1. Department of Chemical Engineering, University of Nizwa
Equilibrium Calculations: Dew Point, Bubble Point and Flash Calculations
Dr. Khashayar Nasrifar
Department of Chemical Engineering, University of Nizwa
Spring

2. Objectives Estimating k-values Calculating dew point condition
Calculating bubble point condition
Flash calculation

3. P-x,y diagram for binary mixtures

4. T-x,y diagram for binary mixtures

5. x-y diagram and k-values for binary mixture
x-y diagrams are at constant pressure but variable temperature.
x-y diagrams can easily be constructed from T-x, y diagrams
Tempearature x y
k=y/x
Heavy component saturated temperature T1 x1 y1
y1/x1 T2 x2 y2
y2/x2 T3 x3 y3
y3/x3 T4 x4 y4
y4/x4 1

6. K-values for hydrocarbons

7. Dew Point Calculations
For dew point calculations, the gas phase composition (yi’s) and either T or P are given. The question is to calculate xi’s and P or T. Assuming T is given. Then we assume the pressure, and then estimate ki’s. We need to check out for If the condition holds, the assumed pressure is the dew point pressure. Otherwise change it until the condition holds. If P is given, the calculation procedure is similar, only T should be assumed and we need to look for T that satisfy the above condition.

8. Bubble Point Calculations
For bubble point calculations, the liquid phase composition (xi’s) and either T or P are given. The question is to calculate yi’s and P or T. Assuming T is given. Then we assume the pressure, and then estimate ki’s. We need to check out for If the condition holds, the assumed pressure is the bubble point pressure. Otherwise change it until the condition holds. If P is given, the calculation procedure is similar, only T should be assumed and we need to look for T that satisfy the above condition.

9. Example
The following mixture at K (10°C) is given. Calculate (a) the dew point pressure, (b) the bubble point pressure.
Species
Composition (mole%)
Methane 10
Ethane 20
propane 70

10. Solution (Part a) Species yi P=6.9 bar ki yi/ki P=10.34 bar P=8.7 bar
Methane
0.10 20
0.005
13.2
0.008 16
0.006
Ethane
0.20
3.25
0.062
2.25
0.089
2.65
0.075
Propane
0.70
0.92
0.761
0.65
1.077
0.762
0.919
0.828
1.174 1

11. Solution (Part b) Species yi P=26.2 bar ki kixi P=27.6 bar P=26.54 bar
Methane
0.10
5.60
0.56
5.25
0.525
5.49
0.549
Ethane
0.20
1.11
0.222
1.07
0.214
1.10
0.220
Propane
0.70
0.335
0.235
0.32
0.224
0.33
0.231
1.017
0.963
1.000

12. Flash calculations V: mole/min y1, …, yn T, P L/F=? F: mole/min
z1, …, zn
L: mole/min
x1, …, xn

13. Flash calculation

14. Flash calculation
Newton method

15. Example
Calculate the composition and liquid fraction that leave a flash drum for a feed stream at K and 13.8 bar. The composition of the feed read
Species zi
Methane
10%
Ethane
20%
Propane
70%

16. Solution No Species zi ki 1 Methane 10% 10 2 Ethane 20% 1.76 3 Propane
70%
0.52
Assuming (L/F)0=0.5

17. Solution (continued) 0.5 0.168324 -0.60765 1 0.777007 -0.05301
L/F
(L/F)
(L/F)
0.5 1 2 3
-3.8E-05 4
-2.7E-09

18. Solution
Liquid and vapor phase composition at L/F = 0.727 No
Species zi ki xi
yi=kixi 1
Methane
10% 10
0.0289
0.2892 2
Ethane
20%
1.76
0.1656
0.2915 3
Propane
70%
0.52
0.8055
0.4188

19. Conclusions You have learnt about T-x, y and P-x, y diagrams
You have learnt about k-value estimation for hydrocarbon systems
You have learnt about VLE calculations (dew, bubble and flash).