Abstract
Abstract. The model of single-well push–pull (SWPP) test has been widely used to investigate reactive radial dispersion in remediation or parameter estimation of in situ aquifers. Previous analytical solutions only focused on a completely isolated aquifer for the SWPP test, excluding any influence of aquitards bounding the tested aquifer, and ignored the wellbore storage of the chaser and rest phases in the SWPP test. Such simplification might be questionable in field applications when test durations are relatively long because solute transport in or out of the bounding aquitards is inevitable due to molecular diffusion and cross-formational advective transport. Here, a new SWPP model is developed in an aquifer–aquitard system with wellbore storage, and the analytical solution in the Laplace domain is derived. Four phases of the test are included: the injection phase, the chaser phase, the rest phase and the extraction phase. As the permeability of the aquitard is much smaller than the permeability of the aquifer, the flow is assumed to be perpendicular to the aquitard; thus only vertical dispersive and advective transports are considered for the aquitard. The validity of this treatment is tested against results grounded in numerical simulations. The global sensitivity analysis indicates that the results of the SWPP test are largely sensitive (i.e., influenced by) to the parameters of porosity and radial dispersion of the aquifer, whereas the influence of the aquitard on results could not be ignored. In the injection phase, the larger radial dispersivity of the aquifer could result in the smaller values of breakthrough curves (BTCs), while there are greater BTC values in the chaser and rest phases. In the extraction phase, it could lead to the smaller peak values of BTCs. The new model of this study is a generalization of several previous studies, and it performs better than previous studies ignoring the aquitard effect and wellbore storage for interpreting data of the field SWPP test reported by Yang et al. (2014).
Highlights
A single-well push–pull (SWPP) test could be applied for investigating aquifer properties related to reactive transport in the subsurface instead of the inter-well tracer test, due to its advantages of efficiency, low cost and easy implementation
Similar to other aquifer tests, the SWPP test is a forcedgradient groundwater tracer test, and analytical solutions are often preferred to determine the in situ aquifer properties, due to the computational efficiency
Some assumptions included in previous models have been relaxed in the new model, some other processes of the reactive transport in the SWPP test have to be simplified in analytical solutions
Summary
A single-well push–pull (SWPP) test could be applied for investigating aquifer properties related to reactive transport in the subsurface instead of the inter-well tracer test, due to its advantages of efficiency, low cost and easy implementation. Numerous studies have demonstrated that such an assumption might cause errors for groundwater flow (Zlotnik and Zhan, 2005; Hantush, 1967) and for reactive transport (Zhan et al, 2009; Chowdhury et al, 2017; Li et al, 2019) This is because even without any flow in the aquitards, molecular diffusion inevitably occurs when solute injected to the aquifer is close to the aquitard– aquifer interface. These models only focus on the first phase of the SWPP test (injection) Another assumption included in many previous models of radial dispersion is that the wellbore storage is ignored for the solute transport.
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