Modeling Three‐Dimensional Flow in Confined Aquifers by Superposition of Both Two‐ and Three‐Dimensional Analytic Functions

Abstract

A technique is presented to incorporate three‐dimensional flow in a Dupuit‐Forchheimer model. The method is based on superposition of approximate analytic solutions to both two‐ and three‐dimensional flow features in a confined aquifer of infinite extent. Three‐dimensional solutions are used in the domain of interest, while farfield conditions are represented by two‐dimensional solutions. Approximate three‐ dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three‐dimensional feature becomes nearly horizontal. Consequently, remotely from a three‐dimensional feature, its three‐dimensional solution is replaced by a corresponding two‐dimensional one. The latter solution is trivial as compared to its three‐dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.