An MINLP formulation for the optimization of multicomponent distillation configurations

Abstract

Designing configurations for multicomponent distillation, a ubiquitous process in chemical and petrochemical industries, is often challenging. This is because, as the number of components increases, the number of admissible distillation configurations grows rapidly and these configurations vary substantially in their energy needs. Consequently, if a method could identify a few energy-efficient choices from this large set of alternatives, it would be extremely attractive to process designers. This paper develops such a method by solving a Mixed Integer Nonlinear Program (MINLP) that is formulated to pick, among the regular-column configurations of Shah and Agrawal (2010b), those configurations that have a low vapor-duty requirement. To compute the minimum vapor-duty requirement for each column within the configuration, we use techniques that rely on the Underwood’s method. The combined difficulty arising from the nonlinearity of Underwood equations and the combinatorial explosion of the choice-set of alternatives poses unmistakable challenges for the branch-and-bound algorithm, the current method of choice to globally solve MINLPs. To address this difficulty, we exploit the structure of Underwood equations and derive valid cuts that expedite the convergence of branch-and-bound by enabling global solvers, such as BARON, infer tighter bounds on Underwood roots. This provides a quick way to identify a few lucrative alternative configurations for separation of a given non-azeotropic mixture. We illustrate the practicality of our approach on a case-study concerning heavy-crude distillation and on various other examples from the literature.