Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Abstract

Optimizing multistage processes, such as distillation or absorption, is a complex mixed-integer nonlinear programming (MINLP) problem. Relaxing integer into continuous variables and solving the easier nonlinear programming (NLP) problem is an optimization idea for the multistage process. In this paper, we propose a relaxation method based on the efficiency parameter. When the efficiency parameter is 1 or 0, the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage. And non-integer efficiency represents partial existence. A multi-component absorption case shows a natural penalty for non-integer efficiency, which can assist the efficiency parameter converging to 0 or 1. However, its penalty is weaker than the existing relaxation models, such as the bypass efficiency model. In a simple distillation case, we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.