Thermal stabilization of chemical reactors II. Bifurcation analysis of the Endex CSTR

Abstract

The steady states of the dynamical Endex CSTR problem are analysed in terms of degenerate bifurcation (singularity) theory. Steady–state analysis is used in two ways: (1) as a device to assist in understanding and predicting complex dynamical behaviour; and (2) as a practical design and operational tool, by applying the concept of quasi–static parameter variation. In the bifurcation analysis, consideration is given to the effects of thermal mismatching, kinetic mismatching, and variations in the thermal exchange, mass flux and heat loss rate parameters, on the structure of the parameter space. The qualitative equivalence of the bifurcation structure of the kinetically matched perfectly coupled adiabatic Endex scheme and the single–reaction adiabatic CSTR is demonstrated, with reference to the role of the reaction enthalpy effects. Numerical analysis shows that either kinetic mismatching of the reactions or imperfect heat exchange may introduce Hopf bifurcations into the adiabatic system. This is a result that is both philosophically and practically important because it shows that limit cycles are not restricted to non–adiabatic thermokinetic systems. The coefficients of thermal exchange, mass flux and heat loss are found to induce distortions of the surface of saddle–node bifurcations (the limit–point shell) through codimension–2 bifurcations. The steady–state and oscillatory–state degeneracies are discussed with reference to the design and operational implications for a working system.