Push-pull tests for estimating effective porosity: expanded analytical solution and in situ application

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.