Two-region flow caused by pumping at a partial penetration well in a leaky confined aquifer

An analytical model for depicting two-region flow caused by constant-rate pumping at a partially penetrating well in a leaky confined aquifer is established. The two-region flow is described by the radial Izbash non-Darcy flow in the vicinity of the abstraction well and Darcy flow away from the abstraction well in the pumped aquifer. The model considers the effects of aquitard storage, wellbore storage, and wellbore skin. The semi-analytical solutions of drawdown are developed by means of a linearization procedure combined with Laplace transform and separation of variables. The time-domain drawdowns are then obtained by using the Stehfest method for numerical Laplace inversion. The solutions encompass previous solutions for one or two-region flow to a partially penetrating well in a (non-)leaky confined aquifer. The drawdown response in the abstraction well, non-Darcy region, and Darcy region is investigated, and sensitivity analysis is made to assess the impact of various controlling parameters. The results demonstrate that the intermediate and late-stage drawdowns in the abstraction well and non-Darcy region for the two-region flow model are larger than the corresponding values for the non-Darcy flow model. The drawdown in the Darcy region for the two-region flow model is larger than that for the Darcy flow model throughout the pumping duration. The results of sensitivity analysis show that the drawdowns in the abstraction well, non-Darcy region, and Darcy region are most sensitive to the non-Darcy constant n, and is very sensitive to the well configuration, and horizontal hydraulic conductivity of the Darcy region.