A globally convergent method for finding all steady‐state solutions of distillation columns

Abstract

SignificanceA globally convergent method is proposed that either returns all solutions to steady‐state models of distillation columns or proves their infeasibility. Initial estimates are not required. The method requires a specific but fairly general block‐sparsity pattern; in return, the computational efforts grow linearly with the number of stages in the column. The well‐known stage‐by‐stage (and the sequential modular) approach also reduces the task of solving high‐dimensional steady‐state models to that of solving a sequence of low‐dimensional ones. Unfortunately, these low‐dimensional systems are extremely sensitive to the initial estimates, so that solving them can be notoriously difficult or even impossible. The proposed algorithm overcomes these numerical difficulties by a new reparameterization technique. The successful solution of a numerically challenging reactive distillation column with seven steady‐states shows the robustness of the method. No published software known to the authors could compute all solutions to this difficult model without expert tuning. © 2013 American Institute of Chemical Engineers AIChE J 60: 410–414, 2014