Ind. Eng. Chem. Res. 2001, 40, 1009
1009
CORRESPONDENCE Comments on “Convergence of the Continuous Fluid-Solid Phase Equilibrium Problem Using Quadrature Compositional Characterizations” C. Lira-Galeana† Thermodynamics Research Laboratory, Mexican Institute of Petroleum, Mexico City, C.P. 07730, Mexico
Sir: I read the paper “Convergence of the Continuous Fluid-Solid Phase Equilibrium Problem Using Quadrature Compositional Characterizations” by J. A. Labadie and K. D. Luks (Ind. Eng. Chem. Res. 2000, 39 (No. 3), 790-796) and found a contradiction between eq 14 of this paper and the pure-solid scheme approached by the authors. Labadie and Luks used the following equations for defining the solid formation temperature of a pseudoized mixture of 1 precipitating and n - 1 nonprecipitating normal alkanes: s f li(P,T,x) ) f purei (P,T) i ) n s (P,T) i ) 1, 2, ..., n - 1 f li(P,T,x) ) f purei
(14a) (14b)
s (P,T) in the above The authors stated that fpurei equations (i.e., the fugacity of the pure solid species i at the system pressure P and temperature T) is calculated for only the heaviest (and, hence, unstable) † Telephone: +52 5 333-6507. Fax: +52 368 9203. E-mail:
[email protected].
pseudocomponent, as introduced elsewhere.1 Because T (i.e., the solid formation temperature) represents a saturation point, it becomes clear that eq 14a suffices for solving for T, and no other equations are needed for specifying the whole nature of the system (i.e., the liquid-phase compositions remain unchanged, while the first crystal formed is wholly composed by that heaviest pseudocomponent). By equating the fugacities of nonprecipitating species between liquid and pure-solid species (as eq 14b points out), one clearly implies that lighter species will coexist in the (incipient) solid phase at the crystal point, which is not the case approached by the authors. I hope that the “use” of eq 14b in the paper by Labadie and Luks could be the result of a misprint error and that the calculation difficulties of numerical quadrature might not come from such an erroneous formulation of the saturation temperature. Literature Cited (1) Lira-Galeana, C.; Firoozabadi, A.; Prausnitz, J. M. Thermodynamics of Wax Precipitation in Petroleum Mixtures. AIChE J. 1996, 42, 239.
IE0007365
10.1021/ie0007365 CCC: $20.00 © 2001 American Chemical Society Published on Web 01/04/2001
