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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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