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Feasibility study by interval arithmetics 107How a subregion is subdivided into smaller boxes is demonstrated in Figure 2. This picturetaken at a moment, shows the yet living boxes, and how they are subdivided. The boxcontaining a wide dot contains a solution.4. ResultsFeasible domain of extractive distillation of particular material systems have been explored.Here we show the results related to separation of the acetone – methanol mixture formingminimum boiling azeotrop, with the help of high boiling entrainer water, in batch extractivedistillation process (batch rectifier device, charge in the boiling vessel, entrainer feed to thecolumn) and continuous extractive distillation process (entrainer feed above the main feed).Methanol (B)10.90.80.70.60.50.40.30.20.10Water (E)(F/V) min [0.1578170891437115,0.1585855111005144]S 2SNS 1UN0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Acetone (A)Acetone10.90.8S 10.70.6SN0.50.40.3UN0.20.1S 200 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225F/VFigure 3. Evolution of the singularities at R = 10. a/ Left hand side: Singular point paths. b/ Right hand side:Bifurcation diagramExample results for the case of batch extractive distillation are shown in Figures 3a and 3b.The exact F/V at which the bifurcation occurs could not be determined by repeatedly findingthe singular points because the computation time increases enormously in the neighborhoodof the bifurcation.0,600,500,401.F/L0,300,200,103.2.0,000,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00RFigure 4.Domains of distinct maps. Domain 1 is feasible.Example results for the case of continuous extractive distillation are shown in Figure 4. Themain parameters are R and F/L. The three regions denoted by square labels correspond todifferent phase maps; domain 1 is the feasible domain. The points of the domain border aredetermined by finding bifurcation points. (Note: this figure is valid according to the analysisof one criterion only, namely connection of the specified rectifying profile with an extractiveprofile. Connection of the specified stripping profile with an extractive profile is not analyzedhere.)