Dispersion effects in porous media gravity currents experiencing local drainage

Gravity current flows in porous media are an essential component of numerous processes related to the energy sector, be these connected to resource production (e.g. heavy oil extraction), energy storage (e.g. of Η₂ over seasonal timescales), or byproduct disposal (e.g. CO₂ sequestration of or acid gas). Many theoretical treatments of gravity current flow invoke a sharp interface assumption and so ignore, in the case of miscible fluids, dispersive transport between the gravity current and the surrounding ambient. We derive an analytical model that takes into account transverse and longitudinal dispersion by considering the bulk and dispersed phases separately. The model in question derives from mass- and buoyancy-balance and assumes both a hydrostatic flow and a bulk phase solute concentration that matches that of the source. Dispersed fluid appears only downstream of the source and results from mixing between the bulk and ambient fluids. For given source and medium conditions, the dispersion severity is characterized by quantifying the amount of fluid (either in terms of volume or in terms of buoyancy) that appears in the dispersed phase. On this basis, we find that the volume of dispersed fluid, though typically small in the absence of gravity current drainage through an isolated fissure, can be large when such a fissure is introduced thereby providing a sink for bulk fluid. Results such as these require, as with analogue flows at much larger Re, specification of an entrainment parameter, the value of which comes from complementary COMSOL numerical simulations. Numerical output is additionally applied to verify key model predictions.