Effect of Prebent Deflection on Lateral Vibration of Stabilized Drill Collars

An effective modulation of lateral vibration of a bottomhole assembly (BHA) is that some prebent deflection is made on the lower stabilized section of drill collars. This is because the restorable deflection of a drill collar confined in a borehole depends on the prebent deflection. If the prebend nears the limit that the borehole can contain, there will be no sufficient restorable deflection to produce restoring force for lateral vibration. To understand the nature of this phenomenon, a dynamic model for lateral vibration of a stabilized prebent drill-collar section in an inclined well is presented. The governing nonlinear equations are obtained by using a Lagrangian approach, which are characterized by a prebend-dependent nonlinear bending stiffness term. They also include the effects of clearance/friction of stabilizers with borehole wall, contact friction of drill collar with borehole wall, axial forces from weight-on-bit (WOB) and bit/formation interactions, and hydrodynamic damping of drilling mud. The gyroscopic moments are proved to be negligibly small terms within a range of operating conditions of drilling. Poincare map bifurcation diagram, phase diagram, Liapunov exponent, and power spectrum analysis are used to evaluate the dynamic behaviors. Simulation results both in a vertical well and in an inclined well show that lateral vibration is sensitive to the prebent deflection in some degree, presenting periodic motion, chaotic motion, or alternating in turn as usual. However, when prebent deflection is more than 87% in a vertical well and more than 45% in a 20 degrees-inclined well (of the average clearance between the drill collar and the borehole), lateral vibration will vanish. Such a characteristic is crucially important for practical applications. For example, we may effectively prevent a drill string in an inclined well from severe whirling motion with a properly designed prebent drill collar.