Double Advective Effects Controlling Liquid Injection in Geothermal Reservoirs

We examine the motion of liquid injected into a liquid dominated geothermal reservoir, focusing on the situation in which the injected liquid has different temperature and composition from the reservoir fluid. As a result of these differences, the injected liquid will typically be of different density to the reservoir fluid, and will therefore spread through the reservoir under gravity. Owing to the thermal inertia of porous rock, as the injected liquid spreads through the rock, the thermal front lags behind the actual fluid front associated with the injected liquid. As a result, the density of the injected fluid changes across the thermal front: fluid ahead of the front has density different from that in the reservoir only as a result of differences in composition; fluid behind the front has density which is different owing to contrasts in temperature and composition. This leads to a change in the structure of the current across the thermal front, and we examine a range of different situations which may develop depending on the initial temperature and compositional contrasts. INTRODUCTION Liquid injection into geothermal reservoirs typically involves fluids whose composition and temperature differ from that in the reservoir. This can lead to an important role of the gravitational or buoyancy force, in additional to the applied pressure, in driving the fluid through the reservoir. Previous studies have examined the controls on the gravitational spreading of liquid injected into geothermal systems (Woods, 1998a; Woods, 1999), in the situation in which the density contrast between the reservoir fluid and the injected fluid is constant. In that situation, it has been shown that the fluid spreads in a self-similar fashion through the reservoir. Solutions have been developed for motion along sloping impermeable layers in the reservoir issuing from a point source as well as for radially spreading currents issuing from a central well along a nearly horizontal impermeable boundary. Other work has considered the effect of fluid-rock reactions on the spreading rate and current morphology of fluid migrating under gravity through the reservoir (Raw and Woods, 2000). By extending the earlier models of gravity currents, more involved model solutions have shown how the current can develop a double structure: injected fluid advances from the source through the reacted porous layer towards the reaction front. At the reaction front, the permeability changes due to reaction, and beyond this front the injected, but already-reacted fluid spreads through the original reservoir rock. In another study, the motion of vaporizing gravity currents has also been examined, with fluid at the advancing surface of the current partially boiling as it enters superheated rock (Woods, 1998b). DENSITY EVOLUTION In all these studies, the density of the injected fluid has been assumed to be fixed. However, owing to the thermal inertia of fluid migrating through a porous rock, the density may change across the thermal front, leading to a range of previously unrecognized current behaviours. To illustrate the different possibilities, it is useful to consider a simple model in which the density of the reservoir fluid is given by ( ) ( ) ( ) o o o C C T T − + − − = β α ρ ρ 1 (1) where the density ρ, relative to a reference density ρο defined at temperature To and concentration Co is assumed to decrease with temperature, with thermal expansion coefficient α and increase with the concentration of dissolved mineral or salt with solutal expansion coefficient β. Coupling equation (1) with the result that for advectively controlled heat transfer through a porous layer, an internal thermal boundary layer typically develops, across which the temperature changes from