Pre-asymptotic Transport Upscaling in Inertial and Unsteady Flows Through Porous Media
Pre-asymptotic Transport Upscaling in Inertial and Unsteady Flows Through Porous Media
复制标题
多孔介质惯性和非定常流中的渐进前输运放大
DOI：
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发表时间：
2015
影响因子：
2.7
通讯作者：
C. Dawson
中科院分区：
文献类型：
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作者：
N. Sund;D. Bolster;S. Mattis;C. Dawson
在大多数经典的多孔介质流动和输运公式中，雷诺数被假定为很小（$$mathrm{Re}<1$$Re<1），这意味着惯性的作用被认为可以忽略不计。然而，存在许多实际相关的例子，其中情况并非如此，惯性效应可能很重要，导致流动结构的变化，甚至随着雷诺数变得更大而引起不稳定和湍流。这种流动结构的变化可以对溶质如何通过多孔介质传输产生深远的影响，从而影响如何有效地模拟大规模传输。在这里，我们模拟，使用高分辨率的数值模型，通过一个理想化的多孔介质的流动条件下的雷诺数范围内，包括稳定和非稳定流的流动和运输。对于所有这些条件下，我们提出并测试三个升级模型的运输-平流扩散方程，不相关的空间模型（USM）和空间马尔可夫模型（SMM）。USM和SMM属于更广泛和更一般的连续时间随机游走模型家族。我们测试这些模型的能力，重现前渐近和渐近羽二次中心矩和突破曲线。我们表明，稳定的流动，惯性效应很强，空间马尔可夫模型优于其他两个，忠实地捕捉到许多非Fickian功能的运输，而不稳定的流动，不相关的空间模型表现最好，由于流场的不稳定性抑制了大规模运输的相关性的作用。我们的结论是，相关性必须占适当的高档运输在稳定的流动，而它可以忽略不计在非定常流。
In most classical formulations of flow and transport through porous media Reynolds numbers are assumed to be small ($$mathrm{Re}<1$$Re<1), meaning that the role of inertia is considered negligible. However, many examples of practical relevance exist where this is not the case and inertial effects can be important leading to changes in flow structure and even giving rise to unsteady and turbulent flows as Reynolds numbers become larger. This change in flow structure can have a profound impact on how solutes are transported through the porous medium, influencing how effective large-scale transport should be modeled. Here we simulate, using high-resolution numerical models, flow and transport through an idealized porous medium for flow conditions over a range of Reynolds numbers, including steady and unsteady flows. For all these conditions we propose and test three upscaled models for transport—an advection dispersion equation, an uncorrelated spatial model (USM) and a spatial Markov model (SMM). The USM and SMM fall into the wider and more general family of continuous time random walk models. We test these models by their ability to reproduce pre-asymptotic and asymptotic plume second centered moments and breakthrough curves. We demonstrate that for steady flows where inertial effects are strong, the spatial Markov model outperforms the other two, faithfully capturing many of the non-Fickian features of transport, while for unsteady flows the uncorrelated spatial model performs best, due to the fact that unsteadiness in the flow field dampens the role of correlation on large scale transport. We conclude that correlation must be accounted for to properly upscale transport in steady flows, while it can be neglected in unsteady flows.