The document discusses process modeling and provides an overview of key concepts. It defines what a model is and different types of models including physical, mathematical, conceptual, black box, white box, and grey box models. It explains the purposes of modeling and discusses good modeling practices like parsimony, modesty, accuracy, and testability. The document also covers model development approaches, classification, errors, application areas, and strengths and weaknesses of different modeling techniques.

1. TABLE OF CONTENTS
Process models
Why models?
Classification of models
Model development approaches
Model verification
Error analysis
Model application
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2. WHAT IS MODEL?
 The knowledge and understanding that the scientist has about the world is
often represented in the form of models.
 Models are simplified representation of a complex system/real world
(physical, or mathematical) to simulate but not all characteristics of the
system
 Physical model: is a smaller or larger physical copy of an object. The object
being modelled may be small (an atom) or large (the Solar System).
 Mathematical model: represents the system by set of equations expressing
relationship between a system variables & Parameters
 Conceptual Models: is a representation of a system, made of the
composition of concepts which are used to help people know, understand, or
simulate a subject the model represents
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3. WHY MODEL?
To make quantitative
predictions about system
behaviour
To back up financial or other
decisions
To optimize a new or existing
process
To operate efficiently and
safely an existing process
For illustration / teaching
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4. PREMISES OF MODEL
 Modeling is based on the assumption that any given process can be expressed in a
formal mathematical statement or set of statements
 Models are approximations of how the world works. The simpler the process, the
easier it is to formulate it in simple mathematical terms
 State variables: are a characteristics of a system that may be measures and can
assume different numerical values at different times (Temperature, Pressure,…)
 Parameters: is a quantity characterizing a system. It may or may not remain
constant in time
 Boundary conditions: The system is isolated from its surroundings by the
“boundary,” which can be physical or imaginary
 Initial Conditions: In mathematics and particularly in dynamic systems, an initial
condition, in some contexts called a seed value, is a value of an evolving variable at
some point in time designated as the initial time.
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5. GOOD MODELS
 Parsimony: it should not be more complex than necessary and its parameters should
be derived from the data
 Modesty: it should not pretend too much
 Accuracy: it should not attempt predictions for situations that are more accurate than can be
measured
 Testability: the results should be open to objective testing and the limits of its validity
 Simplification: answer specific questions, and nothing more
 Verification : test of the internal logic of a model. A logical evaluation of the model’s
assumptions. Good models reflect good science.
 Validation: test of the model behavior. Results should correspond to independent
experimental data.
 Transparent: Good documentation removes uncertainty. A model should have nothing to
hide.
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6. PROCESS MODEL MODES AND STATES
Process States
 Dynamic-state: In all processes of interest, the operating conditions (e.g.,
temperature, pressure, composition) inside a process unit will be varying
over time.
 Steady-state: process variables will not be varying with time
Process Modes
 Batch: feedstocks for each processing step (i.e., reaction, distillation) are
charged into the equipment at the start of processing; products are removed
at the end of processing.
 Continues: Involve continuous flows of material from one processing unit to
the next. Usually designed to operate at steady-state; due to external
disturbances, even continuous processes operate dynamically
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7. MODEL CLASSIFICATION: BLACK BOX
 Empirical/experimental
 Process fundamentals are not necessary
 Based on observed input and output variables
 Purely mathematical (as an opposite to a physical model) form where some
parameters (coefficients) are identified based on observed variables.
 These coefficients typically have no physical meaning
 Often polynomials, could be neural networks etc.
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Input Output

8. MODEL CLASSIFICATION: WHITE BOX
Theoretical/Conservation principles.
”transparent”, the model is understandable to a knowledgeable
process engineer
No process or other data required (theoretically)
Usually complex models
In principle excellent extrapolation (scale-up) properties
Can predict new phenomena (in principle)
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Input Output

9. MODEL CLASSIFICATION: GREY BOX
 In practice, purely ”white” or ”black” box models are rare
 Mechanistic first principle building blocks bring reliability in scale-up and
extrapolation, and functional dependencies to the expressions
 A priori knowledge about the model is used as well to determine the structure and
some of the parameter values.
 Microscopic- macroscopic are also another notable model classifications
Microscopic – includes part of process or apparatus
Macroscopic – includes whole process or apparatus
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Input Output

10. 10
Origin
of
Model Theoretical/Conser
vation Principles
White Box
Empirical/Experim
ental
Black Box
Semi-empirical,
integrates both
Grey Box
ORIGIN BASED MODEL CLASSIFICATION

11. ELEMENTS OF MODELLING
1. Balance dependences: Based upon basic nature laws mass,
energy, atom, charge, …
2. Constitutive equations: like Newton, Fourier, Fick's
3. Phase equilibrium equations: important for mass
transfer
4. Physical properties equations: for calculation
parameters as functions of temperature, pressure and
concentrations.
5. Geometrical dependences: involve influence of
apparatus geometry on transfer coefficients convectional
streams.
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12. MODEL DEVELOPMENT APPROACH
Define the purposes/objectives of themodel
Find out type of available models
Specify the theoretical concepts
Numerical Formulation
Model coding
Code validation
Sensitivity analysis
Model testing & Evaluation
ModelApplication
Presentation of results
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13. CONCEPTUAL TYPE OF MODELS
 Generally composed of a number of simplified interconnected conceptual
elements.
 The elements are used to represent the significant or dominant constituent in
any system processes in the light of our conceptual understanding to these
processes.
 Each conceptual elements simulates the effects of one or more of the
constituent process by the use of empirical and assumed functions which are,
hopefully, physical, realistic or at least physically valid.
 Most common categories of conceptual modelling are:
 Block flow diagrams (BFD)
 Process flow diagrams ( PFD)
 Piping and instrumentation diagrams (P&ID)
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14. 14 THE IDEA OF A (MATHEMATICAL) MODEL
1. Reality to mathematics
2. Mathematical solution
3. Interpreting the model outputs
4. Using the results in the real world
Real world
problem
Mathematical
problem
Mathematical
solution
Interpretation
1 2 3
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15. MATHEMATICAL MODELING
 Mathematical models can be classified into various types depending on the
nature of the variables, the mathematical approaches used, and the behavior
of the system.
 1. Deterministic Vs. Probabilistic/Stochastic
 When the variables (in a static system) or their changes (in a dynamic
system) are well defined with certainty, the relationships between the
variables are fixed, and the outcomes are unique, then the model of that
system is said to be deterministic.
 If some unpredictable randomness or probabilities are associated with at least
one of the variables or the outcomes, the model is considered probabilistic.
 2. Continuous Vs. Discrete
 When the variables in a system are continuous functions of time, then the
model for the system is classified as continuous.
 If the changes in the variables occur randomly or periodically, then the
corresponding model is termed discrete.
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16. CONTINUED
 Static Vs. Dynamic
 Inputs and outputs do not vary with passage of time and are average values.
The model describing the system under those conditions is known as static
or steady state.
 The results of a static model are obtained by a single computation of
all of the equations.
 When the system behavior is time-dependent, its model is called dynamic.
 The output of a dynamic model at any time will be dependent on the
output at a
 previous time step and the inputs during the current time step.
 The result of a dynamic model are obtained by repetitive computation of
all equations as time changes
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17. CONTINUED
 Distributed vs. Lumped
 When the variations of the variables in a system are continuous
 Functions of time and space, then the system has to be modeled by a
distributed model.
 For instance, the variation of a property, c, in the three orthogonal
 Directions (x, y, z), can be described by a distributed function C = f (x,y,z).
 If those variations are negligible in those directions within the system
boundary, then c is uniform in all directions and is independent of x, y, and z.
Such a system is referred to as a lumped system
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18. CONTINUED
 Analytical Vs. Numerical
 When all the equations in a model can be solved algebraically to yield a
solution in a closed form, the model can be classified as analytical.
 If that is not possible, and a numerical procedure is required to solve one or
more of the model equations, the model is classified as numerical.
 example of the reactor, if the entire volume of the reactor is assumed to be
completely mixed, a simple analytical model may be developed to model its
steady state condition. However, if such an assumption is unacceptable, and
if the reactor has to be compartmentalized into several layers and segments
for detailed study, a numerical modeling approach has to be followed.
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19. ERROR IN MODELLING
 Model errors in their inherent structure and inthe data Errorsresult in
uncertainty
 Identification of errors and the processes causing the errors aid in verification
 Systematic errors
 Occurs when the sign of the error persists
 Inadequate representation or misrepresentation
 Differences in the spatial and temporal scales
 Random errors
 Shows no tendency to over or underestimate for a no. of successive time
intervals
 Can be identified by checking for the conservation of means and variances
 Random errors will average out in time
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20. CONTINUED
 Input errors
 One of the most significant sources of error
 Input errors; due to required data input in calibration
 Model structure errors
 Incomplete model structure
 Propagation of errors between model components
 Poorly defined initial or boundary conditions
 Parameter errors
 Non-uniqueness of parameters
 Interdependence of parameters
 Poor spatial representation of point measurements
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21. STRENGTH AND WEAKNESS OF MODELLS
 Major advantage of Conceptual type models
 Their operation/application is easily understood by experts
 Useful engineering tools and give reasonable answers to practical problems.
 The development of the conceptual models does not need much real
understanding of the modelled phenomena.
 Major weakness of Conceptual type models
 Physical Interoperation of parameters is rarely possible.
 Attempts improve the models may lead to over-fitting the parameters
 Large errors may occurs if estimating the model is applied to data beyond
that used in if estimating the parameter values.
 Cause/effect assumption may be wrong
All models are wrong, but some are useful
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22. 22
Process Design
Feasibility analysis of novel designs
Technical, economic, environmental assesment
Effects of process parameter changes on performance
Optimization using structural and parametric changes
Analysing process interactions
Waste minimization in design
MODEL APPLICATION AREAS

23. 23
Process Control
Examining regulatory control strategies
Analysing dynamics for setpoint changes or disturbances
Optimal control strategies for batch operations
Optimal control for multi-product operations
Optimal startup and shutdown policies
CONTINUED

24. 24
Trouble-shooting
Identifying likely causes for quality problems
Identifying likely causes for process deviations
Process safety
Detection of hazardous operating regimes
Estimation of accidental release events
Estimation of effects from release scenarios
CONTINUED

25. 25
Operator training
Startup and shutdown for normal operations
Emergency response training
Routine operations training
Environmental impact
Quantifying emission rates for a specific design
Dispersion predictions for air and water releases
Characterizing social and economic impact
Estimating acute accident effects (fire, explosion)
CONTINUED