Generalized disjunctive programming models for the design of complex distillation systems

This dissertation is concerned with the development of Generalized Disjunctive Programming (GDP) models for the optimal design of distillation columns and separation sequences. Chapter 1 reviews the current state of the art in mathematical programming tools and solution algorithms, and their application to the synthesis of distillation column problems. Chapter 2 introduces a systematic modeling framework based on two superstructure representations that are mapped into general GDP models that can be solved with various techniques. Chapter 2 also illustrates the application of the modeling framework with the development of linear models for the synthesis of distillation sequences with and without heat integration. Chapter 3 describes the development of simultaneous optimization and heat integration models based on GDP, which are solved using standard Mixed Integer Nonlinear Programming (MINLP) algorithms. In Chapter 4, the systematic framework developed in Chapter 2 is used to produce GDP models for nonlinear distillation sequence design problems, with and without heat integration. Chapter 4 also proposes a modified initialization scheme for the Logic-Based Outer Approximation algorithm. Chapter 5 presents the development and solution of rigorous tray-by-tray GDP models for designing distillation columns and separation sequences. This chapter proposes a new master problem formulation for the Logic-Based Outer Approximation algorithm, in order to improve performance. Chapter 6 of the dissertation explores the application of rigorous distillation GDP models in the context of complex column configurations, for separating ideal and non-ideal mixtures. Finally, Chapter 7 summarizes the contributions of the dissertation and presents future work directions.