Natural fractures are characterized by high internal heterogeneity. This internal variability is the cause of flow channeling, which in turn leads to contaminant transport taking place primarily along the high-velocity channels. Mass exchange between the high-velocity channels and the low-velocity zones has the potential to enhance contaminant retention, due to solute diffusion into the low-velocity zones and subsequent exposure to additional surface area for diffusion into the bordering rock matrix. Here, we derive a random walk particle tracking method for heterogeneous fractures, which includes an additional term to account for the aperture gradient. The method takes into account advection, diffusion in the fracture and matrix diffusion. The developed numerical framework is applied to assess the effect of low-velocity zones in rough self-affine fractures. The results show that diffusion into low-velocity zones has a visible but modest impact on contaminant retention. The magnitude of this impact does not change considerably, regardless of whether diffusion into the rock matrix is considered in the model, and increases for a decreasing average Péclet number of the fracture.

中文翻译：

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低速区对粗糙裂缝中溶质滞留的意义

天然裂缝的特点是内部非均质性高。这种内部变化是流动通道的原因，而流动通道又导致污染物传输主要沿着高速通道发生。由于溶质扩散到低速区域并随后暴露于额外的表面积以扩散到边界岩石基质中，高速通道和低速区域之间的质量交换具有增强污染物保留的潜力。在这里，我们推导了一种用于异质裂缝的随机游走粒子跟踪方法，其中包括一个附加项来解释孔径梯度。该方法考虑了平流、裂缝中的扩散和基质扩散。开发的数值框架用于评估粗糙自仿射裂缝中低速区的影响。结果表明，扩散到低速区域对污染物保留有明显但适度的影响。无论模型中是否考虑扩散到岩石基质中，这种影响的大小都不会发生很大变化，并且随着裂缝平均佩克莱特数的减少而增加。