higher positive values of the parameter a restrict the applicability of the NRTL equation in the heterogeneous region. On the contrary, the modification proposed by Marina and Tassios with the value a = -1 makes it impossible to describe in a quantitative correct way the behavior of some homogeneous systems, e.g., all systems with .$ > 0.35. With the systems water-polar substance the value of ,$ lies very often in the range 0.2-0.4 and if the value of ,$ is greater than 0.35, it is necessary to use the parameter a < -1 to preserve the position of this minimum. The relations for the determination of the G11 were summarized by Su‘ska (1972). A more detailed discussion of the NRTL equation and calculation procedures have been prepared by Novik (1973). Literature Cited -1
I 0,5
I
06
I
03
4
Marina, J. M . , Tassios, D. P., lnd. Eng. Chern., Process Des. Develop., 12,67 (1973). NovBk, J. P., SuSka, J., MatouS, J., Collect. Czech. Chern. Cornmun., in press, 1973. Renon, H.,Prausnitz, J. M., AlChEJ., 14,135 (1968). SuSka, J . , NovBk. J. P., Matoub, J., Pick, J., Collect. Czech. Chem. Cornrnun., 37, 2663 (1972).
1
0,2
0;1
0
Figure 1 .
-
is not able to describe the behavior of systems which have XO 0.3 and (Gll)xo < 0.2, without a shift of this minimum. Considering the data in Figure 1 it follows, too, that
Institute of Chemical Technology Department of Physical Chemistry &aha 6, 1905, Czechoslovakia
Josef P. Novlk* Josef SuBka Jaroslav MatouS
Received for review April 16, 1973 Accepted October 17,1973
Some Remarks to Marina’s Modification of the NRTL Equation
Sir: Dr. Novak and his coworkers with their letter concerning the LEMF equation (Le., the NRTL equation with a = -l), their presentation in the 4th Congress CHISA 72 concerning the NRTL and Redlich-Kister equations (Novak, et al., 1972), and their recent publication (Suska, et al., 1972) demonstrate the limitation of the aforementioned empirical equations in correlating VLE data. In the case of the LEMF equation the limitation applies to a very limited number of systems for which 0.35 < ( < 0.4 (Le., 0.1 < XO < 0.15) since they did not find any systems with .$ > 0.4. According to Suska, et al. (1972), however, the values of XO cannot be determined uniquely because the calculation of G11 involves differentiation of the experimental data. For example, for the system ethanol (1)-n-heptane (2), use of the P-X data yields a minimum value for G11 at X I = 0.55 while use of the y-n data yields G11 min at X I = 0.35. Because of this uncertainty it appears to the writer that it would be safer that the quantity (Gll)%o, evaluated from the constants obtained by regressing the VLE data, be checked. If it is found negative a value of -1 > a > -2 should be used.
Such a value should cover systems with 0.4 > 6 > 0.35, as seen from Novak’s graph, and, as shown by Marina and Tassios (1973) and Larson and Tassios (1972), should yield standard deviations not too far from the minimum one. Since, however, the magnitude of the 710 and 7z0values iml pose some restrictions in the NRTL equation (CHISA paper) and no such reference is made for the LEMF equation, the whole subject of the limitations of the LEMF equation needs further study. Literature Cited D.,lnd. Eng. Chern., Process Des. Develop., 11, 37 (1972). Marina, J., Tassios, D., lnd. Eng. Chem., Process Des. Develop., 12,67 (1973). Novak. J. P., et a/., paper presented at the 4th Congress, CHISA 72,1972. Suska, J., Novak, J. P., Matous, J , Pick, J., Collect. Czech. Chern. Commun., 37,2664 (1972). Larson, D., Tassios,
Department of Chemical Engineering Dimitrios Tassios and Chemistry Newark College of Engineering Newark, New Jersey 07102 Received for reuieu, September 19, 1973 Accepted October 17, 1973
CORRECTION In the article, “Calculation of High-pressure Phase Equilibria and Molecular Weight Distribution in Partial Decompression of Polyethylene-Ethylene Mixtures,” by D. C. Bonner, D. P. Maloney, and J. M. Prausnitz [Ind. Eng. Chem., Process Des. Develop., 13, 91 (1974)], the last line in the Appendix on p 95 should read: The value of X21 at 260°C is -49.9 atm. ~
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Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 2, 1974
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