Optimizing groundwater pumping in small island groundwater lenses: An analytical approach

For residents living on small islands, groundwater serves as their primary source of freshwater, which exists in the form of a freshwater lens floating above denser seawater. Previous research on optimizing pumping strategies in freshwater lenses focused on pumping from fixed wells using numerical models, and optimal well locations have not been explored. In this study, we analyze pumping optimization for both fixed well cases and moving well cases in a rectangular island using an analytical approach. This approach allows for a clear understanding of the relationship between hydrogeological parameters and optimization results. For fixed well cases, we provide an analytical solution for the critical pumping rate of each well. For moving well cases, Bayesian optimization is employed to efficiently search the extensive space of possible well locations and identify the critical pumping rate. Our results reveal that the well location has a substantial impact on the critical pumping rate in the fixed well cases, indicating that investigating the optimization of well placement is essential. In the discussion of the moving well cases, the maximum total pumping rate of a pumping well network is independent of hydraulic conductivity, and the critical pumping percentage relative to total recharge is independent of both hydraulic conductivity and recharge. The distribution of optimized well locations for islands with a fixed aspect ratio but different sizes follows the same pattern. In the moving well cases, different solutions can achieve the same maximum pumping rate, especially when multiple wells are involved. In addition, our approach is applicable to scenarios where new wells are added to an existing well system. Our solutions and findings significantly contribute to a deeper understanding of the hydraulic performance of pumping activities from freshwater lenses and offer valuable insights for developing more sustainable and robust groundwater management strategies in small islands.