Steady State Productivity Equations for a Vertical Well in Anisotropic Sector Fault, Channel, and Rectangular Reservoirs

This paper presents steady state productivity equations for a fully penetrating vertical well in the following three anisotropic systems: (a) sector fault, (b) channel, and (c) rectangular reservoir using a uniform line sink model. The new equations, which are based on conformal mapping method, are simple, accurate, and easy to use in field practice. If the well is in a sector fault reservoir, the productivity is a function of the angle of the sector, wellbore location angle, off-vertex distance, and drainage radius. If the well is in a channel reservoir with two parallel impermeable lateral boundaries, well flow rate reaches a maximum value when the well is located in the middle of the channel width. If the well is in a rectangular reservoir with constant pressure lateral boundaries, a new equation is provided to calculate the productivity of the well arbitrarily located in the anisotropic reservoir for the case where the flow rate of an off-center well is bigger than that of a centered well. It is concluded that, for a vertical well, different steady state productivity equations should be used in different reservoir geometries.