- Email: [email protected]
Correlation of solubilities of carbon dioxide in aromatic compounds
Fluid Phase Equilibria, 73 (1992) l-25 Elsevier Science Publishers B.V., Amsterdam
1
Correlation of solubilities of carbon dioxide in aromatic compounds Jun-Shun Yau and Fuan-Nan Tsai Department of Chemical Engineering, National Cheng Kung University, Tainan 70101 (Taiwan) (Received July 23, 1991; accepted in original form November 12, 1991)
ABSTRACT Yau, J.-S. and Tsai, F.-N., 1992. Correlation of solubilities of carbon dioxide in aromatic compounds. Fluid Phase Equilibria, 73: l-25. The solubilities of carbon dioxide in twenty-eight aromatic solvents are modeled Soave equation of state with one interaction parameter. Henry’s constant, the partial volume at infinite dilution and the Margules constant are evaluated from the parameters using the approach of Bender, Klein, Schmitt and Prausnitz (1984, Fluid Equilibria, 15 : 241-255).
by the molar above Phase
INTRODUCTION
Vapor-liquid equilibrium data are the essential element in the design and development of many industrial processes. Carbon dioxide is frequently found in many natural gases, crude oil and coal liquids. Hence, recent developments in coal-gasification, heavy fossil fuel, petroleum products and enhanced oil recovery operation have led to renewed interest in the solubility of carbon dioxide. This work is a continuation of our studies of vapor-liquid equilibria (VLE) of carbon dioxide-normal paraffin systems (Tsai and Yau, 1990). Previously, we have reported data on the solubility of carbon dioxide in four aromatic solvents; phenanthrene, pyrene, phenol and catechol (Yau and Tsai, 1992a,b). Robinson and co-workers (Nagarajan and Robinson, Correspondence to: Dr. Fuan-Nan Tsai, Department Cheng Kung University, Tainan 70101, Taiwan. 0378-3812/92/$05.00
of Chemical Engineering,
0 1992 Elsevier Science Publishers B.V. All rights reserved
National
1987; Bar-rick et al., 1987) have presented the solubility of carbon dioxide in benzene, naphthalene, phenanthrene and pyrene at temperatures up to 433 K and pressures up to 10.6 MPa. Chao and co-workers (Sebastian et al., 1980a,b,c,d; Lee and Chao, 1988) have reported the solubility of carbon dioxide in toluene, m-xylene, diphenylmethane, 1-methylnaphthalene, mcresol and tetralin over the temperature range 308.2-703.35 K and pressures up to 24 MPa. Donohue and co-workers (Morris and Donohue, 1985; Kim and co-workers, 1986,1989) have determined the vapor-liquid equilibrium data of carbon dioxide in benzene, toluene, p-xylene, l-methylnaphthalene, anisole, benzaldehyde and tetralin over the temperature range 343.0-413.15 K and pressure range 2.45-22.12 MPa. In the present study, a correlation is developed from VLE data of carbon dioxide-aromatic hydrocarbon systems on the basis of the Soave equation of state (Graboski and Daubert, 1978) with one interaction parameter. Henry’s constant, the partial molar volume of carbon dioxide at infinite dilution and the Margules constant are then obtained by fitting the Krichevsky-Ilinskaya equation (1945) to the data. CORRELATION WITH THE SOAVE EQUATION OF STATE
Experimental vapor-liquid equilibrium data of carbon dioxide in aromatic solvents were used to develop a correlation method in order to describe the vapor-liquid equilibria of these systems. The Soave equation of state with a binary interaction parameter is used for each binary system. For the Soave equation, the specific relations are a RT p=-(1) u-b u(u+b) where U= C
CZiZjUij
i
j
(3)
b = &bi aij =
(Qiiajj)‘.‘(l
-
kij)
(4)
aii = 0.42748aiR2T:/Pc,
(5)
bi = 0.08664RT,i/P,,
(6)
m, = 0.48508 + 1.551710, - 0.15613&
(8)
TABLB 1 Critical properties and acentric factors used in equation of state Substance
T, (K) P, (atm)
w
Substance
T, (K) PC (atm)
w
Carbon dioxide Benzene Naphth~ene Phenanthrene Pyrene Toluene Ethylbenzene nPropylbenzene Cumene n-Bu~fbenzene n-Hexyibenzene n-Heptylbenzene n-Octylbenzene o-Xylene m-Xyiene
304.1 562.2 748.4 873.2 938.2 591.8 617.2 638.2 631.1 660.5 696.7 727.6 729.3 630.3 617.1
0.239 0.212 0.302 0.54 0.344 0.263 0.302 0.344 0.326 0.393 0.489 0.533 0.577 0.310 0.325
p-Xylene 1-Methylnaphthalene 2-Methylnaphthalene Phenol Catechoi 1-Naphthol 2-Naphthol Benzaldehyde Styrene Anisole Diphenyl Diphenylmethane m-Cresol Tetralin
616.2 772 761 694.2 772.2 826.1 822.4 694.8 647 645.6 789 770 705.8 719
0.320 0.310 0,382 0.438 0.641 0.520 0.520 0.316 0.257 0.347 0.372 0.442 0.454 0.303
72.85 48.26 39.97 32.57 25.66 40.467 35.53 31.584 31.683 28.52 23.35 21.50 19.92 36.82 34.94
34.64 35.53 34.545 60.5 77.67 46.29 46.29 44.81 39.38 41.94 38.00 28.23 45.01 34.644
In fitting the equation of state to experimental data, the values for the optimized interaction parameters are dependent on the properties T,,, PC, and wi used in the evaluation of the pure-component parameters (a and b) in the equations. Table 1 presents the properties of each substance utilized in the present work. Except for n-hexylbenzene, n-heptylbenzene, n-oc@benzene, phenanthrene, pyrene, catechol, 1-naphthol and 2-naphthol, the data are taken from the property data bank of Reid et al. (1988). The critical properties and acentric factors of phenanthrene and pyrene were taken from the API Monograph Series (1979a,b). The values of critical temperature and critical pressure were estimated by the Ambrose method (1978, 19791, and the acentric factor was determined from the Lee-Kesler correlations (1975) for n-hexylbenzene, n-heptylbenzene, n-octylbenzene, catechol, 1-naphthol and Z-naphthol. The values of the normal boiling point needed in calculations of T, for n-hexylbenzene, n-heptylbenzene and n-octylbenzene are taken from API-44 Tables (Wilhoit and Zwolinski, 1970, and for catechol, I-naphthol and Z-naphthol they are taken from the Merck Index (Windholz et al., 1983).
CORRELATION
WITH THE ~IC~VSKY-ILINS~YA
EQUATION
Henry’s constant and the partial molar volume at infinite dilution are determined by fitting the Krichevs&Ilinskaya equation (1945) to the VLE
data. The equation is
ln(f1/4 = ln f&,2+A(x; -
l)/RT
+ VY(P - P,S)/RT
(9)
where the subscript 1 refers to the solute and 2 the solvent, H, 2 is Henry’s constant, Cy is the partial molar volume of the solute at infinite dilution, and Pi is the vapor pressure of the solvent. The expressions of the parameters in the Krichevsky-Ilinskaya equation can be derived from an equation of state by means of the following relations (Bender et al., 1984):
(11) A=-__
RT a 2 ax (In & + In P)T,*,=o 1
(12)
Bender et al. presented the method for the reduction and correlation of high-pressure gas-solubility data using the Krichevsky-Ilinskaya equation, a simple cubic equation of state with conventional mixing rules, and an experimental value for Henry’s constant. The partial molar volume and Margules constant are then obtained from the equation of state.
RESULTS AND DISCUSSION
The basic thermodynamic that at constant temperature is the same in both phases:
fiLfi
requirement for vapor-liquid equilibrium is and pressure the fugacity of each component
(13)
The fugacity coefficient of a component in a mixture, &, is defined as the ratio of the fugacity to its partial pressure. Replacing fugacities with fugacity coefficients, eqn. (13) becomes
(14) In this study, bubble-pressure calculations are used to fit the interaction parameter ktj. The pure-component parameters Tc,, PC,and oi used in the Soave equation of state are shown in Table 1. The calculated results are listed in Tables 2-7. In the calculation, the optimal binary parameter kij obtained by minimizing the bubble-pressure variance is independent of pressure and composition for each isothermal system.
Temp.
383.15 423.15 473.15 523.15
433.15 473.15 523.15 573.15
Phenanthrene
Pyrene
0.558 0.611 0.612 0.628 0.664 0.699 0.736
313.40 343.60 344.30 353.00 373.50 393.20 413.60
0.462 0.504 0.558 0.611
0.439 0.485 0.542 0.599
0.499 0.532 0.565
0.557
313.15
373.15 398.15 423.15
0.486 0.504 0.530 0.539
T,
273.15 283.15 298.15 303.15
(K)
Naphthalene
Benzene
Solvent
31.6 40.4 57.0 62.3
7.3-104.4 10 - 50 10 - 50 10 - 50
18.5-104.8 10 -100.8 10 - 50 10 - 50
10 -103.1 10 - 50 10 - 98.3
20.9- 58.4 22.6- 95.3 68.1-108.2 4.9- 61.9 6.6- 58.3 7.2- 58.8 38.2-151.9
14.7- 76.5
8.29.68.813.0-
(atm)
P range
879 985 1033 727 812 1006 1232 885 1185 1460 1837
56.3 61.0 66.2 52.9 58.8 68.0 80.5 71.9 82.4 98.3 119.6
271.0 323.4 348.9
2.88 4.45 2.00 1.49 2.20 3.61 3.74 3.42
15.62 15.39 16.82 16.98 30.38 38.97 42.47 46.58
7 12 5 5
365.4 439.9 542.4 587.1
7 5 5 5
5.7 21.1 66.5
7.3 13.0
490.9 646.3 690.1 701.4
141.3
13.61 14.24 13.04
12 5 12
4.64 1.72 2.38
799 823 772 1085 1155 1301 1213
52.3 58.7 58.7 62.0 68.4 76.6 85.9
103.9 137.9 133.8 173.7 196.3 220.1 211.5
6.3 71.6 321.1 282.9 241.1 158.0 238.7
2.89 4.39 1.89 4.07 2.15 3.28 1.52
704
95.9
34.2
2.29
52.0
A (J mol-‘) 863 852 753 843
CT (ml mol-‘1
Barrick et al. (1987) Yau and Tsai (1992a)
Barrick et al. (1987) Yau and Tsai (1992a)
Barrick et al. (1987) Jan and Tsai (1991)
Inomata et al. (1987) Kaminishi et al. 0987) Rim et al. (1986) Nagarajan and Robinson (1987) Ohgaki and Katayama (1976)
Reference
compound systems with various numbers
46.1 47.5 49.5 50.6
H,,, (atm) 62.7 73.2 83.2 95.8
AAD CAY x 104)
4.38 4.41 4.21 4.58
%AAD UP/P)
9.03 8.05 7.26 11.37 10.90 11.12 7.15
7.66
10.81 10.52 8.23 9.98
kij (x10*)
6 5 17 8 8 7 9
9
7 7 15 7
Data pts.
Soave correlation of solubility data and thermodynamic parameters for carbon dioxide-aromatic of benzene rings
TABLE 2
Temp. w
311.26 352.59 353.15 353.40 373.20 383.15 393.25 393.71 413.15 422.45 476.95 477.04 502.75 542.85
312.65 338.15 366.15
313.20 393.00 472.90
Solvent
Toluene
Ethylbenzene
n-Propylbenzene
0.491 0.616 0.741
10.9- 73.6 72.0-177.6 11.4-182.6
23.7- 71.2 40.4-105.6 41.0-140.6
3.3- 76.4 3.7-121.5 2.6-117.7 6.6- 61.0 5.1- 54.2 5.9-126.3 9.6- 63.7 4.0-151.0 7.0-130.0 19.5- 51.2 12.2- 50.3 11.6-150.2 20.4- 49.7 31.3- so.9
0.526 0.596 0.597 0.597 0.631 0.647 0.665 0.665 0.698 0.714 0.806 0.806 0.850 0.917
0.507 0.548 0.593
P range (atm)
T,
10.22 8.90 8.25 10.15 8.81 12.71
13 23 9
10.43 9.57 11.32 11.31 11.96 11.31 11.87 8.28 11.58 10.80 11.93, 11.23 12.78 17.00
k,, (x10*)
5 6 8
8 10 12 8 7 10 11 8 9 5 5 8 4 3
Data pts.
Soave correlation of solubility data and thermodynamic
TABLE 3
4.71 4.36 3.73
5.12 4.40 5.39
4.44 7.40 6.70 4.36 4.22 5.65 3.70 6.18 6.81 0.67 1.46 3.36 0.85 2.41
%AAD (AP/P)
parameters
8.7 25.6 43.2
8.8 24.4 58.9 147.2 231.4 137.0 108.8 130.8 185.0 59.4 150.7 204.1 216.0 380.7
x 104)
AAD CAY
94.6 179.9 257.2
98.0 122.5 152.7
101.9 150.2 162.5 162.8 192.0 198.9 213.7 190.0 230.4 232.6 261.7 257.9 261.5 245.9
H,,, (atm)
54.0 73.9 119.7
53.3 58.2 65.1
52.6 61.5 62.0 62.1 68.1 71.3 75.4 74.6 84.5 89.3 139.8 139.5 189.7 398.6
Dy (ml mol_‘)
458 608 1320
547 535 586
677 733 828 829 940 953 1038 851 1157 1192 2002 1961 2759 5743
Renon et al. (1989)
Mohamed and Holder (1987)
Kim et al. (19861 Morris and Donohue (1985) Ng and Robinson (1978) Sebastian et al. (198Ob)
Reference
systems
A (J mol-“1
for carbon dioxide-alkylbenzene
9.98.36.47.211.410.2-
7.85.7lO.l8.5-
14.6- 76.9 23.9-107.6 23.9-147.3
0.385 0.400 0.414 0.428 0.443 0.457
0.397 0.411 0.424 0.438
0.496 0.537 0.581
n-Heptyl- 268.15 benzene 278.15 288.15 298.15 308.15 318.15
288.15 298.15 308.15 318.15
312.65 338.15 366.15
n-Octylbenzene
o-Xylene
48.5 61.1 74.0 81.7
29.3 37.9 48.1 60.7 72.9 81.9
47.4 59.8 75.5 91.2
6.410.99.57.5-
0.414 0.428 0.442 0.457
288.15 298.15 308.15 318.15
n-Hexylbenzene
10 - 30 10 - 50
0.414 0.444
273.15 293.15
n-Butylbenzene
16.8- 64.0 17.8- 73.1 7.1- 85.9 8.9-116.0 29.8-151.1 34.1-169.0
0.474 0.484 0.501 0.536 0.575 0.607
299.25 305.65 316.25 338.35 363.15 383.15
Cumene
11 17 16
21 21 19 22
14 16 21 20 20 23
19 19 11 27
5 9
16 16 40 30 25 18
10.07 8.36 6.77
11.76 9.81 10.36 10.39
10.99 11.23 10.97 9.60 9.32 10.81
11.79 10.55 9.07 9.23
11.91 12.31
10.58 10.27 10.86 9.65 8.10 8.14
3.59 6.82 9.91
6.24 9.12 6.57 2.65
3.67 6.03 4.24 12.15 5.79 4.90
6.66 4.57 6.45 8.54
5.64 8.08
5.26 5.09 7.28 5.54 3.03 3.56
102.0 125.6 151.9
65.2 67.9 80.0 91.7
56.8 55.0 64.2 69.4 78.6 95.6
67.9 71.1 71.1 89.5
55.5 78.5
79.2 85.1 100.1 120.2 140.7 162.7
52.0 56.4 62.5
52.4 53.9 55.6 57.2
46.8 50.1 51.5 52.9 54.5 56.3
51.4 53.3 55.9 56.2
48.3 51.3
52.2 53.3 55.3 59.7 65.7 71.7
567 536 542
264 227 244 250
257 273 269 242 241 283
327 302 278 280
430 453
461 455 492 482 483 551
Mohamed and Holder (1987)
Lansangan et al. (1987)
Lansangan et al. (1987)
Lansangan et al. (1987)
Tiffin et al. (1978)
Occhiogrosso et al. (1986)
312.65 338.15 353.20 366.15 373.40 393.20
p-Xylene
0.507 0.549 0.573 0.594 0.606 0.638
303.15 0.491 310.90 0.504 312.65 0.507 323.15 0.524 338.15 0.548 338.70 0.549 343.15 0.556 366.15 0.593 394.30 0.639 462.15 0.749 477.60 0.774 502.05 0.814 543.35 0.881 582.55 0.944
m-Xylene
T,
Temp. WI
Solvent
TABLE 3 (continued)
5 11 6 5 7 9 5 8 10 4 9 4 5 3
6.6- 32.6 3.1- 79.0 13.1- 71.0 6.7- 32.9 23.7-101.9 4.0-111.8 16.0- 34.7 23.9-151.6 3.9-165.3 21.1- 51.9 8.8-167.5 21.2- 51.4 20.5- 50.9 31.1- 50.8
11.8- 71.9 23.4-106.4 4.5- 60.7 23.8-139.8 4.9- 58.5 7.0- 60.1
14 12 8 13 7 7
Data pts.
(atm)
P range
9.97 8.36 8.49 7.85 10.86 11.41
9.61 9.84 10.19 7.36 8.85 9.31 10.49 8.65 8.84 12.54 9.13 13.91 17.51 25.73
kij (x10’) %AAD
3.46 5.43 2.04 5.70 1.67 3.30
1.26 2.73 6.39 6.81 6.36 6.97 4.17 4.27 4.54 0.44 2.19 0.64 0.46 0.74
CAP/P)
235.8 292.4
189.9
25.9 9.3 10.9 24.7 21.6 59.0 35.1 43.6 41.7 29.5 136.1 79.6 129.6 90.4
AAD (AY x 104)
53.5 58.4 61.9 65.3 68.0 74.9
51.5 52.8 53.2 54.8 58.1 58.3 59.4 65.0 74.1 114.0 127.5 163.9 287.3 758.7
83.7 94.1 98.0 96.6 122.3 125.6 138.0 155.1 187.6 258.2 244.2 267.4 259.0 227.9 95.8 118.4 137.2 148.8 175.3 200.4
$7 (ml mol-‘1
H,,, (atm)
520 496 540 551 707 813
499 519 537 428 524 546 608 593 714 1401 1445 2131 3860 9612
(J mol-‘1
A
Kim et al. (1986) Mohamed and Holder (1987)
Mohamed and Holder (1987) Ng et al. (1982) Sebastian et al. (198Ob) Vera and Orbey (1984)
Reference
Temp. CKI
348.15 373.15 398.15 423.15
398.15 423.15 448.f5 473.15
Solvent
Phenol
Catechol
0.516 0.548 0.580 0.613
0.502 0.538 0,574 0.610
T,
10-M 10-50 IO-50 IO-50
10-50 IO-50 lO-5D IO-50
P range (atmf
5 5 5 5
5 5 5 5
Data pts,
-3.77 -3.99 -5.41 -6.53
7.53 7.72 7.19 6.31
k, (x10’)
Save correlation of solubility data and thermodynamic group numbers on benzene
TABLE 4
0.85 2.05 1.58 IS7
1.69 4.42 0.90 1.28
%AAD (AP/P)
12.3 12.5 8.5 25.3
2.2 5.2 13.1 20.8
AAD (Ay x IO*)
637.2 721.4 765.4 797.4
3259 378-8 430.2 466.5
H
43.3 45.6 48.1 51.2
45.3 48.6 52.1 56.3
Yau and Tsai 0992bI
Yau and Tsai 0992b)
1762 1877 1887 1960
Reference 1347 1465 1531 1597
& mol-‘1
compound systems with various hydrowl
$1 mol-‘)
-co
parameters for carbon dioxide-aromatic
308.15 328.15 353.15 373.15
343.10 0.531 24.4-128.0 372.30 0.577 33.0-168.0
Styrene
Anisole
0.476 0.507 0.546 0.577
343.00 0.494 27.9-134.0 372.60 0.536 35.0-180.7
26.6- 76.4 31.2- 99.2 38.3-134.9 43.0-160.3
(atm)
Benzaldehyde
P range
Temp. K)
Solvent
T,
5 5
9 9 8 8
5 5
Data pts.
5.27 4.63
11.33 9.53 8.74 7.95
3.25 3.38
4.82 4.24
7.06 8.39 8.48 7.34
3.04 2.85
%AAD
CAP/P)
(x10*)
56.0 25.5
24.9 34.4
?il mol-‘)
50.6 53.7 58.4 62.8
133.5 52.9 171.4 58.4
107.2 124.2 154.1 176.0
133.7 50.2 182.8 54.8
$&
516 577
661 608 632 660
454 557
;‘J mol-‘1
for other carbon dioxide-aromatic
(Ay ~10~)
AAD
parameters
k,j
Soave correlation of solubility data and thermodynamic single functional groups on benzene
TABLE 5 systems with various
Rim et al. (1989)
Suppes and McHugh (1989)
Rim et al. (1989)
Reference
compound
11.24 9.36 9.65 9.41
5 5
5 5
393.15 0.476 10 - 50 453.15 0.549 10 - 50
413.15 0.502 10 - 50 473.15 0.575 10 - 50
2-Naphthol
65 50 65 65 65
1-Naphthol
13.91 14.53 13.93 14.62 13.21
15 10 15 15 10
11 5 11 11 16
kij (X 10’)
2-Methyl307.15 0.404 naphthalene 323.15 0.425 324.15 0.426 348.15 0.458 373.15 0.490
Data pts. 13.02 12.89 12.65 12.63 11.00 10.74 14.85 15.55 16.62 26.25
(at&
P range
19.7-236.9 11 19.7-236.9 11 19.7-236.9 10 6 17.9-142.4 5 36.7-204.0 7 12.0-142.6 20.5- 50.2 4 21.0- 50.8 4 20.6- 48.9 4 30.2- 48.3 3
Temp. Tr 00
l-Methyl308.20 0.399 naphthalene 318.20 0.412 328.20 0.425 353.15 0.457 372.60 0.483 413.15 0.535 463.05 0.600 543.45 0.704 623.55 0.808 703.55 0.911
Solvent
0.64 0.62
1.02 0.29
6.41 3.61 2.37 1.83 6.43
6.75 8.51 9.01 2.79 6.96 4.10 0.53 0.54 1.43 0.26
CAP/P)
%AAD
0.4
99.2 65.4 67.0 1.6 28.1 2.7 17.5 45.6 131.2 150.9
500.8 621.0
486.1 588.9
136.2 170.6 166.9 217.6 247.8
51.9 61.2
49.4 57.5
47.7 49.7 49.8 53.2 57.0
126.5 48.4 141.9 49.6 157.0 50.9 202.3 54.3 220.8 57.3 279.7 65.1 387.2 79.1 434.6 116.0 408.9 202.8 334.9 562.7
AAD H,,, n: (Ay x 104) (atm) (ml mol-‘1
Jan and Tsai (1991)
Jan and Tsai (1991)
1115 1240 1102 1340
Jan and Tsai (1991) Kulkarni et al. (1974)
Kim et al. (1989) Lee and Chao (1988) Morris and Donohue (1985) Sebastian et al. (1980~)
625 667 645 708 708
592 600 605 646 630 730 1117 1788 3274 8780
Reference
derivative systems
(J mol-‘)
A
Soave correlation of solubility data and thermodynamic parameters for carbon dioxide-naphthalene
TABLE 6
0.473
0.536 0.600
0.601 0.705 0.810 0.914
0.437 0.451 0.465 0.656 0.769 0.885 0.942
0.478 0.479 0.481 0.519 0.525 0.578 0.643 0.725 0.756 0.867 0.924
423.15 473.15
462.75 542.55 623.35 703.75
308.20 318.20 328.20 462.65 542.45 624.45 664.65
343.60 344.25 345.90 373.10 377.55 415.30 461.95 521.20 543.55 623.35 664.65
Diphenylmethane
m-Cresol
Tetralin
Diphenyl
T,
Temp. (IQ 373.15
Solvent
49.6 50.3 49.4 50.0
32.0-189.1 40.2-188.1 46.0-157.2 31.3-218.3 49.2-240.6 40.2-219.5 20.2- 50.6 45.0-224.3 19.9- 50.3 19.7- 40.5 30.8- 50.4
19.7-236.9 19.7-236.9 19.7-236.9 19.3- 51.1 20.1- 49.9 20.5- 50.2 40.5- 50.1
18.920.219.229.5-
10 - 50 10 - 50
10 - 50
(atm>
P range 11.36 9.11 7.52 12.88 13.04 19.26 35.07 10.86 10.58 10.33 10.94 11.48 15.03 19.70 10.43 10.12 12.16 9.94 10.68 12.67 15.00 15.07 16.14 22.21 34.13
5 5
5 4 4 3
9 9 9 4 4 4 2
6 7 7 5 7 6 4 7 4 4 3
k,, (~10~)
5
Data pts.
4.44 8.12 11.25 5.82 7.72 7.72 0.58 5.51 1.03 1.19 0.62
5.76 5.59 7.62 2.15 2.17 0.34 0.42
0.44 0.50 0.44 0.65
1.81 0.45
2.69
%AAD (APiP)
319.1 356.5 354.9 291.2
8.0 6.7 29.8 104.3
35.3 178.7 24.6 18.5 111.2 12.8 13.6 158.9 104.4 146.5 88.1 153.2 152.0 169.5 193.5 205.7 273.8 340.6 365.4 370.7 340.7 306.5
158.4 183.6 195.6 440.6 470.5 406.9 334.6
326.9 381.1
33.1 34.1 30.2 7.6 53.5 130.3 196.3
260.4
0.2
$A)
12.6 183.4
AAD (Ay ~10~)
55.1 55.2 55.7 60.6 61.6 71.1 87.7 121.6 142.0 313.7 666.4
44.5 45.2 46.6 72.5 113.2 262.3 611.1
83.2 123.1 222.3 650.0
54.1 62.3 74.0
$1 moI-‘)
544 534 616 596 636 844 1182 1726 2085 4822 9919
873 866 876 1436 2320 5265 10996
815 1367 2856 8315
723 790 962
Chou et al. (1990) Inomata et al. (1986) Kim et al. (1989) Sebastian et al. (1980d)
Lee and Chao (1988) Sebastian et al. (1980a)
Sebastian et al. (198Oc)
Jan and Tsai (1991)
Reference
compound systems
(J mole’)
A
Soave correlation of solubility data and thermodynamic parameters for other carbon dioxide-aromatic
TABLE 7
13 000.
I
,
I
I
8,
I
I
I
I
I
obenzene qnaphthalene ~phenanthrene
0.4
0.6
0.6
0.7
0.8
0.9
1.0
Tr, 2 Fig. 1. Plot of Henry’s constant vs. the reduced temperature compound systems with various numbers of benzene rings.
for carbon dioxide-aromatic
Henry’s constant, the partial molar volume at infinite dilution and the Margules constant can be calculated from eqns. (A&643), as shown in Appendix A, by using the obtained optimal interaction parameters. The calculated results are listed in Tables 2-7 for twenty-eight carbon dioxidearomatic compound systems. Table 2 includes four systems of carbon dioxide in one- to four-ring aromatic solvents. Figure 1 shows Henry’s constant as a function of the reduced temperature for different numbers of benzene rings. It can be seen that Henry’s constant increases as the reduced temperature and the number of benzene rings increase. Figure 2 shows the calculated results of the Margules constant as a function of the reduced temperature with a different number of benzene rings. As observed in Fig. 2, we note that the Margules constant increases on increasing the reduced temperature and the number of benzene rings. All points shown *in Figs. 1 and 2 are calculated from eqns. (10) and (12) respectively, and the lines shown in these figures combine only the calculated points and indicate that the tendencies of Henry’s constant and the Margules constant change with the reduced temperature. Table 3 presents the Soave correlation of solubility data and the thermodynamic parameters for carbon dioxide-alkylbenzene systems. The obtained data are illustrated in Figs. 3 and 4 for Henry’s constant and the Margules constant as a function of the reduced temperature, respectively. Figure 3 shows that Henry’s constant increases as the reduced tempera-
:&
\lOOO
0 0
g
0.3
0.4
0.5
:
0
0
0
00
0
0
0.6
benzene
0.7
Tr,
0.3
0.9
1.0
2
Fig. 2. Plot of the Margules constant vs. the reduced temperature aromatic compound systems with various numbers of benzene rings.
for carbon dioxide-
ture, the carbon numbers of the alkyl group, and the methyl group numbers increase. If the reduced temperature is larger than 0.85 for the binary systems carbon dioxide-toluene and carbon dioxide-m-xylene, Henry’s
300. 2 “nN . 2
I ,,,,,,I +n-butylbenzene x n-hex lbenzene * n-hep i ylbenzene - ln-octylbenzene lo-xylene
I ,,I
I
200 - rp-xylene
I ! ii x &loo
-
I
A ethylbenzene 0 n-propylbenzene 0 cumene calculated 0 1”“‘1”‘*” 0.3 0.4 0.5
0.6
Tr,
0.7 2
0.3
0.9
1.0
Fig. 3. Plot of Henry’s constant vs. the reduced temperature zene systems.
for carbon dioxide-alkylben-
15
10000 benzene 0 toluene ~3ethylbenzene 0 n-propylbenzene 0 cumene + n-butylbenzene x n-hezylbenzene Z+n-heptylbenzene * n-octylbenzene l o-xylene l m-xylene A p-zylene
0
8000
'2; 8000 a > 4
4000
0.8 0.7 0.8 0.0 1.0
Tr,z Fig. 4. Plot of the Margules constant vs. the reduced temperature kylbenzene systems.
for carbon dioxide-al-
constant decreases with increasing the reduced temperature. Henry’s constants of aromatic compounds with different carbon numbers of the alkyl group on benzene are qualitatively and quantitatively similar. Therefore the relation can be correlated by
f4,2- (C,benzene - e,2Y =434.90 - 3059.7 Tr,2+ 6559.2 7$
(15) where 0.385 I Tr,2 I 0.911. The average absolute deviation is about 6.98% when it is estimated from eqn. (15) for carbon dioxide-alkylbenzene systems in the work. Figure 4 shows that the Margules constant increases with reduced temperature and decreases with increasing carbon numbers of the alkyl group. It indicates that the Margules constant is qualitatively and quantitatively similar to different carbon numbers of the alkyl group on benzene. Thus, the carbon number of the alkyl group, the methyl group numbers and
16 1ooo
I
I
1
I
I
I
8
I
n
I
1
,
,I
0 benzene 0 phenol A cateahol m; ?Ei 600
P
R! G400-
8’
m!,[, 0 0.4
, 0.6
0.6
0.7
0.2
,
0.0
1.0
2
Tr,
Fig. 5. Plot of Henry’s constant vs. the reduced temperature for carbon dioxide-aromatic compound systems with various numbers of hydroxyl groups on benzene.
the orientation on benzene, do not seem to have much effect on Henry’s constant and the Margules constant. The Soave correlation of solubility data and the thermodynamic parameters for carbon dioxide-hydroxylbenzene are given in Table 4. Figure 5
benzene o phenol A catechol
0
0’ 0.4
’
’ o ’ 0.6 0.6
’
’ 0.7
Tr,
a ’
0.0
n ’
0.9
p
2
Fig. 6. Plot of the Margules constant vs. the reduced temperature for carbon dioxidearomatic compound systems with various numbers of hydroxyl groups on benzene.
17 500
r,,,,,,,,,,
o benzene
_I/ 0 “n”““” 0.4 0.5 0.5
0 toluene A phenol 0 benzaldehyde n styrene A aniaole
0.7
0.0
0.0
1.0
Tr,a Fig. 7. Plot of Henry’s constant vs. the reduced temperature for carbon dioxide-aromatic compound systems with various single functional groups on benzene.
shows the calculated results of Henry’s constant as a function of the reduced temperature with different hydroxyl group numbers. It indicates that Henry’s constant increases as the reduced temperature and hydroxyl
4000
l
benzaldehyde
z Ei > 4 2ooo
0 0.9 0.4 0.5 0.5 0.7 0.2 0.0 Tr, 2
1.0
Fig. 8. Plot of the Margules constant vs. the reduced temperature for carbon dioxidearomatic compound systems with various single functional groups on benzene.
18
600 -
0 1 -naphthol
200 -
A 2-naphthol
_
0 l-methylnaphthalene
* 2-methylnaphthalene 0 *“““‘1”” 0.3 0.4 0.6
0.6
0.7
0.0
0.9
1.0
Tr,2 Fig. 9. Plot of Henry’s constant thalene
derivative
vs. the reduced
temperature
for carbon
dioxide-naph-
systems.
group numbers increase. Figure 6 shows that the relations between the Margules constant and the reduced temperature and hydroxyl group numbers are similar to those of Henry’s constant. We have studied the effect of various substituent groups with the hydroxyl group on benzene in Tables 2-4. The other single functional groups on benzene are included in Table 5. The data are illustrated in Figs. 7 and 8 for Henry’s constant and the Margules constant as a function of the reduced temperature, respectively. Henry’s constant and the Margules constant increase with reduced temperature. Henry’s constants of carbon dioxide in different solvents with a single substituent group on benzene are in the order of phenol > benzaldehyde > styrene > anisole > toluene > benzene. It can be seen that all of the functional groups increase the values of Henry’s constant. The Margules constant of the carbon dioxide-solvent system with a single substituent group on benzene is in the order of phenol > benzene > toluene > styrene > benzaldehyde > anisole. It indicates that all of the functional groups, except the hydroxyl group, decrease the Margules constant. The resonance effect of the ring stabilizes the phenoxide ion to a greater extent than the phenol, and thus shifts the equilibrium towards ionization. Again, carbon dioxide has quite a large quadrupole moment, so the intermolecular forces must be significant for the carbon dioxide-phenol system. As a result, the Margules constant of the carbon dioxide-phenol system is larger than that of other systems, as shown in Fig. 8.
19
_ _ _
o naphthalene o l-naphthol A 2-naphthol 0 1-methylnaphthalene o 2-methylnaphthalene
ol”“““““D 0.8
0.4
0.6
0.2
Tr,
0.7
0.2
0.9
1
1.0
2
Fig. 10. Plot of the Margiles constant vs. the reduced temperature for carbon dioxidenaphthalene derivative systems.
Henry’s constant and the Margules constant at different reduced temperatures for carbon dioxide-naphthalene derivative systems are listed in Table 6, and these data are illustrated in Figs. 9 and 10, respectively. The tendencies of Henry’s constant and the Margules constant versus the reduced temperature for carbon dioxide-benzene derivative systems and carbon dioxide-naphthalene derivative systems are similar in every respect. Table 7 presents correlations of solubility data and the thermodynamic parameters for other carbon dioxide-aromatic solvent systems calculated by the Soave equation. The calculated Henry’s constant, the partial molar volume at infinite dilution and the Margules constant determined by the Krichevsky-Ilinskaya equation with the optimum values of kij for each isotherm, are also listed in the table. Figure 11 shows the calculated partial molar volume at infinite dilution as a function of the reduced temperature for twenty-eight carbon dioxidearomatic compound binary systems. It indicates that the partial molar volume at infinite dilution increase with increasing reduced temperature. The relations can be correlated by ln( ET/N:.‘) = 5.0225 - 6.0150 Tr,* + 7.4051 Tz2 where 0.385 5 T,,* I 0.750, and
(16)
ln( Ey/N2.5) = 4.6766 + 7.2604( Tr,*- 0.75) - 47.482( Tr,2- 0.75)2 + 321.97( q,2 - o.75)3 where 0.750 I Tr,2I 0.944.
(17)
20
800
1’1’1’1
11’1’
0 bensene
4 l-nephthol
0 naphthelene r(rphenentbrenr v t&r + pvene 0 toluene A ethylbensene 0 n-propylbensene * cumene + n-butylbenrens x n-hexylbensene * n-hept@benrene * n-oct#bensene Q o-xylene * m-xylene (b p-@en8 l phenol n c&echo1 A bensaldehyde 8 etyrene 0 enieole 0 m-creeol o l-methylnaphthelene + 2-methylnaphthelene 0 diphenylmethane o diphenyl
0.3
0.4
0.5
0.5
0.7
0.8
0.9
1.0
Tr,2 Fig. 11. Plot of the partial molar volume at infinite dilution vs. the reduced temperature twenty-eight binary carbon dioxide-aromatic compound systems.
for
The average absolute deviations in the partial molar volume at infinite dilution are about 13.19% for eqn. (16) and 4.51% for eqn. (17). The number of benzene rings, N, of tetralin is 1.5. Taking a careful view, we find that the partial molar volume at infinite dilution increases with increasing number of benzene rings. The partial molar volumes at infinite dilution of carbon dioxide-benzene derivative systems, except for the carbon dioxide-hydroxylbenzene system, are larger than that of the carbon dioxide-benzene system, and this tendency is contrary to the effect of the functional group on the Margules constant.
CONCLUSION
The vapor-liquid equilibrium data of twenty-eight carbon dioxidearomatic compound systems are correlated by the Soave-Redlich-Kwong equation of state with a binary interaction parameter. Henry’s constant, the partial molar volume of carbon dioxide at infinite dilution and the Mar-
21
gules constant are then determined by fitting the Krichevsky-Ilinskaya equation to the solubility data with the obtained optimal kij value. Henry’s constant increases with reduced temperature, but when the reduced temperature is larger than about 0.85, Henry’s constant decreases on increasing the reduced temperature. The relation between Henry’s constant and the reduced temperature appears to be parabolic. All of the functional groups increase Henry’s constant, and the hydroxyl group has a significant effect. The partial molar volume at infinite dilution and the Margules constant exponentially increase on increasing the reduced temperature. However, the substituent group has the opposite effect on both parameters. All of the functional groups, except hydroxyl, decrease the Margules constant and cause a small increase in the partial molar volume at infinite dilution. The relations between the partial molar volume at infinite dilution and the reduced temperature for carbon dioxide-benzene derivative systems are similar to those of carbon dioxide-naphthalene derivative systems. Therefore the correlations to express the reduced-temperature-dependent partial molar volume at infinite dilution are proposed for carbon dioxide-aromatic compound binary systems at the reduced temperature from 0.385 to 0.944.
ACKNOWLEDGMENT
Acknowledgment is made to the National Science Council of the Republic of China (NSC 81-0402-EOO6-13) for financial support of this work.
LIST OF SYMBOLS
A
0 f H k N
a R T
V u E
Margules constant (J mol-‘) parameters in the modified Soave equation of state fugacity (atm) Henry’s constant (atm) binary interaction parameter number of benzene rings number of moles pressure (atm) universal gas constant temperature (K) total volume (ml) molar volume (ml mol-l) partial molar volume (ml mol-‘)
22
x Y
z
mole fraction in the liquid phase mole fraction in the vapor phase mole fraction (liquid or vapor phase)
Greek letters
4 0
fugacity coefficient acentric factor
Superscripts L
; 00
liquid phase saturated property vapor phase infinite dilution
Subscripts
1 2 C
i,j r
component 1 (solute), carbon dioxide component 2 (solvent), aromatic compound critical property component i, j reduced property
REFERENCES Ambrose, D., 1978, corrected March 1980. Correlation and estimation of vapor-liquid critical properties. I. Critical temperatures of organic compounds. Natl. Phys. Lab. U.K. Rep., 92. Ambrose, D., 1979. Correlation and estimation of vapor-liquid critical properties. II. Critical pressures and volumes of organic compounds. Natl. Phys. Lab. U.K. Rep., 98. API Monograph Series., 1979a (January). Anthracene and phenanthrene. American Petroleum Institute, Washington, DC, Monograph No. 708. API Monograph Series., 19791, (March). Four-ring condensed aromatic compounds. American Petroleum Institute, Washington, DC, Monograph No. 709. Barrick, M.W., Anderson, J.M. and Robinson, Jr., R.L., 1987. Solubilities of carbon dioxide in naphthalene, phenanthrene, and pyrene at pressures to 10.6 MPa and temperatures from 373 to 433 K. J. Chem. Eng. Data, 32: 372-374. Bender, E., Klein, U., Schmitt, W.Ph. and Prausnitz, J.M., 1984. Thermodynamics of gas solubility: Relation between equation-of-state and activity-coefficient models. Fluid Phase Equilibria, 15: 241-255. Chou, G.F., Forbert, R.R. and Prausnitz, J.M., 1990. High-pressure vapor-liquid equilibria for CO, /n-decane, CO,/tetralin, and CO, /decane/tetralin at 71.1 and 104.4”C. J. Chem. Eng. Data, 35: 26-29.
23 Graboski, MS. and Daubert, T.E., 1978. A modified Soave equation of state for phase equilibrium calculations. Ind. Eng. Chem. Process Des. Dev., 17: 443. Inomata, H., Tuchiya, K., Aria, K. and Saito, S., 1986. Measurement of vapor-liquid equilibria at elevated temperatures and pressures using a flow type apparatus. J. Chem. Eng. Jpn., 19: 386-391. Inomata, H., Arai, K. and Saito, S., 1987. Vapor-liquid equilibria for CO,/hydrocarbon mixtures at elevated temperatures and pressures. Fluid Phase Equilibria, 36: 107-119. Jan, D.S. and Tsai, F.N., 1991. Modeling phase behavior of carbon dioxide with aromatic solvents. Ind. Eng. Chem. Res., 30: 1965-1970. Kaminishi, G.I., Yokoyama, C. and Takahashi, S., 1987. Vapor pressures of binary mixtures of carbon dioxide with benzene, n-hexane and cyclohexane up to 7 MPa. Fluid Phase Equilibria, 34: 83-99. Kim, C.H., Vimalchand, P. and Donohue, M.D., 1986. Vapor-liquid equilibria for binary mixtures of carbon dioxide with benzene, toluene and p-xylene. Fluid Phase Equilibria, 31: 299-311. Kim, C.H., Clark, A.B., Vimalchand, P. and Donohue, M.D., 1989. High-pressure binary phase equilibria of aromatic hydrocarbons with CO, and C,H,. J. Chem. Eng. Data, 34: 391-395. Krichevsky, I.R. and Ilinskaya, A.A., 1945. Partial molar volumes of gases dissolved in liquids (the thermodynamics of dilute solutions of nonelectrolytes). Acta Physicochim. URSS, 20: 327-348. Kulkami, AA., Luks, K.D. and Kohn, J.P., 1974. Phase-equilibria behavior of systems carbon dioxide-2-methylnaphthalene and carbon dioxide- n-decane-2-methylnaphthalene. J. Chem. Eng. Data, 19: 349-354. Lansangan, R.M., Jangkamolkulchai, A. and Luks, K.D., 1987. Binary vapor-liquid equilibria behavior in the vicinity of liquid-liquid-vapor loci. Fluid Phase Equilibria, 36: 49-66. Lee, B.I. and Kesler, M.G., 1975. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J., 21: 510-527. Lee, R.J. and Chao, KC., 1988. Extraction of I-Methylnaphthalene and m-cresol with supercritical carbon dioxide and ethane. Fluid Phase Equilibria, 43: 329-340. Mohamed, R.S. and Holder, G.D., 1987. High pressure phase behavior in systems containing CO, and heavier compounds with similar vapor pressures. Fluid Phase Equilibria, 32: 295-317. Morris, W.O. and Donohue, M.D., 1985. Vapor-liquid equilibria in mixtures containing carbon dioxide, toluene, and I-methylnaphthalene. J. Chem. Eng. Data, 30: 259-263. Nagarajan, N. and Robinson, Jr., R.L., 1987. Equilibrium phase compositions, phase densities, and inter-facial tensions for CO, + hydrocarbon systems. 3. CO, + cyclohexane. 4. CO, +benzene. J. Chem. Eng. Data, 32: 369-371. Ng, H.J. and Robinson, D.B., 1978. Equilibrium phase properties of the toluene-carbon dioxide system. J. Chem. Eng. Data, 23: 325-327. Ng, H.J., Huang, S.S.S. and Robinson, D.B., 1982. Equilibrium phase properties of selected m-xylene binary systems, m-xylene-methane and m-xylene-carbon dioxide. J. Chem. Eng. Data, 21119-122. Occhiogrosso, R.N., Igel, J.T. and McHugh, M.A., 1986. Phase behavior of carbon dioxidearomatic hydrocarbon mixtures. Fluid Phase Equilibria, 26: 165-179. Ohgaki, K. and Katayama, T., 1976. Isothermal vapor-liquid equilibrium data for binary systems containing carbon dioxide at high pressures: methanol-carbon dioxide, nhexane-carbon dioxide, and benzene-carbon dioxide systems. J. Chem. Eng. Data, 21: 53-55.
24
Reid, R.C., Prausnitz, J.M. and Poling, B.E., 1988. The Properties of Gases and Liquids. 4th edn., McGraw-Hill, New York. Renon, H., Laugier, S., Schwartzentruber, J. and Richon, D., 1989. New determinations of high pressure vapor-liquid equilibria in binary systems containing n-propylbenzene with nitrogen or carbon dioxide consistent with the Prausnitz-Kesler test. Fluid Phase Equilibria, 51: 285-298. Sebastian, H.M., Lin, H.M. and Chao, KC., 1980a. Gas-liquid equilibrium of carbon dioxide plus m-cresol and carbon dioxide plus quinoline at elevated temperatures. J. Chem. Eng. Data, 25: 381-383. Sebastian, H.M., Simnick, J.J., Lin, H.M. and Chao, KC., 1980b. Gas-liquid equilibrium in mixtures of carbon dioxide + toluene and carbon dioxide + m-xylene. J. Chem. Eng. Data, 25: 246-248. Sebastian, H.M., Nageshwar, G.D., Lin, H.M. and Chao, K.C., 198Oc. Vapor-liquid equilibrium in binary mixtures of carbon dioxide+ diphenylmethane and carbon dioxide+ lmethylnaphthalene. J. Chem. Eng. Data, 25: 145-147. Sebastian, H.M., Nageshwar, G.D., Lin, H.M. and Chao, K.C., 1980d. Gas-liquid equilibria in mixtures of carbon dioxide and tetralin at elevated temperatures. Fluid Phase Equilibria, 4: 257-260. Suppes, G.J. and McHugh, M.A., 1989. Phase behavior of the carbon dioxide-styrene system. J. Chem. Eng. Data, 34: 310-312. Tiffin, D.L., DeVera, A.L., Luks, K.D. and Kohn, J.P., 1978. Phase-equilibria behavior of the binary systems carbon dioxide-n-butylbenzene and carbon dioxide- tran.r-decalin. J. Chem. Eng. Data, 23: 45-47. Tsai, F.N. and Yau, J.S., 1990. Vapor-liquid equilibria of carbon dioxide-normal paraffin systems. J. Chin, Inst. Chem. Eng., 21: 207-213. Vera, J.H. and Orbey, H., 1984. Binary vapor-liquid equilibria of carbon dioxide with 2-methyl-1-pentene, I-hexene, 1-heptene, and m-xylene at 303.15, 323.15, and 343.15 K. J. Chem. Eng. Data, 29: 269-272. Wilhoit, R.C. and Zwolinski, B.J., 1971. Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds. API44 TRC Publication 101, Texas A & M University, College Station, TX. Windholz, M., Budavari, S., Blumetti, R.F. and Otterbein, ES., 1983. The Merck Index, An Encyclopedia of Chemicals, Drugs, and Biologicals. 10th edn., Merck, Rahway NJ. Yau, J.S. and Tsai, F.N., 1992a. Solubility of carbon dioxide in phenanthrene and in pyrene. J. Chem. Eng. Data, in press. Yau, J.S. and Tsai, F.N., 1991b. Solubility of carbon dioxide in phenol and in catechol. J. Chem. Eng. Data, in press.
APPENDIX
A
Henry’s constant; the partial molar volume of solute at infinite dilution and the Margules constant are calculated by the Soave-Redlich-Kwong equation of state:
25
2%
RTbl + (~;-b~)~
a22cw
aJ5
2b2hI 2V,(a12 [
a22b1 + Rl-b; with (,I’= jjy - u;
1 W)
- b2)
+
- a121 - %2@1
bdbl - b2) - v’bl
- b2)
- a221 - 2a22w1
1
b2) - v’b21
RTb,v;( v; + b2)
- b2)
][++g-&]-;
R7b,’
v;(v; +
v;(b, - b2) - v’b2 b2)
2a12[ W3 -
(G - b212
RTb,”
+
+ v;(v;+b2)*
-
v;(b, - b2) - v’b2
A=-2 X
- v;(v;+b~)
+ b2)
[v;(v;+b2)]2 RT
%,bl
-
v;(b, - b,) - v’b2 (vi + b212
I)
(W @W
1
Correlation of solubilities of carbon dioxide in aromatic compounds Jun-Shun Yau and Fuan-Nan Tsai Department of Chemical Engineering, National Cheng Kung University, Tainan 70101 (Taiwan) (Received July 23, 1991; accepted in original form November 12, 1991)
ABSTRACT Yau, J.-S. and Tsai, F.-N., 1992. Correlation of solubilities of carbon dioxide in aromatic compounds. Fluid Phase Equilibria, 73: l-25. The solubilities of carbon dioxide in twenty-eight aromatic solvents are modeled Soave equation of state with one interaction parameter. Henry’s constant, the partial volume at infinite dilution and the Margules constant are evaluated from the parameters using the approach of Bender, Klein, Schmitt and Prausnitz (1984, Fluid Equilibria, 15 : 241-255).
by the molar above Phase
INTRODUCTION
Vapor-liquid equilibrium data are the essential element in the design and development of many industrial processes. Carbon dioxide is frequently found in many natural gases, crude oil and coal liquids. Hence, recent developments in coal-gasification, heavy fossil fuel, petroleum products and enhanced oil recovery operation have led to renewed interest in the solubility of carbon dioxide. This work is a continuation of our studies of vapor-liquid equilibria (VLE) of carbon dioxide-normal paraffin systems (Tsai and Yau, 1990). Previously, we have reported data on the solubility of carbon dioxide in four aromatic solvents; phenanthrene, pyrene, phenol and catechol (Yau and Tsai, 1992a,b). Robinson and co-workers (Nagarajan and Robinson, Correspondence to: Dr. Fuan-Nan Tsai, Department Cheng Kung University, Tainan 70101, Taiwan. 0378-3812/92/$05.00
of Chemical Engineering,
0 1992 Elsevier Science Publishers B.V. All rights reserved
National
1987; Bar-rick et al., 1987) have presented the solubility of carbon dioxide in benzene, naphthalene, phenanthrene and pyrene at temperatures up to 433 K and pressures up to 10.6 MPa. Chao and co-workers (Sebastian et al., 1980a,b,c,d; Lee and Chao, 1988) have reported the solubility of carbon dioxide in toluene, m-xylene, diphenylmethane, 1-methylnaphthalene, mcresol and tetralin over the temperature range 308.2-703.35 K and pressures up to 24 MPa. Donohue and co-workers (Morris and Donohue, 1985; Kim and co-workers, 1986,1989) have determined the vapor-liquid equilibrium data of carbon dioxide in benzene, toluene, p-xylene, l-methylnaphthalene, anisole, benzaldehyde and tetralin over the temperature range 343.0-413.15 K and pressure range 2.45-22.12 MPa. In the present study, a correlation is developed from VLE data of carbon dioxide-aromatic hydrocarbon systems on the basis of the Soave equation of state (Graboski and Daubert, 1978) with one interaction parameter. Henry’s constant, the partial molar volume of carbon dioxide at infinite dilution and the Margules constant are then obtained by fitting the Krichevsky-Ilinskaya equation (1945) to the data. CORRELATION WITH THE SOAVE EQUATION OF STATE
Experimental vapor-liquid equilibrium data of carbon dioxide in aromatic solvents were used to develop a correlation method in order to describe the vapor-liquid equilibria of these systems. The Soave equation of state with a binary interaction parameter is used for each binary system. For the Soave equation, the specific relations are a RT p=-(1) u-b u(u+b) where U= C
CZiZjUij
i
j
(3)
b = &bi aij =
(Qiiajj)‘.‘(l
-
kij)
(4)
aii = 0.42748aiR2T:/Pc,
(5)
bi = 0.08664RT,i/P,,
(6)
m, = 0.48508 + 1.551710, - 0.15613&
(8)
TABLB 1 Critical properties and acentric factors used in equation of state Substance
T, (K) P, (atm)
w
Substance
T, (K) PC (atm)
w
Carbon dioxide Benzene Naphth~ene Phenanthrene Pyrene Toluene Ethylbenzene nPropylbenzene Cumene n-Bu~fbenzene n-Hexyibenzene n-Heptylbenzene n-Octylbenzene o-Xylene m-Xyiene
304.1 562.2 748.4 873.2 938.2 591.8 617.2 638.2 631.1 660.5 696.7 727.6 729.3 630.3 617.1
0.239 0.212 0.302 0.54 0.344 0.263 0.302 0.344 0.326 0.393 0.489 0.533 0.577 0.310 0.325
p-Xylene 1-Methylnaphthalene 2-Methylnaphthalene Phenol Catechoi 1-Naphthol 2-Naphthol Benzaldehyde Styrene Anisole Diphenyl Diphenylmethane m-Cresol Tetralin
616.2 772 761 694.2 772.2 826.1 822.4 694.8 647 645.6 789 770 705.8 719
0.320 0.310 0,382 0.438 0.641 0.520 0.520 0.316 0.257 0.347 0.372 0.442 0.454 0.303
72.85 48.26 39.97 32.57 25.66 40.467 35.53 31.584 31.683 28.52 23.35 21.50 19.92 36.82 34.94
34.64 35.53 34.545 60.5 77.67 46.29 46.29 44.81 39.38 41.94 38.00 28.23 45.01 34.644
In fitting the equation of state to experimental data, the values for the optimized interaction parameters are dependent on the properties T,,, PC, and wi used in the evaluation of the pure-component parameters (a and b) in the equations. Table 1 presents the properties of each substance utilized in the present work. Except for n-hexylbenzene, n-heptylbenzene, n-oc@benzene, phenanthrene, pyrene, catechol, 1-naphthol and 2-naphthol, the data are taken from the property data bank of Reid et al. (1988). The critical properties and acentric factors of phenanthrene and pyrene were taken from the API Monograph Series (1979a,b). The values of critical temperature and critical pressure were estimated by the Ambrose method (1978, 19791, and the acentric factor was determined from the Lee-Kesler correlations (1975) for n-hexylbenzene, n-heptylbenzene, n-octylbenzene, catechol, 1-naphthol and Z-naphthol. The values of the normal boiling point needed in calculations of T, for n-hexylbenzene, n-heptylbenzene and n-octylbenzene are taken from API-44 Tables (Wilhoit and Zwolinski, 1970, and for catechol, I-naphthol and Z-naphthol they are taken from the Merck Index (Windholz et al., 1983).
CORRELATION
WITH THE ~IC~VSKY-ILINS~YA
EQUATION
Henry’s constant and the partial molar volume at infinite dilution are determined by fitting the Krichevs&Ilinskaya equation (1945) to the VLE
data. The equation is
ln(f1/4 = ln f&,2+A(x; -
l)/RT
+ VY(P - P,S)/RT
(9)
where the subscript 1 refers to the solute and 2 the solvent, H, 2 is Henry’s constant, Cy is the partial molar volume of the solute at infinite dilution, and Pi is the vapor pressure of the solvent. The expressions of the parameters in the Krichevsky-Ilinskaya equation can be derived from an equation of state by means of the following relations (Bender et al., 1984):
(11) A=-__
RT a 2 ax (In & + In P)T,*,=o 1
(12)
Bender et al. presented the method for the reduction and correlation of high-pressure gas-solubility data using the Krichevsky-Ilinskaya equation, a simple cubic equation of state with conventional mixing rules, and an experimental value for Henry’s constant. The partial molar volume and Margules constant are then obtained from the equation of state.
RESULTS AND DISCUSSION
The basic thermodynamic that at constant temperature is the same in both phases:
fiLfi
requirement for vapor-liquid equilibrium is and pressure the fugacity of each component
(13)
The fugacity coefficient of a component in a mixture, &, is defined as the ratio of the fugacity to its partial pressure. Replacing fugacities with fugacity coefficients, eqn. (13) becomes
(14) In this study, bubble-pressure calculations are used to fit the interaction parameter ktj. The pure-component parameters Tc,, PC,and oi used in the Soave equation of state are shown in Table 1. The calculated results are listed in Tables 2-7. In the calculation, the optimal binary parameter kij obtained by minimizing the bubble-pressure variance is independent of pressure and composition for each isothermal system.
Temp.
383.15 423.15 473.15 523.15
433.15 473.15 523.15 573.15
Phenanthrene
Pyrene
0.558 0.611 0.612 0.628 0.664 0.699 0.736
313.40 343.60 344.30 353.00 373.50 393.20 413.60
0.462 0.504 0.558 0.611
0.439 0.485 0.542 0.599
0.499 0.532 0.565
0.557
313.15
373.15 398.15 423.15
0.486 0.504 0.530 0.539
T,
273.15 283.15 298.15 303.15
(K)
Naphthalene
Benzene
Solvent
31.6 40.4 57.0 62.3
7.3-104.4 10 - 50 10 - 50 10 - 50
18.5-104.8 10 -100.8 10 - 50 10 - 50
10 -103.1 10 - 50 10 - 98.3
20.9- 58.4 22.6- 95.3 68.1-108.2 4.9- 61.9 6.6- 58.3 7.2- 58.8 38.2-151.9
14.7- 76.5
8.29.68.813.0-
(atm)
P range
879 985 1033 727 812 1006 1232 885 1185 1460 1837
56.3 61.0 66.2 52.9 58.8 68.0 80.5 71.9 82.4 98.3 119.6
271.0 323.4 348.9
2.88 4.45 2.00 1.49 2.20 3.61 3.74 3.42
15.62 15.39 16.82 16.98 30.38 38.97 42.47 46.58
7 12 5 5
365.4 439.9 542.4 587.1
7 5 5 5
5.7 21.1 66.5
7.3 13.0
490.9 646.3 690.1 701.4
141.3
13.61 14.24 13.04
12 5 12
4.64 1.72 2.38
799 823 772 1085 1155 1301 1213
52.3 58.7 58.7 62.0 68.4 76.6 85.9
103.9 137.9 133.8 173.7 196.3 220.1 211.5
6.3 71.6 321.1 282.9 241.1 158.0 238.7
2.89 4.39 1.89 4.07 2.15 3.28 1.52
704
95.9
34.2
2.29
52.0
A (J mol-‘) 863 852 753 843
CT (ml mol-‘1
Barrick et al. (1987) Yau and Tsai (1992a)
Barrick et al. (1987) Yau and Tsai (1992a)
Barrick et al. (1987) Jan and Tsai (1991)
Inomata et al. (1987) Kaminishi et al. 0987) Rim et al. (1986) Nagarajan and Robinson (1987) Ohgaki and Katayama (1976)
Reference
compound systems with various numbers
46.1 47.5 49.5 50.6
H,,, (atm) 62.7 73.2 83.2 95.8
AAD CAY x 104)
4.38 4.41 4.21 4.58
%AAD UP/P)
9.03 8.05 7.26 11.37 10.90 11.12 7.15
7.66
10.81 10.52 8.23 9.98
kij (x10*)
6 5 17 8 8 7 9
9
7 7 15 7
Data pts.
Soave correlation of solubility data and thermodynamic parameters for carbon dioxide-aromatic of benzene rings
TABLE 2
Temp. w
311.26 352.59 353.15 353.40 373.20 383.15 393.25 393.71 413.15 422.45 476.95 477.04 502.75 542.85
312.65 338.15 366.15
313.20 393.00 472.90
Solvent
Toluene
Ethylbenzene
n-Propylbenzene
0.491 0.616 0.741
10.9- 73.6 72.0-177.6 11.4-182.6
23.7- 71.2 40.4-105.6 41.0-140.6
3.3- 76.4 3.7-121.5 2.6-117.7 6.6- 61.0 5.1- 54.2 5.9-126.3 9.6- 63.7 4.0-151.0 7.0-130.0 19.5- 51.2 12.2- 50.3 11.6-150.2 20.4- 49.7 31.3- so.9
0.526 0.596 0.597 0.597 0.631 0.647 0.665 0.665 0.698 0.714 0.806 0.806 0.850 0.917
0.507 0.548 0.593
P range (atm)
T,
10.22 8.90 8.25 10.15 8.81 12.71
13 23 9
10.43 9.57 11.32 11.31 11.96 11.31 11.87 8.28 11.58 10.80 11.93, 11.23 12.78 17.00
k,, (x10*)
5 6 8
8 10 12 8 7 10 11 8 9 5 5 8 4 3
Data pts.
Soave correlation of solubility data and thermodynamic
TABLE 3
4.71 4.36 3.73
5.12 4.40 5.39
4.44 7.40 6.70 4.36 4.22 5.65 3.70 6.18 6.81 0.67 1.46 3.36 0.85 2.41
%AAD (AP/P)
parameters
8.7 25.6 43.2
8.8 24.4 58.9 147.2 231.4 137.0 108.8 130.8 185.0 59.4 150.7 204.1 216.0 380.7
x 104)
AAD CAY
94.6 179.9 257.2
98.0 122.5 152.7
101.9 150.2 162.5 162.8 192.0 198.9 213.7 190.0 230.4 232.6 261.7 257.9 261.5 245.9
H,,, (atm)
54.0 73.9 119.7
53.3 58.2 65.1
52.6 61.5 62.0 62.1 68.1 71.3 75.4 74.6 84.5 89.3 139.8 139.5 189.7 398.6
Dy (ml mol_‘)
458 608 1320
547 535 586
677 733 828 829 940 953 1038 851 1157 1192 2002 1961 2759 5743
Renon et al. (1989)
Mohamed and Holder (1987)
Kim et al. (19861 Morris and Donohue (1985) Ng and Robinson (1978) Sebastian et al. (198Ob)
Reference
systems
A (J mol-“1
for carbon dioxide-alkylbenzene
9.98.36.47.211.410.2-
7.85.7lO.l8.5-
14.6- 76.9 23.9-107.6 23.9-147.3
0.385 0.400 0.414 0.428 0.443 0.457
0.397 0.411 0.424 0.438
0.496 0.537 0.581
n-Heptyl- 268.15 benzene 278.15 288.15 298.15 308.15 318.15
288.15 298.15 308.15 318.15
312.65 338.15 366.15
n-Octylbenzene
o-Xylene
48.5 61.1 74.0 81.7
29.3 37.9 48.1 60.7 72.9 81.9
47.4 59.8 75.5 91.2
6.410.99.57.5-
0.414 0.428 0.442 0.457
288.15 298.15 308.15 318.15
n-Hexylbenzene
10 - 30 10 - 50
0.414 0.444
273.15 293.15
n-Butylbenzene
16.8- 64.0 17.8- 73.1 7.1- 85.9 8.9-116.0 29.8-151.1 34.1-169.0
0.474 0.484 0.501 0.536 0.575 0.607
299.25 305.65 316.25 338.35 363.15 383.15
Cumene
11 17 16
21 21 19 22
14 16 21 20 20 23
19 19 11 27
5 9
16 16 40 30 25 18
10.07 8.36 6.77
11.76 9.81 10.36 10.39
10.99 11.23 10.97 9.60 9.32 10.81
11.79 10.55 9.07 9.23
11.91 12.31
10.58 10.27 10.86 9.65 8.10 8.14
3.59 6.82 9.91
6.24 9.12 6.57 2.65
3.67 6.03 4.24 12.15 5.79 4.90
6.66 4.57 6.45 8.54
5.64 8.08
5.26 5.09 7.28 5.54 3.03 3.56
102.0 125.6 151.9
65.2 67.9 80.0 91.7
56.8 55.0 64.2 69.4 78.6 95.6
67.9 71.1 71.1 89.5
55.5 78.5
79.2 85.1 100.1 120.2 140.7 162.7
52.0 56.4 62.5
52.4 53.9 55.6 57.2
46.8 50.1 51.5 52.9 54.5 56.3
51.4 53.3 55.9 56.2
48.3 51.3
52.2 53.3 55.3 59.7 65.7 71.7
567 536 542
264 227 244 250
257 273 269 242 241 283
327 302 278 280
430 453
461 455 492 482 483 551
Mohamed and Holder (1987)
Lansangan et al. (1987)
Lansangan et al. (1987)
Lansangan et al. (1987)
Tiffin et al. (1978)
Occhiogrosso et al. (1986)
312.65 338.15 353.20 366.15 373.40 393.20
p-Xylene
0.507 0.549 0.573 0.594 0.606 0.638
303.15 0.491 310.90 0.504 312.65 0.507 323.15 0.524 338.15 0.548 338.70 0.549 343.15 0.556 366.15 0.593 394.30 0.639 462.15 0.749 477.60 0.774 502.05 0.814 543.35 0.881 582.55 0.944
m-Xylene
T,
Temp. WI
Solvent
TABLE 3 (continued)
5 11 6 5 7 9 5 8 10 4 9 4 5 3
6.6- 32.6 3.1- 79.0 13.1- 71.0 6.7- 32.9 23.7-101.9 4.0-111.8 16.0- 34.7 23.9-151.6 3.9-165.3 21.1- 51.9 8.8-167.5 21.2- 51.4 20.5- 50.9 31.1- 50.8
11.8- 71.9 23.4-106.4 4.5- 60.7 23.8-139.8 4.9- 58.5 7.0- 60.1
14 12 8 13 7 7
Data pts.
(atm)
P range
9.97 8.36 8.49 7.85 10.86 11.41
9.61 9.84 10.19 7.36 8.85 9.31 10.49 8.65 8.84 12.54 9.13 13.91 17.51 25.73
kij (x10’) %AAD
3.46 5.43 2.04 5.70 1.67 3.30
1.26 2.73 6.39 6.81 6.36 6.97 4.17 4.27 4.54 0.44 2.19 0.64 0.46 0.74
CAP/P)
235.8 292.4
189.9
25.9 9.3 10.9 24.7 21.6 59.0 35.1 43.6 41.7 29.5 136.1 79.6 129.6 90.4
AAD (AY x 104)
53.5 58.4 61.9 65.3 68.0 74.9
51.5 52.8 53.2 54.8 58.1 58.3 59.4 65.0 74.1 114.0 127.5 163.9 287.3 758.7
83.7 94.1 98.0 96.6 122.3 125.6 138.0 155.1 187.6 258.2 244.2 267.4 259.0 227.9 95.8 118.4 137.2 148.8 175.3 200.4
$7 (ml mol-‘1
H,,, (atm)
520 496 540 551 707 813
499 519 537 428 524 546 608 593 714 1401 1445 2131 3860 9612
(J mol-‘1
A
Kim et al. (1986) Mohamed and Holder (1987)
Mohamed and Holder (1987) Ng et al. (1982) Sebastian et al. (198Ob) Vera and Orbey (1984)
Reference
Temp. CKI
348.15 373.15 398.15 423.15
398.15 423.15 448.f5 473.15
Solvent
Phenol
Catechol
0.516 0.548 0.580 0.613
0.502 0.538 0,574 0.610
T,
10-M 10-50 IO-50 IO-50
10-50 IO-50 lO-5D IO-50
P range (atmf
5 5 5 5
5 5 5 5
Data pts,
-3.77 -3.99 -5.41 -6.53
7.53 7.72 7.19 6.31
k, (x10’)
Save correlation of solubility data and thermodynamic group numbers on benzene
TABLE 4
0.85 2.05 1.58 IS7
1.69 4.42 0.90 1.28
%AAD (AP/P)
12.3 12.5 8.5 25.3
2.2 5.2 13.1 20.8
AAD (Ay x IO*)
637.2 721.4 765.4 797.4
3259 378-8 430.2 466.5
H
43.3 45.6 48.1 51.2
45.3 48.6 52.1 56.3
Yau and Tsai 0992bI
Yau and Tsai 0992b)
1762 1877 1887 1960
Reference 1347 1465 1531 1597
& mol-‘1
compound systems with various hydrowl
$1 mol-‘)
-co
parameters for carbon dioxide-aromatic
308.15 328.15 353.15 373.15
343.10 0.531 24.4-128.0 372.30 0.577 33.0-168.0
Styrene
Anisole
0.476 0.507 0.546 0.577
343.00 0.494 27.9-134.0 372.60 0.536 35.0-180.7
26.6- 76.4 31.2- 99.2 38.3-134.9 43.0-160.3
(atm)
Benzaldehyde
P range
Temp. K)
Solvent
T,
5 5
9 9 8 8
5 5
Data pts.
5.27 4.63
11.33 9.53 8.74 7.95
3.25 3.38
4.82 4.24
7.06 8.39 8.48 7.34
3.04 2.85
%AAD
CAP/P)
(x10*)
56.0 25.5
24.9 34.4
?il mol-‘)
50.6 53.7 58.4 62.8
133.5 52.9 171.4 58.4
107.2 124.2 154.1 176.0
133.7 50.2 182.8 54.8
$&
516 577
661 608 632 660
454 557
;‘J mol-‘1
for other carbon dioxide-aromatic
(Ay ~10~)
AAD
parameters
k,j
Soave correlation of solubility data and thermodynamic single functional groups on benzene
TABLE 5 systems with various
Rim et al. (1989)
Suppes and McHugh (1989)
Rim et al. (1989)
Reference
compound
11.24 9.36 9.65 9.41
5 5
5 5
393.15 0.476 10 - 50 453.15 0.549 10 - 50
413.15 0.502 10 - 50 473.15 0.575 10 - 50
2-Naphthol
65 50 65 65 65
1-Naphthol
13.91 14.53 13.93 14.62 13.21
15 10 15 15 10
11 5 11 11 16
kij (X 10’)
2-Methyl307.15 0.404 naphthalene 323.15 0.425 324.15 0.426 348.15 0.458 373.15 0.490
Data pts. 13.02 12.89 12.65 12.63 11.00 10.74 14.85 15.55 16.62 26.25
(at&
P range
19.7-236.9 11 19.7-236.9 11 19.7-236.9 10 6 17.9-142.4 5 36.7-204.0 7 12.0-142.6 20.5- 50.2 4 21.0- 50.8 4 20.6- 48.9 4 30.2- 48.3 3
Temp. Tr 00
l-Methyl308.20 0.399 naphthalene 318.20 0.412 328.20 0.425 353.15 0.457 372.60 0.483 413.15 0.535 463.05 0.600 543.45 0.704 623.55 0.808 703.55 0.911
Solvent
0.64 0.62
1.02 0.29
6.41 3.61 2.37 1.83 6.43
6.75 8.51 9.01 2.79 6.96 4.10 0.53 0.54 1.43 0.26
CAP/P)
%AAD
0.4
99.2 65.4 67.0 1.6 28.1 2.7 17.5 45.6 131.2 150.9
500.8 621.0
486.1 588.9
136.2 170.6 166.9 217.6 247.8
51.9 61.2
49.4 57.5
47.7 49.7 49.8 53.2 57.0
126.5 48.4 141.9 49.6 157.0 50.9 202.3 54.3 220.8 57.3 279.7 65.1 387.2 79.1 434.6 116.0 408.9 202.8 334.9 562.7
AAD H,,, n: (Ay x 104) (atm) (ml mol-‘1
Jan and Tsai (1991)
Jan and Tsai (1991)
1115 1240 1102 1340
Jan and Tsai (1991) Kulkarni et al. (1974)
Kim et al. (1989) Lee and Chao (1988) Morris and Donohue (1985) Sebastian et al. (1980~)
625 667 645 708 708
592 600 605 646 630 730 1117 1788 3274 8780
Reference
derivative systems
(J mol-‘)
A
Soave correlation of solubility data and thermodynamic parameters for carbon dioxide-naphthalene
TABLE 6
0.473
0.536 0.600
0.601 0.705 0.810 0.914
0.437 0.451 0.465 0.656 0.769 0.885 0.942
0.478 0.479 0.481 0.519 0.525 0.578 0.643 0.725 0.756 0.867 0.924
423.15 473.15
462.75 542.55 623.35 703.75
308.20 318.20 328.20 462.65 542.45 624.45 664.65
343.60 344.25 345.90 373.10 377.55 415.30 461.95 521.20 543.55 623.35 664.65
Diphenylmethane
m-Cresol
Tetralin
Diphenyl
T,
Temp. (IQ 373.15
Solvent
49.6 50.3 49.4 50.0
32.0-189.1 40.2-188.1 46.0-157.2 31.3-218.3 49.2-240.6 40.2-219.5 20.2- 50.6 45.0-224.3 19.9- 50.3 19.7- 40.5 30.8- 50.4
19.7-236.9 19.7-236.9 19.7-236.9 19.3- 51.1 20.1- 49.9 20.5- 50.2 40.5- 50.1
18.920.219.229.5-
10 - 50 10 - 50
10 - 50
(atm>
P range 11.36 9.11 7.52 12.88 13.04 19.26 35.07 10.86 10.58 10.33 10.94 11.48 15.03 19.70 10.43 10.12 12.16 9.94 10.68 12.67 15.00 15.07 16.14 22.21 34.13
5 5
5 4 4 3
9 9 9 4 4 4 2
6 7 7 5 7 6 4 7 4 4 3
k,, (~10~)
5
Data pts.
4.44 8.12 11.25 5.82 7.72 7.72 0.58 5.51 1.03 1.19 0.62
5.76 5.59 7.62 2.15 2.17 0.34 0.42
0.44 0.50 0.44 0.65
1.81 0.45
2.69
%AAD (APiP)
319.1 356.5 354.9 291.2
8.0 6.7 29.8 104.3
35.3 178.7 24.6 18.5 111.2 12.8 13.6 158.9 104.4 146.5 88.1 153.2 152.0 169.5 193.5 205.7 273.8 340.6 365.4 370.7 340.7 306.5
158.4 183.6 195.6 440.6 470.5 406.9 334.6
326.9 381.1
33.1 34.1 30.2 7.6 53.5 130.3 196.3
260.4
0.2
$A)
12.6 183.4
AAD (Ay ~10~)
55.1 55.2 55.7 60.6 61.6 71.1 87.7 121.6 142.0 313.7 666.4
44.5 45.2 46.6 72.5 113.2 262.3 611.1
83.2 123.1 222.3 650.0
54.1 62.3 74.0
$1 moI-‘)
544 534 616 596 636 844 1182 1726 2085 4822 9919
873 866 876 1436 2320 5265 10996
815 1367 2856 8315
723 790 962
Chou et al. (1990) Inomata et al. (1986) Kim et al. (1989) Sebastian et al. (1980d)
Lee and Chao (1988) Sebastian et al. (1980a)
Sebastian et al. (198Oc)
Jan and Tsai (1991)
Reference
compound systems
(J mole’)
A
Soave correlation of solubility data and thermodynamic parameters for other carbon dioxide-aromatic
TABLE 7
13 000.
I
,
I
I
8,
I
I
I
I
I
obenzene qnaphthalene ~phenanthrene
0.4
0.6
0.6
0.7
0.8
0.9
1.0
Tr, 2 Fig. 1. Plot of Henry’s constant vs. the reduced temperature compound systems with various numbers of benzene rings.
for carbon dioxide-aromatic
Henry’s constant, the partial molar volume at infinite dilution and the Margules constant can be calculated from eqns. (A&643), as shown in Appendix A, by using the obtained optimal interaction parameters. The calculated results are listed in Tables 2-7 for twenty-eight carbon dioxidearomatic compound systems. Table 2 includes four systems of carbon dioxide in one- to four-ring aromatic solvents. Figure 1 shows Henry’s constant as a function of the reduced temperature for different numbers of benzene rings. It can be seen that Henry’s constant increases as the reduced temperature and the number of benzene rings increase. Figure 2 shows the calculated results of the Margules constant as a function of the reduced temperature with a different number of benzene rings. As observed in Fig. 2, we note that the Margules constant increases on increasing the reduced temperature and the number of benzene rings. All points shown *in Figs. 1 and 2 are calculated from eqns. (10) and (12) respectively, and the lines shown in these figures combine only the calculated points and indicate that the tendencies of Henry’s constant and the Margules constant change with the reduced temperature. Table 3 presents the Soave correlation of solubility data and the thermodynamic parameters for carbon dioxide-alkylbenzene systems. The obtained data are illustrated in Figs. 3 and 4 for Henry’s constant and the Margules constant as a function of the reduced temperature, respectively. Figure 3 shows that Henry’s constant increases as the reduced tempera-
:&
\lOOO
0 0
g
0.3
0.4
0.5
:
0
0
0
00
0
0
0.6
benzene
0.7
Tr,
0.3
0.9
1.0
2
Fig. 2. Plot of the Margules constant vs. the reduced temperature aromatic compound systems with various numbers of benzene rings.
for carbon dioxide-
ture, the carbon numbers of the alkyl group, and the methyl group numbers increase. If the reduced temperature is larger than 0.85 for the binary systems carbon dioxide-toluene and carbon dioxide-m-xylene, Henry’s
300. 2 “nN . 2
I ,,,,,,I +n-butylbenzene x n-hex lbenzene * n-hep i ylbenzene - ln-octylbenzene lo-xylene
I ,,I
I
200 - rp-xylene
I ! ii x &loo
-
I
A ethylbenzene 0 n-propylbenzene 0 cumene calculated 0 1”“‘1”‘*” 0.3 0.4 0.5
0.6
Tr,
0.7 2
0.3
0.9
1.0
Fig. 3. Plot of Henry’s constant vs. the reduced temperature zene systems.
for carbon dioxide-alkylben-
15
10000 benzene 0 toluene ~3ethylbenzene 0 n-propylbenzene 0 cumene + n-butylbenzene x n-hezylbenzene Z+n-heptylbenzene * n-octylbenzene l o-xylene l m-xylene A p-zylene
0
8000
'2; 8000 a > 4
4000
0.8 0.7 0.8 0.0 1.0
Tr,z Fig. 4. Plot of the Margules constant vs. the reduced temperature kylbenzene systems.
for carbon dioxide-al-
constant decreases with increasing the reduced temperature. Henry’s constants of aromatic compounds with different carbon numbers of the alkyl group on benzene are qualitatively and quantitatively similar. Therefore the relation can be correlated by
f4,2- (C,benzene - e,2Y =434.90 - 3059.7 Tr,2+ 6559.2 7$
(15) where 0.385 I Tr,2 I 0.911. The average absolute deviation is about 6.98% when it is estimated from eqn. (15) for carbon dioxide-alkylbenzene systems in the work. Figure 4 shows that the Margules constant increases with reduced temperature and decreases with increasing carbon numbers of the alkyl group. It indicates that the Margules constant is qualitatively and quantitatively similar to different carbon numbers of the alkyl group on benzene. Thus, the carbon number of the alkyl group, the methyl group numbers and
16 1ooo
I
I
1
I
I
I
8
I
n
I
1
,
,I
0 benzene 0 phenol A cateahol m; ?Ei 600
P
R! G400-
8’
m!,[, 0 0.4
, 0.6
0.6
0.7
0.2
,
0.0
1.0
2
Tr,
Fig. 5. Plot of Henry’s constant vs. the reduced temperature for carbon dioxide-aromatic compound systems with various numbers of hydroxyl groups on benzene.
the orientation on benzene, do not seem to have much effect on Henry’s constant and the Margules constant. The Soave correlation of solubility data and the thermodynamic parameters for carbon dioxide-hydroxylbenzene are given in Table 4. Figure 5
benzene o phenol A catechol
0
0’ 0.4
’
’ o ’ 0.6 0.6
’
’ 0.7
Tr,
a ’
0.0
n ’
0.9
p
2
Fig. 6. Plot of the Margules constant vs. the reduced temperature for carbon dioxidearomatic compound systems with various numbers of hydroxyl groups on benzene.
17 500
r,,,,,,,,,,
o benzene
_I/ 0 “n”““” 0.4 0.5 0.5
0 toluene A phenol 0 benzaldehyde n styrene A aniaole
0.7
0.0
0.0
1.0
Tr,a Fig. 7. Plot of Henry’s constant vs. the reduced temperature for carbon dioxide-aromatic compound systems with various single functional groups on benzene.
shows the calculated results of Henry’s constant as a function of the reduced temperature with different hydroxyl group numbers. It indicates that Henry’s constant increases as the reduced temperature and hydroxyl
4000
l
benzaldehyde
z Ei > 4 2ooo
0 0.9 0.4 0.5 0.5 0.7 0.2 0.0 Tr, 2
1.0
Fig. 8. Plot of the Margules constant vs. the reduced temperature for carbon dioxidearomatic compound systems with various single functional groups on benzene.
18
600 -
0 1 -naphthol
200 -
A 2-naphthol
_
0 l-methylnaphthalene
* 2-methylnaphthalene 0 *“““‘1”” 0.3 0.4 0.6
0.6
0.7
0.0
0.9
1.0
Tr,2 Fig. 9. Plot of Henry’s constant thalene
derivative
vs. the reduced
temperature
for carbon
dioxide-naph-
systems.
group numbers increase. Figure 6 shows that the relations between the Margules constant and the reduced temperature and hydroxyl group numbers are similar to those of Henry’s constant. We have studied the effect of various substituent groups with the hydroxyl group on benzene in Tables 2-4. The other single functional groups on benzene are included in Table 5. The data are illustrated in Figs. 7 and 8 for Henry’s constant and the Margules constant as a function of the reduced temperature, respectively. Henry’s constant and the Margules constant increase with reduced temperature. Henry’s constants of carbon dioxide in different solvents with a single substituent group on benzene are in the order of phenol > benzaldehyde > styrene > anisole > toluene > benzene. It can be seen that all of the functional groups increase the values of Henry’s constant. The Margules constant of the carbon dioxide-solvent system with a single substituent group on benzene is in the order of phenol > benzene > toluene > styrene > benzaldehyde > anisole. It indicates that all of the functional groups, except the hydroxyl group, decrease the Margules constant. The resonance effect of the ring stabilizes the phenoxide ion to a greater extent than the phenol, and thus shifts the equilibrium towards ionization. Again, carbon dioxide has quite a large quadrupole moment, so the intermolecular forces must be significant for the carbon dioxide-phenol system. As a result, the Margules constant of the carbon dioxide-phenol system is larger than that of other systems, as shown in Fig. 8.
19
_ _ _
o naphthalene o l-naphthol A 2-naphthol 0 1-methylnaphthalene o 2-methylnaphthalene
ol”“““““D 0.8
0.4
0.6
0.2
Tr,
0.7
0.2
0.9
1
1.0
2
Fig. 10. Plot of the Margiles constant vs. the reduced temperature for carbon dioxidenaphthalene derivative systems.
Henry’s constant and the Margules constant at different reduced temperatures for carbon dioxide-naphthalene derivative systems are listed in Table 6, and these data are illustrated in Figs. 9 and 10, respectively. The tendencies of Henry’s constant and the Margules constant versus the reduced temperature for carbon dioxide-benzene derivative systems and carbon dioxide-naphthalene derivative systems are similar in every respect. Table 7 presents correlations of solubility data and the thermodynamic parameters for other carbon dioxide-aromatic solvent systems calculated by the Soave equation. The calculated Henry’s constant, the partial molar volume at infinite dilution and the Margules constant determined by the Krichevsky-Ilinskaya equation with the optimum values of kij for each isotherm, are also listed in the table. Figure 11 shows the calculated partial molar volume at infinite dilution as a function of the reduced temperature for twenty-eight carbon dioxidearomatic compound binary systems. It indicates that the partial molar volume at infinite dilution increase with increasing reduced temperature. The relations can be correlated by ln( ET/N:.‘) = 5.0225 - 6.0150 Tr,* + 7.4051 Tz2 where 0.385 5 T,,* I 0.750, and
(16)
ln( Ey/N2.5) = 4.6766 + 7.2604( Tr,*- 0.75) - 47.482( Tr,2- 0.75)2 + 321.97( q,2 - o.75)3 where 0.750 I Tr,2I 0.944.
(17)
20
800
1’1’1’1
11’1’
0 bensene
4 l-nephthol
0 naphthelene r(rphenentbrenr v t&r + pvene 0 toluene A ethylbensene 0 n-propylbensene * cumene + n-butylbenrens x n-hexylbensene * n-hept@benrene * n-oct#bensene Q o-xylene * m-xylene (b p-@en8 l phenol n c&echo1 A bensaldehyde 8 etyrene 0 enieole 0 m-creeol o l-methylnaphthelene + 2-methylnaphthelene 0 diphenylmethane o diphenyl
0.3
0.4
0.5
0.5
0.7
0.8
0.9
1.0
Tr,2 Fig. 11. Plot of the partial molar volume at infinite dilution vs. the reduced temperature twenty-eight binary carbon dioxide-aromatic compound systems.
for
The average absolute deviations in the partial molar volume at infinite dilution are about 13.19% for eqn. (16) and 4.51% for eqn. (17). The number of benzene rings, N, of tetralin is 1.5. Taking a careful view, we find that the partial molar volume at infinite dilution increases with increasing number of benzene rings. The partial molar volumes at infinite dilution of carbon dioxide-benzene derivative systems, except for the carbon dioxide-hydroxylbenzene system, are larger than that of the carbon dioxide-benzene system, and this tendency is contrary to the effect of the functional group on the Margules constant.
CONCLUSION
The vapor-liquid equilibrium data of twenty-eight carbon dioxidearomatic compound systems are correlated by the Soave-Redlich-Kwong equation of state with a binary interaction parameter. Henry’s constant, the partial molar volume of carbon dioxide at infinite dilution and the Mar-
21
gules constant are then determined by fitting the Krichevsky-Ilinskaya equation to the solubility data with the obtained optimal kij value. Henry’s constant increases with reduced temperature, but when the reduced temperature is larger than about 0.85, Henry’s constant decreases on increasing the reduced temperature. The relation between Henry’s constant and the reduced temperature appears to be parabolic. All of the functional groups increase Henry’s constant, and the hydroxyl group has a significant effect. The partial molar volume at infinite dilution and the Margules constant exponentially increase on increasing the reduced temperature. However, the substituent group has the opposite effect on both parameters. All of the functional groups, except hydroxyl, decrease the Margules constant and cause a small increase in the partial molar volume at infinite dilution. The relations between the partial molar volume at infinite dilution and the reduced temperature for carbon dioxide-benzene derivative systems are similar to those of carbon dioxide-naphthalene derivative systems. Therefore the correlations to express the reduced-temperature-dependent partial molar volume at infinite dilution are proposed for carbon dioxide-aromatic compound binary systems at the reduced temperature from 0.385 to 0.944.
ACKNOWLEDGMENT
Acknowledgment is made to the National Science Council of the Republic of China (NSC 81-0402-EOO6-13) for financial support of this work.
LIST OF SYMBOLS
A
0 f H k N
a R T
V u E
Margules constant (J mol-‘) parameters in the modified Soave equation of state fugacity (atm) Henry’s constant (atm) binary interaction parameter number of benzene rings number of moles pressure (atm) universal gas constant temperature (K) total volume (ml) molar volume (ml mol-l) partial molar volume (ml mol-‘)
22
x Y
z
mole fraction in the liquid phase mole fraction in the vapor phase mole fraction (liquid or vapor phase)
Greek letters
4 0
fugacity coefficient acentric factor
Superscripts L
; 00
liquid phase saturated property vapor phase infinite dilution
Subscripts
1 2 C
i,j r
component 1 (solute), carbon dioxide component 2 (solvent), aromatic compound critical property component i, j reduced property
REFERENCES Ambrose, D., 1978, corrected March 1980. Correlation and estimation of vapor-liquid critical properties. I. Critical temperatures of organic compounds. Natl. Phys. Lab. U.K. Rep., 92. Ambrose, D., 1979. Correlation and estimation of vapor-liquid critical properties. II. Critical pressures and volumes of organic compounds. Natl. Phys. Lab. U.K. Rep., 98. API Monograph Series., 1979a (January). Anthracene and phenanthrene. American Petroleum Institute, Washington, DC, Monograph No. 708. API Monograph Series., 19791, (March). Four-ring condensed aromatic compounds. American Petroleum Institute, Washington, DC, Monograph No. 709. Barrick, M.W., Anderson, J.M. and Robinson, Jr., R.L., 1987. Solubilities of carbon dioxide in naphthalene, phenanthrene, and pyrene at pressures to 10.6 MPa and temperatures from 373 to 433 K. J. Chem. Eng. Data, 32: 372-374. Bender, E., Klein, U., Schmitt, W.Ph. and Prausnitz, J.M., 1984. Thermodynamics of gas solubility: Relation between equation-of-state and activity-coefficient models. Fluid Phase Equilibria, 15: 241-255. Chou, G.F., Forbert, R.R. and Prausnitz, J.M., 1990. High-pressure vapor-liquid equilibria for CO, /n-decane, CO,/tetralin, and CO, /decane/tetralin at 71.1 and 104.4”C. J. Chem. Eng. Data, 35: 26-29.
23 Graboski, MS. and Daubert, T.E., 1978. A modified Soave equation of state for phase equilibrium calculations. Ind. Eng. Chem. Process Des. Dev., 17: 443. Inomata, H., Tuchiya, K., Aria, K. and Saito, S., 1986. Measurement of vapor-liquid equilibria at elevated temperatures and pressures using a flow type apparatus. J. Chem. Eng. Jpn., 19: 386-391. Inomata, H., Arai, K. and Saito, S., 1987. Vapor-liquid equilibria for CO,/hydrocarbon mixtures at elevated temperatures and pressures. Fluid Phase Equilibria, 36: 107-119. Jan, D.S. and Tsai, F.N., 1991. Modeling phase behavior of carbon dioxide with aromatic solvents. Ind. Eng. Chem. Res., 30: 1965-1970. Kaminishi, G.I., Yokoyama, C. and Takahashi, S., 1987. Vapor pressures of binary mixtures of carbon dioxide with benzene, n-hexane and cyclohexane up to 7 MPa. Fluid Phase Equilibria, 34: 83-99. Kim, C.H., Vimalchand, P. and Donohue, M.D., 1986. Vapor-liquid equilibria for binary mixtures of carbon dioxide with benzene, toluene and p-xylene. Fluid Phase Equilibria, 31: 299-311. Kim, C.H., Clark, A.B., Vimalchand, P. and Donohue, M.D., 1989. High-pressure binary phase equilibria of aromatic hydrocarbons with CO, and C,H,. J. Chem. Eng. Data, 34: 391-395. Krichevsky, I.R. and Ilinskaya, A.A., 1945. Partial molar volumes of gases dissolved in liquids (the thermodynamics of dilute solutions of nonelectrolytes). Acta Physicochim. URSS, 20: 327-348. Kulkami, AA., Luks, K.D. and Kohn, J.P., 1974. Phase-equilibria behavior of systems carbon dioxide-2-methylnaphthalene and carbon dioxide- n-decane-2-methylnaphthalene. J. Chem. Eng. Data, 19: 349-354. Lansangan, R.M., Jangkamolkulchai, A. and Luks, K.D., 1987. Binary vapor-liquid equilibria behavior in the vicinity of liquid-liquid-vapor loci. Fluid Phase Equilibria, 36: 49-66. Lee, B.I. and Kesler, M.G., 1975. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J., 21: 510-527. Lee, R.J. and Chao, KC., 1988. Extraction of I-Methylnaphthalene and m-cresol with supercritical carbon dioxide and ethane. Fluid Phase Equilibria, 43: 329-340. Mohamed, R.S. and Holder, G.D., 1987. High pressure phase behavior in systems containing CO, and heavier compounds with similar vapor pressures. Fluid Phase Equilibria, 32: 295-317. Morris, W.O. and Donohue, M.D., 1985. Vapor-liquid equilibria in mixtures containing carbon dioxide, toluene, and I-methylnaphthalene. J. Chem. Eng. Data, 30: 259-263. Nagarajan, N. and Robinson, Jr., R.L., 1987. Equilibrium phase compositions, phase densities, and inter-facial tensions for CO, + hydrocarbon systems. 3. CO, + cyclohexane. 4. CO, +benzene. J. Chem. Eng. Data, 32: 369-371. Ng, H.J. and Robinson, D.B., 1978. Equilibrium phase properties of the toluene-carbon dioxide system. J. Chem. Eng. Data, 23: 325-327. Ng, H.J., Huang, S.S.S. and Robinson, D.B., 1982. Equilibrium phase properties of selected m-xylene binary systems, m-xylene-methane and m-xylene-carbon dioxide. J. Chem. Eng. Data, 21119-122. Occhiogrosso, R.N., Igel, J.T. and McHugh, M.A., 1986. Phase behavior of carbon dioxidearomatic hydrocarbon mixtures. Fluid Phase Equilibria, 26: 165-179. Ohgaki, K. and Katayama, T., 1976. Isothermal vapor-liquid equilibrium data for binary systems containing carbon dioxide at high pressures: methanol-carbon dioxide, nhexane-carbon dioxide, and benzene-carbon dioxide systems. J. Chem. Eng. Data, 21: 53-55.
24
Reid, R.C., Prausnitz, J.M. and Poling, B.E., 1988. The Properties of Gases and Liquids. 4th edn., McGraw-Hill, New York. Renon, H., Laugier, S., Schwartzentruber, J. and Richon, D., 1989. New determinations of high pressure vapor-liquid equilibria in binary systems containing n-propylbenzene with nitrogen or carbon dioxide consistent with the Prausnitz-Kesler test. Fluid Phase Equilibria, 51: 285-298. Sebastian, H.M., Lin, H.M. and Chao, KC., 1980a. Gas-liquid equilibrium of carbon dioxide plus m-cresol and carbon dioxide plus quinoline at elevated temperatures. J. Chem. Eng. Data, 25: 381-383. Sebastian, H.M., Simnick, J.J., Lin, H.M. and Chao, KC., 1980b. Gas-liquid equilibrium in mixtures of carbon dioxide + toluene and carbon dioxide + m-xylene. J. Chem. Eng. Data, 25: 246-248. Sebastian, H.M., Nageshwar, G.D., Lin, H.M. and Chao, K.C., 198Oc. Vapor-liquid equilibrium in binary mixtures of carbon dioxide+ diphenylmethane and carbon dioxide+ lmethylnaphthalene. J. Chem. Eng. Data, 25: 145-147. Sebastian, H.M., Nageshwar, G.D., Lin, H.M. and Chao, K.C., 1980d. Gas-liquid equilibria in mixtures of carbon dioxide and tetralin at elevated temperatures. Fluid Phase Equilibria, 4: 257-260. Suppes, G.J. and McHugh, M.A., 1989. Phase behavior of the carbon dioxide-styrene system. J. Chem. Eng. Data, 34: 310-312. Tiffin, D.L., DeVera, A.L., Luks, K.D. and Kohn, J.P., 1978. Phase-equilibria behavior of the binary systems carbon dioxide-n-butylbenzene and carbon dioxide- tran.r-decalin. J. Chem. Eng. Data, 23: 45-47. Tsai, F.N. and Yau, J.S., 1990. Vapor-liquid equilibria of carbon dioxide-normal paraffin systems. J. Chin, Inst. Chem. Eng., 21: 207-213. Vera, J.H. and Orbey, H., 1984. Binary vapor-liquid equilibria of carbon dioxide with 2-methyl-1-pentene, I-hexene, 1-heptene, and m-xylene at 303.15, 323.15, and 343.15 K. J. Chem. Eng. Data, 29: 269-272. Wilhoit, R.C. and Zwolinski, B.J., 1971. Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds. API44 TRC Publication 101, Texas A & M University, College Station, TX. Windholz, M., Budavari, S., Blumetti, R.F. and Otterbein, ES., 1983. The Merck Index, An Encyclopedia of Chemicals, Drugs, and Biologicals. 10th edn., Merck, Rahway NJ. Yau, J.S. and Tsai, F.N., 1992a. Solubility of carbon dioxide in phenanthrene and in pyrene. J. Chem. Eng. Data, in press. Yau, J.S. and Tsai, F.N., 1991b. Solubility of carbon dioxide in phenol and in catechol. J. Chem. Eng. Data, in press.
APPENDIX
A
Henry’s constant; the partial molar volume of solute at infinite dilution and the Margules constant are calculated by the Soave-Redlich-Kwong equation of state:
25
2%
RTbl + (~;-b~)~
a22cw
aJ5
2b2hI 2V,(a12 [
a22b1 + Rl-b; with (,I’= jjy - u;
1 W)
- b2)
+
- a121 - %2@1
bdbl - b2) - v’bl
- b2)
- a221 - 2a22w1
1
b2) - v’b21
RTb,v;( v; + b2)
- b2)
][++g-&]-;
R7b,’
v;(v; +
v;(b, - b2) - v’b2 b2)
2a12[ W3 -
(G - b212
RTb,”
+
+ v;(v;+b2)*
-
v;(b, - b2) - v’b2
A=-2 X
- v;(v;+b~)
+ b2)
[v;(v;+b2)]2 RT
%,bl
-
v;(b, - b,) - v’b2 (vi + b212
I)
(W @W