Analytic Solutions to Three-Dimensional Unconfined Groundwater Flow Near Wells

Analytic solutions are presented for three-dimensional steady-state saturated unconfined groundwater flow to one or more partially penetrating and horizontal wells. The method employs distributed singularities (analytic elements) placed outside the flow domain to enforce conditions of zero fluid pressure and specified normal flux along the phreatic surface. The resulting analytic solutions are continuous and differentiable everywhere, including at the flow domain boundaries. The solutions inherently satisfy continuity of flow in the infinite flow domain, but water balance errors can occur within the sub-domain of interest. The phreatic surface itself is represented by a continuous surface rather than a discretized network of nodes or elements. The representation of a vertical partially penetrating well includes the effects of a seepage face that may form along the well bore, and accounts for aquifer stratificaiton in the case of axisymmetric flow. It is shown that the effect of recharge on the phreatic surface can usually be neglected when modeling local three-dimensional flow near a well. The three-dimensional effects of one or more partially penetrating or horizontal wells becomes negligible at one to two aquifer thicknesses away. Consequently, at that distance the 3-D solution resembles Dupuit-Forchheimer flow. A technique is presented to embed the local 3-D solutions to partially penetrating and horizontal wells into a regional Dupuit-Forchheimer model.