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 The new model includes previously unpublished results such as pipe in compression in drop-off bends.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.

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