One- and two-dimensional spatiotemporal thermal patterns in a fixed-bed reactor

Spatiotemporal patterns, that exist in a plug-flow reactor catalyzing an oscillatory exothermic reaction, are analyzed using a piecewise linear heat-generation function and an approximate integration procedure. Pattern selection is determined by the phase planes spanned by the reactor and the ratio of the two slowest time scales: front residence time and period of oscillations. The main patterns in a one-dimensional bed are classified as almost homogeneous oscillations, periodic pulses, excitable waves and oscillatory fronts. Certain analytical results can be obtained for this approximate model. We consider behavior of an adiabatic reactor, in which convection inhibits symmetry breaking, as well as that of an isothermal-fluid reactor in which the fluid temperature is constant but the solid temperature is varying due to reaction. In the latter case convection induces symmetry breaking. In an annular cylindrical reactor the two-dimensional motions, in the form of moving and rotating pulses, reflect the ring symmetry in the angular direction and the reaction-convection interaction in the longitudinal direction.