Productivity equations for an off-center partially penetrating vertical well in an anisotropic reservoir

This paper presents steady state and pseudo-steady state productivity equations for an off-center partially penetrating vertical well in an anisotropic reservoir, using a uniform line sink model. This paper also gives equations for calculating pseudo skin factor due to partial penetration. Compared with the equations for partially penetrating wells in the literature, the new equations, which are based on three dimensional models, are simple and accurate.If the well is in steady state with a circular cylinder drainage volume, and if the top and bottom reservoir boundaries are impermeable, the radius of the cylindrical system and off-center distance appear in the productivity equations. If the reservoir has a gas cap or bottom water, the effects of the radius and off-center distance on productivity can be ignored.A new equation is provided to calculate the productivity of a partially penetrating vertical well arbitrarily located in the anisotropic reservoir with a box-shaped drainage volume under pseudo-steady state. A convenient expression to calculate the Dietz shape factor is also presented.It is concluded that, for a partially penetrating vertical well, different productivity equations should be used under different reservoir boundary conditions.