Concentration multiplicity and stability for autocatalytic reactions in a continuous stirred‐tank reactor

Abstract

Abstract Concentration multiplicity and stability for autocatalytic reactions of the type A + R → R + R with overall rate expression \documentclass{article}\pagestyle{empty}\begin{document}$ -{\rm r}_A = {\rm kC}_A^m {\rm C}_R^n $\end{document} in a continuous stirred‐tank reactor (CSTR) is analyzed in a rigorous way in this paper. Important parameters for multiplicity criteria are reaction orders m and n, dimensionless space time Θ, and the ratio P of feed concentration of R to that of A. Necessary conditions for the system to have multiple exit concentrations (conversions) are defined in the (m, n, P) space. Multiplicity is guaranteed by limiting the dimensionless space time in a proper range in addition to the necessary conditions. Stability analysis shows that there is no periodic oscillation for the system. The upper and lower steady states of multiple solutions are both asymptotically stable. A unique steady state is globally stable.