A hybrid numerical‐symbolic solving strategy for equation‐oriented process simulation and optimization

Abstract

The equation‐oriented (EO) and sequential modular (SM) methods are two typical approaches for numerical process simulation and optimization. For a large‐scale system, the EO method usually suffers from difficulties in variable initialization. The SM method, conversely, can suffer from slow convergence and requires experience in choosing appropriate tear variables. In this article, a novel strategy combining numerical and symbolic approaches is proposed for solving process systems represented by polynomials. First, a digraph method is developed to identify the subset of equations that should be solved simultaneously. Then, a symbolic computation method based on Gröbner basis is proposed to reformulate the simultaneous equations as a completely sequential model with a triangular structure. Last, the reformulated model is solved sequentially without any iterative tearing process. The case studies show that the proposed strategy can significantly improve the solving efficiency and robustness for process simulation and optimization. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2764–2780, 2017