Mathematical Modeling of Continuous Fermentation in Lactic Acid Production

Abstract

The equations of a generalized mathematical model for the continuous fermentation of lactic acid have been presented. The system of equations includes the material balance relationships for biomass, a substrate, lactic acid, a byproduct, and the component of raw materials that produces the substrate. The specific rate of biomass growth takes into account all of the inhibition effects, namely, inhibition by the biomass, substrate, and product. Numerical solutions to the equations of the model in discrete and continuous forms for the basic variant of the values of constants have been presented. The effect of the characteristics of inhibition on the characteristics of the process, including the maximum productivity as a function of the dilution rate, has been evaluated. The generalized mathematical model makes it possible to take into account the majority of particular variants of the study and modeling of lactic acid synthesis in continuous fermentation that were reported in the literature. It has been recommended that the equations of the mathematical model be used to study processes under semibatch conditions, processes with recycling, processes with product recovery in membrane technology, and others.