Abstract
Relationships have been derived and an algorithm has been presented for calculating the technological characteristics of lactic acid production, namely, the concentration of the main substrate that enters a fermenter (S0, g/L), the concentration of the component of raw materials that produces the substrate during fermentation (M0, g/L), and the dilution rate (D, h–1), which ensure optimal conditions in the continuous mode. The productivity with respect to lactic acid (QP, g/(L h)) has been used as an optimality criterion. Calculations are based on the equations of a generalized mathematical model, which include the material balance relationships for biomass, the substrate, the product, the byproduct, and the component of raw materials that produces the substrate. The specific growth rate takes into account the maximum value for biomass (Xmax, g/L) and the maximum value for the product (Pmax, g/L). An equation has been derived for estimating the maximum value of productivity max QP and the corresponding value of dilution rate Dopt, the solution of which has been used for estimating the characteristics of the process in the stream that leaves the fermenter (X, g/L; S, g/L; P, g/L; and B, g/L). The results of calculations made it possible to estimate the amount of the substrate that ensures the optimum mode. The specific feature of the process has been revealed, and a relationship has been derived that shows that the choice of values for technological characteristics $$S_{0}^{{{\text{opt}}}}$$ and $$M_{0}^{{{\text{opt}}}}$$ is possible for the implementation of the optimum mode. The range of values that allow this choice, i.e., the multiplicity region, has been determined. An estimate of the efficiency of using the substrate has been obtained that determines the amount of the substrate consumed for the formation of biomass as a component that synthesizes the product. Numerical calculations using the basic values of constants in equations for the mathematical model, which were derived based on literature studies in solving particular problems, have been presented. It has been recommended that the results of this study be used to develop a practical technology and select a strain of microorganisms.
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