Quantifying the performance of the horizontal less permeable barrier in improving the maximum sustainable withdrawal rate in coastal aquifers

Horizontal less permeable barriers have been proposed as a viable approach for reducing seawater intrusion in coastal aquifers. However, the performance of such barriers on enhancing coastal well pumping remains unclear. This study presents an analytical model based on the potential theory capable of evaluating the effect of a horizontal less permeable barrier on the maximum sustainable withdrawal rate in a finite-domain coastal aquifer. The model contains a steady-state groundwater flow equation that includes a Dirac delta function representing the pumping well, a constant-head coastline boundary, a constant-flux inland boundary and no-flux lateral boundary conditions. A localized equivalent hydraulic conductivity is applied exclusively within the barrier region and its adjacent aquifer interface zone. The solution is derived using the finite Fourier Cosine transform. Numerical simulations employing the variable-density flow code SEAWAT are conducted to validate the proposed analytical solution, and the analytical results align well with the numerical simulation results. The sensitivity analysis based on the analytical solution and dimensionless parameters reveals that the maximum sustainable withdrawal rate can be up to twice as much as the rate without the barrier as the dimensionless equivalent hydraulic conductivity decreases. Additionally, as the dimensionless length of the barrier increases, the withdrawal rate exhibits a significant increasing trend before reaching a plateau. In a rectangular aquifer, the pumping well located closer to the inland boundary and nearer to the axis of symmetry along the shore corresponds to a higher maximum sustainable withdrawal rate. Furthermore, the maximum sustainable withdrawal rate is an order of magnitude more sensitive to the aquifer aspect ratio and the dimensionless hydraulic parameter than to the dimensionless transverse dispersivity. These findings offer valuable insights for constructing less permeable barriers to migrate seawater intrusion and for deploying pumping wells in coastal areas. The proposed analytical framework provides a flexible basis for analyzing coastal aquifer problems involving pumping wells, aquifer heterogeneity, and complex boundary conditions.