Directional Drillstring Dynamics

A rotating rod under load may execute vibration in different ways: transversal (bending), longitudinal (axial), torsional, or a combination of any of those. In this article, the dynamics of a rotating directional drilling system, constrained to rotate in a borehole, is investigated using the finite element formulation. To study the behavior of the system, a rotating 3D Cosserat rod element is used, this is a newly non linear element developed in this work. The equations of coupled bending, axial and torsional motion of the rotating elastic rod element is derived using the Cosserat rod theory. In general, for slender structures, the shear deformation can be neglected, consequently, to model the drillstring the Bernoulli hypothesis is considered and the shear deformations are neglected. The finite rod element developed has 12 degrees of freedom and takes into account all the geometric nonlinearities. Explicit expressions for the element mass, gyroscopic, stiffness, and non linear terms are derived using Hamiltons principle. Moreover, the finite element discretization is employed and numerical solutions are obtained for the nonlinear drillstring dynamics. Overall, the Cosserat model provides an accurate way of modelling long slender rods.