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Concentration multiplicity and stability for autocatalytic reactions in a continuous stirred‐tank reactor
Author(s) -
Lin K. F.
Publication year - 1979
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450570410
Subject(s) - dimensionless quantity , continuous stirred tank reactor , multiplicity (mathematics) , autocatalysis , limiting , oscillation (cell signaling) , mathematics , thermodynamics , stability (learning theory) , physics , chemistry , parameter space , control theory (sociology) , mathematical analysis , kinetics , engineering , classical mechanics , computer science , mechanical engineering , geometry , biochemistry , control (management) , machine learning , artificial intelligence
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.