New method for geometric nonlinear analysis of large displacement drill strings

Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state consistent with well axis can be obtained from the curvature and the tortuosity of well axis. By using the principle of virtual work, the formula to compute the equivalent load vector of the initial stress was derived. In the derivation, the natural (curvilinear) coordinate system was adopted since both the curvature and the tortuosity were generally not zero. A set of displacement functions fully reflecting the rigid body modes was used. Some basic concepts in the finite element analysis of drill string were clarified. It is hoped that the proposed method would offer a theoretical basis for handling the geometric nonlinear problem of the drill string in a 3-D large displacement wellbore.