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 2015-16

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

P-x,y diagram for binary mixtures

T-x,y diagram for binary mixtures

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

K-values for hydrocarbons

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.

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.

Example The following mixture at 283.15 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

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

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

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

Flash calculation

Flash calculation Newton method

Example Calculate the composition and liquid fraction that leave a flash drum for a feed stream at 283.15 K and 13.8 bar. The composition of the feed read Species zi Methane 10% Ethane 20% Propane 70%

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

Solution (continued) 0.5 0.168324 -0.60765 1 0.777007 -0.05301 L/F (L/F) (L/F) 0.5 0.168324 -0.60765 1 0.777007 -0.05301 -1.18258 2 0.732185 -0.00463 -0.98857 3 0.727498 -3.8E-05 -0.97229 4 0.727459 -2.7E-09 -0.97216

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

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).