Pumping-Induced Non-Darcian Flow in a Finite Confined Aquifer

An analytic model for depicting non-Darcian flow caused by pumping in a finite confined aquifer with an outer barrier boundary is established. The model considers the wellbore storage and skin effect. And the semi-analytical solution is derived with the aid of the Izbash's law-based non-Darcian flow and the method for linearization procedure combined with the Laplace transformation. The new presented solution can reduce to some available solutions for the confined aquifer of unlimited extension. The drawdowns in abstraction well and aquifer are explored. The results suggest that the presence of the no-flux outer boundary makes no difference to the early-time drawdowns, the late-time drawdowns in the unlimited confined aquifer are smaller than those in the finite confined aquifer with a zero-flux outer boundary, and the flow in this finite confined aquifer cannot approach quasi-steady state, especially to a smaller finite outer boundary distance radius. The change of power index n in the non-Darcian flow equation cannot affect the early-time drawdowns in abstraction well, while the drawdowns in aquifer are underestimated for Darcian flow case at early pumping time. The late-time drawdowns in the pumping well and aquifer are significantly overestimated under the assumption of Darcian flow. The early-time drawdowns in abstraction well and aquifer are significantly affected by wellbore storage, and a larger wellbore storage coefficient leads to a smaller drawdown. The skin factor can impact the intermediate-time drawdowns in abstraction well, while the early and intermediate-time drawdowns in aquifer are influenced by skin effect.