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**Chapter 12 Gas-Liquid Equilibrium**

PETE 310 Lectures # Chapter 12 Gas-Liquid Equilibrium

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**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

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

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**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”

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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).

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**Forces between molecular species**

A A B B A B

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**Statement of Equilibrium**

IG/IS Raoult’s law 1 2 P 3 T

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**Types of VLE Calculations**

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

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**Recall Molar Compositions**

By convention liquid compositions (mole fractions) are indicated with an x and gas compositions with a y.

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**Mathematical Relationships**

with In general

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**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]

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**Quantitative Phase Equilibrium Exercise**

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**Bubble Point Evaluation (Ideal Behavior Model)**

The bubble point pressure at a given T is

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**Bubble Point from Raoult's law**

zi=xi

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**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.

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

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**Dew Point Calculation (Ideal Behavior Model)**

Find DP pressure and equilibrium liquid compositions

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**Dew Point from Raoult's law**

zi=yi

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**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.

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**Flash Calculations (Ideal Behavior Calculations)**

Start with the equilibrium equation Material balance

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

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Flash Calculations Rearrange and sum over all yi

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

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**Flash Calculations Objective function (flash function) is**

This is 1/ki – ideal equilibrium ratio

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

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

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**Vapor Pressure Models (Antoine Equation)**

1. Constants depend upon the component – Different Units

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**Example in our web site excel file VLE_310**

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