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CHEE 222: CHEMICAL PROCESS DYNAMICS AND NUMERICAL METHODS Module-I: Introduction to Process Modeling

Topics to be Covered in this Module. . General Introduction to Chemical ProcessingProcess ModelsBasic approach to process modelingFundamental vs EmpiricalChemical Process SystemsLumped vs distributed parameter systemsSteady-State vs DynamicFundamental ModelsBalance EquationsMass BalanceEnergy BalanceChemical Species BalanceConstitutive RelationshipsTypes of VariablesState variableDesign variable.

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CHEE 222: CHEMICAL PROCESS DYNAMICS AND NUMERICAL METHODS Module-I: Introduction to Process Modeling

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    2. 2

    3. Chemical Process 3

    4. Considerations in Chemical Processing Several questions related to different aspect of chemical processing arise when we deal with chemical processing: Synthesis: What sequence of processes are required (mixer, heater, reactor, separator) ? Design: What type and size of equipment? Operation: What operating conditions will yield desirable product? Control: What process input can be manipulated ? Safety: What If a process unit fails? Environmental: How can we operate the system to minimize pollutants ? 4

    5. Process Model

    6. Model, Process Model & Chemical Process/System Model A mathematical or physical system obeying certain specified conditions, whose behavior is used to understand a physical, biological, or social system to which it is analogous to. “McGraw-Hill Dictionary of Scientific and Technical Terms” Process Model A process model is a set of equations (+ necessary input data to solve the equations) that allows us to predict the behavior of a chemical process system Chemical Process/System: A single or a combination of chemical unit operations that cause physical and/or chemical change in a substance or mixture of substances, e.g. Chemical reactor Heat exchanger Separator (distillation column) 6

    7. Basic Approach to Process Modeling 7

    8. Types of Process Models Fundamental Model These models are based on known physical-chemical relationships Conservation Equations Mass Conservation Energy Conservation Species Balance Constitutive Relationships Ideal gas law Reaction kinetics or rate law Heat transfer rate Empirical Model: These models are usually employed when the processes are too complex or poorly understood Least-square fit of experimental data 8

    9. Classification of Chemical Process Systems

    10. Classification Based on Spatial Homogeneity Lumped Parameter System A system wherein process variables are spatially homogeneous (do not vary in spatial dimension) but may vary with time. Distributed Parameter System A system wherein process variables are spatially heterogeneous (vary with space) and may vary with time. 10

    11. Classification Based on Temporal Variation Steady-State System Chemical processes that operate at steady-state conditions, i.e. the inputs and the outputs of the process(es) or process variables do not change with time. Dynamic System Chemical processes for which inputs and the outputs of the process(es) change with time, i.e. they have a dynamic behavior. e.g. batch reactors for pharmaceutical chemicals Note: Dynamic behavior can also be encountered during start-ups and shut-downs of processes or when certain inputs are changed either deliberately or accidentally. 11

    12. Types of System and Resulting Equations 12

    13. Mathematical Modeling of Chemical Processes: Balance Equations

    14. Process Modeling: General Discussion Mathematical equations constituting process models arise from the fundamental laws of mass, energy, and momentum conservation. In CHEE 222, we will focus primarily on Mass and Energy (M&E) balances For systems undergoing changes in chemical composition, species balance equations must be included in the process model. In CHEE 223, you will learn about momentum balance For reliable outputs from a process model, we must ensure that the model constitutes “correct equations” describing the system; as well, we must be confident that we are “solving the equations correctly”. 14

    15. Differential and Integral Balance Equations Differential Balance Equations Equations are derived by considering what is happening in a system at any instance in time. Each term of the equation is a RATE (rate of input, output etc.) Integral Balance Equation Equations are derived by considering the state of a system at two distinct time. Each term of the equation is an AMOUNT of the balance quantity 15

    16. Differential Balance Equation – General Form 16

    17. Mass Conservation: Material Balance Equation 17

    18. Energy Conservation: Energy Balance Equation 18

    19. Mole Balance Equation 19

    20. Transient Mass Balance Example 20

    21. Transient Energy Balance

    22. Differential Energy Balance Equation 22

    23. Energy Balance Equation (Cont.) Let us examine each term of the energy balance equation. 23

    24. Energy Balance Equation (Cont.) 24

    25. Energy Balance Equation (Cont.) 25

    26. Energy Balance Equation (cont.) For most of the chemical processes, the kinetic and potential energy changes in the system and between the inlet and outlet streams are negligible That is, and 26

    27. Energy Balance Equation (cont.) Substituting equations (9), (10), and (11) in equation (8), we get 27

    28. Energy Balance Equation (cont.) Simplification of eqn (14) below depends on what valid assumptions can made 28

    29. Case1: If msys, P and r are constant

    30. Energy Balance Equation (cont.) Case1: If msys, P and r are constant, we can write The above assumption may hold true for constant pressure liquid-system (r=constant) for which the input mass flow rate is equal to output mass flow rate (msys=constant) Applying eqn (15) in overall energy balance equation (12) 30

    31. Case2: msys varies with time; P and r are constant

    32. Energy Balance Equation (cont.) Case2: If msys is NOT constant but P and r are. Also, if the system is a lumped-parameter system For lumped-parameter system, because of the well-mixed assumption, we can define the properties of the fluid in the system to be equal to that of the outlet fluid stream, therefore 32

    33. Applying eqn (17) in overall energy balance equation (12) From mass balance, we can also write, Substituting eqn (19) in (18), we get Energy Balance Equation (cont.) 33

    34. Expanding eqn (20) Rearranging we get, For liquids, we can further simplify Energy Balance Equation (cont.) 34

    35. Transient Energy Balance Example 35

    36. Constitutive Relationships

    37. Constitutive Relationships 37

    38. Types of Variables State and Design Variables Measurable variable that indicates the state of a system Input Variables A variable that normally must be specified to solve a problem Manipulated variable Parameters Must be known to mathematically solve a problem Often fixed by nature 38

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