Macrodispersion and Recovery of Solutes and Heat in Heterogeneous Aquifers

Abstract

The recovery efficiency of aquifer storage systems with radial flow fields are studied for heterogeneous aquifers. Macrodispersion, arising from spatially heterogeneous hydraulic conductivity, is modeled as a scale-dependent mechanical dispersion process. Approximate solutions for the recovery efficiency as a function of local dispersion and macrodispersion parameters, the injection-extraction rate (Formula presented.) and duration (Formula presented.), and storage cycle count, are derived and validated against numerical simulations. If macrodispersion dominates and the macrodispersion coefficient scales linearly with distance, the recovery efficiency is independent of both (Formula presented.). For sublinear and superlinear scalings, recovery increases and decreases respectively if (Formula presented.) increases. However, if local dispersion dominates, increasing (Formula presented.) always increases recovery. As macrodispersion becomes increasingly dominant with scale, the recovery efficiency may be a nonmonotonic function of (Formula presented.), with a maximum. In homogeneous aquifers, nonmonotonicity does not occur for 1D and 2D radial flow, but occurs for 3D radial flow fields only as a function of (Formula presented.), not (Formula presented.). These methods may also be used for fitting local dispersion and macrodispersion parameters with push-pull tests using recovery data, with advantages in scope of applicability and ease of data acquisition and interpretation, compared to existing push-pull test methods, which fit to breakthrough curves and do not consider macrodispersion. Furthermore, characterizing macrodispersion with push-pull tests may be advantageous over methods that use observation wells, as observation well placement may be challenging in highly heterogeneous aquifers. The results show that the macrodispersion parameters are not innate aquifer hydraulic properties, as their values vary with flow field geometry.