Effect of Buoyant Convection on the Spreading and Draining of Porous Media Gravity Currents along a Permeability Jump

Abstract

We investigate theoretically the impact of adding convective dissolution to the sharp interface problem of gravity current propagation along a sloping permeability jump. Three different dissolution modes are explored: constant dissolution, dissolution with simultaneous shutdown and dissolution with sequential shutdown. The last two modes are bookend opposites that make different assumptions about ambient mixing. For simultaneous (sequential) shutdown, different portions of the gravity current interface experience dissolution identically (differently). To gage the effectiveness of dissolution for trapping e.g., supercritical CO$_2$, we consider the evolution of storage efficiencies and examine the impact of changing the dissolution strength, the time, $t_1$, for the onset of shutdown and, for $t_1 < \infty$, the e-folding decay time, $t_2$, characterizing dissolution decay. We also highlight the phenomenon of intermediate run-out, a state where there is a balance between the fluid supplied to the gravity current vs. that lost by dissolution and basal draining. The state in question is transient because, for time $t>t_1$, shutdown decreases the rate of dissolution. The ensuing readjustment causes a remobilization of the previously-arrested gravity currents and their subsequent (though not indefinite) elongation. Our analysis concludes by studying unsteady sources, which provides keen insights into similarities and differences between simultaneous vs. sequential shutdown.