Effect of variable permeability on the propagation of thin gravity currents in porous media

A new formulation is proposed to study the influence of deterministic heterogeneity on the propagation of thin two-dimensional gravity currents in a porous medium above a horizontal impervious boundary. Heterogeneity is conceptualized as a monotonic power-law variation of medium permeability transverse or parallel to the direction of propagation. Considering the injection of a constant or time-variable volume of fluid, the nonlinear differential problem admits a similarity solution which describes the shape and rate of propagation of the current. The bounds on parameters necessary to respect model assumptions are derived asymptotically and for finite time, to clarify the range of applicability of the proposed models. An application to the migration of a contaminant gravity current in the subsurface is then discussed, showing the impact of permeability variations on extension and shape of the intrusion.