Unsteady Stream Depletion when Pumping from Semiconfined Aquifer

Abstract

A solution is obtained for flow depleted from a stream when water is pumped from an adjacent well in a semiconfined aquifer. The streambed partially penetrates the aquitard, which forms the top boundary of the pumped aquifer, and the distance between the well and stream is assumed large enough to allow the stream to be modeled with a zero width. The governing partial differential equations for this problem are shown to be equivalent to the equation postulated and solved by Boulton for flow to a well in a delayed-yield aquifer. Consequently, drawdown curves and plots of stream depletion versus time are all found to have two inflection points. However, unlike the solution behavior for Boulton’s problem, aquifer recharge furnished by the stream causes all drawdown and stream depletion curves to approach horizontal asymptotes as time becomes infinite. The solution calculated herein is general enough to reduce to a solution calculated earlier by Hunt when the aquitard becomes impermeable.