Combined role of leaky and non-Darcian effects on the flow to a pumping well with a non-uniform flux well-face boundary

Abstract

In this study, a non-Darcian flow model was developed for a constant-rate test of a partially penetrating well with a non-uniform flux boundary in a leaky confined aquifer. The Izbash equation was applied to describe non-Darcian flow in the radial direction. Both analytical and numerical methods were employed to solve this model. It was found that the analytical solution with linearization was adequate only when non-Darcian effects were relatively small. With the finite difference method, the radial and vertical fluxes along the well screen were analyzed under four different cases involving leaky and non-Darcian effects. The leaky and non-Darcian effects on the drawdowns with non-uniform flux (NUF) boundary were compared with those with uniform flux (UF) boundary. The results indicate that both leaky and non-Darcian effects can reduce the fluxes along the well screen, while non-Darcian effects can diminish the leakage-induced differences of flux and drawdown between the two well screen ends. Non-Darcian effects can reduce the differences between UF and NUF drawdowns at any elevation with the greatest reduction difference at the elevation of the top end of the screen. The UF solution can replace the NUF solution when the distance is far from the well, as this distance is smallest at the elevation of the screen midpoint and can be distinctly reduced by non-Darcian effects. In general, the results are most sensitive to the power index n, moderately sensitive to the other aquifer parameters and least sensitive to the parameters of the aquitard.