Abstract A mathematical model is presented for advective-diffusive-reactive solute transport due to non-Newtonian fluid flows in a fracture surrounded by a tight porous medium. The interaction between the two media is handled by the continuity of solute concentration and diffusive flux at the interface. The semi-analytical solutions and their asymptotic behaviours are derived for concentration inside the tight porous medium, average concentration within the fracture, and average diffusive flux through the interface. The developed model is verified using a numerical simulation of the original governing equations and then it is compared with the existing theoretical models for solute transport in a fracture with porous walls. It is revealed that the Damkohler number in the finite fracture affects the breakthrough of the solute much more considerably compared to that in the matrix. However, the larger the rate of reaction in the fracture the slower the breakthrough of the solute. Also, the shear-thinning fluids lead to faster breakthrough of the solute than the Newtonian fluid and the shear-thickening fluids yield slower breakthrough of the solute respect to the Newtonian fluid. Moreover, the average diffusive flux through interface generally increases as the advection coefficient becomes larger. In addition, the Damkohler number in the fracture influences the average diffusive flux through interface more noticeably compared to that in the matrix. Nevertheless, the higher the rate of reaction in the fracture the lower the average diffusive flux through interface. Finally, the breakthrough of the solute occurs faster within the infinite fracture respect to the finite fracture.

中文翻译：

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由致密多孔介质包围的裂缝中的非牛顿流体流动引起的对流-扩散-反应性溶质输运

摘要 提出了由非牛顿流体在致密多孔介质包围的裂缝中流动引起的对流-扩散-反应性溶质输运的数学模型。两种介质之间的相互作用是通过界面处溶质浓度和扩散通量的连续性来处理的。半解析解及其渐近行为是针对致密多孔介质内的浓度、裂缝内的平均浓度和通过界面的平均扩散通量导出的。使用原始控制方程的数值模拟验证开发的模型，然后将其与现有的多孔壁裂缝中溶质输运的理论模型进行比较。结果表明，与基质中的相比，有限裂缝中的 Damkohler 数对溶质的突破影响更大。然而，裂缝中的反应速率越大，溶质的突破越慢。此外，剪切稀化流体导致溶质的突破比牛顿流体更快，而剪切稠化流体相对于牛顿流体产生更慢的溶质突破。此外，通过界面的平均扩散通量通常随着对流系数变大而增加。此外，与基质中的相比，裂缝中的 Damkohler 数对通过界面的平均扩散通量的影响更为显着。然而，裂缝中的反应速率越高，通过界面的平均扩散通量越低。