Maximising Net Groundwater Extraction Using an Injection-Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate of an injection-extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive an analytical solution for the maximum net extraction rate and corresponding stagnation-point locations and recirculation ratio, assuming steady-state, sharp-interface conditions. With a broad range of well placement and pumping rates, the injection-extraction well-pair system often outperforms a traditional single extraction well in terms of net extraction rate, which is up to 50% higher for an aquifer with thickness of 20 m, hydraulic conductivity of 10 m/d, and freshwater influx of 0.24 m²/d. Sensitivity analyses show that for a constant freshwater discharge to the sea, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding limits to drawdown restrictions of the pumping well that are not considered here. For a given extraction well in a given coastal aquifer with constant freshwater discharge, the location of the injection well to achieve an optimal net extraction rate depends on its allowable injection rate. A shorter distance between the two wells produces enhanced net extraction for a larger allowable injection rate. If the injection well location is fixed, the recirculation ratio (under conditions of maximum net extraction) between the two wells asymptotes to a constant value with increasing injection rate, and the magnitude of this constant value depends on the locations of the two wells. The analytical analysis in this study provides initial guidance for the design of well-pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal aquifer pumping that apply only to extraction or injection wells.