Buoyant convection in porous media: Multiple layers with inclined permeability jump*

We report upon an experimental study of a filling box flow in a heterogeneous porous medium comprised of two layers of greater (upper layer) and lesser (lower layer) permeability. The associated permeability jump is inclined and the flow, which derives from a discrete line source, has modest Reynolds number but large Peclet number. When plume that issues from the source strikes the permeability jump, a significant fraction of the plume fluid is discharged into an unequal pair of (primary) interfacial gravity currents. These primary gravity currents suffer from drainage loss into the lower layer, as a result they each reach a terminal runout length. We model the associated dynamics using a sharp interface model. Analytical model results predict the time evolution of the gravity currents and their runout lengths. Results are validated with experimental data conducted for different permeability jump angles. Of course, experiments are characterized by perimetric boundaries such that the later time dynamics are of the filling-box variety. Thus the later propagation of primary gravity currents are dictated by the gravity current in the lower layer. We furthermore discuss the nature of filling of upper and lower regions for different plume density.