Self-similar dynamics of liquid injected into partially saturated aquifers

Abstract

The injection of liquid from a central well into a partially saturated aquifer of finite thickness is described using similarity solutions. The solutions illustrate that injection leads to a growing zone around the source in which the fluid fills the whole depth of the aquifer. Beyond this zone, the current adjusts to the depth in the far field as the fluid slumps under gravity. The radial extent of the zone in which the aquifer is fully flooded depends on the ratio of the buoyancy-driven flow speed to the pressure-driven flow speed associated with the injection. New laboratory experiments, using a model porous medium, support the model predictions in the case of an initially unsaturated layer. The analysis is then developed to allow for a fully saturated aquifer, containing fluid of lower density than the injectate, and a further class of similarity solutions is developed. Again, these are shown to be consistent with new laboratory experiments. In concluding, we briefly consider how the results may be combined, to explore the self-similar dynamics of a relatively dense fluid injected into an aquifer which is partially saturated with fluid of smaller density.