Patterns due to convection-diffusion-reaction interaction in a fixed-bed catalytic reactor

The process of pattern selection in a heterogeneous model of a catalytic reactor was studied by analyzing the behavior of a simple condensed model. This condensed model captures the main features of a detailed model if the following features can be matched: (1) the fluid-phase behavior, (2) the catalytic kinetics and (3) the interaction between the phases. A general axial-dispersion model describes the fluid phase and it may acquire the plug-flow reactor, mixed reactor or membrane reactor (stagnant-fluid) asymptotes. The solid phase is assumed to exhibit thermal bistability or follow an oscillator that incorporates a fast and diffusing surface temperature and a localized activity as its dynamic variables. Patterns may emerge already with simple bistable kinetics in a plug-flow reactor with a continuous supply of reactants. This is an important result showing that oscillatory behavior may emerge, due to interaction of thermal multiplicity and reactant flow, in a single-variable distributed system. Stationary waves emerge in a stagnant-fluid membrane reactor. Pattern selection in systems with oscillatory kinetics is determined by the three factors noted above, by the phase planes spanned by the reactor, and by the ratio of the two slowest time scales: front residence time and the period of oscillations. The simple form of the model allows the suggestion of a general classification of emerging patterns and identification of the corresponding conditions in terms of realistic reactor models. A rich plethora of patterns may be induced in a plug-flow reactor with symmetry-breaking interaction; such interaction can be achieved when the fluid temperature is maintained constant. In an adiabatic reactor, exothermic positive-order oscillatory reactions are likely to exhibit almost homogeneous oscillations, certain pulse patterns and stationary fronts.