Abstract

This work extensively examines the chemical equilibrium of a multicomponent solution as part of the dynamic model of the acid retardation method. A detailed study of the chemical equilibrium, represented as a system of nonlinear equations, is a crucial step in building an effective dynamic model for a multicomponent solution. This work presents an algorithm for efficiently calculating the chemical equilibrium using extractive phosphoric acid (EPA) as an example. This algorithm can be utilized in the dynamic model to compute the chemical equilibrium at each point of the spatial grid and at each integration step. Furthermore, for substance concentrations in the experiment involving the purification of extractive phosphoric acid, it is shown that the nonlinear system of chemical equilibrium equations yields simple algebraic relationships that accurately relate the concentration of the considered substance’s molecules to the overall concentration of substances of all elements in the solution. Additionally, it is demonstrated that for each metal, only molecule sorption of one type of salt can be considered due to the low concentration of other types, thus reducing the number of differential equations in the dynamic model of the acid retardation method.

中文翻译：

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离子交换树脂酸阻滞研究中的数学模型问题

摘要

这项工作广泛地检查了多组分溶液的化学平衡，作为酸阻滞方法动态模型的一部分。对以非线性方程组表示的化学平衡的详细研究是建立有效的多组分溶液动态模型的关键步骤。这项工作提出了一种以萃取磷酸（EPA）为例有效计算化学平衡的算法。该算法可以在动态模型中用于计算空间网格的每个点和每个积分步骤的化学平衡。此外，对于涉及提取磷酸纯化的实验中的物质浓度，结果表明，化学平衡方程的非线性系统产生简单的代数关系，可以准确地将所考虑物质的分子浓度与溶液中所有元素的物质总浓度联系起来。此外，结果表明，对于每种金属，由于其他类型盐的浓度较低，因此只能考虑一种类型盐的分子吸附，从而减少了酸阻滞方法动态模型中微分方程的数量。