RESPONSE OF A PARTIALLY PENETRATING WELL IN A HETEROGENEOUS AQUIFER -INTEGRATED WELL-FACE FLUX VS UNIFORM WELL-FACE FLUX BOUNDARY-CONDITIONS

A two-dimensional integrated well-face Aux (IWFF) model is developed f or computing the drawdown at the well-face and around a fully or parti ally penetrating well with wellbore storage, situated in a layered con fined aquifer. In this model, we calculate drawdown and well-face flux distributions by numerically solving a two-dimensional diffusion equa tion in cylindrical coordinates subject to appropriate initial and bou ndary conditions and to the well-face boundary constraint of an integr ated well-face flux rather than the physically inconsistent uniform we ll-face flux boundary condition (the UWFF model). The differences betw een the IWFF and UWFF models in a partially penetrating well situated in a homogeneous isotropic aquifer are insignificant for wellbore draw down (less than 3%) but are pronounced for the well-face flux. In fact , the latter strongly deviates from uniformity as the ratio of the scr een length to the aquifer thickness decreases. For partially penetrati ng wells situated in multilayer aquifers, significant differences betw een the two models may arise, especially if the screen is not located in the most conductive layer. These differences depend on the hydrauli c conductivity contrast of the adjacent layers. Consequently, the unif orm well-face flux boundary condition should be used with extreme caut ion.