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PETE 310 Lectures # 25 -26

PETE 310 Lectures # 25 -26. Chapter 12 Gas-Liquid Equilibrium. Gas-Liquid Equilibrium Ideal Behavior. Applications to low pressures Simplifications the gas phase behaves as an Ideal Gas the liquid phase exhibits Ideal Solution Behavior. Ideal Behavior.

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PETE 310 Lectures # 25 -26

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  1. PETE 310Lectures # 25 -26 Chapter 12 Gas-Liquid Equilibrium

  2. Gas-Liquid Equilibrium Ideal Behavior Applications to low pressures Simplifications • the gas phase behaves as anIdeal Gas • the liquid phase exhibitsIdeal Solution Behavior

  3. Ideal Behavior • The equilibrium criteria between 2 phases a and b is,

  4. Equilibrium Conditions • The last criteria implies “tendency of a component to be in phase a or b is balanced” – “net mass transfer across phases is zero”

  5. Ideal Behavior Model • Gas phase behaves as an ideal gas (IG), and liquid phase behaves as an ideal solution (IS). • These assumptions imply that • IG: molecular interactions are zero, molecules have no volume. • IS: forces of attraction/repulsion between molecules are the same regardless of molecular species. Volumes are additive (Amagat’s Law).

  6. Forces between molecular species B B A A A B

  7. Statement of Equilibrium IG/IS Raoult’s law 1 2 3 P T

  8. CP1 Ta Liquid P1v P1v Bubble Curve Pressure Flash CP2 Dew Curve P2v Vapor P2v 1 Ta 0 Temperature x1, y1 Types of VLE Calculations

  9. Recall Molar Compositions • By convention liquid compositions (mole fractions) are indicated with an x and gas compositions with a y.

  10. Mathematical Relationships with In general

  11. Depletion Path Isothermal Reservoir Depletion Process for a Reservoir Oil with 2 Components A z = fix ed 1 T = T CP a B M P B C Pressure P D y 1 T 0 x z 1 a 1 1 Temperature z1=overall mole fraction of [1], y1=vapor mole fraction of [1], x1=liquid mole fraction of [1]

  12. Quantitative Phase Equilibrium Exercise

  13. Bubble Point Evaluation (Ideal Behavior Model) • The bubble point pressure at a given T is

  14. Bubble Point from Raoult's law zi=xi

  15. Bubble Point Evaluation • Under Raoult’s law, the bubble point has a linear dependence with the vapor pressures of the pure components. • Once the bubble point pressure is found, the equilibrium vapor compositions are found from Raoult’s law.

  16. Dew Point Calculation • At the dew point the overall fluid composition coincides with the gas composition. That is.

  17. Dew Point Calculation (Ideal Behavior Model) • Find DP pressure and equilibrium liquid compositions

  18. Dew Point from Raoult's law zi=yi

  19. Flash Calculations • In this type of calculations the objective is to: findfraction of vapor vaporized (fv) and equilibrium gas and liquid compositions given the overall mixture composition, P and T.

  20. Flash Calculations (Ideal Behavior Calculations) • Start with the equilibrium equation • Material balance

  21. Flash Calculations • Now replace either liquid or gas compositions using equilibrium equation Here replaced xi

  22. Flash Calculations • Rearrange and sum over all yi

  23. yi(T1,P2) P1 > P2 zi(T1,P1) T1,P2 xi(T1,P2) Separation process

  24. Flash Calculations • Objective function (flash function) is This is 1/ki – ideal equilibrium ratio

  25. Flash Calculations • There are several equivalent expressions for the flash function (a) (b) (c)

  26. Flash Calculations • Once fv is found the equilibrium gas and liquid compositions are evaluated from and

  27. Vapor Pressure Models (Antoine Equation) 1. Constants depend upon the component – Different Units

  28. Example in our web site excel file VLE_310

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