A single‐potential solution for regional interface problems in coastal aquifers

An analytic technique for solving three‐dimensional interface problems in coastal aquifers is presented in this paper. Restriction is made to cases of steady state flow with homogeneous isotropic permeability where the vertical flow rates can be neglected in relation to the horizontal ones (the Dupuit‐Forchheimer assumption). The aquifer is divided into zones defined by the type of flow occurring. These types of flow may be either confined, unconfined, confined interface, or unconfined interface flow, where the interfaces separate freshwater from salt water at rest. The technique is based upon the use of a single potential which is defined throughout all zones of the aquifer. This potential in each zone can be represented in a way similar to that suggested by Girinskii in 1946 and 1947. The potential introduced in this paper is single valued and continuous throughout the multiple‐zone aquifer, and its application does not require that the boundaries between the zones be known in advance. The technique thus avoids the difficulties that result from the discontinuity of both the velocity gradients and the Girinskii potentials at the boundaries between the zones and from the unknown locations of these boundaries. The use of the single‐valued potential is illustrated in this paper for an analytic technique, but it may be used with some advantage in numerical methods such as finite difference or finite element techniques. Applications discussed in this paper involve two interface flow problems in a shallow coastal aquifer with a fully penetrating well. The first problem is one of unconfined interface flow where the upper boundary is a free water table. The second is one of confined interface flow where the upper boundary is horizontal and impervious. Each problem involves two zones. One zone is adjacent to the coast and is bounded below by an interface between freshwater and salt water at rest. The other zone is bounded below by an impervious bottom. It is shown that saltwater intrusion in the well occurs when the discharge of the well surpasses a certain value for which the interface becomes unstable. The conditions that must be met to prevent such saltwater intrusion are established for each problem and are represented graphically.