A New Homotopy-Based Strategy for the Robust Determination of All the Feasible Solutions for CSTR Systems

Abstract

A new homotopy-based strategy is presented that can be used in the robust determination of multiple steady-state solutions for continuous stirred tank reactor (CSTR) systems. The strategy relies on the features of homotopy parameter and variables bounding, and requires only that one feasible solution of the system is either known beforehand or can be solved with an existing solving algorithm. The strategy systematically results in all the multiple solutions, or alternatively confirms that the problem does not have multiple solutions, within the predefined problem domain. The strategy was successfully demonstrated with CSTR cases gathered from the literature. Finding all the feasible solutions was verified in simple CSTR systems by applying tools available in the literature. Variables bounding constrained the homotopy path to travel only within the pre-defined variable domain. The strategy is applicable for determining multiple steady states for a variety of chemical engineering systems.