Reversible autocatalytic reactions in an isothermal CSTR: Multiplicity, stability and relaxation times

Abstract

In a recent paper, Gray and Scott have considered the autocatalytic reactions: A → B; rate ∝ ab n , n = 0, 1 or 2 where a and b are the concentrations of A and B respectively. Interest centred mainly on irreversible systems but for which the catalytic species was not indefinitely stable, decaying instead by a rate proportional to its concentration b. In practice all chemical reactions are to some extent reversible. The present work investigates the effect of reversibility for the cases in which B does not decay. Bounds are established on the ranges of residence-time t res for which multiple stationary-states are possible. The stability of the different solutions is assessed and the relaxation times t * characterizing the decay of perturbations are given. For deceleratory reactions reversibility enhances the decay rates (decreases t *): for autocatalytic systems the decay rates may be unaltered or even reduced by a finite reverse reaction-rate. Also treated is the influence of non-zero inlet concentrations b 0 of the autocatalyst. This may lead to greater changes in the patterns of behaviour possible than those observed in the absence of reversibility. The algebraic analysis remains tractable throughout so the various effects can readily be interpreted in physical terms.