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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. Classes of Relations

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

  7. 2. Reaction rates • Reaction rate • General reaction expression

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

  9. Thermodynamic properties • Enthalpy • linear • nonlinear

  10. Thermodynamic properties • Equations of state • ideal gas • cubic EoS • SRK • Peng Robinson • NRTL

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

  12. 5. Equipment and Control • Sensors

  13. 6. Control Elements • Transmitters (4-20mA, 20-100kPa)

  14. Controllers • Traditional (P, PI, PID)

  15. Actuators on valves

  16. Valves • Static valves • Control valves • characteristics

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