Multiplicity for isothermal autocatalytic reactions in open systems. Influence of reversibility and detailed balance

The prototype autocatalytic reaction A + 2B → 3B (rate = k_cab²) leads to a variety of exotic patterns of behaviour, including multistability, ignition, extinction and hysteresis. It also lies at the heart of the simplest models which display sustained oscillatory reaction under well-stirred, isothermal conditions in an open system. The lower-order catalysis A + B → 2B (rate = k_q ab) and the uncatalysed step A → B (rate = k_u a) have the same overall stoichiometry and may occur in parallel with the above reaction. The rate constants k_q and k_u influence the range of residence times over which the exotic patterns can be found. As these two additional steps become more important, such features disappear leaving a monotonic dependence of the stationary-state concentrations on residence time. The conditions for multiplicity etc. in this augmented model can be evaluated analytically in terms of the quotients k_q/k_ca₀ and k_u/k_ca₀², where a₀ is the concentration of reactant A in the feed to the reactor. Reversibility also affects the range over which these patterns arise. Each of the three reactions is subject to the same equilibrium constant K_e = k_c/k_-c = k_q/k_-q = k_u/k_-u. The influence of K_e is revealed clearly by the use of a graphical or flow-diagram approach.