U.S. Environmental Protection Agency


Date of this Version



WATER RESOURCES RESEARCH, VOL. 50, 741–747, doi:10.1002/2013WR013867, 2014


This article is a U.S. government work, and is not subject to copyright in the United States.


Flow problems in an anisotropic domain can be transformed into ones in an equivalent isotropic domain by coordinate transformations. Once analytical solutions are obtained for the equivalent isotropic domain, they can be back transformed to the original anisotropic domain. The existing solutions presented by Cihan et al. (2011) for isotropic multilayered aquifer systems with alternating aquitards and multiple injection/pumping wells and leaky wells were modified to account for horizontal anisotropy in aquifers. The modified solutions for pressure buildup distribution and leakage rates through leaky wells can be used when the anisotropy direction and ratio (Kx=Ky) are assumed to be identical for all aquifers alternating with aquitards. However, for multilayered aquifers alternating with aquicludes, both the principal direction of the anisotropic horizontal conductivity and the anisotropy ratio can be different in each aquifer. With coordinate transformation, a circular well with finite radius becomes an ellipse, and thus in the transformed domain the head contours in the immediate vicinity of the well have elliptical shapes. Through a radial flow approximation around the finite radius wells, the elliptical well boundaries in the transformed domain are approximated by an effective well radius expression. The analytical solutions with the effective radius approximations were compared with exact solutions as well as a numerical solution for elliptic flow. The effective well radius approximation is sufficiently accurate to predict the head buildup at the well bore of the injection/pumping wells for moderately anisotropic systems (Kx=Ky ≤ 25). The effective radius approximation gives satisfactory results for predicting head buildup at observation points and leakage through leaky wells away from the injection/pumping wells even for highly anisotropic aquifer systems (Kx=Ky ≤ 1000).