Capillary pinning and blunting of immiscible gravity currents in porous media

Gravity-driven flows in the subsurface have attracted recent interest in the context of geological carbon dioxide (CO₂) storage, where supercritical CO₂ is captured from the flue gas of power plants and injected underground into deep saline aquifers. After injection, the CO₂ will spread and migrate as a buoyant gravity current relative to the denser, ambient brine. Although the CO₂ and the brine are immiscible, the impact of capillarity on CO₂ spreading and migration is poorly understood. We previously studied the early time evolution of an immiscible gravity current, showing that capillary pressure hysteresis pins a portion of the macroscopic fluid-fluid interface and that this can eventually stop the flow. Here we study the full lifetime of such a gravity current. Using tabletop experiments in packings of glass beads, we show that the horizontal extent of the pinned region grows with time and that this is ultimately responsible for limiting the migration of the current to a finite distance. We also find that capillarity blunts the leading edge of the current, which contributes to further limiting the migration distance. Using experiments in etched micromodels, we show that the thickness of the blunted nose is controlled by the distribution of pore-throat sizes and the strength of capillarity relative to buoyancy. We develop a theoretical model that captures the evolution of immiscible gravity currents and predicts the maximum migration distance. By applying this model to representative aquifers, we show that capillary pinning and blunting can exert an important control on gravity currents in the context of geological CO₂ storage.