Transversal hot zones have been reported to form in packed-bed reactors used to conduct exothermic reactions. Packed-bed reactors are usually operated under non-adiabatic conditions. Previous attempts to predict the formation of transversal hot zones have been made on both shallow and long reactors under adiabatic conditions; that is, wall heat transport is zero. We show that a rich variety of slowly oscillating transversal hot zones, such as rotating patterns, targets, and spirals, may form in shallow, non-adiabatic reactors. Under certain conditions, azimuthally symmetric target patterns coexist with azimuthally non-symmetric rotating patterns. Surprisingly, a small wall heat transport can force a traveling wave or band motion observed under adiabatic conditions into a rotating pattern. A transition from the rotating patterns and/or target patterns to spiral waves depends on the residence time, the reactor length scale, and the wall heat transfer coefficient. A shallow reactor model predicts that the spatiotemporal patterns oscillate at a very low frequency (order of 10 −5 Hz), which is in agreement with predictions based on laboratory experiments.

Transversal temperature pattern formation has been observed in laboratory and industrial catalytic packed-bed reactors (PBRs) used for conducting exothermic reactions. These patterns or nonuniform states can strongly affect reactor performance and pose severe safety issues. Recent studies show that symmetry-breaking bifurcations may cause transversal pattern formation in a reactor operated under nonadiabatic conditions. In this study, we show that wall temperature, which dictates the instantaneous and overall heat exchange rate, strongly influences the selection and dynamics of various target and rotating patterns exhibited in a shallow nonadiabatic PBR. We demonstrate this by linear stability analysis-guided extensive numerical simulations of a shallow reactor model assuming periodic blocking-reactivation kinetics for the catalytic reaction. Transversal spatiotemporal patterns predicted in lab-scale (∼6 cm diameter) and/or bench-scale (∼60 cm) reactors, include rotating patterns, inward/outward/multi-ring targets, quasi-stationary moving patterns, and symmetric and asymmetric spirals. We show that wall temperature modulates the transition between these targets and rotating transversal nonuniform states at both scales. We argue that rich and intricate patterns observed much more in bench-scale reactors than those in lab-scale reactors are possibly due to reduction in the heat removal time upon increase in diameter by 10-fold. We further classify the simulated transversal patterns into three regimes, viz., (i) heating, (ii) heating and cooling, and (iii) cooling, based on the nature of wall heat exchange rate dynamics dictated by the (instantaneous) local temperature near the reactor wall. Wall heat exchange rate dynamics being an experimental observable makes it a signature of a nonuniform state present inside the reactor.