Ind. Eng. Chem. PIocess Des. Dev. 1983, 22, 457-462
A preliminary conservative economic analysis shows that the proposed method of recovery of ethanol from fermentation broths is significantly less costly than other methods. Furthermore, important other advantages are realized when ethanol is converted to gasoline as compared to the direct use of ethanol as a fuel. The cost of producing gasoline from biomass is still significantly higher than the cost of petroleum-based gasoline. Nevertheless, biomass has an important advantage over petroleum: it is renewable.
457
Chang, C. D.; Kuo, J. C. W.; Lang, W. H.; Jacob. S. M.; Wise, J. J.; Silvestri, A. J. Ind. Eng. them. Process Des. D e v . 1978, 17, 255. Chang, C. D. Chem. Eng. Scl. 1980, 35, 619. Danner, C. A.. Ed. “Methanol Technobgy and Economics”, Chem. Eng. Rogr. S y v . Ser. No. 98, AIChE: New York, 1970; p 66. Fanta, G. F.; Bwr. R. C.; Orton, 0. L.; Doene, W. M. Science 1980, 210, 646. Qregor. H. P.; Jeffrles, T. W. Oovwnmnt Repart Announcement Index (US), 1979, 79(18), 215. Report order NTIS-PE-295645. Ladlsch, M. R.; Dyck, K. Science 1979, 205, 898. Leeper, S. A.; Wankat, P. C. In d. Eng. Chem. Process Des. Dev. 1982, 21, 331. Llederman, D.; Jacob, S. M.; Voltz, S. E.; Wise. J. J. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 340. Meieel, S. L.; McCullough, J. P.; Lechthaler. C. H.; Welsz, P. 8. CHEMTECH 1978, 6 , 86. Remkrez, R. Chem. €41.1980, 87(6), 57. Schelkr, W. A. “Energy Requirements for Grain Alcohol Productlon”, presented at 176th Natbnal Meeting of the American Chemical Soclety. Miaml Beech, FL. a p t 10-15, 1978. Venuto, P. B.; Landls, P. S. A&. Catel. 1988, 18, 259. Voltr, S. E.; Wise, J. J. “Development Studies on Conversion of Methanol and Related Oxywnates to Qaiesdlne”, Flnal Report to ERDA under Contract EX078C-01-1773, NTIS No: FE-1773-25, 1976. Yurchak, S.; Voltz, S. E.; Warner, J. P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 527.
Acknowledgment
The authors would like to thank Veronica Burrows for her significant contribution on the economic and energy analysis of the process, and Mobil Oil Corporation for providing the catalyst for this study. Registry No. Ethanol, 64-17-5; diethyl ether, 60-29-7. L i t e r a t u r e Cited Black, C. Chem. €ng. Rog. 1980, 78(9), 78. Chambers, R. S.; Heredeem, R. A.; Joyce, J. J.; Penner- P. S. Science 1979, 206, 789. Chang. C. D.; Sllvestry, A. J. J . Cetal. 1977, 47. 249.
Received for review June 28, 1982 Revised manuscript received November 15, 1982 Accepted January 7, 1983
Modified UNIFAC Model for the Prediction of Henry’s Constants Carlos Antunes and Mmitrlos tamlor’ New Jersey
Insme of
Technobgy, Newark, New Jersey 07102
A group-contribution model for the correlation and prediction of Henry’s constants in single solvents is presented. The model involves a onaparameter per gas/solvent group pair UNIFAC expresslon extended to incorporate free volume effects. The model Is appHed to t h e gases, CH,, N,, and 02,in alkane solvents and in water. oood results, inckKHng a successful description of the temperature dependency of the Henry’s constants, are obtained with typical accuracy of f 10% .
Introduction
Table I. Values of the Constants in Eq 2
The importance of gas solubilities in the chemical and petroleum industry has led to the development of several methods for the estimation of Henry’s constants in pure solvents. Most of these methods apply to nonpolar solvents (Prausnitz and Shair,1961; Yen and McKetta, 1962; Preston and Prausnitz, 1971; Gunn et al., 1974; Cycewski and Prausnitz, 1976, etc.). The last method is also applicable to polar solvents, but results are not very reliable with predictions to within a factor of 2, if care is exercised. Prediction of Henry’s constants, with a less general scope, however, is discussed by Mathias and OConnell(l979) and by Brandani and Prausnitz (1981). In recent years, group-contribution techniques, especially the UNIFAC model (Fredenslund et al., 1975), have been very successful in terms of accuracy and breadth of applicability for the phase equilibrium prediction of mixtures of subcritical compounds. A method for the prediction of Henry’s constants in pure nonpolar and polar solvents, involving conversion of available Henry’s constant values to symmetric infinite dilution activity coefficients and a modified UNIFAC model also extended to include freevolume effects, is presented in this paper. The method is demonstrated with three individual gases: 02,N2, and CHI in two solvents: water and alkanes. 0196-4305/83/1122-0457$01.50/0
A, A, A, A, A,
= 3.54811 =-4.74547 = 1.60151 = -0.87466 = 0.10971
T h e Proposed Method
Symmetric infinite dilution activity coefficient for a gaseous solute i in a given solvent (rim) are calculated from the corresponding Henry’s constant (Hi) at a pressure of 1 atm by using the following relationship .yi-
Hi -
fiL
where ft is the fugacity of hypothetical liquid i, at the system temperature and pressure of 1atm, obtained from the correlation of Prausnitz and Shair (1961). Their graphical correlation was fitted to the following polynomial In (fiL/Pc,) = A.
+ AITr;l + A2T,,+ A3Tr: + A,Tr:
(2)
where P, is the critical pressure of solute i and Triis the solute reduced temperature. Values for the constants A,, Al, A2,As, and A4 in eq 2 are presented in Table I. No 0
1983 American Chemlcal Society
458
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
Table 11. R and Q Values for the Groups of This Study functional group
R
Q
CH,
1.1285 0.6891 0.8313 0.9011
1.1600 0.8053 0.9082 0.8480
CH,
0.6744
0.5400
CH
0.4469
0.2280
H,O
0.9200
1.4000
CH, 0, N,
For the combinatorial part we use the modification of Kikic et al. (1980)
ref
In y; = In O[ Xi
Bondi (1964) Bondi (1968) Bondi (1968) Fredensiund et al. (1975) Fredenslund et al. (1975) Fredenslund et al. (1975) Fredenslund et al. (1975)
+ 1- " - -2qi xi 2
(
::
::)
ln-+1--
where
data, however, are used where for the solute T,> 3.0 since the correlation of Prausnitz and Shair becomes uncertain above this value. Hence from the Henry's constant of gaseous component i in a given solvent, one infinite dilution activity coefficient, yim,can be calculated. On the other hand, the residual part of the UNIFAC model (yt)requires two interaction parameters for a pair of functional groups, i and j
We modify, therefore, the UNIFAC model for the case of gaseous component i in solvent group j into a one-parameter expression by replacing Uij and Uii with the corresponding energies of vaporization (Tassios, 1969, 1971; Wong and Eckert, 1971) = -(2/Z)AUi"
(44
U;j = -(2/Z)AUj'
(4b)
Uii
A value of 10 is assigned to the coordination number 2, while while the energies of vaporization for the hypothetical liquid are calculated from AUiv = Via:
(5)
Values of ai and Vi are given by Prausnitz and Shah (1961). For the groups, AU; values are given by Bondi (1968). Furthermore, our preliminary calculations suggested that, as expected at infinite dilution conditions, the approximation: Uii = Ujj= 0 leads to no loss of accuracy and it is adopted in this study. Finally, since Uij = Uji,the interaction between gas i and group j is given by +i;
=
= exp[-Uij/RT]
(6)
Hence for a system like CH,-alkanes, one interaction parameter (UCH,/CH2) is required. This parameter can be calculated from, say, the CH4/n-hexane Henry's constant, and then be used in the prediction of the Henry's constant for any CH,-alkane system. The temperature range of applicability of the original UNIFAC model is 275-400 K and it is accomplished by considering (U,,- U,.,,,) to be temperature independent. For the description of the Henry's constants dependency on temperature, the following expression is considered in this study +ij
= ex.[
];-
Bij
= exp[ -
+ Cij(T - 273.15) RT
3
(8)
(7)
(11)
V k ( i ) is the number of groups of type k in molecule i. The group parameters Rk and Qk are calculated from the corresponding van der Waals group volume and surface areas (Fredenslund et al., 1975) and are presented for the groups of this study in Table 11. The UNIFAC model was developed from the two-liquid lattice theory which does not account for changes in free volume caused by mixing. While for the typical vaporliquid equilibrium case such free volume effects may be negligible because of the similarity in the molar volumes of the compounds involved, they can be significant for gasaolvent systems (Chappelow and Prausnitz, 1974). To incorporate such effects into the UNIFAC model we write
In yi = In y;
+ In [y + In yiFV
(13)
where the superscript (FV) stands for free volume. For In yiFvwe adopt the expression of Oishi and Prausnitz (1978) which at infinite dilution of solute i in solvent k becomes In yiFV= 3ci In
[
] (8
6y3 - 1 - ci[ vkv3-
- 1)( 1
-&)'I
1
(14) Oishi and Prausnitz developed this expression for polymer-solvent mixtures from the Flory (1970) equation of state. 3ci is the number of external degrees of freedom, equal to 3 fo: the gases of this study (Beret and Prausnitz, 19751, and V is the reduced molar volume 6 = V/V* = V/(15.17br) (15) where V is the molar volume, V* is the hard core molar volume, b is a proportionalityconstant of the order of unity (Oishi and Prausnitz, 1978),and r is given by eq 12a. For the gaseous components, the hypothetical liquid volumes of Prausnitz and Shair (1B6l)are used. For the solvents, temperature dependent molar volumes are calculated from V = CY
+ PT + E P
(16)
where CY,p, and e are constants calculated from molar volume data at three temperatures (Antunes, 1982). Rssults and Discussion The applicability of the model is demonstrated with three gases, CHI, N2, and O2 in alkane solvents. These
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 450 I
Table 111. Data Used for Correlation
T,K
system
ref
,
273-373
N, -a1 kanes n-C, n-C, i-C, n-CM 0,-water
273-377 273-323 273-323 300-375
4 3 4 4
273-373
53
0, -a1 kanes n-C, n-C, n-C, i-C,
298 308 273-323 283-303
1 1 3 4
CH,-water
273-373
49
4
I
1
41
CH,-a1 kanes 3 n-C, 311-377 311-377 8 n-C, 277-378 8 n-C, 4 273-348 n-C, 4 273-348 n-c,, 4 325-400 n-c,, Pray e t al. (1952). Benson and Krause 11976\, Gotoh (1976). Clever et al. (1957). e "International Critical Tables" (1933). f Hildebrand and Scott (1950). Sasse (1965). Tokunaga (1975). Shoor et al. Hayduk and (1969). Perry and Chilton (1973). Buckley (1971). Prausnitz and Chueh (1968). Gunn e t al. Chappelow and Prausnitz (1974). (1974). O Brelvi and O'Connell (1975). P Tremper and Nitta et al. (1973). Kretschmer Prausnitz (1976). et al. (1946). Prausnitz et al. (1967). Katayama and Kobatake and Hildebrand (1961). Nitta (1976). Cycewski and Prausnitz (1976). Tokunaga and Kawai (1975). Lannung and Gjaldbaek (1960). Y N = number of data points. J
Q
Table IV. Interaction Parameter Values Bij 464.402 169.590 39.372 1255.570 949.903 654.656
I
NY
N,-water
group pair N,/CH2 02/CHz CH,/CHz N,/H20 Oz/H,O CH,/H,O
I
Ct i 2.384 0.768 -0.109 17.203 16.049 9.180
systems were chosen because the available literature data base, Table 111, covers a variety of alkane solvents, up to C22,and a large temperature range. The model is also tested with each of these three gases in water because the available data, Table 111,include the maximum of Hi with temperature. The value of b in eq 15 is obtained as shown in Figure 1 where the average absolute ?% error between experimental and calculated Henry's constants
where N is the number of experimental data points, is plotted vs. b for the three gases in alkanes. The obtained value of b = 1.32 is close to the value of 1.28 determined by Oishi and Prausnitz (1978) for polymer-solvent systems. For water, a value of b = 1.18 is recommended since larger values of b, because of the very small mol& volume of water, lead to logarithms of negative arguments in eq 14. Values for the parameters B i . and Cij, obtained by regression of the data in Table I d a n d for b = 1.32 (1.18 for
S
b Figure 1. Evaluation of the optimum b value: (0) N2/alkanes; (0) 02/alkanes; (A)CH4/alkanes; (-) overall. Table V. Correlation Results av abs % error system CH,-a1 kanes N2-alkanes 0,-alkanes CH,-water N,-water 0,-water
A" 9.29 15.24 5.74 6.20 5.54 5.59
B"
Ca
3.66 10.34 5.13 1.40 1.76 0.41
10.29 16.58 4.09 1.40 1.76 0.41
a A: UNIFAC only; B: UNIFAC with 9' from eq 9 free volume; C: UNIFAC with @' from eq 9a + free volume.
+
Table VI. Correlation Results with Temperature-Independent Parameters (Cij = 0 ) and with the Generalized Temperature Dependency of Skjold-Jorgensen e t al., e q 1 9 av abs % error system CH,-alkanes N, -a1 kanes 0,-alkanes CH,-water N,-water 0,-water
only 3.85 14.04 5.63 28.81 35.10 30.81
Bij
eq 19 3.67 22.97 6.96 36.95 45.14 39.29
water), are presented in Table IV. The quality of correlation, shown in Table V, can be considered very satisfactory, taking into account the uncertainty in the experimental data. The same table includes the results obtained by the UNIFAC model without the free volume term. The significant improvement realized by the introduction of this term is in agreement wit$ that reported by Oishi and Prausnitz (1978) for polymemolvent systems where free volume effects are also important. The importance of the free volume is demonstrated in Figure 2,
460
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
c
I
L
0.5
I
I
1
I
I
I
B
l
l
1
1
1
IO
'
1
I
14
1
18
H x IC? AT M
'
n C
Figure 2. Effect of the number of carbon atoms (n,)on the free volume: (0) CH,/n-alkanes, T = 344 K; (0)N2/n-alkanes, T= 298 K, (+) N2/isooctane, T = 298 K.
I
1
f
=\
5001
'd 1
I
290
330
I
I
370
L
T,'K Figure 4. Temperature dependency of Henry's Constants for 0 2 / water: (0) exptl; (-) correlated; (- -) predicted by using the data in the 273-300 K range only.
-
100
I
I
150
I
250
I
350
I
450
I
550
I
I
'
I
'
I
I
I
I
I
'
"
I
J
T,"K
Figure 3. Prediction results: (0) N2/n-Cl6 @); ( 0 ) CH4/n-C7(n); (a)CH4/n-C20(m);(X) CH4/n-C16(k);(+) CHdn-C, (4; (-) predicted. (Letters in parenthesis are references in Table 111.)
where In 77" for CHI and N2in alkanes is plotted against the number of carbon atoms of the solvent. The contribution increases, as expected, with the number of carbon atoms, but it is significant even for solvents like hexane. The importance of using temperature dependent parameters is shown in Table VI where the results for two approaches are presented. In the first one, temperatureindependent parameters (Cij = 0) are used. In the second one, we use the expression for J.,.
where Z(T) = 35.2 - 0.1272T
+ 0.00014P
(19) as developed by Skjold-Jorgensen et al. (1980) from the simultaneous correlation of vapor-liquid and enthalpies of mixing data. Both approaches are inadequate in describing the temperature dependency of the Henry's constants. On the other hand, the proposed temperature dependency not only describes successfully the variation of H with temperature in the temperature range of the data base (273 to 400 K) but also provida successful predictions outside this temperature range as demonstrated in Figure 3. Good results are obtained down to 180 K and up to
t ,
O!l
1
,a'
,
,
J
i
0.8
I
,
,
,
I
,
0.9
,
,
,
1.0
Tr Figure 5. Effect of the solvent reduced temperature on the accuracy of prediction for CH, in ethane, propane and n-butane: (A) ethane; (0) propane; (0) n-butane (Prausnitz et al., 1968).
500 K. The maximum error is below 20%. This is also observed in Figure 4 where the H-T dependency for 02-water in the range 273-373 K, predicted by correlating the data in the range 273-300 K only, is presented. It is worth noticing that these limited data provide a successful estimation of the maximum in the H-T dependency. The proposed correlation should not be used in the vicinity of the critical temperature of the solvent. Under these conditions, the system pressure is too high as compared to low-actually zero-pressure assumed in the development of the free volume expression. In addition, eq 16 should not be used for extrapolation beyond T,= 0.85 (Prausnitz et al., 1967). This effect of the solvent reduced temperature is demonstrated in Figure 5, where the % error in predicted Henry's constants for CH4 in three solvents is plotted against the solvent reduced temperature. A limit of T, = 0.8 is therefore recommended. The contribution of the combinational part in gas-liquid equilibrium calculations can be very significant due to the
Ind. Eng.
,
\
b
I
l
4
’
l
8
l
l
12
l
l
16
l
l
20
l
l
24
“C
Figure 6. Combinatorial contribution: (0)CH,/n-alkanes; (0) N2/n-alkanes; (-) Eq 9; (- - -) eq 9a.
large difference-for the typical case-in the molar volumes of solute and solvent. This is demonstrated in Figure 6, where In y c is plotted vs. the number of solvent carbon atoms for CHI and for N2in alkanes. For comparison, In yris 0.11 and 1.32 for the two systems. On the other hand, for a typical mixture of subcritical compounds, the contribution of the combinational part is very small as compared to the residual part. In the acetone (l)/n-pentane system, for example, and at x1 = 0.047 In y c = -0.040 and In yIr= 1.579 (Freedenslund) et al., 1975). Figure 6 also includes values of In yc calculated by using the original (Fredenslund et al., 1975) expression for 4/
The larger negative value for In yie thus obtained is in agreement with the observation of Kikic et al. (1980) for mixtures of small and large molecules. And as shown in Table V, eq 9 tends to give better results than eq 9a. For water, the residual part is by far the dominant one and no difference between the two equations can be expected. The uncertainty in the hypothetical liquid fugacity for the gaseous solutes does not seem to create serious problems. Use of the specific correlations for f: for O2and N2 of Prausnitz et al. (1980) gave practically the same results. It appears that some of the uncertainty is removed through the temperature-dependent interaction parameters. This may explain the poor results obtained by using temperature independent parameters (Cij = 0).
ut)
Conclusions The UNIFAC model modified to a one-parameter form for the gaseous component-solvent group interaction, which is considered a linear function of temperature, and extended to incorporate free volume of mixing effects can be used for the correlation and prediction of Henry’s constants in single solvents. Good results, including a
Chem. Process Des. Dev., Vol. 22, No. 3, 1983
461
successful description of the temperature dependency of the Henry’s constants, are obtained for the systems of this study. Nomenclature B,] = interaction parameter between gaseous solute i and solvent group j , cal/g-mol b = proportionality constant C, = interaction parameter between gaseous solute i and solvent group j, cal/g-mol K 3c, = number of external degrees of freedom fb = fugacity of hypothetical liquid i at system temperature and pressure at 1 atm, atm H,= Henry’s constant, atm N = number of data points n, = number of carbon atoms P , = critical pressure, atm Q k = group It van der Waals surface area parameter q = pure-component surface area parameter Rk = group k van der Waals volume parameter r = pure component volume parameter R = gas constant, 1.987 cal/g-mol K S = average absolute percent error T = absolute temperature, K T, = critical temperature, K T, = reduced temperature V* = hard core molar volume, cm3/g-mol = molar volume, cm3/g-mol V = reduced molar volume X = mole fraction Greek Letters y = activity coefficient 6 = solubility parameter 0 = surface fraction 4 = segment fraction ql1= interaction parameter, gaseous solute i with solvent group J
Literature Cited Antunes, C. A. M. M.S. Thesis, New Jersey Instltute of Technology, Newark, NJ, 1982. Benson, B. B.; Krause, D., Jr. J . Chem. Phys. 1978, 6 4 , 689. Beret, S.; Prausnitz, J. M. AICh€ J . 1975, 2 1 , 1123. Bondl, A. J . Phys. Chem. 1964. 68, 441. Bondl, A. “Physical Properties of Molecular Crystals Liquids, and Glasses”; Wlley: New York, 1966. Brandani, V.; Prausnkz, J. M. FIuH Phase €@lib. 1981, 7 , 259. Brelvl, S. W., O’Connell, J. P. A I C M J. 1975, 2 1 , 157. Chappelow, C. C.. 111; Prausnb, J. M. AICh€ J . 1974, 2 0 , 1097. Clever, H. L.; Battino. R.; Sayior, J. H.; Gross, P. M. J . Phys. Chem. 1957, 6 1 , 1078. Cycewskl, 0. R.; Prausnltz, J. M. Ind. Eng. Chem. Fundam. 1978, 15, 304. Flory, P. J. Discuss. Faraday Soc. 1970, 49, 7. Fredenslun6, A.; Jones, R. L.; Prausnitz, J. M. AICh€ J . 1975, 2 1 , 1086. Gotoh, K. Ind. Eng. Chem. Fundam. 1976, 15, 269. Gunn, R. D.; Yamada, T.; Whkman, D. AIChE J . 1974, 2 0 , 906. Hayduk, W.; Buckley, W. D. Can. J . Chem. Eng. 1971, 49, 667. Hlldebrand, J. H.; Scott, R. L. “Solublltty of Nonelectrolytes”, 3rd ed.;Reinhold Pubilshing Corp.: New York, 1950. “Internatlonal Crltlcal Tables”; McQraw-Hill: New York, 1933; Vol. 3. p 254. Katayama, T.; NHta, T. J . Chem. Eng. Data 1976, 2 1 , 194. Klkic, 1.; Alessi, P.; Rasmussen, P.; Fredenslund, A. Can. J . Chem. Eng. 1900, 5 8 , 253. Kobatake. Y.; Hlidebrand, J. H. J. Phys. Chem. 1981, 6 5 , 331. Kretschmer, C. 6.; Nowakowska. J.; Wlebe, R. Ind. Eng. Chem. 1948, 18, 506.
Lannung, A.; Gjaldbaek, J. C. Act8 Chem. Scand. 1960, 14. 1124. Mathlas, P. M.; O’Connell, J. P. A&. Chem. Ser. 1979, No. 182, 97. N h , T.; Tatsulshl. A.; Katayama, T. J . Chem. Eng. Jpn. 1973, 6 , 475. Oishi, T.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. D e v . 1978, 17, 333. Perry, R. H.; Chilton, C. H. “Chemical Engineer’s Handbook”, 5th ed.; McGraw-Hili: New York. 1973. Prausnltz. J. M.; Chueh, P. L. “Computer Calculations for High Pressure Vapor-Liquid Equillbrla”; Prentlce-Hall: Englewood Cllffs, NJ, 1968. Prausnltz. J. M.; Eckert, C. A.; Orye, R. V.; OConneil, J. P. “Computer Calculations for Multlcomponent Vapor-Llquld Qullibrla”; PrentlcaHall: Englewood Cliffs. NJ, 1967. Prausnltz, J. M.; Anderson, T.; Grens, E.; Eckert, C.; Hsieh, R.; O’Connell. J. “Computer Calculatlons for Multicomponent Vapor-Liquid and Liquid-Liquid Equillbrla”, PrentlcaHall, Inc.: Engiewood Cliffs, NJ, 1980. PrausnRz, J. M.;Shair. F. H. AIChE J . 1961, 7 , 682. Pray, H. A.; Schweickert, C. E.; Minnlch, B. H. Ind. Eng. Chem. 1952, 4 4 , 1146. Preston, G. T.; Prausnltz, J. M. Ind. Eng. Chem. Fundam. 1971, 10, 389.
462
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Sasse, R. A. Anal. Chem. 1965. 3 7 , 604. Show, S. K.: Walker, R. D., Jr.; Qubblns. K. E. J . phvs. Chem. 1969, 73, 312. SkJoMJorgensen, S.; Rasmussen, P.; Fredenslund, AA. Chem. Eng. Sci. 1980. 3 5 , 2389. Tasslos, D. Paper presented at Annual AIChE Meetlng. Washlngton, DC, 1969. Tassbs, D. AIChE J . 1971, 17, 1367. Tokunaga, J. J. Chem. Eng. Data 1975, 20, 41.
Tokunaga, J.: Kawal, M. J . Chem. Eng. Jpn. 1971, 8, 326. Tremper, K. K.;Rausnk, J. M. J . chsm.Eng. Data 1976, 2 1 , 295. Yen, L. C.; McKetta, J. A I C M J . 1962, 8 . 501. Wong, K. F.; Eckert, C . Ind. fng.Chem. Fundem. 1971, TO, 20.
Received for review January 21, 1981 Revised manuscript received September 16, 1982 Accepted November 1, 1982
Use of the Soave Modification of the Redlich-Kwong Equation of State for Phase Eq~#MrCumCakulations. Systems Containing Methanol Te Chang, Ronald W. Roumeau,' and James K. Ferrell Department of Chemlcal E ~ i n w h g North , Carollna State Unlverslty, Rahsbh, North Carollna 27650
The Soave modification of the Redlich-Kwong equation of state is used to predict phase equilibrium in mixtures found in acid gas removal processes used to clean gases produced from coal. B h r y equilibrium calculations compare favorably with data obtained from the literature, provided a temperatur-ndent interaction parameter is used in some cases. Predictions of equiilbrium behavior in systems containing methanol were satisfactory if the solute composition in the liquid was Umited to approximately 5 mol % nitrogen or 30 mol % for the other components. Parameters evaluated, and their correlations with temperature, were used to Illustrate predictions of multicomponent system behavior. The results should be applicable in many systems of industrial interest where the concentration is maintained at levels consistent with those found as upper limits on the accuracy of the Soave equation.
Introduction Gasification of coal produces a product that contains a variety of species, such as carbon dioxide, hydrogen d i d e , carbonyl sulfide, carbon disulfide, aromatic hydrocarbons, and mercaptans, in addition to the desired gases: carbon monoxide and hydrogen. Separation of these components is accomplished in a multistep process involving quenching and water scrubbing, followed by treatment in an acid gas removal system. The acid gas removal system typically involves absorption-stripping operations which utilize either a physical or chemical solvent. The physical solvent that has shown the most promise is methanol; it has been used in all of the commercial coal gasification operations to date. Despite this fact, models describing the equilibrium behavior of the species mentioned above in refrigerated methanol have not been adequately developed. In an earlier work (Rousseau et al., 1981), a thermodynamic model was developed for the description of systems containing methyl alcohol, carbon dioxide, nitrogen, and hydrogen sulfide. This model used the Soave modification of the Rediich-Kwong (SRK) equation of state (1972) to describe deviations of gas mixtures from ideal behavior and third-order Margules equations to express activity coefficients describing liquid nonidealities. Binary interaction parameters in the Soave equation were estimated from available equilibrium data. Unfortunately, there was considerable uncertainty in the evaluation of these parameters, especially for the methyl alcohol-nitrogen mixtures. In addition, the resulting model covered the modest temperature range from 0 to -15 O C . The SRK equation of state was originally developed to describe phase equilibrium behavior of hydrocarbon mixtures, and subsequent inclusion of a parameter to account 0196-4305/83/1122-0462$01.50/0
for interactions between unlike molecules extended its capability to the description of phase-equilibrium behavior for nonhydrocarbons. Graboski and Daubert (1978b) studied interactions in mixtures of carbon dioxide, hydrogen sulfide, nitrogen, and carbon monoxide. Evelein and Moore (1979) modified the SRK equation to include an interaction constant in the mixing rules for both SRK parameters; they successfully applied their resulting expression to the prediction of phase equilibrium in a variety of mixtures formed from components found in natural gases. Evelein and Moore (1976) obtained reasonable correlations of H20-C02 and H20-H2S data by adding a correction factor accounting for the temperature dependence of the Soave parameter. The purpose of this study was to test the validity of using the SRK equation of state to describe both liquid and gas phases in mixtures found in the separation of gases produced from coal. Data used in evaluating this approach were taken from the literature.
The SRK Equation The Soave modification of the Redlich-Kwong equation of state has the following form P = R T / ( u - b ) - aa/u(u + b ) (1) where the quantity a is a function of temperature. ai = (1
+ mi(l - Tr,0.6))2
(2)
G r a b k i and Daubert (1978a) used a regression program to evaluate mi based on API vapor pressure data for hydrocarbons and gases. They correlated mi with the Pitzer acentric factor
mi = 0.48508 + 1.551710, - 0.156130,~ 0
1983 American Chemical Society
(3)
