A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., ³⁶Cl⁻) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., ⁹⁰Sr⁺⁺) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

提出了一种基于代码CrunchClay的模型，用于考虑了运输中的静电影响的裂缝-粘土矩阵系统。静电对迁移的影响包括与能斯特-普朗克方程所捕获的扩散势的发展有关的静电影响，以及与负电荷粘土颗粒接壤的扩散层的形成，其中发生部分阴离子排斥。该模型基于双重连续体公式，该公式考虑了扩散层和大量水孔空间，比经典的平均静电势模型提供了更灵活的框架。扩散层模型是通过对Poisson-Boltzmann方程中的离子浓度进行体积平均而获得的，但也包括在该连续体内进行纵向传输的处理。体积和扩散层孔隙度内的迁移率的计算基于Nernst-Planck方程的新公式，该公式考虑了网格单元界面处扩散系数和累积因子的平均值。给出了函数残差方程和相关的雅可比矩阵，从而可以用牛顿法求解非线性微分-代数方程组。例如，我们考虑具有单个离散裂缝的2D系统，在其中发生流动和对流传输，这与富粘土基质中的扩散相关。模拟结果表明，阴离子缺乏阻滞作用（例如，我们考虑具有单个离散裂缝的二维系统，在其中发生流动和对流传输，这与富粘土基质中的扩散相关。模拟结果表明，阴离子缺乏阻滞作用（例如，我们考虑具有单个离散裂缝的二维系统，在其中发生流动和对流传输，这与富粘土基质中的扩散相关。模拟结果表明，阴离子缺乏阻滞作用（例如，³⁶氯^- ）裂缝流动系统内的污染羽的，因为它们在很大程度上从充电的粘土岩排除在外，而阳离子（例如，迁移⁹⁰的Sr ⁺⁺）更强烈地衰减。二价阳离子尤其是从裂缝中扩散出来的损失，是由于它们在富含粘土的基质中的扩散层中的积累而加剧的。