Non-Darcian Flow to a Partially Penetrating Pumping Well in a Leaky Aquifer Considering the Aquitard

Non-Darcian Flow to a Partially Penetrating Pumping Well in a Leaky Aquifer Considering the Aquitard–Aquifer Interface Flow

Wen, Zhang / Wu, Fuxian / Feng, Qinggao

Abstract

In this study, non-Darcian flow to a partially penetrating pumping well in a leaky aquifer was investigated. The aquifer system is composed of a main aquifer with an aquitard bounded on the top of the aquifer. The storage of the aquitard was considered in this study, which is the main contribution of this study. The horizontal flow in the main aquifer is assumed to be non-Darcian, while both the vertical flows in the main aquifer and the aquitard were assumed to be Darcian due to the relative low velocities. The non-Darcian flow was described by the Izbash equation. A linearization procedure associated with Laplace transform and separate variable method were used to solve the non-Darcian flow model. Semianalytical solutions (Laplace-domain solutions) were obtained then inverted to time domain by using the Stehfest method. The results indicated that the power index $n$ in the Izbash equation results in a smaller drawdown at late times, the flow approaches quasi steady state earlier, and the leakage has little impact on the drawdowns in the main aquifer when $n$ is larger. The drawdowns are quite different from each other for different $z$ positions even at the same radial distance. The sensitivity analysis indicated that the drawdown in the main aquifer is very sensitive to the power index $n$ , moderately sensitive to the parameters of the main aquifer, and relatively not sensitive to the parameters of the aquitard.