We study the two-dimensional flow and leakage of buoyant fluid injected at a constant volumetric rate into a fluid-saturated porous medium confined vertically by horizontal boundaries. The upper boundary contains a localized vertical fracture that allows fluid to leak into an open or partially confined porous layer above. The rate of leakage is modelled as proportional to the combined action of the gravitational hydrostatic head of the current below the fracture and the background pressure introduced by the injection. After the injected current reaches the fracture, leakage is initially controlled kinematically by the rate at which injected fluid flows towards the fracture. Once the rate at which buoyant fluid flows towards the fracture exceeds a critical value, the current overshoots the fracture and leakage switches to being controlled dynamically by the pressure drop across the fracture. Two long-term regimes of flow can emerge. In one, the current approaches a steady height above the lower boundary and essentially all fluid injected into the medium leaks at long times. In the other, the current accumulates to fill the entire depth of the medium below the fracture. Only a fraction of the injected fluid then leaks at long times, implying significantly greater long-term storage than has been proposed from studies of leakage from unconfined media. An understanding of the flow regimes is obtained using numerical solutions and analysis of long-term similarity solutions. The implications of our results to the geological storage of carbon dioxide is discussed.
- geophysical and geological flows
- gravity currents
- porous media