Heterogenous azeotropic distillaion-homotopy-continuation methods

An algorithm for the simulation of three-phase distillation towers and associated phase separators is presented. The algorithm utilizes the homotopy-continuation method of Allgower and Georg[1] to accurately track the homotopy path, with extensions to avoid limit points when multiple solutions are encountered and when liquid phases are introduced on the trays. The Allgower and Georg algorithm is also extended to track solution paths in parametric studies. Emphasis is placed on the calculation of liquid—liquid equilibria, with a reliable, yet efficient, homotopy-continuation algorithm introduced. An effective method for incorporating the LLE algorithm in the homotopy-continuation algorithm for heterogenous distillation is also introduced. The combined algorithms have located two steady-state solutions for an industrial azeotropic distillation tower a very narrow range of the reflux ratios, one with a single liquid phase on the trays, the other with two liquid phases on 70% of the trays. In addition, for the dehydration of ethanol with benzene, it has detected a region in which five steady-state solutions exist for the same specifications. Three of these solutions were reported by Magnussen .[2] and observed in dynamic simulations by Prokopakis and Seider[3].