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Constitutive Relations

Constitutive relations are essential in linking extensive quantities to intensive variables in physical models. They play a crucial role in defining key physico-chemical properties such as enthalpies, densities, and viscosities. These relations also establish transfer rates for mass and energy while enabling the formulation of conservation equations for mass, energy, and momentum. Additionally, they cover various types of relations, including transfer relations, reaction rates, and thermodynamic properties, alongside interaction with control systems in engineering applications.

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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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