Stability analysis of the continuous ethanol fermentation process with a delayed product inhibition

Abstract

• A continuous ethanol fermentation system with a discrete delay is studied. • A delayed product inhibition is considered as a main reason for oscillatory behavior. • Effect of delay and product inhibition on the system behavior is discussed. In the paper, we propose and analyze a mathematical model of the continuous ethanol fermentation process to study the mechanisms of the self-sustained oscillations of ethanol concentration. The model is based on the assumption that microorganism cells response to the inhibitory effect of product (ethanol) concentration with a delay. From the local stability analysis of the system, we show that the delay time is one of the crucial factors for the occurrence of oscillations and for a critical delay time the fermentation process undergoes a Hopf bifurcation. Further analysis shows that the operating variables and kinetic parameters have also a significant effect on the dynamical behavior of the fermentation system. A proper manipulation of the operating variables allow us to eliminate the oscillatory behavior.