Capture Zone Envelopes for Pumping Wells in Fields of Uniform Areal Recharge

The capture zone envelope of a pumping well consists of the streamlines that bound the area of the aquifer that is eventually captured by the well. An approach is outlined to delineate the capture zone envelopes of pumping wells in aquifers with uniform areal recharge. Three types of uniform areal recharge are considered: recharge resulting in straight head contours, circular head contours, and elliptical head contours. Two types of stagnation points are present for wells in uniform areal recharge: saddle points and high points. Each capture zone envelope passes through a saddle point. A new complex polynomial expression is derived of which the stagnation points are among the roots. The streamlines that form the capture zone envelope are traced from saddle stagnation points by numerically integrating the analytic flow field against the direction of flow. The approach may be applied to steady Dupuit-Forchheimer flow (both confined and unconfined) in homogeneous aquifers with a horizontal base. Short Python scripts have been developed and are made available to find all stagnation points, delineate the capture zone envelopes, and visualize the results. Examples are presented for flow fields with multiple wells in a variety of background flows created by uniform areal recharge.