论文标题
各向异性多孔介质中的轴对称重力电流
Axisymmetric gravity currents in anisotropic porous media
论文作者
论文摘要
我们探索在各向异性多孔介质中轴对称重力电流的运动，其中水平渗透性大于垂直渗透性。众所周知，由恒定点源提供的经典轴对称重力电流在原点附近具有非物理奇异性。我们通过考虑靠近原点的压力主导区域来解决这一问题，该区域允许从源来垂直流动，从而使有限深度的电流残留，而在该区域之外，则流动为重力为主导。在早期，内部压力驱动的区域控制电流的扩散，但是在后期，内部区域占据了逐渐较小的电流，使半径增加为$ \ sim t^{3/7} $，而原点附近的深度大约增加为$ \ sim t^{1/7} $。各向异性的存在突出了这一现象，因为垂直渗透性在后期通过原点附近的压力驱动流动对流动保持了影响。使用这些结果，我们对控制Co $ _2 $通过可渗透含水层迁移的主要动态提供了一些定量见解，就像碳捕获和存储的背景下一样。
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.
