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



A 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