Dispersion of a liquid plume injected to the base of a geothermal reservoir

We develop a model to describe the spreading of a plume of liquid after it has been injected into a geothermal reservoir. We examine the morphology of the plume as it spreads along the base of the reservoir under the force of gravity. We present an exact analytic solution for the long time flow of the injectate along an inclined impermeable boundary, such as the base of the reservoir. We illustrate how this may be used to track the motion of a discrete mass of tracer injected into the reservoir with the injectate. We show that for a continuous source of fluid, after a time t, a pulse of tracer added to the injectate will have advanced downslope a distance proportional to t while spreading cross-siope a distance proportional to t1’3,