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# Lecture 1_Introduction to Process Modeling.pdf

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# Lecture 1_Introduction to Process Modeling.pdf

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### Lecture 1_Introduction to Process Modeling.pdf

1. 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. 2. Process Systems Engineering (PSE) Lecture 1 Introduction to Process Modeling 2 Ph.D. Xiang Zhang
3. 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. 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. 5. Process Systems Engineering (PSE) 5 Models & Equations Distillation Adsorption Supply Chain Ph.D. Xiang Zhang
6. 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. 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. 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. 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. 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. 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. 12. Process Systems Engineering (PSE) Modeling in Chemical Engineering Ph.D. Xiang Zhang
13. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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