A New Generalized Three-Dimensional Analytical Solution in Cartesian Coordinates for Drawdown in a Confined Aquifer for A Partially-Penetrating Vertical Thin Rectangular Parallelepiped Well Screen

A new generalized three-dimensional analytical solution is developed for a partially-penetrating vertical and thin rectangular parallepiped 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 (K_x, K_y, K_z) along the x-y-z coordinate directions. The fully penetrating thin rectangular parallepiped well 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 match very well. Similarly, it is shown that this new solution for tiny fully-penetrating rectangular parallelepiped screen cases (line source) match very well with Theis (1935) solution. Moreover, it is also shown that  tiny partially-penetrating rectangular parallepiped well screen cases (line source) of this new solution  match very well with Hantush (1964) solution. The new analytical solution can cover a partially-penetrating horizontal well by representing its screen interval with a tiny rectangular parallelepiped. This new solution takes into account both the vertical anisotropy (a_zx = K_z/K_x) as well as the horizontal anisotropy (a_yx = K_y/K_x ) and has potential application areas to analyze pumping test drawdown data from partially-penetrating vertical and horizontal wells by representing them as thin rectangular parallelepiped as well as line sources. The solution has also potential application areas for a partially-penetrating rectangular vertical fracture. With this new solution, the horizontal anisotropy (a_yx) in addition to the vertical anisotropy (a_zx) can also be determined using observed drawdown data. More importantly, with this solution, to the knowledge of the author, it has been shown 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.