Ind. Eng. Chem. Process Des. Dev. 1981, 20,578
578
CORRESPONDENCE Modlfied Mlxing Rules for the Lee-Kesler Equation Sir: I read with interest the article, “Collection of Phase Equilibrium Data for Separation Technology”, by William Schotte (1980) in a recent issue of this journal. I would like to point out that the modified mixing rules for the Lee-Kesler equation which appeared in this article as eq 18 and 19, respectively zcm
= Y I Z d + YZZCZ
Pcm
= zcmRTcm/Ucm
avoid a discontinuity in the relation between pseudocritical pressure and composition at either end of the composition range.
Literature Cited Joffe, J. Ind. Eng. Chem. Fundam. 1076. 15, 298. Schotte, W. Ind. Eng. Chem. FrocessDes. Dev. 1060, 19, 432.
Department of Chemical Engineering and Chemistry New Jersey Institute of Technology Newark, New Jersey 07102
were introduced by me in my paper entitled “VaporLiquid Equilibria by the Pseudocritical Method” (Joffe, 1976) for precisely the reason given by Schotte, namely to
Joseph Joffe
ticular mixing rule is less important than the development of the complete set of mixing rules needed to fit the equation of state to mixture data. Joffe (1976) proposed a new set of mixing rules for use with the Lee-Kesler equation (Lee and Kesler, 1975). Plocker, Knapp, and Prausnitz (1978) have cited Joffe’s work, but developed a different set of mixing rules. Equation 1 was suggested as a modification of the Plocker-Knapp-Prausnitz mixing rules rather than the Lee-Kesler mixing rules.
Sir: The comments of Joffe concerning the modified mixing rules for the Lee-Kesler equation are appreciated. I (Schotte, 1980) had termed the mixing rule for the compressibility factor z c m = Y I Z ~ I+ ~ 2 2 , ~ (1) as obvious rather than novel. It is difficult to give proper credit for this equation. Although it is not precisely one of Kay’s mixing rules (Kay, 1936) for pseudo-critical properties, it may be considered as a logical extension. Possibly, Pitzer and Hultgren (1958) might be credited. They proposed a correlation for the compressibility factor
Literature Cited
z = z(0) + &1)
(2) for both pure components and mixtures. They considered the mixing rule for the acentric factor = YlOl + YZWZ (3)
Joffe, J. Ind. Eng. Chem. Fundam. 1076, 15, 298. Kay, W. B. Ind. Eng. Chem. 1036, 28, 1014. Lee, B. I.; Kesler, M. 0. A I C M J . 1075, 21, 510. P$er, K. S.; Hultgren, 0. 0. J. Am. Chem. Soc. 1958, 80, 4793. Plocker, U.; Knapp, H.; Rausnk, J. M. I d . Eng. Chem. Frocess Des. D e v . 1078, 17, 324. Schotte, W. I d . Eng. Chem. Process Des. D e v . 1080, 19, 432
to be an extension of Kay’s rules. Equation 1results from a combination of eq 2 and 3. I would like to point out that the adoption of one par-
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1981 American Chemical Society
William Schotte
