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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...