Low velocity non-Darcian flow to a well fully penetrating a confined aquifer in the first kind of leaky aquifer system

Abstract

In this study, we use a finite difference method to solve low velocity non-Darcian flow to a well in the first kind of leaky aquifer system. Flow in the confined aquifer is assumed to be Darcian and horizontal, whereas flow in the aquitard is assumed to be non-Darcian and vertical. The threshold hydraulic gradient existence of non-Darcian flow in low permeability porous media is employed to describe the non-Darcian flow in the aquitard. A numerical solution has been obtained by using a finite difference method. This solution is compared with the previous solution for Darcian flow case in leaky aquifer system. The error has been analyzed. The comparison of this study and Darcian flow case (Hantush and Jacob, 1955) in leaky aquifer system indicates that the error is very small and can be neglected. However, the hydrogeological parameter calculation of leaky aquifer system is remarkably influenced by low velocity non-Darcian flow in aquitard. For the inflection point method (Hantush, 1956), the absolute values of estimated errors for coefficient of transmissibility of confined aquifer and vertical hydraulic conductivity of aquitard show negative relationship with the pumping rate. For the type curve-fitting method (Walton, 1962), the estimated errors for coefficient of transmissibility and elastic drainable porosity of confined aquifer are very small under small pumping rate. In general, the estimated errors for coefficient of transmissibility and elastic drainable porosity of confined aquifer can be controlled under certain level through adjusting pumping rate. The estimated error of vertical hydraulic conductivity of aquitard is quite large no matter which method is used, even up to nearly 300%.