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Proceedings of GO 2005, pp. 103 – 108.Application of interval arithmetics for exploring feasibilityof extractive distillation variantsErika R. Frits, 1,2 Ali Baharev, 1 Zoltán Lelkes, 1 Mihály Markót, 3 Zsolt Fonyó, 1,2 Endre Rév, 1,2 andTibor Csendes 41 Budapest Univ. Techn. Econ., Dept. Chem. Eng., Budapest, H-1521, Hungary, ufo@mail.bme.hu2 Bud. Univ. Techn. Econ. - Hung. Acad. Sci. Res. Group Techn. Chem., Budapest, H-1521, Hungary, efrits@mail.bme.hu3 European Space Agency, Advanced Concepts Team, Keplerlaan 1, 2201 AZ Noordwijk, the Netherlands,Mihaly.Csaba.Markot@esa.int4 Univ. Szeged, Inst. Appl. Informatics, Pf. 652., Szeged, H-6701, Hungary, csendes@inf.u-szeged.huAbstractFeasibility study of extractive distillation variants is a successful application area of interval arithmeticsbased reliable computation of real function zeroes and global extrema. Feasibility of theseprocesses can be well estimated by studying a differential equation system coupled with algebraicequations. Existence and location of the singular points play a crutial role in feasibility of theseprocesses.From mathematical point of view, the main problem consists of reliably finding the existenceand loci of all the singular points in a given domain, and determining the bifurcations of the phasemap. Both the singular points and the bifurcations have been reliably found by applying an intervalarithmeticbased branch and bound optimization algorithm.The mathematical model is shown, and the capability of the method is demonstrated on exampleresults related to the separation of acetone – methanol mixture (forming minimum boilingazeotrope) with water as a heavy boiling entrainer, in both batch and continuous extractive distillationprocesses.Keywords:interval arithmetics, branch and bound, phase map, singular point, bifurcation, extractive distillation,feasibility.1. IntroductionDistillation as a process for separating liquid components is based on the different volatilityof the components to be separated. Separation of close-volatility mixtures by conventionaldistillation is difficult and expensive. Separation of azeotrope-forming mixtures by conventionaldistillation is impossible. A mixture is called azeotrope-forming if the volatility of thecomponents are identical at some composition, the so-called azeotrope.Extractive distillation processes apply a third component, the so-called entrainer, to makethe separation feasible. There are several variants of these processes according to the volatilityrelations between the components, and according to the several technical opportunities to bechosen.Production of components in specified purity and acceptable recovery is possible only ifthe process pameters are kept inside a domain whose form and extension is not known inadvance. This is called ’the feasible domain’. The process is called feasible if such a domainexists. The main process parameters are the so-called reflux ratio and feed ratio.