Smooth penalty function method for rigorous optimization of distillation processes

Abstract

AbstractInteger decisions on stage numbers and feed locations, and global optimality are still challenging for rigorous optimization of distillation processes. In the present article, we propose a smooth penalty function method to address both these problems. The proposed method is based on the relaxation of the integer decision problem into continuous nonlinear programming (NLP) problem by adopting the bypass efficiency model developed by Dowling and Biegler. A smooth penalty term (SPT) is proposed and added to the total annual cost (TAC) function to form a new objective function, namely, the smooth penalty function. Using the new objective function, the problem is initially solved with negative weight coefficients for the SPTs regarding each column section to get an optimum near the global optimum of the SPT. Then, starting from this solution, the problem is solved again iteratively by increasing the values of the weight coefficients until all the stage numbers become integers. The performance of the method is validated by an illustrating problem and in three case studies, including a reactive distillation optimization problem.