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367
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Baddov.R. F.; Brain, P. L. T.; Logeah, B. A.; Eymery, J. P. Chem . Eng . Scl. l 9 G . 20, 281. Blrd, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiley: New York, 1900 Chapter 21. Emery, J. P. Sc.D. Thesls, M.I.T. Cambridge, MA, 1964. Fletcher, R.; Reeves, C. M. -ut. J . 1964, 7 , 149. Flower, J. R.; Whitehead, B. D. Chem. Eng. (London) 1973, No. 272, 208; No. 273, 271. Gains, L. D. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 381. Gains, L. D. Chem. Eng. Scl. 1979, 3 4 , 37. Ganglah, K.; Husaln, A. a n . J . Chem. Eng. 1974, 52, 654. Gilllland, E. R. Ind. Eng. Chem. 1934, 2 6 . 681. Gremllllon, J. A. Chem. Eng. Rog. 1979. 75(5),37. Hkschfelder. J. 0.; Cwtlss, C. F.; Blrd, R. B. “Molecular Theory of Gases and Liquids”; Wlley: New York, 1964: Chapter 8. Husain. A.; Qanglah, K. “Optimlzatlon Techniques for Chemical Engineers”: Macmlllan: Delhl, 1970,Chapter 6. “International Critlcal Tables of Numerical Data, Physics, Chemistry and Technology”: McGrawNIH: New York, 1928;Voi. 3,p 213;Vol. 5, p 138; vol. 7. D 239. ..r Kern:-D. Q. “Process Heat Transfer”: Mc&aw+llll-Kogakusha Ltd.: Tokyo, 1950:DD 103. 137. Kjaer, J.’ “basuknents and Calculation of Temperature and Converslon In Fixed-Bed Catalytic Reactors”; Jui. Gjellerups Forlag: Copenhagen, 1958; Chapters 8 and 11. Kjaer, J. “Thermodynamic Calculations on an Electronic Digltai Computer”. Akademisk Forlag: Copenhagen, 1983;p 35. Kubec, J.; Burlanova, J.; Bwlanec, Z. Int. Chem. Eng. 1874, 14, 629. Lasdon, L. S.; Mkter, S. K.; Waren, A. D. I€€€ Trans. Autom. Controi 1967, AC-12, 132. McAdams. W. H. “Heat Transmission”, 3rd ed; McGraw-Hill: New York. 1954;p 244. Motard, R. L.; Schacham, M.; Rosen, E. M. AIChE J . 1975. 2 1 , 417. Nelder, J. A.; Mead, R. Comput. J. 1964, 7 , 308. Paavo Uronen “Mcdeilng and Slmulation of Catalytic Autothermic Gas Reactors”; Ch 105,Acta Polytechnlca Scandinavica, University of Oulu,
Flnland, 1971. Perry, J. H.; Chllton, C. H.; Kirkpatrick, S. D. “Chemical Engineers’ Handbook”, 5th ed;McGraw-Hill: New York, 1973;Sectbn 3. Reddy, K. V. Ph.D. Thesis, Kakatlya University, Warangai (A.P.)., India, 1980. Reddy, K. V.; Husaln, A. “Proceedings 1978 Summer Computer Simulatlon Conference”; Newport Beach, CA, 1978. p 286. Reddy, K. V.; Husaln, A. Ind. Eng. Chem. Process Des. Dev. 1980, 19. 580. Reid. R. C.; Sherwood, T. K. “The Properties of Gases and Liquids”, 2nd ed; McGraw-Hill: New York, 1968;Chapter 3. Schrodt, J. T. AIChE J . 1973, 19. 754. Shah, M. J.; Duffin. J. H.; James, C. “Technical Report TR, 02.B04”;IBM Systems Development Dlv., San Jose, CA, 1965. Shah, M. J. Ind. Eng. Chem. 1967, 5 9 , 72. Slngh, C. P. P.; Saraf. D. N. Id. Eng. Chem. P r m s s Des. Dev. 1979. 18,
384. Temkln, M. I.; Fyzhev, V. M. Zh. f l z . Khim. 1939, 13, 851. Temkln, M. I.; Fyzhev, V. M. Khlm. Nanka. Prom. 1957, 2(2),219. Treybai, R. E. “Mass Transfer Operatlons”, 2nd ed; McGraw-HiICKogakushl Ltd.: Tokyo, 1968;Chapter 3. Van Heerden, C. Ind. Eng. Chem. 1859, 4 5 , 1242. Webs, S.M. “Reaction Kinetics for Chemical Englneers”; McGraw-Hill: New York, 1959;p 282. Zayarnyi, N. S. Int. Chem. Eng. 1962, 2 , 378.
Received for reuiew April 30, 1981 Accepted December 28, 1981
This paper has been presented at 2nd World Congress of Chemical Engineering held at Montreal, Canada, Oct 4-9,1981. The authors are thankfulto the Plant Management for extending all facilities. Thanks are also due to M. Sriram for his careful reading and helpful remarks.
Simple Correlations for UNIQUAC Structure Parameters S. W. Brelvl Lummus Technical Center, C. E. Lummus, Ekwmfiekl, New Jersey 07003
The van der Waals volume and surface area for some simple polar and nonpolar compounds, commonly encountered in petrochemicals processing, have been calculated from the molecular structure. The UNIQUAC structure parameters, r and 9, are obtained d r e w from the van der Waals volume and surface area. They provide the pure compound information needed to include these compounds in the UNIQUAC framework for calculating liquid phase activity coefficients. The structure parameters for 101 compounds have been correlated as functions of critical volume and of radius of gyration. The correlation based on critical volume may be used to predict UNIQUAC parameters with a relative deviation of f6%.
Vapor-liquid equilibrium calculations are essential for the design of distillation and absorption columns in chemical processing plants. Equilibrium conditions in mixtures of essentially nonpolar compounds and light gases are conveniently, and accurately, calculated by the generalized method of Chao and Seader (1961) and ita many modifications. In these methods, the vapor phase fugacity coefficient is calculated from a modified Redlich-Kwong equation and the pure component liquid fugacity from corresponding states correlations. The same correlations are used for the liquid fugacity of both subcritical and supercritical components although the supercritical component does not exist as a pure liquid at mixture conditions. Liquid phase activity coefficients are represented by the Hildebrand equation using pure component solubility parameters and molar volumes. The general framework of the Chao-Seader method can be extended for vapor-liquid equilibrium calculations in mixtures containing polar components such as methanol, water, and hydrogen chloride. However, the Hildebrand 0196-430518217 121-0367$01.25/0
equation can no longer be used to represent the excess free energy of the liquid mixture. An equation capable of representing the nonidealities in mixtures containing polar compounds must be used instead. The UNIQUAC expression for excess free energies provides one such method (Abrams and Prausnitz, 1975). This equation is being used increasingly in chemical process calculations to represent activity coefficients in highly nonideal mixtures. The expression for activity coefficients contains two structure parameters, r and q, for each pure component. These are directly related, by constant values, to the van der Waals volume and surface area of the molecule. The van der Waals surface area and volume are characteristic properties of a molecule and, in principle, can be calculated directly from the molecular structure. In practice, they are generally determined by a structural group contribution method (Bondi, 1968). The use of this method is straightforward. However, the group contributions cited by Bondi were obtained by considering structure groups bonded directly to carbon atoms. The use of these group contri0 1982 American Chemical Society
388
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
Table I. UNIQUAC Structure Parameters for Some Simple Polar and Nonpolar Molecules r 4 (ii) (ii)b (i) (i)“ H, N, 0,
co
3 H,O H,S NH, SO,
0.416 0.941 0.913 1.060 1.323 0.990 0.766 1.172 0.900 1.551
C C
C C
1.30 0.99 0.920 1.19 0.91 1.20
0.570 0.991 0.977 1.069 1.279 1.019 0.874 1.168 0.995 1.446
C C
C C
1.12 1.030 1.40 1.20 1.20 1.01
Table 11. Compounds Included in Correlations for UNIQUAC Structure Parameters hydrocarbons (nonring): methane, ethane, propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, n-decane, ethylene, propylene, 1-butene, cis-2-butene, 1,3-butadiene, 1-pentane, 1hexane, 1-heptane,acetylene, propyne, 1-butyne oxygen-containing compounds: acetone, MEK, DEK, acetaldehyde, propionaldehyde, butyraldehyde, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol, 2-butanol, 2-methyl-2-propano1, acetic acid, propionic acid, butyric acid, methyl acetate, ethyl acetate, n-butyl acetate, methyl ether, methyl ethyl ether, diethyl ether, acetic anhydride
(i) By rigorous calculation from molecular structure. (ii) Abrams and Prausnitz (1975) and Anderson and Prausnitz (1976). Not reported.
nitrogen-containing compounds: acetonitrile, propionitrile, nitromethane, methylamine, ethylamine, propylamine, dimethylamine, diethylamine, trimethylamine, triethylamine, HCN
butions could cause errors for molecules in which the structure groups were not bonded directly to a carbon atom. Many polar molecules, e.g. water, hydrogen chloride, and ammonia, are of this type. The purpose of this work is twofold. (1) The van der Waals surface area and volume of some polar molecules (for which the group contribution method would be inappropriate) have been calculated directly from molecular structure. The UNIQUAC r and q can then be obtained directly. This provides the basic pure component information needed to calculate liquid activity coefficients of these polar molecules in a general K-value calculation method. (2) The UNIQUAC structure parameters r and q for polar and nonpolar molecules have been correlated with other pure component properties, viz., critical volume and radius of gyration. The correlation with critical volume appears to be more reliable. In its present stage of development, it can be used to estimate the UNIQUAC r and q for molecules in which all functional structure groups are not bonded directly to carbon atoms. The sensitivity of calculated activity coefficients to the correlated parameters, rand q, has not been studied in this work since calculated activity Coefficients depend also on the binary interaction parameters. The normal procedure in correlating experimental VLE of a binary mixture is to choose a set of pure component parameters, r and q, and regress on the binary parameters. If the numerical values of r and q are changed slightly, a different set of interaction parameters will resuit from regression of the experimental data. Thus, any ambiguity or error in the pure component parameters is, in practice, lumped into the two interaction parameters. Conversely, any set of pure component parameters with its consistent interaction parameters can generally reproduce the original VLE data to equivalent accuracy. Pure component structure parameters generated from the correlations presented here can be used to determine binary interaction parameters from VLE data and subsequently to represent VLE in binary and multicomponent systems. UNIQUAC Parameters from Molecular S t r u c t u r e The van der Waals volume and surface area of a molecule can be calculated from its molecular structure, i.e., atomic sizes and bond lengths. The method of calculation for diatomic molecules is shown in Figure 14-1 and the associated text of Bondi (1968). The method of calculation was extended to polyatomic molecules in the present work. Atomic radii and bond lengths were taken from the work of Sutton (1958). UNIQUAC parameters r and q were obtained from the calculated van der Waals volume and surface areas. These values of r and q are termed rigorous since they are obtained directly from molecular structure.
chlorinated hydrocarbons (nonring): carbon tetrachloride, chloroform, dichloromethane, methyl chloride, ethyl chloride, 1,2-dichloroethane, 1,1,2-trichloroethane, vinyl chloride, trichloroethylene
a
“simple” compounds: H,, N,, 0,, CO, CO,, HCl, H,O, H,S, NH,, SO,, Cl,, NO, NO,, SO, aromatics: benzene, toluene, ethylbenzene, o -xylene, aniline, phenol, chlorobenzene, dichlorobenzene, benzonitrile, benzoic acid, naphthalene cycloparaffins and substituted compounds: cyclopropane, cyclobutane, cyclopentane, cyclopentanone, cyclopentene, cyclohexane, cyclohexanol, cyclohexanone, cyclohexene
Some typical results are shown in Table I. Note that the values for water, ammonia, and SO2 are quite different from those cited by Abrams and Prausnitz (1975) and Anderson (1976), which presumably were obtained by the group contribution method. Correlations for UNIQUAC S t r u c t u r e Parameters Table I1 lists, by chemical type, 101 compounds whose UNIQUAC r and q were correlated as functions of critical volume and of radius of gyration. The group labeled “simple” contains molecules in whose structure the functional groups are not directly attached to carbon atoms. The UNIQUAC r and q for these compounds were determined directly from molecular structure as discussed in the preceding section. The r and q for the remaining compounds were found from group contributions. The critical volume is a natural choice as a correlating variable since it reflects molecular size and shape. It is known accurately for many compounds; for others it can be reliably estimated by well-known methods. The parameters r and q were represented as simple linear functions of critical volume, V , r = a , + a2Vc (1) = bl
+ b,V,
where V , is in cm3/g-mol. Critical volumes were taken largely from the compilation by Reid et al. (1977). Estimation methods recommended by the same authors were used for compounds not included in their compilation. A correlation of q as a linear function of V,2f3proved to be less accurate than eq 2. Data for 101 compounds were used to generate the coefficients of eq 1 and 2. Preliminary screening revealed that, at equal volumes, r and q for molecules with ring structures such as benzene and cyclohexane were smaller than for those with nonring structures such as n-hexane and methyl chloride. The two
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 369 Table 111. Correlations for UNIQUAC Parameters with Critical Volume r correlation compound group
1. 2. 3. 4.
5.
6.
7.
8. 9. 10.
11.
a
81 nonring 67 nonring 14 “simple” 22 hydrocarbons methane isopentane acetylene 24 oxygen compounds MEK butyraldehyde 1-propanol ethyl acetate diethyl ether 11 nitrogen compounds acetonitrile ethylamine HCN 1 0 nitrogen compounds acetonitrile ethylamine 10 chlorine compounds chloroform vinyl chloride 20 ring 11 aromatic chlorobenzene phenol o -xylene 9 cycloparaffins and derivatives cyclopentane cyclohexanone
% dev = 100 X (exptl
Table
-
100al 3.565 2.381 -13.943 14.272
1.199
q correlation
lo&,
% deva
100bl
100b,
% deva
1.202 1.205 1.417 1.1671
5.85 3.85 15.77 2.49 15.61 -2.28 -4.03 2.79 0.61 4.93 -3.77 0.77 -1.05 7.54 6.39 -5.26 28.16 5.07 9.69 -2.80 3.13 5.07 -4.24 3.77 2.66 1.92 -3.72 -2.70 2.36
26.229 26.014 19.253 32.243
0.970 0.970 1.053 0.943
21.636
0.991
-1.473
1.071
11.735
1.025
5.05 3.81 11.49 1.76 8.87 -2.57 -0.29 2.74 1.61 5.40 -2.99 -0.17 -0.80 7.03 6.59 -5.66 24.25 4.81 9.65 -3.39 3.17 5.47 -2.85 5.98 3.46 3.19 -4.57 -2.74 3.56
1.222
-33.388
1.343
-17.919
1.289
-3.142
1.215
23.858 62.331
1.198 1.059
-4 6.026
1.492
23.140
0.953
39.213 46.192
0.864 0.807
-48.3 59
1.250
1.37 -4.03
2.43 -6.37
ealcd)/exptl. Experimental value from group contribution or molecular structure.
IV. Correlations for UNIQUAC Parameters with Radius of Gyration r correlation compound group 1. 2. 3. 4.
5.
6. 7. 8. 9.
65 nonring compounds 53 nonring compounds 1 2 “simple” compounds 21 hydrocarbons methane isopentane acetylene 1 6 oxygen compounds MEK 1-propanol diethyl ether 9 nitrogen compounds acetonitrile ethylamine 7 chlorine compounds chloroform 10 ring compounds 8 aromatics chlorobenzene phenol
% dev = 100 X (exptl - calcd)/exptl.
q correlation
Cl
Cl
% deva
dl
dl
% deva
1.6220 1.8992 0.9087 2.0334
0.0433 0.0384 0.0955 0.0362
1.0614 1.1865 0.9073 1.2681
0.1806 0.1703 0.1657 0.1677
1.4914
0.0547
1.0455
0.1849
1.3523
0.0753
0.9143
0.2236
1.7438
0.0389
1.3690
0.1231
2.3934 1.8634
0.0358 0.0460
22.80 11.09 20.79 14.86 84.81 -12.44 36.63 5.50 -2.02 -6.10 -6.26 4.64 -3.95 1.05 6.33 11.72 6.01 4.98 3.63 10.32
1.6275 0.6739
0.1146 0.1832
8.50 5.14 13.40 4.95 27.79 -6.14 5.53 3.71 -2.29 -3.30 -4.92 3.12 9.75 -4.29 4.40 9.38 8.09 5.38 5.25 9.78
Experimental value from group contribution or molecular structure,
sets of compounds, ring and nonring, were then treated separately. As shown in Table 11, the nonring compounds include: (i) 22 hydrocarbons; e.g. ethane, isobutane, 1,3-butadiene, and ethylene; (ii) 24 oxygen-containing compounds, e.g.
acetone, ethanol, acetic acid, methyl ether, and ethyl acetate; (iii) 11nitrogen-containing compounds, e.g., acetonitrile, nitromethane, and triethylamine; (iv) 10 chlorinated hydrocarbons, e.g., vinyl chloride and 1,1,2-trichloroethane; (v) 14 ”simple” compounds; this is the set
370
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
whose parameters are given in Table I. The set of ring structured compounds includes: (i) 11 aromatics, e.g., toluene, aniline, and chlorobenzene; (ii) 9 cycloparaffins and substituted compounds, e.g., cyclobutane and cyclopentanone. Table I11 summarizes the correlation results. The percent relative deviation in correlating data for a given set of compounds with the derived values of a, and a2 is reported first. The results for typical members of the set follow. For example, the best values of al and a2 for the set of 24 oxygen-containing compounds were 0.01199 and 0.01222. The corresponding percent relative deviation for the 24 compounds was 2.79. Within this set, the percent relative deviation for MEK was 0.61 and for diethyl ether -1.05. The first set in the table is the result of all 81 nonring compounds included in the correlation. When the 14 compounds of the type reported in Table I were excluded, the average deviation was significantly reduced, i.e., set 2. The 67 compounds of set 2 were then separated into different functional types. The next five sets are results for these separate groups. The inclusion of HCN in the set of 11nitrogen compounds gave average deviations of 7.54 and 7.03% for r and q, respectively. Its omission from the set reduced the deviation considerably, to 5.07 and 4.81%. Set 9 are results for 20 ring structured compounds correlated together. When these were divided into two groups, aromatics and cycloparaffins, the deviations were reduced by about 40%. The radius of gyration of a molecule is the other parameter chosen for correlation. It has been used in two recent studies of second virial coefficients, Hayden and O’Connell (1975) and Tarakad and Danner (19771, to characterize molecular size and shape. Values for the radius of gyration were taken from the work of Thompson (1966). Data for radius of gyration are not as readily available as those for critical volume; values were found for only 75 of the 101 compounds of Table 111. The correlations with radius of gyration are r = c1 c2R3 (3)
+
q = d,
+ d2R2
(4)
where R is in angstroms. The results of the correlations
are summarized in Table IV, which is similar to Table 111. Equations 3 and 4 are generally not as good representations of the UNIQUAC parameters as are eq 1 and 2. The correlation of r for 53 nonring compounds, percent relative deviation of 11, is especially poorer than its counterpart in Table 111. Much of this deviation is due to the poor fit for 21 hydrocarbons, particularly methane and acetylene, the first members of homologous series. Equations 3 and 4 are less accurate than eq 1and 2 for nitrogen compounds. For ring compounds, too, the correlations with critical volume represent the data better than do those with the radius of gyration.
Conclusions The parameters r and q for compounds shown in Table I have been obtained from molecular structure. They provide the pure component characteristics needed to incorporate these compounds into the UNIQUAC framework for calculating liquid activity coefficients. The correlations for r and q with critical volume are more accurate than those with the radius of gyration. At the present stage of development, the correlations of Table I11 are useful for estimating UNIQUAC r and q for compounds to which the group contribution method is inapplicable. For example, the coefficientsof set 7 may be used to estimate r and q for a nitrogen-containing compound in which all nitrogen atoms are not attached directly to carbon atoms. Literature Cited Anderson, T.; Prausnltz, J. M. personal communication. Nov 1976. Abrams, S. D.; Prausnltz. J. M. A I C M J . 1975, 27, 116. Bondl, A. “Physical Properties of Molecular Crystals, Llqulds, and Glasses”: Wlley: New York, 1968. Chao. K. C.; Seeder. J. D. AIChE J . 1981, 7 , 598. Hayden, J. G.; O’Connell, J. P. Ind. Eng. Chem. Process Des. D e v . 1975, 14, 209. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. “The Properties of Gases and Llqulds” 3rd ed.;McGraw-Hill: New York, 1977. Sutton, L. E. “Tables of Interatomlc Distances and Conflgurations In Molecules and Ions”: The Chemical Society: London, 1958. Tarakad, R. R.; Danner, R. P. AIChE J . 1977, 23, 685. Thompson, W. H. Ph.D. Dissertation, Pennsylvanla State Universlty, 1966.
Received f o r review February 5, 1980 Revised manuscript received February 23, 1981 Accepted November 26, 1981
