A method to extend the domain of convergence for difficult multicomponent, multistage separation problems

Abstract A new computational procedure is presented to attain convergent solutions for multistage, multicomponent separation problems for non-ideal fluid mixture systems when starting from very crude initial assumptions. The procedure incorporates a gradual non-ideality enhancing method into the Ishii–Otto pseudo-binary-mixture (PBM) algorithm [Comput. Chem. Eng. 25 (2001) 1285]. Shifting K -values from ideal to non-ideal in the course of iterative calculations gradually approaches the correct solution to a problem. The domain of convergence with the proposed procedure is greatly extended and very difficult problems where both non-ideality of fluid systems and very rough assumptions for initial variables are involved can be solved with the same ease as one solves problems with ideal physical properties. An innovative method, made possible because of the PBM concept, to simplify the Jacobian matrix and significantly reduce the computing time for evaluation of the Jacobian is also presented. The effectiveness of the methods is illustrated with example problems.

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