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.
Highlights
The steady-state and dynamic behaviour analyses of continuous stirred tank reactors (CSTRs) have received considerable interest in the field of chemical engineering
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
Homotopy continuation methods form an attractive set of solving methods, which offer a means of reaching multiple steady-state solutions for a CSTR model from one starting point
Summary
The steady-state and dynamic behaviour analyses of continuous stirred tank reactors (CSTRs) have received considerable interest in the field of chemical engineering. It will be shown that the target of finding all the feasible solutions for the investigated CSTR systems can be reached with the Newton homotopy-based solving method if it is equipped with the features of homotopy parameter and variables bounding presented in Malinen and Tanskanen [30,31]. Homotopy continuation methods form an attractive set of solving methods, which offer a means of reaching multiple steady-state solutions for a CSTR model from one starting point. If the Jacobian matrix term is determined at a starting point close to the problem domain boundary, it may cause the numerical values of some non-zero elements of the Jacobian matrix term to become nearly zero This in turn will pose numerical challenges for homotopy path tracking inside the bounding zone.
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