Analytical solutions for seawater intrusion and the maximum pumping rate of a well in unconfined coastal aquifers bounded by L-shaped coastlines

Abstract

Determining the maximum pumping rate (i.e., the maximum allowable pumping rate that does not cause seawater intrusion into the well under the steady-state condition) of a well is the key for sustainable management of coastal aquifers, as overexploitation of coastal aquifers could lead to the widespread occurrence of aquifer salinization (i.e., seawater intrusion). In this study, we develop steady-state analytical solutions to describe seawater intrusion and the maximum pumping rate of a well located in unconfined coastal aquifers bounded by L-shaped coastlines. Rectangular coastal aquifers bounded by two orthogonal constant-head boundaries (i.e., two coastlines) and two orthogonal no-flow inland boundaries are assumed in conceptual models, where replenishment of aquifers is via surface recharge. Analytical solutions are derived by the potential theory and the conformal mapping method, and validated by variable-density flow numerical simulations. It is found that analytical solutions based on the sharp-interface approximation overestimate seawater intrusion and underestimate the maximum pumping rate. An acceptable, conservative maximum pumping rate is obtained by using the correction factor proposed by Lu and Werner (2013). Moreover, the sensitivity of the well location on the maximum pumping rate is investigated, showing that an optimal well location exists. Analytical solutions developed in the current study provide a convenient tool for assessing pumping effects in coastal aquifers bounded by L-shaped coastlines, servicing to various management objectives.