We examine the motion of a buoyant fluid injected into a water-saturated porous rock as it spreads along a thin inclined low-permeability barrier. We account for leakage of the fluid across the barrier once the current is sufficiently deep so that the pressure exceeds the capillary threshold. We show that at some distance from the source, the pressure decreases below this threshold, and all the remaining flux spreads laterally along the barrier. We examine the controls on the partitioning of the flow between the draining flux and the laterally spreading flux and also the controls on the lateral extent of the draining region for the case of an instantaneous release and a maintained release of fluid. We consider the implications of our work for the dispersal of CO 2 plumes which may be sequestered in deep saline aquifers.
IntroductionThe injection of CO 2 into deep saline aquifers or depleted oil and gas fields has received considerable interest in the context of global warming and the related challenge of reducing anthropogenic carbon emissions into the atmosphere (Kumar et al. 2005;Nordbotten, Celia & Bachu 2005). In deep saline aquifers, CO 2 is supercritical and has a density of the order 20 %-40 % smaller than that of water, depending on the temperature and pressure. As a result, there is concern that the CO 2 will migrate through the subsurface and back to human environment, perhaps over time scales of tens to hundreds of years. In order to assess this risk, models are being developed to describe the migration of CO 2 plumes through the subsurface (Hesse et al. , 2007Mitchell & Woods 2006;Vella & Huppert 2006), and data are being collected from various field trials using seismic imaging to interpret the dispersal patterns in the field (Bickle et al. 2007). A significant challenge associated with the prediction of such CO 2 transport is the complexity of the subsurface strata through which the CO 2 migrates. This can lead to multiple and tortuous flow paths from the injection point to the surface, with the CO 2 being dispersed laterally over substantial distances but also reaching the surface through different flow paths over a range of different time scales. Data from the Sleipner field in Norway (Bickle et al. 2007) has shown that the gas spreads out in a pine tree-type pattern, spreading laterally beneath low-permeability layers while gradually migrating upwards as it leaks through these layers or fractures which cut across the layers.Some of the models which have been developed to describe the migration of plumes of CO 2 in the subsurface have assessed the buoyancy-driven dispersal through both †