Leakage from inclined porous reservoirs

We investigate the effect of localized leakage on the storage of buoyant fluids in inclined porous reservoirs, with application to the geological storage of CO2. We find that once the current has propagated some distance beyond the point of leakage, its profile becomes steady in time, save for the nose, which advances at a constant speed. Crucially, this steady state implies that the efficiency of storage (defined as the instantaneous proportion of the injected fluid that does not leak) tends to a finite value. This contrasts with previous studies of localized leakage in horizontal reservoirs, which found that the efficiency of storage tends to zero at late times. We analyse the steady-state efficiency and the time scales of evolution for a leakage point located either upslope or downslope of the injection point using analytical and numerical methods. These findings are verified by model laboratory experiments. Finally, we consider the implications of our results for the geological storage of CO2 under sloping cap rocks compromised by a fracture or fissure.