Single-well Push-Pull Test with Mixing Effect in the Wellbore

Single-well push-pull (SWPP) test has been widely used to determine physical and biochemical parameters of the aquifer around the wellbore by best-fitting the observed breakthrough curves (BTCs) in the extraction phase with the analytical solutions. The mechanics of the solute transport around the wellbore was found to play important role in the results. However, previous analytical solutions did not consider the mixing effect of the tracer with the groundwater in the wellbore in both injection and extraction phase. In this study, a new model was established by including such mixing effect in the wellbore, and two types of boundary conditions at the wellbore were considered: the resident concentration continuity (RCC) and the flux concentration continuity (FCC). The analytical solutions were derived in Laplace domain using the Laplace transform approach and Green's function, and the Stehfest method was used to facilitate the numerical inverse Laplace transform. The potential errors caused by the numerical inverse Laplace transform were demonstrated to be negligible, by comparing the new solution with previous analytical solutions. The results show the new solution of this study is sensitive with the volume of the water or solute in the wellbore in both injection and extraction phases. The larger well radius results in smaller BTCs in the injection phase, but results in larger BTCs in the extraction phase. The influence of water level in the wellbore on BTCs in both injection and extraction are not negligible. Larger water level could result in the smaller BTCs in both injection and extraction phases. The new solution of the SWPP test not only could be used to interpret the experiment data of the SWPP test, but also serve as simulate the well to well test.