On the New Vertical and Horizontal Wells Analytical Solution and Comparisons with MODFLOW

The three-dimensional wells and fracture analytical solution  developed by Batu (2012) recently, which is called “The K_x-K_y-K_y solution” for vertically and horizontally anisotropic confined aquifers under partially-penetrating wells  was verified with some two-dimensional (Theis 1935; Gringarten and Ramey 1973) and three-dimensional (Hantush 1964) well hydraulics analytical solutions and they are included in Batu (2012).  None of these solutions can handle the horizontal anisotropy under partially penetrating wells. As a result, MODFLOW was used to verify the K_x-K_y-K_y solution for the horizontal anisotropy cases (a_yx = K_y/K_x). First, MODFLOW, Hantush (1964), and the K_x-K_y-K_y solution (Batu 2012) were compared for the horizontal anisotropy a_yx = 1. Then, MODFLOW and the K_x-K_y-K_y solution was compared with a_yx less than1. For all cases very good drawdown matches were achieved. These comparisons also provided some useful guidelines in generating more accurate results from MODFLOW simulations under partially penetrating wells  in vertically and horizontally anisotropic aquifers for both vertical and horizontal wells as well as fractures.