Steady States of a Continuous Fermentation Process for Lactic Acid Production: The Multiplicity for a Given Dilution Rate

The results of an analysis of a generalized mathematical model for a continuous fermentation process for lactic acid production have been presented. The mathematical model includes a system of equations for the material balance of the main substrate ( S ), the substrate produced from raw materials during fermentation ( M ), biomass ( X ), a product ( P ), and a by-product ( B ). The kinetics of the formation of biomass (the equation for the specific rate μ) takes into account inhibition by the substrate, biomass, and product. An analysis has been performed from the standpoint of the possibility of estimating technological characteristics at a given dilution rate D ( D = v / V , where v is the volumetric flow rate through a fermenter, m 3 /h, and V is the volume of the fermenter, m 3 ). The limiting values of and D that ensure the practical implementation of the process have been estimated ( includes the initial concentrations of the main substrate S 0 and the component that produces the substrate during synthesis M 0 ). These characteristics have been designated as coordinates of “singular points.” The coordinates of a point that corresponds to the maximum productivity with respect to lactic acid Q P ( where P is the concentration of lactic acid) have been determined simultaneously. Relationships have been derived for calculating sets of technological characteristics (the initial characteristics D , S 0 , and M 0 and the current characteristics X , S , P , B , and M ) based on a given value of D within permissible limits. It has been shown that, for the values of D that correspond to singular points (the first, second, and optimal points), there is one set and, for the other values of D , there are two sets. Numerical estimates of technological characteristics for the values of constants that correspond to the basic variant have been given. It has been shown that, with an increase in the productivity Q P while approaching the value of max Q P , the region of estimates of technological characteristics narrows. It has been recommended that the results of this study be used to predict the economic estimates of the implementation of particular conditions of a technological process.