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

Abstract

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.

Experimental Study to Parameterize Salt-Wedge Formations in Coastal Aquifer

“…The experiments were performed with various conditions of porous media hydraulic conductivity, salinity, and ground surface slope to assess relationships on salt wedge location and inclination. Salt-wedge profiles induced by saltwater intrusion were observed in porous media equilibrium state, and compared with previously derived formulas of the Glover (1959), Henry (1959) and Strack (1976). It was found that salt-wedge shape and formations were affected by the water level ratio (    ) due to high hydraulic conductivity, saltwater salinity and ground surface slope.…”

Assessment of Available Coastal Groundwater Resources Using Strack's Single-potential Analytical Solution

“…The freshwater potential for multiple wells, in an aquifer with uniform flow, can be obtained using the method of superposition (Strack, 1976;Cheng et. al, 2000)…”

“…Reilly and Goodman (1987) Strack (1976) can be used when simplifying assumptions are applicable (Cheng et al, 2000;Park and Aral, 2003).…”

Transient Dupuit Interface Flow with partially penetrating features

“…When Strack's potential is used, the problem reduces to a potential flow problem, which may be solved using analytic functions, by application of the analytic element method, for example [Strack, 1989;Haitjema, 1995]. An additional benefit is that the transition from regular confined flow (no interface) to confined interface flow is taken care of automatically; the potential is continuous at the transition and only the relationship between head and potential changes (for details see Strack [1976Strack [ , 1989). A solution obtained with Strack's potential is an end situation; the interface has reached its final position, and the salt water is at rest.…”

“…Numerical Essaid [1990], and Huyakorn et al [1996]. Strack [1976] presented a comprehensive potential for steady state interface flow by adopting the Dupuit approximation. When Strack's potential is used, the problem reduces to a potential flow problem, which may be solved using analytic functions, by application of the analytic element method, for example [Strack, 1989;Haitjema, 1995].…”