The origins and limits of thermal steady-state multiplicity in the continuous stirred tank reactor

In this study of multiplicity in the exothermal continuous stirred tank reactor (CSTR) problem, the formalism of singularity theory is extended to bifurcation surfaces and same outstanding questions regarding the structure of the parameter space are answered. The multiplicity boundaries of the adiabatic CSTR model are shown to form a three-dimensional surface, an irreducible object which is fundamental to our understanding of this model and its more complex gradientless perturbations. Extension of the analysis to the diabatic model reveals the need for finite coupling between feed and coolant temperatures in order to achieve a smooth embedding of the diabetic into the adiabatic parameter space. This resolves a paradox previously unreported in the singularity theory treatment of the CSTR; the existence of which leads to a subtle problem of overdetermination at the theoretical level, and prevents the smooth application of singularity theory to reactor design at the applied level. It is shown that the highest-order singularity, the winged cusp, is present only for zero or finitely coupled feed and coolant temperatures; otherwise it is trapped at infinity. The results of this analysis are shown to have particular relevance to practical chemical reactor design and will be applied in forthcoming studies of a novel method of thermal stabilization.