On the propagation of non-isothermal gravity currents in an inclined porous layer

We consider the buoyancy-driven flow in an inclined porous layer which results when fluid of different temperature and composition to that in the reservoir is injected from a horizontal line well. The thermal inertia of the porous matrix leads to a transition in the temperature of the injectate as it spreads from the well and heats up to reservoir temperature. Since the buoyancy and viscosity of the injectate change across this thermal transition, the alongslope characteristic speed of the current also changes. Density and viscosity typically decrease with temperature and, so, for injectate that is positively buoyant at reservoir temperature, the changes in density and viscosity with temperature have complementary effects on the characteristic speed. In contrast, for injectate that is negatively buoyant at reservoir temperature, the changes in viscosity and density with temperature have competing influences on the characteristic speed. The change in characteristic speed, combined with the change in buoyancy across the thermal transition, leads to a series of different flow morphologies with the thermally adjusted injectate either running ahead of or lagging behind the original injectate. By approximating the thermal transition as a discrete jump, we derive the leading-order structure of these currents for the different possible cases. We then build on this to develop a more detailed boundary layer description of the thermal transition based on the theory of thin gravity driven flows in porous media. Under certain injection conditions, we show that the thermal transition is gravitationally unstable and that this may lead to mixing across the thermal transition. We consider the implications of the models for several industrial processes including geothermal heat recovery, aquifer thermal storage and carbon dioxide sequestration.