Towards an Novel Stiff String Model for the Torque and Drag Problem

The petroleum industry relies on several kilometer long drillstrings to transmit the axial force and torque necessary to drill the rock formations and reach deep hydrocarbon reservoirs. The assessment of the energy loss along the drillstring, known as the torque and drag problem, plays an essential role in well planning and drilling as the friction appearing at the contacts between the drillstring and the borehole may dramatically increase the costs or, even, be a limiting factor in some configurations. The identification of the number of contacts as well as their positions and extents constitutes the central concern of this question. The nonlinearities associated with the large deflection of the drillstring and the non-penetration condition as well as the a priori unknown number of contacts, however, make the use of conventional numerical tools rather inefficient. To circumvent these difficulties, a simplified stiff string model is derived. Partitioning the global problem in segments of drillstring either in continuous contact with the borehole or free of contact between their extremities, the originality of the proposed formulation lies in the descripion of the drillstring deflection as perturbation of the well-path.