Mathematical Modeling of the Fermentation Process for Lactic Acid Production: A Generalized Model

Abstract

The results of the development of a generalized mathematical model for the fermentation method of lactic acid production have been presented. The mathematical model includes nonsteady-state equations for the production of biomass, the consumption of the substrate, and the production of lactic acid and metabolism byproducts and equations for the formation of an additional amount of the main substrate from the components of raw materials. We acquired the results of the modeling process using constants of the basic variant from studies. The dependences of the characteristics of the process on time for the basic variant and the dependence of the productivity of lactic acid (QP, g/(L h)) on time with estimation of time t reaching the maximum value of QP (max QP) have been presented. The mathematical model takes into account all possible variants of inhibition, namely, concerning the biomass, product, and substrate. The results of modeling with allowance for the intensity of inhibition from each of the factors have shown the following. An increase in biomass inhibition constant Xmax decreases the duration of the process, an increase in product inhibition constant Pmax slightly increases the duration of the process, and a decrease in substrate inhibition constant Ki (the intensity of inhibition increases) considerably increases the duration of the process. Time of process completion tk for all conditions of modeling was determined by reaching one of the following conditions: X = Xmax or P = Pmax or S = 0. In modeling, it has also been found that the variation of constants in the equation for the formation of byproducts does not affect the variation in the characteristics of the process except for the numerical value of the concentration of byproducts.