Horizontal well hydraulics in leaky confined aquifer near a stream: analytical solutions for induced drawdown and water budget components

Horizontal wells have gained popularity as a technology for exploring water resources and remediating aquifers over the last decades, due to costs and numerous technical benefits compared to traditional vertical wells. This study presents a set of analytical solutions for drawdown distribution and various components of water budget contributing to flow toward a horizontal well in an aquifer-aquitard system interacting with a fully penetrating stream. It is assumed that the water level in the upper unconfined aquifer remains fixed at a specific elevation during the course of the pumping in the lower leaky aquifer. The water budget components account for inflows from aquifer storage, stream depletion, and leakage across the aquifer-aquitard interface. Analytical solutions to this three-dimensional, transient, non-axisymmetric Darcian flow model are given for both transient and steady-state flow conditions, relying on a four-fold integral transform technique that includes a Robin-type boundary condition at the aquifer-aquitard interface. It is shown how various components of water budget collectively counterbalance the effect of pumping discharge, confirming that the mass is conserved under both continuous and non-continuous pumping scenarios. Response maps are prepared to assess how different components of water budget react to changes in the well position. Furthermore, it is found that the components of water budget are most sensitive to the well-to-stream distance and anisotropy ratio of the leaky aquifer. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.