A new efficiency relaxation model for rigorous stage number optimization of distillation columns

Abstract

Determining the optimal state number in distillation column design is a mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve. One strategy to solve this problem is relaxing integer stage numbers into continuous variables and solving an easier nonlinear programming (NLP) problem. However, the existing relaxation model often converges to non-integer stage numbers or poor local optima in practical applications, which motivates this paper to develop a new relaxation model. The proposed relaxation model employs an interpolation function to relax the discrete decision on the existence of a stage by varying interphase mass and heat transfer rate between zero and equilibrium state. By adjusting a shape parameter in the interpolation function, the interpolation function shape and its penalty extent of non-integer stage can be manipulated. The results of three distillation column optimization cases show that the proposed model can effectively avoid converges to non-integer stage numbers or poor optima.