Inferring subsurface heterogeneity from push-drift tracer tests

We consider the late-time tailing in a tracer test performed with a push-drift methodology (i.e., quasi-radial injection followed by drift under natural gradient). Numerical simulations of such tests are performed on 1000 multi-Gaussian 2-D log-hydraulic conductivity field realizations of varying heterogeneity, each under eight distinct mean flow directions. The ensemble pdfs of solute return times are found to exhibit power law tails for each considered variance of the log-hydraulic conductivity field, σ²_Ink. The tail exponent is found to relate straightforwardly to σ²_Ink and, within the parameter space we explored, to be independent of push-phase pumping rate, pumping duration, and local-scale dispersivity. We conjecture that individual push-drift tracer tests in wells with screened intervals much greater than the vertical correlation length of the aquifer will exhibit quasi-ergodicity and that their tail exponent may be used to infer σ²_Ink. We calibrate a predictive relationship of this sort from our Monte Carlo study, and apply it to data from a push-drift test performed at a site of approximately known heterogeneity—closely matching the existing best estimate of heterogeneity.