Chapter 12 Gas-Liquid Equilibrium 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 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 A A B B A B

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

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

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 z = fix ed A 1 T = T CP a M B P B C Pressure P D T x z y 1 a Temperature 1 1 1 z1=overall mole fraction of [1], y1=vapor mole fraction of [1], x1=liquid mole fraction of [1]

Quantitative Phase Equilibrium Exercise

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

Bubble Point from Raoult's law zi=xi

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

Dew Point from Raoult's law zi=yi

Flash Calculations In this type of calculations the objective is to: find fraction 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

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

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

Example in our web site excel file VLE_310