1. Phase Equilibrium

2. Phase Equilibrium Models
Fugacity (Equation of State) Models
a) Soave Redlick Kwong (SRK)
Activity Coefficient (g) Models
a) Renon (NRTL)
b) UNIQUAC
C) UNIFAC
Idealized Methods
a) Depriester Charts

3. You need data to be accurate
For whatever kind of puzzle you’ve got ----
You just stick the right formula in ----
A solution for every fool ---
The Indigo Girls

4. Condition of Equilibrium

5. Equation of State Approach
Soave-Redlich-Kwong (SRK) Equation of State
Soave, G., “Equilibrium Constants from a Modified Redlich-Kwong
Equation of State,” Chemical Engineering Science, 27, (1972).

6. Soave-Redlich-Kwong (SRK) Equation of State

7. Soave-Redlich-Kwong (SRK) Equation of State

8. SRK Based Fugacity Coefficient

9. SRK Example
Calculate the liquid and vapor phase fugacity coefficients for the following CO2 (1) / methane (2) mixture using the SRK equation of state. Is the given composition at equilibrium ?
T = -112 F P = 500 Psia kij =
y1 = 0.072
y2 = 0.928
x1 = 0.607
x2 = 0.393

10. Activity Coefficient Approach
Binary Margules Equation

11. Activity Coefficient Approach
Binary NRTL (Renon) Equation

12. Activity Coefficient Models
Multi-component NRTL (Renon)
Renon, H., and Prausnitz, J.M. “Local Compositions in Thermodynamic Excess
Functions for Liquid Mixtures,” AIChE J., 14 (1), (1968).

13. Activity Coefficient Models
NRTL (Renon) aij as a function of molecular classes
hydrocarbons, carbon tetrachloride, non-associated liquids,
polar liquids.
hydrocarbons / polar non-associating liquids (hexane – acetone)
hydrocarbons / freons (hexane / perfluro-hexane)
alcohols / hydrocarbons (methanol / butane)
acetonitrile or nitromethane / carbon tetrachloride
water / polar non-associating liquids (water / acetone)
water / self associating liquids (water / pyridine)

14. Activity Coefficient Models
UNIQUAC
Residual (intermolecular forces)
Combinatorial (size / shape)
Abrams, D.S., Prausnitz, J.M., “Statistical Thermodynamics of Liquid Mixtures:
A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible
Systems,” AIChE J., 21 (1), (1975).

15. Sources of Data Experimental Data Literature Databases
Gmehling,J., and U. Onken Vapor-liquid Equilibrium
Data Collection DECHEMA Chem. Data Ser., 1-8
( )

16. Sources of Data
Experimental Data

17. DECHEMA Data

18. Infinite Dilution Activity Coefficient (NRTL)

19. NRTL Example For the 2-propanol (1) / water (2) system at 1 atm the
infinite dilution activity coefficients are: g1 = and g2 =
Determine t12 and t 21 for use in the NRTL equation
Determine the activity coefficient at the azeotrope composition (x1 = )

20. 10 Minute Problem
The Van Laar activity coefficient model (Table 2.9, page 57) is being used to predict the distribution of a binary mixture. Determine the activity coefficient value for a 50/50 molar mixture given the flowing infinite dilution activity coefficient data.

21. UNIFAC UNIQUAC Functional-group Activity Coefficient
A Group Contribution Approach
Fredenslund, A., Jones, R.L., Prausnitz, J.M., “Group Contribution Estimation of Activity
Coefficients in Non-ideal Liquid Mixtures,” AIChE J., 21 (6), (1975).

22. UNIFAC
Parameters from molecular
measurements / estimates

23. UNIFAC Combinatorial Component Residual Component Groups in components
Groups in mixture
Residual Component

24. UNIFAC Example Determine the activity coefficients of acetone (1) and
n-pentane (2) at 307 K and x1=0.047

25. UNIFAC Example Combinatorial Term ( )
CH3 (1A)
CH3 (1A)
CH2 (1B)
C=O (8)
CH2 (1B)
CH3 (1A)
CH2 (1B)
CH3 (1A)
Acetone (1)
Pentane (2)

26. UNIFAC Example Residual Terms ( )
CH3 (1A)
CH3 (1A)
CH2 (1B)
C=O (8)
CH2 (1B)
CH3 (1A)
CH2 (1B)
CH3 (1A)
Acetone (1)
Pentane (2)

27. UNIFAC Example Residual Term ( )
CH3 (1A)
CH3 (1A)
C=O (8)
CH2 (1B)
CH2 (1B)
CH3 (1A)
CH2 (1B)
CH3 (1A)

28. Equilibrium Flash
Vapor
Feed
Liquid

29. Practical Problem

30. Relative Volatility

31. K Factor
Depriester Chart

32. Isothermal Flash Calculation
V, yi
Fixed T,P
F, zi
L, xi
Trial and Error solution

33. Flash Example Calculate the bubble point, dew point and fractional
flash (T= 180 F) for the following mixture at 200 Psia.
C2 = 8 mole %
C3 = 22 mole %
n-C4 = 53 mole %
n-C5 = 17 mole %

34. Non-isothermal Flash Curve
Temperature
Flash curve
Heat balance curve V