THE MODELING AND DYNAMICS OF CATALYSTS AND FIXED BED REACTORS

The modelling and dynamics of catalysts and fixed bed reactors are considered in this study. Beginning with unsupported metal catalysts (e.g., wires and foils), the study continues with supported metal catalysts to the final analysis of fixed bed reactors. The pertinent literature is reviewed extensively for each of the three basic subjects and the mathematical techniques are presented in a chemical reaction engineering context.;Previous experimentally observed multiplicity and oscillatory phenomena in metal catalyzed reactions have focused on surface reaction mechanisms. However, the fact that the phenomena occur for a wide range of chemical systems suggests that physical rate processes take part in the underlying mechanism. New physicochemical models for unsupported and supported metal catalysts are proposed which are capable of predicting observed ignition, extinction, and oscillatory behaviour by taking the microscopic surface structure into account. Simple harmonic and subharmonic oscillations as well as a wide variety of apparent nonperiodic chaotic oscillations are predicted by the models. The "fuzzy wire" model for unsupported catalysts includes the morphology of the rough activated surface of catalytic wires in the description of the transport and reaction processes. Quantitative comparisons of model predictions with data for butane and cyclohexene oxidation show quite reasonable agreement. The "pebbly surface" model for supported metal catalysts combines the dynamic behaviour of the individual metal crystallites on the surface of the support with heat conduction and diffusion in the bulk particle. This detailed modelling approach which shows good qualitative agreement with data for CO oxidation, also is well suited for cases where sintering or poisoning of the catalyst occurs. Both models in their simplest form are unable to predict the very long period oscillations observed for H(,2) and CO.;Numerical techniques are presented for determining bifurcation of multiple steady states and periodic solutions in fixed bed reactors. Special consideration is given to the solution of stiff reactor equations resulting in an efficient collocation technique. The types of bifurcation behaviour for a first order, irreversible reaction in a tubular reactor with axial dispersion are classified according to the parameters and summarized in parameter space plots. In particular the influence of the Lewis and Peclet numbers is investigated. It is shown that oscillations due to interaction of dispersion and reaction effects will not exist in fixed bed reactors and moreover, will only occur in very short "empty" tubular reactors. The parameter study not only brings together previously published examples of multiple and periodic solutions but also reveals a hitherto undiscovered wealth of bifurcation structures. Sixteen of these structures, which come about by combinations of as many as four bifurcations to multiple steady states and four bifurcations to periodic solutions, are illustrated with numerical examples. Although the analysis is based on the pseudo homogeneous axial dispersion model, it can readily be applied to other reaction diffusion equations such as the general two phase models for fixed bed reactors.