A Novel Method To Find All Physical Solutions of Constrained Chemical Engineering Models in Polynomial Equations

Abstract

Sometimes, there are more than one solutions of a chemical process simulation. In this work, a novel strategy is proposed for finding all physical solutions of chemical engineering models described in polynomials with prescribed variable bounds. First, the Grobner basis method is proposed to transform the original model into a lower-triangular polynomial system. Based on this triangular structure, the problem of finding solutions of a constrained multivariable polynomial system is converted to solve a set of constrained univariate polynomials sequentially. Next, a real-root-isolation algorithm is developed to compute the disjoint intervals of each univariate polynomial such that each interval contains one solution. Finally, a numerical method with convergence monitoring is proposed to locate each solution. Case studies show that the proposed method can accurately analyze the multisolution features of the systems. All physical solutions can be found directly and effectively.