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This chapter explores gas-liquid equilibrium, focusing on ideal behavior in low-pressure applications. It discusses the conditions under which the gas phase behaves as an ideal gas and the liquid phase shows ideal solution behavior. Key concepts include equilibrium criteria, Raoult’s law, bubble point evaluation, dew point calculations, and flash calculations. Various phase equilibrium exercises are provided to illustrate the theoretical principles and their practical applications in separation processes and vapor-liquid equilibrium calculations.
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PETE 310Lectures # 25 -26 Chapter 12 Gas-Liquid Equilibrium
Gas-Liquid Equilibrium Ideal Behavior Applications to low pressures Simplifications • the gas phase behaves as anIdeal Gas • the liquid phase exhibitsIdeal Solution Behavior
Ideal Behavior • The equilibrium criteria between 2 phases a and b is,
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”
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).
Forces between molecular species B B A A A B
Statement of Equilibrium IG/IS Raoult’s law 1 2 3 P T
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
Recall Molar Compositions • By convention liquid compositions (mole fractions) are indicated with an x and gas compositions with a y.
Mathematical Relationships with In general
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]
Bubble Point Evaluation (Ideal Behavior Model) • The bubble point pressure at a given T is
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.
Dew Point Calculation • At the dew point the overall fluid composition coincides with the gas composition. That is.
Dew Point Calculation (Ideal Behavior Model) • Find DP pressure and equilibrium liquid compositions
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.
Flash Calculations (Ideal Behavior Calculations) • Start with the equilibrium equation • Material balance
Flash Calculations • Now replace either liquid or gas compositions using equilibrium equation Here replaced xi
Flash Calculations • Rearrange and sum over all yi
yi(T1,P2) P1 > P2 zi(T1,P1) T1,P2 xi(T1,P2) Separation process
Flash Calculations • Objective function (flash function) is This is 1/ki – ideal equilibrium ratio
Flash Calculations • There are several equivalent expressions for the flash function (a) (b) (c)
Flash Calculations • Once fv is found the equilibrium gas and liquid compositions are evaluated from and
Vapor Pressure Models (Antoine Equation) 1. Constants depend upon the component – Different Units
