Prediction of 3D Transversal Patterns in Packed-Bed Reactors Using a Reduced 2D Model: Oscillatory Kinetics

Abstract

We have recently showed the formation of transversal patterns in a 3D cylindrical reactor in which an exothermic first-order reaction of Arrhenius kinetics occurs with variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution, with the front position oscillating in the axial direction, while in the 3D case, three types of transversal patterns can emerge: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating−oscillating fronts. In the present study, we analyze the possible reduction of the 3D model to a 2D cylindrical shell model to predict patterns. We map bifurcation diagrams showing domains of different modes using the reactor radius (R) as a bifurcation parameter and show that the front divergence and the domains of the kn-mode pattern in the 3D model [corresponding to the transversal eigenfunction Jk(μknr) exp(ikθ), in which Jk is the Bessel function of the first kind] can be predicted by those of the one wave in the 2D model using the linear transformation R3D = μknR2D.