Buoyancy driven flow from a waning source through a porous leaky aquifer

We develop a series of models to describe the migration of a buoyant fluid through a layered permeable rock following release from a localized waning source. In particular, if the fluid is injected into a high permeability layer, bounded above by a layer of lower permeability, a plume migrates along the interface, with some draining into the low permeability layer if the current is sufficiently deep to overcome the capillary entry pressure. We show the motion of the fluid is controlled by a number of key factors with the dominant dimensionless numbers being the time-scale for the source to decay compared to the time-scale for draining through the low permeability layer, the residual saturation of the gas and water in the formation as that phase is displaced by the other phase, and the capillary entry pressure, as measured by the critical depth of the current required for draining, as compared to the initial depth of the current. Simplified analytical models are presented to illustrate some of the key controls on and transitions in the flow, and the models are used to explore leakage and trapping prior to flow reaching a fault zone.