Approximate analytical and numerical solutions for radial non-Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect


Correspondence to: Zhang Wen, School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, P. R. China.



This study investigated non-Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite-thickness skin. The non-Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non-Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller BD results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where BD is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady-state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite-difference solution for such a non-Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non-Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.