G T G T GH O(CH2)2OH +
The recommended power-law exponents for the reactants in the side
reactions are:
Reaction
No. Power-Law Exponents; Modeling Notes
U1 EG = 2 (Multiply group-based pre-exponential factor by 4.0)
U2 EG = 1, T-EG = 1 (Multiply group-based pre-exponential factor by
2.0)
U3 T-EG = 2 (Multiply group-based pre-exponential factor by 1.0)
U4 Reaction is first order with respect to polyester repeat units, assume
concentration of repeat units is approximately equal to the
concentration of B-TPA, set power-law exponents B-TPA = 1.0 B-EG =
1x10-8
U5 T-EG = 1
U6 T-EG = 1, T-VINYL = 1
U7 Reaction is first order with respect to linear molecule with the
following segment sequence:
T-TPA: B-EG : B-TPA : B-EG : B-TPA : T-EG
option 1: assume this concentration = TPA concentration and use
power-law constant TPA = 1*
option 2: use the following equation, based on the most-probable
distribution, to estimate the concentration of this linear oligomer. This
equation can be implemented as a user-rate constant correlation
P 
[ ] [ ] [ ] [ ] [ ] [ ] *[ ] *[
T EG
NUCL
B TPA
ELEC
2 2
B EG
NUCL
T TPA
ELEC
NUCL T EG T DEG B EG
2 2
2

 
 

 
 
 

 
 
 

 
 
 

 
      

2 0
ELEC T TPA B TPA
[ ] *[ ]
   
U8 H2O = 1, C3 = 1 (Multiply group-based pre-exponential factor by 6.0)

Reaction
T-EG : B-TPA : B-EG : B-TPA : B-EG : B-TPA : T-EG
option 1: assume this concentration = TPA concentration and use
power-law constant TPA = 1*
P 
[ ] [ ] [ ] [ ] [ ] *[ ] *[ ]
T EG
NUCL
2 3 2
B TPA
ELEC
B EG
NUCL
NUCL T EG T DEG B EG B DEG
2 2
2

 
 

 
 
 

 
 
 

 
       

2 0
ELEC T TPA B TPA
[ ] *[ ]
   
U10 EG = 1, C3 = 1 (Multiply group-based pre-exponential factor by 12.0)
~B-EG : B-TPA : B-EG : B-TPA : B-EG : B-TPA : T-EG
option 1: assume this concentration = T-EG concentration and use
power-law constant T-EG = 1*
P 
[ ] [ ] [ ] [ ] [ ] *[ ] *[ ]
T EG
NUCL
B TPA
ELEC
3 3
B EG
NUCL
NUCL T EG T DEG B EG B DEG
2 2
2

 
 

 
 
 

 
 
 

 
       

2 0
ELEC T TPA B TPA
[ ] *[ ]
   
U12 T-EG = 1, C3 = 1 (Multiply group-based pre-exponential factor by
6.0)
* To avoid numerical problems, set power-law exponents to 1108 for reactants
which do not appear in the rate expression
0  = Concentration zeroth moment, mol/L (approximately=0.5*([T-TPA]+[T-EG]+[
T-DEG]+[T-VINYL])
Nylon-6 Reaction Kinetics
Nylon-6 melt-phase polymerization reactions are initialized by the hydrolytic
scission of caprolactam rings. The reaction between water and caprolactam
generates aminocaproic acid. The reaction kinetics in the primary reactor are
sensitive to the initial water concentration.
The carboxylic and amine end groups of the aminocaproic acid molecules
participate in condensation reactions, releasing water and forming polymer
molecules. The resulting acid and amine end groups in the polymer react with
each other and with aminocaproic acid, releasing more water.
The amine end of aminocaproic acid and amine ends in polymer react with
caprolactam through ring addition. This reaction is the primary growth
mechanism in the nylon-6 process.

Cyclic Oligomers
As the reactions proceed, intramolecular reactions involving linear polymer
molecules generate cyclic oligomers. Cyclic oligomers ranging from the dimer
through rings ten units long are reported in the literature. The concentration
of each successive cyclic oligomer (dimer, trimer, etc.) falls off sharply, in
accordance with the most probable distribution.
Reactions involving cyclic compounds are not considered in the reaction
generation algorithm in the step-growth model. These reactions, including
ring opening, ring closing, ring addition, and cyclodepolymerization, must be
specified as user reactions.
The following table summarizes key components in the nylon-6 melt
polymerization process. The component names in this table are used in the
tables that follow.
Component ID Databank ID
Component
Structure Component Name
CL C6H11NO -Caprolactam
O
NH
ACA none Aminocaproic acid
O
OH
H2N (CH2)5 C
T-NH2 C6H12NO-E-1 Amine end group
segment
O
H2N (CH2)5 C
T-COOH C6H12NO2-E-1 Acid end group
segment
O
OH
NH (CH2)5 C
R-NY6 C6H11NO-R-1 Nylon-6 repeat segment
O
NH (CH2)5 C
CD none Cyclic dimer
NH (CH2)5 C
O C (CH2)5 NH
O
H2O H2O Water
H2O
Major Reactions
The major reactions in the nylon-6 melt polymerization process are shown
here:
Reaction Type User-Specified Reactions (Forward and Reverse
Reactions Defined Separately)†
Ring Opening /
Ring Closing
Ring Addition /
Cyclodepolymerization
U1 H2O + CL ACA
U2 H2O + CD T-COOH : T-NH2 (=P2)
U3 ACA + CL T-COOH : T-NH2 (=P2)
U4 T-NH2 + CL R-NY6 : T-NH2
U5 ACA + CD T-COOH : R-NY6 : T-NH2 (=P3)
U6 T-NH2 + CD R-NY6 : R-NY6 : T-NH2

Reaction Type Model-Generated Step-Growth Reactions (Define
Nylon-6 Repeat Unit as EN-GRP)
Condensation
Re-Arrangement
1. ACA + ACA T-COOH : T-NH2 + H2O
2. ACA + T-COOH T-COOH : R-NY6 + H2O
3. T-NH2 + ACA R-NY66 : T-NH2 + H2O
4. T-NH2 + T-COOH R-NY66 : R-NY6 + H2O
5. T-NH2 + T-NH2 : T-COOH T-NH2 : R-NY6 + ACA
6. T-NH2 + R-NY6 : T-COOH R-NY6 : R-NY6 + ACA
7. T-NH2 + R-NY6 : R-NY6 R-NY6 : R-NY6 + T-NH2
† In the reaction stoichiometry equations above, the colon (:) indicates
connections between segments. Literature sources report re-arrangement
reactions are insignificant, these reaction rates can be
set to zero
The reactions U1-U6, which involve cyclic monomer and dimer, are not
generated by the current version of the Step-Growth model. These reactions
must be defined as user reactions. However, the stoichiometry of each of
these reactions is shown.
Reactions 1-7 are considered in the reaction generation algorithm in the Step-
Growth kinetics model. The rate constants for these reactions can be assigned
according to the identifiers summarized here:
Reaction
Attacking
Victim Electrophilic
No.
Nucleophilic Species
Species
Victim Nucleophilic
Species
1 forward ACA T-ACA none
2 forward ACA T-COOH none
3 forward T-NH2 ACA none
4 forward T-NH2 T-COOH none
5 forward T-NH2 T-NH2 T-COOH
6 forward T-NH2 T-NH2 R-NY6
7 forward T-NH2 R-NY6 R-NY6
1 reverse H2O T-NH2 T-COOH
2 reverse H2O R-NY6 T-COOH
3 reverse H2O T-NH2 R-NY6
4 reverse H2O R-NY6 R-NY6
5 reverse ACA T-NH2 R-NY6
6 reverse ACA R-NY6 R-NY6
7 reverse T-NH2 R-NY6 R-NY6
The suggested power-law exponents are shown here:
Reaction
U1 forward H2O = 1, CL = 1
U1 reverse ACA = 1
U2 forward H2O = 1, CD = 1 (Multiply group-based pre-exponential factor by 2.0)

Reaction
U2 reverse Reaction is first order with respect to linear dimer P2 with the following segment
sequence:
T-NH2 :T-COOH
option 1: assume P2 concentration = ACA concentration and use power-law constant
ACA = 1*
option 2: use the following equation, based on the most-probable distribution, to
estimate concentration of P2 The denominator in this equation can be implemented
as a user rate constant, with first-order power-law constants for T-NH2 and T-COOH.
P 

[ T 
NH
2
]

 

 
[ 
]

 

 

2 T NH R NY
T COOH R NY 0
T COOH
[ ] [ ]
2 6 6
  
[  ]  [ 
]
U3 forward ACA = 1, CL = 1
U3 reverse See U2 reverse reaction
U4 forward T-NH2 = 1, CL = 1
U4 reverse T-NH2 = 1 (this approximation assumes most T-NH2 end groups are attached to
repeat units)*
U5 forward ACA = 1, CD = 1
U5 reverse Reaction is first order with respect to linear trimer P3 with the following segment
sequence:
T-NH2 : R-NY6 : T-COOH
option 1: assume P3 concentration = ACA concentration and use power-law constant
ACA = 1*
option 2: use the following equation, based on the most-probable distribution, to
estimate concentration of P3 The denominator in this equation can be implemented
as a user rate constant, with first-order power-law constants for T-NH2, R-NY6, and
T-COOH.


[ T 
NH
2
]
[ 6
]
P 
 

 


 

 
[ 
]

 

 

2 T NH R NY
T COOH R NY 0
R NY
T COOH R NY
T COOH
[ 2 ] [ 6
]
[ ] [ ]
6 6
  
  
[  ]  [ 
]
U6 forward T-NH2 = 1, CD = 1
U6 reverse T-NH2 = 1 (this approximation assumes most T-NH2 end groups are attached to
repeat units)*
*
To avoid numerical problems, set power-law exponents to 1108 for reactants which do not
appear in the rate expression
0  = Concentration zeroth moment, mol/L (approximately = 0.5 * ([T-COOH] + [T-NH2])
The side reactions are thought to be catalyzed by acid end groups in
aminocaproic acid and the polymer. A first-order power-law coefficient can be
used to account for the influence of the acid groups in these components.
Alternately, a user rate-constant subroutine can be developed to account for
the influence of the acid end groups.
Note that the forward and reverse terms of the reversible side reactions must
be defined as two separate user reactions in the model.

Nylon-6,6 Reaction Kinetics
The salt process involves a preliminary reaction to form the salt, which
precipitates from solution. During the salt formation, some of the salt remains
in solution, leading to higher polymers. For a rigorous model, it is a good idea
to consider these oligomerization reactions, even in the salt precipitation
reactor. Accounting for these reactions is important when using the model to
optimize the temperature, pressure, and water content of the nylon salt
crystallizer.
The model needs to consider three phase equilibrium (solid salt, liquid, and
vapor). Three phase equilibrium can be considered in Aspen Plus using the
electrolyte chemistry feature. In version 10.0, however, the CSTR model does
not allow a component to appear simultaneously in chemistry reactions and
kinetic reactions. Another way to represent the solid-liquid equilibrium is to
define an equilibrium reaction between the components representing the
dissolved and solid salt. Chemical equilibrium equations can be defined using
the Power-Law reaction kinetics model in Aspen Plus. Apply the “mole-gamma”
option to force the equilibrium equation to use the ratio of the molar
activities as the basis of the equilibrium constant. By using this assumption,
the equilibrium constant is the same as the solubility constant of the solid
salt.
To model the reaction kinetics of the salt process, the dissolved salt should be
considered as a component in the reaction model. The models described in
the open literature do this by considering the salt as an “AB” type monomer.
This treatment, however, fails to consider some of the reverse reactions
which can occur during polymerization. This approach assumes that reverse
condensation reactions and re-arrangement reactions always generate
products with an equal number of adipic acid and HMDA units. In reality,
polymer chains with an unequal number of units can be formed because the
reactions can occur inside the repeat units which originally came from the
reacting salts. Further, the reverse reactions can generate free adipic acid or
HMDA when the reaction occurs at the end of a polymer chain.
Reverse Rate Constant
The models in the literature use a reverse rate constant which is twice the
reverse rate constant experienced by an individual amine group. This factor of
two accounts for the fact that each repeat unit has two amine groups. In the
approach described here, the reverse rate constants used in the model should
be the rate constant between two functional groups, for example between
water and a single amine group.
Considering salt as a component, there are several reversible reactions which
must be considered in the model. A number of condensation reactions occur
including those between molecules of dissolved salt, dissolved monomers, and
polymer end groups. These reactions can be implemented in the step-growth
model through the user reaction feature. The step-growth model will generate
the reactions which do not involve the salt component.
The molecular weight distribution of nylon-6,6 is known to re-equilibrate
when the polymer is exposed to HMDA under pressure. Further, as vacuum is
applied, free HMDA appears to be generated. These facts indicate that
rearrangement reactions are important in this process.

Modeling Approaches
There are two modeling approaches:
 Simplified
 Detailed
The component definitions for both modeling approaches are:
Component ID Databank ID Component Structure Component Name
Components Common to Simplified and Detailed Approach
ADA C6H10O4-D1 Adipic acid
O
O
HO C OH
C (CH2)4
HMDA C6H16N2 H2N (CH2)6 NH2
Hexamethylene diamine
DIS-SALT none Dissolved nylon-6,6 salt
O
O
NH (CH2)6 NH2
HO C
C (CH2)4
SOL-SALT none Solid nylon-6,6 salt
O
HO C O-O
C (CH2)4
+H3N (CH2)6 NH2
MEOH CH4O Methanol
CH3OH
H2O
H2O H2O Water
Segments In Simplified Salt Process Model
T-COOH none Acid end group
segment
O
O
NH (CH2)6 NH
HO C
C (CH2)4
T-NH2 none Amine end group
segment
O
C (CH2)4
O
C
NH (CH2)6 NH2
R-NY66 none Repeat unit segment
O
C (CH2)4
O
C
NH (CH2)6 NH
Segments In Detailed Salt Process Model and Melt-Process Model
T-ADA C6H9O3-E Adipic acid end group
B-ADA C6H8O2-R
O
C (CH2)4
O
C OH
O O Adipic acid repeat unit
C (CH2)4 C
T-HMDA C6H15N2-E HMDA end group
B-HMDA C6H14N2-R HMDA repeat unit
HN (CH2)6 NH2
HN (CH2)6 NH
Note: The component names used in this table are used in the successive
tables to document the reactions.
In the simplified approach, the dissolved salt is treated as an “AB” monomer
(a monomer with two different types of functional groups). This is
accomplished by defining the repeat unit as an “EN-GRP” reactive group. The
simplified approach is consistent with the modeling approach described in the
open literature.
Using this approach, the Step-Growth model will generate all of the main
reactions. The solid-liquid phase equilibrium can be represented as a chemical

equilibrium reaction using the Power-Law model or as two side reactions in
the step-growth model. The equilibrium constant of this reaction corresponds
to the solubility constant of the salt.
The reactions for a simplified Nylon-6,6 salt process model are shown here:
Reaction Type
Phase Equilibrium Reactions (Use Power-Law
Reaction Kinetics Model)
Solid/Liquid
Equilibrium
Reaction Type
C1 DIS-SALT + H2O SOL-SALT
User-Specified Reactions (Forward and Reverse
Reactions Defined Separately)
Salt formation
Reaction Type
U1 HMDA + ADA DIS-SALT + H2O
Model-Generated Step-Growth Reactions (Define
Nylon-6,6 Repeat Unit as EN-GRP)†
Condensation
Re-Arrangement
1. DIS-SALT + DIS-SALT T-COOH : T-NH2 + H2O
2. DIS-SALT + T-COOH T-COOH : R-NY66 + H2O
3. T-NH2 + DIS-SALT R-NY66 : T-NH2 + H2O
4. T-NH2 + T-COOH R-NY66 : T-NY66 + H2O
5. T-NH2 + T-COOH : T-NH2 R-NY66 : T-NH2 + DIS-SALT
6. T-NH2 + T-COOH : R-NY66 R-NY66 : R-NY66 + DIS-SALT
7. T-NH2 + R-NY66 : R-NY66 R-NY66 : R-NY66 + T-NH2
connections between segments
The detailed modeling approach treats the HMDA and ADA segments as
discreet molecular units. Using this assumption, the dissolved salt is a dimer
made up of one hexamethylene diamine end group and one adipic acid end
group. This approach is more rigorous because it considers every possible
reverse reaction, including terminal monomer loss. To use this approach,
define the HMDA repeat group as a bifunctional nucleophile (NN-GRP), and
the ADA repeat group as a bifunctional electrophile (EE-GRP).
The solid-liquid phase equilibrium (reaction C1) is represented as previously
described. The reactions involving the dissolved salt, U1-U6, must be defined
as user reactions. Reactions 1-7, which do not involve the salt, are generated
by the model automatically.
The reactions for a detailed Nylon-6,6 salt process model are shown here:
Reaction Type
Phase Equilibrium Reactions (Use Power-Law
Reaction Kinetics Model)
Solid/Liquid
Equilibrium
C1 DIS-SALT + H2O SOL-SALT

Reaction Type
User-Specified Reactions (Forward and Reverse
Reactions Defined Separately)†
Salt formation
Condensation
Reaction Type
U1 HMDA + ADA DIS-SALT + H2O
U2 DIS-SALT + DIS-SALT T-HMDA : B-ADA : B-HMDA : T-ADA + H2O
U3 DIS-SALT + ADA T-ADA : B-HMDA : T-ADA + H2O
U4 HMDA + DIS-SALT T-HMDA : B-ADA : T-HMDA + H2O
U5 DIS-SALT + T-ADA T-ADA : B:HMDA : B-ADA + H2O
U6 T-HMDA + DIS-SALT B-HMDA : B-ADA : T-HMDA + H2O
Model-Generated Step-Growth Reactions (Define B-HMDA
as NN-GRP,
B-ADA as EE-GRP)
Condensation
Re-Arrangement
1. HMDA + ADA T-HMDA : T-ADA + H2O
2. HMDA + T-ADA T-HMDA : B-ADA + H2O
3. T-HMDA + ADA B-HMDA : B-ADA + H2O
4. T-HMDA + T-ADA B-HMDA + B-ADA + H2O
5. T-HMDA + T-ADA : T-HMDA T-ADA : B-HMDA + HMDA
6. T-HMDA + B-ADA : T-HMDA B-ADA : B-HMDA + HMDA
7. T-HMDA + B-ADA : B-HMDA B-ADA : B-HMDA + T-HMDA
† In the reaction stoichiometry equations above, the colon (:) indicates connections
between segments
Rate Constant Identifiers
The rate constants can be assigned to model-generated reactions in the
simplified model using the identifiers summarized here:
Reaction
No.
Attacking
Nucleophilic
Species
Victim
Electrophilic
Species
Victim
Nucleophilic
Species
1 forward DIS-SALT DIS-SALT none
2 forward DIS-SALT T-COOH none
3 forward T-NH2 DIS-SALT none
4 forward T-NH2 T-COOH none
5 forward T-NH2 T-COOH T-NH2
6 forward T-NH2 T-COOH R-NY66
7 forward T-NH2 R-NY66 R-NY66
1 reverse H2O T-COOH T-NH2
2 reverse H2O T-COOH R-NY66
3 reverse H2O R-NY66 T-NH2
4 reverse H2O R-NY66 R-NY66
5 reverse DIS-SALT T-NH2 R-NY66
6 reverse DIS-SALT R-NY66 R-NY66
7 reverse T-NH2 R-NY66 R-NY66

A subset of these identifiers can be used to assign the same rate constant to
several different reactions. For example, reactions 3-7 can be lumped
together by specifying “T-NH2” as the attacking nucleophilic species and by
leaving the victim species identifiers blank (unspecified).
Rate constants can be assigned to reactions 1-7 in the detailed model using
the identifiers summarized here:
Reaction No. Attacking
Nucleophilic
Species
Victim
Electrophilic
Species
Victim
Nucleophilic
Species
1 forward HMDA ADA none
2 forward HMDA T-ADA none
3 forward T-HMDA ADA none
4 forward T-HMDA T-ADA none
5 forward T-HMDA T-ADA T-HMDA
6 forward T-HMDA B-ADA T-HMDA
7 forward T-HMDA B-ADA B-HMDA
1 reverse H2O T-ADA T-HMDA
2 reverse H2O B-ADA T-HMDA
3 reverse H2O T-ADA B-HMDA
4 reverse H2O B-ADA B-HMDA
5 reverse HMDA T-ADA B-HMDA
6 reverse HMDA B-ADA B-HMDA
7 reverse T-HMDA B-ADA B-HMDA
together by specifying “T-HMDA” as the attacking nucleophilic species and by
Each reaction involving the dissolved salt must be defined as a user-reaction
in the Step-Growth model. The forward and reverse reactions are treated as
two separate reactions. The stoichiometry of each reaction was shown
previously in the reactions table for the detailed modeling approach. The
power-law exponents are in the following table.
Several of the reverse reactions require a particular sequence of segments in
order to occur. The concentration of molecules with these particular
sequences can be assumed (for example, assume the linear trimer
concentration is the same as the dissolved salt concentration) or they can be
estimated from statistical arguments. The following table shows both
techniques. The statistical approach is more rigorous, but it requires writing a
user rate-constant or user kinetic subroutine to perform the calculations as
shown.
The power-law exponents for user-specified reactions in the detailed model
are:

Reaction
U1 forward HMDA = 1, ADA = 1 Multiply group-based pre-exponential factor by 4.0
U1 reverse H2O = 1, DIS-SALT = 1
U2 forward DIS-SALT = 2
U2 reverse Reaction is first order with respect to water and polymer molecule P4 with the
T-HMDA : B-ADA : B-HMDA : T-ADA
option 1: assume P4 concentration = DIS-SALT concentration and use DIS-SALT =
1, H2O = 1*
option 2: set power-law exponent for H2O = 1 and use the following equation, based
on the most-probable distribution, to estimate concentration of P4 (this equation can
be implemented as a user rate constant).
 

 

  
0
P T ADA
4
B HMDA
2[ 
]
T HMDA B HMDA
[  ]  2[ 
]
T HMDA
[ 
]


 
 
T HMDA B HMDA
[ ] 2[ ]
[ 
]
T ADA B ADA
[  ]  2[ 
]
B ADA
2[ 
]

 
T ADA B ADA
[ ] 2[ ]


 
 
  

 
  

U3 forward DIS-SALT = 1, ADA = 1, multiply group rate constant by 2.0
U3 reverse Reaction is first order with respect to water and polymer molecule P 3,aa with the
T-ADA : B-HMDA : T-ADA
option 1: assume P 3,aa concentration = ADA concentration and use power-law
constants ADA = 1, H2O = 1*
on the most-probable distribution, to estimate concentration of P 3,aa (this equation
can be implemented as a user rate constant).


[ T 
ADA
]
2
2
[ ]
P 
 

 


 
3 aa T ADA B ADA
T HMDA B HMDA
B HMDA
, 2

 

2 0
[ ] [ ]
[ ] [ ]
  
  
U4 forward DIS-SALT = 1, HMDA = 1; multiply group rate constant by 2.0
U4 reverse Reaction is first order with respect to water and polymer molecule P 3,BB with the
T-HMDA : B-ADA : T-HMDA
option 1: assume P 3,BB concentration=HMDA concentration and use power-law
constants HMDA=1, H2O=1*
on the most-probable distribution, to estimate concentration of P 3,BB (this equation
can be implemented as a user rate constant).


[ T 
HMDA
]
2
2
[ ]
P 
 

 


 
3 aa T HMDA B HMDA
T ADA B ADA
B ADA
, 2

 

2 0
[ ] [ ]
[ ] [ ]
  
  
U5 forward DIS-SALT = 1, T-ADA = 1
U5 reverse H2O = 1, T-ADA = 1, set power law constants for B-ADA, B-HMDA to 1E-10 to avoid
numerical problems
U6 forward DIS-SALT = 1, T-HMDA = 1

Reaction
U6 reverse H2O = 1, T-ADA = 1, set power law constants for B-ADA, B-HMDA to 1E-10 to avoid
numerical problems
*
To avoid numerical problems, set power-law exponents to 1108 for reactants
which do not appear in the rate expression
0  = Concentration zeroth moment, mol/L (approximately = 0.5 * ([T-ADA] + [T-HMDA])

Melt-Phase Polymerization
The best way to model the melt-phase polymerization of nylon-6,6 is to treat
the HMDA and ADA segments as discreet molecular as shown in the
components table on page 116.
The following table shows the main reactions in the melt-phase
polymerization of nylon-6,6:
Reaction
Model-Generated Step-Growth Reactions (Define B-HMDA as
Type
NN-GRP, B-ADA as EE-GRP)†
Condensation
Re-
Arrangement
1. HMDA + ADA T-HMDA : T-ADA + H2O
2. HMDA + T-ADA T-HMDA : B-ADA + H2O
3. T-HMDA + ADA B-HMDA : B-ADA + H2O
4. T-HMDA + T-ADA B-HMDA + B-ADA + H2O
5. T-HMDA + T-ADA : T-HMDA T-ADA : B-HMDA + HMDA
6. T-HMDA + B-ADA : T-HMDA B-ADA : B-HMDA + HMDA
7. T-HMDA + B-ADA : B-HMDA B-ADA : B-HMDA + T-HMDA
These reactions are generated by the Step-Growth model if the HMDA repeat
group is defined as a bifunctional nucleophile (NN-GRP), and the ADA repeat
group as a bifunctional electrophile (EE-GRP).
Side reactions that are not shown may be included in the model as “user
reactions”.
Rate constants can be assigned to reactions 1-7 using the identifiers for the
detailed model summarized on page 119.
together by specifying “T-HMDA” as the attacking nucleophilic species and by
Melt Polycarbonate Reaction Kinetics
There is little information regarding melt-phase polymerization of
polycarbonate available in the public domain. From what is available, it is
clear that the chemistry of the melt-polycarbonate process follows the typical
pattern for step-growth condensation involving two dissimilar monomers. The
bisphenol-A monomer behaves as a bifunctional nucleophile, and the diphenyl
carbonate monomer behaves as a bifunctional electrophile. The reactions
generate phenol as a by-product. In later stages of the process,
rearrangement reactions regenerate small amounts of bisphenol-A monomer.
The following table summarizes the most convenient method for
characterizing the components involved in the melt polycarbonate process:

Component
ID
Databank
ID Component Structure Component Name
Components Common to Simplified and Detailed Approach
DPC none Diphenyl Carbonate
O
O C
O
T-DPC C7H5O2-E Phenyl carbonate end
group
O
C
O
B-DPC CO-R Carbonate repeat unit
O
C
BPA C15H16O2 Bisphenol-A
HO OH
T-BPA C15H15O2-E Bisphenol-A end group
O OH
B-BPA C15H14O2-R Bisphenol-A repeat unit
O O
PHOH C6H6O Phenol
OH
The following table shows the main reactions in this process. These reactions
are generated by the model if the carbonate group is defined as a bifunctional
electrophile (EE-GRP) and the BPA group as a bifunctional nucleophile
(NN-GRP) .
Reaction
Model-Generated Step-Growth Reactions (Define B-BPA as
Type
NN-GRP, B-DPC as EE-GRP)†
Condensation
Re-
Arrangement
1. BPA + DPC T-BPA : T-DPC + PHOH
2. BPA + T-DPC T-BPA : B-DPC + PHOH
3. T-BPA + DPC B-BPA : B-DPC + PHOH
4. T-BPA + T-DPC B-BPA + B-DPC + PHOH
5. T-BPA + T-DPC : T-BPA T-DPC : B-BPA + BPA
6. T-BPA + B-DPC : T-BPA B-DPC : B-BPA + BPA
7. T-BPA + B-DPC : B-BPA B-DPC : B-BPA + T-BPA
The following table shows how to assign rate constants to each of the
reactions shown in the previous table:
Nucleophilic
Species
Victim
Electrophilic
Species
Victim
Nucleophilic
Species
1 forward BPA DPC none
2 forward BPA T-DPC none
3 forward T-BPA DPC none

Nucleophilic
Species
Victim
Electrophilic
Species
Victim
Nucleophilic
Species
4 forward T-BPA T-DPC none
5 forward T-BPA T-DPC T-BPA
6 forward T-BPA B-DPC T-BPA
7 forward T-BPA B-DPC B-BPA
1 reverse PHOH T-DPC T-BPA
2 reverse PHOH B-DPC T-BPA
3 reverse PHOH T-DPC B-BPA
4 reverse PHOH B-DPC B-BPA
5 reverse BPA T-DPC B-BPA
6 reverse BPA B-DPC B-BPA
7 reverse T-BPA B-DPC B-BPA
Rate constants can be assigned to several by leaving some of the reaction
identifiers unspecified. For example, the reverse reactions involving phenol
can be lumped together by assigning phenol as the attacking nucleophilic
species and by leaving the names of the victim species unspecified.
The open literature does not describe the side reactions involved in this
process, although side reactions are certainly known to exist. These side
reactions can be added to the model as “user reactions”.
Model Features and
Assumptions
Model Predictions
The step-growth model calculates the component reaction rates and the rate
of change of the zeroth and first polymer moments ( , i ) 0 1
of the polymer
chain length distribution. The number average polymer properties (Pn, Mn)
are calculated from the moments. These component attributes can be used
to calculate secondary properties, such as polymer viscosity, melting point,
end group concentrations, intrinsic viscosity, melt flow index, etc. Correlations
relating secondary properties to the polymer moments can be implemented
using a User Prop-Set Property subroutine, as described in the Aspen Plus
User Guide.
The rate of change of polymer mass is calculated as follows:
R
 , *
1
R Mw
s i i
Nseg

p Mw
p
This is the sum of the rates of change of segment masses.

Each segment type is assigned a value , which indicates the number of
“points of attachment” connecting the segment to other segments in the
polymer chain:
Segment Type 
End 1
Repeat 2
Branch-3 3
Branch-4 4
The rate of change of the zeroth moment ( 0 ) is calculated from the rate of
change of the first moment ( 1 ) and the segment type ():

0 1 1  



2
t 
t t


The factor of ½ accounts for the fact that each “connection” links two
segments (without this correction the points of connection are counted twice).
This method is best illustrated through these examples:
Valid Reaction Type† Stoichiometry†
Δλ1 ½ Δλ0
Yes Initiation MMP2 M + M  E + E +2 +1 +1
No Initiation M P1 M  R +1 +1 0
Yes Propagation
(addition) n n 1 P M P  E + M  R + E +1 +1 0
Yes Propagation
(insertion)
Pn *
MP *
M  R +1 +1 0
n  1
Yes Combination
Pn  Pm Pnm E + E  R + R 0 +1 -1
Yes Combination
Pn  Pm Pnm E + E  R -1 +0 -1
Yes Branching
Pn M Pn1 R + M  B3 + E +1 +1 0
Yes Branching
Pn  Pm Pnm R + E  B3 + R 0 +1 -1
Yes Cross linking
Pn  Pm Pnm R + R  B4 -1 +0 -1
† M = Monomer; E = End group segment; B3 = Branch-3 segment; B4 = Branch-4
segment
This method lets you specify most classes of reactions. However, special care
must be taken to ensure that the reaction is defined in a manner that is
consistent with the previous equation.
By default, the model solves the zeroth moment (ZMOM) and segment flow
rates (SFLOW attributes) as independent variables. This can cause a
discrepancy between these variables, especially in flowsheets with high
polymer recycle flow rates. This discrepancy, in turn, can lead to convergence
problems in downstream reactors.

To avoid this problem, you can force the model to calculate the zeroth
moment directly from the segment flow rates by checking the “explicitly solve
zeroth moment” option on the step-growth Options form. When this option is
selected, the model calculates the zeroth moment as:
  
 1
 0 1 2
This option cannot be invoked if two or more reaction models are referenced
from a single reactor block.
Phase Equilibria
The step-growth model can be used to simulate reactions in single-phase
(vapor or liquid), two-phase (VL), or three-phase (VLL) systems. Each step-growth
reaction model is associated with a particular reaction phase, specified
on the Options sheet. The user can consider simultaneous reactions in
multiple phases by referring to two or more reaction models in a reactor.
Typical applications of this model include melt-phase polymerization and
solution polymerization. Slurry, suspension, and emulsion processes involving
step-growth kinetics can also be simulated with this model.
Interfacial polymerization involves a solvent phase, an organic monomer
phase, and a polymer phase. The reaction rate is usually limited by the rate
of mass transfer of monomers from the organic phase to the reacting polymer
phase. The mass-transfer limits across the liquid-liquid interface are not taken
into account by the standard model. These systems can be simulated by
developing a custom reactor model in Aspen Custom Modeler or Aspen Plus,
or by writing an appropriate concentration basis subroutine for the step-growth
model.
Solid-state polymerization involves crystalline and amorphous solid polymer
phases and a vapor phase. The reaction kinetics may be limited by the rate of
mass transfer of volatile reaction by-products from the amorphous solid phase
to the polymer phase. None of the standard reactor models in Aspen Polymers
are designed for solid-state polymerization. Solid-state polymerization models
can be developed in Aspen Custom Modeler and interfaced to the step-growth
polymerization model through the Aspen Custom Modeler / Aspen Polymers
Interface.
Mass transfer limitations in thin-film or horizontal finishing reactors can be
considered by customizing the Step-Growth model using the available
concentration basis subroutine or by developing an appropriate user reactor
model in Aspen Plus or Aspen Custom Modeler.
Reaction Mechanism
The Step-Growth reaction model applies to condensation polymerization. In
the future the model will be extended to cover pseudocondensation and ring-addition
polymerization. The model accounts for any combination of
monofunctional and bifunctional monomers. Cyclic monomers and
multifunctional monomers, however, are not included in the standard reaction
scheme.

User-defined stoichiometric reactions can be added to the model to account
for reactions which are not included in the standard reaction scheme. These
reactions use a power-law rate expression which can be extended to more
complex rate expressions through the application of a user-written Fortran
subroutine.
Model Structure
This section outlines the structure of the Step-Growth kinetics model. It
examines the theoretical framework in detail. The assumptions and limits of
the algorithms are documented.
Reacting Groups and Species
The first step in the development of any process simulation model is to
determine the list of components. In Aspen Polymers it is also important to
decide how to characterize the polymer components. A polymer can be
broken down into segments any number of ways. For example, the nylon-6
repeat unit can be treated as a segment, or it can be divided into two
segments corresponding to the portions of the repeat unit which came from
the diacid and diamine monomers.
Segments
The preferred method of segmenting the polymer component is to define
segments corresponding to the monomers which are used to produce the
polymer. This technique has two distinct advantages. First, the property
models in Aspen Polymers use the monomer as a reference point for
molecular size. Second, the reaction kinetics usually involve adding
monomers to the end of growing polymer chains. Defining segments
corresponding to the monomers makes it easy to write reactions
corresponding to monomers and segments, for example monomer “A” 
segment “A”.
The Step-Growth model assumes that the polymer is segmented in this
manner. For monadic polymers such as nylon-6, this technique is
straightforward. This method of segmenting the polymer is a bit unusual for
dyadic polymers, such as PET, because it treats them as alternating
copolymers. Thus, a molecule of PET with 100 PET units is defined as having a
degree of polymerization of 200 in this model (100 terephthalate units and
100 glycol units).
Monofunctional monomers, such as benzoic acid, always correspond to an
end-group segment in the model. Bifunctional monomers can end up inside a
linear polymer chain as a repeat unit, or may be located at the end of the
chain as an end group. Each symmetric bifunctional monomer (diacids, diols,
diamines, etc.) corresponds to one repeat segment and one end-group
segment. Asymmetric bifunctional monomers (monomers with two different
types of end groups) correspond to one repeat unit and two end-group
segments. Multifunctional monomers can correspond to several segments, as
shown:

Monomer
Type
Monomer
Formula
Corresponding Segment Formulas
End-Groups Repeat Unit Branch-3 Branch-4
Acid --- --- ---
O
R C
OH C
O
R
Ester --- --- ---
O
R C
OR' C
O
R
Amine R NH2 R NH
--- --- ---
Alcohol R OH R O
--- --- ---
Diacid --- ---
C O
HO R C
OH C
O
O
OH R C O
C
O
R C O
Diester --- ---
C O
R'O R C
OR' C
O
O
OR' R C O
C
O
R C O
Carbonate --- ---
O
O
OR C
RO C
OR C
O
Diamine H2N R NH2 HN R NH2 HN R NH
--- ---
Diol HO R OH O R OH O R O
--- ---
Amino acid --- ---
O
O
H2N R C
OH C
H2N R
O
HN R C
OH
O
C
HN R
Lactic acid --- ---
O
O
HO R C
OH HO R
C
O
O R C
OH
O
C
O R
Branch agent ---
Branch agent
O
R(OH)3 ~O-R(OH)2 ~O-R(OH)O~ O R O
O
OH
R(OH)4 ~O-R(OH)3 ~O-R(OH)2O~ O R O
O
O
O R O
Reacting Functional Groups
The Step-Growth reaction model generates reactions based on the types of
functional groups found in the reactants. The model includes a list of pre-defined
group types, as shown:
Description Type Examples†
Nucleophilic repeat units have
NN-GRP
two electron-strong sites.
Electrophilic repeat units have
two electron-weak sites.
EE-GRP
Mixed repeat units have one
electrophilic site and one
nucleophilic site.
EN-GRP
HO(CH2)XOH HO OH
O
HO C
O
(CH2) C OH
O
X Cl C Cl
O
HO C
O
(CH2) OH X HO COH

Description Type Examples†
Nucleophilic leaving groups are
N-GRP
electron-strong end groups.
Electrophilic leaving groups are
electron-weak end groups.
E-GRP
Nucleophilic modifiers are
groups with a single nucleophilic
site.
NX-GRP
Electrophilic modifiers are
groups with a single electrophilic
site.
EX-GRP
O
(CH2) C OH
HO C X
O
O
Cl C Cl
XOH HO(CH2) HO OH
OH OH
O
COH
O
COH
† Highlighted portion of component is the named reacting functional group.
Each functional group in the model is assigned a name and type. The names
are used to distinguish between different groups with the same chemical
functionality.
The following table shows the types of functional groups found in common
monomers and the condensate products:
Monomer
Type
Monomer
Formula
Leaving Groups Segment Groups
Structure Type Structure Type Structure Type
Acid ~OH N-GRP --- --- EX-GRP
O
R C
OH C
O
R
Ester ~OR’ N-GRP --- --- EX-GRP
O
R C
OR' C
O
R
Amine R NH2 ~H E-GRP --- --- R NH
NX-GRP
Alcohol R OH ~H E-GRP --- --- R O
NX-GRP
Diacid ~OH N-GRP --- --- EE-GRP
C O
HO R C
OH C
O
O
R C O
Diester ~OR’ N-GRP --- --- EE-GRP
C O
R'O R C
OR' C
O
O
R C O
Carbonate ~OR N-GRP --- --- EE-GRP
O
O
RO C
OR C
Diamine H2N R NH2 ~H E-GRP --- --- HN R NH
NN-GRP
Diol HO R OH ~H E-GRP --- --- O R O
NN-GRP
Amino acid ~H (amine) E-GRP ~OH (acid) N-GRP EN-GRP
O
O
H2N R C
OH HN R
C
Lactic acid ~H (alcohol) E-GRP ~OH (acid) N-GRP EN-GRP
O
O
HO R C
OH O R
C

Monomer
Type
Monomer
Formula
Leaving Groups Segment Groups
Structure Type Structure Type Structure Type
Reacting Functional Groups In Common Types of Condensate Products
Water ~H E-GRP ~OH N-GRP
H2O
Alcohol RO-H ~H E-GRP ~OR N-GRP
Reacting Species
Since polymer components do not have a fixed structure, polymerization
reactions must be written in terms of the polymer segments. The segments
and standard components that make up the step-growth reaction network are
referred to as reacting species. Each of these reacting species is made up of
one or more reacting functional groups.
Once the reacting groups are defined, the structure of each reacting species is
specified by defining the number of each reacting group in each reacting
species. It is not necessary to specify a zero when a particular group is not in
the species being defined.
Species Structure Validity
The model checks the species structures to verify they are valid and to see if
there are any missing species. Species structures are considered valid if they
follow these rules:
 Species may not be oligomer or polymer components.
 Species may include one EE-GRP, NN-GRP, or EN-GRP, but no species may
have more than one of these three group types. Species may not contain
more than one of any of these three groups.
 Species which are end group segments must include one E-GRP or one N-GRP.
 Species which are repeat segments may not include an E-GRP or N-GRP.
 Species which are monomers must have a balanced number of
electrophilic groups and nucleophilic groups.
 Structures are unique - no two species may have the same structure.
The model determines every valid combination of the specified functional
groups. Any combination which is not represented by a species structure is
assumed to be a missing component. The model reports a warning message
describing the structure of the species which was not specified and drops all
reactions which would have involved this component. You can choose to
ignore this warning if the missing component is unimportant in the process
being simulated.

Oligomer Fractionation
You can choose to include one or more oligomer components in the model.
When this feature is used, the model will fractionate the polymer distribution
between the polymer component and the various oligomer components. The
fractionation algorithm assumes that the polymer follows the most probable
distribution. These assumptions are valid when the reactions are reversible
and when the rate of rearrangement reactions is faster than the rate of the
condensation reactions.
The oligomer feature can be used to track the loss of volatile short-chain
oligomers from the polymer solution or melt. It can also be used to estimate
oligomer concentrations to calculate reaction rates for ring closing reactions
or other reactions that require a particular sequence of segments. Tracking
oligomers, however, does require more simulation time and may make the
model more difficult to converge.
The Options form lets you adjust the tolerance for the oligomer fractionation
calculations. When several oligomers are tracked simultaneously it may be
necessary to reduce the tolerance to improve reactor convergence.
The logic of the step-growth oligomer fractionation algorithm is summarized
here:
Assumptions
Polymer molecules consist of alternating nucleophilic and electrophilic segments
Repeat segments in AB polymers, which are made up of EN-GRP groups, act as both
a nucleophile and an electrophile. The end groups act as either electrophilic or
nucleophilic segments, depending on which leaving group is attached to the end.
The probability of a particular segment being in a given point in the segment
sequence is determined by the concentration of that segment and the concentration
of all other segments of that type (note: this assumption is equivalent to assuming
the most-probable distribution).
Equation
Definition of probability factors used to determine probability of a given sequence of
segments:
P
f N
f N
P
f E
a a
b b
  a  b

f E
i i i
j j j
Pa = Probability that nucleophilic segment a occupies the next nucleophilic position
in the chain
Pb = Probability that electrophilic segment b occupies the next electrophilic
position in the chain
fa = Number of similar points of attachment in nucleophilic segment a (= 2 for
repeat segments which are composed of an NN-GRP)
fb = Number of similar points of attachment in electrophilic segment b (= 2 for
repeat segments which are composed of an EE-GRP)
Na = Concentration of nucleophilic segment “a”
Eb = Concentration of electrophilic segment “b”
i = Index corresponding to list of all nucleophilic segments

j = Index corresponding to list of all electrophilic segments
Example 1: calculation of expected concentration of oligomer with a sequence “ab”
C =P P ab a b0
Cab = Expected oligomer concentration
0 = Concentration zeroth moment of polymer (concentration of all polymer
molecules)
Example 2: calculation of expected concentration of oligomer with a sequence
“aBABa”
C =P 2 P 2
P 
aBABa a B A
0 Reaction Stoichiometry Generation
The model predicts the stoichiometry of each step-growth reaction based on
the structure of each of the reactants. The step-growth reaction generation
algorithm is summarized here:
Reaction Type Reaction Scheme Reaction Generation Algorithm
Condensation -
Monomer Addition
M M P W xa yb xy ab    2,
Pn,xa Myb Pn ,xy Wab    1
M P P W xa n yb n yx ab    , 1,
Find every combination by which
nucleophilic monomers, Mxa , or end
segments Pxa , can react with
electrophilic monomers, Myb , or end
segments, Pyb , to give a condensate
molecule, Wab
Condensation -
Polymer Addition
P P P W n,xa m, yb n m,xy ab    
Find every combination by which
nucleophilic end segments, Pxa , can
react with end segments, Pyb , to give a
condensate molecule, Wab
Reverse Condensation
- Terminal Monomer
Loss
W P M M
W P P M
  
   
ab 2
,
xy xa yb
ab n , xy n 1
,
xa yb
Find every combination by which a
condensate molecule, Wab , can react
with a polymer molecule at the
boundary between a nucleophilic repeat
segment, x, and an electrophilic end
group segment, y
Reverse Condensation
- Scission
W P P P ab n xy n m xa m yb    ,  , ,
condensate molecule, Wab , can react
segment, x, and an electrophilic repeat
segment, y

Reaction Type Reaction Scheme Reaction Generation Algorithm
Forward
Pn, Pm,   MPolycondensation
za yx Pn  m 1
, yz xa Find every combination by which a
nucleophilic end group segment, Pza ,
can react with a polymer molecule at
the boundary between a nucleophilic
repeat segment, x, and an electrophilic
end segment, y
Reverse
Polycondensation
M P P P za n yx n m yz m xa    ,  , 1,
nucleophilic monomer, Mxa , can react
segment, x, and an electrophilic end
segment, y
Re-arrangement P P P P n,za m,xy n m q, yz q,xa     
nucleophilic end group segment, Pza ,
can react with a polymer molecule at
the boundary between a nucleophilic
repeat segment, x, and an electrophilic
repeat segment, y
By default, the step-growth model generates all types of step-growth
reactions described above. You may “turn off” the reaction generation for a
particular class of reactions by clearing the reaction from the Reaction Options
section of the Options form.
Model-Generated Reactions
There are two steps required to assign rate constants to model generated
reactions. First, the rate constant values are specified in the Step-Growth
Rate Constant form (SG-RATE-CON sentence). Then each set of rate
constants is assigned a number for identification. Once the rate constants sets
are defined, they can be assigned to the generated reactions.
Rate Expression for Model Generated Reactions
The Step-Growth reactions model uses a modified power law rate expression,
shown here:
Equation
T
T

Ea
RT T T
b
i
i



1 1

 

 
Tref specified rate NuclElec f f P C k e  
 
 

U flag n e i o i
ref
i
i
ref

Ea
RT b
 
Tunspecified rate  NuclElec f f P C k e T i
U  ref n e i o flag i
i
i
i
Nomenclature

Symbol Description
[Nucl] Concentration of the attacking nucleophilic species, mol/L*
[Elec] Concentration of the attacking electrophilic species, mol/L*
fn
Number of electrophilic leaving groups in the attacking nucleophilic species.
This factor is 2 for diol and diamine monomers.
fe In reactions involving two victim species, fe is the number of electrophilic
groups in the electrophilic species. This factor is 2 for repeat units which
contain EE-GRP groups.
In reactions involving one victim species, fe is the number of nucleophilic
leaving groups in the electrophilic species. This factor is 2 for diacid, diester,
and carbonate monomers.
P In reactions involving two victim species, P is the probability of the victim
nucleophilic species being adjacent to the victim electrophilic species. This
probability factor is calculated by the model assuming the most probable
distribution:
P
f N
f N
vns vns
i i i
 
where:
fvns = Number of similar points of attachment in victim nucleophilic segment
(= 2 for NN-GRP repeat segments, 1 for all others)
Nvns = Concentration of victim nucleophilic segment
i = Index corresponding to list of all nucleophilic segments
i Index corresponding to the rate constant set number. The summation is
performed over the specified list of rate constant set numbers.
Symbol Description
Ci
Catalyst concentration for rate constant set i. If the catalyst species is
specified, this is the concentration of the species. If the catalyst group is
specified, this the group concentration. If both species and group are specified,
this is the concentration of the species times the number of the specified group
in the specified species. If the catalyst is not specified, this factor is set to one.
ko
Pre-exponential factor in user-specified inverse-time units*
Ea Activation energy in user-specified mole-enthalpy units (default =0)
b Temperature exponent (default = 0)
R Universal gas constant in units consistent with the specified activation energy
T Temperature, K
Tref
Optional reference temperature. Units may be specified, and they are
converted to K inside the model.
flag User flag for rate constant set i. This flag points to an element of the user rate
constant array.
U User rate constant vector calculated by the optional user rate constant
subroutine. The user flag indicates the element number in this array which is
used in a given rate expression. When the user flag is not specified, or when
the user rate constant routine is not present, this parameter is set to 1.0.
* The concentration basis may be changed to other units using the Concentration
basis field on the Options sheet or using the optional concentration basis
subroutine.

The reactions follow second order kinetics: one order with respect to the
nucleophilic reactant and one order with respect to the electrophilic reactant.
Catalysts may make the reaction third order (one order with respect to
catalyst).
The rate constants for the model-generated reactions are assumed to be on a
functional group basis. The model applies correction factors to account for the
number of like functional groups in each of the reactants. For example, in a
reaction between a diol monomer and a diacid monomer, the specified rate
constant is multiplied by four to account for the two acid groups in the diacid
and the two alcohol groups in the diol.
Some reactions occur inside polymer chains at the intersection of two
segments. The model applies a probability factor to estimate the
concentration of the given segment pair. This probability is based on the most
probable distribution. It assumes that the segments in the polymer alternate
between nucleophilic segments and electrophilic segments. Repeat segments
composed of an EN-GRP functional group behave as both nucleophiles and
electrophiles, so these segments can alternate with themselves.
The standard rate expression is modified using the optional user rate constant
feature. The rate constant form includes a parameter called the “user flag”
which identifies an element in an array of user rate constants. This array is
calculated by a user-written Fortran subroutine. The standard rate expression
is multiplied by the user rate constants.
Assignment of Rate Constants to Model-
Generated Reactions
Six qualifiers are used to assign each set of rate constants to internally-generated
step-growth reactions, the:
 Attacking nucleophilic reactant name (A-NUCL-SPEC)
 Attacking electrophilic leaving group name (A-ELEC-GRP)
 Victim electrophilic reactant name (V-ELEC-SPEC)
 Victim nucleophilic group name (V-NUCL-GRP)
 Victim electrophilic species name (V-ELEC-SPEC)
 Victim electrophilic group name (V-ELEC-GRP)
The following table contains an example illustrating how these identifiers are
used to distinguish between reactions. Note that the victim electrophilic
species is only used for reactions which occur at the intersection of two
segments in a polymer molecule.

O O
O O
HO(CH2)2O + H2O
HO(CH2)2OH + HOC COH
C COH
O O
1
2
3
4
O(CH2)2OH + HOC COH O(CH2)2O
O O
5 HO(CH2)2O + H2O
6
HO(CH2)2OH + C C
O O
O O
HOC C
78
O(CH2)2OH + C C
O O
HO(CH2)2OH + C COCH3
O O
HO(CH2)2O + CH3OH
HO(CH2)2OH + C COH
Reaction
O O
C COH
+ H2O
O O
HOC C
O(CH2)2O + H2O
9
10
O O
HOC COCH3
HO(CH2)2O + H2O
11
12
O O
HOC COCH3
Reaction Identifiers
Attacking Species Victim Species
A-Nucl-
Spec A-Elec-Grp V-Elec-Spec V-Elec-Grp V-Nucl-Spec V-Nucl-Grp
1 ~H in
O O
HO(CH2)2OH HOC COH
alcohol
none ~OH in acid
2 ~H
O O
H2O C COH
3 ~H in
O O
~O(CH2)2OH HOC COH
alcohol
O O ~O(CH2)2OH ~O(CH2)2O~
none ~OH in acid
4 ~H
O O
H2O C COH
5 ~H in
O O
HO(CH2)2OH C COH
alcohol
O O ~O(CH2)2O~ ~O(CH2)2O~
none ~OH in acid
6 ~H
O O
H2O C C
7 ~H in
O O
~O(CH2)2OH C COH
alcohol
none ~OH in acid
8 ~H
O O
H2O C C
9 ~H in
O O
HO(CH2)2OH HOC COCH3
alcohol
O O ~O(CH2)2O~ ~O(CH2)2O~
none ~OH in acid
10 ~H
O O
H2O C COCH3
11 ~H in
O O
HO(CH2)2OH HOC COCH3
alcohol
none
12 ~H
O O
C C
C C
O O
C C
C C
O O
C C
C C
O O
C C
C C
O O
C C
C C
O O ~OCH3
C C
O O
CH3OH C COCH3
C C
It is not necessary to specify all of the reaction identifiers. For example, the
only time it is necessary to specify the attacking nucleophilic species and the
attacking electrophilic group is when this species contains more than one type
of group and the two groups are not equally reactive.

Sets of reactions may be grouped together by making more general
specifications. For example, if the attacking electrophilic group and victim
nucleophilic group are the only two identifiers specified, then the rate
constants are assigned to all reactions involving the named groups.
When more than one reaction set is specified, the sets are processed in
reaction set number order, for example, reaction set one is processed before
reaction set two, three, etc. When a match is found for a given reaction, the
rate constant assignment algorithm moves to the next reaction, ignoring the
remaining reaction sets. The algorithm is designed to find the “special cases”
first, and then move on to the general cases.
Several examples illustrating the concept of rate constant assignment follow.
These examples are based on the set of reactions provided previously.
Rxn-
Sets
Reaction Identifiers
RC-Sets
A-Nucl-
Spec
A-Elec-
Grp
V-Elec-
Spec
V-Elec-
Grp
V-Nucl-
Spec
V-Nucl-
Grp
Case 1 Assign rate constant sets 1 and 2 to all of the model-generated reactions
1 1, 2 unspecified unspecified unspecified unspecified unspecified unspecified
Case 2 Assign rate constant sets 1 and 2 to reactions between alcohol groups in ethylene glycol
and any acid groups
Assign rate constant sets 3 and 4 to reactions between alcohol groups in the polymer
and any acid groups
Assign rate constant set 5 to reverse reactions involving methanol
Assign rate constant set 6 to reverse reactions involving water
1 1, 2 unspecified unspecified unspecified unspecified ~OH in
acid
HO(CH2)2OH
~O(CH2)2OH
2 3, 4 unspecified unspecified unspecified unspecified ~OH in
acid
3 5 H2O unspecified unspecified unspecified unspecified unspecified
4 6 CH3OH unspecified unspecified unspecified unspecified unspecified
Case 3 Assign rate constant sets 1 and 2 to reactions between alcohol groups in ethylene glycol
and terephthalic acid
Assign rate constant sets 3 and 4 to all other reactions involving acid groups
Assign rate constant set 5 to reactions between water and glycol end groups
Assign rate constant set 6 to all other reverse reactions involving water
Assign rate constant set 7 to reactions between ethylene glycol and the methylester end
groups in the polymer
Assign rate constant 8 to all other reactions
O O
1 1, 2 unspecified unspecified unspecified unspecified
HO(CH2)2OH HOC COH
2 3, 4 unspecified unspecified unspecified unspecified unspecified ~OH in
acid
3 5 H2O unspecified unspecified unspecified unspecified
~O(CH2)2OH
4 6 H2O unspecified unspecified unspecified unspecified unspecified
5 7 unspecified unspecified unspecified
O O ~OCH3
HO(CH2)2OH C COCH3
6 8 unspecified unspecified unspecified unspecified unspecified unspecified

User Reactions
The model cannot predict all types of reactions based on the specified
structures. Reactions which are not predicted by the model can be included as
user-specified reactions. These can include thermal scission reactions,
monomer or segment reformation, end-group modification, etc.
The user-specified reactions apply a modified power-law rate expression, as
shown here:
Equation
b
Ea


 1 1
  
i

 
k Catalyst k e T
i


Tref specified   i
 
 
net i i o i U flag
T
ref
R T T
ref




, [ ]
Ea
 i
Tref unspecified   i
k  [ Catalyst ] k e RT b
iU flag
net ,
i i o i T Assign User Rate Constants is used: rate  activity  C a
mj k
m m j j i net ,
i
rate   a
Assign User Rate Constants is not used:  C mj k (m  i) m j j
net ,
i
Nomenclature
Symbol Description
m User reaction number
i Rate constant set number
j Component number
 Product operator
Cj
Concentration* of component j, mol/L
i 
Catalyst order term for catalyst i (default = 1)
mj  Power-law exponent for component j in reaction m
ko
Pre-exponential factor in user-specified inverse-time and concentration units*
net ,i k Net rate constant for set i
T Temperature, K
Tref
Optional reference temperature. Units may be specified, they are converted to K in the
model.
flag User flag for rate constant set i. This flag points to an element of the user rate constant
array.
U User rate constant vector calculated by the optional user rate constant subroutine. The
user flag indicates the element number in this array which is used in a given rate
expression. When the user flag is not specified, or when the user rate constant routine
is not present, this parameter is set to 1.0.

* The concentration basis may be changed to other units using the Concentration
basis field on the Options sheet or using the optional concentration basis
subroutine.
You can modify the standard rate expression using the optional user rate
constant feature. The rate constant form includes a parameter called the
“user flag” which identifies an element in an array of user rate constants. This
array is calculated by a user-written Fortran subroutine. The standard rate
expression is multiplied by the user rate constants as shown.
Assignment of Rate Constants to User Specified
Reactions
 There are two options for assigning rate constants to user-specified
reactions. By default, the model assumes there is exactly one set of rate
constants for each reaction (for example, rate constant set “i” is used for
reaction “i”).
Alternately, you may use the Assign User Rate Constant sheet to assign one
or more sets of rate constants to each reaction. This feature is convenient in
two situations:
 Models with a large number of user side reactions when the rate constants
of the various reactions are equal or are related to each other
algebraically.
 Reactions catalyzed by several catalysts simultaneously.
Conventional and Power-Law Components
Conventional components and segments can appear as reactants or products
in the reaction stoichiometry. Each reaction must be mass balanced (the mass
of the products must be equal to the mass of the reactants).
The power-law components can include conventional components, segments,
or oligomers. Power-law coefficients can be specified for components which
do not appear in the reaction stoichiometry, such as catalysts or inhibitors.
The model allows the reactants to have power-law constants of zero, but this
is not recommended because it can lead to numerical problems in the reactor
models. For example, if a reaction “AB” is zeroth order with respect to
component “A”, the reaction could have a positive rate even when component
“A” is not present. This causes “non-negativity violation” integrator errors in
RPlug and RBatch and causes convergence errors in RCSTR. To avoid these
problems, specify a very small power-law coefficient, such as 110-8 .
A user-specified reaction can be accelerated by several different catalysts. In
this situation, use the Assign User Rate Constants form to link multiple sets of
rate constants to each reaction. Each set of rate constants may be associated
with a particular catalyst.
When the side reaction kinetics are complicated, it can be easier to write the
kinetics in the context of the available user kinetic subroutine. This subroutine
is called from the Step-Growth reaction model. The argument list for this
user-written Fortran subroutine includes the step-growth rate constants, user

rate constants, species concentrations, group concentrations, species
structures (number of each group in each species), and others.
User Subroutines
The Step-Growth model can be customized by applying user-written
subroutines. There are three types of subroutines available. The concentration
basis for the model can be changed through a user basis subroutine. This
subroutine can also be used to calculate the volume (RCSTR and RBatch) or
area (RPlug) of the reacting phase. A user rate-constant subroutine can be
used to extend the standard rate expression for model-generated or user-specified
reactions. A user kinetics routine can be used to add reactions to the
model which are too difficult to represent using the power-law approach, or to
calculate user attributes for polymer characteristics which are not tracked by
Aspen Polymers. These routines can be used together in any combination.
User Basis Subroutine
The user basis subroutine can be used to calculate the component
concentrations and the reacting-phase volume (area) basis used in the
component and attribute conservation equations. Use this subroutine when
rate constants are available in unusual concentration units not found in Aspen
Polymers, or when the reacting phase volume or area calculated by the
reactor model is not consistent with the real reactor (for example, in plug flow
reactors with fixed liquid level).
This subroutine can also be used in conjunction with Fortran blocks and user
component attributes to calculate mass-transfer rates and to account for the
influence of mass-transfer limitations on the component concentrations in the
reacting phase.
The argument list for the user basis routine is provided here. This argument
list is prepared in a Fortran template called USRMTS.F, which is delivered with
Aspen Polymers.
User Subroutine Arguments
SUBROUTINE USRMTS
1 SOUT, NSUBS, IDXSUB, ITYPE, XMW,
2 IDSCC, NPO, NBOPST, NIDS, IDS,
3 NINTB, INTB, NREALB, REALB, NINTM,
4 INTM, NREALM, REALM, NIWORK, IWORK,
5 NWORK, WORK, NCPM, IDXM, X,
6 X1, X2, Y, DUM1, FLOWL,
7 FLOWL1, FLOWL2, FLOWV, FLOWS, VLQ,
8 VL1, VL2, VV, VSALT, VLIQRX,
9 VL1RX, VL2RX, VVAPRX, VSLTRX, RFLRTN,
* IFLRTN, CRATES, NTCAT, RATCAT, CSS,
1 VBASIS, IPOLY, NSEG, IDXSEG, AXPOS,
2 TIME )

Argument Descriptions
Variable Usage Type Dimension Description
SOUT Input REAL*8 (1) Stream vector
NSUBS Input INTEGER Number of substreams in stream vector
IDXSUB Input INTEGER NSUBS Location of substreams in stream vector
ITYPE Input INTEGER NSUBS Substream type vector
1=MIXED
2=CISOLID
3=NC
XMW Input REAL*8 NCC Conventional component molecular
weights
IDSCC Input HOLLERITH 2,NCC Conventional component ID array
NPO Input INTEGER Number of property methods
NBOPST Input INTEGER 6, NPO Property method array
NIDS Input INTEGER Number of reaction model IDs
NINTB Input INTEGER User-specified length of INTB array
INTB Retention INTEGER NINTB Reactor block integer parameters (See
Integer and Real Parameters, page 154)
NREALB Input INTEGER User-specified length of REALB array
REALB Retention REAL*8 NREALB Reactor block real parameters (See
NINTM Input INTEGER User-specified length of INTM array
INTM Retention INTEGER NINTM User subroutine integer parameters (See
NREALM Input INTEGER User-specified length of REALM array
REALM Retention REAL*8 NREALM User subroutine real parameters (See
NIWORK Input INTEGER Length of user subroutine integer work
vector
IWORK Work INTEGER NIWORK User subroutine integer work vector (See
Local Work Arrays, page 155)
NWORK Input INTEGER Length of user subroutine real work
vector
WORK Work REAL*8 NWORK User subroutine integer work vector (See
Local Work Arrays, page 155)
NCPM Input INTEGER Number of components present in the
mixed substream (See Packed Vectors,
page 155)
IDXM Input REAL*8 NCPM Component sequence numbers (See
Packed Vectors, page 155)
X Input REAL*8 NCPM Overall liquid mole fractions
X1 Input REAL*8 NCPM First liquid mole fractions
X2 Input REAL*8 NCPM Second liquid mole fractions
Y Input REAL*8 NCPM Vapor phase mole fractions
Dum1 Dummy REAL*8 (1) Argument reserved for future application

FLOWL Input REAL*8 Total liquid flow rate, kmol/sec
FLOWL1 Input REAL*8 First liquid flow rate, kmol/sec
FLOWL2 Input REAL*8 Second liquid flow rate, kmol/sec
FLOWV Input REAL*8 Vapor flow rate, kmol/sec
FLOWS Input REAL*8 Salt flow rate, kmol/sec
VL Input REAL*8 Total liquid molar volume, m3/ kmol
VL1 Input REAL*8 First liquid molar volume, m3/ kmol
VL2 Input REAL*8 Second liquid molar volume, m3/ kmol
VV Input REAL*8 Vapor molar volume, m3/ kmol
VSALT Input REAL*8 Salt molar volume, m3/ kmol
VLIQRX Input REAL*8 Volume* of liquid in reactor, m3
VL1RX Input REAL*8 Volume* of first liquid in reactor, m3
VL2RX Input REAL*8 Volume* of second liquid in reactor, m3
VVAPRX Input REAL*8 Volume* of vapor in reactor, m3
VSLTRX Input REAL*8 Volume* of salt in reactor, m3
RFLRTN Retention REAL*8 (3, 1) Real retention for FLASH
IFLRTN Retention INTEGER (3, 1) Integer retention for FLASH
CRATES Output REAL*8 NCC Component rates of change, kmol/m3-sec
NTCAT Input INTEGER Number of component attributes
RATCAT Output REAL*8 NTCAT Component attribute rates of change,
cat/m3-sec
CSS Output REAL*8 NCC Concentration vector for the active phase
VBASIS Output REAL*8 Holdup basis used to calculate reaction
rates*
IPOLY Input INTEGER Reacting polymer component index
NSEG Input INTEGER Number of segment components
IDXSEG Input INTEGER NSEG Segment component index vector
AXPOS Input REAL*8 RPlug only: axial position, m
TIME Input REAL*8 RBatch only: time, sec
* When using molar concentrations, this parameter is volume of the reacting phase
in m3 in RCSTR and RBatch or the cross-sectional area of the reacting phase in m3
in RPlug.
Example 1 illustrates how to use the user basis routine to convert the
concentration basis from the standard molar concentration basis (mol/L) to a
mass concentration basis (mol/kg). (Note: the current version of Aspen
Polymers supports several concentration basis through the CONC-BASIS
keyword located on the Options form, we retain this example as a
demonstration). Using these units, the reaction rates are calculated in units of
mol/kg-sec. These rates are multiplied by the holdup basis (VBASIS) for the
reactor in the Step-Growth model. For this reason, the holdup basis must be
consistent with the concentration basis, e.g., it must be in kg. The holdup
basis pertains to the reacting phase, it does not include the phases which do
not react.

Example 1: A User Basis Routine For the Mass-Concentration Basis
X
C

i M
i
Liquid
Ci = Mass-concentration of component i
Xi = Mole fraction of component i
MLiquid
= Average molecular weight of components in the
liquid phase
CALL PPMON_VOLL( TEMP, PRES, X, NCPMX, IDXM,
1 NBOPST, GLOBAL_LDIAG, 1, VLQ, DVS, KER)
C-unpack the mole fraction vector into the molar concentrations...
CALL SHS_UNPACK ( X , NCPMX, IDXM, CSS )
C ---------------------------------------------------------------
C
C concentration (mole/kg)=(mole I / mole liquid )*( mole liquid/kg)
C
C ---------------------------------------------------------------
DO 10 I = 1, NCOMP_NCC
CSS(I) = CSS(I) * 1.D3 / STWORK_XMWL
10 CONTINUE
C ---------------------------------------------------------------
C
C reacting phase basis must be consistent with concentration basis (kg)
C liquid mass inventory = liquid volume * density
C
C ---------------------------------------------------------------
VBASIS = VLIQRX * STWORK_XMWL * 1.D-3 / VLQ
RETURN
Note: This excerpt does not include the argument list and declarations
section of the user basis routine.
The plug flow reactor model in Aspen Plus assumes that the vapor and liquid
move at the same velocity through the reactor (e.g., no-slip conditions). This
assumption is not consistent with the physical reality of polymer finishing
reactors or wiped-film evaporators. The subroutine in Example 2 gets around
the no-slip assumption in RPlug, allowing you to specify the volume occupied
by the liquid phase. In this example, the user specifies the first integer
argument in the RPlug block as “1” and specifies the first real argument as
the volume fraction of the reactor occupied by the liquid phase.
Example 2: A User Basis Routine to Specify Liquid Volume in RPlug
UFRAC = 1.D0
IF ( REALB(1) .NE. RGLOB_RMISS ) UFRAC =
REALB(1)
IF ( INTB(1).EQ.1 ) THEN

C - unpack the mole fraction vector into the
molar concentrations...
C - concentration = mole fraction divided by molar
volume of phase
CSS(I) = CSS(I) / VLQ
20 CONTINUE
C - multiply total reactor volume by user-specified
volume fraction -
VBASIS = ( VLIQRX + VVAPRX ) * UFRAC
C - this line makes RPlug calculate liquid residence
time (not L+V)
SOUT(NCOMP_NCC+8)=(SOUT(NCOMP_NCC+9)/
SOUT(NCOMP_NCC+6)) / VLQ
RETURN
END IF
User Rate-Constant Subroutine
The user rate constant subroutine can be used to modify rate constant
parameters for model-generated and user-specified reactions. Use this
routine to modify the standard power-law rate expression for non-ideal
reaction kinetics.
The user rate constant feature can be used to modify the standard power-law
rate expression. This subroutine returns a list of real values which are stored
in an array “RCUSER”. The length of this array is defined by the keyword
NURC (number of user rate constants) in the user rate constant subroutine
form (USER-VECS secondary keyword). Each of the elements in the user rate
constant array can store a different user rate constant. The USER-FLAG
keyword in the SG-RATE-CON and RATE-CON forms is used to specify which
user rate constant is used with a particular set of rate constants.
Elements 1-NURC of RCUSER are calculated by a user rate-constant
subroutine. The standard rate expression is multiplied by the USER-FLAGth
element of the user rate constant vector RCUSER. By default, the USER-FLAG
keyword is set to zero. The zeroth element of the RCUSER array is set to a
value of 1.0, so the rate expression remains unmodified unless the USER-FLAG
keyword is specified.
The argument list for the subroutine is provided here. This argument list is
prepared in a Fortran template called USRRCS.F, which is delivered with
Aspen Polymers.

SUBROUTINE USRRCS
3 NINTB, INTB, NREALB, REALB, NINTR,
4 INTR, NREALR, REALR, NIWORK, IWORK,
6 X1, X2, Y, DUM1, VL,
7 VL1, VL2, VV, VSALT, IPOLY,
8 NSEG, IDXSEG, NOLIG, IDXOLI, NSGOLG,
9 NGROUP, IDGRP, NSPEC, IDXSPC, NFGSPC,
* CSS, CGROUP, TEMP, PRES, NURC,
1 RCUSER, CATWT )
1=MIXED
2=CISOLID
3=NC
weights
IDSCC Input HOLLERITH 2, NCC Conventional component ID array
NBOPST Input INTEGER 6, NPO Property method array (used by FLASH)
IDS Input HOLLERITH 2,NIDS Reaction model ID list:
i,1 reactor block ID
i,2 reactor block type
i,3 reaction block ID
i,4 reaction block type
i,5 user subroutine ID
NINTR Input INTEGER User-specified length of INTM array
INTR Retention INTEGER NINTR User subroutine integer parameters (See
NREALR Input INTEGER User-specified length of REALM array
REALR Retention REAL*8 NREALR User subroutine real parameters (See

vector
IWORK Work INTEGER NIWORK User subroutine integer work vector
(See Local Work Arrays, page 155)
vector
WORK Work REAL*8 NWORK User subroutine integer work vector
page 155)
VL Input REAL*8 Total liquid molar volume, m3/kmol
VL1 Input REAL*8 First liquid molar volume, m3/kmol
VL2 Input REAL*8 Second liquid molar volume, m3/kmol
VV Input REAL*8 Vapor molar volume, m3/kmol
VSALT Input REAL*8 Salt molar volume, m3/kmol
NOLIG Input INTEGER Number of oligomer components
IDXOLI Input INTEGER NOLIG Oligomer component index vector
NSGOLG Input INTEGER NSEG,
NOLIG
Segment frequency vector: contains
number of each segment in each
oligomer
NGROUP Input INTEGER Number of functional groups
IDGRP Input HOLLERITH NGROUP Functional group ID vector
NSPEC Input INTEGER Number of reacting species
IDXSPC Input INTEGER NSPEC Reacting species component index
vector
NFGSPC Input INTEGER NSPEC,
NGROUP
Group frequency vector: contains
number of each functional group in each
species
CSS Input REAL*8 NCC Concentration vector for reacting species
CGROUP Input REAL*8 NGROUP Concentration vector for reacting groups
TEMP Input REAL*8 Temperature, K
PRES Input REAL*8 Pressure, Pa
NURC Input INTEGER Number of user rate constants (See User
Rate-Constant Subroutine, page 144)

RCUSER Output REAL*8 NURC User rate constant vector (See User
CATWT Input REAL*8 Catalyst weight, kg (in RPLUG,
weight/length)
Example 3 illustrates how to use this subroutine to implement complex rate
expressions in the Step-Growth model.
Example 3: Implementing a Non-Ideal Rate Expression
Suppose a side reaction QZ is first order with respect to component Q and
first order with respect to a catalyst C. The effectiveness of the catalyst is
reduced by inhibitor I according to the following equation:
   C

 actual
1 (  )
C  
eff a bT I
Where:
[C ] eff = Effective catalyst concentration, mol/L
[C ] actual = Actual catalyst concentration, mol/L
[I] = Inhibitor concentration, mol/L
T = Temperature, K
a,b = Equation parameters
The net rate expression can thus be written as:
 
C
a bT I

1 1


 
*
 R T Tref
actual k e
rate Q  
o
E
( )
 

 
[ ]
1
Where:
ko = Pre-exponential factor, (L/mol)/sec
E* = Activation energy
R = Gas law constant
Tref = Reference temperature for ko
[Q] = Concentration of component Q, mol/L
The standard rate expression for side reactions is:

E
R T T



1 1

 

 

*

rate  k e ref C i
U j o
i
i
 
 
* ( )
Where:
 = Product operator
Ci = Concentration of component i

i = Power-law exponent for component i
U = User rate constant
j = User rate-constant flag
Suppose the rate constant for the uninhibited reaction is 3 103 (L/mol)/min
at 150C, with an activation energy of 20 kcal/mol, and the inhibition rate
constants are A=0.20 L/mol, B=0.001 L/mol-K. The stoichiometric coefficients
and power-law exponents are specified directly in the Stoic and PowLaw-Exp
keywords. The Arrehnius rate parameters and reference temperature are also
specified directly in the model.
The parameters for the user rate constant equation can be specified using the
optional REALRC list. Including the parameters in the REALRC list allows the
model user to adjust these parameters using the standard variable accessing
tools, such as Sensitivity, Design-Specification, and Data-Regression.
The resulting model input is summarized below:
USER-VECS NREALRC=2 NUSERRC=1
REALRC VALUE-LIST=0.2D0 0.001D0
STOIC 1 Q -1.0 / Z 1.0
POWLAW-EXP 1 Q 1.0 / C 1.0
RATE-CON 1 3D-3<1/MIN> 20.000<kcal/mol>
TREF=150.0<C> URATECON=1
The power-law term from this equation is:
E

* 1 1


 

 
rate  k e R T Tref
CQ o
Where:
[C] = Catalyst concentration, mol/L
k= Pre-exponential factor
o Thus, the required user rate constant is:
1
U j
a bT I
( )
( ( )[ ]
1
 
 
1
Where:
T = Temperature, K
a, b = Equation parameters
An excerpt from the user rate constant subroutine for this equation is shown
below:
C - Component Name -
INTEGER ID_IN(2)
DATA ID_IN /'INHI','BITO'/

C ======================================================================
C EXECUTABLE CODE
C ======================================================================
C - find location of inhibitor in the list of components -
IF ( IDSCC(1,I).EQ.ID_IN(1).AND.IDSCC(2,I).EQ.ID_IN(2) ) I_IN=I
10 CONTINUE
C - get the concentration of the inhibitor -
C_IN = 0.0D0
IF ( I_IN .GT.0 ) C_IN = CSS( I_IN )
C ----------------------------------------------------------------------
C Parameters: each REALR element defaults to zero if not specified
C ----------------------------------------------------------------------
A = 0.0D0
IF ( NREALR .GT. 0 ) A = REALR( 1 )
B = 0.0D0
IF ( NREALR .GT. 1 ) B = REALR( 2 )
C ----------------------------------------------------------------------
C User rate constant #1 U(1) = 1 / ( 1 + (A+BT)[I] )
C ----------------------------------------------------------------------
IF ( NURC.LT.1 ) GO TO 999
RCUSER(1) = 1.0D0 / ( 1.0D0 + ( A + B*TEMP ) * C_IN )
END IF
999 RETURN
User Kinetics Subroutine
The user kinetics subroutine is used to supplement the built-in kinetic
calculations. Use this subroutine when the side reaction kinetics are too
complicated to represent through the user rate constant routine, or when
previously written Fortran routines are to be interfaced to the Step-Growth
model.
The argument list for this subroutine is provided here. The argument list and
declarations are set up in a Fortran template called USRKIS.F, which is
delivered with Aspen Polymers.
SUBROUTINE USRKIS(
3 NINTB, INTB, NREALB, REALB,
4 NINTK, INTK, NREALK, REALK, NIWRK,
5 IWRK, NWRK, WRK, NCPMX, IDXM,
6 X, X1, X2, Y, DUMXS,
7 FLOWL, FLOWL1, FLOWL2, FLOWV, DUMFS,
8 VLQ, VLQ1, VLQ2, VVP, VOLSLT,
9 VLIQRX, VL1RX, VL2RX, VVAPRX, VSLTRX,
* IPOLY, NSEG, IDXSEG, NOLIG, IDXOLI,
1 NSGOLG, NGROUP, IDGRP, NSPEC, IDXSPC,
2 NFGSPC, CSS, CGROUP, TEMP, PRES,
3 RFLRTN, IFLRTN, CRATES, NTCAT, RATCAT,
4 NRC, PREEXP, ACTNRG, TEXP, TREF,
5 IUFLAG, NURC, RCUSER )

1=MIXED
2=CISOLID
3=NC
weights
NBOPST Input INTEGER 6, NPO Property method array (used by FLASH)
i,5 user subroutine ID
NINTK Input INTEGER User-specified length of INTM array
INTK Retention INTEGER NINTK User subroutine integer parameters (See
NREALK Input INTEGER User-specified length of REALM array
REALK Retention REAL*8 NREALK User subroutine real parameters (See
vector
vector
page 155)

FLOWL Input REAL*8 Total liquid flow rate, kmol / sec
FLOWL1 Input REAL*8 First liquid flow rate, kmol / sec
FLOWL2 Input REAL*8 Second liquid flow rate, kmol / sec
FLOWV Input REAL*8 Vapor flow rate, kmol / sec
FLOWS Input REAL*8 Salt flow rate, kmol / sec
VL2 Input REAL*8 Second liquid molar volume, m3/kmol
NOLIG Input INTEGER Number of oligomer components
IDXOLI Input INTEGER NOLIG Oligomer component index vector
NSGOLG Input INTEGER NSEG,
NOLIG
Segment frequency vector: contains
number of each segment in each
oligomer
NGROUP Input INTEGER Number of functional groups
IDGRP Input HOLLERITH 2,NGROUP Functional group ID vector
NSPEC Input INTEGER Number of reacting species
IDXSPC Input INTEGER NSPEC Reacting species component index
vector
NFGSPC Input INTEGER NSPEC,
NGROUP
Group frequency vector: contains
number of each functional group in each
species
CSS Input REAL*8 NCC Concentration vector for reacting species
CGROUP Input REAL*8 NGROUP Concentration vector for reacting groups
PRES Input REAL* Pressure, Pa
RFLRTN Retention REAL*8 3,(1) Real retention for FLASH
IFLRTN Retention INTEGER 3,(1) Integer retention for FLASH
CRATES Output REAL*8 NCC Component rates of change, kmol / m3 -
sec
NTCAT Input INTEGER Total number of component attributes

cat / m3 - sec
NSGRC Input INTEGER Number of sets of step-growth rate
constants
PREEXP Input REAL*8 NSGRC Pre-exponential factors, 1/sec (See
Step-Growth Rate Constants, page 153)
ACTNRG Input REAL*8 NSGRC Activation energies, J/kmol-K
TEXP Input REAL*8 NSGRC Temperature exponents, unitless
TREF Input REAL*8 NSGRC Reference temperatures, K
IUFLAG Input Integer*8 NSGRC User rate constant flags (See User Rate-
Constant Subroutine, page 144)
NURC Input INTEGER Number of user rate constants
* Area in RPlug
The user kinetic subroutine returns the rate of change of the reacting species
and the Class 2 component attributes (zeroth moment and segment flow
rates). The subroutine may be applied to calculate user component attributes
(CAUSRA etc.) to track color or other polymer properties which are related to
the thermal history of the polymer.
Example 4 illustrates how the concentration of a color body can be tracked
through user kinetics routine. The example assumes that the polymer color is
proportional to the amount of unknown color bodies which are generated by
side reactions. These unknown side reactions are sensitive to the thermal
history of the polymer, according to an Arrehnius rate expression. The
activation energy and pre-exponential factors of this expression are stored as
the first and second REAL parameters for the user kinetics model.
Example 4: Tracking Polymer Color Using User Attributes in a Step-
Growth User Kinetics Model
INTEGER IDUSRA(2)
DATA IDUSRA /'CAUS','RA '/
C.....GAS CONSTANT IN KCAL/MOL-K...
RGASKC = 1.987D-3
C.....locate CAUSRA attribute: LUSRA points to location in SOUT...
LUSRA = SHS_LCATT( 1, IPOLY, IDUSRA )
C.....LURAT points to this attribute in the RATCAT vector...
LURAT = LUSRA - NCOMP_NVCP
C ----------------------------------------------------------------------
C Get the rate constants from the list of REAL parameters in the
C user-kinetics section of the Step-Growth Subroutine form
C REAL(1) A_CF Color Formation pre-exponential, 1/min
C REAL(2) E_CF Color Formation activation energy, kcal/mol-K

C ----------------------------------------------------------------------
A_CF = 0.D0
E_CF = 0.D0
IF ( NREALK .GT. 1 ) THEN
IF ( REALK( 1 ) .GE. RGLOB_RMISS ) REALK( 1 ) = 0.D0
IF ( REALK( 2 ) .GE. RGLOB_RMISS ) REALK( 2 ) = 0.D0
A_CF = REALK( 1 ) / 60.D0
E_CF = REALK( 2 )
END IF
C Calculate color formation rate in color-units/cubic-meter/second
RATCAT( LURAT ) = A_CF * DEXP( -E_CF / ( RGASKC*TEMP ) )
RETURN
Step-Growth Rate Constants
The step-growth reaction rate constants can be applied in the user kinetics
subroutine. The rate constants are passed to this model as a set of arrays
which are stored in rate constant set number order (the element number of
the array corresponds to the reaction set number). These parameters are
stored in SI units. The concentration basis for the pre-exponential factors are
in molar concentration (mol/L) units. When a user concentration basis
subroutine is used, the pre-exponential factors are assumed to be in units
which are consistent with the user-calculated concentrations.
The user rate constants are also passed to the user kinetic subroutine. These
parameters can be used “as is”, or they can be used with the step-growth
rate constants to build rate expressions consistent with those used by the
standard model. The array “UFLAG” is used to designate which user rate
constant (if any) is assigned to a given set of step-growth rate constants. For
example, if IUFLAG(2) = 1, then user rate constant 1 is assigned to step-growth
rate constant set 2, and the pre-exponential factor can be adjusted
accordingly. Example 5 illustrates how to apply user rate constants and step-growth
rate constants in a user kinetics model.
Example 5: How to Apply User Rate Constants and Step-Growth Rate
Constant in a Step-Growth User Kinetics Model
C set work space to calculate net rate constants
LPREEX = 0
LNETRC = LPREEX + NSGRC
C ----------------------------------------------------------------------
C Multiply step-growth pre-exponential factors by user rate constants
C and store the results in the work array.
C ----------------------------------------------------------------------
DO 10 IR = 1, NSGRC
IRCU = IUFLAG( IR )
IF ( IRCU .EQ. 0 ) THEN
WORK( LPREEX + IR ) = PREEXP( IR )
ELSE
WORK( LPREEX + IR ) = PREEXP( IR ) * RCUSER( IRCU )
END IF
10 CONTINUE
C ----------------------------------------------------------------------

C Calculate the net rate constants
C ----------------------------------------------------------------------
DO 20 IR = 1, NSGRC
IF ( TREF(IR) .EQ. 0 ) THEN
TTERM1 = 1/TEMP
TTERM2 = TEMP**TEXP(IR)
ELSE
TTERM1 = 1/TEMP - 1/TREF(IR)
TTERM2 = ( TEMP / TREF )**TEXP(IR)
END IF
ETERM = DEXP( -ACTNRG(IR) * TTERM1 / PPGLOB_RGAS )
WORK( LNETRC+ IR ) = WORK( LPREEX+ IR ) * ETERM * TTERM2
20 CONTINUE
Note: The work array is used to store intermediate results in the calculations.
The size of the work array must be specified in the subroutine form and must
be large enough to avoid overwriting the end of the array.
INCL-COMPS List
The reactor models in Aspen Polymers use mass-balance equations for each
reacting component. In order to make the reactor models fast, components
which do not appear in the reactions are excluded from these calculations.
The list of reacting components is automatically generated by the Step-
Growth model. This list includes the polymer component, listed oligomers,
components which appear in the list of reacting species, components which
appear as products or reactants in the user-specified reactions, and
components in the INCL-COMPS component list.
When user concentration basis or user kinetics subroutines are applied in a
model, these subroutines can include reactions involving components which
do not otherwise appear in the list of reacting components. These
components should be added to the INCL-COMPS list to ensure they appear in
the mass-balance equations.
Integer and Real Parameters
Each user model has two sets of integer and real parameters. The first set
comes from the subroutine form of the reactor block. The second set comes
from the subroutine form of the step-growth reactions model. Each of these
parameters are retained from one call to the next, thus these parameters can
be used as model inputs, outputs, or retention.
The reactor block integer and real parameters can be used to specify data
which are specific to a particular unit operation, such as reactor geometry,
mass transfer coefficients, etc. The integer and real parameters in the
subroutine forms can be used to specify global parameters, such as rate
constants or physical property parameters.

Local Work Arrays
You can use local work arrays by specifying the model workspace array length
on the STEP-GROWTH Subroutine form. These work areas are not saved from
one call to the next. All three user subroutines share a common work area, so
you must zero out the work space at the start of each subroutine.
Packed Vectors
Aspen Plus frequently uses a technique called “packing” to minimize
simulation time. The user models previously described use packed vectors to
track the mole fractions of each phase (vectors X, X1, X2, and Y). These
vectors contain NCPM elements (Number of Components Present in the Mixed
substream). The component index associated with each element is listed in
the vector “IDXM”. All other vectors used by the model, including the rates
vectors and the component concentration vectors, are unpacked.
Example 6: Calculating Unpacked Component Concentrations
Calculate unpacked component concentrations of the first liquid phase given
the packed mole fractions of the first liquid phase and the molar volume of
the first liquid phase.
IF ( VL1 .GT. 0.D0 .AND. FLOWL1.GT.0.D0 ) THEN
DO 10 I = 1, NCPM
CSS(I) = X1( IDXM( I ) ) / VL1
10 CONTINUE
END IF
Note: NCPM steps were required to load the concentration vector. Since
NCPM is always less than or equal to NCC (total number of conventional
components), there is a reduction in the required number of steps to perform
the operation.
Specifying Step-Growth
Accessing the Step-Growth Model
To access the Step-Growth polymerization kinetic model:
1 From the Data Browser, click Reactions.
2 From the Reactions folder, click Reactions.
3 The Reactions object manager appears.
4 If the kinetic model already exists, double-click the desired Reaction ID in
the object manager or click Edit to get to the input forms.
5 To add a new model, from the Reactions object manager, click New. If
necessary, change the default ID for the reaction.

6 Select Step-Growth as the reaction type and click OK.
Specifying the Step-Growth Model
The Step-Growth model input forms are divided into two folders:
Specifications and User Subroutines.
Use the Specifications forms to define reacting species and functional
groups, enter reaction rate constant parameters, and include user side
reactions.
Use this
To
sheet
Species Define reacting species and functional groups
Specify the name of the polymer being produced
Specify the names for linear oligomers (optional)
Reactions Generate and display model-generated reactions
Rate Constants Specify reaction rate constants for model-generated reactions
User Reactions Specify reaction stoichiometry and enter rate constants for user-specified
reactions
User Rate
Constants
Specify catalysts and reaction rate constants for user-specified
reactions
Assign User
Rate Constants
Assign one or more sets of rate constants to each user-specified
reaction
Options Specify the reacting phase and concentration basis.
Change reaction convergence parameters.
Select report options.
Use the User Subroutines forms to specify the names and parameters for
optional user subroutines.
Use this sheet To
Kinetics Specify the name of the user kinetics routine and give the
integer and real arguments for the user arrays for this routine
Rate Constants Specify the name of the user kinetics routine, the number of
user rate constants calculated by the routine, and to give the
Basis Specify the name of the user concentration and reacting phase
volume basis routine and give the integer and real arguments
for the user arrays for this routine
Specifying Reacting Components
You must specify the reacting species and functional groups on the Step-
Growth Specifications Species sheet.
First specify the polymers and oligomers produced:
1 In the Polymer field, specify the polymer produced.
2 In the Oligomers field, list oligomers that you want the model to track.

3 In the species definition table, specify the functional groups contained in
each reacting species and define each group type.
The structure of reacting species in terms of the reactive functional groups
they contain must be defined. To do this:
1 In the Group field specify an ID name for each functional group type
present in the reacting species.
2 For each group, select a type from the group type field.
3 List the species in the Species field.
These species can be monomers, condensates, or segments.
The resulting form is a spreadsheet, with each column representing a
functional group and each row representing a reacting species. The cells in
the spreadsheet correspond to the number of each functional group in
each species.
4 In the number field for each species, specify the number of each defined
functional group contained in that species.
Unspecified fields are interpreted as zeros.
Listing Built-In Reactions
The step-growth model generates reactions based on the functional group
definition of reacting species. You can view the system-generated reactions,
by clicking the Generate Reactions button on the Specifications
Reactions sheet.
In the Reaction summary listing for each reaction, the first column indicates
the reaction type. The second column lists the reactants, and the last column
lists the products. The Data Browser window can be resized to better view the
reaction listing.
Specifying Built-In Reaction Rate Constants
You can define the catalysts and rate constants for system-generated
reactions. The model applies a modified power-law rate expression, which can
be customized through a user-written rate constant subroutine. By default,
the model assumes concentrations are in mol/liter. Another concentration
basis can be applied through a user-written basis subroutine.
To specify rate constants:
1 Go to the Rate constants sheet.
2 In the reaction No. field, assign a unique integer identifier for a set of rate
constant parameters.
3 In the Catalyst Species field, specify the name of a catalyst species
associated with the rate constant set.
You can leave this field unspecified if the reaction is uncatalyzed, or if the
catalyst is defined as a functional group.
4 In the Catalyst Group field, specify the name of a catalyst functional
group associated with the rate constant set.
You can leave this field unspecified if the reaction is uncatalyzed, or if the
catalyst is defined as a species.

5 Enter the rate constant parameters: ko for Pre-exponential factor, Ea for
Activation energy, b for Temperature exponent, Tref for Reference
temperature.
6 Request any user rate constant expression in the User flag field.
7 Repeat these steps as needed to specify the list of rate constant
parameters.
Assigning Rate Constants to Reactions
You can assign rate constants to individual reactions using the reaction
stoichiometry, or you can assign rate constants to sets or reactions using the
appropriate reaction identifiers.
To assign the rate constants set:
1 Click the Assign Rate Constants button on the Specifications Rate
constants sheet.
2 Click the Global tab to assign rate constants to a set of reactions or use
the Individual sheet to assign rate constants to individual reactions.
3 Go to the Rate Constant Sets field, select from the list of pre-defined rate
constant sets for each reaction.
Including User Reactions
You can add user reactions to the built-in set. For this you must specify a
reaction stoichiometry and the associated rate constants. The model applies a
modified rate expression, which can be customized through a user-written
rate constant subroutine.
To add user reactions use the following options found on the Specifications
User Reactions sheet:
Click To
New Add new reactions to the scheme
Edit Specify reaction stoichiometry and power-law
exponents
Rate Constants Specify reaction rate constant parameters for the
reactions
Click to select a reaction. Click a reaction then Control-Click to include
additional reactions for multiple selections. Double-click to edit a reaction.
In addition, you can use the following buttons:
Click To
Hide/Reveal
Exclude/Include a reaction from the
calculations
Delete
Permanently remove a reaction from the model

Adding or Editing User Reactions
In the User Reactions sheet, to add a new reaction to the scheme or edit an
existing reaction, open the Edit subform. When you open the Edit subform, a
unique number is assigned in the Reaction no. field, to the reaction being
added.
To add or edit your reaction:
1 On the Edit subform, specify the Component ID and stoichiometric
Coefficient for the reactants.
Reactants must have a negative coefficient.
2 Specify the Component ID and stoichiometric Coefficient for the
products.
Products must have a positive coefficient.
3 Click to check the Completion Status
 or 
Click Close to return to the reaction summary.
Specifying Rate Constants for User
Reactions
All the rate constants for user-specified reactions are summarized in a grid on
the User Rate Constants tab:
1 In the ko field, enter the pre-exponential factor.
2 In the Ea
field, enter the activation energy.
3 In the b field, enter the temperature exponent.
4 In the Tref field, enter the reference temperature.
Note: Use the Catalyst Species field to associate a rate constant with a
particular catalyst. If you leave this field blank the model drops the catalyst
term from the rate expression.
Use the Catalyst Order field to specify the reaction order with respect to the
catalyst (the model assumes first order by default).
Assigning Rate Constants to User Reactions
By default, the model assumes one set of rate parameters for each reaction.
(For example, rate constants in row 1 apply to user reaction 1). Alternately,
you may assign one or more rate constants to each reaction using the Assign
User Rate Constants form.
When several rate constants are assigned to a reaction the model calculates a
net rate constant by summing all of the listed rate constants and multiplying
the sum by a specified activity.
To assign rate constants to user reactions:
1 On the Assign User Rate Constants form, use the Activity field to
specify the activity factor.

2 In the Rate Constant Sets field, select from the list of pre-defined rate
constant sets for each reaction.
Selecting Report Options
You can select which format to use for the step-growth reactions in the report
file. On the Options sheet, go to the Report frame to request a reaction
report. Then, select a Summary or Detailed format.
Selecting the Reacting Phase
The Options form lets you specify the phase in which the reactions occur.
Select the appropriate phase from the list in the Reacting Phase field. All of
the reactions in a particular step-growth object are assumed to take place in
the same phase.
Note: You must specify the Valid Phases keyword for each reactor model
referencing the kinetics to ensure the specified reacting phase exists.
If the Reacting Phase option is set to Liquid-1 or Liquid-2 the model
assumes two liquid phases exist. When the named phase is not present, the
model prints a warning message and sets the reaction rates to zero. There
are two options for handling phase collapse:
 Select the Use bulk liquid phase option to force the model to apply the
specified reaction kinetics to the bulk phase when the named phase
disappears.
 Select the Suppress warnings option to deactivate the warning
messages associated with phase collapse.
These options are especially convenient when modeling simultaneous
reactions in two liquid phases using two step-growth models. In this situation,
you would typically select the Use bulk liquid option for one phase and not
the other (to avoid double-counting reactions when one phase collapses).
Specifying Units of Measurement for Pre-
Exponential Factors
Reaction rates are defined on a molar basis (moles per volume per time) .
The time units for the pre-exponential factors are specified directly on the
Rate Constant forms.
By default, the concentration units are presumed to be in SI units (kmole/m3
or mole/L).
You change the concentration basis to other units using the Concentration
Basis field of the Options sheet. Alternately, you may apply a user basis
subroutine.

Including a User Kinetic Subroutine
Use the User Subroutines Kinetics form to specify parameters for user
kinetics calculations:
1 In subroutine Name, enter the name of the Fortran subroutine.
2 Specify the size of vectors for Integer, Real in Number of parameters,
and Length of work arrays.
3 Enter integer and real parameter values in Values for parameters
columns.
4 Click Include Comps to specify components to be included in material
balance convergence.
Including a User Rate Constant Subroutine
Use the User Subroutines Rate Constants form to specify parameters for
user rate constants calculations:
2 Specify the size of vectors for Integer, Real and No. const. in Number
of parameters.
3 Specify the size of vectors of Integer and Real in Length of work
arrays.
columns.
Including a User Basis Subroutine
Use the User Subroutines Basis form to specify parameters for basis
calculations:
2 Specify the size of vectors for Integer and Real in the Number of
parameters and Length of work arrays.
columns.
References
Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley.
Gupta, S. K, & Kumar, A. (1987). Reaction Engineering of Step-Growth
Polymerization. New York: Plenum.
Jacobsen, L. L., & Ray, W. H. (1992). Unified Modeling for Polycondensation
Kinetics. J. Macromol. Sci.-Rev. Macromol. Chem. Phys.
Kaufman, H. S., & Falcetta, J. J. (Eds). (1977). Introduction to Polymer
Science and Technology: An SPE Textbook. New York: Wiley.
McKetta, J. J. (Ed.). (1992). Encyclopedia of Chemical Processing and Design,
39 & 40. New York: Marcel Dekker.

Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere.

9 Free-Radical Bulk
This section covers the free-radical bulk/solution polymerization model
available in Aspen Polymers (formerly known as Aspen Polymers Plus).
 Free-Radical Bulk/Solution Processes, 164
 Polymer Properties Calculated, 190
 Specifying Free-Radical Polymerization Kinetics, 193
Several example applications of the free-radical bulk/solution polymerization
model are given in the Aspen Polymers Examples & Applications Case Book.
The Examples & Applications Case Book provide process details and the
kinetics of polymerization for specific monomer-polymer systems.
The free-radical bulk/solution polymerization model is applicable to bulk and
solution polymerization processes. Some examples of applicable polymers
are:
 General purpose polystyrene - Made by polymerization of styrene
monomer with or without solvent fed continuously to reactor.
 High impact polystyrene - Made by polymerization of an unsaturated
rubber dissolved in styrene in a solution process. Also produced in mass-suspension
processes.
 Poly(vinyl chloride) - Produced in bulk polymerization using monomer-soluble
free radical initiators. Most of the homopolymers and copolymers
of vinyl chloride, however, are produced by suspension polymerization.
 Poly(vinyl acetate) - Produced industrially by the polymerization of vinyl
acetate in bulk or solution processes. Also produced in suspension and
emulsion processes. Both batch and continuous processes are used.
9 Free-Radical Bulk Polymerization Model 163

 Poly(vinyl alcohol) - Poly(vinyl acetate) is converted into the
corresponding poly(vinyl alcohol) by direct hydrolysis or catalyzed
alcoholysis. The reaction can be catalyzed by strong acids or strong bases.
 Poly(methyl methacrylate) - The vast majority of commercially prepared
acrylic polymers and methacrylic polymers are copolymers. Commercially
they are prepared by solution polymerization. They are also produced by
emulsion polymerization and suspension polymerization.
 Low density polyethylene - Made by high pressure, free radical processes
in either a tubular reactor or a stirred autoclave. Typical commercial
processes include staged compression, initiator injection, partial
conversion of ethylene to polymer, separation of ethylene from polymer,
extrusion of molten polymer, and cooling of ethylene.
 The Free-Radical model may also be used to simulate suspension
polymerization processes in which the polymer is completely soluble in the
organic (monomer) phase. Two reaction models can be applied together
to represent reactions in each liquid phase. An example of this process is:
 Poly(styrene) - Poly(styrene) may be produced in a continuous suspension
process in a series of CSTR type reactors.
Free-Radical Bulk/Solution
Processes
Free-radical polymerization accounts for a large proportion (more than 40%
by weight) of the commodity grade polymers. It is employed in the synthesis
of countless homo- and copolymers using monomers that are either
monosubstituted ethylenes RHC  CH  2 or 1,1-disubstituted ethylenes
R1R2C CH2   .
Free-radical polymerization usually takes place with the monomer in the liquid
phase. Several types of processes are used. A solvent or suspending medium
may be used, and the polymer formed may be soluble, insoluble, or swelled
by the monomer and solvent. Commercially important processes for free-radical
polymerization include bulk, solution, suspension, and emulsion
polymerization.
Bulk and Solution Polymerization
Bulk and solution polymerization processes are characterized by the fact that
the reactions proceed in a single phase. Typically the monomers are fed to a
reactor with or without a solvent. A small amount of initiator is also fed. At
the reaction temperature, the initiator decomposes to form radicals that
initiate the polymerization reactions. The polymer formed is usually soluble in
the monomer/solvent mixture. However, in some systems, such as PVC, the
polymer is insoluble and forms a separate phase.
The most commonly used reactor types include batch, semi-batch, continuous
stirred-tank and tubular reactors. Flowsheets consisting of several reactors in
series are common. The main technical challenges with bulk/solution
polymerization processes are heat removal, handling of the highly viscous
164 9 Free-Radical Bulk Polymerization Model

liquid, and recovery of residual monomer/solvent. Several modes of heat
removal can be employed, including jacket cooling, internal cooling
coils/baffles, external heat exchangers and reflux condensors.
Most free-radical polymerizations have at least four basic reaction steps:
 Initiation
 Propagation
 Chain transfer to a small molecule (i.e. monomer, solvent or transfer
agent)
 Termination
These reactions occur simultaneously during the polymerization. For branched
polymers additional reactions for long and short chain branching can also be
present. A comprehensive kinetic scheme for the free-radical homo- and
copolymerization of up to Nm monomers has been built into Aspen Polymers.
The scheme includes most of the reactions commonly used for modeling free-radical
polymerization. The model also includes several optional reactions:
 Terminal double bond polymerization
 Pendent double bond polymerization (for diene monomers)
 Head-to-head propagation (for asymmetric monomers)
 Cis- and trans- propagation (for diene monomers)
 Primary and secondary decomposition of bifunctional initiators
Reactions such as depropagation and random chain scission are not included
in the current model. These reactions may be added to the built-in scheme in
the future.
The main reactions in the current built-in free-radical kinetic scheme is shown
here :

166
Built-in Free-Radical
The nomenclature used in the free
Polymerization Kinetic Scheme
free-radical kinetic scheme is shown here
here:
9 Free-Radical Bulk Polymerization Model

Symbol Description
Symbols Used in the Population Balance Equations
Ak
Chain transfer agent of type k
B , B Reaction by-products (optional for some reactions)
1 2 Ck
Coinitiator or catalyst of type k
Dn Dead polymer chain of length n ( n1, n2, ...nm )
jk
n D Polymer chain of length n containing an undecomposed bifunctional
initiator fragment of type k attached to penultimate segment of type j
D Polymer chain of length n containing a terminal double bond of type i
 in
D Polymer chain of length n reacting at an internal double bond of type i
) (vinyl in
(e.g., a diene segment of type i in the vinyl configuration)
ij
TDB f Fraction of reactions between species i and j resulting in the formation of
a terminal double bond of type i
Ik
Standard initiator of type k
I B
Bifunctional initiator of type k
k Mj
Monomer of type j
i Live polymer chain of length n having an active segment of type i
Pn
i(cis)
n P Live polymer chain of length n having an active diene segment of type i
in the cis configuration.
i(trans )
n P Live polymer chain of length n having an active diene segment of type i
in the trans configuration.
R Primary radicals
Sk
Solvent of type k (for solution polymerization)
Xk
Inhibitor of type k
1 2  , Stoichiometric coefficients for reaction by-products B1, B2
 Initiator efficiency factor for initiator k
k Ak
Chain transfer agent of type k
B , B Reaction by-products (optional for some reactions)
1 2 Ck
Coinitiator or catalyst of type k
Dn Dead polymer chain of length n ( n1, n2, ...nm )
Symbol Description
Symbols Used in Reaction Rate and Moment Balance Equations
a, b, c Coefficients for the induced (thermal, radiation) initiation rate
C Concentration of a reacting non-polymeric species. The following
subscripts are used to identify the component:

Symbol Description
Ak Chain transfer agent k
Ck Catalyst or coinitiator k
Ik Initiator or bifunctional initiator k
Mi Monomer i
Sk Solvent k
Xk Inhibitor k
k Net rate constant (see Equation 3.1 on page 170 ). The following
subscripts are used to identify the reaction types:
bs Beta scission
bid Bifunctional initiator primary decomposition
cis Cis-propagation
ic Catalyzed initiation
id Standard initiator decomposition
hth Head-to-head propagation
p Propagation (polymerization)
pdb Pendent double bond polymerization
pi Primary chain initiation
scb Short chain branching
si Special initiation (induced initiation)
sid Secondary decomposition of bifunctional initiator
tc Termination by combination
td Termination by disproportionation
tdbp Terminal double bond polymerization
tra Chain transfer to agent
trans Trans-propagation
trm Chain transfer to monomer
trp Chain transfer to polymer (long chain branching)
trs Chain transfer to solvent
x Inhibition
N Number of (A=agents, BI=bifunctional initiators, C=catalysts,
CI=coinitiators, I=standard initiators, M=monomers, S=solvents,
X=inhibitors)
k
r N Number of radicals (1 or 2) formed from the decomposition of initiator of
type k
1 2  , Stoichiometric coefficients for reaction by-products B1, B2
k  Initiator efficiency factor for initiator k
ij
TDB f Fraction of reactions between species i and j resulting in the formation of
a terminal double bond of type i
 Zeroth moment of live polymer with respect to active segment of type i
i0
 j
First moment of live polymer with respect to segment j
1 Zeroth moment of bulk polymer (live + dead)
0

Symbol Description
j
1 
First moment of bulk polymer (live + dead) with respect to segment j
2
Second moment of bulk polymer (live + dead)
 Moment a (a=0, 1, 2, etc) of polymer molecules with terminal double
 ja
bond of type j
i, j  Flow rate of dyads consisting of i and j segments (these values are
stored in the DYADFLOW attribute)
 i Molar fraction of diene segment i in the vinyl configuration (zero for non-diene
segments) (related to VINYLFRA attribute)
k  Concentration of undecomposed initiator fragment k in the bulk polymer
(live + dead) (related to FRAGFLOW attribute)
In the discussion that follows, a polymer chain is considered to be made up of
monomer units or segments derived from the propagating monomers.
Typically there will be one segment type associated with each monomer.
However, it is possible to define several segment types associated with a
single monomer. This may be necessary, for example, for modeling the
tacticity of a polymer, or head-to-head versus head-to-tail incorporation of an
asymmetric monomer RHC  CH2 .
Polymer Chain Terms
The term live polymer chain (Pn )
i refers to growing polymer chains containing
n segments, with a radical attached to a segment of type i, i.e., segment
formed from monomer i. The term dead polymer chain (Dn ) refers to
terminated polymer chains that do not have an attached radical. The term
bulk polymer chain is used to refer to the sum of the live and dead polymer
chains. The subscript n refers to the chain length in terms of the number of
segments or monomer units incorporated in the polymer chain. Live chains
are reactive and can participate in the polymerization reactions while dead
chains are usually considered inert, except when long chain branching
reactions are important.
The radical attached to one end of a live polymer chain is considered to be
mobile and moves away from the initiator fragment with every addition of a
monomer molecule. It is believed that after a few monomer additions the
chemistry of the initiator fragment and developing chain microstructure will
not have a strong influence on the mode of monomer addition.
The free-radical kinetic model assumes that the reactivity of a live polymer
chain depends only on the active segment containing the radical, and is
independent of the polymer chain length and other structural properties. This
assumption was used in writing the rate expressions for the reactions shown
in the Built-in Free-Radical Polymerization Kinetic Scheme figure on page 166.
For example, in the propagation reaction, the rate of propagation ( ) Rp ij is
independent of the polymer chain length. It depends only on the
concentration of monomer j and the concentration of live polymer chains with
active segments of type i. Models using this assumption are referred to as
terminal models in the polymerization literature.

For copolymerization, the built-in kinetics routine allows the user to specify
the number of monomers used. Similarly, the user has the flexibility to
specify the number of each type of reactive species used in the
polymerization, e.g. initiators, chain transfer agents, solvents and inhibitors.
The user can easily setup the built-in kinetics to model a specific free-radical
polymerization by selecting a subset of the reactions shown in the Built-in
Free-Radical Polymerization Kinetic Scheme figure on page 166. It is
necessary that the subset include a chain initiation and a propagation
reaction. Frequently, at least one termination, chain transfer, or inhibition
reaction to produce dead polymer is also selected.
The rate constants for each reaction in the built-in kinetics is calculated at the
reaction temperature and pressure using the modified Arrhenius equation
shown below with user specified parameters: pre-exponential (or frequency)
factor, activation energy, activation volume, and reference temperature:
Rate Constant
 exp 1 1 (3.1)
g
VP

k k Ea


 


 
 

o f
 
R T T
ref
R
 
 




Where:
ko = Pre-exponential factor in l/sec for first order reactions,
and m3 / kmol  s for second order reactions
Ea = Activation energy in mole-enthalpy units
V = Activation volume in volume/mole units
P = Reaction pressure
R = Universal gas constant
ref T = Reference temperature
g f = Gel effect factor from optional built-in or user-defined gel
effect correlation
The second term in the exponential function contains an activation volume
that is important for high pressure polymerization systems. For low to
moderate pressures, the activation volume is typically set to default value of
zero. This term is used to account for the pressure dependence of the
reaction rate constant.
The free-radical model allows the rate expression to be modified by a gel
effect term, g f . The gel effect term can be calculated using one of several
built-in correlations or it can be calculated by an optional user-defined gel
effect subroutine.
The model allows any number of bifunctional initiators, however the
maximum number of unique bifunctional initiators (used throughout the
flowsheet) must be specified on the Polymers, Options subform. This
parameter is used to dimension the FRAGFLOW polymer component attribute,
which is used to track the flow rate of undecomposed initiator fragments. The
FRAGFLOW attribute must be included in the attribute list in the Polymers,

Polymers subform. Bifunctional and standard initiators can be used in the
same model.
Initiation
The initiation step involves the generation of reactive free-radicals followed by
the addition of a monomer molecule (chain initiation) to form chain radicals of
unit length (Pi )
1 . The non-chain or primary radicals (R )  may be generated by
the thermal decomposition of a chemical initiator, a catalyzed initiation
reaction involving electron transfer from ions, or by thermal/radiation induced
mechanisms. Three types of standard initiation reactions are included in the
built-in kinetics:
 Initiator decomposition reaction
 Induced initiation reaction
 Catalyzed initiation reaction
The initiator decomposition reaction accounts for primary radical generation
from the thermal decomposition of chemical initiators.
The induced initiation reaction can be configured to account for the generation
of radicals by thermal and radiation induced mechanisms from the monomers
themselves, with or without the use of a coinitiator or promoter.
The catalyzed initiation reaction can be used to account for redox initiation,
which has found wide application in aqueous emulsion polymerization
systems.
The most commonly used radical generation method is the thermal
decomposition of chemical initiators (usually peroxide or azo compounds)
which decompose to form radicals when heated to an appropriate
temperature. Only small amounts of the chemical initiator (less than 1 wt. %
based on monomer) are needed. However, due to their high activation
energies chemical initiators have a relatively narrow useful temperature range
(approx. 30C) over which the decomposition rates are neither too fast nor
too slow.
Some processes, notably bulk polystyrene polymerization, use initiators with
two active sites. These bifunctional initiators decompose in two stages,
providing greater control over the molecular weight distribution of the
product.
The free-radical model includes two reactions associated with bifunctional
initiators:
 Bifunctional initiator decomposition (primary decomposition)
 Secondary initiator decomposition (primary decomposition)
 The primary decomposition reaction generates a pair of radicals, an
undecomposed initiator fragment, and optional by-products. The
undecomposed fragment is tracked using the FRAGFLOW polymer
component attribute.
 The initiator fragment decomposes in the secondary decomposition
reaction, generating a free radical and a polymeric radical.

Initiator Decomposition Reaction
The initiator decomposition reaction is modeled as a first order thermal
decomposition reaction:
Ik
k
id
k
k k rk k k id I  N R  B  B R  k C
1, 1 2, 2   
This rate expression ( k )
id R describes the rate for the thermal decomposition of
standard initiator k. The symbols 1 B and 2 B represent optional user-specified
reaction by-products. This feature lets you track the formation of low-molecular
weight decomposition by-products, such as carbon dioxide, which
may be generated as the initiators decompose. The byproduct formation rates
are determined by:
Ik
k
R  k C R 
k C B 1 , k 1, k id Ik B 2 , k 2,
k id
k
For mass balance purposes, the polymer mass generation rate is incremented
by the initiator mass consumption rate, less the mass formation rate of by-products.
The rate expression for the formation of primary radicals from the thermal
decomposition of standard initiators is given by:
NI

R rad

N k C
id k
Ik
k

k id
k
r
1
There are a number of user specifiable parameters associated with this
reaction. The user can specify more than one initiator to model systems
where multiple initiators with different half-lives are used to control the
initiation rate over the course of the polymerization. Depending on the
initiator, either one or two primary radicals may be formed, hence the
parameter Nrk should be set to 1 or 2. Bifunctional initiators, which can
produce up to four radicals, are handled explicitly using another set of
reactions described below. A fraction of the radicals generated by
decomposition undergo radical recombination in the radical-cage, leading to
stable byproducts. The initiator efficiency factor, k  , is used to specify the
fraction of radicals which are not destroyed by the cage effect. The efficiency
factor can be adjusted using an efficiency gel effect correlation as described
later in the text.
The rate constant k
id k is calculated using a modified Arrhenius equation
(Equation 3.1 on page 170) with three parameters: pre-exponential factor,
activation energy and activation volume. As noted previously, the activation
volume accounts for the pressure dependence of the rate constant. This
parameter is typically non-zero only at high pressures. Appendix B lists
initiator decomposition rate constant parameters (pre-exponential factor and
activation energies) for many commonly used initiators. These rate
parameters are included in the INITIATOR databank and are automatically
loaded into the model each time the reaction network is generated.
The standard rate expression can be modified using an optional built-in or
user-defined gel effect correlation as described later in the text.

M
Induced Initiation jReaction
Free-radicals can also be generated from some monomers by thermal,
radiative (UV, electron beam or gamma rays) or induced mechanisms. For
example, styrene at temperatures above 120C has a significant thermal
initiation rate. The thermal initiation mechanism for styrene is believed to be
3rd-order in monomer (Hui & Hamielec, 1972). This reaction results in the
formation of significant amounts of cyclic dimers and trimers which have to be
removed during devolatilization. Hence, thermal initiation is not favored
commercially.
Radiation initiation has been used mainly for polymer modification to induce
branching, crosslinking or grafting reactions. The induced initiation reaction,
shown below, can be configured to model both these initiation mechanisms:
M j + C k  P  kjB  kjB kj = kj aj
b
cj 1 1 2 2 R si k si C Ck
C (h )j j1
For thermal initiation, the rate should be bj
R j
 k j
C si si
Mj
(set a j , c j to zero).
For radiation initiation, the rate should be bj cj
R j
 k j
C (h ) si si
Mj
(set a j to zero)
The induced initiation reaction can also account for the effects of using an
initiator or promoter ( ) k C to increase the rate of radical generation.
The parameters 1  and 2  are optional stoichiometric coefficients related to
by-products 1 B and 2 B . The byproduct formation rates are determined by:
R kj  kj
k j
C aj
C bj (h  ) cj
R kj  kj
k j
C aj
C bj (h 
) cj
B 1 1 si
Ck
Mj
B
2 2 si
Ck
Mj
The molar consumption rate of the monomer is equal to kj
si R . If a promoter is
specified in the reaction, its molar consumption rate is also set to kj
si R . The
mass generation rate of the polymer is set equal to the mass consumption
rate of the monomer ( j M ) and promoter ( k C ).
The special initiation reactions generate live polymer directly, thus this
reaction does not contribute to radical generation.
Catalyzed Initiation Reaction
The catalyzed initiation reaction is similar to the initiator decomposition
reaction except that a catalyst concentration term is included in the reaction
rate expression:
k j kj rk j kj kj ci I C  N R C  B  B R  k C C
1, 1 2, 2   
Ik Cj
kj
ci
kj
This rate
expression ( kj )
ci R describes the rate of consumption of initiator k. The catalyst
rate is set to zero, assuming that the catalyst is not consumed by this
reaction. The corresponding rate expression for the formation of primary
radicals is given by:
NI N
CI

 
R rad

N k C C
ic k
j
Ik Cj
kj
ic
kj

kj r
1 1

The parameters 1  and 2  are optional stoichiometric coefficients related to
by-products 1 B and 2 B . The byproduct formation rates are determined by:
R kj  kj
k kj
C C R kj  kj
k kj
C C B 1 1 ic
Ik Cj B
2 2 ic
Ik Cj
For mass balance purposes, the
polymer mass generation rate is incremented by the initiator mass
consumption rate, less the mass formation rate of by-products.
Primary Chain Initiation
To complete the initiation process, the reactive primary radicals (R ) react
with monomer by the primary chain initiation reaction to form polymer chain
radicals of unit length. The chain initiation reaction is shown below:
R M P j
R j
k C R j
     1
pi
The chain radicals grow by successive addition of monomer molecules to form
long chain polymer molecules. It is common practice to set the chain initiation
rate constants equal to the propagation rate constant each monomer.
The primary chain initiation reaction consumes primary radicals:
j
pi
Mj
NM


R rad
 
k C R
pi i
Mi
i
pi
1
Bifunctional Initiator Primary Decomposition Reaction
The bifunctional initiator decomposition reaction is modeled as a first order
thermal decomposition reaction:
Ik
I B
  R   R   B  
B R k
 k k
C
k k k k 1, k 1 2, k 2 bid
bid
This rate expression ( k )
bid R describes the rate for the primary decomposition
of bifunctional initiator k. Each primary decomposition reaction generates an
undecomposed fragment. The generation rate of undecomposed fragments is
equal to the initiator decomposition rate:
R  k C F ( k )
bidIk
The symbols B B 1 and 2 represent optional user-specified reaction by-products.
k
This feature allows you to track the formation of low-molecular
weight decomposition by-products, such as carbon dioxide, which may be
generated as the initiators decompose. The byproduct formation rates are
determined by:
Ik
k
R  k C R 
k C B 1 , k 1, k bid Ik B 2 , k 2,
k bid
k
For mass balance purposes, the polymer mass generation rate is incremented
by the bi-initiator mass consumption rate, less the mass formation rate of by-products.
The rate expression for the formation of primary radicals from the primary
thermal decomposition of bifunctional initiators is given by:

NBI

R rad

N k C
bid k
Ik
k

k bid
k
r
1
The user can specify more than one bifunctional initiator to model systems
initiation rate over the course of the polymerization.
The model assumes that the each site in the bifunctional initiator generates
two radicals. A fraction of the radicals generated by decomposition undergo
radical recombination in the radical-cage, leading to stable byproducts. The
initiator efficiency factor, k  , is used to specify the fraction of radicals which
are not destroyed by the cage effect. This factor can be adjusted using a
built-in or user-defined efficiency gel effect correlation.
The rate constant k
bid k is calculated using a modified Arrhenius equation
parameter is typically non-zero only at high pressures.
The rate expression can be modified using an optional built-in or user-defined
gel effect correlation as described later in the text.
To complete the initiation process, the reactive primary radicals (  ,  )
k R R
react with monomer by the chain initiation reaction to form polymer chain
radicals of unit length. Note that the undecomposed initiator fragment k is
conserved in the polymer chain ( , )
P j k . This fragment is eventually destroyed
1
by the secondary decomposition reaction described in the next sub-section.
The chain initiation reactions are shown below:
R   M  P j
R j
 k j
C R  j
1
pi
pi
Mj
    
R M P , R k C R
k j 1
Mj k
The chain radicals grow by successive addition of monomer molecules to form
long chain polymer molecules.
j
pi
jp
i
j k
Bifunctional Initiator Secondary Decomposition Reaction
The secondary bifunctional initiator decomposition reaction is modeled as a
first order thermal decomposition reaction:
j k
n D  R  P  B  B R  k 
1, 1 2, 2 ( )
k
k
k k F k sid
j
k k n
,
This rate expression ( ) F (k ) R describes the rate for the decomposition of
bifunctional initiator fragment k. In this equation   k  is the concentration of
undecomposed fragments of type k, which is calculated from the FRAGFLOW
polymer attribute.
The model assumes that the secondary decomposition reaction generates a
primary radical and a live end group (polymer radical). A fraction of the
radical pairs generated by decomposition recombine in the radical-cage,

leading to stable byproducts. The initiator efficiency factor, k  , is used to
specify the fraction of radicals which are not destroyed by the cage effect.
This factor can be adjusted using a built-in or user-defined efficiency gel
effect correlation.
The generation rate of primary radicals from this reaction can be written as:
NBI

R rad

k
sid k
 
k
k
k sid
1
Each fragment decomposition event generates a new live end. The model
assumes that the fragments are randomly distributed across the bulk polymer
molecules and that the penultimate segment attached to the fragment
becomes a live end. The generation rate of live ends of type i from the
decomposition of initiator fragment k can be written as:
 
j
1

1

k k

0
d ( j )
0 
k sid k

dt
The byproduct formation rates are determined by:
B k k sid R  k  R  k  1 , 1, 2 , 2,
k
k
 
k B k k sid
k
The mass generation rate of polymer is adjusted to account for mass lost in
the form of reaction by-products.
The user can specify more than one bifunctional initiator to model systems
initiation rate over the course of the polymerization.
The rate constant k
sid k is calculated using a modified Arrhenius equation
parameter is typically non-zero only at high pressures.
The rate expression can be modified using an optional built-in or user-defined
gel effect correlation as described later in the text.
Propagation
The chain radicals grow or propagate by the addition of monomer molecules
to form long polymer chains (Pn )
i . The propagation reaction is represented by:
i
  j
 i 1
p i
j
pij
P M P R k C P n
j n
Mj n
where monomer j is being added to a polymer chain of length n, with an
active segment of type i. The resulting polymer chain will be of length n+1
and the active segment will be of type j. The active segment type usually
represents the last monomer incorporated into the polymer chain.
For copolymerization, there will be Nm *Nm propagation reactions having
different reactivities. For example, with two monomers, the monomer being
added could be monomer 1 or monomer 2 while the active segment type

could be segments from monomer 1 or monomer 2. Hence there will be four
rate constants (k11, k12 , k21, k22 ) where the first subscript refers to the active
segment type while the second subscript refers to the propagating monomer
type. For the terminal model the rate of propagation is dependent only on the
active segment and propagating monomer concentrations.
This copolymerization scheme can be adapted for modeling the
stereoregularity (isotactic, syndyotactic or atactic) of monomer addition in
homopolymerization.
Head-to-Head Propagation
When reactions occur between substituted vinyl monomers or 1,3 dienes, the
repeat units usually join the chain in a head-to-tail configuration, as shown
below (here HTT = head-to-tail). A portion of the monomers may join the
chain in the head-to-head configuration, as shown in the second reaction
below. Head-to-head unions can also result from termination by combination
as described later.
R
HC
CH2*
R
+
head-to-tail dyad
HTT Propagation HC
H2
C
R
HC
CH2*
R
head-to-head dyad
R R
R R
CH
2
CH* +
HTH Propagation
CH
2
HC
HC
CH2*
The head-to-head dyads disturb the normal regularity of the chain. As a
result, the head-to-head fraction of the polymer can have a strong influence
on the crystallinity of the polymer, and thus influence the mechanical
properties of the final product.
The model can track head-to-head additions using the optional HTH
Propagation reaction. The polymer attributes HTHFLOW and HTHFRAC
(head-to-head flow and fraction) must be included in the list of attributes on
the Polymers, Polymers subform.
The model does not explicitly track normal head-to-tail additions. Instead, the
standard propagation reaction is used to track the total (head-to-head and
head-to-tail) propagation rate. The head-to-head propagation reaction
explicitly tracks the head-to-head propagations. This design allows the user to
fit the overall propagation rate first, and then refine the model by adding
head-to-head additions.
The HTHFLOW attribute is a scalar value. The overall rate of change of the
head-to-head flow hth R is calculated by summing the head-to-head additions
across all pairs of monomers. Termination by combination also generates
head-to-head pairs as discussed later. The net rate expression for head-to-head
dyads can be written as:
Nmon
 Nmon
 j
ij
i
ji
 
hth
hth
R  C k  C k 
k
hth Mi j
1 1
 
i
ij
0 0    
i j tc
Mj

Chain Transfer to Small Molecules
Chain transfer to small molecules such as monomer, solvent or chain transfer
agent usually involves the abstraction of hydrogen from the small molecule by
the chain radical and leads to the termination of the live chain. At the same
time, a new primary transfer radical is formed which can start chain
polymerization. The effect of chain transfer on the polymerization kinetics
depends on the reactivity of the transfer radical. When the transfer radical is
very reactive, as is the case when the chain initiation rate constant is greater
than the propagation rate constant, chain transfer will not lower the
polymerization rate or conversion, but will reduce the molecular weight of the
polymer. However, if the transfer radical is less reactive than the monomer-based
propagating radical, as in the case of low chain initiation rate constant,
both the conversion and molecular weight of the polymer will be lowered.
Chain Transfer to Solvent or Agent
Chain transfer to solvent and chain transfer to a transfer agent have the
following rate expressions:
P i
A D R R ij
k C P n
    
k n tra
P S D R R k C P n
ij
tra
i
A n
k
i
ij
    
k n trs
ij
trs
i
S n
k
For transfer to agent or solvent the transfer radicals are assumed to have the
same reactivity as the primary radicals formed by initiation. The case where
the transfer radical has a different reactivity than the primary radical may be
added in a future version.
Chain Transfer to Monomer – Generation of Terminal
Double Bonds
In the chain transfer to monomer reaction, the live polymer end ( ) n P
abstracts a hydrogen from a monomer molecule, resulting in a dead polymer
chain ( ) n D . The monomer, which loses a hydrogen, becomes a live polymer
end group with an unreacted double bond ( ) 1 P . Subsequent propagation
reactions generate long-chain polymer radicals with a terminal double-bond
segment at the opposite end of the chain   n P . These initial reaction steps
are shown below:
·
Chain Transfer Terminal
·
to Monomer segment
Pn + M Dn + P1=
P1=
·
Propagation
+ n-1 M
Pn=
double bond
Terminal
double bond
segment
·

The terminal double bond segments can react with live end groups through
terminal double bond polymerization reactions as described later in this
section. These reactions lead to the formation of a molecule with a long chain
branch.
The model optionally tracks terminal double bonds using the polymer
component attribute TDBFLOW, which contains one element for each type of
segment.
The chain transfer to monomer reaction does not always generate a terminal
double bond. The terminal segment may undergo a re-arrangement reaction,
which destroys the double bond site. The model parameter “TDB fraction”  ij 
TDB f can be used to specify the fraction of chain transfer to monomer
reactions that generate a terminal double bond.
The reaction rate of the chain transfer to monomer reaction is defined as:   i
i
n P M D  f P   1 f P R  k C P 1 1
Where  ij 
Mj n
ij
trm
ij
trm
ij j
TDB
ij j
j n TDB
trm R is the rate of consumption of monomer j and live polymer end
groups of type i and the generation rate of live ends of type j. The generation
rate of terminal double bonds of type j  j 
trm R is defined by:
i
j
trm R   f k C P
Mj n
ij
trm
ij
TDB
Chain transfer to polymer, which is also included in the kinetic scheme, is
discussed in the section that follows on Termination.
Termination
Bimolecular termination of radicals may involve primary radicals (R ) and
chain radicals (Pn )
j . However, the concentration of primary radicals is usually
much lower than the concentration of chain radicals. Hence, only bimolecular
termination involving chain radicals is included in the built-in kinetic scheme.
In termination, the chain radicals are destroyed and live chains are converted
to dead polymer chains.
Intermolecular termination occurs by one of two mechanisms, combination
(coupling) or disproportionation. Many monomers (e.g. MMA) show both types
of termination while other monomers (e.g. styrene) terminate predominantly
by combination. The mode of termination has a strong influence on the
average polymer chain length and chain length distribution, especially when
chain transfer is not significant. When the combination reaction is dominant,
the polydispersity (in a single CSTR) will approach 1.5. The polydispersity
approaches 2.0 when disproportionation is dominant.
Termination by Combination
In termination by combination, two live polymer end groups react with each
other, forming a single dead chain with a head-to-head segment pair. Each of
these reactions, on average, doubles the molecular weight of the polymer.

The figure below shows an example for poly(styrene).
Pn
CH
2
Pm
CH + CH
HC CH
2
2
HC
CH
2
HC
Dn+m
The reaction rate depends on the concentration of the live end groups:
P i
 P j
 D R ij
 k ij
P j
P i n
m
n 
m tc
tc
n
n
The formation of head-to-head segment dyads can be tracked by including
the optional HTHFLOW and HTHFRAC (head-to-head flow and head-to-head
fraction) attributes in the attribute list on the Polymers, Polymers subform.
Head-to-head sequences can contribute to thermal instability and may cause
degradation during storage or subsequent processing.
Termination by Disproportionation
In disproportionation reactions, the radical at the end of one chain attacks a
hydrogen atom at the second-to-last carbon atom in the second chain,
forming two dead polymer molecules with no net change in molecular weight.
Disproportionation results in one of the dead chains having a saturated end-group
while the other will have an end-group with a terminal double bond. For
example:
Pn Pm Dn= Dm
CH3
H
CH C
CH3
+ C CH2
C O
OCH3
C
OCH3
O
CH
CH3
C
CH3
+ HC CH2
C O
OCH3
C
OCH3
O
The reaction rate depends on the concentration of the live end groups:
  i
P i
 P  f D   1 f ij
D  D R ij
 k ij
P j
P
n TDB
n m td
td
n
n
The formation of terminal double bonds can be tracked by including the
TDBFLOW and TDBFRAC (terminal double bond flow and fraction) in the list
of attributes on the Polymers, Polymers subform. Terminal double bonds
can contribute to thermal instability and may cause degradation, branching
and gelation during storage or subsequent processing.
The chain transfer to monomer reaction does not always generate a terminal
double bond. The terminal segment may undergo a re-arrangement reaction,
which  ij 
destroys the double bond site. The model parameter “TDB fraction” in
ij
TDB
j
m
TDB f can be used to specify the fraction of chain transfer to monomer
reactions that generate a terminal double bond. The generation rate of
terminal double bonds of type i by disproportionation  i 
td R is defined by:
i
td R   f k P P
j
n
i
n
ij
td
ij
TDB

Inhibition
Inhibition is included as an additional termination mechanism. This involves
reaction between a chain radical and a small molecule (inhibitor or impurities)
to form a dead chain:
P i
 X  D R ik
 k ik
C P
i
n k n x
x
Xk n
The model assumes that the inhibitor is consumed by the reaction; the
polymer mass generation rate is adjusted accordingly.
Gel effect in Termination
Bimolecular termination reactions between chain radicals become diffusion
controlled at high polymer concentration or high conversion. This leads to an
increase in the polymerization rate and molecular weight. This condition is
known as the gel effect or Trommsdorff effect. At high conversions the
increased viscosity of the reaction medium imposes a diffusional limitation on
the polymer chains, leading to lower effective termination rates. Eventually at
high enough conversions, even the propagation, initiation, and chain transfer
rates may be affected by the diffusional limitation.
The diffusional limitation is modeled by multiplying the low conversion
reaction rate coefficients by a gel-effect factor that will lower their effective
value with increasing conversion. The free-radical model includes an option to
modify the reaction rate expressions using a built-in or user-defined gel-effect
correlation, as described later in this chapter.
Long Chain Branching
Chain Transfer to Polymer
The polymer radical in one chain can transfer to a repeat unit in a second
chain. This chain transfer to polymer reaction always generates a long chain
branch, since subsequent propagation from the live site causes the backbone
molecule to grow a new branch.
The chain transfer to polymer reaction can be written as:
P i
 D  D  P j
R ij
 k ij
m D P i
n
m n m
trp
trp
j m n
Each transfer reaction generates one long chain branch. The optional polymer
component attributes LCB and FLCB are used to track the molar flow rate of
long chain branches and the long chain branching frequency (branch point per
thousand repeat units).
Terminal Double Bond Polymerization
Polymer chains with terminal double bonds are formed by several reactions,
including chain transfer to monomer, termination by disproportionation, beta-scission
and beta-hydride elimination.
These terminal double bond groups can participate in propagation reactions in
much the same manner as a monomer molecule. The resulting terminal
double bond propagation reactions generate a long chain branch since the

propagation reaction goes “through” the terminal double bond, leaving the
polymer molecule attached to the TDB group attached to the backbone of the
growing live polymer molecule.
Pn+m Pm
Dn=
·
+
Terminal Double Bond
Polymerization ·
· Propagation + Termination
Molecule with
long-chain branch
Each terminal double bond propagation reaction generates one long chain
branch. This reaction can also transfer the live end from one type of segment
to another (e.g., from segment i to segment j).
The optional polymer component attributes LCB and FLCB are used to track
the molar flow rate of long chain branches and the long chain branching
frequency (branch point per thousand repeat units).
The rate of terminal double bond polymerization, ij
tdbp R between live end i and
terminal double bond segment j can be written as:
i 
jm
P i
 D   P j
R ij
 k ij
P i
D

n n 
m
tdbp
tdbp
n
The concentration of terminal double bond segments is calculated from the
optional polymer component attribute TDBFLOW.
Short Chain Branching
The radical in a live end group can undergo a “backbiting” reaction in which
the radical in live end segment i is transferred to a hydrogen atom in segment
j in the same chain, forming a short chain branch. Short chain branches,
typically five or six carbon atoms in length, are quite morphologically different
than long chain branches, which are formed by a number of reactions.
The backbiting reaction leads to short chain branches if the backbone radicals
are stable and can continue propagation. The total rate of short chain
branching, R SCB , depends on the live end group concentrations, jm
, and the
rate constants for the short chain branching reaction, i scb k :
 i i
i
n P P R k 
Short chain branching is tracked by the optional polymer component attribute
SCB. The short chain branching frequency (short chain branches per
thousand repeat units) is reported in the optional polymer attribute FSCB.
For some polymers (e.g. polypropylene) the backbone radical can be highly
unstable and will result in the scission of the chain into a dead polymer chain
with a terminal double bond and a short live chain one to six carbon atoms
is
SCB cb
j
n

long. Use the beta scission reaction (see below) to track these types of
reactions.
Beta-Scission
A simplified beta-scission reaction is included in the built-in kinetics. It is
limited to reactions where a live chain undergoes scission to form a dead
chain of the same length and a primary radical:
P i
 f D   (1 f )D  R R  k P
i
n n
This reaction can be used to simulate backbiting reactions which form short-chain
ib
s
ib
n s
i
TDB
in
i
TDB
polymer radicals (see Short Chain Branching).
The beta scission reaction usually generates a terminal double bond
corresponding to the live end i. In some special cases, the double bond may
not form or may be unstable. The “terminal double bond fraction” parameter,
i
TDB f , can be used to specify the fraction of beta-scission reactions which
generate a terminal double bond (by default, this parameter is unity). Thus,
the rate of generation of terminal double bonds from the beta-scission
reaction, i
td R , can be defined as:
R i
  f ij
k ij
P i
P
j
td TDB
td
n
n
Reactions Involving Diene Monomers
Cis and Trans Propagation
Propagation reactions involving 1,3-diene monomers, such as butadiene or
isoprene, can generate three types of repeat segments as shown below.
* +
CH2
* +
* +
CH* Vinyl Configuration
CH2
C C
CH2*
H
H
CH2
C C
H
CH2*
H
Normal Propagation
Cis Propagation
Trans Propagation
Cis Configuration
Trans Configuration
Although these segments may exhibit different physical properties, it is
convenient to lump them together as a single repeat segment, and track the
various segment configurations using the optional polymer component
attributes CIS-FLOW and TRANSFLO. Likewise, the three types of
propagation reactions are lumped together under the standard propagation
reaction. Optional Cis-Propagation and Trans-Propagation reactions are used
to specify the rate parameters for reactions that generate segments with the
cis- or trans- configurations.

This design is intended to keep the model development process as simple as
possible. The user can add cis/trans/vinyl accounting a working model without
changing any of the existing rate parameters.
The new CIS-FLOW and TRANSFLO attributes are dimensioned NSEG and
correspond to the bulk polymer. The flow rate of each diene segment in the
vinyl configuration can be calculated by taking a mole balance across the
various configurations taken by diene segments. The optional polymer
attributes CIS-FRAC, TRANSFRA, and VINYLFRA report the molar fraction
of each type of diene segment in each of the three configurations (an
additional cross link configuration is also tracked as discussed later).
The rate of formation of segments of type j with cis configuration, j
cis R , is
calculated by summing over all types of live end groups i:
    i
P i
M P j ( cis
)
R j
k ij
C 
i
n j n
1 cis
cis
Mj
0
Likewise, the rate of formation of segments of type j with trans configuration,
j
trans R , is calculated by summing over all types of live end groups i:
    i
P i
M P j ( trans
)
R j
k ij
C 
i
n j n
1 trans
trans
Mj
0
In the equations above, ij
cis k and ij
trans k are, respectively, the net rate
constants for cis and trans propagation of monomer j onto a chain with a live
end i. The standard reaction scheme does not include any reactions which
consume the cis and trans end groups. Further, the model does not constrain
the cis and trans reaction rates in any manner; the model user must ensure
that the cis and trans propagation rates are lower than the net propagation
rate.
Pendent Double Bond Polymerization
Diene segments in the vinyl configuration contain a pendent double bond that
“hangs” off the main polymer chain. Live chains can react with these double
bonds in a “pendent double bond polymerization” reaction, analogous to
normal propagation. These reactions generate a short cross-link between two
long linear chains, as shown below.
* +
Reaction Pathway
Propagation CH2
*
PDB Polymerization
Pendent double bond
Cross-linked molecule
*
CH*

The pendent double bond polymerization rate ( ij
PDB R ) depends on the
concentration of live ends of type i ( i0
 ) and the concentration of pendent
 j vinyl ):
(vinyl) double bonds of type j in the bulk polymer phase ( ( )
1
P i
 D ( vinyl ) P j
R ij
 k ij  i  j ( vinyl
)
n n 
m
PDB
pdb
0 1
The model assumes the reaction generates a new live segment of type j. The
reaction model does not distinguish between subsequent propagation from
this new live site from normal propagation reactions involving live end
groups.
Each pendent double bond polymerization reaction involving diene segment j
generates a new cross-link of type j. The flow rate of cross-links is tracked by
the optional polymer component attribute XLFLOW. The cross-linking density
is (moles of links per mass of polymer) is tracked by polymer attribute
XDENSITY.
The concentration of vinyl groups (pendent double bonds) is determined by a
mole balance. The flow of pendent double bonds of type i ( PDB(i) ) is
calculated by subtracting the concentration of other possible configurations
(cis, trans, or cross-link):
PDB(i)  SFLOW (i)  (CIS _ FLOW(i)  TRANSFLO(i)  XFLOW (i))
This flow rate is used to determine the concentration of pendent groups.
When the degree of cross-linking is extensive, the polymer can form a gel
phase. The current version of the Free-Radical kinetics model does not
account for gelation. This limits the model to situations with a low degree of
cross-linking.
Model Features and
Assumptions
Following are the model features and assumptions used in the free-radical
polymerization model available in Aspen Polymers.
Calculation Method
In the Aspen Polymers free-radical bulk/solution polymerization model, the
polymer chain length distribution averages and molecular structure properties
are calculated using the population balance and method of moments
approach, based on the built-in kinetics shown in the Built-in Free-Radical
Polymerization Kinetic Scheme figure on page 166.
Population balance equations are used to account for the concentration of
live polymer chains and combined polymer chains of length n. The f-th live
and combined polymer chain length distribution moments are defined as
jm
follows:

f j
f
0
 n P
n
j
n

 f
  
m
f
0 1

 
n P D
 
n
j
n
N
j
n

 
 
For homopolymerization the index f is a scalar variable and the active
segment superscript j may be dropped for the live polymer moment definition
as there is only one segment type. Hence, for homopolymerization there will
be one zeroth moment, one first moment, one second moment and so on for
the live and combined polymer. However, for copolymerization, the index f
will be a vector whose elements denote the monomer with respect to which
the moment is defined. For copolymerization with respect to every active
segment, there will be one zeroth moment, Nm first moments,
N  N m ( N m - 1)
m
2
second moments and so on.
For example, for copolymerization with three monomers, the vector index f
can have the following values for the first moment:
1
0
0
0
1
0








f = , ,
0
0
1










representing the first moment with respect to segment one, two and three
respectively. The application of the moment definitions to the live and bulk
polymer population balance equations yields the live and bulk polymer chain
length distribution moment equations. The general moment equations are
listed in the following figures. The various zeroth, first, second, etc. moment
equations can be generated from these by substituting the appropriate values
for the index f.
The live polymer chain length distribution moment equation is shown here:

i

N
M N
f n j k C R k C k C C h
dt
 
   CI
    
 
0    (  )
k
i
Mj
ij
Mj trm
1 1
 

b c
Mj
a
Ck
jk jk jk
jk
si
i
jp
i
f
d

NBI


k
i k
 
f
k
k sid k



1

0
1 1
0
N
  j


  

C k         
f
j j
f
N
i
f
M M
i
Mi
ji
p
f
 
Mj j
a
ia
f a
ij
p
k C
a
 1  0 
1
N
 M NM
k ij
i

k
trp  
  
0     
i
j
f
ji i
trp
i
f j
1
1
1
M NM
N
 
 
k ij
i
k
scb f
1 1
 
 
i
j
f
ji
scb
i

NM

 k ij
k
 td  
i
j
f
ij i
tc
1
0 
f
M NM


N
f
  
ij
tdb k
   
1


a
k
1 0
 
i
f a
ja

   
 

i
j
f
ji i
tdb
i
a
0
f
M NM


N
f
  
  
ij j
i
k
pdb    
 

     
i
j
f
ji i
pdb
i
a
a f a
a
k
1
1
1 0
where  j contains some terms for reactions leading to the formation of dead
polymer

 

     
 
M M A S NX
j k k C k k C k C k C
k
N
k
Sk
jk
trs
N
k
Ak
jk
tra
N
 
i
ji i
trp
N
Mi
ji
trm
1
1 1 1 1
1
    
Xk
jk
x
i
j
bs
The moments with respect to terminal double bonds are approximated:


1 0 i i i i etc
...
2

0
        

2 0
1

0
In the final term of the equation, the symbol  i represents the molar fraction
of diene segment i in the vinyl configuration (attribute VINYLFRA). This term
is zero for all segments that are not dienes.
The term k
0  represents the concentration of polymer molecules containing
an undecomposed initiator fragment associated with bifunctional initiator k.
The bulk polymer chain length distribution moment equation is shown here:

NM N
M
     
 
d

f n j f k C R 
k C k C C h
dt

 
 
i
ij
jp
   
j
   
Mj trm
0 i
bj cj
Mj
aj
C
j
si
Mj
i
1 1
f
M NM


N
f
    f a
 
  
   
ij
p j k C
 

k C
1 0 1
  
i
j
Mi f
ji
p
j
a
ia
Mj
a
NM M N
M
f
N
  1  
 
  
j
f 
a
f
ij
i
j
k
tc f
k
 
0
1 2
1 
1 0

 

 
i
i
a
ia
ij
tc
j
a
f
M M M M NM M

  
N
N
N
N
N
f
   
ji
tdb k k
     
j
1 1
 

i j
f
ij
tdb
i
a
j
f a
    1 j


 1

j
a
k
1 1 0
  


i
j
f
ij i
tdb
i
i
a
0
0
f
M M M M NM M


N
N
N
N
N
f
   
ji
pdb k k
1         
j
1 1
 
0 1

i j
f
ij
pdb
i
j
f a
     
 
i
j
j
a
a
a
k
1 1
1 1 0
    

i
j
f
ij i
pdb
i
1
For copolymers, segment-segment dyad rate equation is:
  tc i j

i j k C k C k
dt
,     
 
Mi i j
ji j
Mj p
ij i
p
d
0 0 , 0 0

Quasi-Steady-State Approximation (QSSA)
Users may invoke the Quasi-Steady-State Approximation (QSSA) for the live
moment equations. Invoking QSSA converts the live moment differential
equations (ODE) to algebraic equations, which are solved internally in the
kinetics routine. Assuming QSSA is equivalent to assuming that the live
moments attain their steady-state values instantaneously. This approximation
makes the system of ODEs much easier to integrate by reducing stiffness.
Comparison of the results with and without QSSA for most free-radical
polymerization systems, where the chain lifetimes are short compared to the
residence time, show negligible differences. Therefore it is usually reasonable
to use the QSSA. However, users should check the validity of this
approximation by running cases with the QSSA switch set to YES and NO for
their particular system. By default the QSSA is turned off (QSSA switch is set
to NO). Users have the option of invoking the QSSA for all the live polymer
moment equations, or selectively for only the zeroth, first, or second moment
of live polymer.
Phase Equilibrium
The polymerization model currently considers a single-phase system (vapor or
liquid), two-phase system (vapor and liquid), or three-phase (VLL) system
when calculating concentrations for the reaction kinetics. For single-phase
systems, the reacting phase may be either vapor or liquid. In multi-phase
systems, reactions can occur in one or more phases simultaneously. Each
reaction object is associated with a single reacting phase, identified on the
options form.
By default the reacting phase is assumed to be the liquid phase (for VLL
systems, the reacting phase must be specified). Several reaction models can
be referenced from a single reactor block to account for reactions in each
phase.
Gel Effect
Bimolecular termination reactions between chain radicals become diffusion
controlled at high polymer concentrations or high conversion leading to an
initial increase in the polymerization rate and molecular weight. This condition
is known as the gel effect or Trommsdorff effect. At high polymer
concentrations, the increased viscosity of the reaction medium imposes a
diffusional limitation on the polymer chains, which leads to lower effective
termination rates. Typically the termination rate coefficients are affected first
by the gel effect because they involve diffusion of two bulky polymer radicals.
Eventually at high enough conversions, even the propagation, initiation, chain
transfer reactions, and the initiator efficiency are lowered by the gel effect.
Hence, in general it may be necessary to allow gel/glass effects for all the
polymerization reactions in the built-in kinetic scheme.

Diffusional Limitation
The diffusional limitation is usually modeled by multiplying the low conversion
reaction rate coefficients, ko , by a gel effect factor, GF, that decreases with
increasing conversion. Hence the effective rate coefficient for a reaction is
given by:
keff  koGF
Several empirical and semi-empirical correlations relating the gel effect factor
to conversion and operating conditions are available in the literature.
Currently two of these have been implemented as built-in correlations. Users
will be able to use these gel effect correlations simply by specifying the
correlation number and the parameters. The built-in correlations are:
Correlation Number 1:
GF a
1
a 
a Xp
1 
3
2 Where:
X p = Weight fraction of polymer
This correlation has three user specified parameters, a1, a2 , and a3 .
Correlation Number 2:


GF A   
a X
2 3
BX CX DX
p
  
p p p
a

1 
9
 
 
10
exp
With:
A  a  a T 1 2
B  a  a T 3 4
C  a  a T 5 6
D  a  a T 7 8
Where:
X p = Weight fraction of polymer
T = Temperature in Kelvin
This correlation has ten user specified parameters, a1 to a10 .
Users may also include their own gel effect correlation by specifying a
correlation number greater than the number of built-in gel effect correlations
(currently two) . In this case, users must provide the correlation for the gel
effect factor in the form of a Fortran subroutine. The user gel effect
subroutine argument list is documented here:
User Gel Effect Subroutine Arguments

Subroutine USRGEL ( ICORR, MAXGP , GPAR ,WFTFRP , GF,
+ SOUT ,NSUBS ,IDXSUB,ITYPE ,
+ NINTK ,INTK ,NREALK,REALK ,
+ NPO ,NBOPST,IDS ,NCK ,
+ NITG ,ITG ,NREA ,REA )
Variable I/O Type-Spec Dimension Description
ICORR I I Gel effect correlation number
MAXGP I I Maximum number of gel effect
parameters
GPAR I R MAXGP Gel effect parameters
WTFRP I R Weight fraction of polymer
GF O R Gel effect factor
SOUT I R Outlet stream
NSUBS I I Number of substreams
IDXSUB I I NSUBS Location of substreams in stream
vector
ITYPE I I NSUBS Substream type vector
1 = MIXED
2 = CISOLID
3 = NC
NINTK I I Number of integers for model
INTK I/O I NINT Integer array for model
NREALK I I Number of reals for model
REALK I/O R NREAL Real array for model
NPO I I Number of property methods
NBOPST I I 6, NPO Property method array
IDS I I 2, 13 Block IDs
i, 1 Block ID
i, 2 to i, 4 used by system
i, 5 kinetic subroutine name
NCK I I Total number of components
NITG I I Length of integer array for kinetics
ITG I I NITG Integer array for kinetics
NREA I I Length of real array for kinetics
REA I R NREA Real array for kinetics
Polymer Properties Calculated
The following variables can be calculated by the built-in kinetics routine based
on the polymer attributes and the subset of the built-in kinetics used for a
specific simulation:
 Zeroth, first and second moments for the combined polymer

 Zeroth and first moments for the live polymer
 Number, weight and z-average degree of polymerization and
polydispersity index for the combined polymer (DPN, DPW, DPZ, PDI)
 Number, weight and z-average molecular weight for the combined
polymer (MWN, MWW, MWZ)
 Average molecular weight of segments in combined polymer (MWSEG)
 Copolymer segment composition for combined polymer (SFLOW, SFRAC)
 Mole fraction of combined polymer chains that are live (LDFRAC)
 Number average degree of polymerization for live polymer (LDPN)
 Live polymer active segment composition (LEFLOW, LEFRAC)
 Copolymer segment composition for live polymer (LSFLOW, LSFRAC)
 Copolymer dyad flow rates (DYADFLOW), fractions (DYADFRAC), and the
number-average block length with respect to each type of monomer
(BLOCKN).
 Total number of short and long chain branches (SCB, LCB)
 Short and long chain branching frequencies (FSCB, FLCB)
 Flow rate and fraction of head-to-head dyads (HTHFLOW, HTHFRAC)
 Flow rate of cis-, trans-, and cross-link segments configurations
corresponding to each type of diene monomer (CIS-FLOW, TRANSFLO,
XLFLOW)
 Fraction of diene segments in the cis-, trans-, and vinyl configuration
(CIS-FRAC, TRANSFRA, VINYLFRA)
These parameters are stored as component attributes defined in Chapter 2.
These variables, except for the branching frequencies, are related to the
moments by the relationship shown here:
DPN
i
Nm
  i



1
1
0
( )
LDPN
i
( )
j
N

i
1

 
N
i
m
m
1



1
0
( )
SFRAC I i
( ) ( )
i


Nm
 
i
( )

1
1
1
LSFRAC I i
( ) ( )
i


Nm
 
i
( )

1
1
1
PDI
 
2 0
 
i
Nm
 
i


 

1
2
(1)
LPFRAC
j
Nm
  j



0
1
0
( )
LEFRAC I j
( ) ( )
j


Nm
 
j
( )

0
0
1

The branching frequencies are calculated from the rate of chain transfer to
polymer and the rate of backbiting reactions. The branching frequencies are
reported in terms of number of branches per thousand segments in the
polymer.
Structural Properties
Frequently some of the polymer properties are reported in terms of other
properties that are related to these structural properties. These include
properties such as melt flow rate or melt index, viscosity numbers, or K-values,
etc. User-property subroutines can be set up for calculating some of
these polymer properties from the polymer moments and structural
properties.
User Profile Properties
In addition to the polymer properties reported through the component
attributes, additional results are reported through User Profile variables. The
following user profile variables are currently available in the built-in free-radical
kinetics routine:
Profile
Number
Profile Type Units
1 Conversion of monomer to polymer Fraction
2 Rate of polymerization (propagation) KMOL/S/CUM
3 Heat of polymerization KCAL/S/CUM
4 Reacting phase volume
(or volume flow)
CUM or CUM/S
5 Reacting phase total moles
(or mole flow)
KMOL or
KMOL/S
6 Reacting phase average molecular
weight
KG/KMOL
7 Rate of chain termination by
combination
KMOL/S/CUM
8 Rate of chain termination by
disproportionation
KMOL/S/CUM
9 Rate of chain termination by inhibition KMOL/S/CUM
10 Rate of initiation of radicals KMOL/S/CUM
11 Rate of induced initiation KMOL/S/CUM
12 Rate of chain transfer to monomers KMOL/S/CUM
13 Rate of chain transfer to polymer KMOL/S/CUM
14 Rate of chain transfer to agents KMOL/S/CUM
15 Rate of chain transfer to solvents KMOL/S/CUM
16 Rate of beta scission KMOL/S/CUM
17 Rate of short chain branching KMOL/S/CUM
18 Concentration of initiators KMOL/CUM
19 Concentration of catalysts KMOL/CUM
20 Concentration of coinitiators KMOL/CUM
21 Concentration of monomers KMOL/CUM
22 Concentration of transfer agents KMOL/CUM

Profile
Number
Profile Type Units
23 Concentration of solvents KMOL/CUM
24 Concentration of inhibitors KMOL/CUM
25 Concentration of polymer KMOL/CUM
For more information, see Adding Gel-Effect on page 196.
Rates and Concentrations
The rates and concentrations reported via the user profiles can be used to
calculate additional information, such as the kinetic chain length and fraction
of dead chains with terminal double bond segments. These user profile
variables can only be accessed if you are calling the free-radical kinetics from
a batch reactor (RBatch) or a plug flow reactor (RPlug).
Specifying Free-Radical
Accessing the Free-Radical Model
To access the Free-Radical polymerization kinetic model:
The Reactions object manager appears.
5 Select Free-Rad as the reaction type and click OK.
Specifying the Free-Radical Model
The Free-Radical model input forms are listed below:
Use this sheet To
Species Define reacting species
Reactions Specify reactions and rate constant parameters
Rate Constants Summarize rate constant parameters
Options Specify reacting phase and select additional
options
Gel Effect Supply gel-effect correlation parameters

Specifying Reacting Species
You must specify the reacting species in the Species sheet:
2 In the Monomers field, list the reacting monomers. For each monomer, in
the goes to  field, specify the polymer segment that the monomer
converts to.
3 Continue listing other types of reacting species, e.g. solvents, transfer
agents, etc.
4 Select the Generate Reactions option if you want the reactions to be
generated automatically.
After going through the reaction generation once, it is recommended that
you turn off this feature. Otherwise, the reaction generation is performed
repeatedly.
Listing Reactions
The Free-Radical model generates reactions based on the list of reacting
species. You can view the system-generated reactions, then assign rate
constant parameters to these reactions.
You can view a list of the system-generated reactions on the Reactions
sheet. In the Reaction summary listing for each reaction, the first column
indicates the reaction type. The second column lists the reactants, and the
last column lists the products. The Data Browser window can be resized to
better view the reaction listing. Use the following options:
Click To
Edit Edit the current reaction indicated by the row
selector
reactions
Click To
Hide/Reveal
calculations
Delete
Adding Reactions
To add a new reaction to the scheme click New to open the Add Reaction
subform:

1 In Reaction type, select a type for the new reaction. The Reaction
scheme for that type is displayed.
2 In the reactant fields (for example, Initiator, Catalyst) enter the
reactants of the categories allowed for that reaction type.
3 Where applicable, specify reaction by-products and stoichiometric
coefficients.
4 Click Cancel to discard the new reaction
 or 
Click New to add a new reaction
 or 
Click to check the Completion status
 or 
Click Done to return to the reaction summary.
Editing Reactions
To edit a reaction, click Edit to open the Edit Reaction subform:
1 Modify the Reaction type as needed.
The Reaction scheme for that type is displayed.
2 Modify reactants as needed.
3 Click to check the Completion status
 or 
To assign rate constants to user reactions, click Rate Constants to open the
Rate Constant Parameters subform. Alternately, move to the Rate
Constants summary form for a grid-style form displaying rate constants for
all reactions. For each reaction, enter:
2 In the Ea field, enter the activation energy.
3 In the V field, enter activation volume.
4 In the Tref field, enter reference temperature.
5 In the Efficiency field, enter initiator efficiency for initiation reactions.
6 In the No. radicals field, enter the number of primary radicals formed in
initiation reactions.
7 In the TDB frac field, enter the fraction of reactions that generate a
terminal double bond.
8 In the Gel Effect field, specify the number of the gel-effect sentence
number associated with the specified reaction rate.
9 In the Efficiency Gel Effect field, specify the number of the gel-effect
sentence associated with initiator efficiency.

10 Click the stoichiometry list and select a new reaction. Enter rate constants
for the new reaction. You can use the Prev and Next buttons to select the
previous or next reaction in the list (or move to another row when using
the Rate Constants summary form).
 or 
Adding Gel-Effect
Use the Gel-Effect sheet to add gel effect to reactions:
1 To activate the form, click Use Gel Effect.
2 In Sentence ID, enter a unique integer identifier.
3 In the Corr. No. field, specify a gel effect correlation number (use a
number greater than 100 for user-defined gel effect correlations).
4 In Parameters, list the parameters for the gel effect correlation.
When the specified correlation number is larger than the number of built-in
correlations, you must also enter the gel-effect subroutine name in the
Subroutine box.
5 To repeat steps 1-4 for additional gel-effect correlations, in the Sentence
ID field, click New.
Selecting Calculation Options
You can select additional simulation options for the model such as QSSA,
special initiation options, and gel-effect on the Options sheet.
Option Field Description
QSSA Apply the quasi-steady-state approximation.
This activates additional options in the Apply QSSA to frame
on the right side of the form. Inside this frame, select the
moments for which you would like to apply the QSSA
approximation.
Special
Initiation
Activate the Special Initiation Parameters frame at the
bottom of the form.
In this frame, list the monomers affected, and enter the
special initiation coefficients and radiation intensity.
Reacting Phase Specify the phase in which reactions occur.
All of the reactions in the free-radical reaction object are
assumed to take place in the same phase. You can use two
(or more) free-radical models in the same reactor to account
for simultaneous reactions in multiple phases (see the
SuspensionEPS example).
If the Reacting Phase option is set to Liquid phase 1 or Liquid phase 2
the model assumes two liquid phases exist. When the named phase is not
present, the model prints a warning message and sets the reaction rates to
zero. There are two options for handling phase collapse:

disappears.
referencing the kinetics to ensure the reactor models are consistent with the
reaction models.
Specifying User Profiles
User profiles may be tabulated in RBatch and RPlug reactors. To specify user
profiles, go the reactor’s User Subroutine form User Variables sheet:
1 In the Number of user variables field, enter the number of user variable
profiles to be tabulated.
For a list of user profiles available in the free-radical model, see Polymer
Properties Calculated on page 192.
2 In the Variable No. field, list the profile numbers in order.
You must enter the profiles sequentially, without omissions.
3 For each profile, enter a profile Label and a Units Label.
Although these labels are displayed, the reactor model does not perform
unit conversions on the user profiles. The user profile variables are totals.
For example, the reported propagation rate is summed over all
propagation reactions.
4 To view user profile results, go to the User Variables sheet of the
reactor’s Profiles form.
References
Arriola, D. J. (1989). Modeling of Addition Polymerization Systems, Ph.D.
Thesis. University of Wisconsin-Madison, WI.
Engineering. New York: Wiley.
Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley-
Interscience.
Choi, K.Y. & Kim, K.J. (1987). Steady State Behavior of a Continuous Stirred
Tank Reactor for Styrene Polymerization with Bifunctional Initiators. Chemical
Engineering Science.
Choi, K.Y., Liang, W.R., and G.D. Lei (1988). Kinetics of Bulk Styrene
Polymerization Catalyzed by Symmetrical Bifunctional Initiators. Journal of
Applied Polymer Science Vol. 35, 1547-1562.
Choi, K.Y., & Lei, G.D. (1987). Modeling of Free-Radical Polymerization of
Bifunctional Initiators. AICHE Journal Vol. 33 No. 12, 2067-2076.
Friis, N., & Hamielec, A. E. (1976). Gel-Effect in Emulsion Polymerization of
Vinyl Monomers. ACS Symp. Ser., 24.

Ham, G. E. (Ed.). (1967). Vinyl Polymerization Volume 1. New York: Marcel
Dekker.
Hui, A. E., & Hamielec, A. E. (1972). Thermal Polymerization of Styrene at
High Conversion and Temperatures. An Experimental Study. J. of Applied
Polym. Sci., 16, pp. 749-769.
Kim, K.J., and Choi, K.Y. (1989). Modeling of Free Radical Polymerization of
Styrene by Unsymmetrical Bifunctional Initiators. Chemical Engineering
Science, Vol. 44 No. 2, pp. 297-312.
Lenz, R. W. (1968). Organic Chemistry of Synthetic High Polymers. New York:
Wiley-Interscience.
Marten, F. L., & Hamielec, A. E. (1979). High Conversion Diffusion Controlled
Polymerization. ACS Symp. Ser., 104.
Ray, W. H., & Laurence, R. L. (1977). Polymerization Reaction Engineering. In
Chemical Reactor Theory. New Jersey: Prentice-Hall.
Villalobos, M.A., Hamielec, A.E., and P.E. Wood (1991). Kinetic Model for
Short-Cycle Bulk Styrene Polymerization through Bifunctional Initiators.
Journal of Applied Polymer Sciene V 42, 629-641.

10 Emulsion Polymerization
Model
This section covers the emulsion polymerization model available in Aspen
Polymers (formerly known as Aspen Polymers Plus).
 Emulsion Polymerization Processes, 200
 Polymer Particle Properties Calculated, 218
 Specifying Emulsion Polymerization Kinetics, 219
The Aspen Polymers Examples & Applications Case Book illustrates how to use
the emulsion model to simulate styrene butadiene copolymerization.
The emulsion polymerization model is applicable to emulsion polymerization
processes where nucleation occurs by both the micellar and homogeneous
mechanisms or to seeded polymerization. Some of the applicable polymers
are described below:
 Styrene - A component of synthetic rubber and paper coating
 Butadiene - Synthetic rubber, impact modifier in ABS and HIPS
 Tetrafluroethylene - Polytetrafluroethylene (PTFE), fluoropolymers Viton
 Vinylacetate - Polyvinylacetate (PVA) adhesives, paint formulation
 Methylmethacrylate - Surface coating applications.
 Acrylic Acid - Minor component in paints
 2-chloro-1,3-butadiene (chloroprene) - Neoprene rubber
 Butyl Acrylate - Surface coatings
 Butyl Methacrylate - Comonomer in surface coatings
 Vinyl Chloride - PVC used in floor covering and coatings
10 Emulsion Polymerization Model 199

A wide variety of processes are used in emulsion polymerization. The
processes that can be modeled using the Aspen Polymers emulsion
polymerization model are those that follow micellar, homogeneous, or seeded
polymerization.
An example of a process that follows micellar nucleation and subsequent
growth is the production of SBR latex in semi-batch reactors for paper coating
applications. The following lists polymeric products made by emulsion
polymerization:
 Emulsion paints, made from a number of monomers (styrene, butadiene,
acrylates, etc.) and a variety of other ingredients
 Adhesives, from slightly plasticized poly(vinyl acetate) and poly(ethylene-co-
vinyl acetate) - a pressure sensitive adhesive
 SBR, for carpet backing and for coating paper and card board along with
china clay, thus facilitating printing on surfaces
 Non-woven fabrics, which have their fabrics pre-coated with polymer and
then heat pressed (these are termed “thermoformable” felts)
 ABS (Acrylonitrile-Butadiene-Styrene), used in high impact strength
material made by swelling of a polybutadiene latex with a mixture of
styrene and acrylonitrile and polymerizing further. HIPS (High-Impact
PolyStyrene) made from bulk polymerized polystyrene in the presence of
polybutadiene
Emulsion Polymerization
Processes
Emulsion polymerization is an industrially important process for the
production of polymers used as synthetic rubber, adhesives, paints, inks,
coatings, etc. The polymerization is usually carried out using water as the
dispersion medium. This makes emulsion polymerization less detrimental to
the environment than other processes in which volatile organic liquids are
used as a medium.
In addition, emulsion polymerization offers distinct processing advantages for
the production of polymers. Unlike in bulk or solution polymerization, the
viscosity of the reaction mixture does not increase as dramatically as
polymerization progresses. For this reason, the emulsion polymerization
process offers excellent heat transfer and good temperature throughout the
course of polymer synthesis. This process is always chosen when the polymer
product is used in latex form.
In emulsion polymerization, free-radical propagation reactions take place in
particles isolated from each other by the intervening dispersion medium. This
reduces termination rates, giving high polymerization rates, and
simultaneously makes it possible to produce high molecular weight polymers.
200 10 Emulsion Polymerization Model

One can increase the rate of polymerization without reducing the molecular
weight of the polymer. Emulsion polymerization has more recently become
important for the production of a wide variety of specialty polymers.
Particle Formation
To appreciate the complexities of emulsion polymerization, a basic
understanding of the fundamentals of particle formation and of the kinetics of
the subsequent particle growth stage is required. A number of mechanisms
have been proposed for particle formation. It is generally accepted that any
one of the mechanisms could be responsible for particle formation depending
on the nature of the monomer and the amount of emulsifier used in the
recipe.
The two common mechanisms for particle formation are:
 Micellar nucleation
 Homogeneous nucleation
With micellar nucleation, micelles, which are aggregates of emulsifier
molecules, act as the site of nucleation.
With homogeneous nucleation, the radicals produced in the aqueous phase
polymerize with dissolved monomer and precipitate out to form precursor
particles. The precipitated precursor particles coagulate with each other until
a stable particle is formed.
Micellar Nucleation
Micellar nucleation is considered to be the primary mechanism for particle
formation (Harkins, 1945; Smith & Ewart, 1948) in those emulsion
polymerization systems for which the monomer is very sparingly soluble in
water, and where the concentration of emulsifier is above the critical micelle
concentration (CMC). As the name implies, the micelles, which are formed
when the emulsifier concentration is above the CMC, act as the site for
particle nucleation.
The reaction mixture consists of water, monomer, emulsifier and a water-soluble
initiator. The monomer is dispersed in the form of droplets in the
water by agitation. The droplets formed are stabilized by the emulsifier
molecules which are adsorbed on the droplet surface. In addition to the
droplets, monomer is also found dissolved in the aqueous medium and
solubilized inside the micelles.
Similarly, the emulsifier is found in three locations: in the micelles, dissolved
in the aqueous medium, and adsorbed on the monomer droplets. Since a
water soluble initiator is used, the initiator molecules will be mainly found
dissolved in the water medium.
When a typical emulsion polymerization recipe is heated, the initiator
dissociates in the aqueous medium and produces initiator radicals. Upon
propagating with monomer in the water phase the initiator radicals form
oligomeric radicals and enter the micelles, which are aggregates of emulsifier
molecules inside which a small amount of monomer is entrapped. The
capturing of a radical by micelle and reaction with the entrapped monomer
signifies the formation of a particle from a micelle. As the propagation takes

place in the newly created particle, a thermodynamic potential difference is
created for the diffusion of the monomer from the monomer droplets into the
growing particles.
As the particles grow, some of the micelles disintegrate and cover the
growing particles to stabilize them. Therefore, the micelles are not only
consumed in the formation of polymer particles, but also in the stabilization of
growing polymeric particles. In fact, approximately one percent of the
micelles are used in the formation of particles. When no micelles remain in
the reaction mixture, micellar nucleation ceases.
Stage I
The time required for particle nucleation to be complete is also called the
nucleation time or the nucleation period, and usually lasts 10-15 minutes in
conventional polymerization systems. This is commonly referred to as the
seed stage, or Stage I, in the emulsion polymerization industry. After the
nucleation or seed stage, the number of particles in the reaction mixture
remains constant if particles do not agglomerate.
Stage II
The stage following the seed stage is called the growth stage or Stage II of
the emulsion polymerization. In Stage II, the polymer particles grow through
a steady diffusion of monomer from the monomer droplets to the particles.
Since the number of particles remains constant and the particles are
saturated with monomer, this stage is marked by a constant rate of
polymerization and could easily be observed on a conversion vs. time plot.
Stage II is considered complete when the monomer droplets are totally
depleted.
Stage III
In Stage III, the monomer finishing stage, the reaction mixture consists of
the monomer swollen polymer particles and the aqueous medium. Further
polymerization of the monomer in the particles takes place. This results in a
decrease of the particle size due to higher density of the polymer compared to
the monomer. During Stage III, the concentration of monomer dissolved in
the aqueous phase falls rapidly, as does the concentration in the polymer
particles. The final product obtained at the end of Stage III is called latex.
The following figure illustrates the stages in a micellar nucleation emulsion
polymerization reaction:

Particle Number and Nucleation Time
The number mber of particles, usually in the range of
1016 to 1018 per liter of latex
is an important parameter in emulsion polymerization. Smith and Ewart have
derived mathematical
following assumptions (Smith & Ewart, 1948):
 Particles as well as micelles are equally effective in capturing radicals from
the aqueous phase
 Temperature of the reaction is constant
 Volumetric growth rate
With these assumptions, the particle number
the following equatio
10 Emulsion Polymerization Model
latex,
expressions for the number of particles under the
of polymer particles is constant
and nucleation time
equations:
are given by
203



N 0.37 R N A E s
 0.6
0.4
I 
 a
p v

s  

(3.2)
t
1 0 . 4 A E
0 .
6
s
I a

 
 

 
0 .
65
nuc R N

 
v

(3.3)
R N I a is the rate of generation of radicals in the water phase, and vs is the
volumetric growth rate of swollen polymer particles. They are determined
from the following equations:
R fk I I d  2 (3.4)
vs 
k M n
N
MW
d
p p
a
1

m
p p
(3.5)
Where:
f = Initiator efficiency
kd = Rate constant for initiator dissociation
I = Initiator concentration
Na = Avogadro's number
kp = Propagation constant
Mp = Monomer concentration inside the particles
n = Average number of radicals per particle
MWm = Molecular weight of the monomer
dp = Density of polymer
 p = Volume fraction of polymer in the particle phase
Homogeneous Nucleation
Homogeneous nucleation is the mechanism for particle formation when
monomers are more water soluble and level of emulsifier is not high enough
for the formation of micelles in the recipe.
The following figure shows a detailed picture of kinetic events that take place
during particle formation by homogeneous nucleation:

When the reaction mixture is heated the initiator molecules dissolved in the
water medium dissociate and produce the initiator radicals. These initiator
radicals react with the dissolved mono
oligomeric radical in the water phase.
As the size of the oligomeric radical increases it becomes insoluble in water
and precipitates out of the water phase. This event signifies the formation of
a primary polymer particle
phase. However, these primary particles are not stable, and, hence, coagulate
with each other until enough surface charge is developed to stabilize the
particles. These surface charges are provided by the i
molecules. In addition, the coagulated particles are also stabilized by ionic
and non-ionic emulsifier added to the emulsion recipe.
Once a stabilized particle is formed, it grows by getting a steady supply of
monomer from monomer
monomer and quickly propagate into an
from the growing oligomeric radical in the water
ionic end of the initiator
droplets by diffusion. As the particles grow and
205
mer onic

become large, the oligomeric radicals that are formed in the water phase are
directly absorbed by the particles. After sufficient number of particles are
formed that are able to absorb all of the radicals in the water phase, no new
particles are formed in the water phase and the number of particles becomes
constant. Also in homogeneous nucleation the particle number reaches a
constant value, as in micellar nucleation. The subsequent growth stage is
similar to the growth stage in the micellar nucleation.
Particle Formation Rate
The rate of particle formation by homogeneous nucleation can be derived by
considering the water phase kinetics and rate of precipitation of the polymers
at an assumed critical chain length (jcr). Assuming the aggregation number
(N ) agg for the formation of stable particles from the precipitated precursor
particles, the rate of particle formation by homogeneous nucleation is given
by:
 
R
dN
dt
  / 1
N 
k nN N
a i de a
N
k M
pw w

k M k R k A k A
agg
  
pw w tw w ap p am m
jcr
homo  

 

 
In the above equation Rw 
refers to the concentration of live radicals in the
water phase and is given by:
 
R
k nN N
/ 1

  
 
i de a


w k M k R 
k A k A
pw w tw w ap p am m
jcr
1




 

 

1
Where:
 
k M
pw w
   
k M k R k A k A
pw w tw w ap p am m
Refer to the table of page 208 for the explanation of the symbols in the above
equations.
Particle Growth
Stage II, the growth stage, starts after the completion of the seed stage in
the in situ seed process . In the in situ seed process, the micelles are used for
the generation of the seeds. In the case of an external seed process, a well
characterized seed is used as the starting material for emulsion production. If
quality control tests indicate that the particle number and particle size
distribution of the seed particles will not result in the desired end-product
specifications, the batch is normally terminated. Therefore, in the growth
stage it can be assumed that the desired number of particles, with the desired
particle size distribution has already been formed.
It is generally agreed that the growth process is a well understood process
and amenable to control. The growth reaction is responsible for developing
molecular properties (molecular weights, composition, etc.) and morphology
(core-shell, particle size distribution). Since the growth reaction lasts about

10-12 hours, there is great potential for optimizing the reaction time by
increasing temperature or by keeping the particles saturated with monomer.
Once inside a particle, radicals induce the usual free
steps such as propagation, termination, chain transfer, etc. A growing radical
can escape from a particle and return to the aqueous medium to participate in
an aqueous phase termination react
Stage II, monomer continuously diffuses from the monomer droplets into the
particle phase, providing a steady monomer supply for the growing polymer
particle.
As the particles grow, the emulsifier molecules are co
onto or desorbed from the particles to maintain thermodynamic equilibrium.
This dynamic exchange between various phases when added to the regular
polymerization kinetics makes emulsion polymerization a more complex
process than bulk or
illustrates the transport processes and reactions in a latex particle
Radical Balance
The radical balance
that are responsible for the radical generation and the radic
free-radical polymerization
reaction or enter into another particle. During
continuously adsorbed
solution polymerization processes. The following figure
in the aqueous phase is controlled by the kinetic events
radical consumption in
207
ion ntinuously particle:
al

that phase. Radicals are generated in the dispersant phase by two kinetic
events:
 Initiator decomposition in the aqueous phase
 Desorption of radicals from the particle phase into the aqueous phase
Radicals are depleted from the aqueous phase by two kinetic events:
 Termination of a live radical with another live radical in the aqueous phase
 Diffusion of a radical from the aqueous phase into a particle or a micelle
Aqueous Phase Rate
The rate of production of radicals in the aqueous phase is considered equal to
the rate of depletion of the radicals from the aqueous phase. This is an
application of the stationary state hypothesis or quasi-steady-state
approximation (QSSA):
k N n R N k R N k R N de p I a a w a tw w a     2 2 (3.6)
The previous equation can also be written as:
    mn  Y2 (3.7)
With:

v N 2 k R 
N
2v
  

s a k R
  a w a
a w
N k
p tp
N k
p tp
(3.8)
 
v 2
R N
N k
I s a
p tp
(3.9)
m
k v
N
k
de s a
tp

(3.10)
Y
N k k
k N
2
2v 2
p tp tw
a s a

(3.11)
The emulsion polymerization model nomenclature is shown here:
Symbol Description
aArea of a single micelle (m3)
m
ap
Area of a single particle (m3)
Am
Area of micelles (m2/m3 of aqueous phase)
Ap
Area of particles (m2/m3 of aqueous phase)
As Area coverage by emulsifier (m2/kmol)
dp
Density of polymer (kg/m3)
E Emulsifier concentration (kmol/m3)
F(v,t) Volume density function for particle size distribution (m-3)

Symbol Description
f Initiator efficiency
[I] Initiator concentration in the aqueous phase (kmol/m3)
ka
Absorption constant for particles (s-1)
jcr Critical chain length
 p
Volume fraction of polymer in polymer particle
kd
Initiator dissociation constant (s-1)
kde
Rate constant for the desorption of radicals from the
particles (m3/s)
kam
Rate constant for the absorption of radicals by micelles
(m/s)
kap
Rate constant for the absorption of radical by the particles
(m/s)
kp
Rate constant for propagation in particle phase (m3/kmol-s)
kpw
Rate constant for propagation in the aqueous phase
(m3/kmol-s)
kij Rate constant for activated initiation (m3/kmol-s)
act
kox
ij Rate constant for oxidation (m3/kmol-s)
kre
ij Rate constant for reduction (m3/kmol-s)
ktw
Rate constant for the termination in the aqueous phase
(m3/kmol-s)
pm Partition coefficient for the i-th component between polymer
Ki
particles and monomer droplets
Mp
Concentration of monomer in the polymer phase (kmol/m3)
Mwm
Molecular weight of monomer (kg/kmol)
Mw
Monomer concentration in aqueous phase (kmol/m3)
n Average number of radicals per particle
Np
Number of particles per unit volume of aqueous phase
(no./m3)
Na
Avogadro number
Nagg
Aggregation number
Nn
Number of particles containing n radicals per unit volume
(no./m3-s)
Rhomo
Rate of particle generation by homogeneous nucleation
(no./m3-s)
Rw 
Radical concentration in the aqueous phase (kmol/m3)
RI
Rate of initiator dissociation (kmol/m3-s)
tnuc
Nucleation time(s)
v Volume of a single unswollen particle (m3)

Symbol Description
vm
Volume of a single micelle (m3)
vh
Volume of a single particle formed by homogeneous
nucleation (m3)
v Volumetric growth rate of a single particle (m3/s)
vVolume of a swollen particle (m3)
s
vs Volumetric growth rate of a swollen particle (m3/s)
 Rate of radical absorption by Np particles (Kmol/s)
Total rate of radical generation (Kmol/s- m3)
i
0
Zeroth moment of the particle size distribution (no./m3 of
aqueous phase)
1
First moment of the particle size distribution (m3/m3 of
aqueous phase)
2
Second moment of the particle size distribution (m6/m3 of
aqueous phase)
3
Third moment of the particle size distribution (m9/m3 of
aqueous phase)
Particles containing n radicals are produced by three kinetic events:
 Absorption of a radical from the aqueous phase by a particle containing
(n-1) radical. The total rate of this event is given as:
N   1
p
nN
 Radical desorption from a particle containing (n+1) radicals. The total rate
of this event is given as:
Nn+1 kde (n+1)
 Termination in a particle containing (n+2) radicals. The total rate of this
reaction is given as:
[( 2)( 1)] 2    N k n n n tp
v
Particle Phase
Particles containing n free-radicals are depleted in the particle phase in three
analogous ways. By equating the rate of formation to the rate of depletion of
particles containing n free-radicals the recurrence formula is obtained:
 
  
/ ( 1)
N  N N N k n N k n n 
/ 1 ( 2)( 1) 1 1 2
          

  n a p n de n tp N

 

 
       v
v
a
n a p de tp
a
N N N k n k n n
N
(3.12)
This recurrence formula was first developed by Smith and Ewart, in a slightly
modified form (Smith & Ewart, 1948). Equation 3.12 can be solved for the

average number of radicals per particle, n . The general solution as given by
O'Toole is as follows (O'Toole, 1965):
n aI ( a
)
m
m
I a

4  
1( )
(3.13)
In Equation 3.13, Im(a) and Im1(a) are modified Bessel functions of the first
kind with parameters m and a. Equation 3.10 gives the definition of m. a is
calculated as a function of , defined in Equation 3.8, according to:
a  8 (3.14)
The simultaneous solution for n (Equation 3.13) and the stationary steady
state equation for the radical balance in the aqueous phase (Equation 3.6)
completely define the kinetics of the emulsion polymerization.
Kinetics of Emulsion Polymerization
A general emulsion polymerization kinetics scheme involves simultaneous
free-radical polymerization taking place in the dispersant phase, particle
phase and the monomer droplet phase. However, in general the monomer
droplet phase is regarded as an inert phase supplying monomer to the
particle phase during reaction. In conventional emulsion polymerization,
initiator decomposition takes place in the dispersant phase and the initiator
radicals enter the polymer particle phase.
The polymer particle phase is considered to be the site for all the
polymerization reactions. There is a dynamic exchange of radicals between
the particle phase and the dispersion phase. The average number of radicals
per particle is dependent on the steady state that is reached as a result of this
exchange. The free-radical kinetics scheme used in the model is that used in
the free-radical polymerization model.
Emulsion polymerization can handle activated initiation, redox initiation,
absorption and desorption, and much of the kinetics described in the free
free-radical Reaction Kinetic Scheme section on page 165, but not short chain
branching or beta scission.
Activated Initiation
The mechanism for activated initiation is given as:
I  A k
kj act
 n R   x *
k j
kj
Where:
Ik = Initiator molecule
Aj = Activator molecules which promote the dissociation of
the initiator molecules
R = Primary radical produced in the initiation reaction
x * = Waste products that do not participate in the
polymerization reactions

In emulsion polymerization water soluble persulfate initiators are normally
employed as initiators. In addition, water soluble sodium bisulfite is used as
an activator in many emulsion polymerization reactions for accomplishing
activated initiation of persulfates.
For the above given mechanism, Rkj act
, the radical generation rate for
activated initiation, is given by the following equation:
R
dR
dt
kj
kj

n f k C C act
kj kj act
Ik Aj
 
Where:
kact
kj = Rate constant for activated initiation
CIk
= Concentration of initiator in the aqueous phase
CAj
= Concentration of activator in the aqueous phase
nkj = Number of radicals produced per initiator molecules
fkj = Efficiency factor
Redox Initiation
The mechanism for redox initiation is given as:
I Fe k
n R Fe Y * k
  ox     k
(oxidation—slow)
Fe  RekreFe  x* (reduction—fast)
Similar to activated initiation, redox initiation is used in emulsion
polymerization reactions to promote decomposition of initiators at a much
lower temperature. For example, redox initiation is employed in cold rubber
production. It is also used in emulsion polymerization reactions where high
radical flux is needed.
k
R I k (the initiator, oxidant, or sometimes catalyst) decomposes in the presence
of the reduced (ferrous) ions, Fe++, to form one free radical, , and the

oxidized (ferric) ion, Fe+++. The reductant, Re, reacts with the ferric Fe+++ ion
reducing it to ferrous Fe++. x* and Y* are inactive byproducts of the reactions.
The activator system (or redox couple), a Ferrous salt (e.g. ferrous sulfate
heptahydrate) plus a reductant (e.g. SFS, Sodium Formaldehyde
Sulphoxylate), activates the initiator and regenerates the ferrous ion as
previously shown.
Multiple initiators are common: for example, KPS (Potassium persulfate) and
tBHP (tert -butyl hydroperoxide). KPS is used initially. At high conversion, the
monomer concentration in the polymer phase is low and the 
2 4 S O radicals
cannot diffuse into the polymer phase because they are hydrophyllic. tBHP,

on the other hand, partitions into both the aqueous and the polymer phases
and is, therefore, used for finishing in redox systems.
In the case of two initiators, two oxidation reactions and one reduction
reaction should be specified.
As the ferrous and ferric ions get regenerated in the redox reaction, it is
assumed that the total iron concentration remains constant in the reaction. As
the rate of reduction is much faster than the rate of oxidation, a stationary
state hypothesis is assumed for the ferrous and ferric ions.
Assuming stationary state hypothesis for the ferric and ferrous ion
concentration in the redox initiation mechanism, one can derive an equation
for the rate of generation of the radicals by the redox initiation as follows:
k
 
k C C n f k C
red Fe k k ox
k I
t k
Re
Re
k C k C
dR
dt
k
ox

k I k
red
 
Where:
CFet
= Total concentration of the iron in the aqueous phase
k
ox k = Rate constant for oxidation step of initiator k
red k = Rate constant for reduction step
CIk
= Concentration of initiator k in the aqueous phase
Re C = Concentration of reductant in the aqueous phase
k n = Number of radicals produced per initiator molecule, k
(default=1)
k f = Efficiency factor for initiator k (default=1)
In thermal decomposition, typically each initiator molecule produces two
radicals. The cage effect is when the radicals annihilate each other before
they are able to diffuse out of the cage into the aqueous phase. This effect is
captured by the radical efficiency term for thermal decomposition.
In redox initiation, only one radical is generated from the initiator.
Consequently, there is no cage effect because there is only one radical in the
cage. Therefore, in redox initiation, there is typically no need for the two
parameters: k n (number of radicals per initiator molecule) and k f (radical
efficiency). However, these parameters are provided and defaulted to a value
of 1 to provide additional handles for the user to fit their model to plant data.
Absorption and Desorption
In addition, there is an exchange of radicals between the aqueous phase and
the polymer phase. Radicals generated in the aqueous phase are absorbed by
the micelles during micellar nucleation and by the particle during nucleation
and subsequent growth. Radicals in the polymer phase can desorb from the

particle and enter the aqueous phase. The kinetics of absorption and
desorption are described as follows:
Absorption by particles:
R N k
N j i
  R k a C C i
 1 ap ap p Ni Rj
 ap
 
Absorption by micelles:
R N N j m
  kam 1 R k a C C am am m Nm Rj
 
Desorption:
N k
N R i
1 R k iC de de Ni
de  
i


Where:
am = Area of a single micelle
ap = Area of a single particle
Nm = Number of micelles with i radicals per cubic meter of
aqueous phase
Ni = Number of particles with i radicals per cubic meter of
aqueous phase
Reaction Rate Constant
The rate constant for each reaction in the built-in kinetics is calculated at the
reaction temperature and pressure using the modified Arrhenius equation
with user specified parameters for frequency factor, activation energy,
activation volume, and reference temperature:

 


k k exp Ea 
1 1
 
 
VP
o R T T

 




ref
R
Where:
ko = Pre-exponential factor in l/sec for first order reactions,
and m3 / kmol  s for second order reactions
Ea = Activation energy in mole-enthalpy units
V = Activation volume in volume/mole units
P = Reaction pressure
T = Reaction temperature
ref T = Reference temperature
The second term in the exponential function contains the activation volume
and is important for high pressure polymerization systems. For detailed

information of the reactions, see the free-radical Reaction Kinetic Scheme
section on page 165.
Rate constants related to absorption by particles, absorption by micelles and
desorption from particles are given by the Arrhenius expression as:
Ea
k k
  
exp
o RT 
 
assuming zero activation volume.
Model Features and
Assumptions
Following are the model features and assumptions used in the emulsion
Model Assumptions
The emulsion polymerization process is extremely complex and involves
phenomena for which a complete theoretical understanding has not been
reached. Important assumptions are made in the emulsion polymerization
model:
 The reaction mixture is perfectly mixed
 Particles are formed by the micellar or the homogeneous mechanism
 No agglomeration or breakage of particles occurs
 No secondary nucleation occurs
 All particles have the same average number of radicals and hence the
same volumetric growth rate
 The particle size distribution is unimodal, with moments of PSD sufficient
to describe the PSD
 There are no mass transfer limitations on the polymerization reactions
 Molecular weight is controlled by chain transfer reactions
Thermodynamics of Monomer Partitioning
Modeling of the kinetics involved in emulsion polymerization is complicated by
the fact that the reaction mixture is multiphase. It is important to account for
partitioning of the components among various phases. Up to four coexisting
phases may be present in the reaction mixture. After the consumption of the
monomer droplets, only three phases will remain in the system.
A short-cut partition coefficient methodology was used to handle the four
phases. One benefit of using this approach is that NRTL parameters are not
required for the polymer or its segments. The method assumes the polymer
solubility is zero in the monomer, aqueous, and vapor phases and performs a
rigorous 3-phase flash calculation to yield:
 Vapor phase - if present, contains water and monomers

 Dispersion phase - contains water, initiators, emulsifiers, activators and
some dissolved monomer
 Monomer phase - contains monomer and some dissolved water
The user provides a partition coefficient for each component that may be
present in the polymer phase. Following the rigorous 3-phase flash, an
iterative algorithm calculates the amount of each component to transfer from
the monomer phase, if present, and the aqueous phase to the polymer phase
in order to satisfy the partition coefficient constraints. As monomer is
transferred to the polymer phase, water is transferred from the monomer
phase to the aqueous phase so that its concentration in the monomer phase
is the saturation concentration calculated by the rigorous flash.
The user-supplied partition coefficients are provided as either:
 Monomer (L1) basis
 1 
pi i i x k x1
 Aqueous (L2) basis
 2 
pi i i x k x2
In either case, the partition coefficients are on a mass basis.
This scheme works equally well for monomer starved or monomer saturated
situations. When the monomer phase collapses, the algorithm transfers
monomer from the aqueous phase to the polymer phase. If the user provided
partition coefficients on a monomer basis, the partition coefficient with
respect to the aqueous phase is calculated as:
LL
i i i k 2  k1 / k
LL
i k values are only available when there is sufficient monomer present in the
swollen polymer particles to form a separate monomer phase if polymer were
removed. If the 3-phase flash does not detect a separate monomer phase,
LL
i k values will not be available, and the algorithm will transfer all monomer
from the aqueous phase to the polymer phase.
In addition, there are two rigorous phase equilibrium approaches to handle
the thermodynamics of monomer partitioning. The first rigorous approach
assumes the presence of two liquid phases. The distribution of water,
monomers, and polymers is determined by isofugacity relationships, and the
fugacities of various species are computed by the physical property option set
chosen for the system. The second approach performs rigorous four phase
(vapor-liquid-liquid-polymer) flash calculations based on a newly available
flash algorithm.
Polymer Particle Size Distribution
Polymer particle size and size distribution, among other factors, determine
the rheological properties of the latex . Although actual particle size
distribution is important, it is often measured in terms of certain averages
such as number average and weight average diameters. Further, rigorous
tracking of the particle size distribution by discrete methods is
computationally expensive.

In conventional emulsion polymerization where unimodal distributions are
normally encountered, the moments of the particle size distribution give
sufficient information about the nature of the particle size distribution. The
particle size distribution can be described in terms of different independent
variables such as diameter or volume of the particle. Since volumetric growth
rate of the particle in emulsion polymerization remains almost constant in
Stage I and Stage II of the process, the population balance equation is
formulated in terms of the volume of the particles.
General Population Balance Equation
The general population balance equation for the emulsion polymerization is
given as follows:
  v ,   v  F  v
,
t
      
F t
  
t

     

k A N R R am m a w m h
v
v v v v
homo (3.15)
In Equation 3.15 the right-hand side represents the nucleation of particles
from miceller and homogeneous nucleation. Refer to the table on page 208
for an explanation of the variables used. The volumetric growth rate is v for
a single unswollen particle (Equation 3.5):
v 
k M n
N
MW
d
p p
a
m
p
(3.16)
The general population balance equation can be converted to the equivalent
moment equations. The j-th moment of the particle size distribution is given
as:

 ( , )
0
 jF j d
    j
(3.17)
Applying moment definition in Equation 3.17 to the general population
balance equation in Equation 3.15, the first four moments of the particle size
distribution are given as:
d
dt
0  k A N [ R  ]  R am m a w
homo (3.18)
d
dt
 v  v k A N [ R  ]  v R (3.19)
0 m am m a w h
homo 
1 
d
dt
 2v  v2 k A N [ R  ]  v2 R m am m a w h
homo (3.20)

2 
1
d
dt
 3v  v3 k A N [ R  ]  v3 R m am m a w h
homo (3.21)

3 
2
Where:
kam = Kinetic constant for the absorption of the oligomeric
radicals into the micelles
Am = Area of the micelles

Rhomo = Rate of particle formation by homogeneous
nucleation
Polymer Particle Properties
Calculated
The emulsion model is designed to generate the following results that are of
interest for the emulsion polymerization process:
 Copolymer composition
 Number average molecular weight
 Particle size distribution averages for unswollen particles
The results are available as component attributes under the names listed
here:
Name Symbol Description Class Units
PSDZMOM 0
Zeroth moment of the
particle size
distribution (volume)
2 no./s
PSDFMOM 1
First moment of the
PSD (volume)
0 m3/s
PSDSMOM 2
Second moment of the
PSD (volume)
2 m6/s
PSDTMOM 3
Third moment of the
PSD (volume)
2 m9/s
VOLN Vn
Number average
volume of the particles
0 m3
VOLV Vv
Volume average
volume of the particles
0 m3
VOLZ Vz
Z-average volume of
the particles
0 m3
DIAV Dv
Volume average
diameter
0 m
PDV PDv
Polydispersity for PSD
(Volume)
0 ---
SFRAC --- Copolymer
composition
0 ---
MWN --- Number average
molecular weight
0 kg/kmol
User Profiles
In addition to the polymer properties reported through the component
attributes, other model calculations are reported through User Profile
variables. The following user profile variables may be requested from the
model:

 Glass transition temperature of the polymer (C)
 Average number of radicals per particle
 % Soap coverage of the polymer particles
 Volume of the monomer droplet phase (m3)
 Concentration of monomers in the monomer droplets (kmol/m3)†
 Volume of the aqueous phase (m3)
 Monomer concentration in the aqueous phase (kmol/m3)†
 Volume of the polymer particle phase (m3)
 Monomer concentration in the polymer particles (kmol/m3)†
 Monomer conversion
† One profile is reported for each monomer.
User profiles are only accessible if the reaction model is called from a batch
reactor (RBatch) or a plug flow reactor (RPlug). The user profiles are returned
in the order shown. A label must be provided to differentiate the profile
variables. For the monomer concentrations in the aqueous, monomer, and
polymer phases one profile is returned for each monomer.
Specifying Emulsion
Accessing the Emulsion Model
To access the Emulsion polymerization kinetic model:
5 Select Emulsion as the reaction type and click OK.
Specifying the Emulsion Model
The Emulsion model input forms are divided into two folders: Specifications
and Phases.
Use the Specifications forms to define reacting species and enter reaction
rate constant parameters. Use the following options:
Use this sheet To

Options Select additional options
Gel Effect Gel-effect correlation parameters
Use the Phases forms to enter information related to phase partitioning and
particle growth. Use the following options:
Use this sheet To
Phase Equilibria Specify component phase split
Particles Specify emulsifiers and define particle radical
exchange information
You must specify the reacting species in the Specifications Species sheet:
1 In the Polymer field, specify the polymer produced. Also specify
Dispersant and the Redox couple (ferrous salt and reductant) if redox
initiation is used.
2 In the Monomers field list the reacting monomers. For each monomer, in
converts to.
3 Continue listing other types of reacting species, e.g. initiators, transfer
agents, etc.
repeatedly.
Listing Reactions
The Emulsion model generates reactions based on the list of reacting species.
You can view the system-generated reactions, then assign rate constant
parameters to these reactions.
You can view a list of the system-generated reactions on the Specifications
Reactions sheet. In the Reaction summary listing for each reaction, the first
column indicates the reaction type. The second column lists the reactants,
and the last column lists the products. The Data Browser window can be
resized to better view the reaction listing. Use the following options:
Click To
selector
reactions

Click To
Hide/Reveal
calculations
Delete
Adding Reactions
To add a new reaction to the scheme, click New to open the Add Reaction
subform:
1 In Reaction type, select a type for the new reaction.
2 In other reactant (for example, Initiator, Catalyst) fields, enter the
 or 
 or 
 or 
Editing Reactions
 or 
Rate Constant Parameters subform:
1 In the Pre-Exp (k_ref) field, enter the pre-exponential factor.
2 In the Act-Energy (Ea) field, enter the activation energy.
3 In the Act-Volume (V) field, enter activation volume.
4 In the Ref. Temp. (Tref) field, enter reference temperature.
5 In the Efficiency field, enter initiator efficiency for initiation reactions.

6 In the No. radicals field, enter the number of primary radicals formed in
initiation reactions.
previous or next reaction in the list.
8 Click the Summary tab to see a listing of all the rate constant
parameters.
 or 
Selecting Calculation Options
You can select additional simulation options for the model, such as gel-effect,
on the Options sheet.
For Gel effect, you need to specify parameters on the Gel Effect sheet.
Adding Gel-Effect
Use the Gel-Effect sheet to add gel effect to reactions:
1 Enter a unique integer identifier in No.
2 In the Reaction field, specify the reaction to which you would like to
apply gel effect.
3 In the Corr. No. field, specify a gel effect correlation number.
4 In Parameters, list the parameters for the gel effect correlation.
Specifying Phase Partitioning
Use the Phases Phase Equilibria sheet to specify phase partitioning for the
components in the emulsion system:
1 If you select a Rigorous approach, specify a Method.
2 If you select the Partition Coefficients approach, in the Basis field
select the phase partitioning basis, for example, MONOMER or AQUEOUS
3 For each component present in the polymer phase (except the polymer),
specify the split fraction using the Component and Coefficient fields.

Specifying Particle Growth Parameters
Use the Phases Particles sheet to specify data for particle generation and
particle related events:
1 Define Emulsifier, and specify critical micelle concentration, CMC, and
surfactant Area.
2 For homogeneous nucleation, specify Aggregation number and Critical
length.
You must specify radical absorption and desorption rate constant parameters
for micelles and particles.
References
Barton, J., & Capek, I. (1994). Radical Polymerization in Disperse Systems.
New York: Ellis Harwood.
Blackley, D. C. (1975). Emulsion Polymerization: Theory and Practice.
London: Applied Science Publishers Ltd.
Gilbert, R. G. (1995). Emulsion Polymerization: A Mechanistic Approach.
Boston: Academic Press.
Hamielec, A. E., & Tobita, H. (1992). Polymerization Processes. In Ullmans
Encyclopedia of Industrial Chemistry, A21, 305. New York: VCH Publishers.
Harkins, W. D. (1945). J. Chem. Phys., 13, 301.
Odian, G. (1991). Principles of Polymerization, 3rd. Ed. New York: John Wiley
& Sons.
O’Toole, J. T. (1965). Kinetics of Emulsion Polymerization. J. Appl. Polym.
Sci., 9, 1291.
Poehlein, G. W. (1986). Emulsion Polymerization. In H.F. Mark, N. M. Bikales,
C. G. Overberger, and G. Menges, (Eds.). Encyclopedia of Polymer Science &
Technology, 6, 1. New York: Wiley-Interscience.
Ponnuswamy, S. R., & Hamielec, A. E. (1997). Emulsion Polymerization:
Theory and Practice. Lecture notes for intensive short course on polymer
reaction engineering held at Burlington, ON, Canada, April 28-30.
Smith, W. V., & Ewart, R. H. (1948). J. Chem. Phys., 16, 592.

11 Ziegler-Natta
This section covers the Ziegler-Natta polymerization kinetic model available in
Aspen Polymers (formerly known as Aspen Polymers Plus). The term Ziegler-
Natta polymerization is used here to describe a variety of stereospecific multi-site
and single site catalyzed addition polymerization systems including the
traditional Ziegler-Natta catalyzed systems, chromium based catalyzed
systems (Phillips type) and the more recent metallocene based catalyzed
systems.
 Ziegler-Natta Processes, 226
 Specifying Ziegler-Natta Polymerization Kinetics, 244
Several example applications of the Ziegler-Natta polymerization model are
given in the Aspen Polymers Examples & Applications Case Book. Additionally,
the Examples & Applications Case Book provides process details and the
kinetics of polymerization for specific monomer-polymer systems.
The Ziegler-Natta polymerization model is applicable to processes utilizing
coordination catalysts for the production of stereospecific polymers.
Some examples of applicable polymers are:
 Linear low density polyethylene - Ethylene is copolymerized with an alpha-olefin,
such as 1-butene, 1-hexene, or 1-octene. Commercial processes
include low pressure, slurry-phase processes, solution-phase processes,
low pressure, gas phase processes.
 High density polyethylene - Ethylene homopolymers or copolymers with
high alpha olefins with density 0.940 g / cm3 and higher. Commercial
11 Ziegler-Natta Polymerization Model 225

processes include solution, slurry or suspension, and gas phase
polymerization.
 Ethylene-propylene elastomers - Polymerization proceeds by solution or
slurry processes. Both are operated continuously in liquid-phase back-mixed
reactors.
 Polypropylene - Commercial processes include liquid pool, diluent slurry,
and gas phase polymerization.
Ziegler-Natta Processes
Ziegler-Natta polymerization accounts for a significant fraction of the
polyethylene polymers and all the polypropylene homopolymers and
copolymers produced commercially. The commercial production of these
polyolefins is done exclusively by continuous processes using several different
processes and reactor types operating over a wide range of conditions.
High density polyethylene (HDPE) and linear low density polyethylene (LLDPE)
are produced via catalyzed polymerization processes. The operating
conditions for the catalyzed processes are relatively less severe compared to
the high pressure processes for LDPE production. The pressure generally
ranges from 10-80 atm while the temperatures range from 80-110C. The
pressure and temperature may be as high as 200 atm and 250C in some of
the solution polymerization processes.
Catalyst Types
There is a variety of catalysts used for ethylene polymerization including
supported and unsupported heterogeneous catalyst systems and
homogeneous catalyst systems. The Ziegler-Natta transition metal (Ti) based
catalysts are the most widely used.
However, there are numerous variations of these catalysts. Some vanadium
based catalysts are also used. Chromic oxide on silica catalysts are used in
the Phillips loop reactor process, while the Union Carbide Unipol process may
use either Ziegler-Natta (Ti) or chromium compounds on silica catalysts.
More recently, several manufacturers have been developing commercial
processes using metallocene based catalysts, mainly zirconium and titanium.
These catalysts are believed to be single site catalysts that are capable of
producing high yields, combined with narrow molecular weight and copolymer
composition distributions.
All commercial isotactic polypropylene homopolymer (PP) is manufactured
using heterogeneous Ziegler-Natta catalyst systems. The catalyst consists of
a solid transition metal halide, usually TiCl3 , with an organoaluminum
compound cocatalysts, such as diethylaluminum chloride (DEAC), or a MgCl2
supported TiCl4.AlEt3 catalyst.
226 11 Ziegler-Natta Polymerization Model

Ethylene Process Types
There are three types of catalyzed ethylene polymerization processes in
commercial use today:
 Liquid slurry
 Solution
 Gas-phase
A partial list of HDPE and LLDPE processes, along with a summary of their
characteristics is shown here:
Process Reactor Diluent /
Solvent
Catalyst Temp.
(C)
Press.
(atm)
Residence
Time
(hr)
Company
Liquid
slurry
Loop i-butane
n-hexane
Supported
Ti or Cr
80-100 30-35 1.5-2.5 Phillips Solvay
CSTR n-hexane Supported
Ti
80-90 8-35 2.0-2.7 Dow
Hoechst
Nissan
Mitsubishi
Montedison
Solution CSTR n-hexane
cyclohexane
Ti/V 130-
250
30-200 0.08-0.17 Dow
Dupont
Stamicarbon
Gas Stirred
bed
--- Supported
Ti or Cr
70-110 20-35 3-5 AMOCO
BASF
Fluidized
bed
--- Supported
Ti or Cr
85-100 20-30 3-5 BP
Union Carbide
In the slurry process, a hydrocarbon diluent is used, typically a C4 C7 
paraffin, isoparaffin or cycloparaffin. Under the conditions used the
polyethylene is essentially insoluble in the diluent. As a result a slurry is
formed.
In the solution process, the conditions used are such that the polyethylene is
completely dissolved in the solvent.
In gas-phase processes, gaseous ethylene and comonomers are contacted
with a polymer-catalyst powder. Polymerization occurs in the monomer-swollen
polymer particles which contain embedded catalyst fragments with
active sites.
Ethylene polymerization processes have been reviewed extensively. More
detailed descriptions of these processes are available in the open literature
(Albright, 1985; Choi & Ray, 1985a; Nowlin, 1985; Short, 1983).

Propylene Process Types
There are three types of catalyzed polypropylene homopolymerization
processes in commercial use today:
 Liquid slurry
 Liquid pool (bulk)
 Gas-phase
A partial listing of propylene homopolymerizatio processes, along with a
summary of their characteristics is shown here:
Process Reactor Diluent /
Solvent
Catalyst Tacticit
y
(%)
Temp.
(C)
Press.
(atm)
Residenc
e
Time (hr)
Company
Bulk
(Liquid
Pool)
Loop Liquid
monomer
Supported Ti Up to 99 60-80 30-40 1-2 Himont
Mitsui
CSTR Liquid
monomer
Unsupported
or supported
Ti
Up to 98 60-75 30-40 2 Dart
El Paso
Montedison
Sumitomo
Diluent
Slurry
CSTR n-hexane,
n-heptane
Unsupported
or supported
Ti
Up to 98 60-80 15-20 3-4 Montedison
Gas Fluidized bed N2 Supported Ti Up to 98 60-80 20 3-5 Sumitomo
Union
Carbide
Vertical stirred
bed
--- Unsupported
or supported
Ti
Up to 98 70-90 20 4 BASF
ICI
USI
Horizontal
compartment-ed
stirred bed
--- Unsupported
or supported
Ti
Up to 98 70-90 20 4 AMOCO
In the slurry process, a hydrocarbon diluent, typically butane, hexane or
heptane, is used at operating temperatures of 70-90C. Under these
conditions the isotactic polypropylene is essentially insoluble in the diluent. As
a result a slurry is formed.
In the liquid pool process, liquid propylene is used in place of the diluent. In
this process also, the polypropylene is insoluble in the liquid propylene and a
slurry is formed. The higher monomer concentrations in this process allow for
smaller reactors and lower operating temperatures compared to the slurry
process.
In the gas-phase processes, gaseous propylene is contacted with a polymer-catalyst
powder. Polymerization occurs in the monomer-swollen particles
which contain embedded catalyst fragments with active sites.

Propylene polymerization processes have been reviewed extensively in the
literature. More detailed descriptions of these processes are available in the
open literature (Albright, 1985; Brockmeier, 1983; Choi & Ray, 1985b).
Besides polypropylene homopolymer (PP), high impact polypropylene (HIPP)
and some ethylene-propylene (EP) copolymers are produced by including an
additional reaction stage to the polypropylene homopolymerization process. A
summary of catalyst processes for propylene copolymerization is shown here:
Process Reactor
Diluent /
Solvent Catalyst
Temp.
(C)
Press. (atm) Resi-dence
Time
(hr)
Co-monomers
Company
Stage
1
Stage
2
Bulk
(Liquid
Pool)
+
Second
Stage
Loop - fluid
bed
--- Supported Ti 60-80 30-40 20 1-2 Ethylene &
others
Himont
Mitsui
CSTR -
CSTR
--- Supported Ti 60-75 30-40 30-40 2 Ethylene Sumitomo
CSTR -
stirred
horizontal
bed
--- Unsupported
or supported
Ti
40-75 30-40 20 2-5 Ethylene Dart
El Paso
Diluent
Slurry
CSTR Liquid
monomers
& diluents
Ti/V 0-20 5-20 --- 1 Ethylene,
Butene,
dienes
Montedison
Dutral
Multistage
Gas
Fluid bed -
fluid bed
--- Supported Ti 60-80 20 20 3-5 Ethylene &
others
Sumitomo
Union
Carbide
Vertical
stirred bed
- stirred
bed
--- Unsupported
of supported
Ti
70-90 20 20 4 Ethylene &
others
BASF
ICI
USI
Horizontal
stirred bed
-
horizontal
stirred bed
--- Supported Ti 70-90 20 20 4 Ethylene &
others
AMOCO
Chisso
In the EP process, last reaction stage is designed to introduce the desired
amount of EP copolymer into the PP product. For example, the Himont
spheripol process uses liquid pool loop reactors followed by a gas-phase
fluidized bed reactor for the copolymerization stage. The residence time
distribution of the polymer particles leaving each stage should be as narrow
as practical to ensure that the weight ratio of EP to PP for particles leaving the
second stage is as uniform as possible. The Amoco/Chisso process has largely
met this requirement.

The built-in catalyst/polymerization kinetic scheme represents the typical
scheme described in the open literature (Xie et al., 1994). Although a number
of reaction mechanisms have been proposed to describe stereospecific
Ziegler-Natta polymerization, there is still no definitive reaction mechanism to
completely describe the kinetic behavior of these complex
catalyst/polymerization systems.
Most of the proposed mechanisms include a detailed set of reactions.
However, not all of these reactions apply to every catalyst system nor can
they be verified. The kinetic scheme for chromium and metallocene catalyzed
systems can be considered to be a subset of a comprehensive Ziegler-Natta
kinetic scheme.
Reaction Steps
There are a few key elementary reactions that apply to almost all catalyzed
addition polymerization systems. These include the three basic reaction steps:
 Chain initiation
 Propagation
 Chain transfer (spontaneous and to small molecules such as monomer,
solvent and chain transfer agents)
For chromium and metallocene catalyst systems, additional reactions for long
chain branching via terminal double bond polymerization must also be
included.
In addition to the polymerization reactions, there are reactions affecting the
catalyst active sites on which the polymerization reactions take place. These
include catalyst site activation, inhibition and deactivation. The catalyst
reactions and the polymerization reactions occur simultaneously during the
polymerization.
A comprehensive kinetic scheme for the catalyzed multi-site homo- and
copolymerization of any number of monomers has been built into Aspen
Polymers.
Catalyst States
The multi-site catalyst states and the types of reactions affecting them are
shown here:

In setting up a si
simulation, the user specifies the catalyst flow rate for the
feed streams, and a catalyst parameter, the moles of sites per unit mass of
catalyst. This parameter together with the catalysts flow rate is used to
compute the total moles of sites.
The total moles les of sites are made up of potential sites, active sites of different
reactivities, and dead sites. Site activation reactions convert potential sites to
active sites, while site deactivation reactions convert active sites to dead
sites. There are several
into the kinetic scheme and these are discussed later in this section.
Site Types
In the figure, potential sites and dead sites are considered to be independent
of site type. The user specifies the number of site types to be included for a
particular simulation.
 A vacant site
molecule attached to it.
 A propagation site
 Inhibited sites
attached, temporarily blocking it from becoming propagation sites. The
small molecule may dissociate from an inhibited sited, which then
becomes a vacant site once again. Therefore, the site inhibition reaction is
considered reversible.
11 Ziegler-Natta Polymerization Model
different site activation/deactivation reactions built
. is an active site that does not have a polymer or othe
has a growing polymer molecule attached to it.
have small molecules such as hydrogen or poisons
231
mulation, other
ogen

232
When a vacant site is involved in a chain initiation reaction it is converted to a
propagation site. When a propagation site is involved in a chain transfer
reaction, a vacant site and a dead polymer molecule are formed.
The built-in scheme includes most of t
he modeling Ziegler-internal
double-bond polymerization with diene comonomers, and site
transformation reactions (Debling et al., 1994; Xie et al., 1994) have not
been included in the current model. These reactions may be added to the
built-in scheme in the future. The current built
polymerization kinetic scheme is shown here
Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme
(continued)
n the reactions commonly used for
-Natta polymerization. Reactions such as depropagation,
ded built-in Ziegler-Natta catalyst and
here:

(continued)
continued
233

234
(continued)
Kinetic Scheme Nomenclature
The nomenclature used in the Ziegler
given here:
Symbol Description
Am
Cocatalysts m
Em
Electron donor m
Ziegler-Natta polymerization kinetic scheme is

Symbol Description
Cds
Dead catalyst sites
Cps
Potential catalyst sites
k Inhibited catalyst sites of type k
Dn
Cis
k Dead polymer chain of length n ( n1, n2, ..., nm ) for
copolymerization produced from a catalyst site of type k
H2
Hydrogen
Mj
Monomer j
Nm
Number of monomers
Nsites
Number of active site types
Ok Reaction order for the non-polymer component at site
type k
Pk
0
Vacant catalyst sites of type k
k
,
Pn i
Live polymer chain of length n having an active segment
of type i attached to a active site of type k
Sm
Solvent m (for solution or slurry polymerization)
Tm
Chain transfer agent m
Xn
Inhibitor n
k Zeroth moment of live polymer with respect to active
0,i
segment of type i and active site of type k
In the following discussion:
 A polymer chain is considered to be made up of monomer units or
segments derived from the propagating monomers
k refers to growing polymer chains containing n segments
 Live chain (Pn,i )
or monomer units, with an active segment of type i attached to a catalyst
active site of type k
k refers to a terminated polymer chain
 Dead chain (Dn )
 The superscript k refers to the active site type from which the dead
polymer chain was formed
 The subscript n refers to the chain length in terms of the number of
segments or monomer units incorporated in the polymer chain
Live chains are reactive and can participate in the polymerization reactions
while dead chains are usually considered inert, except in cases where long
chain branching reactions are important.
Polymerization Mechanism
The catalyst active site is attached to one end of a live polymer chain via a
metal-carbon bond. It is generally accepted that polymerization proceeds via

a two-step mechanism. In the first step, monomer is complexed to the
transition metal site. The second step is the coordinated insertion of the
monomer into the metal-carbon bond. As a result, the polymer chain and the
previously added segments grow away from the active site with every
addition of a monomer molecule.
It is believed that the chain microstructure will not have a strong influence on
the mode of monomer addition. For this reason, the built-in kinetic model
assumes that the reactivity of a live polymer chain depends only on the active
segment and the active site type, and is independent of the polymer chain
length and other structural properties. Meaning in the propagation reaction,
the rate of propagation Rp k
, ij
is independent of the polymer chain length. It
depends only on the concentration of monomer j, and the concentration of
live polymer chains with active segments of type i attached to an active site
of type k. Models using this assumption are referred to as terminal models in
the polymerization literature.
Copolymerization Mechanism
For copolymerization, the built-in kinetic scheme allows the user to specify
the number of monomer types used. Similarly the user has the flexibility to
specify the number of each type of reactive species present in the
polymerization: catalysts, cocatalysts, chain transfer agents, solvents, etc.
The user is able to tailor the built-in kinetics to model a specific catalyzed
polymerization system by selecting a subset of the reactions shown in the
Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme figure on
page 232. However, it is important that the subset include a chain initiation,
propagation, and at least one chain transfer or active site deactivation
reaction to produce dead polymer.
Rate Expressions
The rate expression for each reaction is generally written as a product of the
rate constant and the concentrations of the reacting species. In many of the
reactions, one of the reacting species is a polymer chain while the other is a
small molecule such as monomer, chain transfer agent, cocatalyst, etc. A
reaction order with respect to the small reacting molecule is included for
some of the reactions. This reaction order has a default value of one.
The rate constants for each reaction at sites of type k are calculated at the
reaction temperature using the Arrhenius equation shown below. The user
specified rate constant parameters are pre-exponential factor (ko )
k , activation
energy (Eak ) at sites of type k, and the reference temperature.
Rate Constant

 

k = k exp - E a
 

 


 
1 1
R T T


ref
k
ko
k
Where:

ko = Pre-exponential factor in 1/sec for first order reactions
and m3 / kmol  sec for second order reactions
Ea = Activation energy in mole enthalpy units
ref T = Reference temperature in Kelvin
Catalyst Pre-Activation
Some of the chromium catalysts used in these processes exhibit slow
activation with induction period. This slow activation can be modeled by
catalyst preactivation reaction. The precatalyst goes to catalyst that further
undergoes site activation, initiation and propagation.
Catalyst Site Activation
The catalyst site activation step involves the generation of reactive vacant
active sites from potential sites. Depending on the catalysts system, the
activation may be done before the catalyst is fed to the reactor or within the
reactor.
There are several different site activation reactions included in the built-in
kinetic scheme. They include site activation by cocatalyst, by electron donors,
by hydrogen, by monomer, and spontaneous site activation. Different catalyst
systems tend to be activated by a different subset of the reactions in this
scheme. For example, TiCl3 catalyst systems are usually activated with an
organoaluminum cocatalyst such as diethylaluminum chloride (DEAC), in the
reactor. Chromic oxide catalysts are calcined by heating with air for several
hours at temperatures of 400C to 975C and cooled in dry air. Some of these
catalysts may be activated with a reducing agent before introduction into the
reactor, while others are activated within the reactor.
Site Activation Reactions
Some of the site activation reactions (activation by monomer, electron donor,
hydrogen) have been proposed to explain the observed rate enhancement
behavior in different catalyst systems. For example, the activation of
additional sites by comonomer has been proposed to explain the rate
enhancement observed with the addition of a comonomer to ethylene and
propylene homopolymerization reactors.
Chain Initiation
Chain initiation involves the reaction of a monomer molecule at a vacant
active site to form a live polymer molecule of unit length at that site. This
reaction converts a vacant active site to a propagation site. The chain
initiation reaction is shown below:

Po k
 M i
 P i
R k

k k
P k

1 ci
ci
o
C Mi
k
OMi
k is dependent on the
The rate of chain initiation at site type k (Rci )
concentration of vacant sites of type k and the concentration of monomer i.
The user can also specify the reaction order with respect to the monomer
concentration. The live polymer chains grow by successive addition of
monomer molecules to form long polymer molecules.
Propagation
The live polymer at each active site type grow or propagate through the
addition of monomer molecules to form long polymer chains. The propagation
reaction is represented by:
P k
 M  P k
R k
 k k
C P k
n , i j n  1, j
p , ij
p , ij
Mj n , i
(main propagation)
Where monomer j is being added to a polymer chain of length n, with an
active segment of type i at an active site of type k. The resulting polymer
chain will be of length n+1 and the active segment will be of type j. The
active segment type usually represents the last monomer type incorporated
into the polymer chain.
For copolymerization, there will be Nm *Nm *Nsite propagation reactions that
may have different reactivities. For example, with two monomers and three
site types, the monomer being added could be monomer 1 or monomer 2
while the active segment type could be segments from monomer 1 or
monomer 2 at each site type.
As a result, there will be twelve rate constants (kp,k ij )
, where the subscript i
refers to the active segment type while the second subscript j refers to the
propagating monomer type. The superscript k refers to active site type. For
the terminal model the rate of propagation is dependent only on the
concentration of live polymer with active segment i at active site k and the
concentration of the propagating monomer j.
In Aspen Polymers Version 3.0 and higher, another propagation reaction has
been added to account for formation of atactic polymer. This reaction has the
same form as the main propagation reaction:
  k
OpaMi
P k
 M  P R  k  k
C n , i   , 0, j
Mi
(atactic propagation)
k paij
k paij
k
j n i i
k . When the atactic propagation
but uses a different rate constant (k ) paij
reaction is included in the simulation, the main propagation reaction should
be considered to account for the formation of all polymer whether it is
isotactic or atactic. Hence the main propagation reaction is also termed the
total propagation. The atactic propagation reaction only accounts for the
formation of atactic polymer. The atactic content of the polymer is then
calculated from the ratio of atactic to total polymer.

Chain Transfer to Small Molecules
Chain transfer to small molecules such as monomer, solvent or chain transfer
agent usually involves the extraction of hydrogen from the small molecule by
the active site and leads to the termination of the live chain. At the same
time, a new vacant site is formed which can undergo chain initiation to start
polymerization. The effect of chain transfer on the polymerization kinetics
depends on the reactivity of the transfer sites.
When the transfer site is very reactive, as is the case when the chain initiation
rate constant is greater than the propagation rate constant, chain transfer will
not lower the polymerization rate or conversion, but will reduce the molecular
weight of the polymer. However, if the transfer site is less reactive, as in the
case of low chain initiation rate constant, both the conversion and molecular
weight of the polymer will be lowered.
In the built-in kinetics, chain transfer to hydrogen, cocatalysts, solvent,
transfer agent, electron donor, monomer and spontaneous chain transfer are
included as shown in the Built-In Ziegler-Natta Catalysts and Polymerization
Kinetic Scheme figure on page 232.
Chain Transfer to Monomer
For chain transfer to monomer a new polymer chain of unit length is
generated while for the other transfer reactions a vacant site of that type is
generated. The dead polymer chain formed by some of the chain transfer
reactions will have an end-group with a terminal double bond. In addition to
the rate constant parameters and the reaction order, the user may also
specify a parameter to track the fraction of dead polymer chains with terminal
double bonds that are generated from the chain transfer reactions. The
default value for this parameter is zero.
Site Deactivation
The catalyst site deactivation step involves the deactivation of active sites,
vacant and propagation, to form dead sites. Depending on the catalyst
system and operating conditions, the deactivation rate may be high or low.
There are several different site deactivations reactions included in the built-in
kinetic scheme. They include site deactivation by cocatalyst, by electron
donors, by hydrogen, by monomer, by poisons, and spontaneous site
deactivation. Different catalyst systems tend to be deactivated by a different
subset of the reactions.
The deactivation rate constants are assumed to be dependent only on the site
type and not on the polymer segment attached to a site. Therefore, the same
rate constant is applied to both vacant and propagation sites of the same
type. Note that deactivation rates shown in the Built-In Ziegler-Natta
Catalysts and Polymerization Kinetic Scheme figure on page 232 are per unit
of active (vacant and propagation) site concentration.

Site Inhibition
Inhibited sites have small molecules such as hydrogen or poisons attached.
As a result, inhibited sites are temporarily blocked from becoming
propagation sites. The site inhibition reaction is considered reversible.
Therefore, the small molecule may dissociate from an inhibited site which
then becomes a vacant site once again. The user must specify rate constant
parameters for both the forward (inhibition) and reverse (dissociation)
reactions.
Cocatalyst Poisoning
For some catalyst systems, additional amounts of cocatalysts are fed to the
reactor to counteract the effect of any poisons present . This is modeled as a
cocatalyst poisoning reaction in the built-in kinetics. The product of this
reaction is designated as a byproduct in the list of reactive species. The
byproduct is considered to be inert and does not participate in any reaction.
Terminal Double Bond Polymerization
For some catalyst systems, primarily metallocene, polymer chains with long
chain branches are formed. However, the long chain branching frequency is
usually small. The long chain branches are believed to be due to propagation
reactions involving a live chain and a terminal double bond on a dead polymer
chain. Polymer chains with terminal double bonds are formed by some of the
chain transfer reactions. To form long chain branches, the metal center must
be open to provide a favorable reactivity ratio for the macromonomer.
The concentration of terminal double bond (TDB) end-groups on the dead
polymer chains are tracked through an additional segment called the TDB-Segment.
TDB-Segments are generated through the chain transfer reactions
and are consumed through the TDB polymerization reaction. When the TDB
reaction is used, one additional segment needs to be defined in the
Components form for the TDB-Segment. Typically, for a copolymerization
system with N monomers, N repeat segments would be defined in the
Components form. However, with the TDB polymerization reaction, N repeat
segments and one end segment should be defined in the Component form.
The end segment must be specified as the TDB-Seg species in the Species
folder of the Ziegler-Natta kinetics.
Example for Terminal Double Bond Polymerization
This example starts with the delivered example file Polymerspp.bkp.
1 Include a segment to represent the terminal double bond. The segment
database includes several preconfigured TDB segments (each containing
one less hydrogen than the corresponding monomer). Be sure to select
Type Segment.

2 Declare the TDB segment an END segment on the Components |
Polymers | Characterization | Segments sheet.
3 Specify the segment in the T.D.B. segment field on the Ziegler-Natta
Reactions | Species sheet.
4 Reactions are not generated automatically for TDB polymerization
reactions. On the Reactions sheet, click New and add as many reactions
of type TDB-POLY as you need to account for multiple sites and active
segments.

5 In addition, you need reactions to generate the TDB segment. On the
Rate Constants sheet, set Tdb Frac to a value greater than 0 to cause
the TDB segment to form. Tdb Frac is the fraction of reaction events that
lead to terminal double bond formation. Also on this sheet specify the pre-exponential
factor and activation energy for the TDB-POLY reactions.

Model Features and
Assumptions
Following are the model features and assumptions used in the Ziegler-Natta
Phase Equilibria
options form.
phase.
Rate Calculations
The Ziegler-Natta polymerization kinetic model supplies to the reactor models
the reaction rates for the components and the rate of change of polymer
attributes (e.g. the chain length distribution moments) . The component
reaction rates are computed from the kinetic scheme by summing over all
reactions that involve the component. The site based moment rates are
derived from a population balance and method of moments approach similar
to that described in the Calculation Method section on page 185.
on the polymer attributes selected, and the subset of the built-in kinetics used
for a specific simulation:
 Zeroth, first and second moments for the composite and site based
combined polymer
 Zeroth and first moments for the composite and site based live polymer
 Number and weight degree of polymerization and polydispersity index for
the composite and site based bulk polymer (DPN, DPW, PDI and SDPN,
SDPW, SPDI)
 Number and weight average molecular weight for the composite and site
based bulk polymer (MWN, MWW and SMWN, SMWW)
 Copolymer segment composition for composite and site based bulk
polymer (SFRAC and SSFRAC segment mole fractions)
 Total number long chain branches (LCB)

 Long chain branching frequencies (FLCB)
 Mole fraction of live bulk polymer chains (LPFRAC and LSPFRAC)
 Number average degree of polymerization for live polymer (LDPN and
LSDPN)
 Copolymer segment composition for live polymer (LSFRAC and LSSFRAC)
 Live polymer active segment composition (LEFRAC and LSEFRAC)
These variables are stored as component attributes (See Chapter 2). It is
assumed that attributes needed for the kinetic scheme are selected. The
specification of the Ziegler-Natta Model is described later in this section.
In many cases, users may need to know polymer product properties related
to the above structural properties. For example, users may be interested in
melt flow rate or melt index, viscosity, density, etc. These properties can be
calculated in user-supplied Fortran subroutines which take the polymer
moments and structural information and return the desired property. An
example use of a user supplied subroutine to return melt index is shown in
the HDPE section of the Aspen Polymers Examples & Applications Case Book.
Specifying Ziegler-Natta
Accessing the Ziegler-Natta Model
To access the Ziegler-Natta polymerization kinetic model:
5 Select Ziegler-Nat as the reaction type and click OK.
Specifying the Ziegler-Natta Model
The Ziegler-Natta model input forms are as listed below. Use these forms to
define reacting species and enter reaction rate constant parameters.
Use this sheet To
Options Specify the reacting phase

You must specify the reacting species on the Species sheet:
2 In the Monomers field list the reacting monomers. For each monomer, in
converts to.
3 If you select the terminal double bond polymerization reaction, in the
T.D.B.-Seg field, list TDB segment that is formed by the chain transfer
reactions and is consumed by the terminal double bond polymerization
reaction. Otherwise, go to step 4.
Note: The TDB segment should be of type end segment and should not be
used as a repeat segment for a particular monomer (see Step 2).
4 Continue listing other types of reacting species, for example, solvents,
transfer agents, etc.
repeatedly.
Listing Reactions
The Ziegler-Natta model generates reactions based on the list of reacting
species. You can view the system-generated reactions, then assign rate
constant parameters to these reactions.
You can view a list of the system-generated reactions on the Reactions
sheet. In the Reaction summary listing for each reaction, the first column
indicates the reaction type. The second column lists the reactants, and the
last column lists the products. The Data Browser window can be resized to
Click To
selector
reactions
Click To
Hide/Reveal
calculations
Delete
Permanently remove a reaction from the
model

Adding Reactions
subform:
2 In other reactant (for example, Initiator, Catalyst) fields, enter the
 or 
 or 
 or 
Editing Reactions
 or 
1 In the Site No. field, enter the site number.
3 In the Ea field, enter the activation energy.
4 In the Order field, enter the order for component in reaction.
5 In the Fraction field, enter terminal double bond fraction.
parameters.

 or 
References
Albright L. F. (1985). Processes for Major Addition-Type Plastics and Their
Monomers, 2nd Ed. Florida: Krieger Pub.
Brockmeier, N. F. (1983). Latest Commercial Technology for Propylene
Polymerization. In R.P. Quirk (Ed.), Transition Metal Catalyzed
Polymerizations - Alkenes and Dienes. New York: Academic Pub.
Choi, K-Y, & Ray, W. H. (1985a). Recent Developments in Transition Metal
Catalyzed Olefin Polymerization - A Survey. I. Ethylene Polymerization. J.
Macromol. Sci. Rev. Macromol. Chem. Phys., C25 (1), 1.
Choi, K-Y, & Ray, W. H. (1985b). Recent Developments in Transition Metal
Catalyzed Olefin Polymerization - A Survey. II. Propylene Polymerization. J.
Macromol. Sci. Rev. Macromol. Chem. Phys., C25 (1), 57.
Debling, J. A., Han, G. C., Kuijpers, F., Verburg, J., Zacca, J., & Ray, W. H.
(1994). Dynamic Modeling of Product Grade Transition for Olefin
Polymerization Processes. AIChE J., 40, No. 3, 506.
Nowlin, T. E. (1985). Low Pressure Manufacture of Polyethylene. Prog. Polym.
Sci., 11, 29.
Short, J. N. (1983). Low Pressure Ethylene Polymerization Processes. In R.P.
Quirk (Ed.), Transition Metal Catalyzed Polymerizations - Alkenes and Dienes.
New York: Academic Pub.
Xie, T., McAuley, K.B., Hsu, J. C. C., & Bacon, D. W. (1994). Gas Phase
Ethylene Polymerization: Production Processes, Polymer Properties, and
Reactor Modeling. Ind. Eng. Chem. Res., 33, 449.

12 Ionic Polymerization
Model
This section covers the ionic polymerization kinetic model available in Aspen
Polymers (formerly known as Aspen Polymers Plus). The cationic, anionic and
group transfer addition polymerization kinetics can be modeled using this
model.
 Ionic Processes, 250
 Specifying Ionic Polymerization Kinetics, 260
Some examples of applicable polymers are given in below:
 Polystyrene - Anionic polymerization is used to produce narrow molecular
weight distribution polystyrenes in small quantities. Cationic
polymerization is used to produce low molecular weight polystyrenes for
coatings and glues. Block copolymers of styrene and butadiene are
produced commercially with anionic polymerization.
 Polyisobutylene - Low-to-medium molecular weight poly isobutylene is
produced commercially by polymerization of high purity isobutylene in
isobutane or hexane diluent using aluminum chloride or hexane trifluoride
as a catalyst.
 Polybutene - Polybutenes are produced in solution by copolymerizing
isobutylene and n-butene using aluminum chloride or hexane trifluoride as
a catalyst.
 Polybutadiene - Block copolymers of styrene and butadiene are produced
commercially with anionic polymerization.
 Polyoxides - Examples are poly ethylene oxide (PEO) and poly propylene
oxide (PPO). Continuous tubular or column reactors or semibatch
12 Ionic Polymerization Model 249

autoclaves are used. The polymerization can be carried out with different
mechanisms: anionic (base catalysis), cationic (acid catalysis), or
coordinate.
Ionic Processes
Many specialty polymers are manufactured by ionic polymerization processes.
For the description of a specific ionic process, refer to the References section.
Ionic polymers fall in the category of addition polymers, i.e., the reactive
species grow in length by continuous addition of monomer units. However,
there are several features that distinguish the ionic polymerization processes
from other addition polymerization processes like free-radical and Ziegler-
Natta:
 Different propagating species are often present in ionic processes. These
species may be free ions, tight ion pairs, loose ion pairs, dormant esters,
etc. Moreover the propagating species are often in equilibrium.
 Association or aggregation phenomena is common in BuLi type of
initiators for anionic polymerization. The associated initiator is not reactive
and is in equilibrium with its dissociated form. The association phenomena
also takes place with growing polymer chains, which reduces the actual
number of chains growing at any given time. This phenomena affects both
the conversion and polymer properties.
 Exchange reaction takes place between live and dormant polymer. The
active species transfer from one polymer to another. This reaction controls
the molecular weight distribution of the final polymer. If the exchange
reaction rate constant >> propagation rate constant, then for increasing
monomer conversion the polydispersity approaches a limiting value of 1.0.
 Ionic reactions are a strong function of solvent, initiator and operating
conditions and are susceptible to poisons.
 Chain transfer and termination reactions may be negligible or absent in
certain polymerization processes thus leading to formation of living
polymers.
In the following sections, the general chemistry of ionic polymerization and
the built-in initiator / polymerization kinetic scheme are described. The kinetic
scheme is based on literature survey of ionic polymerization mechanisms.
Ionic kinetic scheme can model either cationic, anionic or group-transfer
polymerization. The ionic kinetic scheme in Aspen Polymers is a super-set of
all the above mentioned reactions.
Reaction Steps
There are a few key elementary reactions that apply to all ionic
polymerization systems. These include the three basic reaction steps:
 Formation of active species
 Chain initiation
250 12 Ionic Polymerization Model

 Propagation
There is almost no chain transfer in living polymerization. There are additional
reactions for each chemistry which will be discussed later. There can be
different forms of propagating species, e.g., free-ions, ion-pairs, and dormant
esters. A given ionic polymerization system can have different combinations
of these propagating species.
To account for different propagating species, the same framework is used as
the Ziegler-Natta multi-site kinetics model. In the ionic model, each site
refers to a unique type of active species. To model three propagating species
for an initiator, the model will have three sites with each site corresponding to
the unique propagating active species type. In this framework, the polymer
produced by dormant esters will be stored in live polymer attributes for the
selected dormant ester site.
Polymer Molecules Tracked
There are three different types of polymer molecules tracked by ionic kinetic
scheme:
 Pn,k
i - live polymer molecule chains of length n with active segment k
attached to the active center of type i.
For example, free-ions can be site 1, ion-pairs as site 2 and dormant
esters as site 3. The propagation rate constant for dormant esters ( k p for
site 3) may be zero.
 in
Q - associated (or aggregate) polymer molecule chains of length n
formed by association of propagating species of type i.
The site based aggregate polymer attributes contain the information about
polymer formed by association of different propagating species. For
example, only the ion pairs propagating species may associate in case of
BuLi type of initiators.
 in
D - dead polymer molecule chains of length n formed by active
propagating species of type i.
The site based bulk polymer attributes contain information about the bulk
polymer which is a sum of live, aggregate and dead polymer.
Initiator Attributes
The initiator in ionic model has three attributes which are solved along with
moment equations:
Pi Pt i C
i
 P0FLOW; ,  PT0FLOW;  CIONFLOW
0 0 I
These variables are provided as attributes so that they can be used in user
kinetics to add side reactions. For example, a transfer species (Pt, i )
0 may
undergo a side reaction with other components; addition of a salt with same
counter ion (C i ) I
may tilt the polymerization in one direction by allowing
counter-ion to be in equilibrium with ion concentrations from other salts. The
initiator decomposition reactions (involving Pi
0 or Im ) can also be modeled in

252
Aspen Plus as user reactions which can be solved simultaneously with built
ionic kinetics in Aspen Polymers.
The built-in initiator and polymerization kinetic scheme
Built-In Ionic Polymerization Kinetic Scheme
built-in
is shown in here
:
12 Ionic Polymerization Model

The nomenclature used in the ionic polymerization kinetic scheme is shown
here:
Symbol Description
AChain transfer agent, m
m
AIm
Associated initiator, m
bFC
Coefficient (= 0 when catalyst does not participate in the
reaction)
bTCI
Coefficient (= 0 when C-ion does not participate in the
reaction)
i Counter ion (C-ion) corresponding to active species of
CI
type i
Cn
Catalyst, n
Dn i
Dead polymer chain length of n produced by active
species of type i
dEQL
reaction)
dEXA
Coefficient (= 0 when Po does not participate in the
reaction)
dFC
reaction)
dI 2
Coefficient (= 0 when C-ion is not formed in the reaction)
I p
Initiator, p
Mj
Monomer, j
nm,p Association number for initiator dissociation reaction
Pi
Active species of type i (chain length 0)
0
Pt,i
0
Transfer active species of type i (chain length 0)
i

P
j,j
Active species of type i with active segment j (chain length
1)
i Growing species chain of length n of type i with active
Pn,k
segment k
i Associated polymeric species of chain length n with active
Qn, k
segment k
Tm
Terminating agent, m
Xm
Exchange agent, m
The ionic model is a terminal model, implying that the rate constants are
functions of only terminal segment of the polymer chain.

o Copolymerization
For i
copolymerization, the built-in kinetic scheme allows the user to specify
the number of monomer types used. Similarly the user has the flexibility to
specify the number of each type of reactive species present in the
polymerization:
 Associated initiators
 Initiators
 Catalysts
 Exchange agents
 Chain transfer agents
 Termination agents
The user is able to tailor the built-in kinetics to model a specific
polymerization system by selecting a subset of the reactions shown in the
Built-in Ionic Polymerization Kinetic Scheme figure on page 252.
The rate constants for each reaction for active species of type i are calculated
at the reaction temperature using the Arrhenius equation shown below. The
user specified rate constant parameters are pre-exponential factor (k ) and
the activation energy (Eai ) at active species of type i:
Rate Constant

 
k i
k i
-

 
exp
1 1
 
o
i
Ea
R T T
ref

 

 
Where:
ko = Pre-exponential factor in 1/sec for first order reactions
and m3/kmol-sec for second order reactions
Ea = Activation energy in mole enthalpy units
R = Universal constant
T = Reaction temperature in Kelvin
Tref = Reference reaction temperature in Kelvin (default is
1E38)
Formation of Active Species
The active species are the initiator in dissociated form:
AI 
n m,p
I m
p The association and dissociation of initiator is observed in alkyl-Lithium type
of initiators in nonpolar solvents for anionic polymerization. n-butyl-Li exists
as hexamer whereas s-BuLi and t-BuLi exist as tetramers for styrene
polymerization. The dissociated initiator further reacts with monomer to form
growing polymer with unit chain length in chain initiation step. This reaction
can also be used to represent self-ionization of some strong acids

(AlCl , AlBr , TiCl ) in cationic polymerization, with nm,p being the degree of
3 3 3 ionization:
I + b C  P i
+ d C i m FC n
0
FC I
The active species Pi
0 is formed by this reaction. Several initiators
(KNH , NaNH 2 2 ) decompose to form an active species (or dissociate into
ions) in anionic polymerization (b , d ) FC FC  0  1 . Polystyrene is
manufactured using KNH2 initiator.
With no reverse reaction, the electron transfer initiation with light
(electrochemical initiation) is also a special case of the above scheme for
anionic polymerization. Initiator and catalyst are used in cationic
polymerization with no counter-ion (d ) FC  0 . In case of anionic
polymerization, a starter may be used to generate an active species.
For polyether polyols (polypropylene oxide), initiator is ROH and catalyst is
KOH (weak base) and the reaction is only in forward direction.
The above scheme can also represent donar-accepter equilibria and self
dissociation of acids in cationic initiation (A+B A-+B+ ) .
Chain Initiation
The active species incorporate monomer to form propagating species with
unit chain length:
Pi M P
i
0  
j 
j,j
I The initiator i
(in dissociated form) directly reacts with monomer to form
propagating species with unit chain length. A counter-ion may be formed
(d  1 ) :
I 2 I + M  P i
+ d C m j  j,j
I 2
The transfer active species incorporate monomer to form propagating species
with unit chain length:
Pt,i M P
i
0  
j 
j,j
Propagation
The growing polymer with an active species at the end of the chain may grow
or propagate through the addition of monomer molecules to form long
polymer chains. The propagation reaction is represented by:
P i
 M  P i n,k
j n+ 
j , j
where monomer j is being added to a polymer chain of length n, with an
active segment of type k and active species of type i. The resulting polymer
chain will be of length n+1 and the active segment will be of type j. The

active segment type usually represents the last monomer type incorporated
into the polymer chain.
Copolymerization
For copolymerization, there will be N * N * N propagation reactions that
m m site may have different reactivities. For example, with two monomers and three
site types, the monomer being added could be monomer 1 or monomer 2
while the active segment type could be segments from monomer 1 or
monomer 2 at each site type. As a result, there will be twelve rate constants
( ki ) p , kj
, where the subscript k refers to the active segment type while the
second subscript j refers to the propagating monomer type. The superscript i
refers to active species type.
For the terminal model the rate of propagation is dependent only on the
concentration of live polymer with active segment k on active species i and
the concentration of the propagating monomer j.
Association or Aggregation
The propagating species initiated by alkyl-Lithium type of initiators in anionic
polymerization also exhibit the association phenomena like the initiator. The
association of live polymeric species is usually dimeric in nature. The
associated polymer Qi
n  m, k
is tracked as a separate polymer and does not
participate in any other reactions:
P i
+P i
 Q i n, k
m, k
n 
m, k
Exchange
Exchange reactions exchange the growing active species between two
different growing polymers. If both free ions and ion pairs are growing, then
the counter-ion can exchange between the two polymeric species. There can
be exchange reaction between dormant polymer (with ester as growing
species which does not propagate) and ion pairs/free ions. The exchange
reaction can also take place between an exchange agent (e.g., alcohol end
group in solvent or starter) and a growing polymer. If exchange reaction with
a small molecule does not produce a Pspecies, then d 0. The exchange
0 EXA between growing species and dormant species takes place in polyether
polyols (propylene oxide). The dormant species can be an alcohol:
P i
+ P j
 P j
+ P i
n,k
m,p
n,k
m,p
i
  j
 i 0
P X P d P n,k
m n,k
EXA
Equilibrium with Counter-Ion
The following reaction represents the equilibrium between free ions and ion
pairs, hence the name equilibrium with counter-ion (d ) EQL  1 . The

spontaneous ionization reaction can also be represented by this reaction when
d 0 EQL :
P i
 P j
 d C j
n,k
n,k
EQL I
Chain Transfer
There are four types of chain transfer reactions:
 Spontaneous
 Monomer
 Dormant polymer formation
 Chain transfer agent
Spontaneous chain transfer can lead to formation of a dead polymer molecule
and an active species caused by proton loss, e.g., cationic polymerization of
poly isobutylene:
Spontaneous P i
 D + P i n,k
0
n i
n Chain transfer i
to monomer can take place with hydride abstraction from an
olefin, for example, cationic polymerization of polyisobutylene and butyl
rubber:
Monomer P i
+ M  D + P i n,k
j 
j, j
Chain transfer to monomer in polyethers (propylene oxide) can form dormant
species (alcohol) . The dormant species is modeled as a live polymer with a
different site type but it does not have the usual chain initiation and
propagation reactions. This dormant polymer can participate in exchange
reactions:
Form dormant polymer P i
+ M  P j
+ P i n,k
p n,k

p, p
n The growing i
polymer chain can also be transferred to a chain transfer agent,
A, leading to formation of a transfer active species of the same type, i. The
reaction rate order wrt. to chain transfer agent can be specified by the user:
Chain transfer agent P i
+ A  D + P t,i n,k
m 0
Chain Termination
The growing polymer chain with ion pairs as active species can be
spontaneously terminated by combination with counter ion (b  0 ) , e.g.,
TCI cationic polymerization of polystyrene, tetrahydrofuran, polyisobutylene. A
growing free ion active species can terminate by reacting with its own counter
ion (b  1 ) :
TCI Counter-ion P i
+ b C i
D n,k
TCI I
n i

The chain can terminate after reacting with a chain terminating agent to form
a dead polymer. Any small molecule can act as a chain terminating agent.

n i
The reaction rate order wrt. to terminating agent can be specified by the
user:
Terminating agent P i
+T 
D n,k
m Coupling
Coupling reactions are encountered in thermo-plastic elastomer production.
For example, to make styrene-butadiene-styrene (SBS) TPE, styrene is added
first, and then half of the butadiene is added. Introducing a coupling agent to
this reaction system will form SBS polymer. In this example i=j=1 and k=2.
P i
 P j

P k
n m
n  m
Another mechanism represented by this reaction is higher order association of
polymeric chain. Dimeric association can be modeled by the association
reaction, but the coupling reaction should be used to model higher order
association of polymer chains. In a given simulation, the coupling and
association reactions are mutually exclusive.
Model Features and
Assumptions
Following are the model features and assumptions used in the ionic
Phase Equilibria
options form.
phase.
Rate Calculations
The ionic polymerization kinetic model supplies to the reactor models the
reaction rates for the components and the rate of change of polymer
attributes (e.g. the chain length distribution moments) :
 The component reaction rates are computed from the kinetic scheme by
summing over all reactions that involve the component.

 The site based moment rates are derived from a population balance and
method of moments approach similar to that described in the Calculation
Method section on page 185.
Additionally, the moment definitions are modified to include the aggregate
polymer as separate and as a part of bulk polymer. The attributes calculate
and report up to third moments of live, aggregate and bulk polymer. The
moment definitions are:
Polymer Moment Definition
i
Live Polymer, Pn,k

i f
n P , , 
 f k
i
n k
n
i
Aggregate Polymer, Qn,k

i f
n Q , , 
 f k
i
n k
n
Dissociated Aggregate
Polymer, Qi
n  m ,
k
   
i f
n Q , ,  
 f k
i
n m k
n m
Bulk Polymer 
  
 
  
i f

n i f k
  
    
k

f
i
n P Q D
n k
i
n k
Nseg
k
i
Nseg
k
i
, , 
f k
 
Nseg
k
, ,
f
n i

n
n D

on the polymer attributes selected, and the subset of the built-in kinetics used
for a specific simulation:
 Zeroth, first and second moments for the composite and site based bulk
polymer
 Zeroth and first moments for the composite and site based live polymer
and aggregate polymer
 Number and weight degree of polymerization and polydispersity index for
the composite and site based bulk polymer (DPN, DPW, PDI and SDPN,
SDPW, SPDI)
 Number and weight average molecular weight for the composite and site
based bulk polymer (MWN, MWW and SMWN, SMWW)
 Copolymer segment composition for composite and site based bulk
polymer (SFRAC and SSFRAC segment mole fractions)
 Mole fraction of bulk polymer chains that are live (LPFRAC and LSPFRAC)
 Mole fraction of bulk polymer chains that are aggregated (APFRAC and
ASPFRAC)
 Number average degree of polymerization for live polymer (LDPN and
LSDPN)
 Number and weight average degree of polymerization for aggregate
polymer (ADPN, ADPW, ASDPN and ASDPW)

 Copolymer segment composition for live and aggregate polymer (LSFRAC,
ASFRAC, LSSFRAC and ASSFRAC)
 Live polymer active segment composition (LEFRAC and LSEFRAC)
These variables are stored as component attributes. See Chapter 2 for a
description of these component attributes. It is assumed here that attributes
needed for the kinetic scheme are selected. For each live polymer attribute,
there is also a corresponding aggregate polymer attribute.
Specifying Ionic Polymerization
Kinetics
Accessing the Ionic Model
To access the Ionic polymerization kinetic model:
5 Select Ionic as the reaction type and click OK.
Specifying the Ionic Model
The Ionic model input forms are as listed below. Use these forms to define
reacting species and enter reaction rate constant parameters:
Use this sheet To
Options Specify the reacting phase
You must specify the reacting species on the Species sheet:
2 In the Monomers field, list the reacting monomers.
For each monomer, in the goes to  field, specify the polymer segment
that the monomer converts to.
3 Continue listing other types of reacting species, for example, solvents,
transfer agents, etc.

Listing Reactions
You can build a list of reactions on the Reactions sheet. In the Reaction
summary listing for each reaction, the first column indicates the reaction
type. The second column lists the reactants, and the last column lists the
products. The Data Browser window can be resized to better view the reaction
listing. Use the following options:
Click To
selector
reactions
Click To
Hide/Reveal
calculations
Delete
Adding Reactions
subform:
2 In other reactant (for example, Initiator, Catalyst) fields enter the
 or 
 or 
 or 
Editing Reactions
To add or edit a reaction, click Edit to open the Edit Reaction subform:

 or 
1 In the ko(fwd) or (rev) field, enter the pre-exponential factor for
forward or reverse reaction.
2 In the Ea(fwd) or (rev) field, enter the activation energy for forward or
reverse reaction.
4 In the Order field, enter the order.
5 In the Asso. No. field, enter the polymer association number.
6 In the Coeff. b and Coeff. d fields, enter coefficients b and d.
parameters.
 or 
References
Bikales, M., Overberger, & Menges. (1985). Encyclopedia of Polymer Science
and Engineering, 2nd Ed. New York: Wiley Interscience.
Chang, C. C., Miller, J. W., & Schorr, G. R. (1990). Fundamental Modeling in
Anionic Polymerization Processes. J. of Appl. Pol. Sci., 39, 2395-2417.
Chang, C. C., Halasa, A. F., & Miller, J. W. (1993). The Reaction Engineering
of the Anionic Polymerization of Isoprene. J. of Appl. Pol. Sci., 47, 1589-1599.
Compton, R. G. (Ed.). (1992). Mechanism and Kinetics of Addition
Polymerizations. Comprehensive Chemical Kinetics, 31.
Fathi, H., Hamielec, A. E., & Davison, E. J. (1996). Modelling of Anionic
Solution Polymerization of Butadiene - The Effects of Chain Termination and
Long Chain Branching on Molecular Weight Distribution Development. Polymer
Reaction Eng., 4, No. 4.

Kennedy, J. P., & Squires, R. G. (1967). Contributions to the Mechanism of
Isobutene Polymerization I. Theory of Allylic Termination and Kinetic
Considerations. J. Macromol. Sci., A1(5), 805-829.
Kirk-Othmer. (1991). Encyclopedia of Chemical Technology, 4th Ed. New
York: Wiley Interscience.
Moore, J. G., West, M. R., & Brooks, J. R. (1979). The Anionic Solution
Polymerization of Butadiene in a Stirred-Tank Reactor. ACS Symp. Ser., 104.
Muller, et. al. (1995). Kinetic-analysis of Living Polymerization Processes
exhibiting slow equilibria. Application to group transfer and cationic
polymerizations. 5th International Workshop on Polymer Reaction
Engineering, 131, 9-11 October, Berlin: DECHEMA.
Odian, G. (1981). Principles of Polymerization, 3rd Ed. New York: Wiley
Interscience.
Pepper, G. C. (1957). Cationic Polymerization. Proc. of the Intl. Symp. on
Macromol. Chemistry. Prague.
Szwarc, M. (1996). Ionic Polymerization Fundamentals. New York: Hanser.
Treybig, M. N., & Anthony, R. G. (1979). Anionic Styrene Polymerization in a
Continuous Stirred-Tank Reactor. ACS Symp. Ser., 104.

13 Segment-Based Reaction
Model
This section describes the segment-based power-law reaction model available
in Aspen Polymers (formerly known as Aspen Polymers Plus).
 Segment-Based Model Allowed Reactions, 267
 Specifying , 285
The segment-based power-law reaction model can be used to simulate
polymerization reactions using a simple power-law type rate expression. This
may be useful when simulating new processes that do not fit well into the
other built-in models in Aspen Polymers, or when a very detailed mechanistic
reaction model is not necessary.
The segment-based power-law model is the best choice for simulating step-growth
addition processes—for example, the production of polyurethane.
This model may also be used to represent processes involving changes to
polymer segments. The underlying kinetics are basic power law reactions in
which segments and monomeric components may participate. Some
examples of applicable polymers are:
 Polyvinyl alcohol (PVA) - Alcoholysis of polyvinylacetate
 Chlorinated polyethylene (CPE) - Chlorination of polyethylene
 Polymethylmethacrylate (PMMA) - Recovery of methylmethacrylate from
PMMA
 Polyisobutylene - Chain scission of polyisobutylene
13 Segment-Based Reaction Model 265

Step-Growth Addition Processes
Step-growth addition processes involve reactions between two functional
groups to produce a new functional group without the loss of low molecular
weight condensates. For example, in the production of polyurethane polymers
a diol is reacted with a diisocyanate to produce an alternating copolymer with
urethane linkages between the monomer units:
O
HO R OH + O=C=N X N=C=O R OCNH
O
X NHCO
diol diisocyanate polyurethane
These reactions are usually irreversible. The individual reaction steps can be
simulated using the segment-based power-law model.
Polymer Modification Processes
The conventional route for synthesizing commercial polymers is through the
polymerization of a monomeric compound. These polymerization reactions fall
under different categories depending on the nature of the monomer and its
growth mechanism.
However, once synthesized, polymers may undergo further reactions. In
some instances, these reactions may be undesirable side reactions, in which
case they may be considered as degradation reactions. In other cases, the
only mechanism for producing certain polymers may be through the
modification of a starting polymer. Typically, this situation occurs if a
monomer is not readily available for that polymer. For example, polyvinyl
alcohol is produced by alcoholysis of polyvinyl acetate.
Modification reactions are often used to improve polymer properties such as
oil resistance (chlorosulfonation of polyethylene), heat resistance (chlorination
of polyethylene), solubility ("-cellulose), and flammability (natural rubber).
There are also a few cases where it is economically desirable to react scrap
polymer for monomer recovery (methyl methacrylate from polymethyl
methacrylate) (Rodriguez, 1989).
Reaction Categories
Regardless of the end effect of the polymer modification reaction, the events
taking place fall into one of two categories based on the site where they occur
on the polymer chain. The reactions may take place on:
 Side groups
 Polymer backbone: scission, depolymerization, cross-linking, or bond
changes
There are some fundamental issues that distinguish reacting polymers from
their low molecular weight counterparts. One obvious characteristic of
reacting polymers is the potential for steric hindrance. A reacting side group
may be too close to the polymer chain, for example. There may also be
changes in solubility as reaction progresses.
Furthermore, crystallinity has an effect on the polymer reactivity; in general,
for a semicrystalline polymer, only the amorphous region is able to react.
266 13 Segment-Based Reaction Model

Finally, an important difference that characterizes polymers is the fact that a
higher local concentration of reacting functional groups is observed than that
indicated by the overall polymer concentration (Odian, 1991).
Segment-Based Model Allowed
Reactions
The reaction categories allowed in the segment-based reaction model, along
with a brief summary of the conditions where each of these reactions may
occur, is shown here:

Segment Based Model Reaction Categories
Conventional Species
Reactions involving all non polymeric species fall under this category.
Monomeric components may react among themselves to produce
intermediate species. These reactions are represented as Category I in the
Segment Based Model Reaction Categories figure on page 268.

Side Group or Backbone Modifications
Polymer modification reactions aimed at altering end properties involve in
most cases side group or backbone modifications. In such reactions, groups
attached to the polymer chain are substituted. One example is that of the
alcoholysis of polyvinyl acetate to produce polyvinyl alcohol:
CH3
C
O
O
OH
CH + CH3OH + CH3CO2CH3
CH2 CH CH2
Another example is the chlorination of polyethylene to produce chlorinated
polyethylene (CPE):
CH2 + Cl2 CHCl + HCl
Side group and backbone reactions are illustrated as reaction Category II in
the Segment Based Model Reaction Categories figure on page 268.
Chain Scission
A common polymer degradation reaction is chain scission. In this case, bonds
are broken along the polymer chain resulting in shorter polymer molecules
with lower molecular weight. Chain scission may be induced by several
factors. One example is the scission of polyisobutylene upon oxidation:
CH3
CH2 C CH2
CH2
CH3
CH2 C
+ CH2
CH2
Some scission reactions may involve a monomeric component, such as an
acid or base:
CH2 – CH2 + HCl CH2Cl + CH3
Chain scission reactions are represented as Category III reactions in the
Depolymerization
Depolymerization is the reverse of the propagation step of a polymerization
reaction. In such reactions, monomer molecules are lost from the polymer
chain. Depolymerization is often considered a degradation reaction. There
are, however, cases where it is brought on by design to recover monomer
from scrap polymer. An example depolymerization reaction is that of
polymethyl methacrylate to regenerate methyl methacrylate:

CH3 CH3
C O
O
CH3
CH2 C CH2 C
C O
O
CH3
CH3
CH2 C
C O
O
CH3
CH3
C O
O
CH3
+ CH2 C
Depolymerization is illustrated as Category IV in the Segment Based Model
Reaction Categories figure on page 268.
Propagation
Propagation reactions involve the addition of monomers to the end of a
growing polymer chain. Propagation is illustrated as Category V in the
Combination
There are other mechanisms through which polymer segments react with
each other. Some of these reactions, grouped as combination reactions,
include kinetic events where two polymer molecules combine into one. These
reactions are represented as Category VI in the Segment Based Model
Reaction Categories figure on page 268.
Branch Formation
Branch formation occurs when a polymer molecule attaches to another
polymer chain, converting a repeat unit to a branch point. Monomers can also
react with repeat units to initiate branch formation. Branch formation is
illustrated as Category VII in the Segment Based Model Reaction Categories
figure on page 268.
Cross Linking
Cross linking occurs when a repeat unit in one chain reacts with a repeat unit
in another chain, forming a cross link (branch 4) segment. Cross linking is
illustrated as Category VIII in the Segment Based Model Reaction Categories
figure on page 268.
Kinetic Rate Expression
The segment-based reaction model uses a modified power-law rate
expression where the rate of reaction is calculated as the product of the
reacting species concentrations with a rate constant representing the specific
reactivity of the reaction. The kinetic rate expression in the segment-based
model is described below:

Equation
b
Ea


 1 1
  
i

 
k Catalyst k e T
i


Tref specified   i
i  
 
, [ ]
net i i o i U flag
T
ref
R T T
ref




Ea
i

Tunspecified *  [ ]   ref ,
i
k Catalyst i
e RT b
iU flag
net i i k o i T Assign User Rate Constants is used:    
 
ratem 
activitym C mj
k ,
aj
j i net i
 
ratem C k mj
,  
aj
 
Assign User Rate Constants is not used: net m j
Nomenclature
Symbol Description
m User reaction number
i Rate constant set number
j Component number
 Product operator
Cj
Concentration* of component j, mol/L
i 
Catalyst order term for catalyst i (default = 1)
mj  Power-law exponent for component j in reaction m
ko
Pre-exponential factor in user-specified inverse-time and concentration units**
net ,i k Net rate constant for set i assigned to reaction m
knet,m Net rate constant for reaction m
T Temperature, K
Tref
Optional reference temperature. Units may be specified, they are converted to K in the
model. Defaults to global reference temperature (Global Tref) specified on the Specs sheet.
flag User flag for rate constant set i. This flag points to an element of the user rate constant
array.
U User rate constant vector calculated by the optional user rate constant subroutine. The user
flag indicates the element number in this array which is used in a given rate expression.
When the user flag is not specified, or when the user rate constant routine is not present,
this parameter is set to 1.0.
* The concentration basis may be changed to other units using the Concentration basis field on the
Specs sheet or using the optional concentration basis subroutine.
** The reference temperature may be specified globally on the Specs sheet or locally for each rate
constant set on the Rate-Constants sheet. If global and local reference temperatures are both
unspecified then this form of the equation is applied.

Customizing the Rate Expression; User Rate Constant
Subroutine
You can modify the standard rate expression using the optional user rate
constant feature. The rate constant form includes a parameter called the
“user flag” that identifies an element in an array of user rate constants. This
array is calculated by a user-written Fortran subroutine. The standard rate
expression is multiplied by the user rate constants as shown above. See
Program FilesAspen Plus <version>engineuserUSBRCN.f for a
template for this routine.
Concentration Basis for Rate Calculations
Component concentrations depend on the calculation basis: molarity, mole
fraction, mass fraction, mass concentration, etc. The polymer mole fraction is
converted into its segment mole fractions according to the following equation:
Mw
Frac Frac SFRAC i
p
avg
,  * ( )*
s i p Mwseg
Where:
Fracs,= Segment mole fraction
i SFRAC(i) = Polymer segment fraction (component attribute)
Mwp = Polymer molecular weight
Mwsegavg =
Nseg
1 
Average segment molecular weight = SFRAC i Mw
( )* i
User Concentration Basis Subroutine
Alternately, a user basis subroutine can be used to calculate the component
concentrations and the reacting-phase holdup basis used in the component
and attribute conservation equations. Use this subroutine when rate constants
are available in unusual concentration units not found in Aspen Polymers, or
when the reacting phase volume or area calculated by the reactor model is
not consistent with the real reactor (for example, in plug flow reactors with
fixed liquid level). The segment-based model and step-growth model can use
the same basis routine. See Program FilesAspen Plus
<version>engineuserUSRMTS.f for a template for this routine.
Model Features and
Assumptions
The following assumptions are built into the segment-based reaction model:
 All reactions between two segments are intermolecular; ring formation
reactions are specifically excluded unless the ring molecules are tracked
as separate oligomer components

 Reactions may occur anywhere in the polymer chain
 Mass balance holds for components involved in the reactions on segment
basis
 Moment of chain length distribution calculations cover up to the first
moment (ZMOM, SFLOW, FMOM). Higher moments (SMOM, TMOM) are
not predicted by the current version of the model
 Since higher moments not covered, segment-based model should be last
in reaction block sequencing
The segment-based reaction model calculates and returns the following
information:
 Rate of change for all components involved in reaction scheme, and rate
of change for all segments
 Polymer segment composition (SFLOW, SFRAC, EFRAC)
 Zeroth moment of chain length distribution (ZMOM)
 First moment of chain length distribution (FMOM)
 Number average degree of polymerization (DPN)
 Number average molecular weight (MWN)
 When the Reacting Site is specified on the Specifications form, the
model will calculate rates for the zeroth moment, first moment, and
segment flow rates at the specified site (attributes SZMOM, SFMOM, and
SSFLOW for the specified site number). These attributes are used to
calculate the composite attributes listed above.
This information is returned through the stream compositions for the
component rate of change, and through the polymer component attributes for
the segment rate of change and moment calculations.
The rate of change of polymer mass is calculated as follows:
R
 , *
1
R Mw
s i i
Nseg

p Mw
p
This is the sum of the rates of change of segment masses.
Each segment type is assigned a value , which indicates the number of
“points of attachment” connecting the segment to other segments in the
polymer chain:
Segment Type 
End 1
Repeat 2
Branch-3 3
Branch-4 4

The rate of change of the zeroth moment ( 0 ) is calculated from the rate of
change of the first moment ( 1 ) and the segment type ():

0 1 1  



2
t 
t t


The factor of ½ accounts for the fact that each “connection” links two
segments (without this correction the points of connection are counted twice).
This method is best illustrated through these examples:
Valid Reaction Type† Stoichiometry†
Δλ1 ½ Δλ0
Yes Initiation MMP2 M + M  E + E +2 +1 +1
No Initiation M P1 M  R +1 +1 0
Yes Propagation
(addition) n n 1 P M P  E + M  R + E +1 +1 0
Yes Propagation
(insertion)
Pn *
MP *
M  R +1 +1 0
n  1
Yes Combination
Pn  Pm Pnm E + E  R + R 0 +1 -1
Yes Combination
Pn  Pm Pnm E + E  R -1 +0 -1
Yes Branching
Pn M Pn1 R + M  B3 + E +1 +1 0
Yes Branching
Pn  Pm Pnm R + E  B3 + R 0 +1 -1
Yes Cross linking
Pn  Pm Pnm R + R  B4 -1 +0 -1
† M = Monomer; E = End group segment; B3 = Branch-3 segment; B4 = Branch-4 segment
This method lets you specify most classes of reactions, however special care
must be taken to ensure that the reaction is defined in a manner that is
consistent with the previous equation. In particular, the segment-based
model does not allow initiation reactions of the type 1 MP since the
equation does not account for the initial formation of polymer molecules
through this mechanism. Note, however, that this mechanism is valid since
the same reaction can represent an insertion type propagation step in which
the active polymer end group is conserved.
User Subroutines
The segment-based power-law model can be customized by applying user-written
subroutines. There are two types of subroutines available. The
concentration and holdup basis for the model can be changed through a user
basis subroutine. A user rate-constant subroutine can be used to extend the
standard reaction rate expression. These routines can be used together in any
combination.

User Basis Subroutine
The user basis subroutine can be used to calculate the component
concentrations and the reacting-phase holdup (typically volume in a CSTR or
batch reactor or active area in a PFR). This routine can also be used to
calculate rates of change of components and component attributes. Use this
subroutine when rate constants are available in unusual concentration units
not found in Aspen Polymers, or when the reacting phase volume or area
calculated by the reactor model is not consistent with the real reactor (for
example, in plug flow reactors with fixed liquid level).
This subroutine can be used in conjunction with Fortran blocks and user
component attributes to calculate mass-transfer rates and to account for the
influence of mass-transfer limitations on the component concentrations in the
reacting phase.
The argument list for the user basis routine is provided here. This argument
list is prepared in a Fortran template called USBBAS.F, which is delivered with
Aspen Polymers.
SUBROUTINE USBBAS
3 NINTB, INTB, NREALB, REALB, NINTM,
4 INTM, NREALM, REALM, NIWORK, IWORK,
6 X1, X2, Y, DUM1, FLOWL,
7 FLOWL1, FLOWL2, FLOWV, FLOWS, VLQ,
8 VL1, VL2, VV, VSALT, VLIQRX,
9 VL1RX, VL2RX, VVAPRX, VSLTRX, RFLRTN,
* IFLRTN, CRATES, NTCAT, RATCAT, CSS,
1 VBASIS, IPOLY, NSEG, IDXSEG, AXPOS,
2 TIME )
NSUBS Input INTEGER Number of substreams in stream
vector
IDXSUB Input INTEGER NSUBS Location of substreams in stream
vector
1=MIXED
2=CISOLID
3=NC
weights
IDSCC Input HOLLERITH 2,NCC Conventional component ID array
NBOPST Input INTEGER 6, NPO Property method array

Integer and Real Parameters, page
154)
154)
NINTM Input INTEGER User-specified length of INTM array
INTM Retention INTEGER NINTM User subroutine integer parameters
(See Integer and Real Parameters,
page 154)
NREALM Input INTEGER User-specified length of REALM array
REALM Retention REAL*8 NREALM User subroutine real parameters (See
154)
vector
vector
page 155)
Dum1 Dummy REAL*8 (1) Argument reserved for future
application
FLOWL Input REAL*8 Total liquid flow rate, kmol/sec
FLOWL1 Input REAL*8 First liquid flow rate, kmol/sec
FLOWL2 Input REAL*8 Second liquid flow rate, kmol/sec
FLOWV Input REAL*8 Vapor flow rate, kmol/sec
FLOWS Input REAL*8 Salt flow rate, kmol/sec
VL Input REAL*8 Total liquid molar volume, m3/ kmol
VL1 Input REAL*8 First liquid molar volume, m3/ kmol
VL2 Input REAL*8 Second liquid molar volume, m3/ kmol
VV Input REAL*8 Vapor molar volume, m3/ kmol
VSALT Input REAL*8 Salt molar volume, m3/ kmol

RFLRTN Retention REAL*8 (1) Real retention for FLASH
IFLRTN Retention INTEGER (1) Integer retention for FLASH
CRATES Output REAL*8 NCC Component rates of change, kmol/m3-
sec
NTCAT Input INTEGER Number of component attributes
cat/m3-sec
CSS Output REAL*8 NCC Concentration vector for the active
phase
VBASIS Output REAL*8 Holdup basis used to calculate reaction
rates*
AXPOS Input REAL*8 RPlug only: axial position, m
TIME Input REAL*8 RBatch only: time, sec
* When using molar concentrations, this parameter is volume of the reacting phase in m3
in RCSTR and RBatch or the cross-sectional area of the reacting phase in m2 in RPlug.
Note: The argument lists for the segment-based user basis routine and step-growth
user basis routine are identical. Both types of models can reference
the same basis routines.
Example 1 illustrates how to use the user basis routine to convert the
concentration basis from the standard molar concentration basis (mol/L) to a
mass concentration basis (mol/kg). (Note: the current version of Aspen
Polymers supports several concentration basis through the BASIS keyword
located on the Specs sheet. This example is a demonstration). Using these
units, the reaction rates are calculated in units of mol/kg-sec. These rates are
multiplied by the holdup basis (VBASIS) for the reactor in the segment-based
power-law model. The holdup basis must be consistent with the concentration
basis, e.g., in this case it must be in kg. The holdup basis pertains to the
reacting phase, it does not include the phases that do not react.
Example 1: A User Basis Routine For the Mass-Concentration Basis
X
C

i M
i
Liquid
Ci = Mass-concentration of component i

Xi = Mole fraction of component i
MLiquid
= Average molecular weight of components in the
liquid phase
CALL PPMON_VOLL( TEMP, PRES, X, NCPMX, IDXM,
1 NBOPST, GLOBAL_LDIAG, 1, VLQ, DVS, KER)
C-unpack the mole fraction vector into the molar concentrations...
C ---------------------------------------------------------------
C
C concentration (mole/kg)=(mole I / mole liquid )*( mole liquid/kg)
C
C ---------------------------------------------------------------
CSS(I) = CSS(I) * 1.D3 / STWORK_XMWL
10 CONTINUE
C ---------------------------------------------------------------
C
C reacting phase basis must be consistent with concentration basis (kg)
C liquid mass inventory = liquid volume * density
C
C ---------------------------------------------------------------
VBASIS = VLIQRX * STWORK_XMWL * 1.D-3 / VLQ
RETURN
The plug flow reactor model in Aspen Plus assumes that the vapor and liquid
move at the same velocity through the reactor (e.g., no-slip conditions). This
assumption is not consistent with the physical reality of polymer finishing
reactors or wiped-film evaporators. The subroutine in Example 2 circumvents
the no-slip assumption in RPlug, allowing you to specify the volume occupied
by the liquid phase. In this example, you specifiy the first integer argument in
the RPlug block as “1” and the first real argument as the volume fraction of
the reactor occupied by the liquid phase.
Example 2: A User Basis Routine to Specify Liquid Volume in RPlug
UFRAC = 1.D0
IF ( REALB(1) .NE. RGLOB_RMISS ) UFRAC =
REALB(1)
IF ( INTB(1).EQ.1 ) THEN
C - unpack the mole fraction vector into the
molar concentrations...
C - concentration = mole fraction divided by molar
volume of phase
CSS(I) = CSS(I) / VLQ
20 CONTINUE
C - multiply total reactor volume by user-specified
volume fraction -
VBASIS = ( VLIQRX + VVAPRX ) * UFRAC

C - this line makes RPlug calculate liquid residence
time (not L+V)
SOUT(NCOMP_NCC+8)=(SOUT(NCOMP_NCC+9)/
SOUT(NCOMP_NCC+6)) / VLQ
RETURN
END IF
User Rate-Constant Subroutine
The user rate constant subroutine can be used to modify rate constant
parameters for model-generated and user-specified reactions. Use this
routine to modify the standard power-law rate expression for non-ideal
reaction kinetics.
The user rate constant feature can be used to modify the standard power-law
rate expression. This subroutine returns a list of real values, which are stored
in an array “RCUSER”. The length of this array is defined by the keyword
NURC (number of user rate constants) in the user rate constant subroutine
form (USER-VECS secondary keyword). Each of the elements in the user rate
constant array can store a different user rate constant. The USER-FLAG
keyword in the Rate Constants form is used to specify which user rate
constant is used with a particular set of rate constants.
Elements 1 through “NURC” of RCUSER are calculated by a user rate-constant
subroutine. The standard rate expression is multiplied by the USER-FLAGth
element of the user rate constant vector RCUSER. For example, if the
USER-FLAG field contains the number “4”, the power-law rate term will be
multiplied by the fourth element of array RCUSER. By default, the USER-FLAG
keyword is set to zero. The zeroth element of the RCUSER array is set to a
value of 1.0, so the rate expression remains unmodified unless the USER-FLAG
keyword is specified.
The argument list for the subroutine is provided here. This argument list is
prepared in a Fortran template called USBRCN.F, which is delivered with
Aspen Polymers.
SUBROUTINE USBRCN
3 NINTB, INTB, NREALB, REALB, NINTR,
4 INTR, NREALR, REALR, NIWORK, IWORK,
6 X1, X2, Y, DUM1, VL,
7 VL1, VL2, VV, VSALT, IPOLY,
8 NSEG, IDXSEG, NCC, CSS, TEMP,
9 PRES, NURC, 1 RCUSER, CATWT )

NSUBS Input INTEGER Number of substreams in stream
vector
IDXSUB Input INTEGER NSUBS Location of substreams in stream
vector
1=MIXED
2=CISOLID
3=NC
weights
NBOPST Input INTEGER 6, NPO Property method array (used by
FLASH)
INTB Retention INTEGER NINTB Reactor block integer parameters
page 154)
NREALB Input INTEGER User-specified length of REALB
array
154)
NINTR Input INTEGER User-specified length of INTM array
INTR Retention INTEGER NINTR User subroutine integer parameters
page 154)
NREALR Input INTEGER User-specified length of REALM
array
REALR Retention REAL*8 NREALR User subroutine real parameters
page 154)
NIWORK Input INTEGER Length of user subroutine integer
work vector
vector

NCPM Input INTEGER Number of components present in
the mixed substream (See Packed
Vectors, page 155)
IDXM Input REAL*8 NCPM Component sequence numbers
(See Packed Vectors, page 155)
Dum1 Dummy REAL*8 (1) Argument reserved for future
application
VL2 Input REAL*8 Second liquid molar volume,
m3/kmol
NCC Input INTEGER Number of components (unpacked)
CSS Input REAL*8 NCC Concentration vector for reacting
species
PRES Input REAL*8 Pressure, Pa
NURC Input INTEGER Number of user rate constants (See
User Rate-Constant Subroutine,
page 144)
Rate-Constant Subroutine, page
144)
CATWT Input REAL*8 Catalyst weight, kg (in RPLUG,
weight/length)
Example 3 illustrates how to use this subroutine to implement complex rate
expressions in the segment-based power-law model.
Example 3: Implementing a Non-Ideal Rate Expression
Suppose a side reaction QZ is first order with respect to component Q and
first order with respect to a catalyst C. The effectiveness of the catalyst is
reduced by inhibitor I according to the following equation:
   C

 actual
1 (  )
C  
eff a bT I
Where:

[C ] eff = Effective catalyst concentration, mol/L
[C ] actual = Actual catalyst concentration, mol/L
T = Temperature, K
a,b = Equation parameters
The net rate expression can thus be written as:
 
C
a bT I

1 1


 
*
 R T Tref
actual k e
rate Q  
o
E
( )
 

 
[ ]
1
Where:
ko = Pre-exponential factor, (L/mol)/sec
E* = Activation energy
R = Gas law constant
Tref = Reference temperature for ko
The standard rate expression for side reactions is:

E
R T T



1 1

 

 

*

rate  k e ref C i
U j o
i
i
 
 
* ( )
Where:
 = Product operator
Ci = Concentration of component i
i = Power-law exponent for component i
U = User rate constant
j = User rate-constant flag
Suppose the rate constant for the uninhibited reaction is 3 103 (L/mol)/min
at 150C, with an activation energy of 20 kcal/mol, and the inhibition rate
constants are A=0.20 L/mol, B=0.001 L/mol-K. The stoichiometric coefficients
and power-law exponents are specified directly in the Stoic and PowLaw-Exp
keywords. The Arrehnius rate parameters and reference temperature are also
specified directly in the model.
The parameters for the user rate constant equation can be specified using the
optional REALRC list. Including the parameters in the REALRC list allows the
model user to adjust these parameters using the standard variable accessing
tools, such as Sensitivity, Design-Specification, and Data-Regression.
The resulting model input is summarized below:
USER-VECS NREALRC=2 NUSERRC=1

REALRC VALUE-LIST=0.2D0 0.001D0
STOIC 1 Q -1.0 / Z 1.0
POWLAW-EXP 1 Q 1.0 / C 1.0
RATE-CON 1 3D-3<1/MIN> 20.000<kcal/mol>
TREF=150.0<C> URATECON=1
The power-law term from this equation is:
E

* 1 1


 

 
rate  k e R T Tref
CQ o
Where:
[C] = Catalyst concentration, mol/L
k= Pre-exponential factor
o Thus, the required user rate constant is:
1
U j
a bT I
( )
( ( )[ ]
1
 
 
1
Where:
T = Temperature, K
a, b = Equation parameters
An excerpt from the user rate constant subroutine for this equation is shown
below:
C - Component Name -
INTEGER ID_IN(2)
DATA ID_IN /'INHI','BITO'/
C ======================================================================
C EXECUTABLE CODE
C ======================================================================
C - find location of inhibitor in the list of components -
IF ( IDSCC(1,I).EQ.ID_IN(1).AND.IDSCC(2,I).EQ.ID_IN(2) ) I_IN=I
10 CONTINUE
C - get the concentration of the inhibitor -
C_IN = 0.0D0
IF ( I_IN .GT.0 ) C_IN = CSS( I_IN )
C ----------------------------------------------------------------------
C Parameters: each REALR element defaults to zero if not specified
C ----------------------------------------------------------------------
A = 0.0D0
IF ( NREALR .GT. 0 ) A = REALR( 1 )
B = 0.0D0
IF ( NREALR .GT. 1 ) B = REALR( 2 )
C ----------------------------------------------------------------------
C User rate constant #1 U(1) = 1 / ( 1 + (A+BT)[I] )
C ----------------------------------------------------------------------
IF ( NURC.LT.1 ) GO TO 999
RCUSER(1) = 1.0D0 / ( 1.0D0 + ( A + B*TEMP ) * C_IN )

END IF
999 RETURN
Integer and Real Parameters
Each user model has two sets of integer and real parameters. The first set
comes from the subroutine form of the reactor block. The second set comes
from the subroutine form of the step-growth reactions model. Each of these
parameters are retained from one call to the next, thus these parameters can
be used as model inputs, outputs, or retention.
The reactor block integer and real parameters can be used to specify data
which are specific to a particular unit operation, such as reactor geometry,
mass transfer coefficients, etc. The integer and real parameters in the
subroutine forms can be used to specify global parameters, such as rate
constants or physical property parameters.
Local Work Arrays
You can use local work arrays by specifying the model workspace array length
on the Subroutine forms. These work areas are not saved from one call to the
next. Both user subroutines share a common work area. User subroutines are
responsible for initializing the work space at the start of each subroutine.
Packed Vectors
Aspen Plus frequently uses a technique called “packing” to minimize
simulation time. The user models previously described use packed vectors to
track the mole fractions of each phase (vectors X, X1, X2, and Y). These
vectors contain NCPM elements (Number of Components Present in the Mixed
substream). The component index associated with each element is listed in
the vector “IDXM”. All other vectors used by the model, including the rates
vectors and the component concentration vectors, are unpacked.
Calculating Unpacked Component Concentrations
Calculate unpacked component concentrations of the first liquid phase given
the packed mole fractions of the first liquid phase and the molar volume of
the first liquid phase.
IF ( VL1 .GT. 0.D0 .AND. FLOWL1.GT.0.D0 ) THEN
DO 10 I = 1, NCPM
CSS(I) = X1( IDXM( I ) ) / VL1
10 CONTINUE
END IF
Note: NCPM steps were required to load the concentration vector. Since
NCPM is always less than or equal to NCC (total number of conventional
components), there is a reduction in the required number of steps to perform
the operation. Using packed arrays for calculations reduces overhead by
eliminating the need to check for zero values when carrying out mathematical
operations.

Specifying Segment-Based
Kinetics
Accessing the Segment-Based Model
To access the Segment-based power-law kinetic model:
5 Select Segment-Bas as the reaction type and click OK.
Specifying the Segment-Based Model
The Segment-Based model input forms are as listed below. Use these forms
to specify reaction conditions and build a reaction scheme.
Use the Specifications forms to define reaction stoichiometry, enter reaction
rate constant parameters, assign rate constants to reactions, and to specify
the concentration, reacting phase, reacting site, and other model options.
Use this sheet To
Specs Define reacting phase, concentration basis, and reacting
polymer
Reactions Define reaction stoichiomerty and enter reaction rate constant
parameters
Rate Constants Specify reaction rate parameters and catalysts
Assign Rate
Constants
Associate each reaction with one or more sets of rate constants
Use the User Subroutines forms to specify the names and parameters for
optional user basis and rate constant subroutines.
Use this sheet To
Rate Constants Specify the name of the user kinetics routine, the number of
user rate constants calculated by the routine, and to give the
Basis Specify the name of the user concentration and holdup basis
routine and give the integer and real arguments for the user
arrays for this routine
Specifying Reaction Settings
Use the Specs sheet to define the reaction model settings:
1 In the Reacting polymer field, specify the reacting polymer.

2 In the Reference temperature field, specify the default global reference
temperature for rate constant parameters.
3 In the Phase field, specify the phase in which reactions occur.
If the specified phase is Liquid phase 1 or Liquid phase 2 you may also
choose to specify additional options (under the Options frame) to control
how calculations are performed when the phases collapse into a single
liquid phase. For details, see Selecting the Reacting Phase next.
4 In the Basis field, specify the basis for component concentrations in the
reaction rate calculation.
Optionally, you can apply a user subroutine to calculate the concentration
and holdup basis. For details, see User Basis Subroutine on page 275.
5 If desired, specify a site number in the Reacting Site field, and specify
which method to use in the Segment concentration basis frame. For
details, see Selecting the Reacting Site on page 286.
Selecting the Reacting Phase
The Specs form lets you specify the phase in which the reactions occur.
Select the appropriate phase from the list in the Reacting Phase field. All of
the reactions in the segment-based reaction object are assumed to take place
in the same phase. You can use two (or more) segment-based models in the
same reactor to account for simultaneous reactions in multiple phases.
referencing the kinetics to ensure the specified reacting phase exists.
If the Reacting Phase option is set to Liquid phase 1 or Liquid phase 2
the model assumes two liquid phases exist. When the named phase is not
present, the model prints a warning message and sets the reaction rates to
zero. There are two options for handling phase collapse:
disappears.
These options are especially convenient when modeling simultaneous
reactions in two liquid phases using two step-growth models. In this situation,
one would typically select the Use bulk liquid option for one phase and not
the other (to avoid double-counting reactions when one phase collapses).
Selecting the Reacting Site
The segment-based power-law reaction model can be used in conjunction
with other Aspen Polymers reaction models to define side reactions. When
combining the segment-based model with a Ziegler-Natta or ionic
polymerization model, use the Reacting Site field on the Specs form to
assign the reaction rates to a particular active site.

Note: The Segment Concentration Basis field lets you select the
calculation method for the concentrations used within the reaction model.
 When you select Use composite segment concentration the segment
mole fractions used to calculate the reaction rates are calculated from the
following equation:
Mw
Frac Frac SFRAC i
p
avg
,  * ( )*
s i p Mwseg
 When you select Use segment concentration at specified site the
following equation is applied:
avg
p
Mw
Frac Frac * SSFRAC(i, j)* , 
s i p Mwseg
Where j refers the specified reacting site number.
In both cases the attribute rates of change are mapped to the component
attributes associated with the user-specified reacting site number (e.g.,
SSFLOW(i,j), SZMOM(i,j), etc.)
Building A Reaction Scheme
You can build a list of reactions on the Reactions sheet. To do this you must
specify a reaction stoichiometry. The Data Browser window can be resized to
Click To
selector
reactions
Click To
Hide/Reveal
Activate or de-activate a set of reactions.
Inactive reactions are highlighted with a gray
background.
Delete
Adding or Editing Reactions
To add a new reaction to the scheme or to edit an existing reaction, click
New or Edit to open the Edit Stoichiometry subform:
Note that in the Reaction no. field, a unique number is assigned to the
reaction being added.

reactants.
Reactants must have a negative coefficient.
products.
Products must have a positive coefficient.
 or 
Specifying Reaction Rate Constants
The rate constants are summarized in a grid on the Rate Constants sheet:
Note: Reaction rates are defined on a molar basis (moles per volume per
time). The time units for the pre-exponential factors are specified directly on
the Rate Constant form.
By default, the concentration units are assumed to be in SI units (kmole/m3
or mole/L).
You can change the concentration basis to other units using the
Concentration Basis field of the Specs sheet. Alternately, you may apply a
user basis subroutine.
2 In the Ea
field, enter the activation energy.
3 In the b field, enter the temperature exponent.
4 In the Tref field, enter the reference temperature. If this field is left blank
the reference temperature will default to the user-specified global
reference temperature on the Specs form.
5 If desired, specify a Catalyst Species and Catalyst Order.
6 If desired, specify a user rate constant element number on the User Flag
field (For details, see the User Rate-Constant Subroutine on page 144).
Note: Use the Catalyst Species field to associate a rate constant with a
particular catalyst. If you leave this field blank (empty) the model drops the
catalyst concentration term from the rate expression.
Use the Catalyst Order field to specify the reaction order with respect to the
catalyst (the model assumes first order by default).
There are two options for assigning rate constants to reactions. By default,
the model assumes there is exactly one set of rate constants for each reaction
(for example, rate constant set “i” is used for reaction “i”).
Alternately, you may use the Assign User Rate Constant sheet to assign
one or more sets of rate constants to each reaction. This feature is convenient
in two situations:

 Models with a large number of user side reactions when the rate constants
of the various reactions are equal or are related to each other
algebraically.
 Reactions catalyzed by several catalysts simultaneously.
The assignment option is recommended for two reasons:
 You can enter several sets of rate constants for each reaction without re-entering
the reaction stoichiometry.
 You can assign a set of rate constants to multiple reactions, reducing the
number of adjustable parameters in the model, which makes it easier to
fit against data.
When several rate constants are assigned to a reaction the model calculates a
net rate constant by summing all of the listed rate constants and multiplying
the sum by a specified activity.
To assign rate constants to reactions:
1 On the Assign User Rate Constants form, use the Activity field to
specify the activity factor (default value is unity).
2 In the Rate Constant Sets field, select from the list of pre-defined rate
constant sets for each reaction. These numbers refer to the row numbers
on the Rate Constants form.
Including a User Rate Constant Subroutine
Use the User Subroutines Rate Constants form to specify parameters for
user rate constants calculations:
2 Specify the size of vectors for Integer, Real and No. const. in Number
of parameters.
3 Specify the size of vectors of Integer and Real in Length of work
arrays.
columns.
Including a User Basis Subroutine
Use the User Subroutines Basis form to specify parameters for basis
calculations:
2 Specify the size of vectors for Integer and Real in the Number of
parameters and Length of work arrays.
columns.
References

Kroschwitz, J. (Ed.). (1990). Concise Encyclopedia of Polymer Science and
Odian, G. (1991). Principles of Polymerization, 3rd Ed. New York: Wiley.
Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere.
Rudin, A. (1982). The Elements of Polymer Science and Engineering. New
York: Academic Press Inc.

14 Steady-State
Flowsheeting
Aspen Polymers (formerly known as Aspen Polymers Plus) allows you to
model polymerization processes in both steady-state and dynamic mode. In
this chapter, flowsheeting capabilities for modeling processes in steady-state
mode are described.
 Polymer Manufacturing Flowsheets, 291
 Modeling Polymer Process Flowsheets, 293
 Steady-State Modeling Features, 294
Following this introduction, Aspen Polymers flowsheeting capabilities for
modeling steady state processes are discussed in several sections.
 Steady-State Unit Operation Models, 295
 Plant Data Fitting, 339
 User Models, 359
 Application Tools, 375
Polymer Manufacturing
Flowsheets
Polymer production processes are usually divided into the following major
steps:
 Monomer synthesis and purification
 Polymerization
 Recovery/separation
 Polymer processing
The modeling issues of interest in each of these steps were discussed in
Chapter 1, and are summarized in the following figure. The focus here is on
the various unit operations required in these processing steps.
14 Steady-State Flowsheeting 291

292
Monomer Synthesis
During monomer synthesis
since the presence of contaminants, such as water or dissolved gases, may
adversely affect the subsequent polymerization stage by poisoning catalysts,
and storage the engineer is concerned with purity
14 Steady-State Flowsheeting

depleting initiators, causing undesirable chain transfer or branching reactions
which would cause less effective heat removal. Another concern is the
prevention of monomer degradation through proper handling or the addition
of stabilizers. Control of emissions, and waste disposal are also important
factors.
Polymerization
The polymerization step is the most important step in terms of capital and
operating costs. The desired outcome for this step is a polymer product with
specified properties (e.g. molecular weight distribution, melt index, viscosity,
crystallinity) for given operating conditions. The obstacles that must be
overcome to reach this goal depend on the type of polymerization process.
Polymerization processes may be batch, semi-batch, or continuous. In
addition, they may be carried out in bulk, solution, suspension, or emulsion.
Bulk continuous systems provide better temperature and molecular weight
control at the expense of conversion; batch systems offer less control over
molecular weight. In addition, they may result in a high viscosity product and
require high temperatures and pressures. Solution systems also provide good
temperature control but have associated with them the cost of solvent
removal from the polymer.
In summary, for the polymerization step, the mechanisms that take place
during the reaction introduce changes in the reaction media which in turn
make kinetics and conversion, residence time, agitation, and heat transfer the
most important issues for the majority of process types.
Recovery / Separations
The recovery/separation step is the step where the desired polymer produced
is further purified or isolated from by-products or residual reactants. In this
step, monomers and solvents are separated and purified for recycle or resale.
The important issues for this step are phase equilibrium, heat and mass
transfer.
Polymer Processing
The last step, polymer processing, can also be considered a recovery step. In
this step, the polymer slurry is turned into solid pellets or chips. Heat of
vaporization is an important issue in this step (Grulke, 1994).
Modeling Polymer Process
Flowsheets
The obvious requirement for the simulation of process flowsheets is the
availability of unit operation models. Once these unit operation models are
configured, they must be adjusted to match the actual process data. Finally,
tools must be available to apply the fitted model to gain better process
14 Steady-State Flowsheeting 293

understanding and perform needed process studies. As a result of the
application of the process models, engineers are able to achieve goals such as
production rate optimization, waste minimization and compliance to
environmental constraints. Yield increase and product purity are also
important issues in the production of polymers.
Steady-State Modeling Features
Aspen Polymers has tools available for addressing the three polymer process
modeling aspects.
Unit Operations Modeling Features
A comprehensive suite of unit operations for modeling polymer processes is
available in Aspen Polymers. These include mixers, splitters, heaters, heat
exchangers, single and multistage separation models, reactors, etc. For more
information on available unit operation models, see Steady-State Unit
Operation Models on page 295.
Plant Data Fitting Features
Several tools are available for fitting process models to actual plant data.
Property parameters may be adjusted to accurately represent separation and
phase equilibrium behavior. This can be done through the Data Regression
System (DRS). See the Aspen Plus User Guide for information about DRS.
Another important aspect of fitting models to plant data has to do with the
development of an accurate kinetic model within the polymerization reactors.
The powerful plant data fitting feature (Data-Fit) can be used for fitting
kinetic rate constant parameters. For more information, see Plant Data Fitting
on page 339.
Process Model Application Tools
The tools available for applying polymer process models include capabilities
for performing sensitivity, for performing optimizations, and for applying
design specifications. For more information, see Application Tools on page
375.
References
Dotson, N. A, Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization
Prentice Hall.
294 14 Steady-State Flowsheeting

15 Steady-State Unit
Operation Models
This section summarizes some typical usage of the Aspen Plus unit operation
models to represent actual unit operations found in industrial polymerization
processes.
 Summary of Aspen Plus Unit Operation Models, 295
 Distillation Models, 301
 Reactor Models, 302
 Mass-Balance Reactor Models, 302
 Equilibrium Reactor Models, 304
 Kinetic Reactor Models, 304
 Treatment of Component Attributes in Unit Operation Models, 335
Summary of Aspen Plus Unit
Operation Models
Aspen Plus includes a number of basic unit operation models that are typically
used to represent one or more unit operations found in real processes. These
models may be used alone to represent equipment such as pumps, heaters,
valves, mixers, etc., or they may be used as generic “tools” to build models of
more complex unit operations.
The following table summarizes the available unit operation models:
Basic Unit Operation Models and Stream Manipulators
Dupl Copies inlet stream to any number of outlet streams
Flash2 Performs two-phase (vapor-liquid) or three-phase (vapor-liquid-solid)
phase equilibrium calculations
Flash3 Performs three-phase (vapor-liquid-liquid) phase equilibrium
calculations
FSplit Splits inlet stream to any number of outlet streams
15 Steady-State Unit Operation Models 295

Basic Unit Operation Models and Stream Manipulators
Heater Represents heaters, coolers, or mixers with known heat duty or
specified temperature
Mixer Adiabatic mixing of any number of feed streams
Mult Multiplies stream flow rates by a constant
Pipe Calculates pressure drop through pipelines
Pump Represents pumps or liquid standpipes (pressure must be specified)
Distillation and Fractionation Models
Sep Mass-balance model for separation operations with any number of
product streams
Sep2 Mass-balance model for separation operations with two product
streams
RadFrac Predictive multistage distillation model
MultiFrac Predictive model for complex distillation operations with multiple
columns
Reactor Models
RStoic Mass-balance model based on specified conversion for any number of
stoichiometric reactions
RYield Mass-balance model based on specified product yield for any number of
stoichiometric reactions
REquil Chemical equilibrium calculated from user-specified equilibrium
constants
RGibbs Chemical equilibrium calculated by Gibbs free-energy minimization
RCSTR Predictive, reaction rate-based model to simulate continuous stirred
tank reactors
RPlug Predictive, reaction rate-based model to simulate continuous plug-flow
reactors
RBatch Predictive, reaction rate-based model to simulate batch and semi-batch
stirred tank reactors
Dupl
The Dupl block copies one inlet stream to two or more outlet streams. By
design, the mass flow rate and attribute rates out of this block will be greater
than the flow rates into the block, violating mass and attribute conservation
principles.
Frequently, the Dupl block is used as a shortcut to reduce the simulation time
required to model a process consisting of two or more parallel process lines.
For example, consider the process shown here:
Operating Conditions
R1A R1B R2A R2B R3A R3B
Temperature,
C
250 250 260 260 270 265
Pressure, torr 760 760 1200 1200 1500 1700
Volume, liter 2000 2000 1500 1500 1000 1200
296 15 Steady-State Unit Operation Models

The second unit (“R2A” and “R2B”) in the “A” and “B” lines consist of identical
unit operations operating at the same conditions. The third unit (“R3A” and
“R3B”) operates differently in the two lines. Since the process lines are
identical up to the third unit, there is no need to include both process lines in
the model. Instead, we can consider one line, such as “A” and duplicate the
outlet stream at the point where the process conditions diverge from each
other.
Another application of the Dupl model is to carry out simple case studies. For
example, assume there are two proposed scenarios for carrying out a given
reaction. In the first scenario, the reaction is carried out at a high
temperature in a small reactor with a short residence time. In the second
scenario, the reaction is carried out at a low temperature in a large reactor

with high residence times. The two reactors can be placed in a single flow
sheet model. The duplicator block is used to copy one feed stream to both
reactors. The two “cases” can be compared by examining the stream
summary.
Flash2
The Flash2 block carries out a phase-equilibrium calculation for a vapor-liquid
split. The “chemistry” feature of this block can be used to extend the phase
equilibrium to vapor-liquid-solid systems. The free-water option can be used
to extend the phase equilibrium calculations to include a free water phase in
addition to the organic liquid phase.
The Flash2 model can be used to simulate simple flash drums with any
number of feed streams. The model is also a good tool for representing spray
condensers, single-stage distillations, knock-back condensers, decanters, and
other types of equipment which effectively operate as one ideal stage.
The Flash2 model assumes a perfect phase split, but an entrainment factor
can be specified to account for liquid carryover in the vapor stream. The
entrainment factor is specified by the user, it is not calculated by the model.
If a correlation between the vapor flow rate and the entrainment rate is
available, this correlation can be applied to the model using a Fortran block
which reads the vapor flow rate calculated by the Flash block, calculates the
entrainment rate, and writes the resulting prediction back to the Flash block.
Note that this approach creates an information loop in the model which must
be converged.
The Flash2 block does not fractionate the polymer molecular weight
distribution. Instead, the molecular weight distribution of the polymer in each
product stream is assumed to be the same as the feed stream.
Flash3
The Flash3 block carries out phase-equilibrium calculations for a vapor-liquid-liquid
splits. The liquid phases may be organic-organic (including polymer-monomer)
or aqueous-organic. For aqueous-organic systems, the Flash3
model is more rigorous than the Flash2/free water approach described above.
The key difference is that the Flash3 model considers dissolved organic
compounds in the aqueous phase while the free water approach assumes a
pure water phase.
Generally, three-phase flashes are more difficult to converge than two-phase
flashes. Three-phase flash failures may indicate bad binary interaction
parameters between the components. The problem may also stem from
bogus vapor pressures or heats of formation. In general, it is a good idea to
study two-phase splits for the system in question before attempting to model
a three-phase decanter or reactor.
As with the two-phase flash, the three-phase flash is more stable if
temperature and pressure are specified. Other options, such as duty and
vapor fraction, are more difficult to converge. Temperature estimates may aid
convergence in duty-specified reactors.

The Flash3 block does not fractionate the polymer molecular weight
FSplit
The flow splitter block, FSplit, is used to represent valves or tanks with
several outlets. The outlet flow rates can be specified on a mass, mole, or
volume basis, or they can be specified as a fraction of the feed stream. In
general, the fraction specifications are best because they are independent of
the feed stream flow rates. This makes the model more flexible and reliable
when using tools like SENSITIVITY or DESIGN-SPEC which might directly or
indirectly manipulate the stream which is being split. The FSplit block can also
be used with reactor models to account for back-mixing.
The FSplit block assumes that the class 2 polymer attributes split according to
mass mixing rules. For example, if the outlet stream is split 60:40, then the
class 2 attributes, such as the segment flow rates, are also split 60:40. This
approach is identical to assuming that the properties of the polymer in each
outlet stream are the same as the properties of the polymer in the inlet
stream.
Heater
Heater can be used to represent heaters, coolers, mixers, valves, or tanks.
The Heater block allows you to specify the temperature or heat duty of the
unit, but does not carry out rigorous heat exchange equations. Any number of
feed streams can be specified for the Heater block. This block follows the
same mixing rules as the Mixer model.
Mixer
The mixer block, Mixer, is used to mix two or more streams to form a single
mixed outlet. The mixer block can be used to represent mixing tanks, static
mixers, or simply the union of two pipes in a tee. The Mixer model assumes
ideal, adiabatic mixing. The pressure of the mixer can be specified as an
absolute value or as a drop relative to the lowest feed stream pressure.
The Mixer model is functionally equal to the Heater model, except it only
allows adiabatic mixing. For this reason, the Heater model may be a better
choice for modeling mixing tanks.
The Mixer block assumes that the class 2 polymer attributes are additive. For
example if stream “A” and “B” are mixed to form stream “C”, and the zeroth
moments of a polymer in stream “A” and “B” are 12 kmol/sec and 15
kmol/sec, then the polymer in the product stream has a zeroth moment of
12+15=27 kmol/sec.
Mult
The Mult block is used to multiply the flow rate of a stream. A common
application of this block is to collapse two parallel process line models into a

single line to avoid unnecessary duplicate calculations. For example, consider
the process shown here:
In this process, the “A” and “B” lines consist of identical equipment with the
same operating conditions. The Mult blocks “HALF” and “TWICE” are used to
divide the feed stream flow rate by two after R1, representing the split
between lines, and to double the product flow rate, representing the junction
of the parallel lines into a single line at R3. This technique avoids the
duplicate calculations for R2 “A” and “B” reactors, which should give the same
results. This technique can save a great deal of simulation time.
Pump
The Pump block changes the pressure of a stream. This block can be used to
represent an actual pump, or it can be used to represent pressure increases
due to liquid head in standpipes.
Pipe
The Pipe model is used to calculate pressure drops in pipelines. The
algorithms in this model are not designed for non-ideal fluids such as
polymers, so the pipe model should be used with caution in polymer process
models. A better option to calculate pressure drops in polymer pipelines is to
use RPlug with a user-written pressure-drop subroutine.

Sep
The Sep block is a generic separation model that allows component
fractionation between two or more product streams. The products can be split
according to flow rate or fractional specifications. The Sep block is commonly
used to represent distillation columns or other separation equipment when
the product stream purity is well known and the details of the separation
process are not important.
The Sep block does not fractionate the polymer molecular weight distribution.
Instead, the molecular weight distribution of the polymer in each product
stream is assumed to be the same as the feed stream.
Sep2
The Sep2 block is a generic separation model that allows component
fractionation between two product streams. The products can be split
according to flow rate or fractional specifications. The Sep2 block is commonly
used to represent distillation columns or other separation equipment when
the product stream purity is well known and the details of the separation
process are not important. Compared to the Sep block, the Sep2 block has
more flexible input options, but it only allows two outlet streams.
The Sep2 block does not fractionate the polymer molecular weight
Distillation Models
Aspen Plus includes several shortcut distillation models (DISTL, SFRAC, etc.)
which can be used to represent distillation columns. These blocks do not
fractionate the polymer molecular weight distribution. Instead, the molecular
weight distribution of the polymer in each product stream is assumed to be
the same as the feed stream. The class-2 component attributes in each
product stream are set proportional to the mass flow rate of the attributed
component in each product stream.
With the exception of the RadFrac model, the rigorous distillation models in
Aspen Plus do not account for component attributes.
RadFrac
The RadFrac block is a rigorous multistage distillation model for two- and
three-phase systems. RadFrac allows polymer feed streams at any tray, but it
does not account for polymerization reaction kinetics. The molecular weight
distribution and other polymer properties are not fractionated between the
phases. Instead, the class-2 component attributes of the polymer components
are split at each stage in proportion to the polymer component mass
fractions. For example, if 90% of the polymer fed to a given tray goes to the
liquid phase leaving that tray, then 90% of the zeroth moment and other
class-2 attributes are assigned to the liquid phase on that tray.

Reactor Models
Aspen Plus includes three classes of reactor models which include various
levels of rigor and predictive capability. These classes are: (1) mass-balance
models; (2) equilibrium models; and (3) rigorous kinetic models.
The least predictive models, RStoic and RYield, calculate output flow rates
based on user-specified input flow rates. If polymer components are involved
in the reactions, then the component attributes associated with the polymer
components must be specified for the product stream. These models calculate
the mass and energy balances, but they do not perform rigorous kinetic
calculations.
The RGibbs and REquil models assume chemical and phase equilibrium. When
polymer components are involved in the reactions, then the specified
stoichiometry must be consistent with the reference molecular weight of the
polymer component. In addition, the component attribute values for the
polymer product must be specified by the user. Since the solution algorithms
for these models do not consider the influence of the segmental composition
of polymer components, they cannot be applied to copolymers.
Rigorous kinetic models include RCSTR (continuous stirred tank reactor),
RPlug (plug-flow reactor model), and RBatch (batch stirred tank reactor).
Each of these models can consider one, two, or three reacting phases. These
reactor models are with the reaction kinetic models to predict product stream
composition and flow rates based on calculated reaction rates.
Mass-Balance Reactor Models
RStoic
The RStoic reactor model is used to represent reaction equipment when
reaction kinetics are unknown or are unimportant, for example when
reactions are very fast and proceed until the limiting reagent is exhausted.
RStoic requires knowledge of the net reaction stoichiometry, and the extent of
reaction or conversion of a key component.
RStoic calculates the product stream flow rates based on user-specified
reaction stoichiometries and extent of reaction or conversion of a key
component. The reaction stoichiometry statements may include monomers,
oligomers, or polymers, but may not include segments. Instead, the segment
information (SFLOW or SFRAC) must be specified as component attributes in
the COMP-ATTR sentence.
Reactions Involving Polymers
If polymer components are involved in any of the reactions, use the COMP-ATTR
form to specify molecular weight values (MWN, MWW or PDI) or degree
of polymerization (DPN, DPW or PDI ) for the polymer products. Specify the
SFRAC attribute for homopolymers or copolymers with a known product
polymer composition. For copolymers with product compositions which

depend on the feed flow rates of monomers or polymer segments, specify
dummy values for the SFLOW attribute and use a user-written Fortran block
to predict product segment flow rates which are consistent with the calculated
product flow rates. Write the calculated results into the product stream of the
RStoic block.
When some of the specified reactions involve polymers, the reaction
stoichiometry must be written in a manner consistent with the reference
molecular weight of the polymer component. Otherwise, the mass and energy
balance calculations will not be consistent.
Simulating Polymer Phase Change
The RStoic model may be used with the substream feature to simulate phase
changes in polymers. For example, the user may define a reaction to convert
polymer from the liquid or amorphous state (in the MIXED substream) to
crystalline polymer (in the CISOLID) substream. Conversely, melting can be
simulated as a reaction that converts polymer in the CISOLID substream to
polymer in the MIXED substream.
When RStoic is used in this manner, the model automatically fractionates the
component attributes between the product substreams. If the user does not
specify the product component attributes, the model sets the values of the
class-2 attributes in each substream proportional to the flow rate of the
attributed component in the substream. In effect, the model assumes that
there is no selectivity of properties between the product phases. The polymer
in each product phase will have the same characteristics (segment
composition, mole weight, etc) as the polymer in the feed stream.
RYield
The RYield reactor model is used to represent reaction equipment when
reaction kinetics are unknown or are unimportant, and the reactions result in
a product distribution with a known yield.
RYield calculates the product stream flow rates based on user-specified
reaction stoichiometries and yield distributions. The reaction stoichiometry
statements may include monomers, oligomers, or polymers, but may not
include segments. Instead, the segment information (SFLOW or SFRAC) must
be specified as component attributes in the COMP-ATTR sentence.
If polymer components are involved in any of the reactions, use the COMP-ATTR
form to specify molecular weight values (MWN, MWW or PDI) or degree
of polymerization (DPN, DPW or PDI ) for the polymer products. Specify the
SFRAC attribute for homopolymers or copolymers with a known product
polymer composition. For copolymers with product compositions which
depend on the feed flow rates of monomers or polymer segments, specify
dummy values for the SFLOW attribute and use a user-written Fortran block
to predict product segment flow rates which are consistent with the calculated
yield. Write the calculated results into the product stream of the RYield block.
When some of the specified reactions involve polymers, the reaction
stoichiometry must be written in a manner consistent with the reference

molecular weight of the polymer component. Otherwise, the mass and energy
balance calculations will not be consistent.
Equilibrium Reactor Models
REquil
The REquil model calculates product stream flow rates using equilibrium
constants determined from Gibbs free energy. The equilibrium constants are
based on user-specified reaction stoichiometries and yield distributions. The
reaction stoichiometry statements may include monomers or oligomers, but
may not include polymers or segments. If the feed stream includes polymer
components, the attributes of the polymer components will be copied to the
outlet stream.
RGibbs
The RGibbs model uses the Gibbs free energy minimization technique to
determine the composition of each phase. This algorithm cannot predict the
product of equilibrium polymerization reactions. Polymer phase equilibrium,
however, can be predicted by the model. The RGibbs phase equilibrium
algorithm assumes that the composition and molecular weight distribution of
a polymer component is equal in each of the product phases. The class-2
component attributes of the polymer component are set in proportion to the
mass flow of the polymer component in each of the product phases. The mass
flow rates in the product phases are set by the Gibbs free energy
minimization algorithm.
To properly split component attributes among the RGibbs solution phases, use
the "Phase equilibrium only" option. With this the model can predict multiple
liquid phases such as three liquid phases. Surface tension effects are not
considered. If you are certain that there will be no vapor phase, uncheck the
"Include vapor phase" box to speed up calculations. Use one outlet stream for
each predicted phase, to separate out the component attributes of that
phase.
Kinetic Reactor Models
RCSTR
The RCSTR model represents a continuous stirred tank reactor with one or
more phases.
The model assumes perfect mixing within and between the phases, phase
equilibrium, and isothermal, isobaric operation. Non-ideal mixing can be
represented using a network of RCSTR models.

Temperature
The CSTR model allows you to specify duty or temperature. If duty is
specified, it is a good idea to provide a temperature estimate, T-EST, to
improve the convergence of the model. The maximum temperature step size,
T-STEP, may also influence the CSTR convergence. This parameter defaults to
50C, which results in substantial changes in reaction rates for reactions with
typical activation energies. The temperature/duty iteration loop is referred to
as the “Energy Balance” or “EB-LOOP” in the CSTR diagnostics.
Pressure
Pressure can be specified as an absolute value or as a pressure drop relative
to the feed stream with the lowest pressure. In Aspen Plus, pressure drops
are expressed as non-positive pressure specifications given in absolute
pressure units.
Residence Time
The RCSTR model allows you to specify the effective hold-up in several
different ways. For single-phase reactors, you can specify the total reactor
volume or the total residence time. If the residence time is specified, then the
estimated reactor volume should be specified to improve the residence-time/
volume loop convergence (RT-LOOP).
When two or more condensed phases are present, the RCSTR model assumes
that each condensed phase has the same residence time. This “no-slip”
assumption implies that the volume ratios of the condensed phases in the
reactor are equal to the volume flow ratios of the condensed phases exiting
the reactor.
For multiphase reactors, specify the condensed phase volume or residence
time in addition to the total reactor volume. Do not specify the total residence
time, as this residence time is the average of the vapor and liquid phases. If
the reacting phase residence time is specified, provide an estimate for the
reacting phase volume. This will improve the reactor convergence. If
residence time convergence is troublesome, try adjusting the volume step
size.
Multiphase Reactors
The RCSTR model can be used to simulate single- or multiple-phase reactors.
The valid-phases keyword is used to define the number and type of fluid
phases present in the reactor.
Amorphous solid polymers are treated as a “liquid” phase in Aspen Polymers
(formerly known as Aspen Polymers Plus). Crystalline solids can be addressed
by defining a “CISOLID” substream to track the flow rate of each inert
crystalline solid.
Dissolving or crystallizing solids can be captured using the Chemistry feature
to define chemical equilibrium reactions between the solid and fluid phases.
Note, however, that the current version of RCSTR does not allow components
to appear in both kinetic reactions and in chemistry equilibrium reactions.

The user may attach multiple outlet streams directly to the reactor model.
The phase or phases flowing to these streams are identified on the streams
form. When solids are present the solid phases will be added to the liquid
outlet.
In older releases of Aspen Plus, the RCSTR model had one process fluid outlet
stream containing all of the phases exiting the reactor. This option is still
supported in the current release for upward compatibility. As shown in the
following figure, a Flash2 or Flash3 block can be used to split the mixed outlet
stream of the reactor:
Reactors with Non-Ideal Mixing
Networks of RCSTR and RPlug blocks can be used to account for non-ideal
mixing found in industrial reactors. For example, many industrial reactors are
divided into zones by vertical or horizontal baffles. In addition, some reactors
have poor mixing characteristics which result in dead zones. The figures that
follow demonstrate ways to model some types of real reactors.
Since many of the “network” models involve recycle loops, they may require
substantially more simulation time than a single RCSTR block. In addition, the
recycle loop convergence may make the model more difficult to converge. For
these reasons, the simplest model that agrees with process data is always the
best choice.
This figure shows a two-phase CSTR with horizontal partitions:

This figure shows a two-phase CSTR with vertical partitions:
This figure shows a two-phase CSTR with an external heat exchanger:

This figure shows a two-phase CSTR with a dead-zone:
RCSTR Algorithm
The RCSTR model uses a trial-and-error technique to solve the mass and
energy balance equations. Trial-and-error solutions are difficult to reach when
the reaction rates are high, the variables cover several orders of magnitude,
when many equations must be solved simultaneously, and when the variables
are strongly related to each other. All of these conditions are found in
polymerization reaction kinetics, making reactor convergence especially
challenging.
A good understanding of the design of the RCSTR model is required in order
to troubleshoot convergence problems. Otherwise, it may be difficult to

understand how to apply the various convergence parameters to improve the
reliability of the model.
The RCSTR algorithm consists of a series of nested loops, as shown in the
following figure. The loops are solved from the inside to the outside using
various trial-and-error solver algorithms. Some convergence parameters are
associated with each of these loops.
The outer-most loop involves the volume and residence time of the CSTR.
There are many options for specifying the characteristic volume of a
multiphase CSTR. The following table shows the various calculations for
volume and residence times in RCSTR:

Specifications: Total reactor volume (Vol)
R
V
F v f
R
j j
j
  V
f v
j j
f v
V j
   R j
k k
k
V
Ff v
j
j j

Specifications: Total residence time (Res-time)
V F v f R R j j
   ** V
j
f v
j j
f v
V j
   R j
k k
k
V
Ff v
j
j j

Specifications: Total reactor volume (Vol), key phase volume
(Ph-vol)
R
V
F v f
R
j j
j
  V specifed j  *  j
V
Ff v
j
j j

Specifications: Total reactor volume (Vol), key phase volume fraction (Ph-vol-
frac)
R
V
F v f
R
j j
j
  V rV j j R   j
V
Ff v
j
j j

Specifications: Total reactor volume (Vol), key phase residence time (Ph-res-
time)
R
V
F v f
R
j j
j
  V Ff v j j j j   **  j  specified
Specifications: Total residence time (Res-Time), key phase volume fraction
(Ph-vol-frac)
V F v f R R j j
   ** V rV j j R   j
j
V
Ff v
j
j j

R V = Total reactor volume;
j V = Volume of phase “j”;
j v = Molar volume of
phase “j”
j r = Volume fraction of phase “j”; R  = Total residence time;
j  = Residence
time of phase “j”
F = Total molar flow rate at reactor outlet;
j f = Molar fraction of phase “j”
* If more than one condensed phase is present, and the key phase is liquid, then
the specified volume applies to the sum of the condensed phase volumes.
** This equation is solved by trial-and-error technique.

When residence time is specified instead of volume, the RCSTR model adjusts
the volume to satisfy the residence time specification.
Convergence problems in the residence time loop can be alleviated by
providing initial volume estimates in the ESTIMATES form. If convergence
problems persist, then the maximum volume step size (Max-Vstep) should be
reduced. If the key phase residence time is specified, then the RCSTR model
uses the specified reactor volume as an upper limit for the key phase volume.
EB LOOP
The second loop is the energy balance conservation equation (EB-LOOP). In
this loop, the reactor temperature is adjusted to match the specified reactor
duty. If the temperature is specified instead of the duty, this loop is by-passed.
Since the reaction rates are very sensitive to temperature, large changes in
the reactor temperature between energy-balance iterations (EB-ITER) may
cause the mass-balance loop (MB-LOOP) to diverge. This problem can be
solved by providing a good temperature estimate (T-EST) in the ESTIMATES
form. If the problem persists, the maximum temperature step size (Max-
Tstep) should be reduced (the default, 50C, is rather large).
MB-LOOP
The next loop is the mass-balance loop (MB-LOOP). This loop uses a
multivariable solver to converge the conservation equations for component
mole flow and for the class two component attributes.
Two solvers are available: Broyden and Newton. The Broyden algorithm tends
to be relatively fast, but it may be unstable if the number of components and
attributes is large and the reaction rates are high. The Newton algorithm
tends to be slower, but more stable for many classes of problems. The
Newton algorithm calculates the response of each variable to each other
variable by perturbing the variables one at a time by a very small amount.
These perturbation steps require lots of simulation time, which makes each
iteration of the Newton algorithm slow.
The number of mass-balance iterations (MB-Maxit) is defined on the
convergence form. By default, the model allows 50 mass-balance iterations.
This default is sufficient for the Newton algorithm, but is usually too small for
the Broyden algorithm. For polymer reaction kinetics, the number of required
mass-balance iterations may be as high as 500.
Using a Damping Factor
The stability of the Broyden algorithm can be adjusted using a damping factor
(DAMP-FAC) defined on the “Convergence” form. Decreasing the damping
factor decreases the step-size, resulting in a larger number of smaller, more
stable steps. Thus, the maximum number of iterations should be increased as
the damping factor is decreased.
The damping factor is sensitive on a log scale. If the Broyden algorithm
appears unstable, try setting the damping factor to 0.5, 0.3, 0.1, 0.05 etc.
Optimum damping factors for polymerization kinetics typically fall between
0.1 and 0.001.

The conservation equations have the form:
accumulation input   output  Generation
For the component mole balance equations:
R
S
in
F
S
out
F
S
 ,
G V
S
i
i
i
  
i
i
i
j i j j
i
For the class-2 component attributes equations:
R
S
in
A
S
out
A
S
 ' ,
G V
S
i
i
i
  
i
i
i
j i j j
i
Where:
Ri = Residual value for equation i, kmol/sec
Fi
in = Molar flow rate of component i into the reactor, kmol/sec
Fi
out = Molar flow rate of component i out of the reactor, kmol/sec
Gi, j = Molar generation rate of component i in phase j, kmol/m3
sec
in = Flow rate of attribute i into the reactor, kmol/sec or
Ai
particle/sec
out = Flow rate of attribute i out of the reactor, kmol/sec or
Ai
particle/sec
Gi, j
= Generation rate of attribute i in phase j, kmol/m3 sec or
particle/m3 sec
Vj = Volume of phase j in the reactor
Si = Scaling factor for equation i
The mass-balance loop is converged when the maximum scaled residual of
the conservation equations falls below the specified tolerance (MB-TOL):
R
S
i
i


Maximum error = MAX MB TOL i
 
 
 
A secondary criteria is the root-mean-square scaled error, or RMS error:
RMS Error =
1 
2
N
R
S i
i
 

i i

 
The CSTR mass-balance algorithm iterates until the maximum error falls
below the specified mass-balance tolerance or the maximum number of mass-balance
iterations is reached. If the maximum error criteria is reached, and
the RMS error is decreasing by a factor of ten on each iteration, the CSTR
model continues to iterate until the RMS error reaches the specified function
tolerance (FUNC-TOL). This allows the model to reach very tight convergence
tolerances when the convergence behavior is good.

Scaling Factors
The scaling factors play an important role in the convergence behavior of the
model. If the scaling factors are large, and the variables are small, then the
model will be loosely converged. If the scaling factors are small, and the
variables are large, the convergence criteria will be unacceptably tight, and
the model will not converge. There are two scaling options in the RCSTR
model, as shown here:
Variable Type Component Scaling Substream Scaling
Enthalpy Estimated outlet stream enthalpy 105
Component Mole Flows The larger of:
Estimated component mole flow in outlet
stream (or retention value if available)
(Trace) x (Substream flow rate)
Total estimated outlet
stream mole flow rate
Class 2 Attributes The larger of:
Estimated attribute value in outlet stream
(or retention value if available)
(Attribute scaling factor from the TBS table)
x (Estimated mole flow rate of the attributed
component)
(Trace) x (Total estimated outlet mole flow
rate) x (Attribute scaling factor from the TBS
table)
1011
Note: If the estimated component flow or
attribute value is zero or missing, the
default scaling factor is applied.
(Attribute scaling factor
from the TBS table) x
(Substream flow rate)
By default, the component scaling option is used. With this option, the
minimum scaling factors depend on the value of the “TRACE” parameter. The
trace scaling factor is effectively a minimum mole fraction. For components
with concentrations below the trace level, the scaling factors are set to a
minimum value.
The default scaling factors for component attributes are defined as constants
in an Aspen Plus Table Building System (TBS) data file, “COMPATTR.DAT”.
Although the default scaling factors are set to appropriate values for most
classes of reaction kinetics, the optimal values for a particular type of kinetics
may be different than the defaults. The default attribute scaling factors can be
adjusted using the Components Scaling form.
The scaling factors should make the scaled values as close to unity as
possible. For this reason, the scale factors are set to the predicted values
from previously converged passes through the RCSTR block. On the first pass
through the flowsheet, the scaling factors will be set to the estimated value
for the variable. Thus, component flow and component attribute estimates
can be used to set the initial scale factors.
The scaling factors for component attribute values are normalized with the
total mole flow rate of the outlet stream. This keeps the scaling factors
reasonable for models of any type of process, from bench scale to production
scale units.

The inner-most loop is the phase equilibrium loop, or flash equations. For this
reason, it is essential to have accurate physical properties over the entire
range of temperatures and pressures found in the process.
The flash calculations start from retention values once the mass-balance error
falls below the retention threshold (Ret-Thresh) specified in the convergence
form. If the retention threshold is set very high, then the flash may fail,
resulting in step-size cuts in the mass balance loop. If the retention threshold
is reduced, the reactor calculations may require more time. For most
simulation problems, setting the retention threshold to 11010 results in fast
flash convergence without errors. If errors occur, try using the default value,
1105 . If errors persist, the most likely cause is a physical property problem.
Initialization Options
The convergence behavior of the RCSTR model depends on how the model is
initialized. There are three initialization options for the RCSTR model.
 Solver Initialization—Do not use integration
By default, the solver algorithm initializes itself using previously saved
simulation results (retention). This saves time if the RCSTR block is inside
a flowsheet recycle loop, where the block will be run several times in
succession. It also saves time if the block is inside a sensitivity,
optimization, design-spec, or data-fit study.
Alternately, the user can force the model to restart from estimates every
time by checking the restart flag on the block-options form.
When retention is not available, or when the restart option is active, the
model uses user-specified estimates to initialize the solver algorithm.
Estimates can be provided for the reactor volume, phase volume, reactor
temperature, component flow rates, and component attribute values. The
component attribute estimates can be specified using class-2 or class-0
attribute values.
If estimates are not provided, the model initializes the variables using the
mixed feed stream (for example, the initial value of a component flow rate
may be set to the total flow rate of that component in all feed streams to
the reactor).
 Integration Initialization—Always use integration
In the integration algorithm, the RCSTR is treated as a dynamic stirred-tank
reactor. The conservation equations are numerically integrated from
an initial condition to the steady-state condition. The initial compositions
in the reactor are set equal to those in the feed stream.
If temperature is specified in the reactor, then the temperature profile
during initialization can be ramped from the feed stream temperature to
the specified temperature over the interval of several residence times. If
duty is specified, then the duty can be ramped from adiabatic conditions
to the specified duty. Ramping allows the reactor to “cold-start” for
improved integration performance.
The numerical integration carries forward until the residual terms
(accumulation terms) drop below the specified mass-balance tolerance. At
this point, the model enters the solver and continues until the model
converges.

Note that initial guesses for component flow rates and component
attributes should not be provided when using the integration initialization
option unless the reactor exhibits multiple steady-state solutions. In this
case, initial estimates may be used to force the reactor towards a
particular solution.
 Hybrid Initialization—Initialize using integration
The hybrid option takes advantage of the robust integration algorithm to
initialize the reactor during the first pass. On subsequent passes, when a
previously converged solution is available, the solution algorithm bypasses
integration and jumps directly into the trial-and-error solver. Since the
solver algorithm is much faster than the integration algorithm, the hybrid
option offers improved performance for most problems.
Note: By default, the RCSTR model does not use integration (e.g., the trial
and error solution algorithm starts directly from the user-specified initial
guesses or from retention values). Optionally, the RCSTR model can be
initialized using an integration approach or a hybrid approach that uses
integration only when retention values are not available.
Troubleshooting Convergence Problems
To diagnose RCSTR convergence problems, set the terminal reporting level to
“7” in the Block-Options form. This causes the RCSTR model to report the
residence time iterations (RT-ITER), energy balance iterations (EB-ITER), and
mass-balance iterations (MB-ITER) to the control panel. In addition, the
model reports the maximum and root-mean-square errors for each loop.
The Simulation diagnostic reporting level controls the diagnostic messages
written to the history file (.HIS file). The maximum mass-balance error is
reported at level 5. At level 6, the model reports the value of each reacting
component flow rate and each component attribute. At level 7, the model
reports values and rates of change (reaction rates) for components and
attributes. At level 8, the model reports the values, rates, and residuals
(error) of each solved variable.
When troubleshooting convergence problems, simplify the problem by
specifying temperature and volume instead of duty and residence time. If
convergence problems persist, they must be related to the mass-balance
loop, the reaction kinetic model or rate constants, or the underlying physical
property calculations.
Numerical integration is much more reliable than trial-and-error solvers. If
the RCSTR mass-balance fails to converge, try running the same kinetics in
an RPlug model. If possible, set the phase criteria “liquid-only” to eliminate
physical property problems from the list of possible sources of error. If the
RPlug model cannot converge with the specified kinetics, then the problem is
almost certainly related to reaction kinetics.
Possible sources of error in the reaction kinetics include:
 Errors in the molecular weight of a product or reactant
 Errors in the specified stoichiometry of a reaction (mass balance is
violated)

 Unreasonable rate constants, especially activation energies (verify the
units)
 Reactions with zeroth-order reactants which are not present
 Unreasonable concentrations of catalysts or inhibitors (put the feed
stream in a flash block and verify that the concentrations in the reacting
phase make sense).
 Errors in user-written Fortran subroutines.
If these sources of error are eliminated, and convergence problems persist,
try simplifying the model by removing unnecessary side reactions or trace
components from the model. Convergence is much easier if the number of
equations is reduced, the speed of most convergence algorithms varies with
the cube of the number of equations (the number of equations equals the
number of reacting components plus the number of class-2 component
attribute elements).
Common Problems
The following table summarizes solutions for some common problems
encountered when using RCSTR:
Problem Solution
Initial flash failure This is usually a physical property problem.
Check the heat of formation (DHFORM) and
ideal gas heat capacity parameters (CPIG) of
the polymer and oligomer components.
If supercritical components are present,
consider treating them as Henry’s law
components
Verify that the property method you are using
is appropriate for the specified temperature and
pressure
Verify the specified phases are consistent with
the specified temperature and pressure
Verify the specified local and global flash
tolerance
Mass balance not converged in maximum
number of iterations, but the error is decreasing
from one iteration to the next.
Increase the maximum number of iterations. If
more than 500 iterations are required for the
Broyden algorithm, try adjusting the damping
factor. Provide better initial guesses.
number of iterations, the maximum error is
varying erratically between iterations, and the
history file shows reasonable rates.
If using the Broyden algorithm, try decreasing
the damping factor by logarithmic steps (0.5,
0.3, 0.1…0.0001) until the problem converges.
If the problem persists, try using the Newton
algorithm. Provide better initial guesses.
Mass balance is not converging, the maximum
error appears to oscillate between values or
gets “stuck” and does not change.
If using Newton algorithm, change the
stabilization strategy from “dogleg” to “line
search.” This works especially well for ionic and
Ziegler-Natta kinetics.

Problem Solution
number of iterations, the maximum error is
varying erratically between iterations, and the
history file shows some reaction rates or
attribute rates are much larger than others (or
are erratic between iterations).
Check the specified rate constants in the kinetic
models, especially activation energies. Verify
the units of the activation energies. Verify flow
rates of catalysts and initiators in the feed
streams to the reactor. If using user kinetics,
check your subroutine for errors. Verify the
reactor volume (residence time).
number of iterations. Reaction rates are very
high, as expected.
Try using the Newton algorithm with good initial
guesses. If this fails, delete the initial guesses
and try using the integration initialization.
number of iterations. Some reacting
components (catalysts, initiators) are present in
very small quantities.
Try adjusting the “trace” parameter in order-of-magnitude
steps from the default (1103 )
down to the concentration of the trace
components. If this fails, reset trace to the
default value and try integration initialization.
Energy balance loop does not converge, or
mass-balance loop does not converge after the
second energy balance loop iteration, or
temperature step-size cutting (T-CUT) iterations
appear in the diagnostic messages
Verify that the reactor converges with the
temperature specified. If not, see items listed
above, otherwise,
provide a better temperature estimate (T-Est).
If the problem persists, try adjusting the
maximum temperature step-size (Max-Tstep)
from 50C to 10C or even 5C.
Residence time loop does not converge, or
mass-balance loop does not converge after the
second residence-time loop.
Verify that the reactor converges with the
residence time specified. If not, see items listed
above, otherwise, provide better volume
estimates. If the problem persists, try adjusting
the maximum volume step-size (Max-Vstep).
Verify that the correct residence time is
specified (condensed-phase residence time for
two-phase reactors).
Verify two phases exist if the reactor valid
phases=vapor-liquid.
Flash failures appear during the mass-balance
loop; the step-size cutting (X-CUT) diagnostic
message appears.
This may be a physical property problem; it
may reflect overly-tight flash tolerances; or the
flash may be unstable when starting from
retention values Loosen the local and global
flash tolerance levels or increase the maximum
number of flash iterations.
Reactor converges but an error message says
that the mass-balance does not close
Check the molecular weights of each reactant
and product. Verify that reaction stoichiometry
is correct.
RPlug
The RPlug model represents an ideal plug-flow reactor with one or more
phases. The model assumes perfect radial mixing within and between the
phases, phase equilibrium, and no-slip conditions between the phases (e.g.,
the phases all have the same residence time). Dead zones, back-mixing, and
other types of non-ideal plug-flow behavior can be represented using RPlug in
combination with other blocks. The RPlug model does not allow multiple feed

streams. A mixer block must be used in conjunction with the RPlug block to
account for multiple feed streams.
Temperature
RPlug allows many options for specifying the reactor duty or temperature:
Type Specifications Calculations
ADIABATIC None Temperature is calculated at each
axial position based on the
enthalpy balance.
T-SPEC Process stream temperature as a
function of axial position (linear
interpolation between the points)
Duty is integrated along the length
of the reactor. The model reports
the net duty across the reactor
T-COOL-SPEC
Heat transfer routine
optional
Heat media stream temperature
(assumed constant along length
of reactor). Overall heat-transfer
coefficient. Area is determined
from length, diameter , and
number of tubes: A=NDL
of the reactor. The temperature of
the process stream is determined
from the energy balance. The
model reports the net duty across
the reactor
CO-COOL
Thernal fluid stream
required
optional
Thermal fluid stream
temperature, composition, and
flow rate.
Overall heat-transfer coefficient.
Area is determined from length,
diameter, and number of tubes:
A=NDL.
of the reactor and is reported as a
net value. The temperature of the
process and thermal fluid streams
are determined from the energy
balance.
COUNTER-COOL
Thermal fluid stream
required
optional
Thermal fluid composition, flow
rate and effluent temperature.
Area is determined from length,
diameter, and number of tubes:
A=NDL.
of the reactor and is reported as a
net value. The temperature of the
process and thermal fluid streams
are determined from the energy
balance. A design specification
may be used to fit thermal fluid
feed temperature by adjusting
thermal fluid outlet temperature.
RPlug allows one process stream and one heat media stream. Reactions can
occur only in the process stream. Heat transfer calculations are carried out
between the process stream and the heat media stream. The heat media
stream represents a thermal fluid stream or a heating stream and the heat
media stream flows co- or counter-current to the process stream.
If a heat media stream is not specified, the model assumes a constant heat
media temperature and solve for the process fluid temperature.
The heat transfer rate or heat transfer coefficient value is calculated as a
function of axial position, stream conditions, etc., by a user-written Fortran
subroutine. This feature is used to develop rigorous models non-reactive heat
exchangers.

Pressure
The pressure at the reactor entry can be specified as an absolute value or as
a pressure drop relative to the feed stream. In Aspen Plus, pressure drops are
expressed as non-positive pressure specifications given in absolute pressure
units.
The pressure drop across the reactor can be specified as a constant or
calculated in a user-written Fortran subroutine. If the pressure drop is
specified, the model assumes it is linear along the length of the reactor.
Residence Time
The RPlug model assumes a cylindrical geometry. The length, diameter, and
number of tubes are specified. The process fluid is assumed to move through
the tubes, and the thermal fluid is assumed to flow on the outside of the
tubes.
The total reactor volume cannot be specified, but the aspect ratio
(length/diameter) has no influence on the model predictions. Thus, the
diameter can be set to 1.12838 units, which corresponds to an area of 1.0000
units2 . With this area, the length in units and volume in units3 have the same
numerical value, thus the specified length is equal to the volume.
The phase volumes cannot be specified independently. Instead, the RPlug
model assumes that the phases move through the reactor without slipping
past each other. This assumption is valid for situations where one phase is
dispersed as droplets or bubbles in a second, continuous phase, such as dew
in a vapor phase or small gas bubbles in a liquid phase. This assumption is
not valid for multiphase plug flow reactors with controlled levels.
With this assumption in place, the reactor residence time is equal to the
residence time of each phase present in the reactor. The residence time is
calculated by numerical integration.
One work-around for the no-slip assumption is to write a user kinetic
subroutine (or a step-growth mass-transfer routine) which calls the flash
model directly. Then, specify the reactor as liquid-only and set the diameter
to the hydraulic diameter of the reactor.
Calculating Residence Time
Equation to Calculate Residence Time in RPlug:

2 z L
 D N dz

  
0 4 , ,
F f v z z j j z j z
Where:
 = Reactor residence time
D = Tube diameter
N = Number of tubes
Z = Axial position in reactor of length L
Fz = Total molar flow rate of process stream at axial location z

f j,z = Molar fraction of phase j at axial location z
v j,z = Molar volume of phase j at axial location z
Multiphase Reactors
The RPlug models have one process fluid outlet stream that contains all of the
phases exiting the reactor. As shown here, a flash block is used in conjunction
with these blocks to split the liquid and vapor phases from the mixed outlet
stream of the reactor:
In this application, it is good practice to specify PRES=0 (no pressure drop)
and DUTY=0 in the flash block to ensure that the phase split occurs at
conditions which are consistent with the reactor outlet. Another option is to
specify temperature and to use a transfer block to copy the RPlug outlet
stream temperature to the flash specifications.
Reactors with Non-Ideal Mixing
Back-mixed plug flow reactors can be modeled using a recycle stream or by
breaking the reactor down into a series of RCSTR blocks. For example:

The recycle-stream approach has the advantage of RPlug’s profile-based input
and output plotting, but it requires a flowsheet convergence loop that may be
difficult to converge, especially if the circulation ratio is large. The series-of-
CSTRs approach does not require recycle loop convergence, but the results
are not as easily interpreted as the RPlug model.
Reactors with dead zones can be represented using parallel plug-flow
reactors, as shown here:

The dead zone is represented by a plug-flow reactor with a large residence
time. The active zone is represented as a plug-flow reactor with a shorter
residence time. The volumes of the two reactors sum to the total volume of
the real reactor. This approach assumes the dead zone reaches steady state.
As always, the simplest model which agrees with process data is the best
choice.
The following figure shows a reactor with injection ports:

To diagnose numerical problems in RPlug, set the terminal reporting level to
“7” in the Block-Options form. With this setting, the RPlug block will report
the normalized axial location, residence time (in seconds), pressure (in
Pascal), temperature (in K), and vapor molar fraction at each converged step.
reported at level 5. At level 6, the model reports reacting component flow
rates and component attribute values. At level 7, the model also reports the
rates of change of these variables. At level 8, the model also reports initial
scale factors for all variables.
First, simplify the problem by specifying temperature instead of duty or heat-transfer
parameters (thermal fluid temperature, U, or thermal fluid stream).
Specify the reactor as “liquid-only”. This will eliminate many possible sources
of error and help focus the problem on kinetics and integration parameters.
Scaling Factors
RPlug uses Gear’s variable-step-size algorithm to numerically integrate the
mass, energy, and attribute conservation equations along the axial dimension
of the reactor. At each axial step, the conservation equations are solved by a
trial-and-error technique.
Like RCSTR, RPlug solves the conservation equations using scaling factors to
normalize the variables. The values of these scaling factors can have a strong
influence on the speed and reliability of the integration.
The Gear integrator in Aspen Plus offers three error scaling options (ERR-METHOD
in RPlug):
 Static scaling
 Dynamic scaling
 Hybrid scaling
The RPlug static and dynamic scaling options are summarized in the following
table:
Variable Type Static Scaling Dynamic Scaling
Enthalpy 105 (SI units) x total mass flow The larger of:
Enthalpy at 2
Cutoff
Component Mole
Flows
The scaling factor at z = 0 to 1.0 is set to
0.1 x total mass flow
The scaling factor at z = z + z is
set to the larger of:
Component mass flow at z
Cutoff
Scaling factors are updated at
each step

Class 2 Attributes The scaling factor at z = 0 to 1.0 is set to
the larger of:
Attribute value in inlet stream
(Attribute scaling factor from the TBS
table) x (mole flow rate of the attributed
component in the inlet)
(Cutoff) x (total mole flow rate at the
inlet) x (Attribute scaling factor from the
TBS table)
Scaling factors are held constant
The scaling factor at z = z + z is
set to the larger of:
Attribute value at z
Cutoff
Scaling factors are updated at
each step
The static scaling method uses a constant set of scaling factors throughout
the reactor. The dynamic scaling method updates the scaling factors based on
the previously converged step. The scaling factors are never set lower than
the specified minimum scale factor.
The static scaling method may result in faster integration for many types of
problems, but there are potential numerical problems when using this
method. Consider an irreversible reaction “A B” in a plug-flow reactor in
which component “B” is not present in the feed. The scaling factor for
component “A” will be set very large and the scaling factor for “B” will be set
to the minimum scaling factor. This will result in relatively loose tolerance for
the mass balance in “A” and tight tolerance for the mass balance in “B”.
Further, as the reaction approaches completion the component “B” will have a
large flow rate but a small scaling factor. This makes the conservation
equation for “B” difficult to solve, which will result in small integration steps.
Consider the same situation with dynamic scaling. The initial scaling factors
are the same as the static case. With each new step, however, the scaling
factors are updated to the variable values from the previous step. This keeps
the scaled variables close to one throughout the integration. For example:
One pitfall of dynamic scaling, however, occurs when a variable value
decreases and approaches zero. As the value and the scaling factor get

progressively smaller, small absolute errors become large scaled errors. This
also makes the solution difficult, and leads to small steps in the integrator.
This problem can be controlled by setting the minimum scaling factor to a
reasonable value. The default value, 10-10 is much too small for most
problems. A value of 10-5 is reasonable for most situations, and will result in
better model performance.
The hybrid option uses static scaling for all variables except enthalpy, which is
scaled dynamically. This option may be the best choice when the stream
enthalpy is far from the default scale factor, 105 .
In general, the dynamic scaling method results in tighter convergence, but it
requires more simulation time than the static scaling method. This does not
apply to every case, however, and it may also depend on the solver
algorithm. It is a good idea to experiment with these parameters to find the
most reliable convergence strategy for each reactor in each model. When
component attributes are present, as in polymerization kinetics, dynamic
scaling is used by default.
Solver Method
At each step during the integration, the energy, mass, and attribute
conservation equations are solved by trial-and-error. One of the two
“corrector” algorithms, direct substitution or Newton’s method, can be
selected. The Newton algorithm perturbs each variable to determine the
slope, resulting in a smaller number or larger steps compared to the Direct
algorithm. Since the perturbation passes require some time, it is difficult to
predict if the Newton’s method or the Direct method is best for a given
problem. In general, the Newton’s method appears to give the best
performance with polymerization kinetics, but it is a good idea to try using
each algorithm with both dynamic and static scaling to determine the best
combination of convergence parameters for a particular problem.
The corrector tolerance is set as a ratio from the integration tolerance (Corr-
Tol-Ratio). By default, the corrector tolerance is ten times tighter than the
integration tolerance (the corrector tolerance ratio is 0.1). For some
problems, especially those involving reactors with heat transfer calculations,
the optimal corrector tolerance ratio may be higher than 0.1, but this ratio
should not be set larger than 1.0. The flash tolerance should be tighter than
the corrector tolerance. Otherwise, round-off errors in the flash calculations
make the corrector tolerance difficult to achieve. The model always uses the
smaller of the specified RPlug flash tolerance (in the convergence form) or the
global flash tolerance.
Other Integration Parameters
By default, the initial step size in RPlug is set to one percent of the reactor
length (Hinit=0.01). If the solver cannot converge the equations with this
step size, it will cut the step size by a factor of ten. This process will repeat up
to six times. If the solver still cannot converge, the reactor calculation fails
with an error message “solver cannot converge with minimum step size”.
Frequently, reaction rates or heat transfer rates are much faster near the
entrance of the reactor than at the exit of a reactor due to step changes in
temperature or pressure or due to the high concentrations of reactants at the
inlet of the reactor. For these types of problems, the minimum step size may

need to be reduced. For step-growth kinetics, try using an initial step size of
110-4 . Smaller initial step-sizes may be required for addition kinetics,
especially if quasi-steady-state approximations are not applied.
The maximum number of integration steps defaults to 1000. For very “stiff”
kinetics, e.g., kinetics with fast reaction rates involving trace components, the
maximum number of steps may need to be increased, especially if the
corrector is using direct substitution. If more than 5000 steps are required,
try changing the corrector method, scaling method, or increase the cutoff
level.
RPlug stores many types of results at regular intervals (printing points). The
number of intervals defaults to ten, but the number of print points can be
increased to get smoother plots. Since the integration steps do not
necessarily correspond to the print points, the model uses polynomial
interpolation to determine the results for a print point based on the steps
before and after this point. If the integration step sizes are very large, the
interpolation algorithm may give strange results, such as sine waves. This
problem can be fixed by reducing the maximum step size (Max-StepSize) to a
value smaller than the increments between print points (this forces the model
to use linear interpolation). By default, the maximum step size is much larger
than the reactor length.
When hybrid scaling is used, the tolerance of the energy balance is controlled
by the energy balance tolerance ratio.
Common Problems
The following table summarizes common problems encountered when using
the RPlug unit operation block:
Problem Solution
Solver cannot converge
for initial step
Try reducing the initial step size by orders of magnitude from the
default (10-2 ) to 10-8 . If the problem persists, try increasing the cutoff
parameter from 10-10 to 10-5 . If the problem still persists, verify the
values and units of the rate constants in the kinetic model. Verify the
heat-transfer coefficient if applicable. Verify the temperature,
composition, and flow rates of the feed streams. Check the history file
diagnostics for unusually high reaction rates.
Integration error: non-negativity
violation.
This problem is usually related to infeasible reaction kinetics. If using a
user kinetic routine, verify the code, otherwise, a zeroth-order reactant
may be completely consumed. Check the history file diagnostics; look
for the component flow rate or attribute element which has a value of
zero and a negative rate of change.
Integration error:
maximum number of
steps is reached
Try increasing the cutoff parameter from 10-10 to 10-5 . If the problem
persists, try different combinations of scaling method and corrector
method. As a last resort, try increasing the number of steps to 5000. If
the problem still continues, search for errors in the kinetics; check the
diagnostics for unreasonable reaction rates.
Integration error:
corrector tolerance
cannot be achieved
Tighten the flash tolerance to a value below the corrector tolerance.
Loosen the integration tolerance to 110-3 . Increase the corrector
tolerance ratio to 0.2, 0.3, 0.5. If the problem continues, verify the
kinetics and heat-transfer parameters. Check history diagnostics.
Flash failures appear
during the integration
This may be a physical property problem; it may reflect overly-tight
flash tolerances, loosen the local and/or global flash tolerance levels or
increase the maximum number of flash iterations.

Reactor converges but
an error message says
that the mass-balance
does not close
Check the molecular weights of each reactant and product. Verify that
reaction stoichiometry is correct.
RBatch
RBatch is a rigorous model for batch and semi-batch reactors. Any number of
continuous feed streams can be specified in addition to a batch charge
stream. Optionally, a vapor vent may be considered. The RBatch model does
not have a vent condenser option; Aspen Custom Modeler is required to
rigorously model batch polymerization reactors with vent condensers or
overhead columns.
The RBatch model assumes feed and product accumulator holding tanks with
continuous outlets. The accumulator concept provides a bridge between the
continuous steady-state modeling environment in Aspen Plus and the
inherently dynamic nature of batch reactors. The conversion between
continuous streams and discreet charges and dynamic product accumulations
is controlled by specified cycle times and continuous feed stream profiles
specified in the reactor.
Temperature
RBatch allows many options for specifying the reactor duty or temperature, as
summarized here:
Type Specifications Calculations
T-SPEC Reactor temperature The model reports the temperature profile, and
the instantaneous and cumulative duty profiles.
T-PROFILE Reactor temperature as a
function of time. Linear
interpolation is used to determine
temperatures between specified
points.
The model reports the temperature profile, and
the instantaneous and cumulative duty profiles.
T-COOL-SPEC
Heat media stream temperature.
Heat exchange surface area.
The temperature of the reactor is determined
from the energy balance at each time step. The
model reports the temperature profile, and the
instantaneous and cumulative duty profiles.
DUTY-SPEC
Instantaneous heat duty
(assumed constant for entire
cycle). Set the duty to zero to
model an adiabatic reactor.
model reports the temperature profile.
DUTY-PROFILE
Instantaneous heat duty as
function of time. Linear
interpolation is used to determine
duty between specified points.
USER-DUTY
Heat transfer subroutine name The user routine returns the instantaneous heat
duty at each time step. The temperature of the
reactor is determined from the energy. The

The temperature or duty can be specified as a time-varying function. Heat
transfer can be accounted for by assuming a constant thermal fluid
temperature, heat transfer area, and heat transfer coefficient, or by writing a
Fortran routine that returns the instantaneous duty at each time step.
If the temperature or temperature profile is specified, RBatch assumes a
temperature controller. If the reactor is single-phase, or if the reactor volume
is specified, the model assumes perfect temperature control, otherwise, the
model uses a proportional-integral-derivative (PID) controller equation to
represent a temperature controller:
     
reactor
 
Q M K T T
K
I
t s
s t t
T T dt KD
d T T
s
0
    
 
t t t t
t t
dt

 
Where:
Qt = Instantaneous heat duty (J/sec)
Mt
reactor = Mass in reactor at time t (kg)
Tt = Temperature in reactor at time t (K)
Tt
s = Temperature setpoint at time t (K)
t = Time (sec)
K = Proportional gain (J/kg-K)
I = Integral time (sec)
D = Derivative time (sec)
By default, the proportional gain is 2500 J/kg-K, which results in very tight
control at the expense of excessive simulation time. The speed of the model
can be increased by reducing the gain (try a value of 25 J/kg-K).
Pressure
If the reactor volume is not specified, the RBatch model assumes the reactor
operates as a closed system with a variable volume. The pressure at the
reactor is specified as constant value or as a time-varying profile.
If the reactor volume is specified, and there is a vent stream attached to the
reactor, the flow rate of the vent stream is determined from the specified
pressure or pressure profile. The vent flow is positive when the calculated
reactor pressure exceeds the specified reactor pressure.
If the reactor volume is specified, there is no vent stream attached to the
reactor, and the pressure profile is not specified, then the pressure is
determined by the temperature and molar volume of the material inside the
reactor.
If the reactor volume is controlled, a pressure controller model can be linked
to a continuous feed stream. The flow rate of the feed stream is adjusted to
maintain a constant pressure inside the vessel. The continuous feed stream
flow rate can decrease to zero, but it cannot reverse direction if the pressure

exceeds the specified setpoint. The model uses a proportional-integral-derivative
(PID) controller equation to represent the pressure controller:
     
 
F K P P
K
I
s
P P dt KD
d P P
s
t
t t
 
0
    
t t t t t
dt
s

 
Where:
Ft = Instantaneous flow rate (kmol/sec)
Pt
= Pressure in reactor at time t (Pa)
s = Pressure setpoint at time t (Pa)
t = Time (sec)
K = Proportional gain (kmol/sec)/Pa
I = Integral time (sec)
D = Derivative time (sec)
Pt
Reactor Volume
If the reactor pressure is not specified, then RBatch will predict the reactor
pressure based on a specified reactor volume. The pressure will be
manipulated by a trial-and-error algorithm to satisfy the specified volume.
If pressure and volume are both specified, you must either attach a vent
stream to the reactor or attach a continuous make-up stream and pressure
controller to the reactor.
Residence Time
The residence time of the reactor is controlled by user-specified stop criteria.
You can specify whether RBatch should halt the reaction when the stop
criterion variable is approached from above or below. If several stop criteria
are specified, RBatch stops at the first stop criteria it reaches.
In addition to stop criteria, you must specify a maximum time for the reactor.
This prevents runaway calculations in the event that none of the stop criteria
are feasible.
The stop criteria may include one or more of the following:
 A maximum reaction time
 A maximum or minimum component mole or mass fraction in the reactor
 The amount of material (mass, moles, or volume) in the reactor or vent
accumulator
 A maximum vent flow rate
 A maximum or minimum reactor temperature, pressure, or vapor fraction
 The value of a Prop-Set property (includes user Prop-Set properties or
system properties such as viscosity, etc.)

Batch Operations
RBatch can represent batch or semi-batch reactors, depending on what
streams are connected to it in the flowsheet. If a vent stream or time-varying
continuous feed stream is connected to the RBatch block, then the model
operates in semi-batch mode.
The batch reactor model is interfaced into the Aspen Plus continuous flow,
steady-state modeling environment through the concept of holding tanks, as
shown here:
The holding tanks convert the:
 Continuous batch charge stream to a discreet batch charge
 Final vent accumulator inventory to a continuous, time-averaged vent
stream
 Final reactor inventory to a continuous, time-averaged reactor product
stream
Four types of streams are associated with RBatch:
 Continuous Batch Charge
 Time-Varying Continuous Feed
 Time-averaged Continuous Reactor Product
 Time-averaged Continuous Vent Product
Continuous Batch Charge: The material transferred to the reactor at the
start of the cycle. The mass of the batch charge equals the flow rate of the
batch charge stream, multiplied by the batch cycle time. The mass of the
batch charge is equivalent to accumulating the batch charge stream in a
holding tank during a reactor cycle. The contents of the batch charge holding
tank are instantaneously transferred to the reactor at the start of each batch
cycle.
Time-Varying Continuous Feed: Streams that are fed to the reactor over
some discreet interval during the batch cycle. The composition, temperature,
pressure, component attribute values, and time-averaged flow rate of the

stream are specified in the flowsheet. The flow rate of the continuous feed
streams can be specified as a constant value, a time-varying profile, or
manipulated by the pressure controller model to meet a time-varying
pressure setpoint.
Time-averaged Continuous Reactor Product: This stream is determined
by dividing the final reactor inventory by the cycle time. This is analogous to
instantaneously dumping the reactor contents to a large holding tank at the
end of the cycle, and continuously draining the tank throughout each cycle.
Time-averaged Continuous Vent Product: This stream is determined by
dividing the final vent accumulator inventory by the cycle time. During the
batch cycle, the time-varying continuous vent stream is accumulated in the
vent accumulator. The model assumes the vent accumulator contents are
instantly drained to a large holding tank at the end of the cycle, and the
holding tank contents are continuously removed throughout the cycle.
Cycle Time
RBatch is a dynamic batch reactor model that is interfaced into the Aspen Plus
continuous steady-state modeling environment. The interface requires
converting batch charges and accumulator inventories into continuous stream
flow rates. The cycle time is used to convert the batch charge flow rate into
the initial reactor inventory. The cycle time is also used to convert the vent
accumulator inventory and the reactor inventory into vent and reactor
product streams.
For example, assuming a reactor has a cycle time of two hours and that no
continuous feed streams are specified, then:
 If the batch charge stream is set to 50 kg/hour, the initial reactor
inventory is 100 kg.
 If at the end of the reaction cycle, the vent accumulator contains 30 kg of
material, the time-averaged continuous vent stream flow rate is 15 kg/hr.
The composition of the time-averaged vent stream will be the same as the
final composition in the vent accumulator.
 The final reactor inventory will be 70 kg, and the time-averaged reactor
product flow rate will be 35 kg/hr.
RBatch allows you to specify a feed time and down time instead of the cycle
time. In this case, the time-averaged batch charge stream is divided by the
feed time to calculate the initial batch inventory. The time-averaged product
flow rates are based on the cycle time, which is calculated from the sum of
the feed time, the down time, and the reaction time. This option is not
recommended unless it is used to correct the mass balance for the influence
of time-varying continuous feed streams.
To diagnose numerical problems in RBatch, set the terminal reporting level to
“7” in the Block-Options form. With this setting, RBatch reports the time (in
seconds), pressure (in Pascal), temperature (in K), and vapor mole fraction at
each converged integration step.

reported at level 5. At level 6, the model reports reacting component flow
rates and component attribute values. At level 7, the model also reports the
rates of change of these variables. At level 8, the model reports initial scale
factors for all integrated variables.
First, simplify the problem by specifying temperature instead of duty or heat-transfer
parameters (thermal fluid temperature, U, or heat transfer
subroutine). Specify the reactor as “liquid-only”. Specify the reactor pressure,
but not the reactor volume. This will eliminate many possible sources of error
and help focus the problem on kinetics and integration parameters. Once the
model works with these settings, then revert the settings to duty, volume,
and so on, making sure the model converges with each new specification.
Scaling Factors
RBatch uses Gear’s variable-step-size algorithm to numerically integrate the
mass, energy, and attribute conservation equations for the reactor and the
mass-balance equations for the vent condenser (if applicable). At each time
step, the conservation equations are solved by a trial-and-error technique.
RBatch solves the conservation equations using scaling factors to normalize
the variables. The values of these scaling factors have a strong influence on
the speed and reliability of the integration.
The Gear integrator in Aspen Plus offers three error scaling options (ERR-METHOD):
 Static scaling
 Dynamic scaling
 Hybrid scaling
The RBatch static and dynamic scaling factors are summarized here:
Enthalpy 105 (SI units) x mass holdup Enthalpy at previous time step
Component Mass
Inventory In
Reactor and Vent
Accumulator
The scaling factor for each component
inventory equation is set to:
0.1 * (mass of batch charge stream)
The scaling factor at t = t + t is set to the
larger of:
Component mass flow at t
Cutoff
Scaling factors are updated at each step
Class 2 Attribute
Inventory in
Reactor and Vent
Accumulator
The scaling factor of each component
attribute is set to:
(Attribute scaling factor from the TBS
table) x (cycle time) (this is the attribute
inventory at time = 0)
The scaling factor at t = t + t is set to the
larger of:
Attribute inventory at time = t
Cutoff
Scaling factors are updated at each step
The static scaling method uses a constant set of scaling factors throughout
the reactor. The dynamic scaling method updates the scaling factors based on
the previously converged step. The “cutoff” parameter is the minimum scaling
factor used in dynamic scaling.

The static scaling method may result in faster integration for many types of
problems, but there are potential numerical problems when using this
method. Consider an irreversible reaction “A B” in a plug-flow reactor in
which component “B” is not present in the feed. The scaling factor for
component “A” will be set very large and the scaling factor for “B” will be set
to the minimum scaling factor. This will result in relatively loose tolerance for
the mass balance in “A” and tight tolerance for the mass balance in “B”.
Further, as the reaction approaches completion the component “B” has a
large flow rate but a small scaling factor. This makes the conservation
equation for “B” difficult to solve, which will result in small integration steps.
The hybrid option uses static scaling for all variables except enthalpy, which is
scaled dynamically. This option may be the best choice when the stream
enthalpy is far from the default scale factor, 105 .
Consider the same situation with dynamic scaling. The initial scaling factors
are the same as the static case. With each new step, however, the scaling
factors are updated to the variable values from the previous step. This keeps
the scaled variables close to unity throughout the integration. For example:
One pitfall of dynamic scaling, however, occurs when a variable value
decreases and approaches zero. As the value and the scaling factor get
progressively smaller, small absolute errors become large scaled errors. This
also makes the solution difficult, and leads to small steps in the integrator.
This problem can be controlled by setting the minimum scaling factor (cutoff
in the convergence form) to a reasonable value. The default value, 10-10 is
much too small for most problems. A value of 10-5 is reasonable for most
situations, and results in better model performance.
In general, the dynamic scaling method results in tighter convergence, but it
requires more simulation time than the static scaling method. This does not
apply to every case, however, and it may also depend on the solver
algorithm. It is a good idea to experiment with these parameters to find the
most reliable convergence strategy for each reactor in each model. When
component attributes are present, as in polymerization kinetics, dynamic
scaling is used by default.
Solver Method

At each step during the integration, the energy, mass, and attribute
conservation equations are solved by trial-and-error. Two “corrector”
algorithms, direct substitution and Newton’s method, can be selected. The
Newton algorithm perturbs each variable to determine the slope, resulting in
a smaller number or larger steps compared to the Direct algorithm. Since the
perturbation passes require some time, it is difficult to predict if Newton’s
method or the Direct method is best for a given problem. In general,
Newton’s method appears to give the best performance with polymerization
kinetics, but it is a good idea to try using each algorithm with both dynamic
and static scaling to determine the best combination of convergence
parameters for a particular problem.
The corrector tolerance is set as a ratio from the integration tolerance (Corr-
Tol-Ratio). By default, the corrector tolerance is ten times tighter than the
integration tolerance (the corrector tolerance ratio is 0.1). For some
problems, especially those involving reactors with heat transfer calculations,
the optimal corrector tolerance ratio may be higher than 0.1, but this ratio
should not be set larger than 1.0. The flash tolerance should be tighter than
the corrector tolerance. Otherwise, round-off errors in the flash calculations
make the corrector tolerance difficult to achieve. The model always uses the
smaller of the specified RPlug flash tolerance (in the convergence form) or the
global flash tolerance.
Other Integration Parameters
By default, the initial step size in RBatch is set to one tenth of a second
(Hinit=0.1). If the solver cannot converge the equations with this step size, it
will cut the step size by a factor of ten. This process will repeat up to six
times. If the solver still cannot converge, the reactor fails with an error
message “solver cannot converge with minimum step size”.
Frequently, initial reaction rates or heat transfer rates are very fast, so the
minimum step size may need to be reduced. For step-growth kinetics, the
default value should be sufficient. Smaller initial step-sizes may be required
for addition kinetics, especially if quasi-steady-state approximations are not
applied.
The maximum number of integration steps defaults to 1000. For very “stiff”
kinetics, e.g., kinetics with fast reaction rates involving trace components, the
maximum number of steps may need to be increased, especially if the
corrector is using direct substitution. If more than 5000 steps are required,
try changing the corrector method, scaling method, or increase the cutoff
level.
RBatch stores many types of results at regular intervals (printing points). The
number of intervals depends on the reaction time. Since the integration steps
do not necessarily correspond to the print points, the model uses polynomial
interpolation to determine the results for a print point based on the steps
before and after this point. If the integration step sizes are very large, the
interpolation algorithm may give strange results, such as sine waves. This
problem can be fixed by reducing the maximum step size (Max-StepSize) to a
value smaller than the increments between print points (this forces the model
to use linear interpolation). By default, no maximum step size is enforced.
RBatch has the option to stop exactly at print points and vent accumulator
points instead of interpolating these points. When the “exact” option is set to

“yes”, the model adjusts the integration steps to exactly match these points.
This requires extra steps in the integrator that may slow down the model, but
it results in more accurate simulations.
When hybrid scaling is used, the tolerance of the energy balance is controlled
by the energy balance tolerance ratio.
Common Problems
The following table summarizes common problems encountered when using
RBatch:
Problem Solution
Solver cannot converge for
initial step
Try reducing the initial step size by orders of magnitude from the
default (10-1 ) to 10-8 . If the problem persists, try increasing the cutoff
parameter from 10-10 to 10-5 . If the problem still persists, verify the
values and units of the rate constants in the kinetic model. Verify the
heat-transfer coefficient if applicable. Verify the temperature,
composition, and flow rates of the feed streams. Check the history
file diagnostics for unusually high reaction rates.
Integration error: non-negativity
violation.
This problem is usually related to infeasible reaction kinetics. If using
a user kinetic routine, verify the code, otherwise, a zeroth-order
reactant may be completely consumed. Check the history file
diagnostics; look for the component flow rate or attribute element
that has a value of zero and a negative rate of change.
Integration error: maximum
number of steps is reached
Try increasing the cutoff parameter from 10-10 to 10-5 . If the problem
persists, try different combinations of scaling method and corrector
method. As a last resort, try increasing the number of steps to 5000.
If the problem still continues, search for errors in the kinetics; check
the diagnostics for unreasonable reaction rates.
Integration error: corrector
tolerance cannot be
achieved
Tighten the flash tolerance to a value below the corrector tolerance.
Loosen the integration tolerance to 110-3 . Increase the corrector
tolerance ratio to 0.2, 0.3, 0.5. If the problem continues, verify the
kinetics and heat-transfer parameters. Check history diagnostics.
Flash failures appear during
the integration
This may be a physical property problem; it may reflect overly-tight
flash tolerances, loosen the local and/or global flash tolerance levels
or increase the maximum number of flash iterations.
Reactor converges but an
error message says that the
mass-balance does not close
Set the cycle time instead of the feed time.
Check the molecular weights of each reactant and product.
Verify that reaction stoichiometry is correct.
Treatment of Component
Attributes in Unit Operation
Models
As described in previous chapters, Aspen Polymers includes two classes of
component attributes. Class-2 attributes are “primary conserved quantities”
and always have flow-type units (attribute value / unit time). These attributes
include the zeroth moment of the polymer (polymer molecule flow rate), the

segment flow rates, etc. Class-0 attributes are secondary quantities that can
be derived from the primary quantities.
The class-2 attributes follow flow-based mixing rules. In other words, if two
streams are mixed, the product stream class-2 attributes are equal to the
sum of the feed stream class-2 attributes. These mixing rules apply to each
unit operation that allows multiple feeds of the same type (for example,
multiple process fluid feeds). In the distillation models, these mixing rules
apply on a tray-by-tray basis (e.g., if two or more feed streams enter the
same tray).
The blocks with more than one outlet (Flash2, Flash3, Sep, etc.) assume that
the class 2 polymer attributes split according to mass mixing rules. For
example, if 90% of the mass of the polymer flows to the liquid phase, then
90% of the polymer molecules also flow with the liquid phase. This approach
is identical to assuming that the properties of the polymer, such as the
molecular weight distribution, are not fractionated in any way; instead, the
molecular weight distribution of each polymer component in each of the
product phases is identical to that of the polymer in the feed stream.
The following table summarizes the attribute handling for the different
models:
Block Component Attribute Handling
Basic Unit Operation Models
Dupl All attributes in feed stream are copied to each outlet stream.
FSplit
SSplit
Sep
Sep2
Class 2 attributes divide in proportion to flow rate of attributed component. Class 0
attributes are recalculated for each outlet stream.
Equation to calculate outlet stream attributes: A
F
F
out
in
A out
in 
F = Flow rate of attributed component (in = mixed feed, out = outlet)
A = Class-2 component attribute value (in = mixed feed, out = outlet)
Flash2
Flash3
Class 2 attributes divide in proportion to flow rate of attributed component. Class 0
Polymer components are not fractionated by the phase equilibrium models used by
these blocks.
F
F
out
in
A out
in 
When multiple substreams exist, the model distributes polymer attributes between
substreams using the same rule.
Mult Class 2 attributes multiply in proportion to flow rate of attributed component. Class 0
F
F
out
in
A out
in 

Mixer
Heater*
Class 2 attributes are summed across all feed streams. Class 0 attributes are
recalculated for the outlet stream.
Equation to calculate outlet stream attributes: A A out in
 
feeds
Distillation Models
RadFrac Component attribute conservation equations are included in this model at the tray-by-tray
level. The class-2 attributes are calculated at each tray by the following equation:
A
F
F
out
in
A out
in 
F = Flow rate of attributed component (in = mixed feed to tray, out = outlet from tray)
A = Class-2 component attribute value (in = mixed feed to tray, out = outlet from
tray)
The RadFrac model does not allow polymer reaction kinetics.
MultiFrac This unit operation block does not consider component attributes. Polymers must be
converted to oligomer components if polymer fractionation is to be considered in this
model.
Reactor Models
RStoic
RYield
If user specified attributes in the COMP-ATTR form, they are used for the product
stream. Otherwise, class 2 attributes divide in proportion to the flow rate of the
attributed component. Class 0 attributes are recalculated for each outlet stream.
F
F
out
in
A out
in 
RGibbs
REquil
Polymer and heterogeneous catalyst components may not participate in the reactions in
these blocks. The class 2 attributes divide in proportion to the flow rate of the attributed
component. Class 0 attributes are recalculated for each outlet stream.
F
F
out
in
A out
in 
RCSTR
RPlug
RBatch
When using Aspen Polymers reaction kinetics, these models calculate the class-2
component attributes using standard conservation equations. These models can be used
with a user-written Fortran subroutine through the “USER” reaction option. If the user
kinetics include component attributes, then the “COMP-ATTR” field in the user kinetics
form of the reactor model must be set to “yes”. In RCSTR, initial guesses for the outlet
attribute values can be specified in the COMP-ATTR form.
* This also applies to any block that allows multiple feed streams and uses an “implied” mixer to
calculate the net feed stream.

References
Chan, W.-M., Gloor, P. E., & Hamielec, A. E. (1993). A Kinetic Model for Olefin
Polymerization in High-Pressure Autoclave Reactors. AIChE J., 39, No. 1.
Chaudhari, R. V., & Shah, Y. T. (1986). Recent Advances in Slurry Reactors,
Concepts and Design of Chemical Reactors. S.A. Whitaker & A. Cassano
(Eds.). Switzerland: Gordon and Breach Science Publishers.
Henderson, J. N., & Bouton, T. C. (Eds.). (1979). Polymerization Reactors and
Processes. ACS Symp. Ser.
Rodriguez, F. (1996). Principles of Polymer Systems. New York: Taylor &
Francis.
Trambouze, P., van Landeghem, H., & Wauquier, J. P. (1988). Chemical
Reactors: Design/Engineering/Operation. Paris: Editions Technips.
Walas, S. M. (1988). Chemical Process Equipment Selection and Design.
Boston: Butterworths.

16 Plant Data Fitting
Aspen Polymers (formerly known as Aspen Polymers Plus) simulation models
can be fit to plant or laboratory data using Data-Fit. One or more sets of
measured data are provided which may include model inputs or results. Data-
Fit adjusts or estimates input parameters to find the best match between the
model predictions and data. Data-Fit can also reconcile measured data
against the model.
Data-Fit minimizes the weighted sum of square errors, where each error is
the difference between a reconciled input or calculated output and the data.
In statistical terms, Data-Fit performs either ordinary least squares or
maximum likelihood (errors-in-variables) estimation.
 Data Fitting Applications, 339
 Data Fitting For Polymer Models, 340
 Steps for Using the Data Regression Tool, 345
(including troubleshooting tips)
This section emphasizes using the Data-Fit tool to fit process reaction kinetic
parameters. A more general description of this tool is available in the Aspen
Plus User Guide.
Data Fitting Applications
The data regression tool in Aspen Plus can be used to fit model parameters
and reconcile process data. These applications may be carried out
simultaneously.
Parameter regression usually involves adjusting model parameters to improve
the agreement between model predictions and process data. For example,
reaction rate constants may be manipulated to match the measured polymer
molecular weight and monomer conversion. Manipulated parameters may
include reaction rate or equilibrium constants, physical property constants, or
equipment specifications. Fitted parameters may include model predictions
such as reactant conversion, product yield, by-product content, polymer
component attributes, stream compositions or flow rates, or equipment heat
duty, temperature, pressure, or holdup.
16 Plant Data Fitting 339

Data reconciliation runs involve manipulating one or more sets of model
inputs to match model predictions to process data. For example, the average
feed rate of a makeup stream can be estimated based on the flow rate and
composition of the feed and product streams. Manipulated data typically
includes feed stream flow rates and compositions, equipment operating
conditions, heat transfer coefficients, etc.
The Data-Fit model can be used to reconcile input data and fit model
parameters simultaneously. Simultaneous regression and reconciliation is
typically used to fine-tune models which already match process data and
trends relatively well.
Data Fitting For Polymer
Models
Polymer process models frequently include non-ideal phase equilibrium,
reaction kinetics, and complicated unit operations. Fitting these complex
models against process and laboratory data is not a trivial task. A great deal
of consideration must be given to the way this problem is approached.
A detailed example describing how to fit a free-radical reaction kinetics
problem is included in the Aspen Polymers Examples & Applications Case
Book.
A general procedure for fitting complex models is given below.
Step 1. Process Data Review
Collect data for the process. Sources of data include process information
management system (PIMS), process design documents (PDDs), process flow
diagrams (PFDs). Verify reproducibility / standard deviations of data by
collecting multiple data sets for each case. Verify steady state by collecting
data at regular intervals over several plant residence times. Verify data
feasibility against mass and energy balance calculations.
Step 2. Literature Search
Collect information about the process. Sources of data include in-house lab
data, databanks, trade journals, conference notes, polymer handbooks, on-line
electronic databases, experimental designs, etc.
Step 3. Preliminary Model Fitting
Carry out physical property data regression, property constant parameter
estimation runs. Test the parameters against all pertinent data from steps 1
and 2. To the extent possible, verify pure component physical properties and
phase equilibrium predictions using Property Analysis tools.
Step 4. Preliminary Model Development
Develop a basic model of the process, ignoring details such as non-ideal
mixing, heat transfer, etc. Specify temperature instead of duty, volume
instead of residence time. Use parameters from steps 1-3.
340 16 Plant Data Fitting

Step 5. Trend Analysis
Use the sensitivity feature to evaluate trends between model outputs
(conversion, polymer attributes, etc.) and model inputs (rate constants,
operating conditions, etc.) Compare the predicted trends against available
process or lab data. If the trends are not well matched, adjust specific model
parameters to improve the predicted trend. Model fitting may be carried out
using Sensitivity, Design-Specification, Data-Fit, or by trial and error.
Step 6. Model Refinement
Use the Data-Fit tool to carry out simultaneous parameter estimation and
data reconciliation. Relax model assumptions, such as perfect mixing, as
needed. Bring model up to the appropriate level of detail, fitting key
parameters at each development step.
Data Collection and Verification
The first step in fitting a model is to collect and review data. Sources of data
may include process information management system (PIMS), process design
documents (PDDs), and process flow diagrams (PFDs), shift log sheets, and
laboratory analysis reports. It is important to verify the reproducibility of the
data by collecting several duplicate sets of each datum. Duplicate data are
especially important for analytical measurements such as melt flow index and
intrinsic viscosity.
For continuous processes, it is a good idea to verify that the process operates
under steady-state conditions by collecting data at regular intervals. The data
should be collected at regular intervals over a period that exceeds the
cumulative residence time of the key unit operations in the process.
Verify data feasibility against mass and energy balance calculations. It is
impossible to force a rigorous model to match data that violates the
fundamental conservation equations.
When possible, obtain calibration data for unit operating conditions, especially
level calibration data for reactors and flow rate calibration data for flow
meters. The method and assumptions used to calibrate these instruments
must be taken into consideration for data reconciliation runs.
Literature Review
Before you regress process data, it is a good idea to collect information about
the process. Sources of data include in-house lab data, databanks, trade
journals, conference notes, polymer handbooks, on-line electronic databases,
experimental designs, and so on.
The open and in-house process literature may contain a wealth of information
about key model parameters. Further, these sources may provide additional
sources of fundamental data which can be used to independently evaluate
model parameters.
Simulation studies described in trade journals are an excellent source of
insight and know-how related to model development. These studies
frequently point out which assumptions are valid and which parameters are

important. In addition, these papers may elucidate reaction mechanisms or
physical phenomena that should be considered in a rigorous process model.
The physical property and rate constant data reported in the open literature
are never perfect, but they do serve as a good starting point for fitting the
model.
Preliminary Parameter Fitting
It is important to determine as many of the model parameters as possible
early in the model development process. Try to decouple the parameters from
each other whenever possible. For example, find ways to establish phase
equilibrium parameters independently of reaction equilibrium constants. Make
simplifying assumptions to reduce the number of unknown parameters.
Physical property parameters should be firmly established before fitting rate
constants. When data are available, use the physical property data regression
system (DRS) to fit the density, enthalpy, heat capacity, and vapor pressure
of pure components. If phase equilibrium data are available, use DRS to
regress phase equilibrium parameters.
When property data are unavailable for a component, the property constant
estimation system (PCES) can be used to estimate property parameters from
molecular structure. These estimations, however, should be checked against
process data. If data are available for components with similar structures,
they can be used to estimate the properties of components that are not found
in the databank.
The following table lists some of the key physical property parameters in
Aspen Polymers and describes how they influence polymerization kinetics:
Property Parameters Influence on Polymerization Reaction
Kinetics
Density DNLRKT,
DNLVK
Concentration is proportional to density. Reaction
kinetics depend on component concentrations.
Vapor
pressure
PLXANT,
HENRY
The vapor pressure controls phase equilibrium of
volatile components in vapor-liquid systems. The
phase equilibrium strongly influences
concentrations, which controls kinetics.
Enthalpy DHFORM,
DHFVK,
DHFVKM,
DHSUB,
DHCON,
DHFMDP
The component enthalpies influence the predicted
heat duties and temperatures in the model.
Heat capacity CPIG, CPL,
CPLVK,
CPCVK
The heat capacity controls the influence of
temperature on enthalpy.
Transition
temperatures
TMVK, TGVK Phase transitions occur at the melting point and
glass point. Predicted enthalpy, density, and heat
capacity for polymer and oligomer components
depend on the phase regime.
Phase
equilibrium
In multiphase reactors the phase equilibrium
determines the component concentrations in each
phase, which influences the reaction rates.

Property Parameters Influence on Polymerization Reaction
Kinetics
Solubility (of
a solid)
K-SALT The solubility parameter influences the
concentration of partially soluble solids in the
liquid phase. When catalysts, inhibitors, or
monomers are fed as solids, this parameter
controls their concentration, which in turn controls
their reaction rate.
If reaction kinetic parameters are unavailable from in-house or open
literature, it may be necessary to carry out experiments to determine the
magnitude of the rate constants. Carry out the reactions under controlled
conditions to isolate the influence of reaction kinetics from phase equilibrium,
mass transfer, heat transfer, etc. For example, carry out the experiments in
sealed tubes so the liquid phase concentrations are unaffected by phase
equilibrium.
Reaction experiments should be performed over a range of temperatures to
allow determination of the activation energies.
Preliminary Model Development
Once the preliminary parameter fitting is complete, these parameters can be
used to develop a preliminary model. At this stage of the model development
process, it may be best to use simplified models for some of the ancillary
operations that are not directly involved in the polymerization reactors. For
example, it may be more convenient to represent distillation columns using
the non-predictive Sep or Sep2 models instead of the RadFrac or MultiFrac
rigorous distillation models.
The most important rule for model development is to “keep it simple”. Model
development must be carried out in several stages. Add detail to the model
one step at a time. Each generation of the model can yield valuable insights
into the process and can provide substantial benefit to the model developer.
At each stage in the process, fit the appropriate model parameters and
validate the model against all sources of available data. Verify the predicted
trends against process data, operator experience, and engineering know-how.
Over time, the level of detail and power of the model can be increased.
During the preliminary development, use the most basic specifications
possible. For example, in the RCSTR model specify temperature and reacting
phase volume instead of duty and residence time. This approach will make
the model run faster and will help to isolate the influence of property
parameters from reaction kinetic parameters.
Once the preliminary model is complete, it can be tested against process
data. Major discrepancies between the data and the model predictions should
be addressed during this step.
Trend Analysis
Use the preliminary model to carry out trend evaluation studies. The
sensitivity feature can be used to examine the influence of process variables
on the model predictions. Compare these trends against process data. If the

predicted trends are not consistent, adjust the appropriate model parameters
to improve the match. For example, if the predicted slope of the monomer
conversion versus temperature curve is less than the measured slope, the
activation energy of the polymerization reaction may be too low.
Use the sensitivity tool to examine the influence of the model parameters on
the model predictions and to determine which parameters are important in
the model. Parametric studies can be carried out by manipulating two or more
variables in a sensitivity study.
It is good practice to include as many model predictions as possible in each
sensitivity study. The simulation runs take the same amount of time
regardless of the number of defined variables. It is much easier to understand
the predicted trends when the sensitivity results are detailed.
Once you know which parameters are critical to the model predictions, the
data regression tool can be used to adjust these parameters to match specific
trends. Keep the number of manipulated parameters to a minimum until all of
the key parameters are established independently.
Model Refinement
The Data-Fit tool is the best choice for refining the fit between the model
predictions and the process data, especially when several sets of data are
available. Data-Fit can adjust several model parameters simultaneously,
capturing subtle interactions among the parameters to get the best overall
match between the process data and model predictions.
When the model predictions cannot match the process data, the assumptions
in the model may be too broad. Perhaps the process is limited by heat- or
mass-transfer, or a reactor is not ideally mixed. Maybe there are additional
side reactions that should be considered in the model, or the rate expression
needs to be modified to account for some unusual aspect of reaction kinetics.
These issues can be addressed during the model refinement process by
adding new layers of detail to the model. Avoid adding more detail than
necessary, however, because model fitting is a process of diminishing returns.
Model refinement is an open-ended process. The model parameters can be
tuned more accurately as more data become available from the process. Bad
data points are easier to spot when there are more sets of data to compare.
It is impossible for a simulation model to match process data perfectly. There
are several sources of error that lead to differences between the model
results and process data, including:
 Variations in process operating conditions due to disturbances, excursions
from steady state, control system actions, etc.
 Imperfect calibration of flow meters, level controllers, etc.
 Analytical error in lab measurements
 Simplifications and assumptions in the model, such as ideal mixing,
isothermal and isobaric vessels, phase equilibrium, etc.
 Errors in the model parameters.

Steps for Using the Data
Regression Tool
There are three steps involved in using the data regression tool:
 Creating a base-case model
 Entering lab or process data and operating conditions into data sets
 Defining regression cases
Step 1. Creating a base-case model
If the regression tool is being used to fit reaction kinetic parameters from lab
batch reactor data, use the RBatch model with an appropriate reaction kinetic
model.
If the model parameters are being regressed from process data, develop a
model of the process. Before setting up the data fit run, make sure the model
predictions are reasonable and that the model is robust (converges without
errors) over the ranges of each manipulated parameter. You can use
sensitivity blocks to screen the model for accuracy and to test how robust the
model is.
The rate constants and property parameters entered into the base case model
become the initial estimates for the regression.
Step 2. Entering lab or process data and operating conditions into
data sets
There are two types of data sets used with the regression tool, “Point-Data”
and “Profile-Data”:
Use To specify
Point-Data Operating conditions for steady-state unit operation models.
Feed streams for continuous processes or batch charge streams.
Analytical data, measured flow rates, or composition data for product
streams.
Polymer or catalyst component attribute data for product streams.
Profile-Data Operating profiles for batch reactors or plug-flow reactors, including
temperature, pressure, and duty profiles, continuous feed stream
profiles, etc.
Time-series measured data for a batch reactor or data along the axial
profile of a plug-flow reactor.
Note: Component attribute profiles and user variable profiles are not
available as profile data in this release of Aspen Polymers. To fit
profile data for these types of variables, treat each data point in the
profile as a point datum, and specify the coinciding stop-time
(RBatch) or length (RPlug) of the reactor as another point datum in
the same data set.
Step 3. Defining regression cases
For each case, specify the parameters to be adjusted and the data sets to be
fitted. Several regression cases can be included in the same simulation run.
The cases are run sequentially; a prompt will appear on the screen that lets

you specify which cases to include in the run, and the sequence order of the
cases. Each successive case uses the fitted parameters and reconciled data
from the previous case. If the data regression is run again, the previously fit
values are used as initial estimates unless the simulation is reinitialized.
Identifying Flowsheet Variables
You must identify each measured and manipulated variable considered in the
regression. Most types of variables, such as stream flow rates, equipment
operating conditions, and component attribute values can be accessed directly
using the variable accessing system.
In the data regression and data set forms, you cannot access vector data,
such as the stream vector and component attribute vector. You must access
each stream variable or component attribute element as a separate scalar
variable.
When specifying feed stream data, avoid using mole, mass, or volume
fractions as variables in the data set. If the composition of the feed stream
changes from one validation case to another, specify the flow rates of the
components in the stream. If the composition is constant but the flow rate
changes, specify the composition and base-case flow rate in the model, and
specify the total stream flow rate as a point-data variable. This avoids
problems with normalizing fractions and reduces the number of variables
handled by the data-fit algorithm.
Some unit operation models have both input and results variables for the
same operating condition. For example, in the RCSTR model you can access
the specified heat duty (DUTY), or the calculated reactor duty (QCALC). If a
variable is an INPUT variable in the regression it must be specified in the unit
operation model.
For example, if the reactor duty is a manipulated INPUT variable in the
regression, it must be specified as an input variable (DUTY), and the reactor
duty must be specified in the reactor model. If the reactor duty is a measured
RESULTS variable, it must be specified as a results variable (QCALC), and is
usually not specified in the model (the temperature is specified instead).
The following table provides a cross-reference of commonly-used INPUT and
RESULTS variables for key specifications related to several unit operation
models:
Model Operating Condition Input Variable Results Variable
RBatch Cumulative reactor duty DUTY QCALC
RCSTR with one
phase
Duty
Pressure
Temperature
Reactor volume
Reactor residence time
DUTY
PRES*
TEMP
VOL
RES-TIME
QCALC
use outlet stream pressure
TCALC
VOL-CALC
RT-CALC
RCSTR with
multiple phases
Reacting phase volume REACT-VOL VOLL-CALC for liquid volume
VOLV-CALC for vapor volume
VOLLS-CALC for total liquid+solid
volume

Model Operating Condition Input Variable Results Variable
Reacting phase
residence time
PH-RES-TIME VOLL-CALC for liquid residence
time
RTV-CALC for vapor residence
time
RTLS-CALC for liquid or solid
residence time
RPlug Duty
Pressure (process fluid)
Temperature (process
fluid)
Residence time (process
fluid)
DUTY
PRES* (feed)
SPEC-TEMP**
RES-TIME
QCALC
REAC-PRES**
REAC-TEMP**
RT-CALC (entire reactor)
REAC-RESTIM** (residence time
at a profile point)
Flash2 and
Flash3
Duty
Pressure
Temperature
DUTY
PRES*
TEMP
QCALC
use outlet stream pressure
use outlet stream temperature
RadFrac and
MultiFrac
Condenser duty
Reboiler duty
Reflux ratio
Boilup ratio
Stage temperature
Stage pressure
Design specification
setpoint
Q1
QN
basis-RR***
basis-BR***
STAGE-TEMP
STAGE-PRES
VALUE
COND-DUTY
REB-DUTY
RR
BR
TEMP
PRES
various - it depends on the
specification
* The pressure variable is treated as a pressure drop if the specified value is non-positive.
** Specify location (RPlug) or stage number (RadFrac / MulitFrac)
*** Basis can be MOLE, MASS, or STDVOL - the variable specified in the data set
must match the variable specified in the column .
Some measured data, such as polymer melt index and intrinsic viscosity, are
not predicted by the standard property sets in Aspen Polymers. The best way
to include these properties in a data regression is to write a user Prop-Set
property subroutine. Each user property can be linked to a property set.
Property sets can be accessed as stream-property variables.
Manipulating Variables Indirectly
In-line Fortran blocks can be used to enforce assumptions in the model or to
manipulate variables indirectly. Using these techniques to reduce the number
of manipulated variables can greatly enhance the speed and reliability of the
regression.
Example 1: Using Fortran Blocks to Enforce Modeling Assumptions
Suppose:
 Your process involves a catalyst and an initiator.

 The key variables involved in the regression cases are the process
operating conditions and the monomer feed rate. The catalyst and initiator
flow rates are always proportional to the monomer feed rate.
Create a Fortran block and define the monomer, catalyst, and initiator flow
rates as flowsheet variables. Specify the monomer flow rate as a “read
variables” and the catalyst and initiator flow rates as “write variables” as
shown below:
FORTRAN SETCAT
DEFINE FLOMON MASS-FLOW STREAM=FEED COMPONENT=MONOMER
DEFINE FLOINI MASS-FLOW STREAM=ADDITIVE COMPONENT=PEROXIDE
DEFINE FLOCAT MASS-FLOW STREAM=CATALYST COMPONENT=METAL
READ-VARS FLOMON
WRITE-VARS FLOINI FLOCAT
C Specify the base-case flow rates in kg/hr below
F BCMON = 1200.0
F BCCAT = 20.0
F BCINI = 5.0
C Calculate the flow rates of initiator and catalyst
F FLOINI = FLOMON * BCINI / BCMON
F FLOCAT = FLOMON * BCCAT / BCMON
Define the monomer flow rate as a variable in a point-data set. During the
data regression run, the regression model will write the monomer flow rate
for each case. The Fortran block will be executed each time the regression
block manipulates the monomer flow rate. The Fortran block will read the new
monomer flow rate, calculate the initiator and catalyst flow rates, and write
their values.
Using this technique to indirectly manipulate the additive flow rates reduces
the number of variables in the regression, making the regression faster and
more reliable. The cost of this approach is that the indirectly manipulated
variables (catalyst and initiator flow rates) cannot be reconciled (the model
has no information regarding the standard deviations of these variables).
Example 2: Using Parameters and Fortran Blocks to Indirectly
Manipulate Process Variables
Suppose:
 Your polymerization process uses two monomers.
 The key variables involved in the regression cases are the monomer ratio
and the polymer production rate. You want to vary these parameters in
the data regression.
In the base-case model, define the monomer ratio and production rate as
“parameter” variables in a Fortran block. Specify the base-case monomer
ratio and production rate in the same Fortran block. Specify this block to
sequence “first”, as shown below:
FORTRAN INITIAL
DEFINE RATIO PARAMETER 1
DEFINE PRODRT PARAMETER 2
SEQUENCE FIRST
C specify monomer mole ratio
F RATIO = 1.05
C specify polymer production rate, kg/hr
F PRODRT = 2000.0

Create a second Fortran block. Define the monomer flow rates as flowsheet
variables. Access the monomer mole ratio and production rate parameters.
Specify the parameter variables as “read variables” and the monomer flow
rate variables as “write variables”. After solving the algebra, the Fortran block
can be defined as shown below:
FORTRAN ADJUST
DEFINE RATIO PARAMETER 1
DEFINE PRODRT PARAMETER 2
DEFINE FLOM1 MOLE-FLOW STREAM=FEED COMPONENT=MONO-1
DEFINE FLOM2 MOLE-FLOW STREAM=FEED COMPONENT=MONO-2
READ-VARS RATIO PRODRT
WRITE-VARS RATEM1 RATEM2
C w = mole weight of each monomer
F WM1 = 150.23
F WM2 = 230.30
C calculate average molecular weight of monomers
F RATINV = 1.0 / RATIO
F WMAVG = ( 1.0 + RATINV ) * ( WM1 + WM2*RATINV )
C calculate monomer flow rates in kmol/hr
F FLONET = PRODRT / WMAVG
F FLOM1 = FLONET / ( 1.0 + RATINV )
F FLOM2 = FLONET - RATEM1
The production rate and mole ratio parameters can be accessed as parameter
variables in the data-set. The standard deviation for the production rate and
mole ratio variables may be specified; the units of the standard deviations are
the same as the units of the parameters.
Entering Point Data
There are two types of point data: input variables and result variables. Input
variables include feed stream flow rates, equipment operating conditions, and
other parameters that are inputs to the simulation model. Result variables
include product stream flow rates or composition, polymer or catalyst
component attributes, stream properties, or any other simulation calculation
that can be compared to measured process data.
If some results data are missing from one or more sets of data, they can be
left blank on the input forms. The model will estimate the values of these
results and tabulate them after the regression run.
Unknown input data may also be estimated. Leave the input field blank and
specify large standard deviations (for example, 50%) for each missing datum.
Supply a realistic initial guess and make sure the standard deviation results in
reasonable bounds for each missing variable.
The upper and lower bounds for reconciled unknown input variables are
determined from the specified standard deviation and the “bound factor”,
which defaults to ten:
 Lower bound = Measured value - (Bound Factor)*(Standard Deviation)
 Upper bound = Measured value + (Bound Factor)*(Standard Deviation)

Make sure these limits are reasonable. In particular, the limits for a stream
flow rate must not allow the stream flow rate to become zero or negative.
Entering Profile Data
The plug-flow reactor model (RPlug) predicts results at various points along
its length axis. The batch reactor model (RBatch) predicts results at various
points in time during the batch cycle. You can define profile data sets to
specify the operating profiles as input data, or to fit the model to measured
results data.
To do this, specify the time and value for each datum in the profile. You can
specify standard deviations for results variables. Data reconciliation is not
allowed for input profile data.
The following table lists the profile data sets that are currently available for
these reactor models.
Model Variable
Type
Description Profile Name
RBatch,
RPlug
Input Temperature of process fluid TEMPERATURE
Pressure of process fluid PRESSURE
Instantaneous reactor duty DUTY
Results Partial pressure of a component PARTIAL-PRES
Molar concentration of a component in the liquid
phase
MOLECONC-L
Molar concentration of a component in the vapor
phase
MOLECONC-V
Mole fraction of a component in the liquid phase MOLEFRAC-L
Molar fraction of a component in the vapor phase MOLEFRAC-V
Mass concentration of a component in the liquid
phase
MASSCONC-L
Mass concentration of a component in a slurry phase MASSCONC-LS
Mass fraction of a component in the liquid phase MASSFRAC-L
Cumulative reactor heat duty CUM-DUTY
RBatch Input Feed stream component flow rates not applicable
Results Instantaneous vent mole flow rate VENT-MOLFLOW
Instantaneous vent volume flow rate VENT-VOLFLOW
Property Set property in the reactor REACTOR-PROP
Property Set property in the accumulator ACCUM-PROP
Property Set property in the vent VENT-PROP
RPlug Results Property Set property in the reactor PROP-VALUE
If you are fitting component attribute or user Prop-Set property profiles, you
must treat the measured variables as point data for the reactor outlet stream.
Use the reactor length or stop-time as an additional point data. Each profile
point must be treated as a separate data case in the data set.

If some results data are missing from one or more sets of profile data, they
can be left blank on the input forms. The model will estimate the values of
these results and tabulate them after the regression run.
Entering Standard Deviations
Standard deviations may be specified for input and result variables. The
standard deviation is the level of uncertainty in the measurement. You can
enter the value as an absolute or percent error (append a percentage sign,
%, to the value). Statistically determined standard deviations may be
available from an on-line process information management system (PIMS),
from lab databases, or from other information resources. When the standard
deviations are not available, you can enter your best estimate of the expected
error based on your experience or the specifications of the instrument.
The objective function of the data regression is to minimize the sum of
weighted square errors. For results variables, each error is defined as the
difference between the reconciled or specified datum and the value calculated
by the model. Each error is scaled against the square of the standard
deviation:
Objective function =
Measurement Prediction
i (Standard deviation)
2  
i i
i
If the specified standard deviation of a variable is too small, the model over-emphasizes
the importance of the variable during the fitting process. This
may cause the model to make unreasonable adjustments in some parameters
to force good fits to variables with small standard deviations.
You must be careful to consider both the precision and accuracy of each
variable. For example, a variable may have a low standard deviation because
it is very precise (it reproduces well in successive trials), but the
measurement may be inaccurate (it may not reflect the true value of the
measured parameter). Consider the case where a level controller may show
little deviation in the liquid volume in a reactor, but the calibration of the level
transducer may not be accurate to within ten percent of the real liquid
volume. In this case, the standard deviation of the specified liquid volume
should be large enough to reflect the accuracy of the volume, not the
deviation of the liquid level.
If standard deviations are specified for input variables, the model reconciles
these variables. If you do not specify the standard deviation of an input
variable, the model assumes the specified values are exact. Reconciling input
variables accounts for measurement errors in the operating conditions and
can lead to better models, but it can substantially increase how long the run
takes to complete.
Standard deviations must be specified for each of the result variables. Specify
reasonable standard deviations to keep the model from forcing a match by
making wild adjustments to the parameters. The specified standard deviations
are probably too small (or the data quality is poor) if several of the
parameters reach their upper or lower bounds.

Defining Data Regression Cases
You can fit any number of data sets in the same regression case. Point-Data
and Profile-Data may both be included. Each regression case must involve at
least one estimated parameter and at least one reconciled input variable.
There are no upper limits to the number of estimated parameters and
reconciled inputs, however the required simulation time is very sensitive to
the number of variables included in each regression case.
Each input variable with a non-zero standard deviation is reconciled
(adjusted). The reconciled inputs are tabulated in the regression results.
Each estimated parameter must be defined in the base case, or have a default
value (such as a physical property parameter). The specified values for the
base case run are used as the initial guesses for the regression. If the base-case
value lies outside the specified bounds, the boundary condition closest to
the base case value is used.
Sequencing Data Regression Cases
For data fit problems, Aspen Plus will:
 Run the base-case simulation
 Execute the data regression
 Replace the base-case parameter values with the estimated parameter
values and rerun the base-case simulation
If Sensitivity blocks are present, Aspen Plus runs them after the regression is
complete. The estimated parameter values are used to calculate the results
for these blocks.
Flowsheet convergence loops and Design-Specification loops are used in the
preliminary and final base-case simulations and they are sequenced inside the
data regression loop. The sequencing of Fortran blocks and Transfer blocks
depends on which variables are accessed.
If more than one regression is included in a simulation, the regressions can
be affected sequentially. Each successive regression uses the estimated
parameters from the previous regression.
Regression blocks can be manually sequenced if the automatic sequence does
not meet the needs of a particular run, however automatic sequencing is
usually the best choice.
Interpreting Data Regression Results
The key results of the data regression tool are:
 The Chi-square statistic and critical Chi-square value for the fit.
 Estimates and standard deviations for each estimated parameter.
 A table of the measured values, estimated values, and normalized
residuals for each data set.
The Chi-square value is an indicator of the quality of the fit. A model is
considered well fit if the Chi-square value falls below the critical Chi-square
value. The reliability of different fits or different modeling approaches can be

tested by comparing the Chi-square values of the fits. For example, suppose a
reactor is thought to have non-ideal mixing. This assumption can be
evaluated by developing two models, one which assumes ideal mixing (one
CSTR stage) and one which assumes non-ideal mixing (a series of CSTR
stages). The two models can be fit against the same data using the same
parameters. The model with the lower Chi-square statistic represents the data
more accurately, and can be considered the most realistic.
Ideally, the standard deviations of the estimated parameters are small, and
the confidence interval of each parameter is narrow. In practice, however, the
standard deviation of the parameters may be relatively large. This does not
necessarily indicate a poor fit. For example, if the activation energy and pre-exponential
factor for a reaction are both included as estimated parameters in
the data regression, then the standard deviation of the estimated pre-exponential
factor will be large. In this example, small differences in one
parameter (the activation energy) requires large differences in another
parameter (the pre-exponential factor) to keep the model predictions
relatively constant.
The residual values are indicative of the difference between the measured
data and model predictions. For fitted data, the residuals are defined as:
Residual = (Measured value - Predicted value ) 2
/ (Standard deviation )
i i i
i For reconciled data, the residuals are defined as:
Residual = (Measured value - Estimated value ) 2
(Standard deviation i i i
i / )
Review the residual values to verify they are sensible. Large residual values
may indicate a major problem with the model or data, or may reflect an
unreasonably tight standard deviation. Never specify extremely tight standard
deviations. This causes the data regression algorithm to waste time
attempting to obtain tight fits on some variables. If some data are considered
extremely accurate, they should be assigned standard deviations of zero.
The regression results may be plotted against the initial estimates and
measured data. Plots of this type include a 45 dotted line that indicates a
“perfect fit”, e.g., each prediction is exactly equal to the measured data.
Points which fall far from this line are the least well fit. Verify these outliers to
make sure the data is correctly entered into the model and that the units of
measurement are consistent.
If the data regression tool fails to converge, check the objective function. A
large objective function value indicates a poor fit between the model
predictions and measured data. If the objective function is large, review the
residual values for each type of measured data. Large residual values may
indicate a very basic error in the data entry. For example, the data may be
entered in the wrong units or there may be typing errors in the specified
values. Always review the model thoroughly to eliminate these types of
problems before adjusting convergence parameters or making other major
changes to the regression.

Convergence errors can occur for a number of reasons. When a problem
occurs, ask:
 Does the base case model converge well and give reasonable results?
 Is the base case model formulated to handle data that may be out of
mass or energy balance?
 Are the initial estimates of the parameters good enough?
 Are the specified standard deviations reasonable?
 Do the model inputs completely determine the measured results?
 Do the specified bounds allow the regression to take the model into
infeasible regions, causing the unit operation blocks or flowsheet
convergence to fail?
 Are the assumptions and simplifications in the model reasonable?
Regression runs with many variables and runs for highly non-linear models
may still be difficult to converge. In some cases, the convergence criteria may
be unnecessarily tight.
The following table summarizes several convergence parameters that can be
used to tune a regression run. It is not necessary to adjust the convergence
parameters for most regressions.
Parameter Description
ALG-ITERATION Maximum number of algorithm iterations. The default value is
sufficient for nearly all problems
MAX-PASSES Maximum number of flowsheet passes. This parameter may need
to be increased for regressions involving a large number of
variables.
SSQTOL Convergence tolerance for sum of weighted square errors
(Absolute objective function tolerance)
This is the absolute tolerance for the objective function. The
default tolerance is very tight, so regressions that converge to this
tolerance should be reviewed thoroughly. Verify that the specified
standard deviations are sensible. Change the default value of this
parameter if you which to fit the model to achieve a particular
objective function value.
RFCTOL Relative objective function tolerance. The problem is considered
converged if the model predicts that the maximum possible
objective function is less than the product of the relative function
tolerance and the current value of the objective function. For
example, if RFCTOL is 0.1, then the model is converged when the
predicted change in the objective function is less than ten percent
of the objective function value for the current iteration.
XCTOL Minimum variable step-size tolerance. The problem is converged if
the relative step size in the variables falls below XCTOL and the
objective function is decreasing slowly (less than 50% per
iteration).
XFTOL Minimum objective step-size tolerance
INIT-STEP Factor used to determine initial step sizes. This factor can
profoundly affect the performance of the algorithm. If the initial
steps are too large or too small, the model must adjust the step
size until appropriate step sizes are determined.
PERT-FACTOR During the regression, the model determines the response of each
variable to each other variable by making small adjustments, or

Parameter Description
pertubations, to the variables. The size of these adjustments is
determined by the algorithm, this parameter is used to determine
the maximum pertubation step sizes for each variable. You may
need to increase this value when the fitted data are not very
sensitive to the manipulated parameters, or decrease this value
when the sensitivity is very strong.
BOUND-FACTOR
Factor used to determine lower and upper bounds for reconciled
inputs. If the value is too large, the model may enter an infeasible
region, for example a stream flow rate may go to zero. If the
value is too small, the parameter ranges may be too narrow to fit
the data.
INIT-METHOD Method used to initialize the regression. Specify BASE-CASE to use
the base case values to initialize the reconciled input parameters.
Specify MEASUREMENTS to use the measured data to initialize the
reconciled inputs.
Ensuring Well-Formulated Regressions
Poorly formulated regressions may result in large residual values and a large
objective function. Before starting a regression run, use sensitivity studies to
test the model. Verify that the manipulated parameters have a strong
influence on the measured data. Don’t try to fit parameters which have only a
weak impact on the model predictions.
Make sure the parameter ranges are sensible. It is a waste of time to fit a
parameter within a narrow range (less than 5%). On the other hand, if the
range is too large, the regression algorithm may push the model into an
infeasible region. For example, if the distillate to feed ratio in a column is
allowed to decrease to zero, the column model will fail.
The way the data regression is formulated has a major influence on how
quickly and easily the problem converges. De-couple the manipulated
variables as much as possible. For example, don’t fit the rate constants and
phase equilibrium parameters at the same time if the two sets of parameters
can be fit independently in two smaller data regression runs.
Use the weighing factors if some sets of data are more reliable than others. A
larger weight may be assigned to a set of data that are based on long-term
averages from the process information management system, lower weights
might be assigned to data based on poorly kept records from the distant past.
Make sure the manipulated parameters can be determined from the available
data. For example, the activation energy of a reaction cannot be determined
from isothermal data.
The base-case file needs to be formulated in a robust manner. If the base
case model does not converge reliably away from the base case condition,
then it is likely that the regression run will fail. Use the sensitivity tool to
verify that the model is stable over the entire range of each manipulated
parameter and to verify that the model is sensitive to each parameter.
Where possible, use relative or normalized inputs instead of absolute inputs.
For example, in column models use the distillate to feed ratio (D:F) instead of

distillate flow rate. Use pressure drop specifications instead of pressure.
These specifications make the model more reliable and help to avoid problems
that occur if the measured data are inconsistent.
Fitting Activation Energy
It is tempting to try to fit activation energies and pre-exponential factors in
the same regression run. This can lead to significant headaches if the problem
is not approached right. Consider, for example, the standard Arrehnius rate
expression:

E
act
k 
k exp
RT
net o
Using this expression, the net rate constant, knet , is sensitive to the activation
energy, Eact . If the activation energy is adjusted a little bit, a large
adjustment must be made to the pre-exponential factor to offset this
difference. In other words, the activation energy controls the magnitude of
the reaction rate as well as the temperature sensitivity of the reaction rate.
A better approach is to use the modified Arrehnius expression:
k k net o

E
act
R T T

1 1

 
exp
 ref

 
The parameter Tref is a reference temperature that typically represents the
middle of the temperature range used to estimate the activation energy.
Using this formula, the net rate constant, knet , remains constant at the
reference temperature regardless of the value of the activation energy. With
this approach, the pre-exponential factor, ko , controls the magnitude of the
reaction rate at the reference temperature. The activation energy, Eact ,
controls the temperature sensitivity of the rate constant. This makes it much
easier to fit the model.
Scaling the Fitted Parameters
When several types of parameters are adjusted in the same run, the
magnitude of the manipulated parameters may influence how well the data
regression converges. Ideally, the manipulated parameters should be within
several orders of magnitude of each other.
Suppose, for example, the manipulated parameters include rate constants for
several different types of reactions. These expected values of the rate
constants may differ by several orders of magnitude. In this situation, the
regression procedure may over-emphasize the manipulated variables with the
smallest magnitude.
You can get around this problem using two CALCULATOR blocks as shown in
Example 3. Use one CALCULATOR block to define a PARAMETER variable for
each manipulated variable in the regression. Initialize each parameter to one.
Use a second CALCULATOR block to READ these parameter values, to multiply
them by base case values, and then WRITE the results to the manipulated
variables. In the data regression block, manipulate the PARAMETER variables.

This technique allows the data regression to operate on normalized variables
instead of absolute variables which makes it much easier for the regression
algorithm to choose appropriate step sizes and ensures that the variables are
given equal weighting by the algorithm.
Example 3: Using Fortran Blocks to Scale Manipulated Parameters
Problem Description: Suppose two pre-exponential factors are adjusted to
match conversion and intrinsic viscosity, which are defined as user Prop-Set
properties. The pre-exponential factors have very different magnitudes, so
scaling is required to get a good fit.
Instead of manipulating the rate constants directly, use PARAMETER variables
to define and manipulate correction factors for the rate constants. Use a
CALCULATOR block to initialize these correction factors to unity. Manipulate
these PARAMETER variables in the regression. Use a second CALCULATOR
block to adjust the pre-exponential factors using the correction factors
manipulated by the data regression model.
USER-PROPERTY INT-VISC SUBROUTINE=USRPSP FLASH=YES
USER-PROPERTY CONVERSN SUBROUTINE=USRPSP FLASH=YES
PROP-SET INT-VISC INT-VISC
PROP-SET CONVERSN CONVERSN
DATA-SET DS-1
DEFINE CAT MASS-FLOW STREAM=CATALYST SUBSTREAM=MIXED COMPONENT=CAT
DEFINE TEMP BLOCK-VAR BLOCK=CSTR1 SENTENCE=PARAM VARIABLE=TEMP
DEFINE VISC STREAM-PROP STREAM=PRODUCT PROPERTY=INT-VISC
DEFINE CONV STREAM-PROP STREAM=PRODUCT PROPERTY=CONVERSN
USE STD-DEV 0.001 0.1 0.002 0.0050 /
DATA 0.025 290.0 0.844 0.8550 /
DATA 0.023 295.0 0.842 0.8700 /
DATA 0.055 280.0 0.850 0.9050 /
DATA 0.033 292.0 0.835 0.9000
STEP-GROWTH MYMODEL
RATE-CON 1 PRE-EXP=9.67D14 ACT-ENERGY=41.0
RATE-CON 2 PRE-EXP=3.25D0 ACT-ENERGY=0.0
etc…
CALCULATOR INITIAL
DEFINE P1 PARAMETER 1
P1 = 1.0D0
P2 = 1.0D0
EXECUTE FIRST
CALCULATOR ADJUST
DEFINE EXP1 REACT-VAR REACTION=MYMODEL VAR=PRE-EXP SENT=RATE-CON ID1=1
DEFINE EXP2 REACT-VAR REACTION=MYMODEL VAR=PRE-EXP SENT=RATE-CON ID2=2
C specify base case pre-exponential factors for side rxn 1 and 2
F BASE1 = 9.67D14
F BASE2 = 3.25D0
C calculate pre-exponential factors using correction factors

C manipulated by the data regression block
F EXP1 = BASE1 * P1
F EXP2 = BASE2 * P2
READ-VARS P1 P2
WRITE-VARS EXP1 EXP2
REGRESSION FIT-1
DATA DS-1
VARY PARAMETER 1 LABEL=”CORRECT” “FACTOR” “RXN #1”
LIMITS 0.1 10.0
VARY PARAMETER 2 LABEL=”CORRECT” “FACTOR” “RXN #2”
LIMITS 0.1 10.0

17 User Models
This section discusses the features available in Aspen Polymers (formerly
known as Aspen Polymers Plus) for incorporating user modules into a
simulation model.
 User Unit Operation Models, 359
 User Kinetic Models, 365
 User Physical Property Models, 370
Note: For more information on user models, see your Aspen Plus User Models
documentation.
User Unit Operation Models
There are cases where users may need to create special models to represent
a process. Usually these models can be configured by combining several of
the standard unit operation building blocks. For more complex reactor
geometries or in order to represent highly non-ideal systems users may need
to provide their own model as a Fortran subroutine.
There are two user unit operation blocks available: USER and USER2. The first
allows a limited number of inlet and outlet streams. The second allows
multiple inlet and outlet streams. Both unit operations take full advantage of
the Aspen Plus flowsheeting capabilities. The required Fortran subroutine
must process the feed streams and return the condition and composition of
the outlet streams.
User Unit Operation Models Structure
There are three stages to the execution of Aspen Plus unit operation models:
input processing, simulation calculations, and report writing. Normally, the
implementation of a new model requires that all three stages be accounted
for. However, in the case of USER2 models, a generic framework handles the
input setup and processing stage. A Fortran subroutine must be written to
perform the simulation calculations and for writing the report. If no report
17 User Models 359

writer is provided Aspen Plus automatically echoes the input data in the
report.
The following figure summarizes the simulation sequence of a unit operation
model:
User Unit Operation Model Calculations
A user unit operation model can be programmed to represent any unit
operation. Most applications would include combinations of the following:
separations, reactions, heat transfer, mass transfer, mixing and splitting.
There are some common steps that are found in the simulation calculations
within unit operation models, including user models. These steps include:
 Feed processing
 Physical properties and phase equilibrium calculations
 Unit operation calculations (kinetics, heat transfer, mass transfer, etc)
 Results storage and outlet stream initialization
Utilities are available to facilitate each of these steps. The available Fortran
utilities and monitors are:
Stream Handling
NPHASE Determines number of substreams
LPHASE Finds the location of a substream within a stream
SSCOPY Copies a substream from one stream to another
NSVAR Determines the size of the stream vector
360 17 User Models

Component Attribute Handling
GETDPN Find the number average degree of polymerization
GETMWN Find the number average molecular weight
GETPDI Find the polydispersity
GETSMF Find the segment mole fractions
GETSWF Find the segment weight fractions
CAUPT Load attributes into physical property system
LCATT Finds the location of a component attribute in the
stream vector
Component Handling (See Aspen Plus User Models)
CPACK Packs out trace components
ISPOLY Determines if a component is a polymer
ISSEG Determines if a component is a segment
ISOLIG Determines if a component is an oligomer
ISCAT Determines if a component is a catalyst
ISINI Determines if a component is an ionic initiator
KCCID Finds the component index (position in stream vector)
Property Monitors (See Aspen Plus User Models)
KVL Calculates vapor-liquid equilibrium ratio (K-value)
KLL Calculates liquid-liquid equilibrium ratio
ENTHL Calculates liquid mixture enthalpy
VOLV Calculates liquid mixture molar volume
FUGLY Calculates liquid mixture fugacity coefficient
IDLGAS Performs ideal gas calculations
VISCL Calculates liquid mixture viscosity
Flash Routine (See Aspen Plus User Models)
FLASH Flash monitor
Error Handling (See Aspen Plus User Models)
IRRCHK Function to check diagnostic level
ERRPRT Error printing routine
WRTTRM Writer to terminal file or control panel
Report Writer (See Aspen Plus User Models)
RPTHDR Report pagination /header writer
Stream Processing
In order to perform its calculations the user model must be able to read and
process the Aspen Plus stream structure. The stream structure is documented
in Aspen Plus User Models. Example 1 shows a USER2 model routine.
Note: The data in the streams coming in and out of the model are stored in
SI units.
17 User Models 361

There are several utilities available for stream processing. These perform
functions such as finding the number of stream variables, i.e. the size of the
stream vector, copying one stream to another, finding the total number of
substreams, and finding specific substreams within a stream. Several stream
handling utilities are documented in Chapter 4 of Aspen Plus User Models.
In addition to the standard composition and state information found in the
stream structure, there are also component attributes. If the user model
processes polymers, then component attributes must be processed and their
outlet stream values must be calculated and stored. The attributes available
include polymer properties such as degree of polymerization, molecular
weight, polydispersity, and copolymer composition. These are documented in
the Polymer Structural Properties section of Chapter 2. In order to process
attributes, there are Fortran utilities available that perform functions such as
copying attributes from one stream to another, retrieving number average
molecular weight and degree of polymerization, retrieving copolymer
composition, locating specific component attributes within the stream vector,
and determining the size of a vector component attribute. The component
attribute handling utilities are documented in Chapter 4 of Aspen Plus User
Models .
There are also utilities for processing components: for excluding trace
components, for determining component type (polymer, oligomer, segment,
catalyst), etc. These can be found with the component attribute processing
utilities.
Example 1: USER2 Model Routine
C----------------------------------------------------------------------
SUBROUTINE USRMOD (NMATI, SIN, NINFI, SINFI, NMATO,
2 SOUT, NINFO, SINFO, IDSMI, IDSII,
3 IDSMO, IDSIO, NTOT, NSUBS, IDXSUB,
4 ITYPE, NINT, INT, NREAL, REAL,
5 IDS, NPO, NBOPST, NIWORK, IWORK,
6 NWORK, WORK, NSIZE, SIZE, INTSIZ, LD)
C----------------------------------------------------------------------
C
IMPLICIT NONE
C
C DECLARE VARIABLES USED IN DIMENSIONING
C
INTEGER NMATI, NINFI, NMATO, NINFO, NTOT,
+ NSUBS, NINT, NPO, NIWORK,NWORK,
+ NSIZE
C
#include "ppexec_user.cmn"
EQUIVALENCE (RMISS, USER_RUMISS)
EQUIVALENCE (IMISS, USER_IUMISS)
C
#include "dms_plex.cmn"
EQUIVALENCE (IB(1), B(1))
REAL*8 B(1)
C
#include "dms_rglob.cmn"
C
#include "dms_global.cmn"
C
362 17 User Models

#include "dms_ipoff1.cmn"
C
#include "dms_ncomp.cmn"
C
C DECLARE FUNCTIONS
C
INTEGER SHS_LCATT, DMS_KCCIDC
INTEGER XMW, LMW
C
C DECLARE ARGUMENTS
C
INTEGER IDSMI(2,NMATI), IDSII(2,NINFI),
+ IDSMO(2,NMATO), IDSIO(2,NINFO),
+ IDXSUB(NSUBS),ITYPE(NSUBS), INT(NINT),
+ IDS(2,3), NBOPST(6,NPO),
+ IWORK(NIWORK),INTSIZ(NSIZE),NREAL, LD, I
INTEGER KH2O
REAL*8 SIN(NTOT,NMATI), SINFI(NINFI),
+ SOUT(NTOT,NMATO), SINFO(NINFO),
+ WORK(NWORK), SIZE(NSIZE)
C
C DECLARE LOCAL VARIABLES
C
INTEGER IMISS
REAL*8 REAL(NREAL), RMISS, WATER
C
INTEGER IDXP, LZMOM, LMWN, IMWN(2), IZMOM(2)
REAL*8 AMWP, ZMOM
C INITIALIZE ARRAY OF ATTRIBUTE NAMES
DATA IZMOM / "ZMOM"," " /
DATA IMWN / "MWN "," " /
C
C----------------------------------------------------------------------
C
C BEGIN EXECUTABLE CODE
C
C----------------------------------------------------------------------
C OFFSETS TO COMPONENT MOLECULAR WEIGHTS
XMW(I) = DMS_IFCMNC('MW') + I
C
C FIRST COPY FIRST INLET TO FIRST OUTLET
C
DO 100 I = 1, NTOT
SOUT(I,1) = SIN(I,1)
100 CONTINUE
C
C INITIALIZE THE SECOND OUTLET
C
DO 200 I = 1, NCOMP_NCC+1
SOUT(I,2) = 0D0
200 CONTINUE
C
DO 300 I = NCOMP_NCC+2, NCOMP_NCC+9
SOUT(I,2) = RMISS
300 CONTINUE
C
C FIND LOCATION OF COMPONENT ATTRIBUTES
17 User Models 363

C IDXP is position of polymer component in component list.
C Can be obtained with ispoly function
C find location of attributes in stream
LZMOM = SHS_LCATT( 1, IDXP, IZMOM )
LMWN = SHS_LCATT( 1, IDXP, IMWN )
IF (LZMOM .NE. 0) ZMOM = SOUT(LZMOM+1,1)
C
C EXAMPLE OF FINDING A COMPONENT POSITION BY NAME
C
KH2O = DMS_KCCIDC ( 'H2O' )
C
C CAN ALSO PASS POSITION AS PARAMETER IN INT VECTOR
C E.G. KH2O = INT(2)
IF ( KH2O .EQ. 0 ) GO TO 999
C
C PUT COMPONENT (WATER) IN THE SECOND OUTLET
C
WATER = SIN(KH2O,1)
SOUT(KH2O,1) = 0D0
SOUT(NCOMP_NCC+1,1) = SIN(NCOMP_NCC+1,1) - WATER
SOUT(KH2O,2) = WATER
SOUT(NCOMP_NCC+1,2) = WATER
C
999 RETURN
END
Physical Property Calculations
Physical properties and phase equilibrium calculations can be performed
within a user model. Property methods, models, and parameters specified in
the input either through a built-in or a user-defined property method, can be
used for the user model calculations. This can be done through property
monitors. The user model requests the property of interest by calling a
specific monitor, sets the state information and calculation codes in the call to
the monitors, and in turn obtains thermodynamic properties such as fugacity
coefficients, enthalpies, entropies, molar volumes, etc. A flash calculation
routine is also available. See the table on page 360 for a listing of frequently
used property monitors. The FLASH routine and the property monitors are
documented in Aspen Plus User Models. See also User Physical Property
Models on page 370.
Unit Operation Calculations
The purpose of a user unit operation block is to allow the flexibility to
program user correlations or algorithms to represent a process.
Independently from the physical property calculations for which monitors are
provided, users can take advantage of the Fortran subroutine structure to
incorporate the calculations needed to represent their process. Aspen Plus
System Management documents programming guidelines to be followed when
defining the model calculations. The calculations performed within a user unit
operator model for a polymer system are similar to those that could be
performed within a kinetic model. See User Kinetic Models on page 365.
364 17 User Models

Diagnostics
Throughout the simulation calculations, a user model may call the Aspen Plus
error handler to issue diagnostic messages ranging from fatal errors to
warnings and information. The error handler is documented in Aspen Plus
User Models. These diagnostics can be written to the terminal or the control
panel. The USER labeled commons contains output file numbers through
which the terminal, control panel and simulation files can be accessed. See
Aspen Plus User Models for a description of the USER labeled common.
User Unit Operation Report Writing
A report section can be included for a user model in the Aspen Plus simulation
report. This requires a Fortran report writer subroutine. To write the report a
report pagination utility is available. This utility is documented in Aspen Plus
User Models. Note that in the user interface the integer and real arrays for the
user model are displayed on the results screen of the user model.
User Kinetic Models
User kinetic models are primarily intended for situations where the
polymerization phenomena taking place are highly complex and cannot be
represented by the built=in models. Users can write their own equations for
the rate of change of components and the attributes of the polymer that they
are intending to track. This is done through a USER reaction block. The USER
block can be used in conjunction with built-in models. The user model gives
the basic framework for specifying the reaction stoichiometry and the rate
constant parameters. The user kinetic model requires a Fortran subroutine
which performs all the computations that are required for computing the rates
of change for components in the reactive phase and rates of change for
polymer attributes. The structure of this subroutine is documented in Aspen
Plus User Models. For polymerization kinetics user model, there are specific
calculations that are typically performed. These include:
 Locating the polymer component attributes within the stream vector. This
is done through the utility routine SHS_LCATT. Users need to determine
and provide IDXP which is the component index for the polymer.
LDPN = SHS_LCATT( 1, IDXP, ICATYP( 1, IDPN ) )
LZMOM = SHS_LCATT( 1, IDXP,ICATYP( 1, IZMOM ) )
 Retrieving the polymer attribute values from the stream vector SOUT. The
following code shows how to retrieve DPN from SOUT. Other attributes
can be similarly obtained.
IF( LDPN .GT. 0 .AND. SOUT(LDPN+1) .GT. 0D0) DPN = SOUT(LDPN+1)
 Calculating the specific volume of the reacting phase from the stream
vector SOUT. From the stream vector, calculate the total number of moles
and volume of the reacting phase. This example assumes that the reacting
phase is a single liquid phase.
CALL SHS_CPACK (SOUT, NCK, IDXX, XX, TOTFLO)
CALL PPMON_VOLL (
17 User Models 365

+ TEMP, PRES, XX, NCK, IDXX, NBOPST, 4, 1,
+ SVOL, DV, KER)
VFLOW1 = SLIQRX
VFLOW = SVOL * SOUT(NCK+1)
 Calculating molar concentration of each component and class 2 attributes
in the reacting phase. This is obtained by dividing the mole fraction of the
component in the reacting phase by the molar volume of the reacting
phase. It is also shown how to compute concentration of ZMOM, a class 2
attribute for the polymer.
DO 50 I = 1, NC
CONC(I) = XX(I)/SVOL
50 CONTINUE
IF(LZMOM .GT. 0 .AND. VFLOW .GT. RGLOM_RMIN)
ZMOM=SOUT(LZMOM+1)/VFLOW
 Loading the rate constants for each reaction in the reacting phase. The
vector REALR will hold the values of the kinetic constants.
DO 200 I = 1, NR
AK(I) = REALR(I)
200 CONTINUE
 Calculating the rate of reaction for each component and returning that
information to the reactor. The rate equations are user derived. For
example assume that the following user reactions are to be included in the
user kinetics:
A1  A2k1 A3 Waste1 k1
A3 k 2Waste2
The rate constants for user reactions are obtained as:
AK(1) = k1
AK(2) = k2
The reaction rate for the components ( 1=A1, 2=A2, 3=A3 ) are
calculated as:
RATES(1) = -AK(1)*CONC(1)*CONC(2)*VFLOW
RATES(2) = -AK(1)*CONC(1)*CONC(2)*VFLOW
RATES(3) = (AK(1)*CONC(1)*CONC(2) - AK(2)*CONC(3))*VFLOW
 Calculating rate of change for Class 2 attributes for the polymer. The user
is responsible for deriving the expression for the rate of change of
attribute values.
DO 400 I = 1, NTCAT
RATCAT(I) = 0D0
400 CONTINUE
C
The following example code explains the above steps in greater detail.
Note: The data coming in and out of the model are stored in SI units.
Example 2: User Kinetic Subroutine
366 17 User Models

C------------------------------------------------------------------------
SUBROUTINE USRKIP (SOUT, NSUBS, IDXSUB, ITYPE, NINT,
2 INT, NREAL, REAL, IDS, NPO,
3 NBOPST, NIWORK, IWORK, NWORK, WORK,
4 NC, NR, STOIC, RATES, FLUXM,
5 FLUXS, XCURR, NTCAT, RATCAT, NTSSAT,
6 RATSSA, KCALL, KFAIL, KFLASH, NCOMP,
7 IDX, Y, X, X1, X2,
8 NRALL, RATALL, NUSERV, USERV, NINTR,
9 INTR, NREALR, REALR, NIWR, IWR,
* NWR, WR, NRL, RATEL, NRV,
1 RATEV)
C------------------------------------------------------------------------
IMPLICIT NONE
C
C DECLARE VARIABLES USED IN DIMENSIONING
C
INTEGER NSUBS, NINT, NPO, NIWORK,NWORK,
+ NC, NR, NTCAT, NTSSAT,NCOMP,
+ NRALL, NUSERV,NINTR, NREALR,NIWR,
+ NWR
C
EQUIVALENCE (RMISS, USER_RUMISS)
EQUIVALENCE (IMISS, USER_IUMISS)
C
C
C
C.....RCSTR...
#include "rcst_rcstri.cmn"
#include "rxn_rcstrr.cmn"
C
C.....RPLUG...
#include "rplg_rplugi.cmn"
#include "rplg_rplugr.cmn"
EQUIVALENCE (XLEN, RPLUGR_UXLONG)
EQUIVALENCE (DIAM, RPLUGR_UDIAM)
C
C.....RBATCH...
#include "rbtc_rbati.cmn"
#include "rbtc_rbatr.cmn"
C
C.....PRES-RELIEF...
#include "prsr_presri.cmn"
#include "rbtc_presrr.cmn"
C
C.....REACTOR (OR PRES-RELIEF VESSEL OR STAGE) PROPERTIES...
#include "rxn_rprops.cmn"
EQUIVALENCE (TEMP, RPROPS_UTEMP)
EQUIVALENCE (PRES, RPROPS_UPRES)
EQUIVALENCE (VFRAC, RPROPS_UVFRAC)
EQUIVALENCE (BETA, RPROPS_UBETA)
EQUIVALENCE (VVAP, RPROPS_UVVAP)
EQUIVALENCE (VLIQ, RPROPS_UVLIQ)
EQUIVALENCE (VLIQS, RPROPS_UVLIQS)
C
C INITIALIZE RATES
17 User Models 367

C
C
C DECLARE ARGUMENTS
C
INTEGER IDXSUB(NSUBS),ITYPE(NSUBS), INT(NINT),
+ IDS(2),NBOPST(6,NPO),IWORK(NIWORK),
+ IDX(NCOMP), INTR(NINTR), IWR(NIWR),
+ NREAL, KCALL, KFAIL, KFLASH,NRL,
+ NRV, I
REAL*8 SOUT(1), WORK(NWORK),
+ STOIC(NC,NSUBS,NR), RATES(1),
+ FLUXM(1), FLUXS(1), RATCAT(NTCAT),
+ RATSSA(NTSSAT), Y(NCOMP),
+ X(NCOMP), X1(NCOMP), X2(NCOMP)
REAL*8 RATALL(NRALL),USERV(NUSERV),
+ REALR(NREALR),WR(NWR), RATEL(1),
+ RATEV(1), XCURR
C
C DECLARE LOCAL VARIABLES
C
INTEGER IMISS, IDPN(2), IZMOM(2), XMW
REAL*8 REAL(NREAL), RMISS, XLEN, DIAM, TEMP,
+ PRES, VFRAC, BETA, VVAP, VLIQ,
+ VLIQS
DATA IDPN / "DPN ", " " /
DATA IZMOM / "ZMOM", " " /
C BEGIN EXECUTABLE CODE
C ASSUME WE ARE USING A BATCH REACTOR. FOR OTHER REACTORS THE
C PROCEDURE IS SIMILAR
C OFFSETS TO COMPONENT MOLECULAR WEIGHTS
XMW(I)=DMS_IFCMNC('MW')+I
C
C FIND INDEX OF SPECIES BY NAME
IDXP=DMS_KCCIDC('POLY')
C
C
C DETERMINE POINTERS TO POLYMER ATTRIBUTES
LDPN = SHS_LCATT( 1, IDXP, IDPN )
LZMOM = SHS_LCATT( 1, IDXP, IZMOM )
C
C GET POLYMER ATTRIBUTES VALUES FROM SOUT
C
IF( LDPN .GT. 0 .AND. SOUT(LDPN+1) .GT. 0D0) DPN = SOUT(LDPN+1)
C------------------------------------------------------------------
C GET REACTING PHASE SPECIFIC MOLAR VOLUME, SVOL ASSUMING IT IS
C LIQUID
C
CALL SHS_CPACK (SOUT, NCK, IDX, X, TOTFLO)
CALL PPMON_VOLL (
+ TEMP, PRES, X, NCK, IDX, NBOPST, 4, 1, SVOL, DV, KER)
VFLOW1 = SLIQRX
C
C
C GET VOLUME OF REACTING PHASE, VFLOW
368 17 User Models

C
VFLOW = SVOL * SOUT(NCK+1)
C
C-----------------------------------------------------------------
C
C.....CALCULATE MOLAR CONCENTRATIONS OF COMPONENTS AND CLASS 2
C ATTRIBUTES
DO 50 I = 1, NC
CONC(I) = XX(I)/SVOL
50 CONTINUE
IF(LZMOM .GT. 0 .AND. VFLOW .GT. RGLOM_RMIN)
ZMOM=SOUT(LZMOM+1)/VFLOW
C------------------------------------------------------------------
C INITIALIZE THE RATES FOR COMPONENTS TO ZERO
C
DO 100 I = 1, NC
RATES(I) = 0D0
100 CONTINUE
C
C------------------------------------------------------------------
C LOAD REACTION RATE CONSTANTS FROM THE REALR
DO 200 I = 1, NR
AK(I) = REALR(I)
200 CONTINUE
C
C------------------------------------------------------------------
C CALCULATE REACTION RATES FOR COMPONENTS
C
DO 300 I = 1, NC
DO 310 J = 1, NC
M = COMPUTE CORRECT INDEX
RATES(I) = RATES(I) - AK(M) * CONC(I)*CONC(J)*VFLOW
300 CONTINUE
C
C
C CALCULATE RATES FOR CLASS-2 ATTRIBUTE EXAMPLE
C------------------------------------------------------------------
DO 400 I = 1, NTCAT
RATCAT(I) = 0D0
400 CONTINUE
C
C INITIALIZE ATTRIBUTES OF INTEREST IN THIS WAY
C FOR ARRAY ATTRIBUTES THIS GIVES FIRST LOCATION IN ARRAY
C RACAT(LZMOM - (NC+9) + 1) = 0
RETURN
END
17 User Models 369

User Physical Property Models
There is often a need among industrial users to calculate one or more physical
properties based on in-house or literature correlations and expressions that
are not available in Aspen Polymers. In such cases, users can take advantage
of physical property user models.
A user subroutine needs to be supplied for each user model that will calculate
the desired property. For each physical property, a fixed subroutine name and
argument list exists; these can be found in Aspen Plus User Models. An
example of a simple user subroutine that calculates and returns the liquid
molar enthalpy of a mixture (HLMX) is provided below. For instructions on
how to use user physical property models from the graphical user interface,
see Volume 2 of this User Guide, Aspen Polymers Physical Property Methods
and Models.
User model development in polymer simulation is very similar to that in the
simulation of standard components. In case some polymer attributes are
needed for the calculation of a user property, these can be retrieved by
calling the appropriate utility routine (see the table on page 360 for a
summary of the utilities available). The following can be helpful while
developing a physical property user model in Aspen Polymers:
 The index vector, IDX, contains the indexes of the components present in
the current calculation run. For example, if the first component present
currently is listed third in the component list, then: IDX(1) = 3.
 Parameter values are retrieved using the utility DMS_IFCMNC. For
example, suppose you want to pick up the molecular weight of a
component. You need to define an integer array with elements the
locations of the molecular weights of all the components in the component
list on the plex vector, B:
Then, the molecular weight of the component listed third in the
component list is B(XMW(3)).
 In polymer user models, it is often necessary to identify whether a
particular component is polymer, oligomer, or segment. This is done by
the utility logical functions SHS_ISPOLY, SHS_ISOLIG, and PPUTL_ISSEG.
For instance, suppose you want to perform a certain manipulation on the
polymer components present in your run:
IF (SHS_ISPOLY(I)) GO TO 10
Which will send the calculation to line number 10 if the component with
index I is a polymer component.
 The mole fraction vector X (or Z) is based on the apparent molecular
weight of the polymer components. If you need to perform calculations for
a polymer run where the mole fractions are needed, then you must use
the true mole fractions (which are based on the true molecular weight of
the polymer) rather than the apparent mole fractions X. This is done by a
conversion utility routine called POLY_XATOXT:
CALL POLY_XATOXT( N, IDX, XMW, X, XTRUE)
Where: XMW is the vector of the apparent molecular weights, IDX is the
index vector, X is the stream apparent mole fraction vector, and XTRUE is
370 17 User Models

the vector that contains the mole fractions based on the true molecular
weight of the polymer.
 Polymer attributes needed for calculations in user physical property
models are retrieved using utility subroutines. For a list of available
utilities see the table on page 360. As an example, to get the number
average degree of polymerization, DPn, for a particular component you
must give:
CALL POLY_GETDPN( 1, 1, I, DPN )
Where I is the component index. For a detailed description of all the
polymer utilities available see Chapter 4 of Aspen Plus User Models.
 Users can call several Aspen Plus subroutines to perform specific tasks.
For example, routine IDLGAS will return the ideal-gas properties of the
components and their mixture, while PL001 will return the vapor pressure
of the desired components (see Aspen Plus User Models).
 After calculating a molar property, the appropriate conversion must be
made so that the returned property is based on the apparent mole basis.
For instance, after the calculation of the liquid enthalpy of a polymer
component based on the true molecular weight, the following conversion
should be made:
HL_app = HL_true * MW_app / MW_true
A sample user subroutine that calculates and returns the mixture liquid
enthalpy is given in the Example 3.
Note: The data coming in and out of the model are stored in SI units.
Example 3: User subroutine for mixture liquid enthalpy calculation
C----------------------------------------------------------------------
SUBROUTINE HL2U (T ,P ,Z ,N ,IDX ,
1 IRW ,IIW ,KCALC ,KOP ,NDS ,
2 KDIAG ,QMX ,DQMX ,KER )
C
C----------------------------------------------------------------------
C HV2U IS A USER MIXTURE ENTHALPY SUBROUTINE
C
C THIS USER SUBROUTINE CALCULATES THE LIQUID ENTHALPY OF A BINARY
C MIXTURE CONTAINING ONE POLYMER AND ONE SOLVENT.
C
C
C NAME OF MODULE: HL2U
C
C
IMPLICIT NONE
C
DIMENSION Z(N), IDX(N), KOP(10)
DIMENSION D(15)
C... USER DIMENSION
DIMENSION XTRUE(10)
C
C
17 User Models 371

#include "dms_ncomp.cmn"
#include "dms_plex.cmn"
C
EQUIVALENCE (IB(1), B(1))
INTEGER XMW, DHFORM, CPIG, II, DMS_IFCMNC
INTEGER IMON, IPOL, IIMON, IIPOL, I, N, J, ISEG
REAL*8 DELT1, DELT2, DELT3, DELT4, H_MON, H,POL,
* HM_MIX, AVG_MW, T, TREF, QMX
C
C----------------------------------------------------------------------
C
C STATEMENT FUNCTIONS FOLLOW
C
DHFORM(I) = DMS_IFCMNC('DHFORM') + I
CPIG(I,J) = DMS_IFCMNC('CPIG') + 11*(J - 1) + I
C
C *** NOTE *******************************************
C
C PARAMETERS ARE LOCATED USING THE UTILITY DMS_IFCMNC
C AND THE NAME OF THE PARAMETER. FOR EXAMPLE,
C DMS_IFCMNC('MW') RETRIEVES THE LOCATIONS WHERE THE
C COMPONENT MOLECULAR WEIGHTS ARE STORED.
C
C ****************************************************
C
DO 100 I=1,10
XSEG(I) = 0.D0
100 CONTINUE
C
TREF = 298.15
C
C----------------------------------------------------------------------
C
C *** NOTE *******************************************
C COMPONENT ID FOR MONOMER *HARD-WIRED* AT POSITION 2
C COMPONENT ID FOR POLYMER *HARD-WIRED* AT POSITION 3
C ****************************************************
C
IMON = 2
IPOL = 3
ISEG = 4
C
C
C## BOTH Z AND XSEG ARE PACKED: XSEG(IPOL) CONTAINS MOLE FRAC OF SEGMENT
C
CALL XATOXT(N, IDX, B(XMW(1)), Z, XTRUE)
C
C POLYMERIC SPECIES PROP-SET PROPERTIES
C
DELT1 = T - TREF
DELT2 = (T**2 - TREF**2)/2.D0
DELT3 = (T**3 - TREF**3)/3.D0
DELT4 = (T**4 - TREF**4)/4.D0
H_MON = B(DHFORM(IMON)) + B(CPIG(1,IMON))*DELT1 +
+ B(CPIG(2,IMON))*DELT2 + B(CPIG(3,IMON))*DELT3 + B(CPIG(4,IMON))
372 17 User Models

+*DELT4
H_POL = B(DHFORM(IPOL)) + B(CPIG(1,IPOL))*DELT1 +
+ B(CPIG(2,IPOL))*DELT2 + B(CPIG(3,IPOL))*DELT3 + B(CPIG(4,IPOL))
+*DELT4
C
C *** NOTE *******************************************
C IN CASE A COMPONENT ATTRIBUTE WAS NEEDED FOR THE
C CALCULATION OF THE POLYMER ENTHALPY, THE APPROPRIATE
C UTILITY ROUTINE SHOULD BE CALLED.
C
C FOR EXAMPLE, SUPPOSE THE NUMBER-AVERAGE DEGREE OF
C POLYMERIZATION (DPn) OF THE POLYMER WAS NECESSARY.
C THE UTILITY ROUTINE GETDPN CAN BE USED TO RETURN
C THE DESIRED ATTRIBUTE:
C
C CALL POLY_GETDPN (1, 1, IPOL, DPN)
C
C THE ARGUMENTS HAVE THE FOLLOWING MEANING:
C
C 1 = CONVENTIONAL SUBSTREAM
C 1 = DPN FOR 1 COMPONENT IS REQUESTED (NCP=1)
C IPOL = POLYMER COMPONENT INDEX
C DPN = RETURNED VALUE OF THE NUMBER AVERAGE
C DEGREE OF POLYMERIZATION
C
C ****************************************************
C
IIMON = 0
IIPOL = 0
DO 10 I=1,N
II = IDX(I)
IF (II.EQ.IMON) IIMON = I
IF (II.EQ.IPOL) IIPOL = I
10 CONTINUE
C
HM_MIX = H_MON*XTRUE(IIMON) + H_POL*XTRUE(IIPOL)
AVG_MW = B(XMW(IMON))*Z(IIMON) + B(XMW(IPOL))*Z(IIPOL)
C
C
C CONVERT FROM TRUE TO APPARENT MOLE BASIS
QMX = HM_MIX * AVG_MW / B(XMW(ISEG))
C
C
999 CONTINUE
RETURN
END
References
Aspen Plus System Management. Burlington, MA: Aspen Technology, Inc.
17 User Models 373

18 Application Tools
This section discusses the tools available for applying Aspen Polymers
(formerly known as Aspen Polymers Plus) features to solve real-life problems.
The topics covered include:
 Example Applications for a Simulation Model, 375
 Application Tools Available in Aspen Polymers, 376
 Model Variable Accessing, 378
Example Applications for a
Simulation Model
The main purpose of a simulation model is to provide the engineer with a
deeper understanding of the molecular and macroscopic processes which are
vital to a polymer manufacturing process. This understanding will eventually
lead to improvements in various aspects of the process related to safety,
productivity, and polymer product quality. These are some typical scenarios in
which a simulation model is used to meet this objective.
A model may be used to:
 Identify superior grade transition policies and better plant startup and
shutdown procedures which minimize offspec polymer product
 Reduce the number of lengthy and costly experiments on bench, pilot, and
plant scale for polymer product and polymerization process development
 Train process engineers, chemists, plant operators
 Identify sources of variance in polymer product quality
 Provide data for the design of rupture discs and vent lines
 Find optimal temperature profiles for a continuous reactor train which
minimize reaction medium viscosity while meeting product specifications
 Investigate monomer feed policies for a semi-batch copolymerization
process for keeping the chemical composition distribution narrow
 Design a free-radical initiator mix to maximize productivity under the
constraints of safe reactor operations
18 Application Tools 375

Application Tools Available in
Aspen Polymers
Several analysis and flowsheeting tools are available in Aspen Polymers to
configure a model for performing analyses and studies of a process. These
include:
 CALCULATOR - used to incorporate Fortran or Microsoft Excel calculations
in the simulation
 DESIGN-SPEC - used to apply specifications on process variables
 SENSITIVITY - used to examine the effect of varying one or more process
variables
 OPTIMIZATION - used to perform optimization calculations
For each of these tools, with the exception of CALCULATOR, Aspen Plus sets a
loop around a model, flowsheet section, or entire flowsheet. Within this loop,
selected operating variables are manipulated and key process variables are
sampled.
The calculation procedure for analysis and flowsheeting tools is illustrated
here:
The categories of accessible flowsheet variables are described in Model
Variable Accessing on page 378.
Note that in most cases Aspen Plus automatically generates the calculation
sequence. You can also specify a sequence manually. For details on how use
these tools in your simulations, see the Aspen Plus User Guide. Example uses
of these features are given in the Aspen Polymers Examples and Applications
Case Book.
CALCULATOR
Calculator blocks provide a mechanism for you to incorporate Fortran
statements or Microsoft Excel spreadsheets into the flowsheet calculations.
This can be used to calculate and set input variables based on special user
inputs. For this reason, calculator blocks can be used as feed-forward
376 18 Application Tools

controllers. You can also use calculator blocks to calculate and write results to
the Aspen Plus report, control panel, or external file.
Calculator blocks can be used to display charts, tables, or graphs through
Excel.
To use this block you must specify which model variables to sample or
manipulate, enter the Fortran statements or create the Excel sheet, and set
the sequence in which the block must be executed during the flowsheet
calculations.
An example use of a calculator block as a feed-forward controller would be to
hold the flowrate of a catalyst proportional to a monomer flow for a situation
where that monomer flow varies.
DESIGN-SPEC
Design-Spec blocks allow you to set a process variable that is normally
calculated during the simulation. For each specification, you must identify
which process variable can be adjusted to meet that specification. For this
reason, Design-Spec blocks can be used as feedback controllers.
To use this block you must specify which model variables must be fixed, what
values they must be fixed at, and which model input variables can be
manipulated. You can include Fortran statements in Design-Spec blocks.
An example use of a Design-Spec block would be to set a maximum amount
for impurities in a product stream.
SENSITIVITY
Sensitivity blocks provide a mechanism for you to analyze the effect of
operating variables, which you select on the process. This block generates a
matrix of manipulated variables versus sampled variables. If there is more
than one manipulated variable, the sensitivity analysis is performed for each
combination of manipulated variables. It is recommended that you use
multiple Sensitivity blocks if you do not want to combine the manipulated
variables.
To use this block you must specify which are the manipulated variables, which
are the sampled variables, and how they must be tabulated. You can include
Fortran statements in Sensitivity blocks.
An example use of a Sensitivity block would be to determine the effect of
reactor temperature or pressure on the polymer product properties.
OPTIMIZATION
Optimization blocks provide a mechanism for you to minimize or maximize an
objective function calculated using key process variables. To define the
objective function you would use Fortran statements.
To use this block you must define the objective function, specify manipulated
variables, and define constraints, if any.

An example use of Optimization would be to find the optimal reactor
temperature to meet polymer product property specifications while
minimizing reaction medium viscosity.
Model Variable Accessing
When using the various model analysis tools to perform sensitivity studies,
optimization studies, or data fitting, or when applying design specifications, or
adding calculator blocks to a simulation model, users must access many
different flowsheet variables. These flowsheet variables are grouped by type:
 Unit operation block variable
 Stream variable (including polymer component attributes)
 Reaction variable
 Physical property variable
A partial list of accessible variables is given here:
Variable
Identifier Description
Type
Block BLOCK-VAR Unit operation block variable
Unit operation block vector
Stream STREAM-VAR Non component dependent stream variable
MOLE-FLOW Component mole flow
MOLE-FRAC Component mole fraction
MASS-FLOW Component mass flow
MASS-FRAC Component mass fraction
STDVOL-FLOW Component standard volume flow
STDVOL-FRAC Component standard volume fraction
STREAM-PROP Stream Prop-Set property
STREAM-VEC Entire stream vector
SUBSTRM-VEC Entire substream vector
Stream COMPATTR-VAR Component attribute element (Notes 1-4)
COMPATTR-VEC Component attribute (Notes 1-4)
SUBSATTR-VAR Substream attribute element
SUBSATTR-VEC Substream attribute
Reaction REACT-VAR Reaction variable (Note 5)
Physical UNARY-PARAM Unary physical property parameter
Properties BI-PARAM Binary physical property parameter
Notes:
1. Component attributes may be accessed in several ways. They may be
accessed through STREAM-VEC or through SUBSTRM-VEC. In this case,
users are responsible for locating the desired attribute and attribute
element within the stream or substream vector. See the table that follows
for the MIXED substream vector structure.
2. Component attributes may also be accessed with COMPATTR-VAR. With
COMPATTR-VAR, users must provide the element number for attributes

having more than one element. See the Polymer Structural Properties
section of Chapter 2 to find out the dimensions of polymer component
attributes. If the attribute is dimensioned by number of polymer segments,
NSEGS, (e.g. SFLOW, or SFRAC polymer attributes), the ordering of
elements follows the order in which the list of polymer segments was
specified (See the Component Classification section of Chapter 2). For
component attributes dimensioned by number of catalytic sites, each
element represents a site number, i.e. site no. 1, no. 2, etc. For two-dimensional
component attributes dimensioned by number of segments
and number of catalytic sites (NSEGS*NSITES), the first dimension is
NSEG, therefore, the ordering of elements is as follows: the list of specified
segments is repeated for each site beginning with site no. 1.
3. Component attributes may also be accessed with COMPATTR-VEC. In this
case, users are not required to provide an element number since the whole
component attribute is returned as a vector having one or more elements.
The ordering of elements within the attribute vector follows the description
given in Note 2.
4. COMPATTR-VAR and COMPATTR-VEC are equivalent for component
attributes having only one element.
5. REACT-VAR may be used to access kinetic constant parameters for reaction
kinetic models, including free-radical, step-growth and Ziegler-Natta. The
type of information required to access these parameters is model
dependent. For free-radical, the reaction type (INIT-DEC, for example),
and the reacting species are required, in addition to the name of the
parameter to be accessed. The same is true for Ziegler-Natta which also
requires a catalyst site type number. For step-growth, a reaction number is
required. For the standard Aspen Plus reaction models, a reaction number,
and/or substream identifier may be needed to locate the parameters.

The MIXED substream structure is summarized here:
Array Index Description
1, ..., NCC Component mole flows (kgmole/sec)
NCC + 1 Total mole flow (kgmole/sec)
NCC + 2 Temperature (K)
NCC + 3 Pressure (N/m2)
NCC + 4 Mass enthalpy (J/kg)
NCC + 5 Molar vapor fraction
NCC + 6 Molar liquid fraction
NCC + 7 Mass entropy (J/kg-K)
NCC + 8 Mass density (kg/m3)
NCC + 9 Molecular weight (kg/kgmole)
NCC + 10



value
1
ncat1
value
Values for component attribute 1 of component 1
(polymer or other attributed component)



value
1
ncat1
value



value
1
ncat1
value
Note: NCC is the number of conventional components (including polymers,
segments and oligomers) entered on the Components Specifications Selection
sheet. This parameter is stored as NCOMP_NCC in labeled common
DMS_NCOMP (See Aspen Plus User Models, Appendix A).
References
Convergence and Optimization in Aspen Plus, Course notes. Burlington, MA:

19 Run-Time Environment
This chapter discusses various topics related to working in the Aspen
Polymers (formerly known as Aspen Polymers Plus) environment.
The topics covered include:
 Aspen Polymers Architecture, 381
 Installation Issues, 382
 Configuration Tips, 382
 User Fortran, 383
 Troubleshooting Guide, 383
Aspen Polymers Architecture
Aspen Polymers is a layered product. In other words, this product works in
conjunction with a main program. This main program is Aspen Plus for
steady-state simulation and Aspen Dynamics or Aspen Custom Modeler for
dynamic simulation. Aspen Polymers brings to these simulators the polymer
process technology in the form of component characterization, physical
property models and databanks, kinetic models, and the associated input
forms.
As a result of this layered architecture the installation and configuration of
Aspen Polymers is closely tied to that of Aspen Plus for steady-state
simulation and that of Aspen Dynamics and Aspen Custom Modeler for
dynamic simulation. In this chapter we will focus on topics related to the
Aspen Plus environment.
The overall Aspen Polymers architecture is shown here:
19 Run-Time Environment 381

Installation Issues
Hardware Requirements
Aspen Polymers is available on all the hardware platforms supported by Aspen
Plus. For the user interface and engine, these are Windows 2000 with Service
Pack 1 and Windows XP. Consult the Aspen Engineering Suite Installation
Guide for the hardware requirements.
Installation Procedure
Refer to the Aspen Engineering Suite Installation Guide, Aspen Polymers
chapter for information on how to install Aspen Polymers on your system.
Configuration Tips
Startup Files
The information needed to launch the main Aspen Plus application window is
recorded in startup files. These files define the type of simulation, default
settings for the user interface, hosts for the simulation engine, run settings,
etc. One type of startup file is used to define defaults for the type of
simulation. This is the simulation template.
Simulation Templates
Simulation templates are available to help you get started setting up your
model. These templates typically contain options such as unit sets, physical
property method selection, and Table File Format (TFF) selection for stream
result tables. Polymer simulation templates are available. You can create your
own personal template to allow faster definition of a new simulation model.
382 19 Run-Time Environment

To use a simulation template, after starting Aspen Plus, on the startup box
select the template startup option. Then choose one of the polymer simulation
templates. This will automatically setup a global unit set, an appropriate
polymer property method, and a polymer TFF for the stream tables.
To learn more about TFF files see the Aspen Plus System Management.
User Fortran
User Fortran Templates
There are several ways for you to customize your models by adding
calculations in Fortran. The End-Use Properties section of Chapter 2 described
how to setup a user Prop-Set for calculating end-use properties. Chapter 4
described how to setup user unit operation models, user kinetic models, and
user property models. Templates are available for your use in creating the
Fortran files used in these features. You will find these templates in the
following location:
Version Location
Windows %asptop%user
User Fortran Linking
User Fortran calculations in the form of user routines are linked dynamically
to Aspen Polymers during a simulation. Within user Fortran, you will often
access utilities located within Aspen Polymers. In order to access these
utilities, you will need to know the name of the object libraries where they are
located. This applies to the utilities described in Chapter 4 of Aspen Plus User
Models. The name of the utility as shown in the example call sequence
includes the name of the object library where it is located.
You can also create your own dynamic link libraries to hold your user Fortran
files. The Aspen Plus System Management guide describes how to work with
Fortran code modifications.
Troubleshooting Guide
Following are tips to help you diagnose and resolve problems you may run
into while setting up or running Aspen Polymers.
User Interface Problems
A list of symptoms relating to problems you may encounter when using the
user interface is provided below. Possible causes and solutions are given for
each symptom.

Symptom Cause Solution
The polymer input forms
The installation was not
cannot be found on the
complete.
GUI.
You must locate your installation CD and do an
incremental installation of Aspen Polymers.
Select Aspen Polymers from the product list and
chose the subcomponents button to select the
Aspen Polymers steady state installation option.
Aspen Polymers is installed but
not enabled.
Enable Aspen Polymers. From the Tools menu,
select Options. On the Startup tab there is a
box entitled Enable forms for layered
products. Make sure you select Aspen
Polymers
A file created without
using polymer features
appears incomplete in
the components record.
You visited the polymer record
while creating the file, then
later switched off Aspen
Polymers.
You must enable Aspen Polymers (From the
Tools menu, Select Options, click on the Startup
tab). In the Data Browser, select Polymers
(Polymers will appear as incomplete), right
mouse click, select Delete.
Windows crashes during
input specifications.
An invalid operation was
performed either by the Aspen
Plus program or by another
program running
simultaneously.
Usually, when you crash, a backup file is
created. Startup Aspen Plus again, then you
should be able to recover your file. If the invalid
operation was caused by Aspen Plus, repeat the
input steps that lead to the crash, verify that it
is reproducible, and submit the problem to
Technical Support.
Windows crashes during
simulation calculations.
The simulation engine
encountered an error that could
not be transferred to the GUI.
Export an input summary. Run the input
summary alone, then examine the run history
for simulation errors. Change the input
specifications associated with the error and
rerun.
Aspen Plus ran out of resources
to create run files. This can
happen especially for large
simulations. You may see error
messages referring to the
amount of virtual memory
available.
Free-up some disk space and run again. Also,
consult the Aspen Plus System Management
reference manual. An entire section is devoted
to managing virtual memory on Win95/98 and
WinNT.
Aspen Plus ran out of memory
to load dynamic link libraries.
Make some disk space available or increase the
amount of memory available to the application,
then run again.
Windows crashes after
simulation is complete.
Aspen Plus could not load the
simulation results.
If you are running on a remote hosts, there
may have been a communication failure at the
end of the simulation calculations. You can
submit the run again or you can manually load
the results file (.SUM) from the remote host.
If you are running on a local PC host, Aspen
Plus may have run out of memory to load the
results. Make some disk space available or
increase the amount of memory available to the
application and run again.
If the load failure was not due to any of the
above, there may be some information
recorded in the results file (.SUM) that is
causing the problem. Contact Technical Support
and be prepared to supply the results file
and/or your saved simulation file.

Simulation Engine Run-Time Problems
A list of symptoms relating to problems you may encounter with the
simulation engine at run-time are provided below. Possible causes and
solutions are given for each symptom.
During simulation
The application could not find
calculations an error
a valid free license to complete
message occurs for a
the simulation.
license failure.
If the license error message refers to "Feature 10".
This means that you do not have a license for Aspen
Plus itself. If you are using a licensed installation,
then this could be a temporary license failure. This
can happen for multi-user sites, or if you are using a
license manager located on a network. In that case,
you simply need to try again later.
If you are using an installation with a single
activator, then your license key file may be
corrupted, the port where the activator is plugged in
could be damaged, or the activator could be
damaged. To correct your license key files, perform
a license key installation again. If the problem is
your activator, contact Technical Support to have it
replaced.
If the license error message refers to another
feature number, you may still have run into a
temporary license failure (see above). In that case,
try again. If this was not a temporary license failure,
then you created a simulation file which uses
features for which you are not licensed. If the
message refers to "Feature 15", then you are trying
to use Aspen Polymers without a valid license. Other
feature numbers refer to specific add-on products.
You must contact AspenTech to obtain a valid Aspen
Polymers license.
A message box
comes up stating
that an error
occurred in the
Aspen Plus engine.
See "Windows crashes during
simulation calculations" under
User Interface Problems. See
also "After one run a
subsequent run following an
input change crashes" later in
this section.
See "Windows crashes during simulation
calculations" under User Interface Problems. See
also "After one run a subsequent run following an
input change crashes" later in this section.
A run history
message appears
referring to a
dynamic load module
error.
Aspen Plus ran out of
resources to load dynamic link
libraries.
See "Windows crashes during simulation
calculations" under User Interface Problems.

You are referencing user
Fortran and do not have the
compiled object file in your
working directory. The working
directory is the location from
which you opened an existing
file. If you created a file from a
template or opened an existing
file from a floppy or a write
protected area (e.g. xmp or
app) the working directory is
as specified in Tools Options
Startup.
Compile the user Fortran and place it in your run
directory.
A run history
message appears
which refers to
"Virtual Memory
Exhausted".
You ran out of virtual memory
space to load the run files.
See the Aspen Plus System Management, which
discusses virtual memory management.
After one run a
subsequent run
following an input
change crashes.
The problem size has changed
as a result of the input or for
other reasons Aspen Plus
unsuccessfully tried to reuse
the previous run data space.
Usually an error message
appears which states that a
"Fatal error has been
encountered".
Usually after the crash you should be able to recover
your file and run with the input change. To prevent
this from happening for the same run, reinitialize the
simulation before making repeated runs. This is still
a problem that should be reported to Technical
Support.
References
Aspen Engineering Suite Installation Guide for Windows. Burlington, MA:
Aspen Plus System Management. Burlington, MA: Aspen Technology, Inc.

A Component Databanks
This appendix documents the Aspen Polymers (formerly known as Aspen
Polymers Plus) component databanks. There are currently two databanks
available:
 POLYMER Databank - containing polymer pure component parameters
 SEGMENT Databank - containing segment pure component parameters
In addition users may retrieve parameters from the Aspen Plus databanks.
Pure Component Databank
The pure component databanks contain pure component data for over 1500
species. Typically components such as monomers, solvents, catalysts,
initiators, etc. would be retrieved from the pure component databanks. The
parameters in these databanks include those listed in POLYMER Property
Parameters on page 387.
POLYMER Databank
POLYMER contains property parameters for polymers.
Note that a generic polymer component is available in the databank for
custom designed polymers.
POLYMER Property Parameters
The following table shows the parameters stored in the POLYMER databank:
Parameter No. Elements Description
CPIG 11 Ideal gas heat capacity
DGFVK 1 Free energy of formation, ideal gas reference state
DHFVK 1 Heat of formation, ideal gas reference state
DHVLWT 5 Heat of vaporization
MW* 1 Polymer reference molecular weight
OMEGA 1 Acentric factor
PC 1 Critical pressure
A Component Databanks 387

PLXANT 9 Antoine coefficient
TC 1 Critical temperature
VC 1 Critical volume
VLTAIT 9 Tait molar volume model coefficients
ZC 1 Critical compressibility factor
* MW is a reference molecular weight calculated as the average
segment molecular weight using:
MWSEG
NSEG
MW  
For the generic polymer component MW is set to 1.
POLYMER Databank Components
The following table shows the polymers contained in the POLYMER databank:
Alias Polymer Name
ABS Acrylonitrile-butadiene-styrene
BR-1 Poly(butadiene)
CA-1 Cellulose-acetate
Cellulose Cellulose
Chitosan Chitosan
CPE Chlorinated-Poly(ethylene)
CTA Cellulose-triacetate
Dextran Dextran
EVA Ethylene-vinyl-acetate
EEA Ethylene-ethyl-acrylate
EPR Ethylene-propylene
HDPE High-density-Poly(ethylene)
Heparin Heparin
Hyaluronic Hyaluronic-Acid
I-PB Isotactic-Poly(1-butene)
I-PMMA Isotactic-Poly(methyl-methacryl)
I-PP Isotactic-Poly(propylene)
Keratan Keratan-Sulfate
LDPE Low-density-poly(ethylene)
LLDPE Linear-low-density-poly(ethylene)
NBR Nitrile-butadiene-rubber
NYLON6 Nylon-6
NYLON66 Nylon-66
PAA Poly(acrylic-acid)
P(ACA&S) Poly(acrylamide-styrene)
388 A Component Databanks

Alias Polymer Name
PALA Poly(alanine)
PAMIDE Poly(amide)
PAMS Poly(alpha-methylstyrene)
P(AMS&AN) Poly(a-methylstyrene-AN)
PAN Poly(acrylonitrile)
PARA Poly(acrylamide)
PARG Poly(arginine)
PASN Poly(asparagine)
PASP Poly(aspartic-acid)
PB-1 Poly(1-butene)
PBA Poly(n-butyl-acrylate)
PBMA Poly(n-butyl-methacrylate)
P(BMA&S) Poly(n-butyl-methac-styrene)
PBS-1 Poly(butadiene-styrene)
PBT Poly(butylene-terephthalate)
PC-1 Poly(carbonate)
P(C&DMS) Poly(carbonate-dimet-siloxane)
PCHMA Poly(cyclohexyl-methacrylate)
PCYS Poly(cysteine)
PD-1 Poly(decene-1)
PDMA Poly(decyl-methacrylate)
PDMS Poly(dimethylsiloxane)
P(DMS&S) Poly(dimethylsiloxane-styrene)
PE Poly(ethylene)
PEA Poly(ethyl-acrylate)
PEEK Poly(ether-ether-ketone)
PEG Poly(ethylene-glycol)
P(EG&PG) Poly(eth-glycol-prop-glycol)
PEMA Poly(ethyl-methacrylate)
PEO Poly(ethylene-oxide)
P(EO&POX) Poly(eth-oxide-prop-oxide)
P(E&P) Poly(ethylene-propylene)
PET Poly(ethylene-terephthalate)
P(E&VAC) Poly(ethylene-vinyl-acetate)
PGLN Poly(glutamine)
PGLU Poly(glutamic-acid)
PGLY Poly(glycine)
PH Poly(heptene-1)
PHA Poly(n-hexyl-acrylate)
PHENOXY Phenoxy
PHIS Poly(histidine)
PHMA Poly(n-hexyl-methacrylate)
PI Poly(imide)

Alias Polymer Name
PIB Poly(isobutylene)
PIBMA Poly(isobutyl-methacrylate)
PILE Poly(isoleucine)
PIP-1 Poly(isoprene)
PLEU Poly(leucine)
PLYS Poly(lysine)
PMA Poly(methyl-acrylate)
P(MAA&MMA) Poly(methac-acid-met-methac)
P(MAA&S) Poly(methac-acid-styrene)
P(MAA&VAC) Poly(methac-acid-vin-acetate)
PMET Poly(methionine)
PMMA Poly(methyl-methacrylate)
PMMS Poly(m-methylstyrene)
PMP Poly(4-methyl-1-pentene)
PMVPD Poly(2-methyl-5-vinylpyridine)
PNA Poly(sodium-acrylate)
POCS Poly(o-chlorostyrene)
POE Poly(oxyethylene)
POLYMER Generic polymer component
POM Poly(oxymethylene)
POMS Poly(o-methylstyrene)
POP Poly(oxypropylene)
PP Poly(propylene)
PPA Poly(n-propyl-acrylate)
PPBRS Poly(p-bromostyrene)
PPEMA Poly(n-pentyl-methacrylate)
PPG Poly(propylene-glycol)
PPHE Poly(phenylalanine)
PPO Poly(phenylene-oxide)
PPMA Poly(n-propyl-methacrylate)
PPMOS Poly(p-methoxystyrene)
PPMS Poly(p-methylstyrene)
PPOX Poly(propylene-oxide)
PPRO Poly(proline)
PPS Poly(phenylene-sulfide)
PS-1 Poly(styrene)
PSBMA Poly(sec-butyl-methacrylate)
PSER Poly(serine)
PSF Poly(sulfone)
P(S&VP) Poly(sytrene-vinylpyrrolidone)
P(S&VPD) Poly(styrene-4-vinylpyridine)
PT-1 Poly(tetrahydrofuran)
PTFE Poly(tetrafluoroethylene)

Alias Polymer Name
PTHR Poly(threonine)
PTRP Poly(tryptophan)
PTYR Poly(tyrosine)
PU-1 Poly(urethane-fiber)
PVA Poly(vinyl-alcohol)
PVAC Poly(vinyl-acetate)
P(VAC&VAL) Poly(vin-acetate-vin-alcohol)
PVAL Poly(valine)
PVAM Poly(vinyl-amine)
PVC Poly(vinyl-chloride)
PVCAC Poly(vin-chloride-vin-acetate)
PVDC Poly(vinylidene-chloride)
PVDF Poly(vinylidene-fluoride)
PVF Poly(vinyl-fluoride)
PVI Poly(vinyl-isobutyl-ether)
PVME Poly(vinyl-methyl-ether)
PVO Poly(vinylpropionate)
PVP Poly(vinylpyrrolidone)
PVPD Poly(4-vinyl-pyridine)
SAN Styrene-acrylonitrile
SBR Styrene-butadiene-rubber
UF Urea-formaldehyde
SEGMENT Databank
SEGMENT contains property parameters for polymer segments.
Note that a special nomenclature was devised to identify polymer segments.
The segment name consists of the name of the monomer from which it
originates, followed by a label to identify it as a repeat unit (-R) or an end
group (-E). In cases where several molecular structures are possible, a
numeric subscript is used to differentiate the isomers. A similar convention is
used for assigning component aliases.
SEGMENT Property Parameters
The following table shows the parameters stored in the SEGMENT databank:
ATOMNO 10 Vector of atomic number of chemical elements in
segment (used with NOATOM)
CPCVK 6 Crystalline heat capacity
CPIG 11 Ideal gas heat capacity*

CPLVK 6 Liquid heat capacity
DGFVK 1 Free energy of formation, ideal gas reference state
DHCON 1 Enthalpy of condensation
DHFVK 1 Enthalpy of formation, ideal gas reference state
DHSUB 1 Enthalpy of sublimation
DNCVK 4 Crystalline density
DNGVK 5 Glass density
DNLVK 4 Liquid density
MW 1 Molecular weight
NOATOM 10 Vector of number of each type of chemical
element in segment (used with ATOMNO)
TGVK 1 Glass transition temperature
TMVK 1 Melt transition temperature
VKGRP 24 Van Krevelen functional groups
VOLVW 1 Van der Waals volume
UFGRP 24 UNIFAC functional groups
* Estimated from Joback functional group.
SEGMENT Databank Components
The following table shows the SEGMENT databank components:
Alias Segment Name Molecular Structure
CF2-R Methylene-fluoride-R
CO-R Carbonyl-R
CHF2-E Methylene-fluoride-E
CH2O-R Oxymethylene-R
C2O2-R Oxalic-acid-R
CF2
O
C
CHF2
OCH2
O O
C C
C2HO3-E Oxalic-acid-E
C2H2-R-1 cis-Vinylene-R
C2H2-R-2 trans-Vinylene-R
C2H2-R Vinylidene-R
O O
C COH
C CH2

C2H2CL-E Vinyl-chloride-E
C2H2F-E Vinyl-fluoride-E
C2H2CL2-R Vinylidene-chloride-R
C2H2F2-R Vinylidene-fluoride-R
C2H3-E Vinyl-E
C2H3CL-R Vinyl-chloride-R
C2H3F-R Vinyl-fluoride-R
C2H3NO-R Glycine-R
CH CHCl
CH CHF
CH2 CCl2
CH2 CF2
CH CH2
CH2 CHCl
CH2 CHF
NH CH2
C2H3O-E Acetate-E ~COCH3
C2H3O-E-1 Oxyvinyl-E
C2H3O-E-2 Vinyl-alcohol-E
C2H4-R Ethylene-R
C2H4N-E Vinylamine-E-1
C2H4NO-E Glycine-E-1
C2H4NO2-E Glycine-E-2
C2H4O-R-1 Ethylene-oxide-R
C2H4O-R-2 Oxyethylene-R
C2H4O-R-3 Vinyl-alcohol-R
C2H4O2-R Ethylene-glycol-R
O
C
O CH CH2
CH CH
OH
CH2 CH2
CH CH
NH2
NH2 CH2 C
O
CH2 C
O
NH
OH
CH2 CH2 O
O CH2 CH2
CH2 CH
OH
O CH2 CH2 O

C2H5-E Ethylene-E
C2H5N-R Vinylamine-R
C2H5O-E-1 Ethylene-oxide-E-1
C2H5O-E-2 Ethylene-oxide-E-2
C2H5O2-E Ethylene-glycol-E
C2H6N-E Ethyleneamine-E
C2H6OSi-R Dimethyl siloxane-R
C2H7OSi-E Dimethyl siloxane-E
C3H2O2-R Malonic -acid-R
C3H2O2Na-E Sodium acrylate-E-1
C3H3N-R Acrylonitrile-R
C3H3NO-R Acrylamide-R-1
CH2 CH3
CH2 CH
NH2
CH2 CH2
OH
CH3 CH2 O
O CH2 CH2 OH
CH2 CH2
NH2
CH3
Si O
CH3
CH3
Si OH
CH3
O O
CCH2C
CH CH
C
O ONa
CH2 CH
C N
CH CH
C
O NH

C3H3O2-E Acrylic acid-E-1
C3H3O2Na-R Sodium-acrylate-R
C3H303-E Malonic-acid-E
C3H4NO-E Acrylamide-E-1
C3H4NO-B Acrylamide-B
C3H4N2O-B Urea-formaldehyde-R
C3H4O2-R Acrylic-acid-R
C3H4O2Na-E Sodium-acrylate-E-2
C3H5-E Propylene-E-1
C3H5Cl-R 2-chloropropylene-R
CH CH
C
O OH
CH2 CH
C
O
ONa
O O
CCH2COH
CH CH
NH2
C
O
CH2 CH
C
O
NH
CH2
O
N C
N
CH2
CH2
O
CH
C
OH
CH2
O
CH2
C
ONa
CH CH
CH3
CH2 CHCl CH2

C3H5NO-R-1 Acrylamide-R-2
C3H5NO-R-2 Acrylamide-R-3
C3H5NO-R-3 Alanine-R
C3H5NOS-R Cysteine-R
C3H5NO2-R Serine-R
C3H5O2-E Acrylic-acid-E-2
C3H6-R Propylene-R
C3H6NO-E-1 Acrylamide-E-2
C3H6NO-E-2 Alanine-E-1
CH2
O
CH2
C
NH
CH2 CH
O
C
NH2
O
NH CH C
CH3
O
NH CH C
CH2
SH
O
NH CH C
CH2
OH
CH2 CH2
C
O OH
CH2 CH
CH3
CH2 CH2
C
O NH2
NH2 CH C
O
CH3

C3H6NOS-E Cysteine-E-1
C3H6NO2-E-1 Alanine-E-2
C3H6NO2-E-2 Serine-E-1
C3H6NO2S-E Cysteine-E-2
C3H6NO3-E Serine-E-2
C3H6O-R-1 Oxypropylene-R
C3H6O-R-2 Propylene-oxide-R
C3H6O-R-3 Vinyl-methyl-ether-R
C3H6O2-R Propylene-glycol-R
NH2 CH C
O
CH2
SH
O
NH CH C
CH3 OH
O
NH2 CH C
CH2
OH
O
NH CH C
CH2 OH
SH
O
NH CH C
CH2 OH
OH
O CH2 CH
CH3
CH2 CH O
CH3
CH2 CH
O
CH3
O CH2 CH O
CH3

C3H6O2-R-1 1,3-Propanediol-R ~O(CH2)3O~
C3H6O2-R-2 1,2-Propanediol-R
C3H7-E Propylene-E-2
C3H7O-E-1 Oxypropylene-E
C3H7O-E-2 Propylene-oxide-E
OCHCH2O
CH3
CH2 CH2
CH3
CH2 CH
CH3
HO
CH2 CH
CH3
C3H7O-E-i i-Propanol-E ~OCH(CH3)2
C3H7O-E-n n-Propanol-E ~O(CH2)2CH3
C3H7O2-E Propylene-glycol-E
O OH
CH2 CH
CH3
C3H7O2-E-1 1,3-Propanediol-E ~O(CH2)3OH
C3H7O2-E-P 1,2-Propanediol-E-P
C3H7O2-E-S 1,2-Propanediol-E-S
C4H2O2-R-cis Maleic-acid-R
C4H2O2-R-tra Fumaric-acid-R
C4H3O3-E-cis Maleic-acid-E
C4H3O3-E-tra Fumaric-acid-E
OH
OCHCH2OH
CH3
OCH2CHCH3
OH
O
C
C
O
C
C
H H
O
H C
C
C
O
C
H
O
C
C
O
C
COH
H H
O
H COH
C
C
O
C
H

C4H4O2-R Succinic-acid-R
C4H5-B Butadiene-B
C4H5-E-1 Butadiene-E-1
C4H5NO3-R Aspartic-acid-R
C4H5O2-E-1 Methyl-acrylate-E-1
C4H5O2-E-2 Methyl-acrylic-acid-E-1
C4H5O2-E-3 Vinyl-acetate-E-1
C4H5O3-E Succinic-acid-E
C4H6-R-1 Butadiene-R-1
C4H6-R-2 Butadiene-R-2
C4H6NO3-E Aspartic-acid-E-1
O O
C(CH2)2C
CH2 CH CH CH
CH CH CH CH2
CH2 CH C CH2
NH CH C
O
CH2
C
O OH
C CH2
C
O OCH3
CH3
C
CH
C
O OH
CH CH
O
CH3
C
O
O O
C(CH2)2COH
CH2 CH CH CH2
CH2 CH
CH CH2
NH2
CH
CH2
C
O OH
C
O

C4H6NO4-E Aspartic-acid-E-2
C4H6N2O2-R Asparagine-R
C4H6O2-R-1 Methyl-acrylate-R
C4H6O2-R-2 Methyl acrylic-acid-R
C4H6O2-R-3 Vinyl-acetate-R
C4H7-E-1 1-Butene-E
C4H7-E-2 Isobutylene-E
NH
CH
CH2
C
O OH
C
O
OH
NH
CH
CH2
C
O
C
O
NH2
CH
C
O
CH2
O CH3
CH2
O
CH3
C
C
OH
CH2 CH
O
C CH3
O
CH CH
C2H5
CH C
CH3
CH3
CH2 CH2 CH CH2
CH2 CH CH CH3

C4H7NO2-R Threonine-R
C4H7N2O2-E Asparagine-E-1
C4H7N2O3-E Asparagine-E-2
C4H7O2-E-1 Methyl-acrylate-E-2
C4H7O2-E-4 Vinyl-acetate-E-2
C4H8-R-1 1-Butene-R
NH CH C
O
CHOH
CH3
NH2 CH C
CH2
C
O
O
NH2
NH CH
CH2
C
O
C
O
NH2
OH
CH2 CH2
C
O O CH3
CH3
CH2 CH
C
O OH
CH3
C CH3
C
O OH
CH2 CH2
C
O O CH3
CH2 CH
C2H5

C4H8-R-2 Isobutylene-R
C4H8NO2-E Threonine-E-1
C4H8NO3-E Threonine-E-2
C4H8O-R Tetrahydrofuran-R
C4H8O2-R Butylene-glycol-R
C4H8O3-R Diethylene-glycol-R
C4H9O-E-1 Tetrahydrofuran-E-1
C4H9O-E-2 Tetrahydrofuran-E-2
C4H9O2-E Butylene-glycol-E
C4H9O3-E Diethylene-glycol-E
C5H6O2-R Glutaric-acid-R
C5H7NO-R Proline-R
C5H7NO3-R Glutamic-acid-R
CH3
CH2 C
CH3
NH2 CH C
O
CHOH
CH3
CH C O
CHOH
CH3
NH
OH
CH2 CH2 CH2 CH2 O
O C4H8 O
O C2H4 O C2H4 O
C4H8 OH
C4H9 O
O C4H8 OH
O C2H4 O C2H4 OH
O O
C(CH2)3C
N
O
C
NH CH C
O
C2H4
C
O OH

C5H7O2-E-1 Methyl-methacrylate-E-1
C5H7O2-E-2 Ethyl-acrylate-E-1
C5H7O2-E-3 Vinyl-propionate-E-1
C5H7O3-E Glutaric-acid-E
C5H8-R Isoprene-R
C5H8NO-E Proline-E-1
C5H8NO2-E Proline-E-2
C5H8NO3-E Glutamic-acid-E-1
CH3
CH C
C
O O CH3
CH CH
C
O O C2H5
CH CH
O
C C2H5
O
O O
C(CH2)3COH
CH2 C CH CH2
CH3
HN
O
C
O
N
C OH
NH2 CH C
O
C2H4
C
O OH

C5H8NO4-E Glutamic-acid-E-2
C5H8N2O2-R-1 Glutamine-R
C5H8N2O2-R-2 Trimethylene-diisocyanate-R
C5H8O2-R-1 Methyl-methacrylate-R
C5H8O2-R-2 Ethyl-acrylate-R
C5H8O2-R-3 Vinyl-propionate-R
C5H9-E 1-Pentene-E-1
C5H9NO-R Valine-R
NH
O
CH C
C2H4
C
O OH
OH
NH
O
CH C
C2H4
C
O
NH2
O
NH C3H6 NH
O
C C
CH3
C
CH2
C
O OCH3
CH2 CH
C
O O C2H5
CH2 CH
O
C2H5
C
O
CH CH
C3H7
NH CH C
O
CH
CH3 CH3

C5H9NOS-R Methionine-R
C5H9N2O2-E Glutamine-E-1
C5H9N2O3-E Glutamine-E-2
C5H9O2-E-3 Ethyl-acrylate-E-2
C5H9O2-E-4 Vinyl-propionate-E-2
C5H10-R 1-Pentene-R
NH CH C
O
C2H4
S
CH3
O
NH2 CH C
C2H4
C
O NH2
CH3
CH2 CH
O CH3
C
O
CH3
OCH3
CH2 CH2
O
CH3
C
C
C
O O C2H5
CH2 CH2
O
O
C C2H5
CH2 CH
C3H7

C5H10NO-E Valine-E-1
C5H10NOS-E Methionine-E-1
C5H10NO2-E Valine-E-2
C5H10NO2S-E Methionine-E-2
C6H4S-R Phenylene-sulfide-R
C6H5O-E Phenol-E
C6H5S-E-1 Phenylene-sulfide-E-1
C6H5S-E-2 Phenylene-sulfide-E-2
C6H6N2-R-M m-Phenylene-diamine-R
C6H6N2-R-O o-Phenylene-diamine-R
C6H6N2-R-P p-Phenylene-diamine-R
O
NH2 CH C
C2H4
S
CH3
NH CH C
O
OH
CH
CH3 CH3
NH CH C
O
OH
C2H4
S
CH3
S
O
S
SH
NH NH
NH NH
NH NH

C6H7N2-E-M m-Phenylene-diamine-E
C6H7N2-E-O o-Phenylene-diamine-E
C6H7N2-E-P p-Phenylene-diamine-E
C6H7N3O-R Histidine-R
C6H8NO-E Vinylpyrrolidnone-E-1
C6H8N3O-E Histidine-E-1
C6H8N3O2-E Histidine-E-2
C6H8O2-R Adipic-acid-R
C6H9NO-R Vinylpyrrolidnone-R
C6H9O2-E-1 Ethyl-methacrylate-E-3
NH NH2
NH NH2
NH NH2
O
CH CH
N C
O O
C (CH2)4 C
CH2 CH
N C
O
CH C CH3
C
O O C2H5

C6H9O2-E-2 n-Propyl-acrylate-E-1
C6H9O3-E Adipic-acid-E
C6H10-R 1,4-Hexadiene-R
C6H10NO-E Vinylpyrrolidnone-E-3
C6H10O2-R-1 Ethyl-methacrylate-R-1
C6H10O2-R-2 n-Propyl-acrylate-R
C6H10O3-R Amylose-R
C6H10O5-R-1 Cellulose-R
CH CH
C
O O C3H7
O O
C (CH2)4 C OH
CH2 CH
CH2
CH
CH
CH3
CH2 CH2
N C
O
CH3
CH2 C
C
O O C2H5
CH2 CH
C
O O C3H7
CH2OH
O
O
CH2OH
O
O
OH OH

C6H10O5-R-2 Dextran-R
C6H11-E-1 4-Methyl-1-pentene-E-1
C6H11-E-2 1-Hexane-E-1
C6H11NO-R-1 Caprolactam-R
C6H11NO-R-2 Isoleucine-R
C6H11NO-R-3 Leucine-R
C6H11O-E Vinyl-isobutyl-ether-E-1
O CH2
O
OH OH
HO
CH CH
CH2 CH
CH3
CH3
CH CH
C4H9
NH (CH2)5 C
O
NH CH
O
C
CH C2H5
CH3
O
C
CH3
CH
CH2
NH
CH
CH3
CH3
CH3
CH CH
O
CH2 CH
CH3
CH2 CH
C
O O C2H5

C6H11O2-E-3 n-Propyl-acrylate-E-2
C6H11O3-E Amylose-E
C6H11O5-E Cellulose-E-1
C6H11O6-E-1 Cellulose-E-2
C6H11O6-E-2 Dextran-E-2
C6H12-R-1 1-Hexane-R
C6H12-R-2 4-Methyl-1-pentene-R
C6H12NO-E-1 Caprolactam-E-1
CH3
CH3 C
C
O O C2H5
CH2 CH2
C
O O C3H7
CH2OH
C O
HO
CH2OH
O
HO
OH OH
CH2OH
O
OH
OH OH
O
CH2 O
O
OH
OH OH
HO
CH2 CH
C4H9
CH2 CH
CH2 CH
CH3
CH3
O
NH2 (CH2)5 C

C6H12NO-E-2 Isoleucine-E-1
C6H12NO-E-3 Leucine-E-1
C6H12NO2-E-1 Caprolactam-E-2
C6H12NO2-E-2 Isoleucine-E-2
C6H12NO2-E-3 Leucine-E-2
C6H12N2O-R Lysine-R
C6H12N4O-R Arginine-R
C6H12O-R Vinyl-isobutyl-ether-R
NH2 CH C
CH
O
CH3 C2H5
NH2 CH C
O
CH3
CH3
CH2 CH
O
C
OH
NH (CH2)5
O
C
OH
NH CH
CH
CH3 C2H5
O
C
OH
NH CH
CH2
CH CH3
CH3
O
NH CH C
C4H8 NH2
NH CH C
O
CH2
CH2
CH2
NH
C NH
NH2
CH2 CH
O CH2 CH
CH3
CH3

C6H12O2-R Hexamethylene-diol-R
C6H13-E-3 1-Hexane-E-2
C6H13N2O-E Lysine-E-1
C6H13N2O2-E Lysine-E-2
C6H13N4O-E Arginine-E-1
C6H13N4O2-E Arginine-E-2
O (CH2)6 O
CH2 CH2
CH2 CH
CH3
CH3
CH3
CH3
CH3 CH
CH2 CH
CH3 CH
C4H9
NH2 CH C
O
C4H8 NH2
O
NH CH C
OH
C4H8 NH2
O
CH C
CH2
CH2
CH2
NH
C NH
NH2
NH2
O
OH
CH C
CH2
CH2
CH2
NH
C NH
NH2
NH

C6H13O-E Vinyl-isobutyl-ether-E-2
C6H13O2-E Hexamethylene-diol-E
C6H14N2-R Hexamethylene-diamine-R
C6H15N2-E Hexamethylene-diamine-E
C7H5O-E Benzoic-acid-E
C7H5O2-E Phenylcarbonate-E
C7H6N-E 4-Vinyl-pyridine-E-1
C7H7N-R 4-Vinyl-pyridine-R
C7H8N-E 4-Vinyl-pyridine-E-2
C7H10O2-R Pimelic-acid-R
C7H11O2-E-1 n-Butyl-acrylate-E-1
CH2 CH2
O
CH2 CH
CH3
CH3
O (CH2)6 OH
NH (CH2)6 NH
NH (CH2)6 NH2
O
C
C
O
O
CH CH
N
CH2 CH
N
CH2 CH2
N
O O
C(CH2)5C
CH CH
C
O O C4H9

C7H11O2-E-2 n-Propyl-methacrylate-E-1
C7H11O3-E Pimelic-acid-E
C7H12O2-R-1 n-Butyl-acrylate-R
C7H12O2-R-2 n-Propyl-methacrylate-R
C7H13-E 1-Heptene-E-1
C7H13O2-E-1 n-Butyl-acrylate-E-2
C7H14-R 1-Heptene-R
C7H15-E-1 1-Heptene-E-2
CH C
CH3
C
O O C3H7
O O
C(CH2)5COH
CH
C
CH2
O O C4H9
CH3
CH2 C
C
O O C3H7
CH CH
C5H11
CH2 CH2
C
O O C4H9
CH3
CH2 CH
C
O O C3H7
CH3
CH3 C
C
O O C3H7
CH2 CH
C5H11
CH2 CH2
C5H11

C7H15-E-2 1-Heptene-E-3
C8H4O2-R Terephthalate-R
C8H4O2-R-1 Phthalate-R
C8H4O2-R-2 Isophthalate-R
C8H5O3-E Terephthalic-acid-E
C8H5O3-E-1 Phthalic-acid-E
C8H5O3-E-2 Isophthalic acid-E
C8H6Br-E p-Bromostyrene-E-1
C8H6Cl-E-1 o-Chlorostyrene-E-1
CH3 CH
C5H11
O O
C C
C
C
O
O
C
O O
C
O O
C C
OH
C
C OH
O
O
C
O O
C
OH
CH CH
Br
CH CH
Cl

C8H6Cl-E-2 p-Chlorostyrene-E-1
C8H7-E Styrene-E-1
C8H7Br-R p-Bromostyrene-R
C8H7Cl-R-1 o-Chlorostyrene-R
C8H7Cl-R-2 p-Chlorostyrene-R
C8H8-R Styrene-R
C8H8Br-E p-Bromostyrene-E-2
C8H8Cl-E-1 o-Chlorostyrene-E-2
CH CH
Cl
CH CH
CH
Br
CH2
CH
Cl
CH2
CH
Cl
CH2
CH2 CH
CH2 CH2
Br
CH2 CH2
Cl

C8H8Cl-E-2 p-Chlorostyrene-E-2
C8H8N-E 2-Methyl-5-vinylpyridine-E-1
C8H8O-R Phenylene-oxide-R
C8H9-E Styrene-E-2
C8H9N-R 2-Methyl-5-vinylpyridine-R
C8H10N-E 2-Methyl-5-vinylpyridine-E-2
C8H12O2-R Suberic-acid-R
C8H12O6-R Cellulose-acetate-R
CH2 CH2
Cl
CH CH
N
CH3
CH3
O
CH3
CH2 CH2
CH2 CH
N
CH3
CH2 CH2
CH3
N
O O
C(CH2)6C
O
CH2 O C CH3
O
OH OH
O

C8H13O2-E-1 n-Butyl-methacrylate-E-1
C8H13O2-E-2 Isobutyl-methacrylate-E-1
C8H13O2-E-3 sec-Butyl-methacrylate-E-1
C8H13O3-E Suberic-acid-E
C8H13O6-E Cellulose-acetate-E
C8H14N2O2-R Hexamethylene-diisocyanate-R
C8H14O2-R-1 n-Butyl-methacrylate-R
C8H14O2-R-2 Isobutyl-methacrylate-R
C8H14O2-R-3 sec-Butyl-methacrylate-R
CH3
C
O O C4H9
CH C
CH3
C
O O CH2 CH CH3
CH C
CH3
CH3
C
O O CH
CH C
CH3
C2H5
O O
C(CH2)6COH
O
CH2 O C CH3
O
OH OH
OH
O O
C NH (CH2)6 NH C
CH3
CH2 C
C
O O C4H9
CH2 C C
H3
CH3
C
O O CH2 CH CH3
CH3
CH2 C
CH3
C
O O CH
C2H5

C8H15-E 1-Octene-E-1
C8H16-R 1-Octene-R
C8H17-E-1 1-Octene-E-2
CH CH
C6H13
CH2 CH
CH3
C
O O C4H9
CH3
CH3 C
C
O O C4H9
CH3 CH2 CH
C
O O CH2 CH
CH3
CH3
CH3
CH3 C
C
O O CH2 CH
CH3
CH3
CH3
CH2 CH
C
CH3
O O CH C2H5
CH3
CH3 C
C
CH3
O O CH
C2H5
CH2 CH
C6H13
CH2 CH2
C6H13

C8H17-E-2 1-Octene-E-3
C9H7O3-E Dimethyl-terephthalate-E
C9H9-E-1 Alpha-Methylstyrene-E-1
C9H9-E-2 m-Methylstyrene-E-1
C9H9-E-3 o-Methylstyrene-E-1
C9H9-E-4 p-Methylstyrene-E-1
C9H9NO-R Phenylalanine-R
C9H9NO2-R Tyrosine-R
CH3 CH
C6H13
O O
C C
O CH3
CH3
CH C
CH3
CH CH
CH CH
CH3
CH CH
CH3
NH CH C
CH2
O
CH C
CH2
OH
NH
O

C9H9O-E p-Methoxystyrene-E-1
C9H10-R-1 alpha-Methylstyrene-R
C9H10-R-2 m-Methylstyrene-R
C9H10-R-3 o-Methylstyrene-R
C9H10-R-4 p-Methylstyrene-R
C9H10NO-E Phenylalanine-E-1
C9H10NO2-E-1 Phenylalanine-E-2
CH CH
OCH3
CH3
CH2 C
CH3
CH2 CH
CH
CH3
CH2
CH
CH3
CH2
NH2 CH C
CH2
O
NH CH C
CH2
O
OH

C9H10NO2-E-2 Tyrosine-E-1
C9H10NO3-E Tyrosine-E-2
C9H10O-R p-Methoxystyrene-R
C9H11-E-1 alpha-Methylstyrene-E-2
C9H11-E-2 alpha-Methylstyrene-E-3
C9H11-E-3 m-Methylstyrene-E-2
NH2 CH C
CH2
OH
O
CH C
CH2
OH
NH
O
OH
CH
OCH3
CH2
CH3
CH
CH2
CH3
CH3 C
CH3
CH2 CH2

C9H11-E-4 o-Methylstyrene-E-2
C9H11-E-5 p-Methylstyrene-E-2
C9H11O-E p-Methoxystyrene-E-2
C9H12-R Ethylidene-norbornene-R
C9H14O2-R Azelaic-acid-R
C9H15O2-E-1 n-Hexyl-acrylate-E-1
C9H15O2-E-2 n-Pentyl-methacrylate-E-1
C9H15O3-E Azelaic-acid-E
C9H16O2-R-1 n-Hexyl-acrylate-R
CH3
CH2 CH2
CH2 CH2
CH3
CH2 CH2
OCH3
CH2
CH
CH
CH
CH
CH2 C
CH
CH3
O O
C(CH2)7C
CH CH
C
O O C6H13
CH3
CH C
C
O O C5H11
O O
C(CH2)7COH
CH
C
CH2
O O C6H13

C9H16O2-R-2 n-Pentyl-methacrylate-R
C9H17-E 1-Nonene-E-1
C9H17O2-E-1 n-Hexyl-acrylate-E-2
C9H18-R 1-Nonene-R
C9H19-E-1 1-Nonene-E-2
C9H19-E-2 1-Nonene-E-3
C10H12-R Dicyclopentadiene-R
CH CH
C7H15
CH2 CH2
C
O O C6H13
CH3
CH2 CH
C
O O C5H11
CH3
CH3 C
C
O O C5H11
CH2 CH
C7H15
CH2 CH2
C7H15
CH
C7H15
CH3
CH2
CH
CH
CH
CH2
CH
CH
CH
CH
CH

C10H15O2-E Cyclohexyl-methacrylate-E-1
C10H16O2-R Cyclohexyl-methacrylate-R
C10H16O2-R-1 Sebacic-acid-R
C10H17O2-E-1 Cyclohexyl-methacrylate-E-2
C10H17O2-E-2 Cyclohexyl-methacrylate-E-3
C10H17O2-E-3 n-Hexyl-methacrylate-E-1
C10H17O3-E Sebacic-acid-E
C10H18O2-R n-Hexyl-methacrylate-R
C10H19-E 1-Decene-E-1
CH3
CH C
C
O O
CH3
CH2 C
C
O O
O O
C(CH2)8C
CH3
CH2 CH
C
O O
CH3
CH3 C
C
O O
CH3
CH C
C
O O
C6H13
O O
C(CH2)8COH
CH3
CH2 C
C
O O
C6H13
CH CH
C8H17

C10H20-R 1-Decene-R
C10H21-E-1 1-Decene-E-2
C10H21-E-2 1-Decene-E-3
C11H10N2O-R Tryptophan-R
C11H11N2O-E Tryptophan-E-1
C11H11N2O2-E Tryptophan-E-2
CH3
CH2 CH
C
O O
C6H13
CH3
CH3 C
C
O O
C6H13
CH
C8H17
CH2
CH2 CH2
C8H17
CH3 CH
C8H17
NH CH C
CH2
N
O
NH2 CH C
CH2
N
O
NH CH C
CH2
N
O
OH

C11H21-E 1-Undecene-E-1
C11H22-R 1-Undecene-R
C11H23-E-1 1-Undecene-E-2
C11H23-E-2 1-Undecene-E-3
C12H6O2-R 2,6-Napthalene-diacid-R
C12H7O3-E 2,6-Napthalene-diacid-E
C12H16O8-R Cellulose-triacetate-R
C12H17O8-E Cellulose-triacetate-E
C12H22N2O8-R Chitosan-R
C12H23-E 1-Dodecene-E-1
CH CH
C9H19
CH
C9H19
CH2
CH2 CH2
C9H19
CH3 CH
C9H19
CH2
O
O
O C CH3
O O
CH3 C O O
C CH3
O
CH2
O
O
O C CH3
HO
O O
CH3 C O O C CH3
CH2OH
O
O
OH NH2
OH NH2
O
CH2OH
O
CH CH
C10H21

C12H23N2O8-E Chitosan-E-1
C12H23N2O9-E Chitosan-E-2
C12H24-R 1-Dodecene-R
C12H25-E-1 1-Dodecene-E-2
C12H25-E-2 1-Dodecene-E-3
C13H9O3-E 2,6-Napthalene-dimethylester-E
C14H23NO10-R Heparin-R
C14H24NO10-E Heparin-E-1
C14H24NO11-E Heparin-E-2
CH2OH
O
O
OH NH2
OH NH2
O
CH2OH
OH
CH2OH
O
O
OH NH2
HO
OH NH2
O
CH2OH
O
CH2 CH
C10H21
CH2 CH2
C10H21
CH3 CH
C10H21
CH2OH
O
O
O OH
HO
CH2OH
O
O
OH NH C CH3
CH2OH
O
O
OH
HO
OH
CH2OH
O
O
OH NH C CH3
CH2OH
O
O
OH
HO
O
CH2OH
O
OH NH
OH
O
C CH3

C14H25O2-E Decyl-methacrylate-E-1
C14H26O2-R Decyl-methacrylate-R
C14H27O2-E-1 Decyl-methacrylate-E-2
C14H27O2-E-2 Decylmethacrylate-E-3
C15H14O2-R Bisphenol-A-R
C15H15O2-E Bisphenol-A-E
CH3
CH C
C
O C10H21 O
CH3
C
C
CH2
O O C10H21
CH3
CH
O C10H21
C
CH2
O
CH3
O C10H21
CH3 C
O
C
CH3
O C
CH3
O
CH3
O C
CH3
OH

B Kinetic Rate Constant
Parameters
This appendix provides decomposition rate parameters for commonly used
initiators. Within each group the initiators are arranged by increasing total
number of carbon atoms.
The parameters are grouped as follows:
 Water Soluble Azo-nitriles
 Solvent Soluble Azo-Nitriles
 Diacyl Peroxides
 Peroxycarbonates
 Alkyl Peroxides
 Hydroperoxides
 Peroxyesters
 C-C Initiators
 Sulfonyl Peroxides
Initiator Decomposition Rate
Parameters
The table at the end of this section shows the decomposition rate parameters
for monofunctional free-radical initiators. These parameters assume first-order
decomposition kinetics. These data are all included in the INITIATOR
database in Aspen Polymers (formerly known as Aspen Polymers Plus).
Initiator decomposition rates depend on several factors including
temperature, pressure, solvent type, and initiator concentration.
Solvent Dependency
Decomposition rates are lowest in solvents that act as radical scavengers,
such as poly chlorinated organic compounds (e.g., TCE). Initiators used for
bulk-phase vinyl chloride polymerizations are typically in these types of
compounds since they closely mimic the solvent environment during
B Kinetic Rate Constant Parameters 431

polymerization. Decomposition rates may be increased by a factor of 2-3 in
polar solvents such as chlorobenzene compared to reactions in non-polar
solvents such as benzene. Decomposition rates of water-soluble initiators are
typically measured in water. The table that follows lists the solvents in which
the rate parameters are measured. The user may wish to apply correction
factors to the rate parameters when the polymerization solvent environment
is different than the measurement basis.
Concentration Dependency
At high initiator concentrations there is an induced initiation effect. Primary
radicals attack and split un-decomposed initiator molecules. This reduces the
measured half-life time and efficiency of the initiator. All of the data reported
in the following table are based on measurements at relatively low initiator
concentrations (0.2 molar or less). Although the standard decomposition rate
expressions do not account for induced initiator, the user may modify the rate
expression using a gel effect term.
Temperature Dependency
Initiator decomposition rates are reported in several formats including rate
constants, half-life times at specified temperatures, and half-life temperatures
at specified times. These data are all related to each other through the
following equations:





k k E ref

exp 1 1
k A E ref exp  
 

 
 
T RT

 
ref

 
T T R T T

 

 


 
ref
 ln(0.5)

T
k
T t
1
, 2


T 
E

ln  ln(0.5)


A
R
3600
60
Where:
A = Pre-exponential factor (1/sec)
Tref k = Decomposition rate at reference temperature (1/sec)
= Decomposition rate at temperature T, K
kT
E = Activation energy (J/kmol-K)
Tref
f
= Reference temperature, K
T = Temperature, K
T t 2 ,
1 = Half life at temperature T, sec
These equations were applied to the published raw data to allow the rate
constants to be published in a concise format here.
432 B Kinetic Rate Constant Parameters

Pressure Dependency
Most sources do not publish activation volume, which describe the pressure
dependency of the reaction rates. Initiator decomposition reactions are known
to exhibit pressure dependence over very wide ranges of pressure. For
example, the half-life of organic peroxides double with a 3000 bar pressure
increase (Degussa, 2004), which implies an activation volume of 1.9x10-5
m3 / kmol . This term can be ignored for processes that operate at reasonably
low pressures.
The following table shows the decomposition rate parameters for
monofunctional free-radical initiators at a reference temperature of 60C
(Tref(K)=333.15). These data are all included in the INITIATOR database in
Aspen Polymers.

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
ID Long Name Trade Name(s) Formula / Molecular Structure MW CAS No kref (1/s) A (1/sec) kcal/mol GJ/kmol 1 min 1 hr 10 hr Solvent Source
Water Soluble Azo-Nitriles
ABAH 2,2’-azo-bis(2-
amidinopropane)
dihydrochloride
Vazo 56 (DuPont)
V-50 (Wako Chem)
C8H20N6Cl2 271.19264 2997-92-4 3.3436E-05 6.44E+14 29.4 0.12300 110.5 73.7 55.9 Water DuPont
VAZO68 4,4’-azo-bis
(4-cyanovaleric acid)
HCl NH HCl
HN
N N
H2N NH2
Vazo 68 (DuPont) C12H22N2O4 258.31776 2638-94-0 7.3642E-06 5.12E+12 27.2 0.11380 132.7 88.7 68.0 Water DuPont
VA61 2,2’-azo-bis[2-(2-
imidazolin-2-yl)propane]
N N
COOH
HOOC
VA-061 (Wako Chem) C12H22N6 250.34712 20858-12-2 1.3404E-03 1.00E+15 27.2 0.11400 78.4 45.0 28.9 Acidic water Wako
VA86 2,2’-Azobis[2-methyl-N-(2-
hydroxyethyl)propionamide]
N N
N
NH
N
HN
VA-086 C12H24N4O4 288.34712 61551-69-7 6.7869E-06 7.95E+14 30.6 0.12800 123.9 86.0 67.7 Water Wako
VAZO44 2,2’-azo-bis(N,N’-
dimethylene
isobutyramidine)
dihydrochloride
Vazo 44 (DuPont)
VA-44 (WakoChem)
O O
N N
HOH2CH2C NH HN CH2CH2OH
C12H24Cl2N6 323.26840 27776-21-2 1.3564E-04 8.10E+12 25.6 0.10700 103.3 63.0 44.0 Water DuPont
VA46B 2,2’-azo-bis[2-(2-
imidazolin-2-yl)propane
disulfate dihydrate
N N
N
NH
N
HN
2HCl
VA-046B (Wako Chem) C12H30N6O10S2 482.53664 20858-12-2 1.4388E-03 1.18E+17 30.4 0.12700 75.9 46.0 31.4 Water Wako
VA41 2,2’-azo-bis[2-(5-methyl-
2-imidazolin-2-yl)propane]
dihydrochloride
N N
N
NH
N H2SO4
HN
H2O
VA-041 (WakoChem) C14H26Cl2N6 349.30628 n/a 2.7035E-04 2.53E+15 28.9 0.12100 91.3 57.4 41.0 Water Wako
VA58 2,2’-azobis[2-(3,4,5,6-
tetrahydropyrimidin-2-
yl)propane] dihydrochloride
N N
N
NH
N
NH
HCl HCl
VA-058 (WakoChem) C14H28Cl2N6 351.32216 102834-39-0 2.5342E-05 1.44E+15 30.1 0.12600 111.8 75.5 58.0 Water Wako
VA57 2,2’-azobis[N-(2-
carboxyethyl)-2-
methylpropionamidine]
tetrahydrate
N N
NH
N N 2HCl
HN
VA-057 (WakoChem) C14H34N6O8 414.45960 n/a 2.8824E-05 5.56E+14 29.4 0.12300 112.0 74.9 57.0 Water Wako
HN
HN NH
HOOC COOH 4 H2O
N N
NH

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
VA85 2,2’-Azobis{2-methyl-N-[2-
(1-hydroxybuthyl)]
propionamide}
VA-085 (Wako Chem) C16H32N4O4 344.45464 n/a 7.8450E-07 6.41E+13 30.4 0.12700 148.2 105.4 85.0 Water Wako
VA60 2,2’-azo-bis{2-[1-(2-
hydroxyethyl)-2-imidazolin-
2-yl]propane}
dihydrochloride
O O
N N
NH HN
CH2CH3
H3CH2C
HOH2C CH2OH
VA-060 (Wako Chem) C16H32Cl2N6O2 411.37472 11858-13-0 1.9254E-05 9.56E+15 31.5 0.13200 111.7 76.9 60.0 Water Wako
Solvent Soluble Azo-Nitriles
N
N N
N N
N
2HCl
CH2CH2OH CH2CH2OH
V30 1-cyano-1-methyl-ethylazofomamide
V-30 (Wako Chem) C5H8N4O 140.14488 10288-28-5 4.4161E-08 1.86E+15 34.5 0.14430 164.9 123.9 104.0 Toluene Wako
AIBN 2,2'-azo-bis-isobutyronitrile Vazo 64 (DuPont)
Perkadox AIBN
(AkzoNobel)
CN
N N CONH2
C8H12N4 164.21024 78-67-1 1.0464E-05 2.74E+15 31.1 0.13023 118.3 82.0 64.4 Chlorobenzene AkzoNobel
AMBN 2,2'-azo-bis(2-
methylbutyronitrile)
Vazo 67 (DuPont)
Perkadox AMBN
(AkzoNobel)
V-59 (Wako Chem)
NC N N CN
V601 dimethyl 2,2'-azobis (2-
methylpropionate)
C2H5
CN
N N
CN
C2H5
V-601 (Wako Chem) C10H18N2O4 230.26400 2589-57-3 8.5556E-06 6.99E+14 30.4 0.12700 122.1 84.3 66.0 Toluene Wako
ACCN 1,1-azo-di-(hexa
hydrobenzenenonitrile)
Vazo 88 (DuPont)
Perkadox ACCN
(AkzoNobel)
V-40 (Wako Chem)
O O
H3CO N N
OCH3
AMVN 2,2'-azo-bis(2,4-dimethyl
valeronitrile)
Vazo 52 (DuPont)
V-65 (Wako Chem)
NC
N N
CN
C14H24N4 248.37152 4419-11-8 1.0349E-04 1.78E+14 27.8 0.11630 102.1 65.0 47.2 Toluene DuPont
VF096 2,2'-azo-bis[N-(2-
propenyl)-2-
methylpropionamide]
VF-096 (Wako Chem) C14H24N4O2 280.37032 129136-92-1 1.5480E-07 4.67E+14 32.7 0.13700 157.8 116.1 96.0 Toluene Wako
O O
N N
NH HN

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
AMOMVN 2,2'-azo-bis(4-methoxy-
2,4-dimethyl valeronitrile)
V-70 (Wako Chem) C16H28N4O2 308.42408 15545-97-8 1.1718E-03 1.26E+15 27.5 0.11500 79.4 46.1 30.0 Toluene Wako
VAM110 2,2'-azo-bis(N-butyl-2-
methylpropionamide)
H3CO H2C
CH2 OCH3
CN
N N
CN
Vam-100 (Wako Chem) C16H32N4O2 312.45584 n/a 2.3941E-08 4.40E+14 33.9 0.14200 174.2 130.9 110.0 Toluene Wako
VAM111 2,2'-azo-bis(N-cyclohexyl-
2-methylpropionamide)
O O
N N
C4H9 NH HN C4H9
Vam-110 (Wako Chem) C20H36N4O2 364.53160 n/a 3.4427E-08 1.71E+13 31.5 0.13200 181.3 133.7 111.0 Toluene Wako
Diacyl Peroxides
O O
N N
NH HN
PP dipropionyl peroxide C6H10O4 146.14300 3248-28-0 4.3006E-05 1.14E+15 30.5 0.12760 119.1 81.9 63.9 Benzene Polymer
O
O
O
O
O
O
O
O
OH
HO
O
O
O
O
O
O
O
O
O
O
O
O
Cl Cl
Handbook
SAP succinic acid peroxide Luperox SAP (Atofina)
SUCP-70-W (Degussa)
C8H10O8 234.16260 123-23-9 8.7924E-06 4.89E+10 24.0 0.10043 142.3 91.0 67.4 Acetone Atofina
IBP diisobutyryl peroxide Trigonox 187-C30
(AkzoNobel)
C8H14O2 142.19796 3437-84-1 2.7220E-03 3.42E+14 26.1 0.10906 72.7 39.0 22.8 Chlorobenzene AkzoNobel
BP dibenzoyl peroxide Luperox AFR40 (Atofina) C14H10O4 242.23100 94-36-0 3.8607E-06 3.40E+14 30.4 0.12721 130.3 91.0 72.1 Benzene Atofina
DCLBP bis(2,4-dichlorobenzoyl)
peroxide
DCLBP (Degussa) C16H6Cl2O4 333.12664 133-14-2 4.2163E-05 3.95E+14 28.9 0.12100 109.1 72.0 54.1 Benzene Degussa
O
O
Cl Cl

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
OMBP bis(ortho-methylbenzoyl)
peroxide
Perkadox 20 (Akzo
Nobel)
OMBP (Degussa)
C16H14O4 270.28476 3034-79-5 1.5072E-05 6.85E+13 28.4 0.11900 120.9 81.0 61.9 Benzene Degussa
PMBP bis(para-methylbenzoyl)
peroxide
O
O
O
O
PMBP (Degussa) C16H14O4 270.28476 895-95-2 5.1895E-06 2.06E+14 29.9 0.12500 128.6 89.0 70.0 Benzene Degussa
OP dioctanoyl peroxide Trigonox SE-8
(AkzoNobel)
O
O
O
O
INP bis(3,5,5-
trimethylhexanoyl) peroxide
Trigonox 36
(AkzoNobel)
Luperox 219 (AtoFina)
O
H3C(CH2)6 O
O (CH2)6CH3
O
DP didecanoyl peroxide Luperox DEC (Atofina)
Perkadox SE-10
(AkzoNobel)
O
O
O
O
C20H38O4 342.51932 762-12-9 1.4646E-05 8.34E+14 30.1 0.12600 117.2 80.0 62.0 Benzene Degussa
LP dilauroyl peroxide Luperox LP (Atofina)
Laurox (AkzoNobel)
O
C9H C 9H19
O
19 O
O
Peroxycarbonates
BPIC tert-butylperoxy isopropyl
carbonate
O
C11H23 C11H23
O
O
O
Trigonox BPIC C8H16O4 176.21264 2372-21-6 7.0005E-08 2.44E+16 35.9 0.15015 154.9 117.0 98.5 Chlorobenzene AkzoNobel
O O
O
O

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
IPPC diisopropyl
peroxydicarbonate
IPPC (Degussa) C8H16O6 208.21144 105-64-6 1.6931E-04 7.70E+14 28.4 0.11900 96.3 61.0 44.0 Benzene Degussa
NPPC di-n-propyl
peroxydicarbonate
Trigonox NPP-CK85
(AkzoNobel)
O
O
O
O
O
O
SBPC di-secbutyl
peroxydicarbonate
Trigonox SBP
(AkzoNobel)
O
O
O
O
O
O
TBPIC tert-butylperoxy-isopropylcarbonate
Trigonox BPIC (Akzo)
Luperox TBIC (AtoFina)
TBPIC (Degussa)
O
O
O
O
O
O
TBPEHC tert-butylperoxy 2-
ethylhexyl carbonate
Trigonox 117
(AkzoNobel)
Luperox TBEC (AtoFina)
O
O
O
O
C13H26O4 246.34704 12/4/3443 6.4441E-08 3.95E+16 36.3 0.15172 154.4 117.0 98.7 Chlorobenzene AkzoNobel
CHPC dicyclohexyl
peroxydicarbonate
O
O
O
O
C4H9
C2H5
CHPC (Degussa) C14H22O6 286.32508 1561-49-5 1.9626E-04 3.30E+16 30.8 0.12900 91.9 59.9 44.2 Chlorobenzene AkzoNobel
O
O
O
O
O
O
O
O O
C2H5
O
C2H5
C4H9
(Polymer
Handbook)
TAPEHC tert-amylperoxy 2-
ethylhexyl carbonate
Trigonox 131
(AkzoNobel)
Luperox TAEC (AtoFina)
EHPC di(2-ethylhexyl)
peroxydicarbonate
Trigonox EHP
(AkzoNobel)
O
O
O
O
O
O

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
BCHPC Di(4-tert-butylcyclohexyl)
peroxydicarbonate
Perkadox 16
(AkzoNobel)
MYPC Dimyristyl
peroxydicarbonate
Perkadox 26
(AkzoNobel)
CEPC dicetyl peroxydicarbonate Perkadox 24
(AkzoNobel)
Alkyl Peroxides
DTBP di-tert-butyl peroxide Trigonox B (AkzoNobel)
Luperox DI (AtoFina)
DTAP di-tert-amyl peroxide Trigonox 201
(AkzoNobel)
Luperox DTA (AtoFina)
BCUP tert-butylcumyl peroxide Trigonox T (AkzoNobel)
BCUP (Degussa)
DCUP dicumyl peroxide Perkadox BC
(AkzoNobel)
DTBCP di-tert-butyl cumyl peroxide C26H38O2 382.58652 3.6200E-09 3.05E+15 36.5 0.15260 184.4 142.0 121.4 Toluene Warson
(1980)
Hydroperoxides
O
O
O
O
O
O
O
O
O
O
O
O C14H29
C14H29
O
O
O
O
O
O C16H33
C16H33
O O
O O
O O
O O
O O

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
TBHP tert-butyl hydroperoxide Trigonox A (AkzoNobel)
Luperox TBH (AtoFina)
TBHP (Degussa)
TAHP tert-amyl hydroperoxide Trigonox TAHP (Akzo)
TAHP (AtoFina)
O OH
TMBHP 1,1,3,3-tetramethylbutyl
hydroperoxide
Trigonox TMBH
(AkzoNobel)
C2H5 O OH
CUHP cumene hydroperoxide Trigonox K (AkzoNobel)
Luperox CU (AtoFina)
CUHP (Degussa)
O OH
IPCHP isopropylcumyl
hydroperoxide
O OH
Trigonox M (AkzoNobel) C12H18O2 194.27372 26762-93-6 5.6157E-09 2.28E+12 31.4 0.13144 207.1 154.0 129.0 Chlorobenzene AkzoNobel
Peroxyesters
TBPA tert-butyl peroxyacetate Trigonox F (AkzoNobel)
Luperox 7 (AtoFina)
O OH
TAPA tert-amyl peroxyacetate Trigonox 133
(AkzoNobel)
O
O
O
TBPIB tert-butyl peroxyisobutyrate Trigonox 41
(AkzoNobel)
C2H5 O O
O
O
O
O

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
TBPPI tert-butyl peroxypivalate Trigonox 25
(AkzoNobel)
TBPPI (Degussa)
TBPEA tert-butyl
peroxydiethylacetate
Trigonox 27
(AkzoNobel)
O O
O
TAPPI tert-amyl peroxypivalate Trigonox 125
(AkzoNobel)
TAPPI (Degussa)
O O
O
TBPB tert-butyl peroxybenzoate Triganox C (AkzoNobel)
Luperox P (AtoFina)
TBPB (Degussa)
O O
O
C2H5
TBPN7 tert-butyl
peroxyneoheptanoate
Trigonox 257
(AkzoNobel)
O
O
O
TAPB tert-amyl peroxybenzoate Trigonox 127
(AkzoNobel)
Luperox TAP (AtoFina)
TAPB (Degussa)
O O
O
C3H7
TBPEH tert-butylperoxy-2-
ethylhexanoate
Trigonox 21
(AkzoNobel)
O
O
C2H5
O
TMBPPI 1,1,3,3-tetramethylbutyl
peroxypivalate
Trigonox 425
(AkzoNobel)
O
O
O
C4H9
C2H5
O
O
O

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
TAPEH tert-amyl peroxy-2-
ethylhexanoate
Trigonox
121(AkzoNobel)
TAPEH (Degussa)
TBPIN tert-butylperoxy-3,5,5-
trimethyl-hexanoate
Trigonox 42S
(AkzoNobel)
O
O
C2H5
O
C4H9
C2H5
TBPND tert-butyl
peroxyneodecanoate
Trigonox 23
(AkzoNobel)
TBPND (Degussa)
O
O
O
DMHBPEH 1,1-dimethyl-3-
hydroxybutyl peroxy-2-
ethylhexanoate
O O
O
C2H5
C4H9
C2H5
Luperox 665 (AtoFina) C14H28O4 260.37392 95732-35-7 1.0997E-05 3.49E+13 28.2 0.11800 125.0 84.0 64.4 TCE AtoFina
TAPND tert-amyl
peroxyneodecanoate
Trigonox 123
(AkzoNobel)
O
O
C4H9
C2H5
O
OH
CUPN7 cumyl peroxyneoheptanoate Trigonox 197
(AkzoNobel)
O
C2H5 O O
C4H9
C2H5
C2H5
TMBPEH 1,1,3,3-tetramethylbutyl
peroxy-2-ethylhexanoate
Trigonox 421
(AkzoNobel)
C2H5
C2H5
O
O C
O
DMHBPND 1,1-dimethyl-3-
hydroxybutyl
peroxyneodecanoate
O
O
O
C4H9
C2H5
Luperox 610 (AtoFina) C16H32O4 288.42768 95718-78-8 4.0233E-04 1.14E+14 26.6 0.11131 90.4 54.0 36.6 a-methylstyrene
AtoFina
O
C C2H5 4H9
O
C2H5
O
OH

Decomposition Rate
Parameters
Decomposition
Activation Energy
Half Life
Temperature, C
TMBPND 1,1,3,3,-tetramethylbutyl
peroxyneodecanoate
Triganox 423
(AkzoNobel)
CUPND cumyl peroxyneodecanoate Trigonox 99
(AkzoNobel)
CUPND (Degussa)
C C2H5 4H9
C-C Initiators
DMDPB 2,3-dimethyl-2,3-
diphenylbutane
Perkadox 30
(AkzoNobel)
C4H9
Sulfonyl Peroxides
ACHSP acetyl
cyclohexanesulphonyl
peroxide
Lupersol 228Z (AtoFina) C8H14O5S 222.26216 3179-56-4 7.3692E-04 7.27E+17 32.0 0.13390 80.1 51.0 36.6 Toluene Warson
O
(1980)
O
O
C2H5
O
O O
C2H5
C2H5
O
S
O
O O
O

References
Note: Anonymous data sources from the internet are documented by the
vendor name and the year in which the data were collected.
AkzoNobel (2004). Initiators for Polymer Production, Product Catalog.
AtoFina (2004). Organic Peroxides, General Catalog.
AtoFina (2004). Organic Peroxides, Product Bulletin, Diacyl Peroxides.
AtoFina (2004). Organic Peroxides, Product Bulletin, Dialkyl Peroxides.
AtoFina (2004). Organic Peroxides, Product Bulletin, Peroxydicarbonates.
AtoFina (2004). Organic Peroxides, Product Bulletin, Tertiary Alkyl
Hydroperoxides.
AtoFina (2004). Fine Chemicals Technical Data.
Degussa (2004). Technical Information. Half-Life Times of Organic Peroxides.
Dupont (2004). Vazo Free radical initiators.
(http://www.dupont.com/vazo/grades.html)
Masson, J.C. (1989). Decomposition Rates of Organic Free Radical Initiators.
Polymer Handbook, 3rd Edition. New York.
Wako Chemical (2004). Water Soluble Azo-Initiator.
(http://www.wako-chem.co.jp/specialty/waterazo/main.htm)
Wako Chemical (2004). Solvent Soluble Azo-Initiator.
(http://www.wako-chem.co.jp/specialty/oilazo/main.htm)
Warson, H. (1980). Per-Compounds and Per-Salts in Polymer Processes.
England: Solihull Chemical Services, 5-17.

C Fortran Utilities
For descriptions of Fortran utilities useful in writing user kinetic subroutines,
see Chapter 4 of Aspen Plus User Models.
C Fortran Utilities 445

D Input Language Reference
This section describes the input language for:
 Specifying Components, 447
 Specifying Component Attributes, 451
 Specifying Attribute Scaling Factors, 453
 Requesting Distribution Calculations, 454
 Calculating End Use Properties, 454
 Specifying Physical Property Inputs, 456
 Specifying Step-Growth Polymerization Kinetics, 460
 Specifying Free-Radical Polymerization Kinetics, 467
 Specifying Emulsion Polymerization Kinetics, 477
 Specifying Ziegler-Natta Polymerization Kinetics, 484
 Specifying Ionic Polymerization Kinetics, 494
 Specifying Segment-Based Polymer Modification Reactions, 501
Specifying Components
This section describes the input language for specifying components.
Naming Components
Following is the input language used to name components.
Input Language for Components
COMPONENTS cid [cname] [outid] / ...
Input Language Description for Components
COMPONENTS cid Component ID. Used to refer to the component in
all subsequent input and is also used to identify the
component in the simulation report. Aspen Plus
input language conventions and naming guidelines
apply to this keyword.
D Input Language Reference 447

cname The databank name or alias used for that
component. Refer to the documentation for the
desired databank to find out the correct databank
name or alias for the desired component. Place an
asterisk (*) in the cname position if you do not
wish to retrieve the component from the databank.
Note that in this case you are required to provide
all necessary physical property parameters.
outid Eight-character name used for the component in
reports. (Default=cid)
Input Language Example for Components
DATABANKS PURE13 / POLYMER / SEGMENT / INITIATOR
COMPONENTS
INI1 LP INIT / ; INITIATOR
STY STYRENE STYRENE / ; MONOMER
CAN ACRYLONITRILE CAN / ; MONOMER
XYLENE P-XYLENE XYLENE / ; SOLVENT
STYSEG STYRENE-R STY-SEG / ; STYRENE SEGMENT
ACNSEG ACRYLONITRILE-R ACN-SEG / ; ACN SEGMENT
SAN SAN SAN ; COPOLYMER
Specifying Component Characterization
Inputs
A POLYMERS paragraph is used to define polymers, their segments,
oligomers, and heterogeneous catalysts, if any, involved in the
polymerization. This paragraph is also used to define the polymer and catalyst
component attributes desired in the simulation. Only the names of the
attributes need to be specified in the POLYMERS paragraph. Initial values for
the component attributes may be entered for the polymer and catalyst
components in each stream via the STREAM paragraph. Following is the input
language for the POLYMERS paragraph.
448 D Input Language Reference

Input Language for Polymers, Oligomers, and Catalysts
POLYMERS
PARAM kwd=value
SEGMENTS seg-id seg-type / …
OLIGOMERS olig-id seg-id number / …
POLYMERS poly-id / …
CATALYSTS cat-id mol-site / …
INITIATORS ini-id/ …
ATTRIBUTES comp-id attr-list / …
DISTRIBUTION polyid disttype NPOINTS=value
FUNCLOG=YES/NO
UPPER=value
Input Language Description for Polymers, Oligomers, and Catalysts
PARAM Used to enter special parameters. Keywords are as follows.
NSITE Number of catalyst site types
N-BIFUN-INIT
Number of bifunctional initiators
SEGMENTS Used to specify all the segments used in the simulation. The
information entered through this keyword is used by the
system to pass segment property information.
seg-id Name of the segment (must be a valid
component ID)
seg-type Segment type. This information is used to
differentiate segment types. The options are
END, REPEAT, BRANCH3, or BRANCH4. The
default value is REPEAT
POLYMERS Used to identify all polymers present in the simulation.
poly-id Name of the polymer (must be a valid component
ID)
OLIGOMERS Used to specify the structure of oligomers present in the
simulation.
olig-id Oligomer component ID
seg-id ID for segment contained in that oligomer. All the
segment names must be valid component IDs
(Optional)
number Number of this segment in the oligomer
(Default=1)
POLYMERS Used to identify all polymers present in the simulation.
poly-id Name of the polymer (must be a valid component
ID)

CATALYSTS Used to identify all the heterogeneous polymerization
catalysts present in the simulation and to specify the moles of
catalytic sites per mole of catalyst.
cat-id Catalyst component ID
mol-site Moles of catalytic sites per unit mass of that
catalyst
INITIATORS Used to identify all the ionic polymerization initiators present
in the simulation.
ini-id Initiator component ID
ATTRIBUTES Used to specify all the polymer/catalyst component attributes
desired for each polymer/catalyst in the simulation. Only the
attribute names need to be specified here. Values for the
component attributes are entered in the COMP-ATTR sentence
of the STREAM paragraph.
comp-id Polymer or catalyst component ID
attr-list List of component attributes. The component
attributes specific to polymers are listed in
Polymer Component Attributes in Chapter 2,
while those for catalysts are listed in Site-Based
Species Attributes in Chapter 2.
DISTRIBUTION Used to request polymer property distribution plots.
polyid Polymer ID
disttype Distribution type
NPOINTS Number of points
FUNCLOG Calculate distribution as rW(r) vs. r on a log scale.
Default is NO
upper Upper limit
Since component attributes represent a significant feature in Aspen Polymers
(formerly known as Aspen Polymers Plus), a complete subsection has been
devoted to their use in the simulator. For more detailed information regarding
component attributes, see the Polymer Structural Properties section of
Chapter 2.

Input Language Example for Polymers, Oligomers and Catalysts
POLYMERS
POLYMERS SAN ; DEFINE SEGMENTS IN
POLYSTYRENE
SEGMENTS STYSEG REPEAT/
ACNSEG REPEAT ; DEFINE TYPE OF SEGMENTS
PRESENT
; DEFINE ATTRIBUTES FOR POLYMERS
ATTRIBUTES SAN DPN DPW PDI MWN MWW ZMOM FMOM SMOM SFLOW SFRAC
&
LDPN LZMOM LFMOM LSFLOW LSFRAC LEFLOW LEFRAC
LPFRAC
DISTRIBUTION PS CHAIN-SIZE NPOINTS=100 UPPER=9999
Specifying Component
Attributes
This section describes the input language for specifying component
attributes..
Specifying Characterization Attributes
See Specifying Component Characterization Inputs on page 448.
Specifying Conventional Component
Attributes
To assign user component attributes to a conventional component use the
ATTR-COMPS paragraph as follows:
Input Language for Catalyst Component Attributes
ATTR-COMPS comp-id attr-list CLASS=CV / ...
Input Language Description for Catalyst Component Attributes
comp-id Standard component ID.
attr-list List of attributes. Valid attributes were given in User Attributes in
Chapter 2.
Initializing Attributes in Streams
Following is the input language used to enter attribute values in streams.

Input Language for Material Streams
STREAM sid
SUBSTREAM ssid keyword=value
basis-FLOW cid flow / . . .
basis-FRAC cid frac / . . .
COMP-ATTR cname cattrname (value-list) / . . .
Keywords: TEMP PRES basis-FLOW
Optional Keywords: NPHASE PHASE
Input Language Description for Material Streams
SUBSTREAM Used to enter state and flash specifications for substreams.
Ssid Substream ID
TEMP Temperature
PRES Pressure
basis-
FLOW
Flow rate on a MOLE, MASS, or VOLUME basis
NPHASE Number of phases
PHASE Used to specify the phase when NPHASE=1
PHASE=V (vapor), L (liquid), or S (solid)
basis-FLOW Used to enter component flows.
cid Component ID
flow Component mole or mass flow
basis-FRAC Used to enter component fractions.
cid Component ID
frac Component mole or mass fraction
COMP-ATTR Used to enter component attribute values.
Cname Component name
cattrname Component attribute name. For polymer
attributes, values must be entered for at least
SFRAC or SFLOW, and DPN or both ZMOM and
FMOM
value-list List of values for each element in the attribute.
Use “*” to skip entries
Input Language Example for Material Streams

STREAM FEED
SUBSTREAM MIXED TEMP=70 PRES=1
MASS-FLOW STY 13.5 /ACN 7.27 /XYLENE 79 /SAN 0.1E-5/INI1 0.23
COMP-ATTR SAN DPN (3000) /
DPW (6000) /
PDI (2) /
MWN (312450) /
MWW (624900) /
ZMOM (0.39E-10) /
FMOM (1.17E-7) /
SMOM (7.02E-4) /
SFLOW (0.55E-7 0.55E-7) /
SFRAC (0.5 0.5) /
LSFLOW (0. 0.) /
LEFLOW (0. 0.)
Specifying Attribute Scaling
Factors
This section describes the input language used to change the default scaling
factors for component attributes.
Specifying Component Attribute Scale
Factors
The ATTR-SCALING paragraph is used to override the default scaling factors
and upper bounds for component attributes. The standard values for these
parameters are defined in the Aspen Plus system definition file through the
TBS data table PPCMATTR.DAT.
The component attribute scaling factors are used in flowsheet tear-stream
convergence and in reactor model convergence as described in Component
Attribute Scale Factors in Chapter 2.
The model uses one set of scaling parameters for all elements of each
component attribute. If one component attribute is used by more than one
component, different scaling factors can be applied for each instance of the
attribute.
Input Language for Attribute Scaling Factors
ATTR-SCALING
SCALING COMP=comp-id ATTR=attr-id
SCALE-FACTOR=scale UPPER-BOUND=upper

Input Language Description for Attribute Scaling Factors
SCALING Used to enter special parameters. Keywords are as follows.
comp-id Attributed component ID
attr-id Attribute ID
scale Number of catalyst site types
upper Upper limit
Input Language Example for Component Attribute Scaling
ATTR-SCALING
SCALING PP LSEFLOW SCALE=1E-008 UPPER=1.E35
SCALING PP LZMOM SCALE=1E-008 UPPER=1.E35
SCALING PP LSZMOM SCALE=1E-008 UPPER=1.E35
SCALING TICL4 CVSFLOW SCALE=1E-008 UPPER=1.E35
SCALING TICL4 CPSFLOW SCALE=1E-008 UPPER=1.E35
Requesting Distribution
Calculations
See Specifying Component Characterization Inputs on page 448.
Calculating End Use Properties
This section describes the input language for calculating end use properties.
Input Language for Prop-Set
PROP-SET propsetid propname-list keyword=value
Optional Keywords:
COMPS PHASE UNITS TEMP PRES
Input Language Description for Prop-Set
Use the Prop-Set paragraph to define a property set. A property set is a
collection of thermodynamic, transport, and other properties. Each property
set you define is identified by an ID you supply.
Propsetid Property set ID.
Propname-list List of property names. (See Aspen Physical Property System
Physical Property Data documentation.)

COMPS List of component Ids (applies to all properties listed in Aspen
Physical Property System Physical Property Data
documentation). (Default=all components actually present
when the property is calculated.)
PHASE PHASE=V Vapor
PHASE=L Total liquid
PHASE=L1 First-liquid
PHASE=L2 Second-liquid
PHASE=T Total mixture
PHASE=S Solid
Phase compositions are determined at stream conditions.
(Default=T, if listed as a valid phase for the property in Aspen
Physical Property System Physical Property Data
documentation; otherwise no default.)
UNITS Units options selected for the units keywords that are listed
for the property in Aspen Physical Property System Physical
Property Data documentation. (Default=IN-UNITS if Prop-Set
is specified for design specifications, Fortran blocks,
optimization paragraphs and constraint paragraphs.
Default=OUT-UNITS if Prop-Set is specified for reports. If a
property has mole, mass, or flow units, the default will be
mole units.)
TEMP Temperatures for property calculations. (Default=stream
temperature. For VVSTD and VVSTDMX, Default=25C.)
PRES Pressures for property calculations. (Default=stream
pressure. For VVSTD and VVSTDMX, Default=1 atm.)
Input Language for USER-PROPERTY
USER-PROPERTY userpropid propname-list keyword=value
Keyword: SUBROUTINE
Optional Keywords: FLASH UNIT-TYPE UNIT-LABEL COMP-DEP LVPCT-DEP
CURVE-PROP DEFAULT-PROP BLEND-METHOD BLEND-OPT
EXTRAPOLATE
Input Language Description for USER-PROPERTY
Use the USER-PROPERTY paragraph to define the property. This property can
be referenced in the Prop-Set paragraph in the same way as built-in
properties. You must supply a Fortran subroutine to calculate the value of the
user Prop-Set properties.

userpropid User property set ID. This property must be different from
built-in properties. (See Aspen Physical Property System
Physical Property Data documentation.)
SUBROUTINE Name of user-supplied subroutine for calculating the
property. For details on writing the user-supplied subroutine,
see Aspen Plus User Models reference manual.
FLASH FLASH=NO Does not flash the stream before the
user-supplied subroutine is called
(Default)
FLASH=
NOCOMPOSITE
Does not flash the stream for total
stream properties (When PHASE=T in the
Prop-Set paragraph), but flashes for any
other phase specification
FLASH=YES Always flashes stream before the user-supplied
subroutine is called
UNIT-TYPE Units keyword for the property. If not entered, unit
conversion is not performed on property values returned from
the user-supplied subroutine.
UNIT-LABEL Unit label for the property printed in the report. A unit label is
used only when unit conversion is performed by the user-supplied
subroutine (that is, when UNIT-TYPE is not given).
COMP-DEP COMP-DEP=YES Property is component property
COMP-DEP=NO Property is a mixture property (Default)
Specifying Physical Property
Inputs
This section describes the input language for specifying physical property
inputs. More information on physical property methods and models is given in
Volume 2 of this User Guide.
Specifying Property Methods
Following is the input language used to specify property methods.
Input Language for Property Methods
PROPERTIES opsetname keyword=value /
opsetname [sectionid-list] keyword=value /...
Optional keywords:
FREE-WATER SOLU-WATER HENRY-COMPS
HENRY-COMPS henryid cid-list

Input Language Description for Property Methods
The PROPERTIES paragraph is used to specify the property method(s) to be
used in your simulation. In this paragraph properties may be specified for the
entire flowsheet, for a flowsheet section, or for an individual unit operation
block. Depending on the component system used, additional information may
be required such as Henry's law information, water solubility correlation, free-water
phase properties. The input language for specifying property methods
is as follows.
opsetname Primary property method name
(See the Aspen Polymers User Guide, Volume 2).
sectionid-list List of flowsheet section IDs.
FREE-WATER Free water phase property method name (Default=STEAM-TA).
SOLU-WATER Method for calculating the K-value of water in the organic
phase.
SOLU-WATER=0 Water solubility correlation is used,
vapor phase fugacity for water
calculated by free water phase property
method
SOLU-WATER=1 Water solubility correlation is used,
calculated by primary property method
SOLU-WATER=2 Water solubility correlation is used with
a correction for unsaturated systems,
calculated by primary property method
SOLU-WATER=3 Primary property method is used. This
method is not recommended for water-hydrocarbon
systems unless water-hydrocarbon
interaction parameters are
available. (Default)
HENRY-COMPS Henry's constant component list ID.
The HENRY-COMPS paragraph identifies lists of components for which Henry's
law and infinite dilution normalization are used. There may be any number of
HENRY-COMPS paragraphs since different lists may apply to different blocks
or sections of the flowsheet.
henryid Henry's constant component list ID
cid-list List of component IDs
Input Language Example for Property Methods

HENRY-COMPS HC INI1
PROPERTIES POLYNRTL HENRY-COMPS=HC
Specifying Property Data
Following is the input language used to specify property data.
Input Language for Property Data
PROP-DATA
PROP-LIST paramname [setno] / . . .
PVAL cid value-list / value-list / . . .
PROP-LIST paramname [setno] / . . .
BPVAL cid1 cid2 value-list / value-list / . . .
COMP-LIST cid-list
CVAL paramname setno 1 value-list
COMP-LIST cid2-list
BCVAL paramname setno 1 cid1 value-list /
1 cid1 value-list / . . .
Physical property models require data in order to calculate property values.
Once you have selected the property method(s) to be used in your simulation,
you must determine the parameter requirements for the models contained in
the property method(s), and ensure that they are available in the databanks.
If the model parameters are not available from the databanks, you may
estimate them using the Property Constant Estimation System, or enter them
using the PROP-DATA or TAB-POLY paragraphs. The input language for the
PROP-DATA paragraphs is as follows. Note that only the general structure is
given, for information on the format for the input parameters required by
polymer specific models see the relevant chapter in Volume 2 of this User
Guide.
Input Language Description for Property Data
PROP-LIST Used to enter parameter names and data set numbers.
PVAL Used to enter the PROP-LIST parameter values.
BPVAL Used to enter the PROP-LIST binary parameter values.
COMP-LIST Used to enter component IDs.
CVAL Used to enter the COMP-LIST parameter values.
BCVAL Used to enter the COMP-LIST binary parameter values.
paramname Parameter name

setno Data set number. For CVAL and BCVAL the
data set number must be entered. For setno >
1, the data set number must also be specified
in a new property method defined using the
PROP-REPLACE paragraph. (For PROP-LIST,
Default=1)
cid Component ID
cid1 Component ID of first component of binary
pair
cid2 Component ID of second component of binary
pair
value-list List of parameter values. For PROP-LIST, enter
one value for each element of the property;
for COMP-LIST, enter one value for each
component in the cid-list.
cid-list List of component ID
Input Language Example for Property Data
PROP-DATA
IN-UNITS SI
PROP-LIST PLXANT / TB
PVAL HOPOLY -40.0 0 0 0 0 0 0 0 1D3 / 2000.0
PVAL COPOLY -40.0 0 0 0 0 0 0 0 1D3 / 2000.0
PROP-DATA
IN-UNITS SI
PROP-LIST MW
PVAL HOPOLY 1.0
PVAL COPOLY 1.0
PVAL ABSEG 192.17
PVAL ASEG 76.09
PVAL BSEG 116.08
PROP-DATA
IN-UNITS SI
PROP-LIST DHCONM / DHSUB / TMVK / TGVK
PVAL HOPOLY -3.64261D4 / 8.84633D4 / 1.0 / 0.0
PVAL COPOLY -3.64261D4 / 8.84633D4 / 1.0 / 0.0
PROP-DATA
IN-UNITS SI
PROP-LIST GMRENB / GMRENC
BPVAL MCH ASEG -92.0 / 0.2
BPVAL ASEG MCH 430.0 / 0.2
Estimating Property Parameters
Following is the input language used to estimate property parameters.

Input Language for Property Parameter Estimation
ESTIMATE [option]
STRUCTURES
method SEG-id groupno nooccur / groupno nooccur /...
Input Language Description for Property Parameter Estimation
The main keywords for specifying property parameter estimation inputs are
the ESTIMATE and the STRUCTURES paragraphs. A brief description of the
input language for these paragraphs follows. For more detailed information
please refer to the Aspen Physical Property System Physical Property Data
documentation.
option Option=ALL Estimate all missing parameters (default)
method Polymer property estimation method name
SEG-id Segment ID defined in the component list
groupno Functional group number (group IDs listed in Appendix B of
Volume 2 of this User Guide)
nooccur Number of occurrences of the group
Input Language Example for Property Parameter Estimation
ESTIMATE ALL
STRUCTURES
VANKREV ABSEG 115 1 ;-(C6H4)-
VANKREV BSEG 151 2 / 100 2 ; -COO-CH2-CH2-COO-VANKREV
ABSEG 115 1 / 151 2 / 100 2 ;-(C6H4)-COO-CH2-CH2-COO-Specifying
Step-Growth
Following is the input language for the STEP-GROWTH REACTIONS paragraph.
Input Language for Step-Growth Polymerization
REACTIONS rxnid STEP-GROWTH
DESCRIPTION '...'
REPORT REPORT=yes/no RXN-SUMMARY=yes/no RXN-DETAILS=yes/noI
STOIC reactionno compid coeff / ...
RATE-CON setno pre-exp act-energy [T-exp] [T-ref] [USER-RC=number]
[CATALYST=compid] [CAT-ORDER=value]
POWLAW-EXP reactionno compid exponent /
[ASSIGN reactionno [ACTIVITY=value] RC-SETS=setno-list]
SPECIES POLYMER=polymerid OLIGOMER=oligomer-list
REAC-GRP groupid type /...
SPEC-GROUP compid groupid number / groupid number / ...

RXN-SET rxn-setno
[A-NUCL-SPEC=compid] [A-ELEC-GRP=groupid] &
[V-ELEC-SPEC=compid] [V-NUCL-GRP=groupid] &
[V-NUCL-SPEC=compid] [V-ELEC-GRP=groupid] &
RC-SETS=rc-setno-list
SG-RATE-CON rc-setno
[CAT-SPEC=compid] [CAT-GRP=groupid] &
sgpre-exp [sgact-energy] [sgt-exp] [sgt-ref] [USER-RC=number]
SUBROUTINE KINETICS=kinname RATECON=rcname MASSTRANS=mtname
USER-VECS NINTK=nintk NREALK=nrealk NINTRC=nintrc &
NREALRC=nrealc NINTMT=nintmt NREALMT=nrealmt &
NIWORK=niwork NWORK=nwork NURC=nurc
INTK value-list
REALK value-list
INTRC value-list
REALRC value-list
INTMT value-list
REALMT value-list
INCL-COMPS compid-list
REAC-TYPE FOR-CON=yes/no REV-CON=yes/no REARRANGE=yes/no
EXCHANGE=yes/no
CONVERGENCE SOLVE-ZMOM=yes/no OLIG-TOL=tolerance
OPTIONS REAC-PHASE=phaseid CONC-BASIS=basis SUPPRESS-WARN=yes/no
USE-BULK=yes/no
The keywords for specifying rate constant parameters for the built-in
reactions, and for specifying user reactions are described here.
Input Language Description for Step-Growth Polymerization
rxnid Unique paragraph ID.
DESCRIPTION Up to 64 characters between double quotes.
REPORT Reaction report options- controls writing of reaction report
in .REP file.
REPORT=YES Print reaction report
REPORT=NO Do not print reaction report
RXN-SUMMARY=
YES
Print stoichiometry for each model-generated
and user-specified reaction.
(Default).
RXN-SUMMARY=
NO
Do not print this summary.
RXN-DETAILS=YES Print stoichiometry, rate constants, and
probability factors for each model-generated
and user-specified reaction.
RXN-DETAILS=NO Do not print this detailed summary.
STOIC Used to specify stoichiometry for user reactions.
Reactionno Reaction number
compid Component ID

coeff Stoichiometric coefficient (positive for
products, negative for reactants)
RATE-CON Used to specify rate constants for user reactions.
SetNo Rate constant set number
pre-exp Pre-exponential factor in inverse-time
units
act-energy Activation energy in mole enthalpy units
T-exp Temperature exponent
T-ref Reference temperature
number User rate constant flag
CATALYST=
Optional catalyst component ID
compid
CAT-ORDER=value Optional reaction order for catalyst
(default=1)
POWLAW-EXP Used to specify power-law exponents for user reactions.
reactionno Reaction number
compid Component ID
exponent Power law exponent
ASSIGN Used to assign rate constant(s) to user reactions.
ACTIVITY=
value
Multiplying factor used to calculate net rate
constant
RC-SETS =
setno-list
List of rate constants (from RATE-CON)
which apply to this user reaction
SPECIES Used to specify key components involved in the reactions.
polymerid Component ID for polymer product
oligomer-list List of oligomers to be tracked
REAC-GRP Used to identify the names and types of reacting functional
groups participating in the reaction network.
groupid Functional group ID
type Functional group type
EE-GRP Electrophilic repeat unit
NN-GRP Nucleophilic repeat unit
EN-GRP Mixed electrophilic/nucleophilic repeat unit
E-GRP Electrophilic leaving group
N-GRP Nucleophilic leaving group
EX-GRP Electrophilic modifier (end cap)

NX-GRP Nucleophilic modifier (end cap)
SPEC-GROUP Used to characterize the reacting functional group
composition of the components (segments and monomers)
participating in the step-growth reaction network.
compid Component ID
groupid Reactive functional group ID
number Number of occurrences of group in species
SG-RATE-CON Used to specify rate constants for model-generated step-growth
reactions and to specify which catalyst they apply to
(if any).
setno Rate constant set number
CAT-SPEC=
compid
Component ID of catalyst species
CAT-GRP=
groupid
Group ID of catalyst group
USER-RC=
number
User rate expression flag
sgpre-exp Pre-exponential factor in inverse-time units
sgact-energy Activation energy in mole-enthalpy units
sgt-exp Temperature exponent
sgt-ref Reference temperature in temperature units
RXN-SET Used to assign sets of rate constants to model-generated
reactions.
A-NUCL-SPEC=
compid
Component ID of reactant which acts as
the attacking nucleophile
A-ELEC-GRP=
groupid
Group ID of electrophilic leaving group in
attacking nucleophilic reactant
V-ELEC-SPEC=
compid
Component ID of reactant which acts as
the nucleophile. When reactions occur
inside polymer molecules, this may be a
segment.
V-ELEC-GRP=
groupid
Group ID of electrophilic group in victim
species (attached to V-NUCL-GRP)
V-NUCL-SPEC=
compid
Component ID of nucleophilic reactant
attached to the victim electrophilic
reactant at the reacting site
V-NUCL-GRP=
groupid
Group ID of nucleophilic group in victim
species (attached to V-ELEC-GRP)
RC-SETS =
rcsetno-list
List of rate constants (from SG-RATE-CON)
which apply to the set of reactions
identified by the previous keywords

SUBROUTINE Used to provide the names of user-supplied Fortran
subroutines. The subroutine argument lists are documented
in the User Subroutines section of Chapter 3.
KINETICS=
User kinetic subroutine name
kinname
RATECON=
rcname
User rate constant subroutine name
MASSTRAN=
mtname
User concentration basis / mass-transfer
subroutine name
USER-VECS Used to specify the size of vectors for user subroutines.
NINTK=nintk Length of integer array for kinetics
NREALK=nrealk Length of real array for kinetics
NINTRC=nintrc Length of integer array for rate constants
NREALRC=
Length of real array for rate constants
nrealrc
NINTMT=nintmt Length of integer array for user basis
routine
NREALMT=
nrealmt
Length of real array for user basis routine
NIWORK=
niwork
Total length of integer workspace
NWORK=nwork Total length of real workspace
NURC=nurc Number of rate constants calculated by
user subroutine
INTK Used to enter integer parameter for kinetics.
REALK Used to enter real parameters for kinetics.
INTRC Used to enter integer parameters for rate constants.
REALRC Used to enter real parameters for rate constants.
INTMT Used to enter integer parameters for mass transfer.
REALMT Used to enter real parameters for mass transfer.
INCL-COMPS Used to list components which participate in reactions in the
user kinetics model, but which do not appear in model-generated
or user-specified reactions.
Compid-list List of additional components to include
in the mass-balance calculations
REAC-TYPE Used to specify which classes of reactions will be generated
by the step-growth model (default is “YES” for all types of
reactions.
FOR-CON=
yes/no
Generate forward condensation reactions

REV-CON=
yes/no
Generate reverse condensation reactions
REARRANGE=
yes/no
Generate re-arrangement reactions
EXCHANGE=
yes/no
Generate end-group exchange reactions
CONVERGENCE Used to specify convergence parameters.
SOLVE-ZMOM=
yes/no
Explicitly solve zeroth moment (default =
no)
OLIG-TOL=
tolerance
Specify tolerance for oligomer
fractionation calculations (default is
1x10-4)
OPTIONS Used to specify reaction model options.
REAC-PHASE=
phaseID
Specify the reacting phase as L, L1, L2,
or V (default is L)
CONC-BASIS=
basis
Specify concentration units for rate
constants as MOL/L (default), MMOL/L,
MOL/KG, or MMOL/KG
SUPRESS-WARN=
yes/no
YES: do not print warnings when the
specified phase is not present
NO: always print warnings when the
specified phase is not present (default)
USE-BULK=
yes/no
YES: force the model to apply the
specified reaction kinetics to the bulk
phase when the specified phase is not
present (default)
NO: rates are set to zero when the
Input Language Example for Step-Growth Polymerization
REACTIONS NYLON STEP-GROWTH
DESCRIPTION “NYLON-6 KINETICS: SIMPLE MODEL WITHOUT CYCLICS”
REPORT RXN-DETAILS=YES
SPECIES POLYMER=NYLON6
REAC-GROUP TNH2 E-GRP / TCOOH N-GRP / BCAP EN-GRP
SPECIES-GRP T-NH2 TNH2 1 / T-NH2 BCAP 1 / T-COOH TCOOH 1 / &
T-COOH BCAP 1 / ACA TNH2 1 / ACA TCOOH 1 / &
ACA BCAP 1 / B-ACA BCAP 1 / H2O TNH2 1 / H2O TCOOH 1
SG-RATE-CON 1 TREF=260 PRE-EXP= 5.461 ACT-ENERGY=23.271
SG-RATE-CON 2 CAT-SPEC=ACA TREF=260 PRE-EXP=40.678 ACT-ENERGY=20.670
SG-RATE-CON 3 CAT-SPEC=T-COOH TREF=260 PRE-EXP=40.678 ACT-ENERGY=20.670
SG-RATE-CON 4 TREF=260 PRE-EXP=0.0124 ACT-ENERGY=29.217
SG-RATE-CON 5 CAT-SPEC=ACA TREF=260 PRE-EXP=0.0924 ACT-ENERGY=26.616
SG-RATE-CON 6 CAT-SPEC=T-COOH TREF=260 PRE-EXP=0.0924 ACT-ENERGY=26.616
RXN-SET 1 ELECTRO-GRP=TNH2 NUCLEO-GRP=TCOOH RC-SETS= 1 2 3

RXN-SET 2 NUCLEOPHILE=H2O RC-SETS= 4 5 6
STOIC 1 CL -1.0 / H2O -1.0 / ACA 1.0
STOIC 2 CL -1.0 / H2O -1.0 / ACA 1.0
STOIC 3 CL -1.0 / H2O -1.0 / ACA 1.0
STOIC 4 ACA -1.0 / CL 1.0 / H2O 1.0
STOIC 5 ACA -1.0 / CL 1.0 / H2O 1.0
STOIC 6 ACA -1.0 / CL 1.0 / H2O 1.0
STOIC 7 CL -1.0 / B-ACA 1.0
STOIC 10 B-ACA -1.0 / CL 1.0
STOIC 11 B-ACA -1.0 / CL 1.0
STOIC 12 B-ACA -1.0 / CL 1.0
STOIC 13 CL -1.0 / ACA -1.0 / T-NH2 1.0 / T-COOH 1.0
STOIC 16 T-NH2 -1.0 / T-COOH -1.0 / ACA 1.0 / CL 1.0
STOIC 19 CL -1.0 / B-ACA 1.0
STOIC 20 CL -1.0 / B-ACA 1.0
STOIC 21 CL -1.0 / B-ACA 1.0
RATE-CON 1 PRE-EXP=0.00424 ACT-ENERGY=19.880 TREF=260
POWLAW-EXP 1 CL 1.0 / H2O 1.0
POWLAW-EXP 2 CL 1.0 / H2O 1.0 / T-COOH 1.0
POWLAW-EXP 3 CL 1.0 / H2O 1.0 / ACA 1.0
POWLAW-EXP 4 ACA 1.0
POWLAW-EXP 5 ACA 1.0 / T-COOH 1.0
POWLAW-EXP 7 CL 1.0 / T-NH2 1.0
POWLAW-EXP 8 CL 1.0 / T-NH2 1.0 / T-COOH 1.0
POWLAW-EXP 9 CL 1.0 / T-NH2 1.0 / ACA 1.0
POWLAW-EXP 10 T-NH2 1.0
POWLAW-EXP 11 T-NH2 1.0 / T-COOH 1.0
POWLAW-EXP 12 T-NH2 1.0 / ACA 1.0

POWLAW-EXP 13 CL 1.0 / ACA 1.0
POWLAW-EXP 14 CL 1.0 / ACA 1.0 / T-COOH 1.0
POWLAW-EXP 15 CL 1.0 / ACA 2.0
POWLAW-EXP 17 T-COOH 1.0 / ACA 1.0
POWLAW-EXP 20 ACA 1.0 / T-COOH 1.0
CONVERGENCE SOLVE-ZMOM=YES
OPTIONS REAC-PHASE=L CONC-BASIS=’MOL/KG’
Specifying Free-Radical
Following is the input language for the FREE-RAD REACTIONS paragraph. The
reaction keywords and rate coefficient parameters for free-radical
polymerization are given. Users may select a subset of the built-in reactions
for a given simulation.

Input Language for Free-Radical Polymerization
REACTIONS reacid FREE-RAD
PARAM QSSA=yes/no QSSAZ=yes/no QSSAF=yes/no RAD-INTENS=value
SPECIES POLYMER=cid INITIATOR=cid-list MONOMER=cid-list INHIBITOR=cid-list &
SOLVENT=cid-list BI-INITIATOR=cid-list COINITIATOR=cid-list CHAINTAG=cid-list &
CATALYST=cid-list INIT-DEC cid idpre-exp idact-energy idact-volume ideffic &
idnrad ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] [COEF1=value BYPROD1=cid] &
[COEF2=value BYPROD2=cid]
INIT-CAT cid1 cid2 icpre-exp icact-energy icact-volume iceffic
icnrad ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &
[COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid]
INIT-SP cid1 cid2 ispre-exp isact-energy isact-volume ref-temp &
[GEL-EFFECT=gelid] [COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid]
INIT-SP-EFF cid coeffa coeffb coeffc
BI-INIT-DEC cid bdpre-exp bdact-energy bdact-volume bdeffic
ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &
SEC-INIT-DEC cid sdpre-exp sdact-energy sdact-volume sdeffic
ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &
CHAIN-INI cid cipre-exp ciact-energy ciact-volume ref-temp [GEL-EFFECT=gelid]
PROPAGATION cid1 cid2 prpre-exp pract-energy pract-volume ref-temp [GEL-EFFECT=gelid]
CHAT-MON cid1 cid2 cmpre-exp cmact-energy cmact-volume ref-temp [GEL-EFFECT=gelid]
CHAT-POL cid1 cid2 cppre-exp cpact-energy cpact-volume ref-temp [GEL-EFFECT=gelid]
CHAT-AGENT cid1 cid2 capre-exp caact-energy caact-volume ref-temp [GEL-EFFECT=gelid]
CHAT-SOL cid1 cid2 cspre-exp csact-energy csact-volume ref-temp [GEL-EFFECT=gelid]
B-SCISSION cid bspre-exp bsact-energy bsact-volume ref-temp [GEL-EFFECT=gelid]
TERM-DIS cid1 cid2 tdpre-exp tdact-energy tdact-volume ref-temp [GEL-EFFECT=gelid]
TERM-COMB cid1 cid2 tcpre-exp tcact-energy tcact-volume ref-temp [GEL-EFFECT=gelid]
INHIBITION cid1 cid2 inpre-exp inact-energy inact-volume ref-temp [GEL-EFFECT=gelid]
SC-BRANCH cid1 cid2 scpre-exp scact-energy scact-volume ref-temp [GEL-EFFECT=gelid]
HTH-PROP cid1 cid2 hppre-exp hpact-energy hpact-volume ref-temp [GEL-EFFECT=gelid]
CIS-PROP cid1 cid2 pcpre-exp pcact-energy pcact-volume ref-temp [GEL-EFFECT=gelid]
TRANS-PROP cid1 cid2 ptpre-exp ptact-energy pcact-volume ref-temp [GEL-EFFECT=gelid]
TDB-POLY cid1 cid2 tdpre-exp tdact-energy tdact-volume ref-temp [GEL-EFFECT=gelid]
PDB-POLY cid1 cid2 pbpre-exp pbact-energy pbact-volume ref-temp [GEL-EFFECT=gelid]
GEL-EFFECT gelid CORR-NO=corrno &
MAX-PARAMS=maxparams GE-PARAMS=paramlist / ...
SUBROUTINE GEL-EFFECT=subname
OPTIONS REAC-PHASE=phaseid SUPRESS-WARN=yes/no USE-BULK=yes/no
Input Language Description for Free-Radical Polymerization
reacid Paragraph ID.
PARAM Used to specify polymerization mechanism, radiation
intensity, and request the Quasi-Steady-State
Approximation (QSSA).
RAD-INTENS=
value
Used to specify a value for the radiation
intensity to be used for the induced
initiation reaction (default is 1.0)
QSSA=
YES/NO
Used to request QSSA for all moments
(default is NO)

QSSAZ=
YES/NO
Used to request QSSA for the zeroth
moment only (default is NO)
QSSAF=
YES/NO
Used to request QSSA for the first moment
only (default is NO)
QSSAS=
YES/NO
Used to request QSSA for the second
moment only (default is NO)
SPECIES Reacting species identification. This sentence is used to
associate components in the simulation with reactive
species in the built-in free-radical kinetic scheme. The
following species keywords are currently valid
INITIATOR List of standard initiators
BI-INITIATOR List of bifunctional initiators
CATALYST List of catalysts
COINITIATOR List of coinitiators
MONOMER List of monomers
POLYMER Reacting polymer ID
CHAINTAG Chain transfer agends
SOLVENT List of solvents which act as chain transfer
agents
INHIBITOR List of inhibitors
MON-RSEG Specifies the pairing between monomers and their
corresponding repeat segments in a polymer.
monomer Monomer ID
r-seg Corresponding repeat segment ID
INIT-DEC Identifier for initiator decomposition reaction.
cid1 Initiator ID
idpre-exp Preexponential factor
idact-energy Activation energy
idact-volume Activation volume (default is 0.0)
ideffic Initiator efficiency (default is 1.0)
idnrad Number of radicals from one initiator
molecule (default is 2.0)
ref-temp Reference temperature
GEL-EFF=gelid Gel effect sentence ID
EFF-GEFF=
gelid
Efficiency factor gel effect sentence ID
COEF1=value Stoichiometric coefficient of first by-product
(default=1.0)

BYPROD1=cid Byproduct 1 component ID
COEF2=value Stoichiometric coefficient of 2nd by-product
(default=1.0)
INIT-CAT Identifier for catalyzed initiator decomposition reaction.
cid1 Initiator ID
cid2 Catalyst ID
icpre-exp Preexponential factor
icact-energy Activation energy
icact-volume Activation volume (default=0.0)
iceffic Initiator efficiency (default=1.0)
icnrad Number of radicals from one initiator
molecule (default=2.0)
EFF-GEFF=
gelid
(default=1.0)
(default=1.0)
INIT-SP Identifier for thermal and radiation induced initiation
reaction.
cid1 Monomer ID
cid2 Co-initiator ID
ispre-exp Preexponential factor
isact-energy Activation energy
isact-volume Activation volume (default is 0.0)
INIT-SP-EFF Parameters for thermal and radiation induced initiation
reaction.
cid Monomer ID
coeffa Exponent for coinitiator concentration
(default is 0.0)

coeffb Exponent for monomer concentration
(default is 0.0)
coeffc Exponent for radiation intensity (default is
0.0)
BI-INIT-DEC Bifunctional initiator primary decomposition
cid1 Bi-initiator ID
bdpre-exp Preexponential factor
bdact-energy Activation energy
bdact-volume Activation volume (default is 0.0)
bdeffic Initiator efficiency (default is 1.0)
EFF-GEFF=
gelid
(default=1.0)
(default=1.0)
SEC-INIT-DEC Bifunctional initiator secondary decomposition
cid1 Bi-initiator ID
sdpre-exp Preexponential factor
sdact-energy Activation energy
sdact-volume Activation volume (default is 0.0)
sdeffic Initiator efficiency (default is 1.0)
EFF-GEFF=
gelid
(default=1.0)
(default=1.0)

CHAIN-INI Identifier for chain initiation reaction.
cid1 Monomer ID
cipre-exp Preexponential factor
ciact-energy Activation energy
ciact-volume Activation volume (default is 0.0)
PROPAGATION Identifier for chain propagation reaction.
cid1 Active segment ID
cid2 Monomer ID
prpre-exp Preexponential factor
pract-energy Activation energy
pract-volume Activation volume (default is 0.0)
CHAT-MON Identifier for chain transfer to monomer reaction.
cid1 Monomer corresponding to polymer active
segment ID
cid2 Monomer ID
cmpre-exp Preexponential factor
cmact-energy Activation energy
cmact-volume Activation volume (default is 0.0)
CHAT-POL Identifier for chain transfer to polymer reaction.
cid2 Segment ID on dead chain
cppre-exp Preexponential factor
cpact-energy Activation energy
cpact-volume Activation volume (default is 0.0)
CHAT-AGENT Identifier for chain transfer to transfer agent reaction.
cid2 Transfer agent ID

capre-exp Preexponential factor
caact-energy Activation energy
caact-volume Activation volume (default is 0.0)
CHAT-SOL Identifier for chain transfer to solvent reaction.
cid2 Solvent ID
cspre-exp Preexponential factor
csact-energy Activation energy
csact-volume Activation volume (default is 0.0)
B-SCISSION Identifier for beta-scission reaction.
bspre-exp Preexponential factor
bsact-energy Activation energy
bsact-volume Activation volume (default is 0.0)
TERM-DIS Identifier for chain termination by disproportionation
reaction.
cid1 First polymer active segment ID
cid2 Second polymer active segment ID
tdpre-exp Preexponential factor
tdact-energy Activation energy
tdact-volume Activation volume (default is 0.0)
TERM-COMB Identifier for chain termination by combination reaction.
cid1 Monomer corresponding to first polymer
active segment ID
cid2 Monomer corresponding to second polymer
active segment ID
tcpre-exp Preexponential factor

tcact-energy Activation energy
tcact-volume Activation volume (default is 0.0)
INHIBITION Identifier for chain inhibition reaction.
cid1 Polymer active segment ID
cid2 Inhibitor ID
inpre-exp Preexponential factor
inact-energy Activation energy
inact-volume Activation volume (default is 0.0)
SC-BRANCH Identifier for short chain branching reaction.
cid1 Reactant polymer active segment ID
cid2 Product active segment ID
scpre-exp Preexponential factor
scact-energy Activation energy
scact-volume Activation volume (default is 0.0)
HTH-PROP Head-to-head propagation reaction
cid2 Monomer ID
hppre-exp Preexponential factor
hpact-energy Activation energy
hpact-volume Activation volume (default is 0.0)
CIS-PROP Cis-propagation for diene monomers
cid2 Diene monomer ID
pcpre-exp Preexponential factor
pcact-energy Activation energy
pcact-volume Activation volume (default is 0.0)

TRANS-PROP Trans-propagation for diene monomers
cid2 Diene monomer ID
pract-volume Activation volume (default is 0.0)
TDB-POLY Terminal double bond polymerization
cid2 Terminal double bond segment ID
tbpre-exp Preexponential factor
tbact-energy Activation energy
tbact-volume Activation volume (default is 0.0)
PDB-POLY Pendent double bond polymerization
cid2 Pendent double bond segment ID
pbpre-exp Preexponential factor
pbact-energy Activation energy
pbact-volume Activation volume (default is 0.0)
GEL-EFFECT Gel effect switch and correlation selection. This sentence is
used to:
Modify the reaction rate expression or initiator efficiency
factor, typically to account for the gel effect at high
conversion.
Select a gel effect correlation from a list of built-in and
user specified gel effect correlations
Specify the maximum number of parameters
Specify the parameter values for the selected correlation
The default action is to not include a gel effect.

gelid Gel effect sentence ID
GETYPE=
reactiontype
Used to identify the type of reaction to
apply gel effect to. A list of valid
reaction types follows
CORR-NO=
corrno
Used to select a correlation number. If a
correlation number greater than the
number of built-in correlations (currently
2) is specified then the user should
supply a Fortran subroutine containing
the user gel effect correlation.
MAX-PARAMS=
maxparams
Used to enter the maximum number of
gel effect parameters for the correlation
selected.
GE-PARAMS=
paramlist
Used to enter a list of parameters for
the correlation selected.
SUBROUTINE User subroutines sentence.
GEL-EFFECT=
subname
Used to specify the name of the
subroutine containing user gel effect
correlations. The user gel-effect
subroutine argument list was shown in
the Gel Effect section in Chapter 3. A
Fortran template called USRGEL.F is
available for your use.
REAC-PHASE=
phaseID
Specify the reacting phase as L, L1, L2,
or V
(default is L)
SUPRESS-WARN=
yes/no
USE-BULK=
yes/no
YES: force the model to apply the
specified reaction kinetics to the bulk
phase when the specified phase is not
present (default)
NO: rates are set to zero when the
Input Language Example for Free-Radical Polymerization
REACTIONS SBD FREE-RAD
DESCRIPTION "test file"
PARAM QSSA=yes
SPECIES INITIATOR=APS MONOMER=STY BD &
SOLVENT=EB POLYMER=SBD CHAINTAG=DDM COINITIATOR=CINI

INIT-DEC APS 1.6220E+11 1.1530E+08 0.0 EFFIC=.80 NRADS=2 &
BYPROD1=CO2 COEF1=0.1 BYPROD2=CO COEF2=0.2
INIT-SP STY CINI 438000.0 1.1480E+08 0.0
CHAIN-INI STY 2.2E7 3.2E7
CHAIN-INI BD 1.2E8 3.88E7
PROPAGATION STY STY 2.2E7 3.2E7
PROPAGATION STY BD 4.4E7 3.2E7
PROPAGATION BD BD 1.2E8 3.88E7
PROPAGATION BD STY 8.5E7 3.88E7
HTH-PROP STY STY 2.2E5 3.2E7
HTH-PROP BD BD 1.2E6 3.88E7
CIS-PROP BD BD 1.2E6 3.88E7
CIS-PROP STY BD 4.4E5 3.2E7
TRANS-PROP BD BD 1.2E6 3.88E7
TRANS-PROP STY BD 4.4E5 3.2E7
CHAT-MON STY STY 2200. 3.2E7
CHAT-MON STY BD 4400. 3.2E7
CHAT-MON BD BD 12000. 3.88E7
CHAT-MON BD STY 8500. 3.88E7
CHAT-AGENT STY DDM 1051.0 2.9590E+07 0.0
CHAT-AGENT BD DDM 900.0 2.9590E+07 0.0
CHAT-SOL STY EB 1051.0 2.9590E+07 0.0
CHAT-SOL BD EB 900.0 2.9590E+07 0.0
B-SCISSION STY 1.00E6 4.5E7 TDB-FRAC=1
B-SCISSION BD 1.00E6 4.5E7 TDB-FRAC=1
TERM-COMB STY STY 1.30E7 9.90E6 GEL-EFFECT=1
TERM-COMB STY BD 1.30E7 9.90E6 GEL-EFFECT=1
TERM-COMB BD BD 1.30E7 9.90E6 GEL-EFFECT=1
TERM-COMB BD STY 1.30E7 9.90E6 GEL-EFFECT=1
TERM-DIS STY STY 1.30E6 9.90E6 GEL-EFFECT=1
TERM-DIS STY BD 1.30E6 9.90E6 GEL-EFFECT=1
TERM-DIS BD BD 1.30E6 9.90E6 GEL-EFFECT=1
TERM-DIS BD STY 1.30E6 9.90E6 GEL-EFFECT=1
TDB-POLY STY STY 2.2E5 3.2E7
TDB-POLY STY BD 4.4E5 3.2E7
TDB-POLY BD BD 1.2E6 3.88E7
TDB-POLY BD STY 8.5E5 3.88E7
PDB-POLY STY BD 4.4E3 3.2E7
PDB-POLY BD BD 1.2E2 3.88E7
INIT-SP-EFF STY COEFFA=0.0 COEFFB=3.0 COEFFC=0.0
GEL-EFFECT 1 CORR-NO=2 MAX-PARAMS=10 &
GE-PARAMS=1 0 2.57 -5.05E-3 9.56 -1.76E-2 &
-3.03 7.85E-3 0.0 2
Specifying Emulsion
Following is the input language for the EMULSION REACTIONS paragraph.
Users are able to select the phases in which the reactions are occurring and
also define the kinetics of particle absorption, desorption, and termination.

Input Language for Emulsion Polymerization
REACTIONS reacid EMULSION
PARAM KBASIS=monomer/aqueous
SPLIT-PM spm-cid kll
SPECIES INITIATOR=cid MONOMER=cid INHIBITOR=cid &
DISPERSANT=cid . . .
INIT-DEC phasid cid idpre-exp idact-energy [idact-volume] ideffic &
idnrad ref-temp
INIT-CAT phased cid1 cid2 icpre-exp icact-energy [icact-volume] iceffic &
icnrad ref-temp
INIT-ACT phasid cid1 cid2 iapre-exp iaact-energy [iaact-volume] iaeffic &
ianrad ref-temp
PROPAGATION phasid cid1 cid2 prpre-exp pract-energy [pract-volume] ref-temp
CHAT-MON phasid cid1 cid2 cmpre-exp cmact-energy [cmact-volume] ref-temp
CHAT-POL phasid cid1 cid2 cppre-exp cpact-energy [cpact-volume] ref-temp
CHAT-AGENT phasid cid1 cid2 capre-exp caact-energy [caact-volume] ref-temp
TERM-DIS phasid cid1 cid2 tdpre-exp tdact-energy [tdact-volume] ref-temp
TERM-COMB phasid cid1 cid2 tcpre-exp tcact-energy [tcact-volume] ref-temp
INHIBITION phasid cid1 cid2 inpre-exp inact-energy [inact-volume] ref-temp
REDUCTION phasid cid1 cid2 rdpre-exp rdact-energy [rdact-volume] rdeffic &
rdnrad ref-temp
OXIDATION phasid cid1 cid2 oxpre-exp oxact-energy [oxact-volume] ref-temp
GEL-EFFECT GETYPE=reactiontype CORR-NO=corrno &
MAX-PARAMS=maxparams GE-PARAMS=paramlist / ...
SUBROUTINE GEL-EFFECT=subname
ABS-MIC ampre-exp amact-energy
ABS-PART appre-exp apact-energy
DES-PART dppre-exp dpact-energy
EMUL-PARAMS emulid cmc-conc area
Input Language Description for Emulsion Polymerization
reacid Paragraph ID.
PARAM Use to enter basis parameters.
KBASIS=
monomer/
aqueous
Basis for phase split ratios
SPLIT-PM Used to enter homosaturation solubility of species in the
polymer phase.
spm-cid Component ID of the species
partitioning into the polymer phase
kll Ratio of mass fraction of species in
polymer phase to mass fraction in
reference phase. KBASIS determines
whether the reference phase is the
monomer of aqueous phase
associate components in the simulation with species in the
built-in free-radical kinetic scheme. The following species
keywords are currently valid
INITIATOR CATALYST MONOMER
CHAINTAG DISPERSANT INHIBITOR
POLYMER EMULSIFIER ACTIVATOR
REDOX-AGENT REDUCTANT

INIT-DEC Identifier for initiator decomposition reaction.
phasid Reaction phase (DISPERSANT)
cid Initiator ID
idpre-exp Preexponential factor
idact-energy Activation energy
idact-volume Activation volume (optional)
ideffic Initiator efficiency
idnrad Number of radicals from one initiator
molecule
INIT-CAT Identifier for catalyzed initiator decomposition reaction.
cid1 Initiator ID
cid2 Catalyst ID
icpre-exp Preexponential factor
icact-energy Activation energy
icact-volume Activation volume (optional)
iceffic Initiator efficiency
icnrad Number of radicals from one initiator
molecule
INIT-ACT Identifier for initiation by activator and initiator.
cid1 Initiator ID
cid2 Activator ID
iapre-exp Preexponential factor
iaact-energy Activation energy
iaact-volume Activation volume (optional)
iaeffic Initiator activation efficiency
ianrad Initiator activation number of radicals
PROPAGATION Identifier for chain propagation reaction.
phasid Reaction phase (POLYMER or
DISPERSANT)
cid1 Monomer corresponding to active
polymer segment ID

cid2 Monomer ID
pract-volume Activation volume (optional)
CHAT-MON Identifier for chain transfer to monomer reaction.
phasid Reaction phase (POLYMER)
polymer segment ID
cid2 Monomer ID
cmpre-exp Preexponential factor
cmact-energy Activation energy
cmact-volume Activation volume (optional)
CHAT-POL Identifier for chain transfer to polymer reaction.
polymer segment ID
cid2 Monomer corresponding to reacting
polymer segment ID or dead chain
cppre-exp Preexponential factor
cpact-energy Activation energy
cpact-volume Activation volume (optional)
CHAT-AGENT Identifier for chain transfer to transfer agent reaction.
polymer segment ID
cid2 Transfer agent ID
capre-exp Preexponential factor
caact-energy Activation energy
caact-volume Activation volume (optional)
TERM-DIS Identifier for chain termination by disproportionation
reaction.

DISPERSANT)
cid1 First active polymer segment ID
cid2 Second active polymer segment ID
tdpre-exp Preexponential factor
tdact-energy Activation energy
tdact-volume Activation volume (optional)
TERM-COMB Identifier for chain termination by combination reaction.
DISPERSANT)
cid1 First active polymer segment ID
cid2 Second active polymer segment ID
tcact-volume Activation volume (optional)
INHIBITION Identifier for chain inhibition reaction.
cid1 Active polymer segment ID
cid2 Inhibitor ID
inpre-exp Preexponential factor
inact-energy Activation energy
inact-volume Activation volume (optional)
REDUCTION Identifier for reduction step of redox initiation.
cid1 Reductant ID
cid2 Redox agent (catalyst) ID
rdpre-exp Preexponential factor
rdact-energy Activation energy
rdact-volume Activation volume (optional)
rdeffic Reduction activation efficiency
rdnrad Reduction activation number of radicals

OXIDATION Identifier for oxidation step of redox initiation.
cid1 Initiator ID
cid2 Redox agent (catalyst) ID
oxpre-exp Preexponential factor
oxact-energy Activation energy
oxact-volume Activation volume (optional)
GEL-EFFECT Gel effect switch and correlation selection. This sentence is
used to
Include a gel effect for any reactions in the built-in kinetic
scheme and for the initiator efficiency
Select a gel effect correlation from a list of built-in and
user specified gel effect correlations
Specify the maximum number of parameters
Specify the parameter values for the selected correlation
The default action is to not include a gel effect.
GETYPE=
reactiontype
Used to identify the type of reaction to
apply gel effect to. A list of valid
reaction types follows
INITIATION Initiator decomposition
INIT-EFF Initiator efficiency
PROPAGATION Propagation, chain initiation and induced
initiation reactions
CHAT-MON Chain transfer to monomer
CHAT-POL Chain transfer to polymer
CHAT-AGENT Chain transfer to agent
TERMINATION Termination
CORR-NO=
corrno
Used to select a correlation number. If a
correlation number greater than the
number of built-in correlations (currently
2) is specified then the user should
supply a Fortran subroutine containing
the user gel effect correlation.
MAX-PARAMS=
maxparams
Used to enter the maximum number of
gel effect parameters for the correlation
selected.
GE-PARAMS=
paramlist
Used to enter a list of parameters for
the correlation selected.

SUBROUTINE User subroutines sentence.
GEL-EFFECT=
subname
Used to specify the name of the
subroutine containing user gel effect
correlations. The user gel-effect
subroutine argument list was shown in
the Gel Effect section in Chapter 3. A
Fortran template called USRGEL.F is
available for your use.
ABS-MIC Used to specify rate of radical absorption by micelles.
ampre-exp Preexponential factor
amact-energy Activation energy
ABS-PART Used to specify rate of radical absorption by particles.
appre-exp Preexponential factor
apact-energy Activation energy
DES-PART Identifier for radical desorption.
dppre-exp Preexponential factor
dpact-energy Activation energy
EMUL-PARAMS Used to specify emulsion parameters for micellar
nucleation.
emulid Emulsifier ID
cmc-conc Critical micelle concentration
area Surface coverage or area per unit mole
of emulsifier
Input Language Example for Emulsion Polymerization

REACTIONS EMLRXN EMULSION
DESCRIPTION "EXAMPLE EMULSION INPUT"
PARAM KBASIS=MONOMER
SPECIES INITIATOR=APS MONOMER=STY NBA EMULSIFIER=EMUL &
DISPERSANT=H2O POLYMER=POLYMER
INIT-DEC DISPERSANT APS 1.0000E+16 1.4020E+08 &
0.0 EFFIC=.80 NRADS=2
PROPAGATION POLYMER STY STY 2341450.0 2.6000E+07
PROPAGATION POLYMER STY NBA 3265600.0 2.6000E+07
PROPAGATION POLYMER NBA NBA 1909530.0 2.2400E+07
PROPAGATION POLYMER NBA STY 1.4918E+07 2.2400E+07
CHAT-MON POLYMER STY STY 3310000.0 5.3020E+07
CHAT-MON POLYMER STY NBA 3310000.0 5.3020E+07
CHAT-MON POLYMER NBA NBA 438.90 2.7600E+07
CHAT-MON POLYMER NBA STY 438.90 2.7600E+07
TERM-COMB POLYMER STY STY 1.6125E+09 7000000.0
TERM-COMB POLYMER STY NBA 7.3204E+09 1.4600E+07
TERM-COMB POLYMER NBA NBA 3.3217E+10 2.2200E+07
TERM-COMB POLYMER NBA STY 7.3204E+09 1.4600E+07
ABS-MIC 1.0000E-07 0.0
ABS-PART 1.0000E-07 0.0
DES-PART 0.0 0.0
EMUL-PARAMS EMUL 0.0 5.0000E+08
SPLIT-PM STY .40
SPLIT-PM NBA .40
Specifying Ziegler-Natta
Following is the input language for the part of the polymerization REACTIONS
paragraph specific to Ziegler-Natta kinetics. Ziegler-Natta inputs may be used
to define the reaction kinetics for a wide variety of homo- and co-polymers
produced by catalyzed polymerization, including HDPE. A subset of the built-in
kinetics can be defined for a simulation by including the reaction keywords for
the desired reactions and specifying the rate coefficient parameters for these
reactions. The reaction keywords and rate coefficient parameters for Ziegler-
Natta polymerization are also provided. Currently for two phase systems the
polymerization reactions are applied to the liquid phase in the reactor. For gas
phase polymerization systems the solid polymer, or the amorphous part of
the polymer, is modeled as a liquid.
Input Language for Ziegler-Natta Polymerization
REACTIONS reacid ZIEGLER-NAT
SPECIES PRECAT=cid CATALYST=cid COCATALYST=cid MONOMER=cid CHAINTAG=cid &
SOLVENT=cid POISON=cid BYPRODUCT=cid HYDROGEN=cid POLYMER=cid &
ELECDONOR=cid TDBSEGMENT=cid
ACT-SPON site-id cid1 aspre-exp asact-energy asorder ref-temp
ACT-COCAT site-id cid1 cid2 acpre-exp acact-energy acorder ref-temp
ACT-EDONOR site-id cid1 cid2 aepre-exp aeact-energy aeorder ref-temp
ACT-H2 site-id cid1 cid2 ahpre-exp ahact-energy ahorder ref-temp
ACT-MON site-id cid1 cid2 ampre-exp amact-energy amorder ref-temp
CHAIN-INI site-id cid1 cipre-exp ciact-energy ciorder ref-temp

PROPAGATION site-id cid1 cid2 prpre-exp pract-energy prorder ref-temp
CHAT-MON site-id cid1 cid2 cmpre-exp cmact-energy cmorder cmtdb-frac ref-temp
CHAT-AGENT site-id cid1 cid2 capre-exp caact-energy caorder catdb-frac ref-temp
CHAT-SOL site-id cid1 cid2 cspre-exp csact-energy csorder cstdb-frac ref-temp
CHAT-COCAT site-id cid1 cid2 ccpre-exp ccact-energy ccorder cctdb-frac ref-temp
CHAT-H2 site-id cid1 cid2 chpre-exp chact-energy chorder chtdb-frac ref-temp
CHAT-EDONOR site-id cid1 cid2 cepre-exp ceact-energy ceorder cetdb-frac ref-temp
CHAT-SPON site-id cid1 cid2 cnpre-exp cnact-energy cnorder cntdb-frac ref-temp
DEACT-POISON site-id cid1 dppre-exp dpact-energy dporder ref-temp
DEACT-COCAT site-id cid1 dcpre-exp dcact-energy dcorder ref-temp
DEACT-MON site-id cid1 dmpre-exp dmact-energy dmorder ref-temp
DEACT-EDONOR site-id cid1 depre-exp deact-energy deorder ref-temp
DEACT-H2 site-id cid1 dhpre-exp dhact-energy dhorder ref-temp
DEACT-SPON site-id dspre-exp dsact-energy dsorder ref-temp
COCAT-POISON cid1 cid2 copre-exp coact-energy coorder ref-temp
FSINH-H2 site-id cid1 fhpre-exp fhact-energy fhorder ref-temp
RSINH-H2 site-id cid1 rhpre-exp rhact-energy rhorder ref-temp
FSINH-POISON site-id cid1 fppre-exp fpact-energy fporder ref-temp
RSINH-POISON site-id cid1 rppre-exp rpact-energy rporder ref-temp
TDB-POLY site-id cid1 cid2 tdpre-exp tdact-energy tdorder ref-temp
ATACT-PROP site-id cid1 cid2 atpre-exp atact-energy atorder ref-temp
CAT-ACTIVATE cid1 cid2 avpre-exp avact-energy avorder ref-temp
OPTIONS REAC-PHASE=phaseid SUPPRESS-WARN=yes/no USE-BULK=yes/no
Input Language Description for Ziegler-Natta Polymerization
reacid Reaction paragraph ID.
associate components in the simulation with the reactive
species in the built-in kinetic scheme. The following species
keywords are currently valid
PRECAT CATALYST COCATALYST
MONOMER CHAINTAG SOLVENT
POISON BYPRODUCT
HYDROGEN POLYMER
ELECDONOR TDBSEGMENT
MON-RSEG Specifies the pairing between monomers and their
corresponding repeat segments in a polymer.
monomer Monomer ID
r-seg Corresponding repeat segment ID
ACT-SPON Reaction identifier for spontaneous site activation of a
catalyst potential site to a vacant active site of type k.
site-id Site type identifier for active site formed
(k = 1, 2, ... , NSITE)
cid1 Component ID of catalyst
aspre-exp Preexponential factor (default is 0.0)
asact-energy Activation energy (default is 0.0)
asorder Reaction order for potential site
concentration (default is 0.0)

ACT-COCAT Reaction identifier for site activation by cocatalyst of a
site-id Site type identifier for active site
(k = 1, 2, ... , NSITE)
cid2 Component ID of cocatalyst
acpre-exp Preexponential factor (default is 0.0)
acact-energy Activation energy (default is 0.0)
acorder Reaction order for cocatalyst concentration
(default is 0.0)
ACT-EDONOR Reaction identifier for site activation by electron donor of a
(k = 1, 2, ... , NSITE)
cid2 Component ID of electron donor
aepre-exp Preexponential factor (default is 0.0)
aeact-energy Activation energy (default is 0.0)
aeorder Reaction order for electron donor
ACT-H2 Reaction identifier for site activation by hydrogen of a
(k = 1, 2, ... , NSITE)
cid2 Component ID of hydrogen
ahpre-exp Preexponential factor (default is 0.0)
ahact-energy Activation energy (default is 0.0)
ahorder Reaction order for hydrogen concentration
(default is 0.0)
ACT-MON Reaction identifier for site activation by monomer of a
(k = 1, 2, ... , NSITE)

cid2 Component ID of monomer
ampre-exp Preexponential factor (default is 0.0)
amact-energy Activation energy (default is 0.0)
amorder Reaction order for monomer concentration
(default is 0.0)
CHAIN-INI Reaction identifier for polymer chain initiation on a vacant
active site of type k. The vacant site becomes a
propagation site of type k.
site-id Site type identifier (k = 1, 2, ... , NSITE)
cipre-exp Preexponential factor (default is 0.0)
ciact-energy Activation energy (default is 0.0)
ciorder Reaction order for monomer concentration
(default is 0.0)
PROPAGATION Reaction identifier for polymer chain propagation on an
active site of type k.
cid1 Component ID of active segment (specified
in terms of the corresponding monomer ID)
prpre-exp Preexponential factor (default is 0.0)
pract-energy Activation energy (default is 0.0)
prorder Reaction order for monomer concentration
(default is 0.0)
CHAT-MON Reaction identifier for chain transfer to monomer on active
site of type k.
cmpre-exp Preexponential factor (default is 0.0)
cmact-energy
Activation energy (default is 0.0)

cmorder Reaction order for monomer concentration
(default is 0.0)
cmtdb-frac Fraction of generated dead polymer chains
with terminal double bonds (default is 0.0)
CHAT-AGENT Reaction identifier for chain transfer to agent on active site
of type k.
cid2 Component ID of chain transfer agent
capre-exp Preexponential factor (default is 0.0)
caact-energy Activation energy (default is 0.0)
caorder Reaction order for agent concentration
(default is 0.0)
catdb-frac Fraction of generated dead polymer chains
CHAT-SOL Reaction identifier for chain transfer to solvent on active
site of type k.
cid2 Component ID of solvent
cspre-exp Preexponential factor (default is 0.0)
csact-energy Activation energy (default is 0.0)
csorder Reaction order for solvent concentration
(default is 0.0)
cstdb-frac Fraction of generated dead polymer chains
CHAT-COCAT Reaction identifier for chain transfer to cocatalyst on active
site of type k.
ccpre-exp Preexponential factor (default is 0.0)

ccact-energy Activation energy (default is 0.0)
ccorder Reaction order for cocatalyst concentration
(default is 0.0)
cctdb-frac Fraction of generated dead polymer chains
CHAT-H2 Reaction identifier for chain transfer to hydrogen on active
site of type k.
chpre-exp Preexponential factor (default is 0.0)
chact-energy Activation energy (default is 0.0)
chorder Reaction order for hydrogen concentration
(default is 0.0)
chtdb-frac Fraction of generated dead polymer chains
CHAT-EDONOR Reaction identifier for chain transfer to electron donor on
active site of type k.
cepre-exp Preexponential factor (default is 0.0)
ceact-energy Activation energy (default is 0.0)
ceorder Reaction order for electron donor
cetdb-frac Fraction of generated dead polymer chains
CHAT-SPON Reaction identifier for spontaneous chain transfer on active
site of type k.
cnpre-exp Preexponential factor (default is 0.0)

cnact-energy Activation energy (default is 0.0)
cnorder Reaction order (not used)
cntdb-frac Fraction of generated dead polymer chains
DEACT-POISON Reaction identifier for site deactivation by poison of a
catalyst active site of type k to a dead site.
cid1 Component ID of poison
dppre-exp Preexponential factor (default is 0.0)
dpact-energy Activation energy (default is 0.0)
dporder Reaction order for poison concentration
(default is 0.0)
DEACT-COCAT Reaction identifier for site deactivation by cocatalyst of a
dcpre-exp Preexponential factor (default is 0.0)
dcact-energy Activation energy (default is 0.0)
dcorder Reaction order for cocatalyst concentration
(default is 0.0)
DEACT-MON Reaction identifier for site deactivation by monomer of a
dmpre-exp Preexponential factor (default is 0.0)
dmact-energy Activation energy (default is 0.0)
dmorder Reaction order for monomer concentration
(default is 0.0)
DEACT- EDONOR Reaction identifier for site deactivation by electron donor of
a catalyst active site of type k to a dead site.
depre-exp Preexponential factor (default is 0.0)

deact-energy Activation energy (default is 0.0)
deorder Reaction order for electron donor
DEACT-H2 Reaction identifier for site deactivation by hydrogen of a
dhpre-exp Preexponential factor (default is 0.0)
dhact-energy Activation energy (default is 0.0)
dhorder Reaction order for hydrogen concentration
(default is 0.0)
DEACT-SPON Reaction identifier for spontaneous site deactivation of a
dspre-exp Preexponential factor (default is 0.0)
dsact-energy Activation energy (default is 0.0)
dsorder Reaction order (not used)
COCAT-POISON
Reaction identifier for cocatalyst poisoning reaction.
copre-exp Preexponential factor (default is 0.0)
coact-energy Activation energy (default is 0.0)
coorder Reaction order (not used)
FSINH-H2 Reaction identifier for site inhibition by hydrogen-forward
reaction.
fhpre-exp Preexponential factor (default is 0.0)
fhact-energy Activation energy (default is 0.0)
fhorder Reaction order for hydrogen concentration
(default is 0.0)

RSINH-H2 Reaction identifier for site inhibition by hydrogen-reverse
reaction.
rhpre-exp Preexponential factor (default is 0.0)
rhact-energy Activation energy (default is 0.0)
rhorder Reaction order for inhibited site
FSINH-POISON Reaction identifier for site inhibition by poison-forward
reaction.
fppre-exp Preexponential factor (default is 0.0)
fpact-energy Activation energy (default is 0.0)
fporder Reaction order for poison concentration
(default is 0.0)
RSINH-POISON Reaction identifier for site inhibition by poison-reverse
reaction.
rppre-exp Preexponential factor (default is 0.0)
rpact-energy Activation energy (default is 0.0)
rporder Reaction order for inhibited site
TDB-POLY Reaction identifier for terminal double bond propagation
reaction.
in terms of the corresponding monomer)
cid2 Component ID of TDB segment
tdpre-exp Preexponential factor (default is 0.0)
tdact-energy Activation energy (default is 0.0)
tdorder Reaction order (not used)

ATACT-PROP Reaction identifier for atactic propagation reaction.
in terms of the corresponding monomer)
atpre-exp Preexponential factor (default is 0.0)
atact-energy Activation energy (default is 0.0)
atorder Reaction order for monomer concentration
(default is 0.0)
CAT-ACTIVATE Reaction identifier for catalyst activation reaction.
cid1 Component ID for pre-catalyst
avpre-exp Preexponential factor (default is 0.0)
avact-energy Activation energy (default is 0.0)
avorder Reaction order for catalyst
REAC-PHASE=
phaseID
Specify the reacting phase as L, L1, L2, or V
(default is L)
SUPRESS-WARN=
yes/no
USE-BULK=
yes/no
YES: force the model to apply the specified
reaction kinetics to the bulk phase when the
NO: rates are set to zero when the specified
phase is not present
Input Language Example for Zielger-Natta Polymerization
REACTIONS ZN-R2 ZIEGLER-NAT
DESCRIPTION "ZIEGLER-NATTA KINETIC SCHEME"
SPECIES CATALYST=CAT COCATALYST=CCAT MONOMER=E2 &
SOLVENT=HEXANE HYDROGEN=H2 POLYMER=HDPE
ACT-SPON 1 CAT .080 0.0 1.0
ACT-SPON 2 CAT .080 0.0 1.0
ACT-SPON 3 CAT .080 0.0 1.0
ACT-SPON 4 CAT .080 0.0 1.0

ACT-COCAT 1 CAT CCAT .150 0.0 1.0
CHAIN-INI 1 E2 255.0 0.0 1.0
CHAIN-INI 2 E2 90.0 0.0 1.0
CHAIN-INI 3 E2 255.0 0.0 1.0
CHAIN-INI 4 E2 90.0 0.0 1.0
PROPAGATION 1 E2 E2 255.0 0.0 1.0
PROPAGATION 2 E2 E2 90.0 0.0 1.0
PROPAGATION 3 E2 E2 255.0 0.0 1.0
PROPAGATION 4 E2 E2 90.0 0.0 1.0
CHAT-MON 1 E2 E2 .090 0.0 1.0
CHAT-MON 2 E2 E2 .240 0.0 1.0
CHAT-MON 3 E2 E2 .090 0.0 1.0
CHAT-MON 4 E2 E2 .240 0.0 1.0
CHAT-H2 1 E2 H2 5.550 0.0 1.0
CHAT-H2 2 E2 H2 18.50 0.0 1.0
CHAT-H2 3 E2 H2 5.550 0.0 1.0
CHAT-H2 4 E2 H2 18.50 0.0 1.0
CHAT-SPON 1 E2 .0040 0.0 1.0
CHAT-SPON 2 E2 .0120 0.0 1.0
CHAT-SPON 3 E2 .0040 0.0 1.0
CHAT-SPON 4 E2 .0120 0.0 1.0
DEACT-SPON 1 .00010 0.0 1.0
DEACT-SPON 2 .00060 0.0 1.0
DEACT-SPON 3 .00010 0.0 1.0
DEACT-SPON 4 .00060 0.0 1.0
OPTIONS REAC-PHASE=L
Specifying Ionic Polymerization
Kinetics
Following is the input language for the IONIC REACTIONS paragraph.

Input Language for Ionic Polymerization
REACTIONS reacid IONIC
SPECIES ASSO-INI=cid INIT=cid CATALYST=cid &
EX-AGENT=cid CT-AGENT=cid TM-AGENT=cid &
POLYMERS
MON-RSEG cid segid / cid segid / …
INIT-DISSOC cid1 cid2 idpre-exp-f idact-ener-f idpre-exp-r idact-ener-r idasso-no &
idref-temp
ACT-CATALYST site-id cid1 cid2 acpre-exp-f acact-ener-f acpre-exp-r acact-ener-r &
accoefb accoefd acref-temp
CHAIN-INI-1 site-id cid i1pre-exp-f i1act-ener-f i1ref-temp
CHAIN-INI-2 site-id cid1 cid2 i2pre-exp-f i2act-ener-f i2coefd
CHAIN-INI-T site-id cid itpre-exp-f itact-ener-f itref-temp
PROPAGATION site-id cid1 cid2 prpre-exp-f pract-ener-f prref-temp
ASSOCIATION site-id cid aspre-exp-f asact-ener-f aspre-exp-r asact-ener-r
EXCH-GENERAL rxn id site-id1 cid1 site-id2 cid2 egpre-exp-f egact-ener-f egref-temp
EXCH-AGENT rxn id site-id1 cid1 site-id2 cid2 eapre-exp-f eaact-ener-f &
eapre-expr eaact-ener-r eacoefd earef-temp
EQUILIB-CION site-id1 cid1 site-id2 eqpre-exp-f eqact-ener-f eqpre-exp-r &
eqexp-ener-r eqcoefd eqref-temp
CHAT-SPON site-id cid cspre-exp-f csact-ener-f csref-temp
CHAT-MONOMER site-id cid1 cid2 cmpre-exp-f cmact-ener-f cmref-temp
CHAT-DORM-P rxn id site-id1 cid1 site-id2 cid2 cdpre-exp-f cdact-ener-f cdref-temp
CHAT-AGENT site-id cid1 cid2 capre-exp-f caact-ener-f caorder caref-temp
TERM-C-ION site-id cid tcpre-exp tcact-energy tccoefb tcref-temp
TERM-AGENT site-id cid1 cid2 tapre-exp-f taact-ener-f taorder taref-temp
COUPLING site-id1 site-id2 site-id3 copre-exp-f coact-ener-f copre-exp-r &
coact-eng-r coref-temp
OPTIONS REAC-PHASE=phaseid SUPPRESS-WARN=yes/no USE-BULK=yes/no
Input Language Description for Ionic Polymerization
reacid Reaction paragraph ID.
associate components in the simulation with the reactive
species in the built-in kinetic scheme. The following species
keywords are currently valid:
ASSOC-INIT INITIATOR CATALYST
EXCH-AGENT CHAT-AGENT TERM-AGENT
POLYMER
MON-RSEG Identifying the reacting monomer and the corresponding
repeat segment associated with it.
cid2 Component ID of corresponding repeat
segment
INIT-DISSOC Reaction identifier for initiator dissociation reaction.
Associated initiator of type m dissociates into type p
initiator.
cid1 Component ID of associated initiator
idpre-exp-f Preexponential factor for forward reaction
idact-ener-f Activation energy for forward reaction

idpre-exp-r Preexponential factor for reverse reaction
idact-ener-r Activation energy for reverse reaction
idasso-no Initiator Association number
idref-temp Reference temperature
ACT-CATALYST Reaction identifier for active species activation by catalyst
of type n of an initiator of type m to form active species
and/or counter-ion of type i.
site-id Site type identifier for active species formed
(i = 1, 2, ..., NSITE)
cid1 Component ID of initiator
acpre-exp-f Preexponential factor for forward reaction
acact-ener-f Activation energy for forward reaction
acpre-exp-r Preexponential factor for reverse reaction
acact-ener-r Activation energy for reverse reaction
accoefb 0 if cid2 does not participate in the reaction.
1 if cid2 participates in the reaction
accoefd 0 if counter-ion is absent. 1 if counter-ion is
present
acref-temp Reference temperature
CHAIN-INI-1 Reaction identifier for chain initiation of active species of
type i by monomer of type j.
(i = 1, 2, ..., NSITE)
cid Component ID of monomer
i1pre-exp-f Preexponential factor
i1act-ener-f Activation energy
i1ref-temp Reference temperature
CHAIN-INI-2 Reaction identifier for chain initiation of active species of
type i by monomer of type j reacting with initiator of type
m.
(i = 1, 2, ..., NSITE)
cid1 Component ID of initiator
i2pre-exp-f Preexponential factor
i2act-ener-f Activation energy

i2coefd 1 if counter-ion is formed. 0 otherwise
tref Reference temperature
CHAIN-INI-T Reaction identifier for chain initiation of transfer active
species of type i by monomer of type j.
(i = 1, 2, ..., NSITE)
cid Component ID of monomer
itpre-exp-f Preexponential factor
itact-ener-f Activation energy
itref-temp Reference temperature
PROPAGATION Reaction identifier for polymer chain propagation on an
active species of type i.
(i = 1, 2, ..., NSITE)
cid1 Component ID of active segment
prpre-exp-f Preexponential factor
pract-ener-f Activation energy
prref-temp Reference temperature
ASSOCIATION Reaction identifier for polymer association with active
species of type i.
(i = 1, 2, ..., NSITE)
cid Component ID of active segment
aspre-exp-f Preexponential factor for forward reaction
(forming aggregate polymer)
asact-ener-f Activation energy for forward reaction
aspre-exp-r Preexponential factor for reverse reaction
asact-ener-r Activation energy for reverse reaction
asasso-no Polymer association
asref-temp Reference temperature
EXCH-GENERAL Reaction identifier for general exchange reaction between
two growing polymer chains with unique active species and
end segments attached to them.
rxn id Reaction ID for a unique rate constant
site-id1 Site type identifier for first active species
(i = 1, 2, ... , NSITE)

cid1 Component ID of active segment on siteid1
site-id2 Site type identifier for second active species
(i = 1, 2, ... , NSITE)
egpre-exp-f Preexponential factor
egact-ener-f Activation energy
egref-temp Reference temperature
EXCH-AGENT Reaction identifier for exchange between growing i polymer
species with k segment attached to it and an exchange-agent
of type m.
(i = 1, 2, ... , NSITE)
(i = 1, 2, ... , NSITE) formed
cid2 Component ID of exchange agent
eapre-exp-f Preexponential factor for forward reaction
eaact-ener-f Activation energy for forward reaction
eapre-exp-r Preexponential factor for reverse reaction
eaact-ener-r Activation energy for reverse reaction
eacoefd 0 if Po is absent. 1 if Po is present
earef-temp Reference temperature
EQUILIB-CION Reaction identifier for equilibrium with counter-ion between
i and j active species with kth segment attached to it.
(i = 1, 2, ... , NSITE)
(j = 1, 2, ... , NSITE)
eqpre-exp-f Preexponential factor for forward reaction
eqact-ener-f Activation energy for forward reaction
eqpre-exp-r Preexponential factor for reverse reaction
eqact-ener-r Activation energy for reverse reaction
eqcoefd 0 if counter-ion is absent. 1 if counter-ion is
present

eqref-temp Reference temperature
CHAT-SPON Reaction identifier for spontaneous chain transfer on active
species of type i.
site-id Site type identifier for active species
(i=1, 2, ... , NSITE)
cspre-exp-f Preexponential factor
csact-ener-f Activation energy
csref-temp Reference temperature
CHAT-MONOMER Reaction identifier for chain transfer to monomer of type j
on active species of type i.
(i=1, 2, ... , NSITE)
cmpre-exp-f Preexponential factor
cmact-ener-f Activation energy
cmref-temp Reference temperature
CHAT-DORM-P Reaction identifier for chain transfer on active species of
type i to form dormant polymer of type j.
site-id1 Site type identifier for growing active species
(i = 1, 2, ... , NSITE)
site-id2 Site type identifier for product active species
(j = 1, 2, ... , NSITE) formed
cdpre-exp-f Preexponential factor
cdact-ener-f Activation energy
cdref-temp Reference temperature
CHAT-AGENT Reaction identifier for chain transfer to chain transfer agent
on active species of type i.
(i=1, 2, ... , NSITE)
cid2 Component ID of chain transfer agent

capre-exp-f Preexponential factor
caact-ener-f Activation energy
caorder Reaction order for chain transfer agent
concentration
caref-temp Reference temperature
TERM-C-ION Reaction identifier for chain termination with counter-ion.
(i=1, 2, ... , NSITE)
tcoefb 0 if counter-ion does not participate in the
reaction. 1 if it does
tcref-temp Reference temperature
TERM-AGENT Reaction identifier for termination with terminating agent.
site-id Site type identifier (i = 1, 2, ... , NSITE)
cid1 Component ID of active agent
cid2 Component ID of terminating agent
tapre-exp-f Preexponential factor
taact-ener-f Activation energy
taorder Reaction order for terminating agent
concentration
taref-temp Reference temperature
COUPLING Reaction identifier for coupling reaction between active
species of type i and type j to form active species of type
k.
site-id1 Site identifier for active species of type i
participating in the reaction
site-id2 Site identifier for active species of type j
participating in the reaction
site-id3 Site identifier for active species of type k
formed by coupling reaction
copre-exp-f Preexponential factor
coact-ener-f Activation energy
copre-exp-r Preexponential factor
coact-ener-r Activation energy
coref-temp Reference temperature

OPTIONS Specify reaction model options.
REAC-PHASE=
phaseid
Specify the reacting phase as L, L1, L2, or V
(default is L)
SUPRESS-WARN=
yes/no
USE-BULK=
yes/no
Input Language Example for Ionic Polymerization
REACTIONS rxnid SEGMENT-BAS
DESCRIPTION '...'
PARAM TREF=value PHASE=V/L/L1/L2 SOLVE-ZMOM=YES/NO &
[SUPRESS-WARN=yes/no] [USE-BULK=yes/no] CBASIS=basis &
[REAC-SITE=siteno S-BASIS=basis]
SPECIES POLYMER=polymerid
STOIC reactionno compid coef / ...
RATE-CON reactionno pre-exp act-energy [t-exp] [TREF=ref-temp] &
[CATALYST=cid CAT-ORDER=value] [USER-RC=userid] / ...
[ASSIGN reactionno [ACTIVITY=value] RC-SETS=setno-list]
SUBROUTINE RATECON=rcname MASSTRANS=mtname
USER-VECS NINTRC=nintrc NREALRC=nrealc NINTMT=nintmt NREALMT=nrealmt &
NIWORKRC=niwork NWORKRC=nwork NIWORKMT=niwork NWORKMT=nwork &
NURC=nurc
INTRC value-list
REALRC value-list
INTMT value-list
REALMT value-list
Specifying Segment-Based
Polymer Modification Reactions
The input language for the SEGMENT-BAS REACTIONS paragraph is described
here.
Input Language for Segment-Based Polymer Modification Reactions

REACTIONS rxnid SEGMENT-BAS
DESCRIPTION '...'
PARAM T-REFERENCE=value PHASE=V/L/L1/L2 CBASIS=basis &
SOLVE-ZMOM=YES/NO SPECIES POLYMER=polymerid
STOIC reactionno compid coef / ...
RATE-CON reactionno pre-exp act-energy [t-exp] / ...
The keywords for specifying rate constant parameters, reaction stoichiometry,
and reacting polymer are described here.
Input Language Description for Segment-Based Polymer Modification
Reactions
reacid Unique paragraph ID.
DESCRIPTION Up to 64 characters between double quotes.
PARAM Used to enter reaction specifications.
T-REF=
value
Reference temperature. If no reference
temperature is given, the term 1/Tref is
dropped from the rate expression:
rate  C k e j j oi
Ea
i

1 1


 
  ij R T T
ref

 

For more information, see the Segment-
Based Reaction Model section in Chapter 3.
PHASE=V/L/L1
/L2
Reacting phase
CBASIS Basis for power law rate expression. Choices
are:
MOLARITY
MOLALITY
MOLEFRAC
MASSFRAC
MASSCONC
SUPRESS-WARN=
yes/no
USE-BULK=
yes/no
SOLVE-ZMOM=
Option to explicitly solve for zeroth moment
based on segment types (default=no)

YES/NO
REAC-SITE=
siteno
Site number associated with all reactions in
this model
S-BASIS=
basis
For multi-site kinetics there are two options
for calculating the segment concentrations
used by the reactor model:
COMPOSITE: use the composite segment
concentrations (from SFLOW)
SITE: use the site-based segment
concentrations (from SSFLOW)
SPECIES Used to specify reacting polymer.
POLYMER=
polymerid
Polymer component ID (for reacting
polymer)
STOIC Used to specify stoichiometry for user reactions.
compid Component ID
coef Stoichiometric coefficient (negative for
reactants and positive for products)
POWLAW-EXP Used to specify power-law exponents.
compid Component ID
exponent Power law exponent
ASSIGN Used to assign rate constant(s) to user reactions.
ACTIVITY=
value
Multiplying factor used to calculate net rate
constant
RC-SETS =
setno-list
List of rate constants (from RATE-CON)
which apply to this user reaction
RATE-CON Used to specify rate constant parameters.
SetNo Rate constant set number
pre-exp Pre-exponential factor in inverse time units
act-energy Activation energy in mole enthalpy units
t-exp Temperature exponent
T-ref Reference temperature (default is global
reference temperature in PARAM sentence)
USER-RC=
number
Used to specify an element number in the
user rate constant array (default=do not
apply user rate constant)
CATALYST= Optional catalyst ID

compid
CAT-ORDER=
value
Optional reaction order for catalyst
(default=1)
SUBROUTINE Used to provide the names of user-supplied Fortran
subroutines. The subroutine argument lists are
documented in the User Subroutines section of Chapter 3.
RATECON=
User rate constant subroutine name
rcname
BASIS= mtname User concentration basis / mass-transfer
subroutine name
USER-VECS Used to specify the size of vectors for user subroutines.
NINTRC=nintrc Length of integer array rate constant
routine
NREALRC=
nrealrc
Length of real array for rate constant
routine
NINTMT=nintmt Length of integer array for basis
subroutine
NREALMT=
nrealmt
Length of real array for basis
subroutine
NIWORKRC=
niwork
Length of integer workspace for rate
constant subroutine
NWORKRC=nwork Length of real workspace for rate
constant subroutine
NIWORKMT=
niwork
Length of integer workspace for basis
routine
NWORKRC=nwork Total length of real workspace for
basis subroutine
NURC Number of rate constants returned by
user rate constant routine
INTRC Used to enter integer parameters for user rate constant
subroutine
REALRC Used to enter real parameters for user rate constant
subroutine
INTMT Used to enter integer parameters for user basis subroutine
REALMT Used to enter real parameters for user basis subroutine
Input Language Example for Segment-Based Polymer Modification Reactions
REACTIONS R-1 SEGMENT-BAS
SPECIES POLYMER=PU
STOIC 1 DEG -1. / MDI -1. / DEG-E 1. / MDI-E 1. / &
URETHANE 1.

STOIC 2 DEG -1. / MDI-E -1. / DEG-E 1. / MDI-R 1. / &
URETHANE 1.
STOIC 3 DEG-E -1. / MDI -1. / DEG-R 1. / MDI-E 1. / &
URETHANE 1.
STOIC 4 DEG-E -1. / MDI-E -1. / DEG-R 1. / MDI-R 1. / &
URETHANE 1.
STOIC 5 MDI-E -1. / H2O -1. / MDA-E 1. / CO2 1.
STOIC 6 MDA-E -1. / MDI -1. / MDI-R 1. / MDI-E 1. / &
UREA-R 1.
STOIC 7 MDA-E -1. / MDI-E -1. / MDI-R 2. / UREA-R 1.
STOIC 8 MDI -1. / URETHANE -1. / MDI-E 1. / ALLOPHAN 1.
STOIC 9 MDI-E -1. / URETHANE -1. / MDI-R 1. / ALLOPHAN 1.
STOIC 10 MDI -1. / UREA-R -1. / MDI-E 1. / BIURET 1.
STOIC 11 MDI-E -1. / UREA-R -1. / MDI-R 1. / BIURET 1
RATE-CON 1 2500. <1/sec> 10.
RATE-CON 2 1000. <1/sec> 10.
RATE-CON 3 5000. <1/sec> 10.
RATE-CON 4 10. <1/sec> 10.
RATE-CON 5 100. <1/sec> 10.
ASSIGN-URC 1 ACTIVITY=4. RC-SETS=1
ASSIGN-URC 4 RC-SETS=1
POWLAW-EXP 1 DEG 1. / MDI 1.
POWLAW-EXP 2 DEG 1. / MDI-E 1.
POWLAW-EXP 3 DEG-E 1. / MDI 1.
POWLAW-EXP 4 DEG-E 1. / MDI-E 1.
POWLAW-EXP 5 MDI-E 1. / H2O 1.
POWLAW-EXP 6 MDA-E 1. / MDI 1.
POWLAW-EXP 7 MDA-E 1. / MDI-E 1.
POWLAW-EXP 8 MDI 1. / URETHANE 1.
POWLAW-EXP 9 MDI-E 1. / URETHANE 1.
POWLAW-EXP 10 MDI 1. / UREA-R 1.
POWLAW-EXP 11 MDI-E 1. / UREA-R 1.
References
Aspen Physical Property System Physical Property Data. Burlington, MA:

Index
A
Absorption 213
Acrylic acid 199
Activated initiation 211
Activation energy
fitting 356
Active species formation 254
Adding
emulsion reactions 221
free-radical reactions 194
gel-effect 196, 222
ionic reactions 261
segment-based reactions 287
user basis subroutine 161, 289
user kinetic subroutine 161
user rate constant subroutine
161, 289
user step-growth reactions 159
Ziegler-Natta reactions 246
Addition polymerization
about 81
ionic process differences 250
step-growth processes 266
Addition polymers 57
Addition reactions 103
Aggregate polymer 34, 35
Aggregation reactions 256
Aliphatic polycarbonates 89
Amorphous polymers 16
Analysis tools
available 11, 375–80
calculation procedure 376
optimization 377
sensitivity 377
Application tools 294
Applications
data fitting 339
example uses 375
tools 375–80
Architecture
Aspen Polymers 381
Aromatic polycarbonates 89
Aspen Plus
distillation models 296, 301
Dupl 296–98
equilibrium reactor models 304
Flash2 298
Flash3 298
fractionation models 296
FSplit 299
Heater 299
kinetic reactor models 304–35
mass-balance reactor models
302–4
Mixer 299
Mult 299
Pipe 300
Pump 300
RadFrac 301
RBatch 327–35
RCSTR 304–17
reaction models 86
reactor models 296, 302
REquil 304
RGibbs 304
RPlug 317–27
RStoic 302
RYield 303
Sep 301
Sep2 301
stream manipulators 295
unit operation models 359–65
Aspen Polymers
application tools 294, 375–80
architecture 381
built-in models 85
Index 507

component attribute treatment in
unit operations 335–37
component databanks 387–429
configuring 381–82
data fitting 294, 339–40
decomposition rate parameters
431–33
emulsion model 199–223
end-use properties 75
features 5, 9–13
files 382
flowsheets 293
fortran utilities 445
free-radical polymerization
model 163–98
input language 447–504
installation 382
ionic model 249–63
key parameters 342
kinetic rate constant parameters
431–44
model definition 12
polyester technology package 95
property approach 58
reaction models 85
segment approach 27
segment-based reaction model
265–90
steady-state features 294
steady-state modeling 291–94
step-growth polymerization
model 89–162
templates 382
troubleshooting 383–86
unit operations 294
user models 86, 359–73
user subroutines 140–55, 274–
84
Ziegler-Natta model 225–47
Aspen PolyQuest 96
AspenTech support 3
AspenTech Support Center 3
Association reactions 256
Attributes See also Component
attributes
aggregate polymers 40, 48
bulk polymers 47
calculation methods 47
catalyst 45
handling in unit operations 336
initialization scheme 47–50
initializing in streams 451
live polymers 39, 48
polymers 36–37
required 44, 47
scale factors 50
scaling 453
site-based aggregate polymers
43, 50
site-based bulk polymers 49
site-based live polymers 42, 49
site-based polymers 40
specifying conventional
component 451
user 45, 46
variables for data regression 346
Ziegler-Natta 44
Average properties 58–59
B
Backbone modifications 269
Batch reactors 330
Beta-scission 183
Bifunctional initiator decomposition
171
Bifunctional initiators 174, 175
Bimodal distributions 56
Bivariate distributions 55
Block length 35
Branch formation 270
Branching
degree of 33
free-radical polymerization 192
frequency 35
number of chains 35
reactions 240
Broyden solver 311
Bulk
free-radical polymerization 163–
98
polymer chain 169
polymer chain length moment
equation 187
polymerization 164
Bulk polymerization 85
Butadiene 199
Butyl acrylate 199
508 Index

Butyl methacrylate 199
C
Calculator block 376
Catalyst sites
inhibited 231
propagation 231
types 231
vacant 231
Catalysts
poisoning 240
preactivation 237
site activation 237
types 226–29
Ziegler-Natta 24, 226
Catalyzed initiation reaction 173
Categorizing polymers 19
Chain
initiation for ionic 255
initiation for Ziegler-Natta 237
scission 269
termination 257
Chain length
average properties 59
distribution 20, 35, 59–61, 65
first moment 47
instantaneous weight distribution
63
instanteous number-average 63
weight-average 63
zeroth moment 47
Chain size 55
Chain transfer
dormant polymer formation 257
ionic reactions 257
spontaneous 239, 257
to agent 239, 257
to cocatalysts 239
to electron donor 239
to hydrogen 239
to monomer 179, 239, 257
to polymer 181
to small molecules 178, 239
to solvent 178, 239
to transfer agent 178
Chain-growth polymerization
bulk 85
commercial polymers 84
comparison to step-growth 82
emulsion 85
overview 83
precipitation 85
solution 85
suspension 85
Characterizing
approach 19
components 10, 12, 27
Chlorinated polyethylene 265
Chloroprene 199
Class 0 component attributes 34,
45, 335
Class 1 component attributes 34
Class 2 component attributes 34,
45–46, 313, 335
CMC See Critical micelle
concentration
Cocatalysts
poisoning 240
Combination reactions 104, 270
Component attributes
about 20
aggregate polymer 34
available 36–44
calculation methods 47
categories 35
class 0 34, 45
class 0 treatment in unit
operations 335
class 1 34
class 2 34, 45–46, 313
class 2 treatment in unit
operations 335
classes 34
composite 35
copolymer composition 33
degree of branching 33
degree of cross-linking 33
degree of polymerization 23, 33
emulsion polymerization 218
for aggregate polymers 40, 48
for blocks 52
for bulk polymers 47
for catalysts 34, 44, 45
for composite aggregate
polymers 36
for composite live polymers 35
for composite polymers 35
for ionic initiators 33, 45
for live polymers 39, 48
for polymer properties 33
for polymers 35–36, 36–37
for site-based aggregate
polymers 36, 43, 50
for site-based bulk polymers 49
Index 509

for site-based live polymers 36,
42, 49
for site-based polymers 36, 40–
43
for site-based species 44
for streams 52
for structural properties 33
for Ziegler-Natta catalysts 33
initialization 46, 52
initialization scheme 47
ionic polymerization 260
live polymer 34
molecular architecture 33
molecular weight 33
required 44, 47
scale factors 50
segment composition 33
273
sequence length 33
specifying 51–53
specifying conventional 52
specifying conventional
attributes 451
specifying scale factors 53
specifying scaling factors 453
step-growth polymerization 124
structural properties tracked 23
types 35
unit operation model treatment
335–37
user-specified 45
Ziegler-Natta 44
Ziegler-Natta polymerization 244
Component databanks
about 25
for initiators 26
for PC-SAFT 26
for polymers 11, 27
for POLYPCSF 26
for pure components 25
for segments 11, 26
selecting 28
Components
adding reacting 154
catalysts 24
categories 21–25
characterizing 12
conventional 22
databanks 387–429
defining 12
defining types 29
fortran utilities 360
ionic initiators 24
naming 29, 447
oligomers 23
POLYMER databank 387–91,
388–91
polymers 22
pure component databank 387
segment approach 27
SEGMENT databank 392–429
segments 24
site-based 24
specifying 28
specifying catalysts 448–51
specifying oligomers 448–51
specifying polymers 448–51
specifying step-growth 156
Composition 8
Condensation polymerization 81,
126
Condensation reactions 103
Configuring
Aspen Polymers 381–82
Consumption of radicals 61–62
Continuous polymerization 92
Conventional components 22
Conventional species 268
Convergence
for RCSTR 308
improving 51
initialization options (RCSTR)
314
parameter tuning 354
RBatch troubleshooting 331–35
RCSTR troubleshooting 315–17
RPlug troubleshooting 323–27
scaling factors (RBatch) 332
scaling factors (RCSTR) 313
scaling factors (RPlug) 323
solver method (RBatch) 334
solver method (RPlug) 325
step size (RBatch) 334
step size (RPlug) 325
troubleshooting data regression
353–55
510 Index

Conversion
energy balance 311
Copolymer
density 78
Copolymerization 64
free-radical 163–98
ionic 249–63
ionic propagation 256
user input for ionic model 254
user input for Ziegler-Natta
model 236
Ziegler-Natta 225–47
Copolymers 16
Coupling reactions 258
CPE See Chlorinated polyethylene
Critical micelle concentration 201
Cross linking 270
Cross-link formation 184
Cross-linking 33, 35
Crystalline polymers 16
Crystallinity 8
Custom
prop-sets 76
Custom models See User models,
See User models
customer support 3
Cycle time 331
Cyclodepolymerization reactions
104
D
DAMP-FAC 311
Damping factor 311
Data
collection 341
defining regression cases 351
fitting 339–40
interpreting regression results
352
literature search 340, 341
point 345
profile 345
regression 339–40
review 340
sequencing regression cases 352
trend analysis 341, 343
verification 341
Data fitting See also Data
regression
applications 339
data collection 341
data review 340
data verification 341
features 294
literature search 340, 341
model development 340, 343
model refinement 341, 344
parameters 342–43
preliminary fit 340, 342–43
procedure 340–44
Data regression See also Data
fitting
activation energy 356
base-case model 345
choosing parameters 355
convergence problems 353–55
data sets 345
defining cases 345, 351
entering data 345
entering operating conditions
345
flowsheet variables 378–80
fortran blocks 347
interpreting results 352–53
manipulating variables 347
point data 349
procedure 340–44, 345–58,
345–58
profile data 350
Prop-Sets 347
scaling fitted parameters 356
sensitivity studies 355
sequencing cases 352
standard deviation 351
troubleshooting 353–55
tuning 354
Databanks
component 25, 387–429
functional group 11
INITIATOR 26
PC-SAFT 26
polymer 11
POLYMER 27, 387–91
POLYPCSF 26
pure component 25, 387
segment 11
SEGMENT 26, 391–429
selecting 28
Dead polymer 35
Dead polymer chain 169
Dead sites 45
Dead zones 308, 321
Defining
additional simulation options 13
Index 511

components 12
feed streams 13
flowsheet options 12
global simulation options 12
polymerization kinetics 13
property models 13
regression cases 351
UOS model operating conditions
13
Degree of
branching 33, 55
cross-linking 33
polymerization 33, 57
Density
as polymer property 8
function 58–59
of copolymer 78
Depolymerization 269
Design-spec block 377
Desorption 213
Developing
models 12
Direct esterification 90
Displaying
distribution data for reactors 70
distribution data for streams 70
distribution data tables 70
Disproportionation 180
Distillation models
about 301
available 296
RadFrac 301
Distribution
average properties and moments
58–59
calcuations 454
chain length 65
copolymerization 64
displaying data table 70
displaying for reactors 70
displaying for streams 70
functions 56, 58
GPC 67, 68
in process models 58
kinetic reactors 65
method of instantaneous
properties 60–64
moment equation 187
moments 58–59
particle size 216–18
plotting data 70
plug flow reactors 66
polymer 65
procedure 67
specifying calculations 69–71
specifying characteristics 69
streams 67
structural property 55–72
tracking 65
verification 68
Distribution calculations
specifying input language 454
Dupl
about 296–98
attribute handling 336
Duty
in RBatch 327
in RCSTR 305
in RPlug 318
Dyads 35
free-radical rate equation 187
Dynamic models 10, 13
E
EB-LOOP 311
e-bulletins 3
Editing
ionic reactions 261
Elastomers 16
Electrophilic reactions 101
Emulsion polymerization
absorption 213
accessing model 219
activated initiation 211
adding reactions 221
applications 199
aqueous phase 208
assigning rate constants 221
attributes 218
built-in reaction listing 220
chain growth 85
desorption 213
editing reactions 221
homogeneous nucleation 204–6
512 Index

industrial processes 200
kinetics 200–215, 211
kinetics scheme (figure) 204
latex 202
latex reactions 207
micellar nucleation 201–4
model 199–223
model assumptions 215
model features 215–18
monomer partitioning 215–16
nomenclature 208
nucleation time 203
particle growth 201, 206
particle number 203
particle phase 210
particle size distribution 216–18
population balance equation 217
products produced 200
properties calculated 218
radical balance 207–11
rate constant 214
rate of particle formation 206
reactions 204
redox initiation 212
seed process 206
Smith-Ewart theory 211
specifying calculation options
222
specifying gel-effect 222
specifying model 219
specifying particle growth
parameters 223
specifying phase partitioning 222
specifying reacting species 220
stage I (seed) 202
stage II (growth) 202, 206
stage III (finishing) 202
user profiles 218
End group reformation reactions
104
End-use properties
about 73–79
adding a Prop-Set 79
calculating 76, 79
density of copolymer 78
intrinsic viscosity 77
melt index 78
melt index ratio 79
relationship to structure 75
selecting 79
zero-shear viscosity 77
Energy balance conversion 311
Entering
point data 349
profile data 350
standard deviations 351
Equilibrium
for ionic polymerization 258
for Ziegler-Natta polymerization
243
phase 188
reactions with counter-ion 256
reactor models 304
Equilibrium models
RGibbs 304
RYield 304
Esterification
batch process 94
direct 90
operating conditions 93
results 91
secondary 91
Estimating
property parameters 459
Ethylene
process types 227
Ethylene-propylene 226, 229
Exchange reactions 256
F
Features 5, 9–13
Feed streams
defining 13
with polymers 23, 46
Files
startup 382
Fitting
activation energy 356
choosing parameters 355
Flash2
about 298
input variables 347
results variables 347
Flash3
about 298
input variables 347
Flowsheeting options 11
Flowsheets
basic unit operation models 295
calculation procedure 376
Index 513

calculator block 376
design-spec block 377
Dupl block 296–98
Flash2 block 298
Flash3 block 298
FSplit block 299
Heater block 299
incorporating spreadsheets 376
302–4
Mixer block 299
model configuration tools 376–
78
Mult block 299
optimization 377
Pipe block 300
polymer process 293
process studies 376–78
Pump block 300
RadFrac block 301
RBatch block 327–35
RCSTR block 304–17
REquil block 304
RGibbs block 304
RPlug block 317–27
RStoic block 302
RYield block 303
sensitivity study 377
Sep block 301
Sep2 block 301
setting fixed variables 377
steady-state 291–94
variables 378–80
variables for data regression
378–80
Fortran
arguments 445
linking 383
monitors 360
templates 383
utilities 360, 445
Fortran blocks
in data regression 347
to enforce assumptions 347
to manipulate process variables
348
to scale paramters 357
Fortran utilities
component handling 360
stream handling 360
Fractionation models 296
Free-radical iniators
431–33
Free-radical polymerization
accessing model 193
applications 163
beta-scission reactions 183
bifunctonal initiator
decomposition reaction 174,
175
branching 192
bulk 164
bulk polymer chain length
moment equation 187
calculation method 185
catalyzed initiation reaction 173
chain transfer reactions 178
dyads 187
gel effect 170
gel effect 188–89
induced initiation reaction 173
initiation reactions 171
initiator decomposition reaction
172
kinetics 165–83
kinetics nomenclature 166
live polymer chain length
moment equation 186
model 163–98
model assumptions 185–90
modifying the rate expression
170
moment-property relationship
equation 191
parameters 190–93
514 Index

pendent double bond
polymerization 184
phase equilibrium 188
propagation reactions 176
properties calculated 190–93
quasi-steady-state
approximation 188
rate constant 170
reactions 165
solution 164
specifying calculation options
196
specifying gel-effect 196
specifying reactions 195
specifying user profiles 197
structural properties 192
termination reactions 178–79
user profile properties 192
Frequency function 58–59
FSplit
about 299
Functional group databank 11
G
Gas-phase process 227
Gear integrator 323, 332
Gel effect
built-in correlations 189
free-radical 170
89
specifying 196, 222
user specified correlations 189
user subroutine arguments 189
Gel effect subroutine
free-radical 170
Gel permeation chromatography 67
Generation of radicals 61
Glycol recovery 91
GPC 67
H
HDPE See High density
polyethylene
Heat exchangers 307
Heater
about 299
help desk 3
Heterogeneous catalysts 226
High density polyethylene
about 225
processes 227
High impact polypropylene 229
HIPP See High impact
polypropylene
Hold-up
in RCSTR 305
Homogeneous catalysts 226
Homogeneous nucleation
particle formation 201
process 204–6
rate of particle formation 206
Homopolymers 15
I
INCL-COMPS 154
Induced initiation reaction 173
Industrial applications
polymer production steps 291–
93
polymer production steps
(figure) 291
Industrial processes
model uses 375
266
Inhibited sites 231
Inhibition
catalyst sites 45, 240
Initators
for ionic polymerization 254
Initialization
hybrid option 315
integration option 314
options for RCSTR 314
solver option 314
Initiation
activated 211
catalyzed 171
decomposition rate 171
free-radical 172, 174, 175
induced 171
ionic 45, 251
Index 515

reaction for catalyzed 173
reaction for decomposition 172
reaction for induced 173
redox 212
INITIATOR databank
about 26
Initiators
databank 26
ionic 24
Injection ports 322
Input language
attribute scaling factors 453
catalysts 448–51
component attributes 451–53
components 447–51
conventional component
attributes 451
distribution calculations 454
emulsion 477–84
end-use properties 454–56
for Aspen Polymers 447–504
ionic 494–501
oligomers 448–51
physical properties 456–60
polymers 448–51
property data 458
property methods 456
property parameter estimation
459
prop-set 454–56
segment-based reactions 501–5
step-growth 460–67
streams 451
Input variables
Flash2 347
Flash3 347
MultiFrac 347
RadFrac 347
RBatch 346
RCSTR 346
RPlug 347
Installing
Aspen Polymers 382
Instantaneous
number-average 63
properties 58, 60–64, 65
weight chain length 63–64
Interfacial processes 84
Intermolecular reactions 103
Intramolecular reactions 103
Intrinsic viscosity 77
Ionic initiator 24
Ionic initiators
component attributes 33
properties tracked 45
Ionic polymerization
accessing model 260
active species formation 254
aggregation 256
applications 249
association 256
chain initiation 255
chain termination 257
chain transfer 257
comparison to other addition
processes 250
copolymerization steps 254, 256
coupling 258
equilibrium with counter-ion 256
exchange 256
initiator attributes 251
initiator types 254
kinetics scheme 250–58
model 249–63
model assumptions 258–59
nomenclature 253
phase equilibria 258
polymers tracked 251
propagation 255
properties calculated 259–60
rate calculations 258
rate constants 254
reactions 252
516 Index

K
Kinetic models
RBatch 327–35
RCSTR 304–17
RPlug 317–27
Kinetics
data fitting 339–40
431–33
defining polymerization 13
emulsion (input language) 477–
84
emulsion polymerization 200–
215, 211
free-radical (input language)
467–77
83
ionic (input language) 494–501
ionic polymerization 250–58
mechanisms 10
melt polycarbonate 122–24
multi-site 65, 66
nylon reactions 111–22
parameter influence on 342
polyester reactions 105–11
polymerization 81
rate constant parameters 431–
44
reactor models 304–35
270
single-site 65, 66
specifying emulsion 219–23
specifying free-radical 193–97
specifying ionic 260–62
specifying step-growth 51–53
specifying step-growth (input
language) 460–67
specifying Ziegler-Natta 244–47
step-growth polymerization 101–
24
user fortran arguments 445
user models 365–69
user subroutine (example) 366
user subroutines 149
Ziegler-Natta (input language)
484–93
Ziegler-Natta polymerization
230–42
L
Latex
definition 202
number of particles per liter 203
reactions 207
Linear condensation polymers 57
Linear low density polyethylene
about 225
processes 227, 228
Linking
fortran 383
Liquid enthalpy
Liquid process 228
Live
polymer chain 169
polymer chain length moment
equation 186
Live polymer 34, 35
LLDPE See Linear low density
polyethylene
Local work arrays 155, 284
Low density polyethylene 164
Low molecular weight polymer 57
M
Mass balance 311
Mass-balance models
RStoic 302
RYield 303
Material streams 46
MB-LOOP 311
Melt index 8, 78
Melt index ratio 79
Melt polycarbonate
rate constants 123
reaction components 122
reaction kinetics 122–24
step-growth reactions 123
Melt-phase
nylon-6,6 processes 122
polymerization 100
processes 84
Metallocene catalysts 226
Method of instantaneous properties
58, 60–64, 65
Method of moments 58, 185
Methylmethacrylate 199
Micellar nucleation 201–4
MIXED
substream variables 380
Mixer
Index 517

about 299
Mixing
non-ideal in RCSTR 306
non-ideal in RPlug 320
Modeling
applications 89, 163, 199, 225,
249, 265
data fitting 294, 339–40
enforcing assumptions 347
features 294
nylon 96–100
nylon-6,6 116
polycarbonates 100–101
polyesters 90–96
polymer phase change 303
polymer processes 293
steady-state 291–94
tools 294
unit operations 294, 295–338
Models
accessing variables 378–80
analysis tools 376–78
application tools 375–80
base case 345
calculations for user models
360–65
defining 12
developing 340, 343
parameter fitting 342–43
possible uses 375
process studies 376–78
refining 341, 344
structure for user models 359
unit operation 11
user 359–73
USER2 routine 362
Molecular structure
SEGMENT databank 392–429
Molecular weight
as component attribute 33
distribution 8, 58
number-average 78
weight-average 35, 78
Moment equations
bulk polymer 187
general 186
live polymer 186
relationship to properties 191
Moments of chain length
distribution
first 39, 47
Monomers
corresponding segment formulas
127
definition 15
functional groups 129
partitioning 215–16
purification 292
synthesis 292–93, 292
Most-probable distribution 57, 114,
120, 131
Mult
about 299
MultiFrac
input variables 347
Multimodal distributions 56
N
Newton solver 311
Nomenclature
for emulsion model 208
for free-radical model 166
for ionic model 253
for segment-based reaction
model 271
for step-growth model 103
for Ziegler-Natta model 234
POLYMER databank 388–91
SEGMENT databank 391
Nucleation
homogeneous 201, 204–6
micellar 201–4
period 202
time 202
time (equation) 203
Nucleophilic reactions
about 101
nomenclature 103
Number average
chain length distribution 63
degree of polymerization 57
Number-average
Nylon
518 Index

aqueous salt solutions 98
melt-phase polymerization 100
production process 96–100
salt preparation 98
Nylon-6
production process 96
rate constants 113
reaction kinetics 111
user-specified reactions 113
Nylon-6,6
melt-phase polymerization 122
modeling approaches 116
production process 98
rate constants 118, 119
reaction kinetics 115
O
Occupied sites 45
Oligomers
as components 23
definition 15
fractionation 131
segments 24
specifying 30
Optimization 377
Orienticity 35
P
Packed vectors 155, 284
Parameters
data fitting 339–40
decomposition rate 431–33
estimating property 459
fitting 340, 342–43
for free-radical polymerization
190–93
influence of kinetics 342
integer 154, 284
kinetic rate constant 431–44
POLYMER property 387
real 154, 284
scaling 356
SEGMENT property 391
to manipulate process variables
348
tuning for data regression 354
Particle growth
in emulsion polymerization 206
specifying parameters 223
PBT See Polybutylene
terephthalate
PC-SAFT
databank 26
PC-SAFT databank
about 26
PEN See Polyethylene naphthalate
Pendent double bond
polymerization 184
PET See Polyethylene terephthalate
Phase equilibria
Phase equilibrium
Phase partitioning
specifying 222
Physical properties
calculations in user models 364
fitting parameters 342–43
Pipe 300
Plant data fitting 339–40
Plot
distribution data 70
PMMA See Polymethyl
methacrylate
Point data
about 345
entering 349
Polyamides 90
Polybutadiene 249
Polybutene 249
Polybutylene terephthalate 95
Polycarbonates
aliphatic 89
aromatic 89
Polydispersity
index 63
Polyesters
Index 519

side reactions 109
Polyethylene
chlorinated 265
low density 164
Polyethylene naphthalate 95
Polyethylene terephthalate
batch processes 93–95
continuous step-growth
polymerization 90–93
solid-state models 96
Polyisobutylene 249, 265
Polymer chain
bulk 169
dead 169
definition 169
live 169
POLYMER databank
about 11, 27, 387
components 388–91
nomenclature 388–91
Polymerization
addition 81
bulk 85
chain-growth 82, 83
condensation 81
condensation polymerization 126
continuous 92
degree of 33
emulsion 85, 199–223
interfacial 84
ionic 249–63
kinetics 10, 13, 81
manufacturing step 293
melt phase 84
precipitation 85
process overview 6–7
process types 84
reaction types 81
reactions 81
solid-state 84
solution 84, 85
step-growth 82, 83, 89–162
suspension 85
Polymers
acrylic acid 199
addition 57
aggregate 34, 35
aliphatic polycarbonates 89
amorphous 16
aromatic polycarbonates 89
as components 23
average properties and moments
58–59
branched 16
bulk polymer chain length
moment equation 187
butadiene 199
butyl acrylate 199
butyl methacrylate 199
by chemical structure 18
by physical structure 16
by property 18
chain-growth 84
characterizing 19
chlorinated polyethylene 265
chloroprene 199
component attribute sets 35–36
component attributes 33, 35
component characterization 10
crystalline 16
data fitting procedure 340–44
data regression procedure 345–
58
dead 35
definition 6
elastomers 16
emulsion properties calculated
218
end-use properties 73–79
ethylene-propylene 226
free-radical properties calculated
190–93
high density polyethylene 225
high-impact polystyrene 163
ionic properties calculated 259–
60
ladder 16
linear 16
linear condensation 57
linear low density polyethylene
225
live 34, 35
live polymer chain length
moment equation 186
low density polyethylene 164
low molecular weight 57
520 Index

mass 124, 273
method of instantaneous
properties 58, 60, 65
method of moments 58
methylmethacrylate 199
mole fraction 272
monomer purification 292
monomer synthesis 292–93, 292
network 16
nomenclature 388–91
phase change 303
polyamides 90
polybutadiene 249
polybutene 249
polyesters 90
polyisobutylene 249, 265
polymerization step 293
polymethyl methacrylate 164,
265
polyoxides 249
polypropylene 226
polystyrene 163, 164, 249
polyurethanes 90
polyvinyl acetate 163
polyvinyl alcohol 164, 265
polyvinyl chloride 163
processing 6–7
processing step 293
production rate 63
production steps 291–93
properties 19
property distributions 55–72
prop-sets 74
purification 292–93
reacting 266
recovery 9, 293
segment-based properties
calculated 273
segments 24, 391
separation 9, 293
specifying 29
star 16
step-growth 83
structural properties 23
structure 15
structure of 15–19
styrene 199
synthesis 293
tetrafluroethylene 199
thermoplastics 16
thermosets 16
tracking structural properties 33
vinyl chloride 199
vinylacetate 199
Ziegler-Natta properties
calculated 243
Polymethyl methacrylate 164, 265
Polyoxides 249
POLYPCSF
databank 26
POLYPCSF databank
about 26
Polypropylene
about 226
process types 228
Polypropylene terephthalate 95
Polystyrene 163, 164, 249
Polyurethanes 90
Polyvinyl acetate 163
Polyvinyl alcohol 164, 265
Polyvinyl chloride 163
Population balance
equation for emulsion
polymerization 217
equation for free-radical
polymerization 185
Potential sites 44
Power-law reaction model See
Segment-based reaction
model:about
PPT See Polyproylene terephthalate
Precipitation polymerization 85
Pressure
drop 305, 319
in RBatch 328
in RCSTR 305
in RPlug 319
Process modeling
data fitting 294
dynamic 10, 13
features 294
flowsheets for polymer processes
293
issues for polymers 7–9
steady-state 10, 13, 291–94
tools 294
unit operations 294
Processing
polymers 293
Profile data
about 345
data sets 350
entering 350
RBatch 350
Index 521

RPlug 350
Propagation
depolymerization 269
270
sites 231
Properties
average polymer 58–59
branching 23
chain size 55
composition 8
copolymer composition 23, 55
copolymerization 64
crystallinity/density 8
degree of branching 55
density of copolymer 78
end-use 73–79
estimating parameters 459
for polymers 58
intrinsic viscosity 77
melt index 8, 78
melt index ratio 79
method of instantaneous 60
molecular structure 23
molecular weight 23
molecular weight 8
moments of molecular weight
distribution 23
particle size 55
polymer structural 33, 55
prop-set 73
segment composition 23
specifying data 458
viscosity 8
zero-shear viscosity 77
Property distributions
bimodal 56
bivariate 55
most-probable 57
multimodal 56
Schulz-Flory 56
Stockmayer bivariate 58
structural 55–72
types 55
unimodal 56
Property methods
input language 456
Property parameter databanks 11
Property set See also Prop-Sets
Prop-Sets
adding 79
custom 76
defining 74
for data regression 347
for polymers 74
properties 73
uses 73
Propylene
processes 228, 229
Pseudocondensation reactions 103
Pump 300
Pure components
databank 25, 387
Purification
monomer 292
process step 292–93
PVA See Polyvinyl alcohol
Q
QSSA See Quasi-steady-state
approximation
Quasi-steady-state approximation
188
R
RadFrac
about 301
input variables 347
Radiation initiation reaction 173
Radicals
absorption 210
balance 207–11
consumption of 61–62
depletion 208
desorption 210
generation 208
generation of 61
rate of production 208
termination 210
Random scission 104
Rate constant parameters
data-fitting 294
522 Index

Rate constants
assigning to emulsion reactions
221
assigning to ionic reactions 262
assigning to step-growth
reactions 158, 159
assigning to Ziegler-Natta
reactions 246
data fitting 339
emulsion 214
for melt polycarbonate 123
for model generated reactions
135
for nylon-6 113
for nylon-6,6 118, 119
for polyesters 109
for user-specified reactions 139,
288
free-radical 170
ionic 254
kinetic parameters 431–44
segment-based 270
specifying for segment-based
power-law reactions 288
specifying for step-growth user
reactions 159
step-growth 153
user subroutines 144, 279
Ziegler-Natta 236
Rate expression
step-growth 133, 138
RBatch
about 327–35
batch reactors 330
common problems 335
cycle time 331
duty 327
dynamic scaling 332
hybrid scaling options 333
input variables 346
pressure 328
profile data 350
residence time 329
scaling options 332
semi-batch reactors 330
solver method 334
static scaling options 332
step size 334
streams 330
temperature 327
troubleshooting convergence
331–35
volume 329
RCSTR
about 304–17
algorithm 308
calculation loops 309
calculation table 309
common problems 316
component scaling 313
condensed phases 305
convergence 308
duty 305
effective hold-up 305
external heat exchanger 307
horizontal partition 306
hybrid initialization 315
initialization options 314
input variables 346
integration initialization 314
multiphase 305
non-ideal mixing 306
pressure 305
residence time 305
scaling options 313
single-phases 305
solver initialization 314
substream scaling 313
temperature 305
315–17
vertical partition 307
with dead zone 308
Reacting phase
specifying for segment-based
power-law model 286
specifying for step-growth 160
Reacting polymers 266
Reaction models
Aspen Plus 86, 359–65
available 359–65
basic unit operation 295
built-in 85
custom 86
distillation 296, 301
Dupl 296–98
equilibrium 304
Flash2 298
Flash3 298
fractionation 296
FSplit 299
Index 523

generic 86
Heater 299
kinetic 304–35
mass-balance 302–4
Mixer 299
Mult 299
Pipe 300
Pump 300
RadFrac 301
RBatch 327–35
RCSTR 304–17
reactor 296, 302
REquil 304
RGibbs 304
RPlug 317–27
RStoic 302
RYield 303
Sep 301
Sep2 301
treatment of component
attributes 335–37
Reactions
active species 254
adding emulsion 221
adding free-radical 194
adding ionic 261
adding segment-based 287
adding user 159
adding Ziegler-Natta 246
addition 103
aggregation 256
assigning emulsion rate
constants 221
assigning ionic rate constants
262
assigning step-growth rate
constants 158
assigning user rate constants
159
assigning Ziegler-Natta rate
constants 246
association 256
backbone 269
beta-scission 183
bifunctional initiator
decomposition 174, 175
branching (segment-based) 270
branching (Ziegler-Natta) 240
catalyst preactivation 237
catalyst site activation 237
catalyzed initiation 171, 173
chain initiation (free-radical 171
chain initiation (ionic) 255
chain initiation (Ziegler-Natta)
237
chain scission 269
chain termination (free-radical)
178–79
chain termination (ionic) 257
chain transfer (free-radical) 178
chain transfer (ionic) 257
chain transfer (Ziegler-Natta)
239
chain-growth 83
classifying 81
cocatalyst poisoning 240
combination 104, 270
condensation 103
conventional species 268
coupling 258
cross linking 270
cyclodepolymerization 104
editing emulsion 221
editing free-radical 195
editing ionic 261
editing segment-based 287
editing user 159
editing Ziegler-Natta 246
electrophilic 101
end group reformation 104
equilibrium with counter-ion 256
exchange 256
for step-growth polymerization
126
homogeneous nucleation 204
including user 158
induced initiation 171, 173
Inhibition 181
initiator decomposition 171, 172
intermolecular 103
intramolecular 103
latex 207
melt polycarbonate kinetics 122–
24
micellar nucleation 201
524 Index

micellar nucleation (figure) 202
modification See Segment-based
reaction model
nucleophilic 101
nylon-6 kinetics 111
nylon-6,6 kinetics 115
particle growth 206
polyester kinetics 105–11
polymerization 81
propagation (free-radical) 176
propagation (ionic) 255
propagation (segment-based)
270
propagation (Ziegler-Natta) 238
pseudocondensation 103
radiation initiation 173
radical balance 207
rearrangement 104
reverse condensation 103
ring addition 104
ring closing 104
ring opening 104
side group 269
site deactivation 239
site inhibition 240
specifying segment-based 285–
89
specifying user rate constants
159
spontaneous initiation 173
step-growth 83
step-growth functional groups
128
step-growth rate constants 157–
58
supplied by emulsion model 215–
18
supplied by free-radical model
185–90
supplied by ionic model 258
supplied by segment-based
model 273
supplied by step-growth model
133–37
supplied by Ziegler-Natta model
243
terminal double bond 240
termination (free-radical) 178–
79
termination (ionic) 257
thermal initiation 173
types affecting catalyst states
230
user-specified step-growth 138–
40
viewing emulsion 220
viewing free-radical 194
viewing ionic 261
viewing segment-based 287
viewing step-growth 157
viewing Ziegler-Natta 245
Reactor models
about 302
available 296
data sets 350
equilibrium 304
input variables 346
kinetic 304–35
mass-balance 302–4
Reactors
condensed phase RCSTR 305
convergence problems for
RBatch 331–35
convergence problems for RCSTR
315–17
convergence problems for RPlug
323–27
displaying distribution data 70
distribution 65
horizontal partition 306
multiphase RCSTR 305
multiphase RPlug 320
RCSTR algorithm 308
single-phase RCSTR 305
vertical partition 307
with dead zones 308, 321
with external heat exchanger
307
with injection ports 322
Rearrangement reactions 104
Recovery/separation 9, 293
Redox initiation 212
Regression See Data regression
Reports
for user models 365
step-growth options 160
REquil
about 304
Residence time
RBatch 329
RCSTR 305
Index 525

RPlug 319
Results variables
Flash2 347
Flash3 347
MultiFrac 347
RadFrac 347
RBatch 346
RCSTR 346
RPlug 347
Reverse condensation reactions
103
Rgibbs
about 304
RGibbs
Ring addition reactions 104
Ring closing reactions 104
Ring opening reactions 104
Routines
USER2 362
RPlug
about 317–27
common problems 326
duty 318
dynamic scaling 323
hybrid scaling 325
input variables 347
multiphase 320
non-ideal mixing 320
pressure 319
profile data 350
residence time 319
scaling options 323
solver method 325
static scaling options 323
step size 325
temperature 318
323–27
with dead zone 321
with injection ports 322
Rstoic
about 302
RStoic
Ryield
about 303
RYield
S
Salt
aqueous solutions 98
preparation 98
Scale factors
about 50
specifying 53
Scaling
factors 453
Scaling factors
component (RCSTR) 313
dynamic (RBatch) 332
dynamic (RPlug) 323
hybrid (RBatch) 333
hybrid (RPlug) 325
RBatch 332
RCSTR 313
RPlug 323
static (RBatch) 332
static (RPlug) 323
substream (RCSTR) 313
Schulz-Flory distribution 56
Scission 104, 269
Secondary esterification 91
Seed process 206
Segment approach 27
SEGMENT databank
about 11, 26, 391
components 392–429
nomenclature 391
Segment flow 35
Segment fraction 35
Segment-based model
including user rate constant
subroutine 289
Segment-based power-law model
specifying reacting phase 286
user subroutines 274–84
Segment-based reaction model
about 265–90
accessing 285
adding reaction schemes 287
applications 265
526 Index

assumptions 272
backbone modifications 269
branch formation 270
chain scission 269
combination 270
conventional species 268
cross linking 270
features 272
including user basis subroutine
289
kinetics 270
mole fraction conversion 272
nomenclature 271
propagation 270
rate constants 270
reaction categories 267–72
reactions allowed 267–72
side group modifications 269
specifying pre-exponential units
288
specifying rate constants 288
specifying reaction settings 285
Segments
composition 15, 33
copolymers 16
definition 24
homopolymers 15
methodology in Aspen Polymers
27
mole fraction 272
molecular structure 392–429
nomenclature 391
sequence 15
specifying 29
structure 15
types 24
Semi-batch reactors 330
Semi-crystalline copolymer density
78
Sensitivity blocks 377
Sep
about 301
Sep2
about 301
Separation/recovery 9, 293
Side group modifications 269
Simulations
dynamic 10
templates 382
Site activation 237
Site deactivation 239
Site inhibition 240
Site-based components
about 24
attributes 44
specifying 30
Slurry process 227, 228
Smith-Ewart theory 211
Solid-state models 96
Solid-state processes 84
Solution polymerization 85, 164
Solution process 227
Solution processes 84
Solver methods
RBatch 334
RPlug 325
Specifying
additional simulation options 13
Aspen Polymers options 381–82
attribute scaling factors (input
language) 453
catalysts 448–51
component attributes 51–53
component attributes (input
language) 451–53
component attributes in blocks
52
component attributes in streams
52
component names 447
components 12, 28
components (input language)
447–51
conventional component
attributes 52, 451
data fit 340–44
data regression 345–58
databanks 28
distribution calculations 69–71
distribution calculations (input
language) 454
distribution characteristics 69
emulsion calculation options 222
emulsion kinetics 219–23
emulsion kinetics (input
language) 477–84
Index 527

emulsion model 219
emulsion rate constants 221
emulsion reacting species 220
end-use properties 79
end-use properties (input
language) 454–56
feed streams 13
fixed process variables 377
flowsheet options 12
free-radical calculation options
196
free-radical kinetics 193–97
free-radical kinetics (input
language) 467–77
free-radical model 193
free-radical reacting species 194
gel-effect 196, 222
global simulation options 12
ionic kinetics 260–62
ionic kinetics (input language)
494–501
ionic model 260
ionic rate constants 262
ionic reacting species 260
oligomers 30, 448–51
particle growth parameters 223
phase partitioning 222
physical properties (input
language) 456–60
point data 349
polymerization kinetics 13
polymers 29, 448–51
pre-exponential units 160, 288
profile data 350
property data 458
property models 13
reacting phase 286
regression cases 351
scale factors 53
285
segment-based reaction rate
constants 288
segment-based reaction scheme
287
segment-based reaction settings
285
segment-based reactions 285–89
segment-based reactions (input
language) 501–5
segments 29
site-based components 30
step-growth components 156
step-growth kinetics 51–53
step-growth kinetics (input
language) 460–67
step-growth model 156
step-growth rate constants 157–
58, 158, 159
step-growth reacting phase 160
step-growth report options 160
stream attributes 451
UOS model operating conditions
13
user profiles 197
Ziegler-Natta kinetics 244–47
Ziegler-Natta kinetics (input
language) 484–93
Ziegler-Natta model 244
Ziegler-Natta rate constants 246
Ziegler-Natta reacting species
245
Spontaneous initiation reaction 173
Spreadsheets
incorporating in flowsheets 376
SSplit
Standard deviations 351
Starting
Startup files 382
Steady-state models
data fitting 294
features 294
flowsheeting 291–94
tools 294
unit operation 295–338
unit operations 294
Step-growth polymerization
accessing model 155
adding user reactions 159
addition processes 266
applications 89
Aspen PolyQuest 96
assigning rate constants 135,
139, 158, 159
batch PET 93–95
528 Index

commercial polymers 83
comparison to chain-growth 82
continuous PET 90–93
editing user reactions 159
electrophilic reactions 101
functional groups 128, 129
including user basis subroutine
161
including user kinetic subroutine
161
including user rate constant
subroutine 161
including user reactions 158
interfacial 84
kinetics 101–24
melt phase 84
melt polycarbonate reaction
kinetics 122–24
model 89–162
model predictions 124
model structure 127–55
model-generated reactions 133–
37
nomenclature 103
nucleophilic reactions 101
nylon 96–100
nylon-6 reaction kinetics 111
nylon-6,6 reaction kinetics 115
oligomer fractionation 131
overview 83
PBT 95
PEN 95
polycarbonates 100–101
polyester reaction kinetics 105–
11
polyesters 90–96
PPT 95
rate constants 122, 133, 153
rate constants example 153
rate expression 133, 138
reacting groups 127
reacting species 127, 130
reaction mechanism 126
reaction stoichiometry 132
reactions 104
solid-state 84
solid-state models 96
solution 84
specifying components 156
specifying pre-exponential units
160
specifying rate constants 157–
58, 159
specifying reacting phase 160
specifying report options 160
specifying subroutines 161
user reactions 138
user subroutines 140–55
Stockmayer bivariate distribution
58
Stoichiometry
step-growth 132
Streams
continuous batch charge 330
defining feed 13
displaying distribution data 70
distributions 67
initializing attributes 451
manipulating 295
MIXED variables 380
processing in user models 361
RBatch 330
time-averaged continuous
reactor product 331
time-averaged continuous vent
product 331
time-varying continuous feed
330
Structure
of components 22
of monomers 15
of oligomers 15, 23
of polymers 15–19, 19, 23
of segments 15, 24
property–end-use relationship 75
Styrene 199
Subroutines
fortran arguments 445
including user basis 161, 289
including user kinetic 161
including user rate constant 161,
289
local work arrays 155, 284
updating component list 154
user 140–55, 274–84
user basis 140, 272, 275
user forms 156
user gel effect 189
Index 529

user kinetic (example) 366
user kinetics 149
user property (example) 371
user rate constant 144, 279
support, technical 3
Suspension polymerization 85
Synthesis
monomer 292
polymer 293
T
tacticity 35
TDB See Terminal double bond
technical support 3
Temperature
in RBatch 327
in RCSTR 305
in RPlug 318
Templates
custom 382
fortran 383
simulation 382
Terminal double bond reactions
240
terminal double bonds 35
Terminal models
free-radical 169
Ziegler-Natta 236
Terminal monomer loss 104
Termination
between chain radicals 181
bimolecular 181
by combination 180
disproportionation 180
79
inhibition 181
Tetrafluroethylene 199
Thermal initiation reaction 173
Thermoplastics 16
Thermosets 16
Tips
configuration 382
data regression 353–55
Transesterification 92
Trommsdorff effect 188
Troubleshooting
convergence (RBatch) 331–35
convergence (RCSTR) 315–17
convergence (RPlug) 323–27
data regression convergence
353–55
diagnostic messages 365
RBatch common problems 335
RCSTR common problems 316
RPlug common problems 326
simulation engine 385
user interface 383
U
Unimodal distributions 56
Unit operation models 11
Unit operations
Aspen Plus models 359–65
available models 359–65
basic models 295
calculations 364
diagnostics 365
Dupl 296–98
features 294
Flash2 298
Flash3 298
FSplit 299
Heater 299
input variables 346
302–4
Mixer 299
Mult 299
Pipe 300
property calculations 364
Pump 300
RadFrac 301
RBatch 327–35
RCSTR 304–17
reports 365
REquil 304
RGibbs 304
RPlug 317–27
RStoic 302
RYield 303
530 Index

Sep 301
Sep2 301
steady-state models 295–338
stream processing 361
treatment of component
attributes 335–37
user model calculations 360–65
user model structure 359
USER 359, 365
User attributes
User fortran
arguments 445
linking 383
templates 383
User models
about 359–73
calculations 360–65
component list 154
diagnostics calculations 365
integer parameters 154, 284
kinetic 365–69
packed vectors 155, 284
physical property 370–73
property calculations 364
real parameters 154, 284
reports 365
stream processing 361
structure 359
unit operation 359–65
unit operation calculations 364
USER block 359
USER2 block 359
User profiles
for emulsion polymerization 218
specifying 197
User prop-sets 76
User reactions
adding step-growth 159
assigning rate constants for
step-growth 159
editing step-growth 159
for polyesters 110
nylon-6 113
nylon-6,6 119
specifying rate constants for
step-growth 159
specifying step-growth 158
40
User routines
fortran linking 383
User subroutines
segment-based power-law model
274–84
55
USER2
about 359
model routine 362
V
Vacant sites 44, 231
Variables
accessing flowsheet 378–80
indirect manipulation 347
input 346, 349, 350
results 346, 349, 350
Vectors
packed 155, 284
Viewing
flowsheet variables 378–80
ionic reactions 261
Vinyl chloride 199
Vinylacetate 199
Viscosity
as polymer property 8
intrinsic 77
zero-shear 77
Volume
in RBatch 329
W
web site, technical support 3
Weight average
chain length 63
Z
Z-average
Z-average degree of
polymerization 35
Zero-shear viscosity 77
Ziegler-Natta
Index 531

Ziegler-Natta catalysts
about 24
attributes 44
dead sites 45
inhibited sites 45
occupied sites 45
potential sites 44
specifying 24
vacant sites 44
Ziegler-Natta polymerization
accessing model 244
applications 225
catalyst preactivation 237
catalyst reactions 230
catalyst site activation 237
catalyst states 230
catalyst types 226
chain initiation 237
chain transfer to small molecules
239
cocatalyst poisoning 240
copolymerization steps 236
ethylene processes 227
gas-phase process 227, 228
kinetics scheme 230–42
liquid process 228
model 225–47
model assumptions 243
model features 243
nomenclature 234
polyethylene processes 227
polypropylene process types 228
propagation 238
propylene processes 228, 229
rate constants 236
rate expressions 236
reactions 232
site deactivation 239
site inhibition 240
site types 231
slurry process 227, 228
solution process 227
steps 235
terminal double bond 240
532 Index

Aspen polymersunitopsv8 2-usr

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