Extension of Hantush and Boulton Solutions

Abstract

Equations leading to the Theis, Hantush-Jacob, and Boulton solutions are reviewed to show that the Hantush-Jacob solution contains the Theis solution and that the Boulton solution contains both the Theis and Hantush-Jacob solutions. Scaling methods are used to delineate regions of overlap between these solutions, and a new solution is obtained for free-surface drawdowns in the top layer for the Boulton solution. Ideas underlying the Boulton equations are used to suggest that the Boulton solution also models flow to a well in a layered system, provided that top and bottom boundaries are a free surface and aquiclude, respectively, and that certain restrictions are placed on the transmissivity and elastic storage of the different layers. These restrictions require that the largest transmissivity for any unpumped layer not exceed 5% of the pumped layer transmissivity and that the specific yield of the top unconfined layer be much greater than the elastic storage coefficient for any of the other layers. Numerical calculations with a MODFLOW model confirm these results and show the effect of neglecting aquitard elastic storage.