Modeling of a Catalytic Counter - Current Chemical Reactor
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AbstractThis thesis considers modeling and analyzing aspects of a counter-current, catalytic,moving bed, chemical reactor, based on a study in the book Mathematical ModelingTechniques by R. Aris. The final reaction kinetics equations have turned out tobe mathematically equivalent to the Michaelis-Menten system, treated in detailin another famous book, Mathematics Applied to Deterministic Problems in theNatural Sciences by C. C. Lin and L. A. Segel.The first part of the thesis discusses modeling aspect such as catalytic reactionkinetics, transport in the reactor and conservation laws. In its most general form, themodel leads to a complex system of partial convection/reaction/diffusion equations.The analysis continues with simplification, scaling and qualitative behavior, whichleads to several situations of regular as well as singular perturbation. The analysisalso includes a revised model with permanent poisoning of the catalyst which wasnot treated in the book above. The perturbation solutions are compared to numericalsolutions obtained by the MatlabTM ODE solver ODE45.The last part is considering a simplified one-dimensional reactor in space whichturned out to lead to some numerical challenges.When comparing the present analysis to the books above, is clear that theirperturbation analysis is based on an inconsistent scaling. The analysis in Lin andSegel does not apply to the situation they describe, and this also seems to be the casefor the analysis in Aris. However, time limitations has prevented a deeper analysisof these aspects.