arXiv 2202.011652022-02-03physics.flu-dyn

各向异性多孔介质中的轴对称重力流

Axisymmetric gravity currents in anisotropic porous media

GP Benham, JA Neufeld, AW Woods

DOI：: 10.1017/jfm.2022.922

摘要：

研究了水平渗透率大于垂直渗透率的各向异性多孔介质中轴对称重力流的运动。经典轴对称重力流在原点附近存在非物理奇点。我们解决这个问题，考虑一个压力占主导地位的区域附近的原点，允许从源的垂直流动，使目前仍然是有限的深度，而超出这个区域的流量是重力为主。在早期，内部压力驱动区域控制电流的扩散，但在后期，内部区域占据电流的逐渐较小的部分，使得半径以$\sim t^{3/7}$的形式增加，而靠近原点的深度以$\sim t^{1/7}$的形式增加。各向异性的存在突出了这一现象，因为垂直渗透率通过原点附近的压力驱动流在后期保持对流动的影响。利用这些结果，我们提供了一些定量的见解占主导地位的动态控制CO $_2$迁移通过可渗透含水层，发生在碳捕获和储存的背景下。

英文摘要：

We explore the motion of an axisymmetric gravity current in an anisotropic porous medium in which the horizontal permeability is larger than the vertical permeability. It is well known that the classical axisymmetric gravity current supplied by a constant point source of fluid has an unphysical singularity near the origin. We address this by considering a pressure-dominated region near the origin which allows for vertical flow from the source, such that the current remains of finite depth, whilst beyond this region the flow is gravity-dominated. At early times the inner pressure-driven region controls the spreading of the current, but at late times the inner region occupies a progressively smaller fraction of the current such that the radius increases as $\sim t^{3/7}$, while the depth near the origin increases approximately as $\sim t^{1/7}$. The presence of anisotropy highlights this phenomenon, since the vertical permeability maintains an effect on the flow at late times through the pressure-driven flow near the origin. Using these results we provide some quantitative insights into the dominant dynamics which control CO$_2$ migration through permeable aquifers, as occurs in the context of carbon capture and storage.

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