Drill-String Dynamics: Reduced-Order Models

Abstract

Research efforts are underway to model and study the dynamics of a drill string, and preliminary results are presented in this work. The dynamics of a drill string system has non-smooth characteristics. Moreover, the drill string system dynamics exhibits qualitative changes with respect to the rotation speed of the drill string and friction coefficients associated with the contact between the drill string and the outer shell and the drill string and the well bottom. The coupling between torsion, lateral, and axial vibrations and the nonlinear interactions between them need to be investigated to better understand the dynamic behavior of the drill string system. As a preliminary step towards understanding the dynamics of the drill string, four-degree-of-freedom models are developed for the system by using two rotating sections: an inner stator that can undergo radial displacements and an outer rotor. Stickslip interactions between the drill string and the outer shell are also considered in the model development. Two sets of differential equations are obtained for the system by using displacements and momenta as system states in one model and displacements and velocities as system states in another model. For different values of friction coefficients, rotation speeds, and rotation torques, the results obtained by using the developed models are presented, discussed, and compared with experimental results.

New Analysis Theory and Method for Drag and Torque Based on Full-Hole System Dynamics in Highly Deviated Well

“…The normal contact force model presented here is different from the models of the studies [17][18][19][20], in which perfect models have been assumed. In the finite element numerical simulation of calculating the drag and torque, the rigid and flexible contact method is applied to deal with the contact relation between drill string and borehole; once it monitors the contact, the contact force according to ( 7) is joined with matrix [ ] of (3) to participate in the subsequent calculations.…”

Suppression of drill-string stick–slip vibration by sliding mode control: Numerical and experimental studies

“…Standard axial excitations and torque profiles are applied onto the discs, in order to study the resulting dynamics of the system. Two example rigs are developed in TU Eindhoven and University of Maryland, described in detail in [35,36], respectively. Some other rigs following the same principle are presented in [37,38].…”

Drill Bit Whirl Mitigation Analysis – An Under Actuated System Perspective

“…The discussion was based on the fact that the source of vibration is the bit and hence the centrifugal forces developed when an unbalanced drill string is rotated can be one of the major sources of vibrations. C-Min Liao et al [7] developed a reduced order model for a drill string system with a mass imbalance on the rotor. The tests were focused to analyze the trajectory of the bit under conditions of varying drill bit mass unbalance and operational velocities.…”

“…Jansen [3] suggested that the dynamics of a bend drill string in forward whirl could be demonstrated by an unbalanced mass on the lower bit. Following this idea, unbalanced rotors were used to represent an eccentric drill pipe in the research by Dykstra [6] and C-Min Liao et al [7].…”