Dispersion in radial flow from a recharge well

The recharge and disposal of treated and untreated waste waters in groundwater aquifers results in a mixing of these waters with the natural groundwater. The distribution and boundaries of the ensuing mixture are determined by the combined mechanisms of convection, dispersion, diffusion, and sorption. In this study, the mass conservation equation for a dissolved substance in two-dimensional groundwater flow is developed. An analytical solution and a numerical solution of this equation are obtained for the radial and temporal distribution of a conservative, dissolved substance, which is injected into a homogeneous isotropic confined aquifer by a single recharging well. Experimental measurements of the concentration distributions of a dilute salt water tracer support the theoretical solutions. It is found that, for homogeneous media, the dispersed or mixed region may be less than 1% of the volume of fluid recharged at distances of only 30–60 meters from the well. Finally, from the experimental results it is shown that the dispersion coefficient along the streamlines is the same for both uniform and nonuniform flows at the same velocity.