Theory and Application of a New Generalized Model for Torque and Drag

Abstract

Abstract Well friction, or torque and drag play an important role in many well operations. Modelling is performed either with a numerical simulator, or by analytical mathematical models. Although the latter provide better physical insight, they are often cumbersome to use. A mathematical study was undertaken, analyzing published friction models. Identifying a lot of symmetry in the solutions, we managed to reduce the complexity significantly. The result is a generalized friction model consisting of only two equations, one for rotating friction (torque) and one for pulling friction (drag) that is valid for all well geometries. The derivation of the generalized friction model will be presented. It covers vertical sections, build-up bends, drop-off bends and straight sections. For all these geometries the new model is valid for tubular both in tension and in compression. The different solutions are obtained by selecting the signs of the coefficient of friction and the well inclination. The new model includes previously unpublished results such as pipe in compression in drop-off bends. Any deviated well geometry can now be analyzed using a spreadsheet with the new model, simply by adding forces starting from bottom of the well. A field case is presented. An S-shaped well is modelled using the two equations. In addition to provide a worked example, physical effects like friction in bends are shown and discussed. Introduction The oil industry is in general producing the easiest accessible oil first, because they are more economical. As existing fields are being produced, however, it becomes important to drain these in an optimum way. Drilling technology plays an important role here because the horizontal reach has shown a four-fold increase during the last two decades. It has become evident that well friction is a limiting factor in extended-reach drilling. Sheppard et.al. (1987) showed that an undersection trajectory can have reduced drag compared to a conventional tangent section. Aarrestad and Blikra (1994) present a good review of the various aspects of torque and drag problems encountered in extended-reach drilling. A general review is given by Payne et. al.(1994). Gou and Miska(1993) and Wiggins et.al. (1992) define equations to calculate the well trajectory. Sheppard et. al.(1987) formulated the torque and drag models that are implemented in most simulators today. Aadnoy and Andersen (2001) derived analytical torque and drag solutions for most wellbore geometries to present a tool to perform analysis without a simulator, and, to improve the understanding of well friction. These equations were later (Aadnoy et. al., 2003) expanded into a mechanistic stuck pipe analysis. Tables were presented where the equations for torque and drag are presented for various geometries. This paper carries this analysis a step further. Analysis shows that the solutions possess a lot of symmetry, leading to further simplifications of the equations. Furthermore, only pipe in tension was studied, whereas the present study shows that pipe in compression can also be handled by the same equations.