The Validation of Horizontal Well Models Using a Physical Model of Heat Flow in an Anisotropic Conductor

Abstract

Two recently proposed models of fluid flow in anisotropic media yield different expressions for horizontal well productivity due to their representation of the wellbore. The model developed by Babu and Odeh used a point source/sink for the wellbore, while Peaceman`s model implemented an isobaric boundary along the surface of the wellbore. Babu and Odeh`s model predicted elliptical isobars, even in the immediate vicinity of the wellbore. Peaceman`s model predicted a rapid transition from circular to elliptical isobars as the distance from the wellbore increased. Both models were mathematically correct and seemed plausible. Therefore, the more appropriate model to use in reservoir simulation was determined experimentally. The temperature-induced flow of heat from an anisotropic conductor into a circular heat sink is analogous to the pressure-induced flow of fluids from an anisotropic porous medium into a circular wellbore since the governing differential equations for both processes are identical in form. Heat transfer experiments were, therefore, used to model this fluid flow problem. The results clearly indicated that a transition from circular to elliptical isopotential occurred, in agreement with Peaceman`s model. It is, therefore, more appropriate to model a wellbore as an isopotential when studying near-wellbore problems, such as the calculation of well more » productivity. The calculation of well productivity, however, involves near-wellbore effects. The point source does not bound the porous medium which is governed by the differential equation. Since it is separated from the medium by a distance equivalent to the radius of the well, it should not be used as a boundary condition. The isobaric surface of the wellbore does bound the medium, and, therefore, provides the better representation of the high conductivity wellbore. « less