Numerical model of two-region flow by constant-head pumping in an unconfined aquifer

In order to reveal the mechanism of two-region Darcian and non-Darcian flow induced by constant-head pumping tests in unconfined aquifers, a numerical model of well flow by constant-head pumping underground based on finite difference solution was proposed. In the model, it is assumed that the aquifer is divided into two regions according to the pumping flow characteristics: the finite non-Darcian flow region near the pumping well and the semi-infinite Darcian flow region far away from the pumping well. Specifically, the flow regime in the non-Darcian flow region was simulated by the Izbash’s equation, and the reliability of the proposed solution was verified by comparison with finite element numerical solutions by COMSOL Multiphysics. Finally, the influence of finite non-Darcian effect on hydraulic head and pumping rate, as well as the influence of hydraulic head in the pumping well on pumping rate, was especially studied. The results show that the influence of non-Darcian flow region in the pumping test cannot be ignored. The turbulent flow makes the hydraulic head of the two-region flow larger than that of the pure non-Darcian flow and smaller than that of pure Darcian flow. Besides, such difference of the hydraulic head is increased with the pumping time. The pumping rate can be increased by reducing the hydraulic head in the pumping well or increasing the non-Darcian coefficient, but the effect is gradually decreased as the pumping continues. The flow rate at the cross-section is decreased with the increase of radial distance, the gradient of the flow rate-radial distance curve is decreased with time, and a turning point will appear at the conversion interface between the two regions. The proposed model provides a simple method for quantitative studies on the characteristics of hydraulic head near the pumping well under the coupling of non-Darcian and Darcian effects, and provides a theoretical basis for determining the pumping rate during constant-head pumping test.