A generalized analytical solution for an inclined well in a vertically and horizontally anisotropic confined aquifer and comparisons with MODFLOW

Abstract

In this paper, a new generalized three-dimensional complete analytical solution is presented for any well screen shape in a vertically and horizontally anisotropic confined aquifer in x–y–z Cartesian coordinates system for drawdown by taking into account the three principal hydraulic conductivities (Kx, Ky, and Kz) along the x–y–z coordinate directions. The special solution covers a partially-penetrating inclined parallelepiped as well as an inclined line source well. It has been showed that the rectangular parallelepiped screen case solution of Batu (2012) is a special case of this general solution. Like Batu (2012), the horizontal well case is a special case of this solution as well. The solution takes into account both the vertical anisotropy (azx = Kz/Kx) as well as the horizontal anisotropy (ayx = Ky/Kx) and has potential application areas to analyze pumping test drawdown data from partially-penetrating inclined wells by representing them as tiny parallelepiped as well as line sources. Apart from other verifications, the inclined well solution results have also been compared with the results of MODFLOW with very good agreement. The solution has also potential application areas for a partially-penetrating inclined parallelepiped fracture. With this new solution, both the horizontal anisotropy (ayx = Ky/Kx) as well as the vertical anisotropy (azx = Kz/Kx) can also be determined using observed drawdown data.