Stationary and non-stationary models of bacterial kinetics in well-mixed flow reactors

Abstract

A reaction scheme is proposed which reflects the autocatalytic nature of bacterial reaction kinetics. It is shown that the usual Monod Kinetic equation may be obtained when the stationary state assumption is applied. A mathematical model which does not assume stationary-state kinetics is then employed to represent the dynamics of the continuous flow, stirred-tank bacterial reactor, or “chemostat.” This “non-stationary chemostat model” is intended to account for lags observed between the predictions of the “Monod chemostat model” and experimental responses to temperature [12], concentration [14] and flow changes. Methods used in the comparisons between stationary and non-stationary models include small perturbation analysis and numerical simulation. In the process, the small perturbation analysis of the Monod chemostat model presented earlier by Koga and Humphrey [8] is extended. It is shown that this model predicts markedly different transient responses to flow and to concentration changes. Conditions under which the stationary-state assumption may be applied are also derived and compared with others presented for simple non-autocatalytic enzyme kinetics [4] and for consecutive chemical reactions [7].