Analytical Solutions for a Fully Coupled Hydraulic-Mechanical-Chemical Model With Nonlinear Adsorption

IF 3.4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-09-17 DOI:10.1002/nag.3829
Lin Han, Zhihong Zhang, Jiashu Zhou
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Abstract

Adsorption characteristics play a crucial role in solute transport processes, serving as a fundamental factor for evaluating the performance of clay liners. Nonlinear adsorption isotherms are commonly found with metal ions and organic compounds, which introduce challenges in obtaining analytical solutions for solute transport models. In this study, analytical solutions are proposed for a fully coupled hydraulic-mechanical-chemical (HMC) model that accounts for both the Freundlich and Langmuir isotherms. To mitigate the difficulties arising from the variable coefficients, the system of second-order partial differential equations involving three variables is linearized. The method of separation of variables, theory of integration, and Fourier series are utilized to derive analytical solutions. The analytical method presented can potentially be extended to a broad spectrum of nonlinear adsorption isotherms. The results reveal a 56.5% reduction in solute breakthrough time under the Freundlich isotherm and a remarkable 2.6-fold extension under the Langmuir isotherm when compared to the linear isotherm. The adsorption constants of the Freundlich and Langmuir isotherms exhibit a positive correlation with breakthrough time, while the exponent of the Freundlich isotherm and the maximal adsorption capacity in the Langmuir isotherm demonstrate a negative association with breakthrough time. This study enhances the precision of solute transport prediction and provides a more scientific assessment of clay liner performance.

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具有非线性吸附作用的全耦合水力-机械-化学模型的分析解决方案
吸附特性在溶质迁移过程中起着至关重要的作用,是评估粘土衬里性能的基本因素。非线性吸附等温线常见于金属离子和有机化合物,这给获取溶质迁移模型的分析解决方案带来了挑战。在本研究中,我们提出了一个完全耦合的水力-机械-化学(HMC)模型的分析解决方案,该模型同时考虑了 Freundlich 和 Langmuir 等温线。为了减轻可变系数带来的困难,对涉及三个变量的二阶偏微分方程系统进行了线性化处理。利用变量分离法、积分理论和傅立叶级数求出分析解。所提出的分析方法可以扩展到多种非线性吸附等温线。结果显示,与线性吸附等温线相比,Freundlich 等温线下的溶质突破时间缩短了 56.5%,Langmuir 等温线下的溶质突破时间显著延长了 2.6 倍。Freundlich 和 Langmuir 等温线的吸附常数与突破时间呈正相关,而 Freundlich 等温线的指数和 Langmuir 等温线的最大吸附容量与突破时间呈负相关。这项研究提高了溶质迁移预测的精度,并为粘土衬垫性能的评估提供了更科学的依据。
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来源期刊
CiteScore
6.40
自引率
12.50%
发文量
160
审稿时长
9 months
期刊介绍: The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.
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