A Simple Algorithm for Vapor-Liquid-Liquid Equilibrium Computation

Calculation of phase equilibria plays a crucial part in modeling and simulation of many chemical engineering processes, and it is computationally intensive, especially for systems that exhibit two liquid phases. In this contribution, a new method to calculate the globally stable phases for systems that exhibit two liquid phases is presented which is based on iterative computation and does not require any predetermined solution set In the proposed method, both the liquid compositions are determined with the help of a simple adaptation equation by constant times the deviation in temperatures of the two vapor phases and constant times the deviation in the corresponding vapor compositions. Convergence is evaluated based on the sum of deviation between the temperatures and vapor compositions of the two vapor phases in equilibrium with two liquid compositions, subject to the material balance constraint being satisfied. A further enhancement in convergence speed is achieved using an adaptation mechanism for updating the two constants weighing the errors. The performance of the proposed method is evaluated by computation of vapor-liquid-liquid equilibria (VLLE) for (nonreactive) mixtures encountered in five esterification reactions, in the water-toluene-aniline system and ethylene glycol-lauryl alcohol-nitromethane systems. The results obtained show that all bubble points and liquid phase compositions of the heterogeneous mixtures and the homogeneous mixtures have been predicted accurately. The proposed method can be applied to any vapor-liquid-liquid systems common in reactive distillation systems, particularly in systems with one of the phases as an almost pure single component.