Solution of the Rachford – Rice equation by differential homotopy
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In this paper, a numerical calculation routine is developed to solve the Generalized Rachford-Rice (G-RR) equation in three-phase and multi-component systems, based on the coupling of the successive substitution method and the continuation by differential homotopy, which was applied to different types of mixtures in Vapour-Liquid-Liquid (VLL), Vapor-Liquid-Solid (VLS) and Liquid-Liquid-Liquid (LLL) balances. The proposed algorithm was tested with three different mixtures at conditions of temperature, pressure, composition and different components, finding that the proposed solution is stable and convergent for any type of start vector. The results predict the equilibrium phases satisfactorily, the minimum error being 1.9% in LLL and the maximum being equal to 15.47% in VLL.
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