Dispersion of a fluid plume during radial injection in an aquifer

Abstract

This study outlines a model for radial injected fluid flow with mechanical dispersion in a vertically confined porous aquifer. Existing studies have investigated fully segregated fluid flows in this setting, where the injected fluid and resident fluid form a propagating sharp interface. The present study uses the geometry of these sharp interfaces as a basis for the velocity field to take into account dispersion and buoyancy/viscosity effects. By differentiating the radial position of the sharp interface with respect to time, a time dependent radial velocity field governing the flow is obtained. Evaluating this radial velocity at the moment the original interface were to intersect a given position gives a velocity field that is a function of the position coordinates inside the aquifer. Using this velocity field, the fluids saturation profile resulting from mechanical dispersion can be found analytically. It is shown that the concentration of the injected fluid smoothly decays around the position of the corresponding sharp interface, allowing for the injected fluid to be present in detectable quantities beyond the extent of these solutions. This concentration spread should be considered in defining outer boundaries on fluids in injection well projects such as carbon sequestration or groundwater applications.