Charles Paradis, Larry D. McKay, Edmund Perfect, Jonathon D. Istok, Terry C. Hazen
The analytical solution to describe 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 to improve the in situ estimation of effective porosity. The truncated equation, which assumes displacement during the injection phase is negligible, may theoretically lead to an underestimation of the true value of effective porosity. In order to experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted among six test wells within a shallow and unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injecting bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6% to 5.0%) were substantially greater than those from the truncated equation (0.1% to 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 of the tests presented here also demonstrated that: (1) the spatial variability of effective porosity, within a relatively small study site, can be substantial and (2) the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). In conclusion, the expanded analytical solution improved the theoretical description of the displacement of a tracer during a push-pull test and the in situ application demonstrated an improvement for the estimation of effective porosity.
Paradis CJ, McKay LD, Perfect E, Istok JD, Hazen TC. 2018. Push-pull tests for estimating effective porosity: expanded analytical solution and in situ application. Hydrogeology Journal 26:381-393.