Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models

This paper presents a modeling procedure for the derivation of generalized disjunctive programming (GDP) models for the optimal design of complex or thermally coupled distillation columns. Optimization models for the separation of ideal and azeotropic mixtures are derived on the basis of superstructures reported previously in the literature. The GDP models use rigorous design equations, where the trays in the column can be considered permanent or conditional, depending on the functions they perform (i.e., heat supply/removal, draw streams and feeds). The conditional trays are modeled with disjunctions to decide whether or not vapor-liquid equilibrium mass transfer should be applied in each potential tray. The GDP models derived are solved with a logic-based outer approximation algorithm. The performance of the proposed procedure is evaluated with three examples: (a) the separation of an ideal mixture, (b) the separation of an azeotropic mixture, and (c) an industrial problem involving ideal mixtures. These examples show that the proposed method produces fairly robust and computationally efficient models.