Dynamic responses to perturbations in the non-isothermal, continuous-flow stirred-tank reactor (CSTR)—II. Nonadiabatic operation: The general case

Abstract

When an exothermic reaction is carried out in an open system, discontinuous jumps between stationary states may occur in response to continuous variation of control parameters such as average residence-time. Our previous paper examined the dynamics of such jumps for reaction in a CSTR operating adiabatically. Here the general case of marginally supercritical conditions during non-adiabatic operation in a CSTR is considered. It is again found that: (i) times to ignition and (ii) times for decay to a stationary state both obey universal formulae characteristic of the category of instability, lengthening rapidly as criticality is approached. For example: time-to-ignition ∝ (degree of supercriticality) − 1 2 . We illustrate our results chiefly by reference to a single, first-order, deceleratory reaction with the usual strong dependence on temperature, but the treatment is quite general and can cope with any concentration-dependence and any temperature-dependence of reaction rate.