Boundary function method for stage number optimization for multi-stage distillation process design

In chemical process designs, optimizing stage numbers in the multi-stage separation process is a common and challenging mixed integer nonlinear programming (MINLP) problem. The researchers transform the MINLP into an easily solved NLP by presetting sufficient number stages and optimizing their spatial distribution of existence index. However, because the preset stages, the optimization variable number is increased significantly with structure redundancy. This motivated us to propose the boundary function method in this paper, which eliminates redundancy and increases solution efficiency. The proposed boundary function method introduces boundary variable for stage number optimization. Then the actual stage number is optimized by varying the boundary variable. Using the proposed method, the variable number for the stage number optimization can be restored to one for each column section while maintaining the NLP property. The proposed method significantly reduced the optimization variable number, iteration number, and computation time in four illustrating distillation problems.