1. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Modelling Lumped Parameter Systems C5A

2. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences General 3D conservation space Governing equation

3. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences General 3D conservation space Governing equation General differential form where  can vary in space and time Governing equation Lumped form where  does not vary in space but varies in time

4. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences The lumped conservation balance General conservation balance Assuming homogeneity in the conserved quantity Lumped conservation balance

5. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Model Characteristics

6. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences The mass balance volume

7. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences A Process Example

8. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Overall mass balance

9. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Component mass balances

10. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Molar Balance Mass balances that involve reactions are most conveniently expressed as molar balances. i.e., where g i is the rate of generation or consumption of species i through reaction. i.e., ~

11. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Tank mass balance z P 1 P 2 P 3 P 0 F 1 F 2 Balance volumes  tank holdup  valves Conservation Constitutive A1: Well mixed in x,y,z directions A2: no mass holdup in valves A3: no physical losses from system A4: no mass losses from evaporation A5: Isothermal operation z x y Assumptions

12. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences The energy balance volume

13. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Energy balance Components of the balance  Convective energy flows  Conductive/radiative flows  Work terms

14. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Energy Balance Terms   Convective flows   Heat flows   Work terms   shaft work   expansion work   flow work

15. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Total energy balance

16. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Reduced energy balances  Neglect P E, K E  PV constant or small  Output specific enthalpies equivalent to bulk phase

17. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Reduced energy balances (cont.)  all enthalpies evaluated at system temperature  explicit appearance of reaction terms and temperature

18. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Tank energy balance Balance volumes tank holdup jacket holdup A5: Fixed mass holdup in jacket A6: well mixed jacket contents A7: negligible KE terms A8: negligible PE terms A9: negligible PV terms A10: jacket temperature is averaged A11: fixed heat capacities Assumptions

19. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Tank energy balances Conservation Constitutive Tank Conservation Constitutive Jacket System

20. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Momentum balance

21. PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Example momentum balance