A 3D Analytical Model for Wellbore Friction

Abstract

Summary This paper presents a new friction model for application in petroleum wells. Although very simple, it applies for all wellbore shapes such as straight sections, drop-off bends, build-up bends, side bends or a combination of these. The drillstring is modelled as a soft string. In high tension the string weight is negligible as compared to the tension. This leads to simplified equations where the friction caused by the weight is negligible. For this case the friction in a bend is formulated in terms of the 3D dogleg. The same model therefore applies for 2D and 3D wellbores. The entire well can be modelled by two sets of equations, one for straight wellbore sections and one for curved wellbores. The latter is based on the absolute directional change, or the dogleg of the wellbore. Three worked examples are given in the paper: a 2D well, a 3D well and combined hoisting and rotation in the 3D well. One main purpose of this paper is to provide a simple explicit tool to model and to study friction throughout the well by separating gravitational and tensional friction effects.