Anisotropy distorts the spreading of a fixed volume porous gravity current

We consider the release and subsequent gravity-driven spreading of a finite volume of fluid in an anisotropic porous medium bounded by an impermeable substrate. When the permeability in the vertical direction is much smaller than the horizontal direction, as is the case in many real geological reservoirs, this restricts the spread of the current to a very thin layer near the impermeable base. Using a combination of asymptotic analysis and finite difference computations of Darcy flow, we show that there exist two distinct flow regimes. At early times the bulk of the current descends slowly and uniformly, injecting fluid into thin finger-like regions near the base. At much later times the current transitions to the classical gravity-driven solution and continues to spread with a self-similar shape. One interesting consequence is that the swept volume of the current grows differently depending on the anisotropy of the medium. This has important consequences for managing contaminant spills, where it is important to minimise the contacted volume of the aquifer, or during geological CO$_2$ sequestration where a larger contacted volume results in more CO$_2$ being stored.