Vibration analysis of drillstrings with string-borehole interaction

Drillstring vibration is one of the major causes for a deteriorated drilling performance, and if left untreated may result in a complete failure of the drilling process. Although the variations in the drilling load, stick-slip, and whirling are known to be the primary causes of severe vibrations, they often give rise to excessive flexural deformations and subsequent string-borehole interaction. Drillstring contact-impact interaction with borehole results in high-frequency excitations, which further deteriorate the drilling performance, and may cause damage to the bottomhole assembly. Modelling of impact is crucial to understanding the associated dynamic response, and to providing means for controlling the collision phenomenon. A continuous force-displacement law is introduced to model the impulsive force during the short-lived interval of impact, wherein the material compliance and damping coefficients are determined from energy balance relations. The impact model is integrated to the dynamic model of the whole drillstring; including drillpipes and drillcollars. The dynamic model of the rotating drillstring is formulated using a Lagrangean approach in conjunction with the finite-element method. The model accounts for the torsional-bending inertia coupling and the axial-bending geometric non-linear coupling. In addition, the model accounts for the gyroscopic effect and the effect of the gravitational force field. The generalized eigenvalue problem is solved to determine modal transformations, which are invoked to obtain the reduced-order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate time-response of the drillstring system in the presence of string-borehole collisions.