A numerical solution for non-Darcian flow toward a well in a leaky aquifer

In this paper, non-Darcian flow toward a well in a leaky aquifer was investigated by using the finite-difference method. The Forchheimer equation was employed to describe the non-Darcian flow in the aquifer, and several dimensionless variables were defined for the result analysis. The impact of the turbulence and the leakage on the drawdown surrounding the pumping well was analyzed. The results indicate that the leakage has little effect on the drawdown at early times but has obviously influence on the drawdown at late times as the wellbore storage is excluded. A smaller value of leakage parameter results in a smaller drawdown at late times. As the wellbore storage is considered, all the curves for the drawdown inside the well approach an asymptotic value at early times and are straight lines in log-log scale. The drawdown in the aquifer is similar to that without considering the wellbore storage. The impact of the turbulence factor on the drawdown depends on the leakage. For the case with very small leakage, a greater turbulence results in a smaller drawdown at early times but a larger drawdown at late times. When the leakage is very large, a greater turbulence factor leads to a smaller drawdown during the entire pumping period.

A numerical solution for non-Darcian flow toward a well in a leaky aquifer Academic Article