Finite element dynamic analysis of drillstrings

Field experience manifests that drillstring vibration is one of the major causes for a deteriorated drilling performance. It is crucial to understand the complex vibrational mechanisms experienced by a drilling system in order to better control its functional operation and improve its performance. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangian approach together with the finite-element method. The drillstring components with circular cross-section are discretized into a number of finite shaft elements with 12 degrees of freedom each. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, and the effect of the gravitational force field. Explicit expressions of the finite element inertia coupling and axial stiffening matrices are derived using a consistent mass formulation. Modal transformations are invoked to obtain a reduced order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate the modal characteristics and to perform time-response analysis of the drillstring system.