Modeling Transient Vibrations While Drilling By Use of a Finite-Rigid-Body Approach
Authors: Bybee Karen 
Published: February 2015

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 137754, ’Modeling Transient Vibrations While Drilling Using a Finite Rigid Body Approach,’ by J. Pabon, N. Wicks, SPE, Y. Chang, SPE, B. Dow, and R. Harmer, SPE, Schlumberger, originally prepared for the 2010 SPE Deepwater Drilling and Completions Conference, Galveston, Texas, 5-6 October. The paper has not been peer reviewed.
Vibrations are a common contributor to premature drillstring failure. The need for a better understanding of the phenomenon has driven the implementation of real-time downhole drilling mechanics measurements. The full-length paper describes a numerical-modeling tool developed to enhance understanding of the transient dynamics experienced by a drillstring during drilling operations. A finite-rigid-body approach was chosen for modeling simplicity, computational cost, and physical relevance of the computed results.
Introduction
The drillstring is modeled as a chain of cylindrical segments. Adjacent segments are held together through sets of axial, shear, torsion, and bending springs. The spring constants are computed on the basis of material properties, and the segment geometry (cross sections and segment lengths) are computed by use of standard linear elastic theory, to capture the respective axial, shear, torsion, and bending stiffness of the drillstring. At any moment in time, the spring forces and moments are computed on the basis of their spring constants and the deviations in relative position and orientation of the adjacent segments with respect to a reference undeformed state.
Segment lengths are chosen sufficiently short (typically two to four times the local tool diameter) so they effectively can be treated as rigid bodies. At any moment in time, the movement of a segment (i.e., linear and angular accelerations) follows the classical Newtonian laws of dynamics. Forces and moments acting on each segment include the internal forces and moments and the forces and moments caused by the mud and interaction with the borehole wall.
When updating linear and angular velocities, some external forces acting on the bottomhole assembly (BHA) segments, such as mud drag and damping as a result of an assumed viscoelastic nature of the borehole wall, can influence respective velocities, and their effect is considered by use of an implicit iterative scheme.
The interaction of the drillstring with the circulating mud can be complex, requiring computationally expensive fluid-dynamics models to capture the full drilling-fluid effect. This would make computational times impractical without dedicated computational resources, so a simplified lumped-parameter model of mud effects was used at the segment level. This includes linear approximations of axial, lateral, and torsional drag caused by fluid inside the drillstring and annulus. The drag is proportional to mud viscosity, effective area of contact between tool segment and mud, and relative speeds. The proportionality constants were chosen on the basis of comparison of the model to field cases.