Analysis of stagnation points for a pumping well in recharge areas

Stagnation points in groundwater flow fields delineate different flow regions by the separation streamlines passing through them. Stagnation-point analysis can hereby provide a useful tool in streamline delineation as well as in hydraulic control. In the present work, we present a stagnation-point analysis for a flow field created by a pumping well in recharge areas. This scenario is of great interest since it is very common in practice for pumping wells to be located inside or near a recharge area. A typical case is that an irrigation system is fed by groundwater pumped from an inside well. By performing stagnation-point analysis, it is found that the behavior of the created flow field under study is not only determined by the magnitudes of specific parameters such as pumping rate, regional flow rate, infiltration rate, recharge area, and well location, but also related to the interrelation of these parameters. Applying the properties of the potential Hessian matrix at stagnation points, we also identified the nature of stagnation points (e.g., maximum, minimum, or saddle point) assuming that the pumping well locates at the center of the recharge area. In addition, we delineated the streamlines by tracing streamlines starting from the stagnation points. The orientation of the separation streamlines is determined by the potential Hessian matrix. Generally, for a well with a relatively high pumping rate, there is one, and only one stagnation point outside the recharge area, since all infiltration and partial regional flow are pumped by the well. For a well inside the recharge area with a relatively low pumping rate, however, it is found that there are always three stagnation points, because infiltration is surplus for providing the well extraction, which results in the separation streamlines outside the recharge area and eventually forms a third stagnation point. Under certain field conditions, cases of two stagnation points can occur, and these critical conditions have also been identified.