process modeling

1. Process Systems Engineering (PSE)
Process Systems Engineering (PSE)
Ph.D. Xiang Zhang 1
Lectures (E-learning enrollment key: pse2223xz):
Ph.D. Xiang Zhang
Team leader at the Department for Process Systems Engineering
Max Planck Institute for Dynamics of Complex Technical Systems
Sandtorstrasse 1, 39106 Magdeburg, Germany
Phone: +49 391 6110 390; Office: S3.07
zhangx@mpi-magdeburg.mpg.de
Tutorials (Friday 5:00-7:00 PM in Building 22A, Lecture hall 2):
Andrea Maggi, maggi@mpi-magdeburg.mpg.de (PhD Student)
Edgar Medina, sanchez@mpi-magdeburg.mpg.de (PhD Student)
Severo Balasbas, sbalasbasiii@mpi-Magdeburg.mpg.de (PhD student)
Examination form: Written Exam
08.02.2023 15-17 Messe1 (further notice if changed)

2. Process Systems Engineering (PSE)
Lecture 1
Introduction to Process Modeling
2
Ph.D. Xiang Zhang

3. Process Systems Engineering (PSE)
Course Description
3
 Process or chemical engineering is all about manufacturing!
 To manage manufacturing systems and enable efficient process design, the
behaviour of systems is usually described by mathematical models.
 This course will provide a systematic approach to the mathematical development
of process models and highlight how to analyse and solve the models.
 Main Contents
 Steady-state process modeling & Solution methods
 Dynamic lumped-parameter system (LPS) modeling & Solution methods
 Dynamic distributed-parameter system (DPS) modeling & Solution methods
Ph.D. Xiang Zhang

4. Process Systems Engineering (PSE) 4
Process simulation (mass
& energy balance)
Sugar drying and control
Example of waste
water treatment facility
Safety and risk assessment
Roles of Process Modeling
Ph.D. Xiang Zhang
Not easy to directly work
with the big processes and
plants
Use mathematical models
to describe how processes
work (i.e., simulate real
processes)
The beauty of PSE

5. Process Systems Engineering (PSE) 5
Models & Equations
Distillation
Adsorption Supply Chain
Ph.D. Xiang Zhang

6. Process Systems Engineering (PSE)
Goal of modeling: to mimic the real system
6
Data
Ph.D. Xiang Zhang
Are the models correct / accurate?

7. Process Systems Engineering (PSE)
Main Steps of Modeling
7
For a given system, generate (create) the
mathematical model; analyze the model; solve the
model; create a model object & finally use
Main steps of (process) modelling
(1) Derive model equations representing the system;
(2) Analyze the model equations;
(3) Develop solution strategies for solving model equations;
(4) Solve and apply the developed model, e.g., for optimizing the system’s
performance; for controlling the system’s dynamic behavior
General models: mathematical representation of a system
Process engineering models: mathematical representation of a process system
Ph.D. Xiang Zhang

8. Process Systems Engineering (PSE) 8
The Process System
 Inputs, u
 Outputs, y
 States, x
 Parameters, p
System (S)
u y
x
y = S[u, x, p, t] (dynamic)
y = S[u, x, p] (steady-state)
A process system can be simply a process unit (e.g., reactor, distillation).
It can also be a chemical plant represented by a process flowsheet.
p
Ph.D. Xiang Zhang

9. Process Systems Engineering (PSE)
Tasks for Modeling
Ph.D. Xiang Zhang
and Optimization
Example one: give input I and parameter p,
once state x is fixed, output O can be calculated

10. Process Systems Engineering (PSE)
A Typical Process System: Distillation
Balance Equations
Constitutive Equations
Constraint Equations
Define Boundary Describe System Develop Building Blocks
Mathematical
model
Decomposition
Aggregation
Buildingblock
10
Ph.D. Xiang Zhang

11. Process Systems Engineering (PSE) 11
Problem
definition
Identify
controlling
factors
Analyze
problem data
Construct the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
7-Step Modeling Procedure
Ph.D. Xiang Zhang

12. Process Systems Engineering (PSE)
Modeling in Chemical Engineering
Ph.D. Xiang Zhang

13. Process Systems Engineering (PSE)
Problem Definition (Step 1)
 Clear description of system
 establish underlying assumptions
 Statements of modeling
 intended goal or use of the model
 acceptable error of the model predictions
 anticipated inputs and disturbances
 type of spatial distribution (lumped or distributed model)
 time characteristics (static or dynamic model)
13
Ph.D. Xiang Zhang

14. Process Systems Engineering (PSE)
CSTR Example (Step 1)
 Goal
• effect of inlet change
• study dynamic behavior
• +/-10% accuracy
 CSTR description
• process/system details
• lumped ? - assumed
• dynamic? - yes
in-flow
out-flow
f, CAi
f, CA
, CB
14
Continuous Stirred Tank Reactor (CSTR)
Ph.D. Xiang Zhang

15. Process Systems Engineering (PSE) 15
Problem
definition
Identify
controlling
factors
Analyze
problem data
Construct the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
Modeling Procedure
Ph.D. Xiang Zhang

16. Process Systems Engineering (PSE)
Controlling Factors (Step 2)
 Chemical reaction
 Mass transfer (diffusion, evaporation, precipitation, etc.)
 Heat transfer (conductive, convective, radiative)
 Fluid flow
 Mixing
 …
16
Controlling factors or mechanisms: physico-chemical processes and
phenomena taking place in the system relevant to the modeling goal
Solid Background in Chemical Engineering
Ph.D. Xiang Zhang

17. Process Systems Engineering (PSE)
CSTR Example (Step 2)
 Irreversible reaction A B
 Perfect mixing
 No heat loss or supplied
(adiabatic)
in-flow
out-flow
f, CAi
f, CA
, CB
17
Ph.D. Xiang Zhang

18. Process Systems Engineering (PSE) 18
Problem
definition
Identify
controlling
factors
Analyze
problem data
Construct the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
Modeling Procedure
Ph.D. Xiang Zhang

19. Process Systems Engineering (PSE)
 Physico-chemical data
Heat capacities, viscosity, …
 Kinetic parameters:
k0, E, ΔHR, …
 Equipment data
volume V, …
 Plant (process) data
in-flow
out-flow
f, CAi
f, CA
, CB
Problem Data (Step 3) – CSTR example
19
Ph.D. Xiang Zhang

20. Process Systems Engineering (PSE) 20
Problem
definition
Identify
controlling
factors
Analyze
problem data
Build the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
Modeling Procedure
Ph.D. Xiang Zhang

21. Process Systems Engineering (PSE)
Model Development (Step 4)
 Assumptions
 Boundaries and balance volumes (How big the system is?)
 Conservation equations
 mass balance
 energy balance
 momentum balance
 Constitutive equations
 reaction rates, transfer rates
 property relations, balance volume relations
 equipment & control constraints
 Initial and boundary conditions
 Classification of variables
 known parameters
 user-defined variables
 unknown variables (degrees of freedom, DOF) and DOF-
dependent variables
21
Ph.D. Xiang Zhang

22. Process Systems Engineering (PSE)
Model Development: Balance Equations
Input Output
Accumulation
Generation
Control shell (control volume)
Infinitesimal control shell (control volume)
Normal to the
control shell
Normal to the
control shell
   
n
consumptio
generation
system
of
out
flow
system
into
flow
quantity
of
change
net






















 No quantity distribution inside the control shell
 Net change of quantity (also known as accumulation)
 Accumulation can be applied for mass, energy (heat), and momentum
 When accumulation is zero, steady-state; Otherwise, dynamic process
22
Ph.D. Xiang Zhang

23. Process Systems Engineering (PSE)
Model Development and Analysis (Step 4)
– CSTR Example
23
illustrated on the blackboard …
in-flow
out-flow
f, CAi
f, CA
, CB
Ph.D. Xiang Zhang

24. Process Systems Engineering (PSE) 24
Problem
definition
Identify
controlling
factors
Analyze
problem data
Construct the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
Modeling Procedure
Ph.D. Xiang Zhang

25. Process Systems Engineering (PSE)
The selection of model solution methods fully
depends on the mathematical forms of the model
 Algebraic equations (AE)
 Ordinary differential equations (ODE)
 Partial differential equations (PDE)
 Differential-algebraic equations (DAE)
Solve the Model (Step 5)
25
Ph.D. Xiang Zhang

26. Process Systems Engineering (PSE) 26
• Mechanistic vs. Empirical
• Stochastic vs. Deterministic
• Linear vs. Nonlinear
• Steady-state vs. Dynamic
• Lumped vs. Distributed
• Continuous vs. Discrete
Model Classification
Ph.D. Xiang Zhang

27. Process Systems Engineering (PSE) 27
Model Type & Mathematical Form
Steady state Dynamic
Lumped AE ODE
Distributed Elliptic PDE Parabolic PDE
Ph.D. Xiang Zhang

28. Process Systems Engineering (PSE) 28
Problem
definition
Identify
controlling
factors
Analyze
problem data
Construct the
model
Solve the
model
Verify the
model solution
Validate the
Model
1
2
4 7
5
3 6
Modeling Procedure
Ph.D. Xiang Zhang

29. Process Systems Engineering (PSE)
Model Verification and Validation
• Generate plant data
• Analyze plant data for quality
• Independent hypothesis (assumption) testing
• Parameter or model structure re-estimation
• Revise the model until suitable for purpose
29
Ph.D. Xiang Zhang