Improving Convergence Behavior of Nonlinear Equation Systems in Intensified Process Models by Decomposition Methods

The two decomposition methods Dulmage-Mendelsohn (DM) decomposition and bordered block transformation (BBTF) have been examined on their capabilities to eliminate convergence problems during the iteration of large, nonlinear equation systems as they occur frequently in process modeling. They both divide the overall system into lower dimensional subsystems, which can be solved separately in sequence. Exemplarily these methods were applied on the model of a reactive distillation column, where the decomposed systems show a higher robustness with respect to systematically selected initial points compared to the original system. Nevertheless, the improvement in DM seems small since a large subsystem with 576 of the 664 model equations remains. The convergence result from the iteration of the BBTF decomposed system depends a lot on the initial values for certain strongly coupled variables called tearing variables. In future, methods will be investigated and may also be developed to further reduce the dimension of the subsystems in DM and provide accurate initial values for the tearing variables in BBTF