Abstract

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, m³/h, and V is the volume of the fermenter, m³). The limiting values of \(S{\kern 1pt} '\) and D that ensure the practical implementation of the process have been estimated (\(S{\kern 1pt} '\) includes the initial concentrations of the main substrate S₀ and the component that produces the substrate during synthesis M₀). 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 (\({{Q}_{P}} = DP,\) 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, S₀, and M₀ 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.

中文翻译：

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乳酸生产的连续发酵过程的稳态：给定稀释率的多重性

摘要

已经提出了用于乳酸生产的连续发酵过程的广义数学模型的分析结果。该数学模型包括以下方程式系统：主基质（S），发酵过程中从原材料生产的基质（M），生物质（X），产物（P）和副产物（B）的物料平衡。）。生物质形成的动力学（特定比率μ的方程式）考虑了底物，生物质和产物的抑制作用。从在给定稀释倍率D（D= v / V，其中v是通过发酵罐的体积流量m ³ / h，而V是发酵罐的体积m ³）。已估计确保实际执行该过程的极限值\（S {\ kern 1pt}'\）和D（\（S {\ kern 1pt}'\）包括主基板S ₀的初始浓度以及在合成过程中产生底物的成分M ₀）。这些特征已被指定为“奇异点”的坐标。同时确定了相对于乳酸Q _P（\（{{Q} _ {P}} = DP，\），其中P为乳酸的浓度）的最大生产率的点的坐标。基于给定的D值，得出了用于计算一组技术特性（初始特性D，S ₀和M ₀以及当前特性X，S，P，B和M）的关系。在允许的范围内。已经表明，对于与奇异点（第一，第二和最佳点）相对应的D值，存在一组，对于D的其他值，则存在两组。已经给出了对应于基本变量的常数值的技术特性的数值估计。结果表明，随着生产率Q _P的增加，同时又接近max  Q _P的值，技术特性估计值的范围变窄。建议将本研究的结果用于预测对特定工艺条件实施的经济估算。