Estimation of parameters characterizing a steady-state synthesis process with nonlinear microorganism growth kinetics

Abstract

The paper describes a theoretical basis developed for estimating the parameters of a steady-state biotechnological process characterized by nonlinear microorganism growth kinetics. This study aimed to obtain a common methodological basis for estimating input parameters that determine actual technology implementation, taking into account all possible restrictions on the concentration of incoming substrate Sf (g/l) and dilution rate D (h-1 ). The theory development was based on a mathematical model describing one of the most common processes of lactic acid production. This mathematical model includes three mass balance equations (for biomass, substrate, and product), as well as an equation of microorganism growth kinetics. The study established relations for calculating the ultimate value of the dilution rate D ult at a given Sf , relations for the maximum and minimum values of Sf , as well as Sf and D providing the maximum productivity value QP, g/(l·h), where QP = PD (P – product concentration, g/l). These relations were designed to calculate the parameters of possible process implementation for two options at the same value of QP: two values of D calculated for a given Sf and two values of Sf calculated for a given D. A numerical experiment is described using the constants of the mathematical model confirmed by foreign studies. This numerical experiment is illustrated using an Sf-D dependence pattern determining an acceptable value range for Sf and D, with the separate calculation of parameters according to Sf sections. For each of these sections, calculation formulas are provided. It is concluded that the developed theoretical basis is sufficiently general in nature to be applied to biotechnological processes that involve other kinetic relations, as well as microorganism strains creating by-products and using raw materials that are employed to reproduce the substrate in the process of synthesis.