Gravity-driven flow in a cross-bedded porous rock

Many geological layers include cross bedding, which leads to different values for permeability along and across the bedding planes. We explore how such cross bedding impacts buoyancy-driven flow through an inclined aquifer. For each bedding angle and ratio of the permeability along and across the bedding, a free buoyancy-driven plume rises at a particular angle to the horizontal. If the angle of inclination of the aquifer to the horizontal is smaller than this angle, then the plume rises along the upper boundary, otherwise, somewhat surprisingly, the buoyant plume rises along the lower boundary of the aquifer. We present new laboratory experiments to support these predictions. We also test a model for the effective permeabilities which control the speed and the rate of spread of the plume along one or other boundary of the aquifer. We consider the impact of our results for modelling geological storage of ${\rm CO}_2$ or aquifer thermal energy storage.