Dynamic responses to perturbations in the non-isothermal CSTR: Times to ignition and times for temperature decay—I. Adiabatic operation

Abstract

When a simple exothermic reaction is carried out in an open system, discontinuous jumps between stationary states (ignitions and extinctions) may occur in response to continuous variation of control parameters such as inflow-temperature or average residence-time. This paper examines the dynamics of such jumps for reaction in a CSTR operating adiabatically. Two problems are analysed: (a) the dependence of time-to-ignition on the degree of supercriticality and (b) the decay of small perturbations to the steady state for marginally sub-critical conditions (“critical slowing down”). It is shown that both the time-to-ignition (and time-to-extinction) and the decay to a stationary state obey universal formulae characteristic of the category of instability, increasing rapidly as criticality is approached: time-to-ignition ∝ (degree of supercriticality) -1/2 We illustrate our results chiefly by reference to a single, first-order, deceleratory reaction. We at first exploit the exponential approximation to the Arrhenius temperature law but the treatment is quite general and can cope with any temperature-dependence of reaction-rate.