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Path‐following approaches to the solution of multicomponent, multistage separation process problems
Author(s) -
Vickery D. J.,
Taylor Ross
Publication year - 1986
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690320404
Subject(s) - homotopy analysis method , homotopy , distillation , path (computing) , nonlinear system , process (computing) , separation process , mathematics , algebraic equation , mathematical optimization , computer science , chemistry , physics , chromatography , quantum mechanics , pure mathematics , programming language , operating system , organic chemistry
In solving the nonlinear algebraic equations that are normally used to model multicomponent separation processes, one is not guaranteed that Newton's method or any of its relatives will converge to the solution. This paper describes two homotopies and their use in the solution of difficult equilibrium stage separation process problems. The first, the Newton homotopy, is able to solve more problems than a standard implementation of Newton's method but is not the most reliable homotopy. Since the equations being solved no longer model a separation process unit, the Newton homotopy sometimes suffers from intermediate solutions that are physically meaningless. The second, the thermodynamic homotopy, is strongly based on the thermodynamic properties of the systems involved. This new homotopy is able to handle not only the more traditional distillation problems (hydrocarbon systems and mildly nonideal systems), but is also extremely effective at solving azeotropic and extractive distillation problems. The implementation of these methods requires only minor modifications to existing software.