Macrodispersion and Recovery of Solutes and Heat in Heterogeneous Aquifers

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 Q $Q$ and duration T $T$, 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 Q,T $Q,T$. For sublinear and superlinear scalings, recovery increases and decreases respectively if Q,T $Q,T$ increases. However, if local dispersion dominates, increasing Q,T $Q,T$ always increases recovery. As macrodispersion becomes increasingly dominant with scale, the recovery efficiency may be a nonmonotonic function of Q,T $Q,T$, 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 T $T$, not Q $Q$. 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.

Automated summary

The study investigates the recovery efficiency of aquifer storage systems with radial flow fields for heterogeneous aquifers, with a focus on the impact of macrodispersion. It is found that recovery efficiency is significantly influenced by macrodispersion, while recovery efficiency is positively correlated with injection-extraction rate and duration when local dispersion dominates. As macrodispersion becomes increasingly dominant with scale, the recovery efficiency may exhibit nonmonotonic behavior.