Equations of State 1-The first method Redlich-Kwong (RK) 2-The second method Soave-Redlich-Kwong (SRK) 3-The third method Peng-Robinson (PR)

1. 1 Student/Mohamed salah
Suez University
Faculty Of Petroleum & Mining
Engineering
Prepared by/
Student/ Mohamed salah abou El_hamed
Department/ petroleum refining
Year/ third

2. 2 Student/Mohamed salah
Calculate the density of the gas &liquid phase at 4000Psia and 160
F for the following composition using (RK& SRK& PR)
Solution
The first method(RK)
P= 4000 psia
T=620 RO
R=10.73
ft3
/lb.mol.RO
pr =P/PC
Tr =T/TC
a=.42747(R2
TC
2.5
)/PC
b=.08664(RTC)/PC
A=.42747Pr/Tr2.5
B=.08664Pr/Tr
COMP MW PC TC xi yi vmwt Lmwt
C1 16.043 667.8 343.1 0.45 0.86 13.79698 7.21935
C2 30.07 707.8 549.8 0.05 0.05 1.5035 1.5035
C3 44.097 616.3 665.7 0.05 0.05 2.20485 2.20485
C4 58.124 529.1 734.7 0.03 0.02 1.16248 1.74372
C5 72.151 490.4 828.8 0.01 0.01 0.72151 0.72151
C6 86.178 436.9 913.4 0.01 0.005 0.43089 0.86178
C7+ 215 285 1160 0.4 0.005 1.075 86
Tottal 20.89521 100.2547
COMP Mwt PC TC xi yi
C1 16.043 667.8 343.1 0.45 0.86
C2 30.07 707.8 549.8 0.05 0.05
C3 44.097 616.3 665.7 0.05 0.05

3. 3 Student/Mohamed salah
Step 1
comp Pr Tr bm gas bm liq amliq amgas
c1 5.989817311 1.807053 0.410763 0.214934 32541.345 118852.2
c2 5.65131393 1.127683 0.036106 0.036106 1232.1012 1232.101
c3 6.490345611 0.93135 0.050208 0.050208 2282.7025 2282.703
c4 7.56000756 0.843882 0.025818 0.038727 1224.8557 544.3803
c5 8.156606852 0.748069 0.015711 0.015711 198.46274 198.4627
c6 9.155413138 0.678783 0.009718 0.019436 284.03742 71.00935
c7+ 14.03508772 0.534483 0.018919 1.513531 1266266.7 197.8542
Tottal 0.567243 1.888653 1304030.2 123378.7
am = (sum(x a
.5
))
2 liq
am = (sum(y a.5))2 gas
Step2 A,B(mixture) calculating
A= am P/R
2
TC
2.5
B=bm*p/(RT)
GAS LIQUID
A 0.447839 4.733354
B 0.341066 1.135588
comp a b A B
c1 160698 0.477631 0.5833 0.287185
c2 492840.5 0.722125 1.788907 0.434191
c3 913081 1.004164 3.314291 0.603772
c4 1360951 1.290894 4.939964 0.776174
c5 1984627 1.571149 7.203778 0.944683
c6 2840374 1.943556 10.30996 1.1686
c7+ 7914167 3.783827 28.72675 2.275097
Tottal

4. 4 Student/Mohamed salah
Step3 cubic equation solving
Z3
-Z2
+Z(A-B-B2
)-AB=0
Step4
Mwa for gas
name MW Yi y*mw
c1 16.043 0.86 13.79698
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.02 1.16248
c5 72.151 0.01 0.72151
c6 86.178 0.005 0.43089
c7+ 215 0.005 1.075
20.89521
Mwa for liquid
name MW Xi x*mw
c1 16.043 0.45 7.21935
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.03 1.74372
c5 72.151 0.01 0.72151
c6 86.178 0.01 0.86178
c7+ 215 0.4 86
100.2547
Step5
V
density
11.13304 lb/ft3
L
density
37.18005 lb/ft3
For gas : A-B-B2 = -0.00955 AB = 0.152742 z=.92448
For Liquid : A-B-B2 = 2.308206 AB = 5.37514 z=1.411835

5. 5 Student/Mohamed salah
The second method(SRK)
P= 4000 psia
T=620 RO
R=10.73 ft3
/lb.mol.RO
pr =P/PC
Tr =T/TC
m=.48+1.574w-.176w2
ALFA=(1+m(1-TC
.5
))2
a=.42747(R TC)2
/PC
b=.08664(RTC)/PC
A=.42747(ALFA)Pr/Tr2
B=.08664Pr/Tr
COMP MW PC TC w xi yi m vmwt Lmwt
C1 16.043 667.8 343.1 0 0.45 0.86 0.48 13.79698 7.2194
C2 30.07 707.8 549.8 0.1064 0.05 0.05 0.645481 1.5035 1.5035
C3 44.097 616.3 665.7 0.1538 0.05 0.05 0.717918 2.20485 2.2049
C4 58.124 529.1 734.7 0.1825 0.03 0.02 0.761393 1.16248 1.7437
C5 72.151 490.4 828.8 0.2104 0.01 0.01 0.803378 0.72151 0.7215
C6 86.178 436.9 913.4 0.2972 0.01 0.005 0.932247 0.43089 0.8618
C7+ 215 285 1160 0.52 0.4 0.005 1.25089 1.075 86
Total 20.89521 100.25
Assum kij = 0
Step 1
comp Pr Tr ALFA a b bm gas bm liq A B
c1 5.9898173 1.80705 0.69681 8675.61 0.477631 0.410763 0.214934 0.546377 0.2872
c2 5.6513139 1.12768 0.92166 21018.6 0.722125 0.036106 0.036106 1.750854 0.4342
c3 6.4903456 0.93135 1.05079 35389.1 1.004164 0.050208 0.050208 3.360958 0.6038
c4 7.5600076 0.84388 1.12775 50209.7 1.290894 0.025818 0.038727 5.117716 0.7762
c5 8.1566069 0.74807 1.22883 68937.3 1.571149 0.015711 0.015711 7.656403 0.9447
c6 9.1554131 0.67878 1.35533 93982.1 1.943556 0.009718 0.019436 11.51241 1.1686
c7+ 14.035088 0.53448 1.78593 232368 3.783827 0.018919 1.513531 37.50738 2.2751
Total 0.567243 1.888653

6. 6 Student/Mohamed salah
Step 2
(aα)m for gases
j
i c1 c2 c3 c4 c5 c6 c7+ sum
c1 4471.0748 465.331 644.717 318.224 194.6165 119.322 215.3752 6428.66
c2 465.33149 48.4298 67.0995 33.1194 20.25491 12.41855 22.41539 669.0691
c3 644.7168 67.0995 92.9664 45.887 28.06317 17.2059 31.05652 926.9953
c4 318.22589 33.1197 45.8873 22.6494 13.85171 8.492663 15.32919 457.5558
c5 194.61658 20.2549 28.0632 13.8516 8.471253 5.193836 9.374835 279.8262
c6 119.32199 12.4186 17.2059 8.49261 5.193837 3.184409 5.747835 171.5651
c7 215.37525 22.4154 31.0565 15.3291 9.374834 5.747834 10.3748 309.6737
sumsum= 9243.346
(aα)m for liquids
Step3 A,B(mixture) calculating
A=(aα)m*P/(RT)2
B=bm*p/(RT)
GAS LIQUID
A 0.835423 9.422752
B 0.341066 1.135588
j
i c1 c2 c3 c4 c5 c6 c7+ sum
c1 1224.165 243.4874 337.3517 249.7703 101.8342 124.8719 9015.704 11297.19
c2 243.4874 48.42982 67.09952 49.6795 20.25491 24.83711 1793.23 2247.019
c3 337.3518 67.09952 92.96639 68.83095 28.06317 34.41181 2484.521 3113.244
c4 249.7703 49.6795 68.83094 50.96142 20.77756 25.478 1839.503 2305
c5 101.8343 20.25491 28.06317 20.77756 8.471253 10.38768 749.9866 939.7754
c6 124.8719 24.8371 34.41181 25.478 10.38767 12.73764 919.6533 1152.377
c7 9015.708 1793.231 2484.521 1839.503 749.9867 919.6537 66398.68 83201.28
sumsum= 104255.9

7. 7 Student/Mohamed salah
Step4 cubic equation solving
Z3
-Z2
+Z(A-B-B2
)-AB=0
Step5
Mwa for gas
name MW Yi y*mw
c1 16.043 0.86 13.79698
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.02 1.16248
c5 72.151 0.01 0.72151
c6 86.178 0.005 0.43089
c7+ 215 0.005 1.075
20.89521
Mwa for liquid
Step6
V
density
13.58965 lb/ft3
L
density
42.68518 lb/ft3
For gas : A-B-B2 = 0.378031 AB = 0.284934 z=.92448
For Liquid : 6.997604 10.70036 z=1.411835
name MW Xi x*mw
c1 16.043 0.45 7.21935
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.03 1.74372
c5 72.151 0.01 0.72151
c6 86.178 0.01 0.86178
c7+ 215 0.4 86
100.2547

8. 8 Student/Mohamed salah
The third method(PR)
P= 4000 psia
T=620 RO
R=10.73 ft3
/lb.mol.RO
pr =P/PC
Tr =T/TC
m=.379642+1.48503w-.1644w2
+.016667w3
ALFA=(1+m(1-TC
.5
))2
a=.45724(R TC)2
/PC
b=.07780(RTC)/PC
A=.45724(ALFA)Pr/Tr2
B=.07780Pr/Tr
COMP MW PC TC w xi yi m vmwt Lmwt
C1 16.04 667.8 343.1 0 0.45 0.86 0.3796 13.79698 7.21935
C2 30.07 707.8 549.8 0.1064 0.05 0.05 0.5358 1.5035 1.5035
C3 44.1 616.3 665.7 0.1538 0.05 0.05 0.6042 2.20485 2.20485
C4 58.12 529.1 734.7 0.1825 0.03 0.02 0.6453 1.16248 1.74372
C5 72.15 490.4 828.8 0.2104 0.01 0.01 0.685 0.72151 0.72151
C6 86.18 436.9 913.4 0.2972 0.01 0.005 0.8069 0.43089 0.86178
C7+ 215 285 1160 0.52 0.4 0.005 1.1097 1.075 86
Tottal 20.89521 100.2547
Assum kij = 0
Step1
comp Pr Tr α a b bm gas bm liq A B
c1 5.9898173 1.80705 0.75569 9279.8 0.4289 0.36885 0.193 0.633807 0.25788
c2 5.6513139 1.12768 0.93474 22482.4 0.64845 0.03242 0.03242 1.899378 0.38989
c3 6.4903456 0.93135 1.04266 37853.7 0.90171 0.04509 0.04509 3.567215 0.54217
c4 7.5600076 0.84388 1.10777 53706.4 1.15918 0.02318 0.03478 5.377158 0.69698
c5 8.1566069 0.74807 1.19363 73738.2 1.41084 0.01411 0.01411 7.954971 0.8483
c6 9.1554131 0.67878 1.30442 100527 1.74525 0.00873 0.01745 11.85161 1.04937
c7+ 14.035088 0.53448 1.68592 248551 3.39776 0.01699 1.3591 37.87292 2.04297
Tottal 0.50937 1.69595

9. 9 Student/Mohamed salah
Step2
(aα)m for gases
(aα)m for liquid
j
i
c1 c2 c3 c4 c5 c6 c7+ sum
c1 1318.477 262.246 363.3419 269.013 109.6797 134.4922 9710.288 12167.54
c2 253.6047 50.44215 69.8876 51.74376 21.09653 25.86913 1867.742 2340.386
c3 347.5491 69.12776 95.77651 70.91152 28.91145 35.45199 2559.621 3207.35
c4 256.0231 50.92318 70.55407 52.2372 21.29771 26.11582 1885.553 2362.704
c5 103.8008 20.64606 28.60511 21.17881 8.634845 10.58828 764.4699 957.9238
c6 126.6981 25.20034 34.91508 25.85061 10.53959 12.92393 933.1033 1169.231
c7 9059.534 1801.948 2496.599 1848.445 753.6325 924.1242 66721.45 83605.73
sumsum= 105810.9
Step3 A,B(mixture) calculating
GAS LIQUID
A 0.887118 9.563292
B 0.306266 1.019722
j
i
c1 c2 c3 c4 c5 c6 c7+ sum
c1 4815.5335 501.181 694.387 342.74 209.61 128.515 231.968 6923.934
c2 484.6667 50.4422 69.8876 34.4956 21.0965 12.9346 23.3468 696.8699
c3 664.20486 69.1278 95.7765 47.274 28.9114 17.726 31.9953 955.0159
c4 326.1924 33.9488 47.036 23.2164 14.1985 8.70527 15.7129 469.0103
c5 198.3749 20.6461 28.6051 14.1191 8.63484 5.29414 9.55588 285.23
c6 121.06708 12.6002 17.4575 8.61681 5.2698 3.23098 5.8319 174.0743
c7 216.42221 22.5243 31.2075 15.4036 9.42041 5.77577 10.4252 311.1791
sumsum= 9815.314
A=(aα)m*P/(RT)2
B=bm*p/(RT)

10. 10 Student/Mohamed salah
Step4 cubic equation solving
For gas :
B-1 =-0.69373
(A-2B-3B2) =-0.00681
(AB-B2-B3)=-0.03843
For Liquid :
B-1 =0.019722 (A-2B-3B2
) =4.404347 (AB-B2-B3)=5.57206
Step5
Mwa for gas
Mwa for liquid
Step6
V
density
13.39264 lb/ft3
L
density
58.7983 lb/ft3
Z3
-(B-1)Z2
+(A-2B-3B2
)Z-(AB-B2
-B3
)=0
name MW Yi y*mw
c1 16.043 0.86 13.79698
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.02 1.16248
c5 72.151 0.01 0.72151
c6 86.178 0.005 0.43089
c7+ 215 0.005 1.075
20.89521
name MW Xi x*mw
c1 16.043 0.45 7.21935
c2 30.07 0.05 1.5035
c3 44.097 0.05 2.20485
c4 58.124 0.03 1.74372
c5 72.151 0.01 0.72151
c6 86.178 0.01 0.86178
c7+ 215 0.4 86
100.2547

11. 11 Student/Mohamed salah
Summary
Z GAS Z LIQUID GAS
DENSITY
Liq
DENSITY
PR 0.9381 1.0252 13.39264 58.7983
SRK 0.9245 1.4122 13.58965 42.68518
RK 1.1285 1.6213 11.133 37.3718