A Dupuit-Forchheimer solution to the extraction of seawater from coastal aquifers

Seawater intrusion can be mitigated by extracting saltwater, creating a negative hydraulic barrier that reduces the extent of saltwater in coastal aquifers. The effects of seawater extraction are analyzed in the current study through a semi-analytical methodology based on sharp-interface, steady-state conditions. The methodology is based on the Dupuit-Forchheimer approximation and applies a power series approach to obtain an exact solution to the seawater extent in the aquifer. Alternatively, the solution can be obtained by a Runge-Kutta method, thereby allowing for rapid assessment of the efficacy of seawater extraction for simple situations (e.g., uniform, homogeneous aquifer, and a continuous line sink well). Comparisons with numerical simulations using SEAWAT (including cases with nominally zero dispersion and with dispersion) display good agreement between the sharp-interface solution using a modified density and the 50 % seawater contour from SEAWAT. The results show that for a given well location there is an optimal (maximum) extraction rate of seawater that minimises the landward extent of seawater. Equivalently, for a given extraction rate, there is an optimal well location. These optima place a well at the seawater-freshwater interface, so in practice will likely lead to the partial extraction of freshwater. Nonetheless, they represent the limits defining the operating region for a negative hydraulic barrier in non-dimensional parameter space and thereby can inform initial decisions regarding applicability. The method presented provides a rapid assessment tool for examining the interplay between the extraction well location and the extraction rate.