Dispersive effects in buoyancy-driven flows in porous media

Buoyancy-driven flow in porous media is bookended by two canonical scenarios: a vertically descending plume and a horizontally-propagating gravity current. Whereas the former is dominated by entrainment, the latter often includes significant dispersion. Sahu and Neufeld (J. Fluid Mech., Vol. 886 ,2020) studied dispersive effects in gravity current flow, however, they considered dispersive effects only in the transverse direction, not in the longitudinal direction. Aiming to expand upon their pioneering study, we investigate dispersive effects both parallel and normal to the principle direction of flow. The resulting set of (1D) equations do not admit self-similar solutions but can be solved using standard numerical techniques. In turn, we can reproduce the kinds of gravity current profiles generated, under more restrictive assumptions, by Sahu and Neufeld (2020). Model results are validated using a complementary COMSOL model that was itself confirmed by comparison with analogue experimental results. In the spirit of the bookend cases described above, the COMSOL-based model can be adapted to study more general examples of gravity current flow i.e., gravity currents that are plume-fed and/or that lose mass and buoyancy as they propagate. The implications of our work to real geological flows (e.g. hydrogen storage in a depleted reservoir) are briefly highlighted.