In the recent article by Paradis et al. (2018), an error was made when developing a conceptual model and an analytical solution to describe the one-dimensional displacement of the center of mass of a non-reactive tracer during a single-well injection, drift, and extraction test (push-pull test).

The analytical solution describing the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase. The solution was expanded to improve the in situ estimation of effective porosity. The truncated equation assumed displacement during the injection phase was negligible, which may theoretically lead to an underestimation of the true value of effective porosity. To experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted across six test wells located in a shallow, unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injection of bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6–5.0%) were substantially greater than from the truncated equation (0.1–1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results presented here also demonstrated the spatial variability of effective porosity within a relatively small study site can be substantial, and the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). The tests presented here are also the first that the authors are aware of that estimate, in situ, the effective porosity of fine-grained fill material.

The breakthrough curve obtained from a single-well push-pull test can be adjusted to account for dilution of the injection fluid in the aquifer fluid. The dilution-adjusted breakthrough curve can be analyzed to estimate the reaction rate of a solute. The conventional dilution-adjusted method assumes that the ratios of the concentrations of the nonreactive and reactive solutes in the injection fluid vs. the aquifer fluid are equal. If this assumption is invalid, the conventional method will generate inaccurate breakthrough curves and may lead to erroneous conclusions regarding the reactivity of a solute. In this study, a new method that generates a dilution-adjusted breakthrough curve was theoretically developed to account for any possible combination of nonreactive and reactive solute concentrations in the injection and aquifer fluids. The newly developed method was applied to a field-based data set and was shown to generate more accurate dilution-adjusted breakthrough curves. The improved dilution-adjusted method presented here is simple, makes no assumptions regarding the concentrations of the nonreactive and reactive solutes in the injection and aquifer fluids, and easily allows for estimating reaction rates during push-pull tests.