Analytical solutions for maximum fresh groundwater extraction in stratified coastal aquifers

Abstract

Existing analytical solutions for defining maximum freshwater extraction in coastal aquifers mostly presume a homogeneous aquifer. In this study, analytical solutions for the pumping-induced interface toe position and the maximum pumping rate of a single well in stratified coastal aquifers are developed, based on the potential theory and the analytical solution proposed by Rathore et al. (2020), where aquifer stratification is concisely characterized by the total transmissivity and the transmissivity centroid elevation (hereafter “TCE”). Three typical aquifer domain scenarios are examined, including semi-infinite, infinite-strip, and rectangular coastal aquifers. The sensitivity analysis based on the proposed analytical solutions demonstrates that in all aquifer domain scenarios, a lower TCE leads to a more seaward interface toe and a larger maximum pumping rate, while the impact of total transmissivity is complicated, depending on the type of the inland boundary condition. The effect of inland and lateral boundary conditions on the maximum pumping rate is enhanced in the stratified aquifers of lower total transmissivity and TCE. Importantly, the boundary effects can be eliminated by properly defining the size of the stratified aquifer domain, providing valuable guidance for the design of numerical models and laboratory experiments that are often of finite sizes. Our analytical solutions can serve as a simple tool for the first-order assessment of allowable freshwater extraction in stratified coastal aquifers.