Solving vertical and horizontal well hydraulics problems analytically in Cartesian coordinates with vertical and horizontal anisotropies

SummaryA new generalized three-dimensional analytical solution is developed for a partially-penetrating vertical rectangular parallelepiped well screen in a confined aquifer by solving the three-dimensional transient ground water flow differential equation 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 fully penetrating screen case becomes equivalent to the single vertical fracture case of Gringarten and Ramey (1973). It is shown that the new solution and Gringarten and Ramey solution (1973) match very well. Similarly, it is shown that this new solution for a horizontally tiny fully penetrating parallelepiped rectangular parallelepiped screen case match very well with Theis (1935) solution. Moreover, it is also shown that the horizontally tiny partially-penetrating parallelepiped rectangular well screen case of this new solution match very well with Hantush (1964) solution. This new analytical solution can also cover a partially-penetrating horizontal well by representing its screen interval with vertically tiny rectangular parallelepiped. Also 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 vertical and horizontal wells by representing them as tiny rectangular parallelepiped as well as line sources. The solution has also potential application areas for a partially-penetrating parallelepiped rectangular vertical fracture. With this new solution, the horizontal anisotropy (ayx = Ky/Kx) in addition to the vertical anisotropy (azx = Kz/Kx) can also be determined using observed drawdown data. Most importantly, with this solution, to the knowledge of the author, it has been shown the first time in the literature that some well-known well hydraulics problems can also be solved in Cartesian coordinates with some additional advantages other than the conventional cylindrical coordinates method.

► This is the only comprehensive solution for well hydraulics in Cartesian coordinates published so far.
► The solution is three-dimensional under partially-penetrating wells condition.
► The solution covers partially-penetrating vertical wells, horizontal wells, and vertical fractures.
► The solution takes into account both vertical and horizontal anisotropies.
► Theis (1935), Hantush (1964), and Gringarten and Ramey (1973) are all special cases and comparisons with them are very good.