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

2. 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

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
A A
B B
A B

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

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

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 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]

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:
find fraction 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. Separation process
zi(T1,P1)
xi(T1,P2)
yi(T1,P2)
P1 > P2
T1,P2

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