# Inferring subsurface heterogeneity from push-drift tracer tests

## TL;DR

This study demonstrates that analyzing tail behavior in push-drift tracer tests can effectively infer subsurface heterogeneity, with power law tail exponents directly related to the variance of hydraulic conductivity.

## Contribution

The paper introduces a method to estimate subsurface heterogeneity from tail exponents in tracer test return time distributions, validated through extensive simulations.

## Key findings

- Power law tails observed in tracer return times.
- Tail exponents relate to heterogeneity variance $\sigma^2_{ ext{ln}K}$.
- Method successfully applied to real site data.

## Abstract

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 2D 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, $\sigma^2_{\ln K}$. The tail exponent is found to relate straightforwardly to $\sigma^2_{\ln K}$ and, within the parameter space we explored, to be independent of push-phase pumping rate and pumping duration. 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 $\sigma^2_{\ln K}$. 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.