On the Approach to Steady States of Reacting Systems in the Continuous Stirred Tank Reactor

A theoretical investigation is presented of the approach of chemical reactions to their steady states in a continuous stirred tank reactor (CSTR). We define a approach time tϵ which is a measure of the time required for any perturbation to decrease below a certain value where ϵ = 1/e is a convenient choice for linear networks. We shown analytically for any first order network that the approach time is less than or equal to the average residence time but never longer regardless whether „overshoot”︁ or „false start”︁ occurs if the sum of the initial CSTR concentrations does not exceed the sum of the input concentrations. For higher order single step CSTR reactions we present analytical solutions for small perturbations from their steady states. We show that the longest relaxation time is equal to the average residence time for all non‐autocatalytic higher order reactions in the CSTR. For autocatalytic reactions, however, the relaxation time constant in the CSTR may become infinite at critical flow rates. This interesting phenomenon is called critical slowing down and it has an analogy in second order equilibrium phase transitions. We show that critical slowing down may occur also in higher order autocatalysis. It may act as a tunable low pass filter i.e. the open autocatalytic reaction may resemble a kinetic buffer system that absorbs even large perturbations. As illustrations a number of examples of reaction types are presented.