Steady-state multiplicity and bifurcation analysis via the newton polyhedron approach

A method based on the Newton polyhedron determines bifurcation of solution branches for simultaneous algebraic equations. This method has broad applicability in multiple steady-state analysis in chemical engineering. Reduction of the steady-state equations to a single nonlinear equation is not required. The method provides in nondegenerate cases the normal form of the algebraic equations—the leading nonlinear terms which alone determine steady-state multiplicity. Bifurcation conditions are developed for isothermal reaction between two adsorbed species in a catalytic CSTR and for two and three parallel reactions of arbitrary order in a nonisothermal CSTR.