The Relation Between Wellblock and Wellbore Pressures in Numerical Simulation of Horizontal Wells

In this paper an analytical equation for calculating the effective radius r{sub o}, in a wellblock is derived. The radius r{sub o} is needed to relate wellblock pressure to well pressure. The equation is general and valid for vertical and horizontal wells and for any well location, aspect ratio of the well's drainage area, and anisotropy. The equation is used to show when Peaceman's formulations are adequate and when they require modification. Generally, if the drainage area of the well is a rectangle with sides of large aspect ratio and/or the formation is highly anisotropic, Peaceman's equations need modifications. Simplified forms of the equation applicable to special cases are reported. Furthermore, an easy-to-use approximate equation for calculating r{sub o} values for nearly centered horizontal wells is given. The formulas of this work, as well as those of Peaceman, are relevant only to simulations on uniform grids in homogeneous media.