Analytical Solutions for Optimizing Saltwater Extraction and Freshwater Lens Protection in Saline Riparian Aquifers

Abstract Saltwater extraction is a key strategy of the Salt Interception Schemes (SIS) in Australia's Murray River Basin, aimed at intercepting saline groundwater loads to the river and adjacent floodplains. Despite their widespread application, a general analytical framework is lacking to evaluate how pumping configuration and regional boundary conditions control riparian freshwater lenses, or to predict the maximum saltwater extraction rate that avoids capturing river‐derived fresh groundwater. Here we derive sharp‐interface analytical solutions that quantify pumping‐induced expansion of riparian freshwater lenses and the maximum saltwater extraction rate. The solutions cover four representative regional scenarios: a semi‐infinite flux‐controlled aquifer (S1), a finite‐width flux‐controlled aquifer (S2), a finite‐length head‐controlled aquifer (S3) and a rectangular head‐controlled aquifer (S4). The analytical solutions are validated against numerical simulations, showing good agreement in lens shape and maximum saltwater extraction rates. Sensitivity analysis indicates that regional boundary conditions primarily control the feasible pumping strategy. The finite‐length head‐controlled system (S3) consistently supports the highest saltwater extraction rate, whereas the finite‐width flux‐controlled system (S2) is the most restrictive. The rectangular scenario (S4) can perform either better or worse than the semi‐infinite scenario (S1), depending on aquifer geometry and extraction well location. These solutions provide a fast and transparent tool for designing and optimizing SIS in saline riparian aquifers.