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Constitutive Relations

Constitutive Relations. What are constitutive relations?. Relate conserved extensive quantities to intensive variables Help define physico-chemical quantities (e.g. enthalpies, densities, viscosities ,…) Define transfer rates (mass, energy, …) Other relations to “constitute” the model.

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Constitutive Relations

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  1. Constitutive Relations

  2. What are constitutive relations? • Relate conserved extensive quantities to intensive variables • Help define physico-chemical quantities (e.g. enthalpies, densities, viscosities ,…) • Define transfer rates (mass, energy, …) • Other relations to “constitute” the model

  3. How do constitutive relations arise ? • Related to the terms in the conservation equations for mass, energy and momentum • Convective flow terms (process streams) • Molecular flow streams (fluxes) • Internal processes • Defining intensive variables in terms of extensive quantities and other physico-chemical properties • Constraints on the system (control relations)

  4. Balance volumes, flows and system processes

  5. CSTR Example A  B Constant V

  6. Transfer relations Reaction rates Constitutive Property definitions Equations Balance volume relations Equipment and control constraints Classes of Relations

  7. 1. Transfer Relations • General form • Particular forms • mass transfer • heat transfer

  8. CSTR Example - Qloss Qloss = UA(T-Tamb) A  B Qloss

  9. 2. Reaction rates • Reaction rate (batch reactor only) • General reaction expression

  10. CSTR Example A  B

  11. 3. Thermodynamic relations • Property relations (density, viscosity, …) • Equilibrium relations • Raoult’s law • Relative volatility, K-value • Activity coefficient

  12. CSTR Example A  B

  13. Thermodynamic properties • Enthalpy • linear • nonlinear

  14. CSTR Example A  B

  15. Thermodynamic properties • Equations of state • ideal gas • cubic EoS • Soave Redlich Kwong • Peng Robinson • NRTL

  16. 4. Balance volume relations • Relations between phases VG VL

  17. 5. Control systems

  18. 5a. Sensors • Sensors

  19. 5b. Transmitters • Transmitters (4-20mA, 20-100kPa)

  20. 5c. Controllers • Traditional (P, PI, PID)

  21. 5d. Actuators

  22. 5e. Valves • Static valves • Control valves • characteristics

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