Kotake, M., ‘‘Constants of Organic Compounds,” Part 2, Asakura Publications. Tokvo. JaDan. 1963. D 500. Ljndner, B., J . Chek Ph&v.,’33,’66fk75 (1960). Lindner, B., ibid., 35,371-2 (1961). Mickley, H.S., Sherwood, T. K., Reed, C. E., “Applied Mathematics in Chemical Engineering,” 2nd ed., McGraw-Hill, New York, N. Y., 1957,p 66. O’Connell, J. P., Prausnitz, J. M., Ind. Eng. Chem. Process Des. Develom.. 6. 245 (1967). , Othmer,‘D. F.,Chudgar, M. M., Levy, S. L., Znd. Eng. Chem., 44,1872 (1952). Pierotti, G. J., Deal, C. H., Derr, E. L., AD1 Document 5782, Photodupl. Service, Library of Congress (1958). Pierotti, G. J., Deal, C. H., Derr, E. L., Ind. Eng. Chem., 51 (I), 95-102 11969). Poppe, G.; Buli SOC.Chim. Belg., 44, 640 (1935). Prausnitz, J. M.,Eckert, C. A., Orye, R. V., O’Connell, J. P., “Com uter Calculations for Multicomponent Vapor-Liquid Equili&ria,” -. ___ Prentice-Hall, Englewood Cliffs, N. J. 1967, Chap. 111. Prausnitz, J. M.,“Molecular Thermodynamics of Fluid-Phase Equilibria,’, Prentice-Hall, Englewood Cliffs, N. J., 1969, Chap. VII, p 263. Prigogine, I., Bellemans, A., J . Chem. Phys., 21! 561 (1953). Reid, R. C.,Sherwood, T. K., “The Properties of Gases and Liauids.” McGraw-Hill. New York. X. Y.. (1958). Renoh, H:, Ph.D. dissertation, University of ’California, Berkeley, Calif. (1966). Renon, H., Prausnitz, J. M.,AIChE J . , 14 (l),135-44 (1968). Renon, H., Prausnitz, J. M., ibid., 15 (5),785 (1969a). Renon, H.,Prausnitz, J. M., Ind. Eng. Chem. Process Des. Develop., 8,413-9 (196913). \ - - -
Rushbrooke, G. S.,“Introduction to Statistical Mechanics,” Clarendon Press, Oxford, England, 1949,p 317. Rushbrooke G. S., Trans. Faraday SOC.,36, 1055 (1940). Scatchard, &., Wood, S. E., Mochel, J. M., J. Amer. C h m . Soc., 68, 1957 (1946). Scatchard, G., Ticknor, L. B., ibid., 74,3724 (1952). Scatchard, G., Wilson, G. M., ibid., 86, 133 (1964). Scott, R. L., Discuss. Faraday SOC.,15,44 (1953). Scott, R. L., J . Chem. Phys., 25 (2),193-205 (1956). Scheller, W. A,, Ind. Eng. Chem. Fundam., 4,459-62 (1965). Schneider, G.,Wilhelm, G., 2.Phys. Chem., 20,219 (1959). Severns, W. H.,Sesonke, A., Perry, R. H., Pigford, R. L., AZChE J.,1, 301 (1955). Tassios, D., Paper presented at 62nd Meeting of the AIChE J., Washinnton. D.C.(1969). Weimer, R. F., Prausnitz, J. M., Hydrocarbon Process. Petrol. Refiner, 44, 237 (1965). White, R. R., Trans. Amer. Inst. Chem. Eng., 41, 539 (1945). Wilson, G.M., J . Amer. Chem. SOC.,86, 127-33 (1964). Wilson, G. M., Deal, C. H., Ind. Eng. Chem. Fundam. 1, 20 (1962). \ - - - - ,
RECEIVED for review September 18, 1970 ACCEPTED April 23, 1971 John M. Prausnitz thanks the National Science Foundation for support. Appendix B will appear following these pages in the microfilm edition of this volume of the Journal. Single copies may be obtained from the Reprint Department, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D.C. 20036, by referring to author, title of article, volume, and page number. Remit $17 for photocopy or $2.00for microfiche.
Use of Infinite Dilution Activity Coefficients with Wilson’s Equation Loren 6. Schreiber’ and Charles A. Eckertz Department of Chemical Engineering, University of Illinois, Urbana, 111. 61801
The Wilson equation, with the two parameters evaluated from limiting activity coefficients, can be quite advantageous for the characterization of binary vapor-liquid equilibria. Often good results may be obtained from a single-parameter modification using a single infinite dilution value. This technique is readily extended to multicomponent mixtures. Applications and limitations are discussed.
T h e ViriIson equation (Wilson, 1964) for the excess Gibbs energy of solutions has been shown on many occasions (Eckert e t al., 1965; Pieretnieks, 1968; Orye and Prausnitz, 1965;Prausnitz et al., 1967) t o provide a superior method for the correlation of vapor-liquid equilibria in totally miscible systems. I t s derivation in terms of “local volume fraction” differs from that of most of the other commonly used expressions in that it is based primarily on entropic arguments, whereas the van Laar, Margules, and Scatchard-Hamer equations represent primarily energetic or enthalpic effects. For this reason, the Wilson equation has been especially successful in representing the activity coefficients for associating solutions. Although both the eiithalpic and entropic expressions fit the region of concentrated solutions quite well in general, the Wilson expression is clearly superior in the dilute regions where entropic effects dominate. 1 Present address, Department of Chemical Engineering, California Institute of Technology, Pasadena, Calif. 91 109. 2 To whom correspondence should be addressed.
572
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No.
4, 1971
It is our purpose here t o exploit this difference by demon strating t h a t by the use of the Wilson equation and the two infinite dilution activity coefficients, a n excellent representation of the vapor-liquid equilibria for the whole composition range is achieved. Moreover, surprisingly good results can be obtained from a single infinite-dilution activity coefficient for the binary pair. Of course, once a good representation is available for binary mixtures, the extension to the multicomponent case is straightforward and accurate. There are three cogent reasons for deciding to work with infinite dilution activity coefficients. First, in recent years a number of new techniques, primarily chromatographic, have been developed for the relatively easy and rapid determination of activity coefficients in the limit of infinite dilution to a moderate degree of accuracy (Kobayashi et al., 1967;hlartire and Pollava, 1965;Porter et al., 1956;Wong and Eckert, 1971; Young, 1968). Second, a number of empirical or semiempirical techniques have been developed for correlating or predicting infinite dilution activity coefficients. These include group
Table 1.
Fit of Binary Data to Two limiting Activity Coefficients Av. abr. error in y from fitting, X 1 Os Temp., OC
System, 1-2
No.
Y 2-
71-
.4cetone-acetonitrile~ hcetone-benzene* Acetone-carbon tetrachloride*
1.05 1.65 3.00 0.44 2.06 1.32 0.94 8.75 3.20 0.96 1.35 5.66 2.00 10.6 18.1 27.5 20.0 1.68 1.17 2.74 2.79 1.47 8.10 2.78 3.20 3.20 10.6 4.50 5.50 3.24 5.20
1.04 1.52 2.15 0.54 1.78 1,18 0.96 3.60 3.00 1.00 1.82 9.30 9.40 4.45 9.05 10.8 5.75 1.49 1.03 1.39 3.02 1.34 7.75 1.91 3.72 3.40 7.45 3.16 4.41 1.92 6.34
All points, Wilson
W itson
and yzrn van Scat.Laar Ham.
2 2 2 4 4 5 7 8 14 5 Acetone- chloroform^ 5 4 Acetone-methanolc 8 8 9 5 4 Acetone-methyl acetatec 7 10 10 Acetone-nitromethane. 10 15 6 Acetone-water d 28 4 7 5 Acetonitrile-benzenee 14 4 4 4 4 Acetonitrile-nitromethanee 4 4 6 Benzene-n-heptane.’ 4 11 7 17 Carbon tetrachloride-acetonitrileo 54 28 24 94 Chlorof or m-met hanolc 10 12 12 E thanol-benzeneh 5 42 12 Ethanol-n-hexanez 42 10 116 Ethanol-isooctane? 7 10 66 181 Ethanol-methylc yclopentanet 14 21 14 99 4 n-Hexane-benzenek 3 4 3 n-Hexane-methylc yclopent anel 4 5 6 7 Methanol-waterd 15 14 15 15 Methyl acetate-methanolc 5 4 5 16 2 2 2 Jlethylcyclopentane-benzene” 2 17 7 2-Met h ylpent ane-nitroet hanen 25 3 9 9 14 6 25 9 Nitroethaiie-benzeneo 11 6 Nitromethane-benzeneo 25 10 13 45 4 Nitromethane-benzenep 3 11 6 Nitromethane-carbon tetrachloridep 12 45 4 15 27 44 1-Xtropropane-carbon tetrachloridep 11 28 25 9 12 12 12 12 25 16 29 1-Xit ropropane-n-hexane0 12 14 2-Sitropropane-carbon tetrachloride0 25 30 7 7 9 31 2-Sitropropane-n-hexane0 25 16 17 15 15 h v . for all data 7.5 11.3 27.2 8.6 a Data of Brown and Smith (1960). * Data of Brown and Smith (1957). Data of Severns et al. (1955). Data of Griswold and Wong (1952). e Data of Brown and Smith (1955a). 1 Data of Brown and Ewald (1951). 0 Data of Brown and Smith (1954b). Data of Brown and Smith (1954a). Data of Sinor and Weber (1960). 7 Data of Kretschmer et al. (1948). Data of Myers (1955). Data of Myers (1957). Data of Myers (1956). n Data of Edwards (1962). Data of Saunders and Spaull (1961). p Data of Brown and Smith (195513). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
45 45 45 50 50 50 45 100 45 60 60 45 50 45 69-79 50 72-79 69-80 69-72 100 50 72-80
Experimental
5 2 5 5 9 4 10 10
2
0
contribution methods (Deal and Derr, 1968; Pierotti et a]., 1959; TVilson and Deal, 1962), and techniques based on the division of the Scatchard-Hildebrand cohesive energy density into both polar and nonpolar contributions (Helpinstill and Van Winkle, 1968; Null and Palmer, 1969; Weimer and Prausnitz, 1965). Moreover, it now seems clear t h a t for a n y new theoretical approach t o the prediction of solution properties, the statistical mechanics would be greatly simplified by considering a single solute molecule in a solvent matrix t o avoid having t o invoke either “local volume fractions” or an order-disorder correction. Finally, calculations of phase equilibria in concentrated solutions are found t o be relatively insensitive to moderate errors in the values used for the limiting activity coefficients. Comparison of Expressions
T o investigate the techniques proposed, comparisons were made with experimental data for 31 totally miscible binary system-. The criteria used for selection of the test systems were that good data be available over the whole composition range a t low to moderate pressures, t h a t the data include not only liquid compositions, pressures, and temperatures, but also reliable value? of the vapor compositions, and further t h a t there be i n each case sufficient data available in both dilute
regions for each binary pair t o permit accurate estimation of the activity coefficient a t infinite dilution. Activity coefficients y were calculated from
using experimental d a t a for 5 , y, P , and T, and the d a t a and techniques tabulated by Prausnitz e t al. (1967) t o calculate the gas-phase fugacity coefficients, +(, the reference state fugacity fto, and the Poynting correction in the exponential term. Activity coefficients so calculated do not depend on a n y particular expression for excess Gibbs energy. These values were then plotted in both dilute regions for each binary pair and graphically extrapolated to infinite dilution, thus yielding two experimental values of ymfor each binary pair. The uncertainty in such an extrapolation was, in general, of the order of 1-5010, though in the worst cases it may have been of the order of 10%. The test systems chosen and the resulting values of ymare listed in Table I. For purposes of comparison, three commonly used twoparameter expressions for the excess Gibbs energy were usedWilson’s equation (Equations 2 and 3), the van Laar equation Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
573
(Equation 4), and the Scatchard-Hamer equation (Equation 5 ) . For binary solutions these are,
Table II.
Fit of Binary Data to Single-Parameter Wilson Equation Av. abs. error in y ,
System no.
where (3) BE
RT
-
B2122
AX,
+
22
(4)
"E
where
For each of these expressions, there are two adjustable parameters per binary pair, and these can be found uniquely in each case from the two values of y". This was done for the 31 data test sets, and the resulting parameters were used with each expression to calculate vapor-liquid equilibria over the entire composition range for comparison with the experimental data. The results are expressed in Table I as the average absolute deviation in vapor-phase mole fractions. Also given for comparison is the least-square total pressure fit of all points, using the method of Prausnitz et al. (1967). The conclusions are perhaps best expressed by the average error in vapor composition for all data: The Wilson equation, fit t o all points, gives agreement to 0.75% in y, while using only the two values of ymreduces the agreement by less than 15% t o 0.86%. On the other hand, the average deviation using the parameters found from the values of y m with the van Laar and ScatchardHamer expressions are significantly larger. Similar results for the Wilson equation have been obtained b y Hankinson et al. (1970). They also reported that the fit using the 7"'s was relatively insensitive to i = l O ~ operturbations in each ym.An analogous conclusion was reached in this study, with the fortuitous result t h a t one may use moderately imprecise values of ym to get quite a good representation of the vapor-liquid equilibria in the concentrated range. Of course, the converse would also be true: T o predict even a moderately good value of y m from data in the middle concentration range, one must have exceedingly good data, and even then this is not always possible. Single-Parameter Wilson Equation
A technique for modifying the Wilson equation to make it a single-parameter expression has been suggested (Tassios, 1969; Hankinson et al., 1970). The parameters, A, are related t o the differences in pair potentials, A,I - A,,, the difference between like-pair and unlike-pair interactions. Tassios suggested using the molar energy of vaporization to characterize the like-pair interactions, A,, leaving At? as the sole adjustable parameter for the binary pair. Wong and Eckert (1971) have modified this approach to retain the physical interpretation of the Wilson parameters; they interpretated A f t as the configurational energy per pair interaction; and this is the technique used here. For each data set, the configurational energy of the pure components has been calculated from the heat of vaporization, corrected by the enthalpy deviation of the real gas and the APv term. An arbitrary coordination number of 10 was 574
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Av., all systems
X 103
-
y2"
All points
Y Im
Y 2-
1368 1215 1018 1515 1246 1281 1521 439 1048 1512 1228 565 998 925 433 302 526 1111 1278 1342 1081 1173 637 1417 1112 1077 566 1278 932 1266 809
1349 1174 873 1558 1239 1232 1505 663 843 1507 1255 840 1249 608 - 104 -336 - 95 1101 1204 1255 1167 1157 824 1318 1125 1031 352 1206 1055 1259 1002
1346 1245 1108 1481 1210 1279 1501 423 1083 1494 1242 210 321 1098 642 866 825 1132 1251 1377 958 1198 712 1440 1198 1146 814 1200 1112 1376 920
All points
ylm
5 8 22 7 7 3 10 17 20 4 7 50 44 38 47 67 48 4 8 12 14 3 11 6 13 9 28 9 14 18 16
2 13 37 11 10 10 32 37 3 4 66 65 51 68 66 77 3 6 18 20 2 21 21 11 15 31 11 12 19 18
1 8 23 10 12 3 11 18 23 4 5 60 120 47 48 105 64 3 4 18 27 3 10 5 8 10 43 11 12 9 14
18
25
24
7
-hl2,
col/mol
chosen for these nonespanded liquids. This 15 very similar t o values determined in studies of liquid structure, and minor variations in the choice do not affect the results. Then the single adjustable parameter A12 for the modified Wilson equation was determined for each of the 31 data sets by three different methods: First, all points were best fit using a leastsquares fit to total pressure. Xext two explicit values of A12 were found from each of the two ym's for the binary pair. The results are presented in Table 11, showing the parameters calculated and the average deviation in vapor composition for the equilibria for the whole composition range computed by each method. If the molecular interpretation of Wilson's equation is valid, and providing that the ya's used are correct, all three evaluations of Alz for each data set should be substantially the same, and the predictions of the vapor composition should be of comparable accuracy. This is true in perhaps three-quarters of the cases. However, several systems which are fit well by both techniques using a two-parameter Rilson equation are not well represented by the one-parameter modification-notably, the alcohol-hydrocarbon systems, plus methanol-chloroform and carbon tetrachloride v ith both acetonitrile and nitromethane. These represent the systems with the greatest deviations from Raoult's law. Clearly the three positive values of AI, found (Systems 15-17) can have
~~
Table 111.
System
Calculations for Multicomponent Systems Based on Binary Data Av. ab,. error in T. O C 2-Parom.Wilson 1 -Poram.Wilson, All points ym's All points Y 1-
Acetone-met hanol-chloroform 0.34 0.76 (6 points). Acetone-methanol-water 1.24 1.16 (11 points)* Acetone-methyl acetate-methanol (12 points)a 0.32 0.26 Ethanol-methylcyclopentane0.19 0.92 benzene (45 points). Hexane-ethanol-benzene0.09 0.57 methyl cyclopent ane (10 points) c 0.44 0.73 Av. for all points Data of Severns et al. (1955). * Data of Griswold and Wong (1952). c
5
no physical significance, as the pair potential is a n intrinsically negative number. With the limited number of systems investigated, it seems that the single-parameter Wilson expression is significantly poorer whenever the deviations from Raoult's law are sufficiently large t h a t either of the ymvalues is of order 10 or greater. The important point to notice here, however, is t h a t whenever the one-parameter Wilson equation is applicable, the evaluation of the parameter from a single -ym does result in almost as good a representation of the vapor-liquid equilibria as a fit of all the points. Further, it should be noted t h a t in almost every such case where there is a significant difference in the quality of the fit between the predictions based 011 each of the y m values, the parameter calculated from the ymvalue nearer unity gives the better prediction. Multicomponent Systems
Once binary data are known or can be predicted, the extension to the multicomponent case is eminently straightforward. When we follow the methods of Prausnitz et al. (1967), the two binary parameters for each pair in the multicomponent system are combined in the multicomponent Wilson expression. Thus, the multicomponent vapor-liquid equilibria are calculated from binary data only. For demonstration here, bubble point calculations were made for five multicomponent systems, with the binary system parameters determined by each of four different techniques. First, the regular Wilson equation was used with binary parameters found from fitting all binary data. Second, the same expression was used with the binary parameters evaluated from the two ymvalues for each pair. Third, the single-parameter modification was used with XI2 for each pair found by the best fit of all binary data. And last, the single-parameter expression was used with Xlz evaluated for each pair from the experimental value of 71". Results are presented in Table 111. As expected, the two-parameter form is superior to the single-parameter expression, giving deviations from the experimental values only about one half as great in both bubble point temperature and vapor composition. Again, however, it is shown that the use of ym values to estimate parameters does not introduce very much additional error, either for the one- or two-parameter form. Conclusions
The Wilson equation with the two parameters for each binary pair determined from the infinite dilution activity coefficients can represent data virtually as well as a best fit of
Av. ob,. error in ,. Y . X 1 Oa 2-Param.Wilson 1 -Param. W ikon All points y,'s All points ylm
1.02
2.84
9
7
24
32
1.13
1.28
11
14
13
23
0.20
0.36
13
14
14
16
1.56
2.25
5
9
26
31
1.92 1.17
2.16 1.78
6 10
19 19
22 24
4 8 Data of Sinor and Weber (1960).
the parameters over the whole compositioii range. The same technique, when used to evaluate the parameters for enthalpic expressions, such as the van Laar and Scatchard-Hamer equations, gives significantly poorer results. The major advantage of using such a method is that there are numerous experimental or calculational methods for determining ym values, and the resulting calculations are relatively insensitive to errors in the values used. Even if only a single ymvalue is available for a binary pair, the single-parameter Wilson equation gives a good representation of the binary system as long as the deviations from Raoult's law are not excessive. For the very nonideal systems studied (where one of the values was of order 10 or greater) , the single-parameter Wilson equation was significantly less satisfactory. The technique is readily extended to multicomponent systems in the usual manner, with results similar to those found for the binary vapor-liquid equilibria. Nomenclature
parameter in van Laar equation parameter in Scatchard-Hamer equation parameter in van Laar equation parameter in Scatchard-Hamer equation reference state fugacity, atm excess Gibbs energy. cal/mol pressure, atm gas constant, atni, cm3/mol, O K temperature, O K liquid molar voliime, cm3 liquid mole fraction vapor mole frartion activity coefficient limiting activity cocfficient a t infinite dilution pair interaction energy ill Wilson equation, cal/ mol parameter in Wilson equation vapor-phase fugacity coefficient liquid volume fraction literature Cited
Brown, I., Ewald, A. H., A&. J . Sci. Res. (Ser. A ) , 4, 198 (1951). Brawn, I., Smith, F., Aust. J . Chem., 7,264 (1934a). Brown. I.. Smith. F.. ibid.. D 269 119,54b). Brown: I.; Smith; F.: ibid.; 8 , 62 (19,55a). Brown, I., Smith, F., ibid., p 501 (195Sb). Brown, I., Smith, F., ibid., 10, 423 (1957). Brown I. Smith, F., ibid., 13, 30 (1960). Deal, 6. k.,Derr, E. L., Znd. Enq. Chein., 60 (4),28 (1968). Eckert, C . A., Prausnitx, J. ?\I.,-Orye, K.V O'Connell, J. P., AZChE-Znd. Chem. Eng. Sump. S f r . , 1, 73 (196,5). I.,
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
575
Edwards, J. B., PhD Thesis, Georgia Institute of Technology, 1962.
Svmv. Ser.., 48 (3). Griswold. J.. Wonz. S. Y.. Chem. Ena. Proar. ” ,, 18 (1952):
0 1
“
1
~
Hankinson, R. W., Langfitt, B. D. Tassios, D. P., presented a t the AIChE-IMIQ Third Joint Meeting, Denver, Colo., 1970. Helpinstill, J. G., Van Winkle, M., Ind. Eng. Chem. Process Des. Develop., 7, 213 (1968).
Kobayashi, R., Chappelear, P. S., Deans, K. H., Ind. Eng. Chem., 59(10), 63 (1967).
Kretschmer, C. B., Nowakowska, J., Weibe, R., J. Amer. Chem. SOC.,70, 1785 (1948).
Martire, D. E., Pollava, L. Z., Advan. Chromatogr., 1, 335 (1965). Myers, H. S., Ind. Eng. Chem., 47, 2215 (1955). Myers, H. S., ibid., 48, 1104 (1956). Myers, H. S., Petrol. Refiner, 36 (3), 175 (1957). Neretnieks, I., Ind. Eng. Chem. Process Des. Develop., 7, 335 (1 968\.
Prausnitz, J. M., Eckert, C. A,, Orye, R. V., O’Connell, J. p., “Com uter Calculations for Multicomponent Vapor-Liquid E a u i l i k k ” Prentice Hall. Enelewood Cliffs. N. J . . 1967. Saun’ders, D’. F.,Spaull, A.’J. g.,2. Phys. Che& (Frankfurt), 28, 332 (1961).
Severns, W. H., Sesonke, A., Perry, R. H., Pigford, R. L., AZChE
J.. 1, 401 (1955).
Sinor, J. E. Weber, J. H., J . Chem. Eng. Data, 5,243 (1960). Tassios, D., presented a t the 62nd Annual Meeting of AIChE, Washington, D. C., November 1969. Weimer, R. F. Prausnitz, J. M., Hydrocarbon Process., 44, 237 (1965).
Wilson, G. M., J. Amer. Chem. SOC,86, 127 (1964). Wilson, G. M., Deal, C. H., Ind. Eng. Chem. Fundam., 1, 20 (1962).
Wong, K. F., Eckert, C. A., ibid., 10, 20 (1971). Young, C. L., Chromatogr. Rev., 10, 129 (1968).
\-_.I
Null, H.’R., Palmer, D. A., Chem. Eng. Progr., 65 (9), 47 (1969). Orye, R. V., Prausnitz, J. M., Ind. Eng. Chem., 57 (5), 18 (1965). Pierotti, G. J., Deal, C. H., Derr, E. L., ibid., 51 (I), 95 (1959). Porter, P. E., Deal, C. H., Stross, F. IT, J.Amer. Chem. SOC.,78, 2999 (1956).
RECEIVED for review January 4, 1971 ACCEPTED April 23, 1971
Work supported financially by the Petroleum Research Fund of the American Chemical Society.
Estimation of Ideal Gas Heat Capacities of Hydrocarbons from Group Contribution Techniques New and Accurate Approach Tran-Phuc Thinh, Jean-louis Duran, and Rubens S. Ramalho’ Lava1 University, Department of Chemical Engineering, Quebec 10, Que., Canada
An additive group technique for calculation of ideal gas heat capacities is proposed. Testing with hydrocarbons at several temperatures reveals that this technique is more accurate than any now appearing in the literature.
S e v e r a l methods for predicting C,* values for hydrocarbons are available in the literature. These methods fall into two categories. Category 1 constitutes methods based upon use of theoretical concepts to obtain contributions to C*, from translational, rotational, and vibrational energies. Typical are the methods described by Dobratz (1941), Stull and Xayfield (1943), Crawford and Parr (1948), Souders e t al. (1949), and Lleghreblian (1951). Category 2 comprises additive-group techniques. Methods are empirical and are based upon the assumption that each molecular structural group contributes to the overall heat capacities in a n additive manner. Typical are the methods of Anderson et al. (1944), Johnson and Huang (1957), and Rihani and Doraiswamy (1965). Reid and Sherwood (1966) point out t h a t the methods of Johnson and Huang (1957) and Rihani and Doraiswamy (1965) are the most accurate within category 2 appearing in the literature. If both categories are considered, the methods of Souders et al. (1949) (category 1) and Rihani and Doraiswamy (1965) (category 2) give the most accurate estimations. To whom correspondence should be addressed. 576
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
The method proposed in this article falls within the category of the additive-group techniques. This proposed technique of estimation is shown t o be definitely more accurate than a n y of the existing methods within both categories. I n general no single previous method can combine the three following desirable characteristics: good accuracy, applicability over a broad temperature range from cryogenic to very high temperatures, and continuous estimation of C,* as a function of temperature (many of the existing techniques are limited t o point values a t certain temperature intervals). .4 method which could combine these three characteristics is needed since even the extensive compilation of thermodynamic properties of hydrocarbons of the API Research Project 44 (1969) does not include all hydrocarbons known (e.g., naphthalene is not tabulated). Also, no C,* data for hydrocarbons below 273°K (and often below 298°K) are available except for the first few members of the paraffinic series. Of
Additive
Franklin (1949) suggested, by extension of Pitzer’s statistical mechanical treatment for long chain paraffins (1940), t h a t any thermodynamic property P of hydrocarbons could be well approximated by
