The present paper is a continuation of the problems analysed in Part I (A. Burghardt and M. Berezowski, Chem. Eng. Process., 26 (1989) 45-57) where a method was presented for dividing the global parameter space into regions with different bifurcation diagrams (pellet temperature versus Thiele modulus) by means of a line called the hysteresis variety. The aim of this work is to determine an exact boundary between subregions of the model parameters with different steady-state solutions, contained within the regions defined by the hysteresis variety. Such a boundary is usually termed the catastrophic set. The model employed, of simultaneous heat and mass transport accompanied by chemical reaction, takes into account concentration gradients inside a catalyst pellet and assumes that the pellet temperature is uniform but different from that of the surrounding fluid. Two methods have been proposed for the determination of subregions of multiple steady states: an exact method called parametric and an approximate procedure using the limiting relations for the effectiveness factor. In the parametric method the generalized Thiele modulus is chosen as a parametric variable whose variation from zero to infinity enables the catastrophic set of the parameters θo and γ to be determined for β* = constant. The method has been tested for three basic shapes of catalyst pellet (slab, cylinder and sphere) and reaction orders of 1 4 ≤ n ≤ 3; an example is shown in the Figures where spherical attention has been given to analysing the structure and location of the subregion with five steady-state solutions of the model equations. The approximate method, valid strictly for θ → 0 or θ → ∞, can still be applied for values of θ differing considerably from zero and infinity if the magnitude of the error incurred relative to the exact method is taken into account. Assuming the error ε = 1%, the ranges of θ have been determined where the approximate procedure can be employed. The main advantage of this method is the possibility of obtaining an explicit analytical relation defining the catastrophic set. An example to calculate the catastrophic set using both methods is presented for the catalyst slab, reaction order n = 0.5 and β* = 0.1. © 1990.
