Analysis of a Chemostat Model with Variable Yield Coefficient and Substrate Inhibition: Contois Growth Kinetics

Abstract

We analyze the steady-state operation of a generalized reactor model that encompasses a continuous flow bioreactor and an idealized continuous flow membrane reactor as limiting cases. The biochemical reaction kinetics is governed by a Contois growth model subject to noncompetitive substrate inhibition with a variable substrate yield coefficient. The steady-state performance of the reactor is predicted and stability of the steady-state solutions as a function of dimensionless residence time reported. Our results identified two cases of practical interest. The first feature corresponds to the case where solutions to both no-washout and washout conditions are bistable. The second feature identifies the parameter region in which periodic solutions can occur when the yield coefficient is not constant. Both these features are often undesirable in practical applications and must be avoided. Scaling of the model equations reveals that both the second-bifurcation parameters are functions of the influent concentration. Our results predict how the reactor behavior varies as a function of influent concentration and identify the range of influent concentrations where the reactor displays neither periodic nor bistable behavior.