In a previous publication (Sorbie and Stamatiou in Transp Porous Media 123:271–287, 2018), we presented a one-dimensional analytical solution for scale inhibitor transport and retention in a porous medium through a kinetic precipitation mechanism. In this process, a chemical complex of the scale inhibitor precipitates within the porous matrix and it then re-dissolves through a kinetic solubilisation process. Considering the re-dissolution of this precipitate in a one-dimensional linear system such as a reservoir layer or indeed in a laboratory core/pack flood, the flowing aqueous phase gradually dissolves the precipitate which is then eluted from the system. The most novel aspect of this previous analytical solution arose from the fact that, at a certain point in time (or pore volume throughput), the precipitate in the system was locally fully re-dissolved, forming an internal moving boundary between where no precipitate remained (closer to the system inlet) and where a precipitate was present (further into the system up to the outlet). In the current paper, we extend this work by presenting analytical solutions for the case where precipitation/dissolution occurs simultaneously with an adsorption/desorption interaction between the scale inhibitor and the rock surface, described by the nonlinear Langmuir isotherm. When examining this more complex problem in the flow scenario where the local precipitate is completely dissolved, several interesting analytical solution structures are obtained as a result of the internal moving boundary. Which of these structures occurs is rigorously categorised according to the solubility, the initial levels of precipitate and adsorbate, as well as the shape of the Langmuir isotherm. After the mathematical development of the analytical solutions, they are applied to some example problems which are compared with numerical solutions. Finally, a number of different generic features in the scale inhibitor effluent concentration profile are predicted and discussed with regard to practical field applications.

中文翻译：

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具有耦合吸附和沉淀的 1D 尺度抑制剂传输模型的分析解决方案

在之前的出版物中（Sorbie 和 Stamatiou in Transp Porous Media 123:271–287, 2018），我们提出了一种通过动力学沉淀机制在多孔介质中阻垢剂传输和滞留的一维分析解决方案。在此过程中，阻垢剂的化学复合物在多孔基质中沉淀，然后通过动力学增溶过程重新溶解。考虑到这种沉淀在一维线性系统（如储层）中或实际上在实验室岩心/充填驱中的重新溶解，流动的水相逐渐溶解沉淀，然后从系统中洗脱。这个先前的分析解决方案最新颖的方面来自这样一个事实，即在某个时间点（或孔体积吞吐量），系统中的沉淀物局部完全重新溶解，在没有沉淀物残留（靠近系统入口）和存在沉淀物（进一步进入系统直至出口）之间形成内部移动边界。在当前的论文中，我们通过提出沉淀/溶解与阻垢剂和岩石表面之间的吸附/解吸相互作用同时发生的情况的解析解来扩展这项工作，由非线性朗缪尔等温线描述。在局部沉淀完全溶解的流动场景中检查这个更复杂的问题时，由于内部移动边界，获得了几个有趣的解析解结构。根据溶解度对这些结构中的哪一种进行严格分类，沉淀物和吸附物的初始水平，以及朗缪尔等温线的形状。在解析解的数学发展之后，它们被应用于一些与数值解进行比较的示例问题。最后，结合实际现场应用预测和讨论了阻垢剂流出物浓度分布中的许多不同的通用特征。