AN ALGORITHM FOR CALCULATING CRITICAL-POINTS IN MULTICOMPONENT MIXTURES WHICH CAN EASILY BE IMPLEMENTED IN EXISTING PROGRAMS TO CALCULATE PHASE-EQUILIBRIA

This paper describes an add-on procedure for the calculation of critic al points in multicomponent mixtures according to the method by Heidem ann and Khalil [1]. The benefit of this approach is that all equations of state (EOS) and mixing rules of an existing program for calculatin g phase equilibria, which can be a commercial product or self-made, ar e available for the calculation of critical points. The method by Heid emann and Khalil requires the first and second partial derivatives of the fugacities with respect to the male numbers (delta ln f(k)/delta n (i))(T,V,ni not equal j)(delta 2 ln f(k)/delta n(l)delta(nj))(T,V,ni n ot equal i,j). In our work the first partial derivatives are obtained numerically with a four-point differencing scheme and the second parti al derivatives are obtained from the first partial derivatives with a numerical directional derivative as suggested by Michelsen [2]. This n ew approach allows the combination of the method by Heidemann and Khal il with any program for calculating phase equilibria and eliminates th e need for the cumbersome determination of the analytical first partia l derivatives of the fugacity with respect to the mole numbers. The im plementation into the commercially available process simulator ASPEN P LUS Version 9.2 [3] is described and some calculation results are show n. (C) 1998 Elsevier Science B.V. All rights reserved.