Approximate solution for solute transport during spherical-flow push-pull tests

An approximate analytical solution to the advection-dispersion equation was derived to describe solute transport during spherical-flow conditions in single-well push-pull tests. The spherical-flow case may be applicable to aquifer tests conducted in packed intervals or partially penetrating wells. Using results of two-dimensional numerical simulations, we briefly illustrate the applicability of the derived spherical-flow solution and provide a comparison with its cylindrical-flow counterpart. Good agreement between simulated extraction-phase breakthrough curves and the spherical-flow solution was found when the length of the injection\extraction region was small compared to both aquifer thickness and maximum solute frontal position at the end of the injection phase. On the other hand, discrepancies between simulated breakthrough curves and the spherical -flow solution increased with increasing anisotropy in hydraulic conductivities. Several inherent limitations embedded in its derivation such as assumptions of isotropy and homogeneity warrant the cautious use of the spherical-flow solution.