1. Chapter 14: Phase Equilibria Applications
Part II

2. If the component is supercritical, then the vapor pressure is not defined

3. example
A binary methane (1) and a light oil (2) at 200K and 30 bar consists of a vapor phase containing 95% methane and a liquid phase containing oil and dissolved methane. The fugacity of methane is given by Henry’s law, and at 200 K, H1 = 200 bar. Estimate the equilibrium mole fraction of methane in the liquid phase. The second virial coefficient of methane at 200K is -105 cm3/mol

4. solution

5. Solution (cont)
Need equation for the fugacity coefficient vapor phase

6. Solution (cont) How do we solve for the mole fraction of the solute
in the liquid phase?
x1 =0.118

7. Another example
For chloroform(1)/ethanol(2) at 55oC, the excess Gibbs energy is
The vapor pressures of chloroform and ethanol at 55oC are P1sat = kPa, and P2sat = kPa
Make BUBLP calculations, knowing that B11=-963 cm3/mol, B22 =-1,523 cm3/mol, B12 =52 cm3/mol

8. Need equations for the fugacity coefficients

9. But we don’t know P
 Guess P (avg sat. pressures)

10. For example, at x1 =0.25, solve for y1, y2, P y1 = 0.558 y2 = 0.442
P = kPa
In our web site, there are model spreadsheets that you can download

11. VLE from cubic EOS

13. Vapor pressure pure species
(1)
Liquid branch
Vapor branch
LV transition
Using equation (1), the cubic EOS yields Pisat= f(T)

15. Compressibility factors
For the vapor phase there is another
expression, (14.36)

18. How to calculate vapor pressure from a cubic EOS
We solve for the saturation pressure at a given T such that the fugacity coefficients are equal in the two phases: 2 compressibility eqns., two fugacity coefficient eqns., equality of fugacity coefficients,
5 unknowns: Psat, Zl, Zv, fl, fv

19. Mixture VLE from a cubic EOS
Equations for Zl and Zv have the same form as for pure components
However the parameters a & b are functions of composition
The two phases have different compositions, therefore we could think in terms of two P-V isotherms, one for each composition

21. Mixing rules for parameters

22. Also we need “partial” parameters

23. The partial parameters are used for the calculation of fugacity coefficients
Because fi is related to the partial molar property of GR (residual G)

24. example
Vapor mixture of N2(1) and CH4 (2) at 200K and 30 bar contains 40 mol% N2. Calculate the fugacity coefficients of nitrogen and methane using the RK equation of state.
For RK, e =0 and s =1

26. Calculate P-x-y diagram at 100 oF for methane(1)-n butane (2) using SRK and mixing rules (14.42) to (14.44)
Compare with published experimental data (P, x, y)
Initial values for P and yi can be taken from given experimental
data
First read critical constants, w, from Table B.1 and a from Table 3.1
Calculate b1, b2, a1, a2
In this case T > Tc1

28. Step 1
K value given by

29. The equations for a are valid only up to the critical temperature; however is OK to
extend the correlation slightly above the critical temperature
Lets calculate the mixture parameters (for step 1). When applied to the liquid phase we use the xi mole fractions

30. Follow diagram Fig. 14.9
Assume P and yi
Calculate Zl and Zv, and the mixture fugacity coefficients
Calculate K1 and K2 and the SKixi
Calculate normalized yi=Kixi/ S Kixi
Reevaluate fugacity coefficients vapor phase, etc
If S Kixi > 1, P is too low so increase P;
if S Kixi < 1, then reduce P

31. Results:
Rms % difference between
calculated and exp. P is
3.9%
Rms deviation between
calculated and exp. y1 is
0.013
Note that the system consists
of two similar molecules
Where are the largest
discrepancies with the
experimental data?