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首页> 外文期刊>Transport in Porous Media >Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media
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Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

机译：均相多孔介质中的放大扩散和非线性反应质量传递

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摘要

In this work, we revisit the upscaling process of diffusive mass transfer of a solute undergoing a homogeneous reaction in porous media using the method of volume averaging. For linear reaction rate kinetics, the upscaled model exhibits a vis-A -vis correspondence with the mass transfer governing equation at the microscale. When nonlinear reactions are present, other methods must be adopted to upscale the nonlinear term. In this work, we explore a linearization approach for the purpose of solving the associated closure problem. For large rates of nonlinear reaction relative to diffusion, the effective diffusion tensor is shown to be a function of the reaction rate, and this dependence is illustrated by both numerical and analytical means. This approach leads to a macroscale model that also has a similar structure as the microscale counterpart. The necessary conditions for the vis-A -vis correspondence are clearly identified. The validation of the macroscale model is carried out by comparison with pore-scale simulations of the microscale transport process. The predictions of both concentration profiles and effectiveness factors were found to be in acceptable agreement. In an appendix, we also briefly discuss an integral formulation of the nonlinear problem that may be useful in developing more accurate results for the upscaled transport and reaction equations; this approach requires computing the Green function corresponding to the linear transport problem.
机译：在这项工作中，我们使用体积平均方法，回顾了在多孔介质中经历均相反应的溶质的扩散质量转移的放大过程。对于线性反应速率动力学，该放大模型在微观尺度上表现出与传质控制方程的vis-A-vis对应关系。当存在非线性反应时，必须采用其他方法来放大非线性项。在这项工作中，我们探索线性化方法以解决相关的闭合问题。对于相对于扩散的较大的非线性反应速率，有效扩散张量显示为反应速率的函数，并且这种依赖性通过数值和分析方法进行了说明。这种方法导致了一个宏观模型，该模型也具有与微观模型相似的结构。清楚地确定了vis-A-vis对应的必要条件。宏观模型的验证是通过与微观尺度运输过程的孔隙尺度模拟进行比较来进行的。浓度分布和功效因子的预测均被认为是可以接受的。在附录中，我们还简要地讨论了非线性问题的一个整体表述，这对于为更高级的输运和反应方程式得出更准确的结果可能很有用。这种方法需要计算对应于线性传输问题的格林函数。

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