Nonlinear Behaviors of the Non-Darcian Flow Toward Fully Penetrating Pumping Wells with Skin Effects in a Confined Aquifer

This study develops a mathematical model for non-Darcian flow toward a fully penetrating pumping well in a confined aquifer, explicitly incorporating both well skin effects and non-Darcian flow behavior, which are conventionally neglected in classical models. A two-zone radial flow model consisting of a skin zone and a background region is established to account for hydraulic property differences caused by well construction. The Izbash equation is adopted to describe the nonlinear velocity-gradient relationship, and the transformed differential quadrature method (TDQM) is employed for the efficient solution. By combining the Laplace transform, differential quadrature discretization, and Stehfest numerical inversion, transient drawdown responses are obtained. The model is verified against benchmark solutions and field pumping-test data, showing good agreement. Parametric analyses reveal that (1) increasing the non-Darcian parameter intensifies near-well flow resistance, producing a steeper and more localized drawdown cone; (2) a larger skin factor (improved near-well hydraulic conductivity) significantly reduces drawdown and enhances well efficiency; and (3) increasing skin thickness primarily improves near-field hydraulic response with limited far-field influence. The proposed framework provides an effective tool for analyzing nonlinear pumping behavior in radially heterogeneous aquifers.