Abstract

A computational scheme has been presented that generalizes theoretical representations of a technology for the continuous fermentation of lactic acid at a given concentration of the main substrate in the stream that enters a fermenter. The sequence of constructing the computational scheme includes a preliminary analysis and a principal analysis. In the preliminary analysis, relationships have been derived that form the region of estimating the boundary characteristics that correspond to a given productivity of the process. The coordinates of the point of the maximum productivity \(\left[ {{{S}_{{{\text{opt}}}}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {{D}^{{{\text{opt}}}}}} \right]\) have been found. The coordinates of singular points have also been determined: \(\left[ {{{S}_{1}}\left( {{{D}_{1}}} \right),{{D}_{1}}} \right]\) for singular point 1, \(\left[ {{{S}_{2}}\left( {{{D}_{2}}} \right),{{D}_{2}}} \right]\) for singular point 2, \(\left[ {{{S}_{3}}\left( {{{D}_{3}}} \right),{{D}_{3}}} \right]\) for singular point 3, and \(\left[ {{{S}_{4}}\left( {{{D}_{4}}} \right),{{D}_{4}}} \right]\) for singular point 4. For the point of the maximum productivity and singular points, relationships have been presented for calculating the initial concentrations of the main substrate S₀ and the corresponding initial concentrations of the component that produces the substrate during fermentation M₀. The values of coordinates have been constraints in constructing relationships for the principal analysis that determine sets for selecting the values of M₀ and D at a given value of S₀. The scheme of the construction of sets consists of three sections, namely, I, II, and III. The boundaries of these sections are determined by relationships (21), (22), and (23), respectively. The sequence of the construction of sets for each of the sections has been presented, and it has been shown that there is one set (Set1) for section I, there are two sets (Set1* and Set2*) for section II, and there are three sets (Set1**, Set2**, and Set3**) for section III. Tables have been given for calculating the elements of sets at a given value of S₀. The theoretical relationships that have been derived are used for numerical calculation to estimate the characteristics of the multiplicity of steady states for each of the sets. It is shown that the range of the assignment of S₀ is the widest for section I, whereas the range of values for the dilution rate D is the greatest for section III. Numerical estimates in a comparative variant for sets in sections II and III have shown that the final concentrations of components under the same initial conditions differ in the values of M₀, M, and S. This makes it possible to obtain comparative estimates for the further processing of produced components (the recovery of lactic acid, the recycling and use of unconverted components, the recovery of a by-product, and so on).

中文翻译：

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给定浓度的主底物时乳酸发酵过程的稳态

摘要

已经提出了一种计算方案，其概括了在进入发酵罐的料流中给定浓度的主要底物下连续发酵乳酸的技术的理论表示。计算方案的构建顺序包括初步分析和原则分析。在初步分析中，已经得出了一些关系，这些关系形成了估计边界特征的区域，该边界特征对应于给定的过程生产率。最大生产率点的坐标\（\ left [{{{S} _ {{{\ text {opt}}}}}，{\ kern 1pt} {\ kern 1pt} {\ kern 1pt} {{ D} ^ {{{\ text {opt}}}}}} \ right] \）。还确定了奇异点的坐标：\（\ left [{{{S} _ {1}} \ left（{{{D} _ {1}}} \ right），{{D} _ {1}}} \ right] \）单数点1，\（\ left [{{{S} _ {2}} \ left（{{{D} _ {2}}} \ right），{{D} _ {2}}} \ right] \ ）的奇异点2，\（\ left [{{{S} _ {3}} \ left（{{{D} _ {3}}} \ right），{{D} _ {3}}} \ right] \）代表奇异点3，而\（\ left [{{{S} _ {4}} \ left（{{{D} _ {4}}} \ right），{{D} _ {4 }}} \ right] \）的奇点4。对于最大生产率的点和奇点，已经提出了用于计算主基板S ₀的初始浓度和产生该底物的组分的相应初始浓度的关系。发酵过程中的底物M ₀。坐标的值已成为构建用于主分析的关系的约束，该主分析确定了用于在给定S ₀值下选择M ₀和D值的集合。集的构造方案包括三个部分，即I，II和III。这些部分的边界分别由关系（21），（22）和（23）确定。已经给出了每个部分的集合的构造顺序，并且已经显示出第一部分有一个集合（Set1），第二部分有两个集合（Set1 *和Set2 *），并且第三部分有三组（Set1 **，Set2 **和Set3 **）。给出了用于以给定值计算集合元素的表格S ₀。已推导的理论关系用于数值计算，以估计每个集合的多个稳态的特性。结果表明，对于部分I，S ₀的分配范围最大，而对于部分III ，稀释率D的值范围最大。对第二节和第三节中的集合进行的比较变体中的数值估计表明，在相同的初始条件下，组分的最终浓度在M ₀，M和S的值上有所不同。这使得可以获得对所生产成分的进一步加工的比较估计（乳酸的回收，未转化成分的再循环和使用，副产物的回收等）。