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Poisoning-induced exchange of steady states in a catalytic chemical reactor

Published online by Cambridge University Press:  17 February 2009

D. D. Do  and
R. H. Weiland
D. D. Do
Affiliation:
Department of Chemical Engineering†, University of Queensland, St. Lucia 4067
R. H. Weiland
Affiliation:
Department of Chemical Engineering†, University of Queensland, St. Lucia 4067
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Abstract

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Slow catalyst poisoning can result in the sudden failure of a chemical reactor operating isothermally with substrate-inhibited kinetics. At failure, a satisfactory steady state is exchanged for one of low conversion. The method of matched asymptotic expansions is used to give a detailed description of the exchange process in the phase plane. The structure of the jump is ascertained by separate asymptotic expansions across two adjoining transition regions in which the independent variables contain unknown shifts.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 2 , October 1980 , pp. 237 - 253
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover Publications, New York, 1970).Google Scholar
[2]Aris, R., “Phenomena of multiplicity, stability and symmetry”, Annals New York Acad. Sci. 231 (1974), 86–98.CrossRefGoogle ScholarPubMed
[3]Aris, R., The mathematical theory of diffusion and reaction in permeable catalysts, Vols. I and II (Clarendon Press, Oxford, 1975).Google Scholar
[4]Bruns, D. D., Bailey, J. E. and Luss, D., “Steady state multiplicity and stability of enzymatic reaction systems”, Biotechnol. and Bioeng. 15 (1973), 1131–1145.CrossRefGoogle ScholarPubMed
[5]Buckmaster, J. D., Kapila, A. K. and Ludford, G. S. S., “Linear condensate deflagration for large activation energy”, Acta Astro. 3 (1976), 593–614.CrossRefGoogle Scholar
[6]Cole, J. D., Perturbation methods in applied mathematics (Blaisdell Publishing Co., Mass., 1968).Google Scholar
[7]Devera, A. L. and Varma, A., “Substrate-inhibited enzyme reaction in a tubular reactor with axial dispersion”, Chem. Eng. Sci. 34 (1979) 275–278.CrossRefGoogle Scholar
[8]Do, D. D. and Weiland, R. H., “Consistency between rate expressions for enzyme reactions and deactivation”, Biotechnol. and Bioeng. (1980) (in press).CrossRefGoogle Scholar
[9]Haberman, R., “Slowly varying jump and transition phenomena associated with algebraic bifurcation problems”, SIAM J. Appl. Math. 37 (1979) 69–106.CrossRefGoogle Scholar
[10]Ho, T. C., “Uniqueness criteria of the steady state in automotive catalysis”, Chem. Eng. Sci. 31 (1976), 235–240.CrossRefGoogle Scholar
[11]Kapila, A. K., “Reactive-diffusive system with Arrhenius kinetics: dynamics of ignition”, SIAM J. Appl. Math. (1980) (in press).Google Scholar
[12]Kapila, A. K., “Arrhenius systems: dynamics of jump due to slow passage through criticality”, (1980) unpublished manuscript.CrossRefGoogle Scholar
[13]Kapila, A. K. and Matkowsky, B. J., ‘Reactive-diffusive system with Arrhenius kinetics: multiple solutions, ignition and extinction”, SIAM J. Appl. Math. 36 (1979), 373–389.CrossRefGoogle Scholar
[14]Kassoy, D. R., “Extremely rapid transient phenomena in combustion, ignition and explosion”, SIAM-AMS Proceedings 10 (1976), 61–72.Google Scholar
[15]Liñán, A. and Williams, F. A., “Theory of ignition of a reactive solid by constant energy flux”, Combustion Sci. Tech. 3 (1971), 91–98.CrossRefGoogle Scholar
[16]Liñán, A. and Williams, F. A., “Ignition of a reactive solid exposed to a step in surface temperature”, SIAM J. Appl. Math. 36 (1979), 587–603.CrossRefGoogle Scholar
[17]Periera, C. J. and Varma, A., “Uniqueness criteria for the steady state in automotive catalysis”, Chem. Eng. Sci. 33 (1978), 1645–1657.CrossRefGoogle Scholar