Drill Collar Length is a Major Factor in Vibration Control
Authors: Dareing Don W. 
Published: December 2007

Dareing, Don W., SPE

Summary
Drill collar length directly affects the overall vibration response of drillstrings. Drill collar length is partly responsible for severe vibrations in hard rock drilling but can also be the solution to vibration control. This paper gives a new interpretation to the cause and control of drillstring vibrations and presents the results in terms of formulas that can be directly applied by the drilling engineer.

Introduction
It is standard practice to design the length of drill collars or bottomhole assemblies (BHA's) so that the neutral point is located in the collars. The neutral point is the point where compressive stress is equal to local hydrostatic pressure. The calculation is based on static forces only, including buoyant weight of the collars and static bit weight. One formula commonly used to calculate drill collar length is
...........................(1)
According to this formula, the distance to the neutral point is 85 % of the total drill collar length, allowing for a margin of bit weight overload. Higher bit weights require longer BHA's. Natural frequencies and inertia loading in BHA's are not considered in this calculation. As a result, the present practice of calculating drill collar length often leads to natural tuning of the collars with bit displacement frequencies. This means that many drill collars are unintentionally designed to vibrate, and collar length selection, based on statics alone, may account for rough running. Drill collars can vibrate in three modes:axial or longitudinal,torsional, andtransverse or lateral.
Because the collars are confined by the wellbore, lateral vibrations are not usually a major source of stress and are not covered in this paper. Drill collars are free to move axially and torsionally, and these two modes of vibration can become severe. Kelly bounce and whipping of the draw works cables indicate axial vibrations in drillstrings. Torsional vibrations are normally not seen from the rig floor because the rotary table drive tends to "fix" the vibrational angular motion at the surface. Nonetheless, large dynamic torque can be generated at the rotary table. As in any mechanical system, severe vibrations in drillstrings are the result of resonance or frequency tuning. Resonance exists when the frequency of the applied force is equal to a natural free vibration frequency. The drill collar section, however, controls the overall vibration response because its cross-sectional area is several times the cross-sectional area of drillpipe. The collars act as receivers and amplifiers of vibration energy from the drill bit. In one sense the drill collar section is the dog wagging the tail, which in this case is the drillpipe section. This observation, supported by calculations and field data, is explained further in the paper. Assumptions made in the analysis are as follows.1. The BHA is a constant-OD and -ID drill collar2. The drill bit is a roller cone rock bit.3. The formation is medium to hard.4. The natural frequency of damped free vibration of the BHA is not significantly different from its natural frequency of undamped free vibration.5. Axial and torsional stiffness of stabilizers do not significantly alter the natural modes and vibration.6. Hole inclination and curvature do not affect natural frequency of BHA's. One goal of the paper is to give alternative vibration control techniques for alleviating rough running. Shock absorbers are proved alternatives. Rough, running can also be alleviated by adjustments in BHA design. A third alternative is rotary speed selection, based on techniques given in the paper.

Natural Frequency of Drill Collar Assembly
BHA's are often made up of different sizes of drill collars, stabilizers, and downhole tools. In general, critical rotary speed should be based on the natural frequency of the composite BHA. For simplicity, the following discussion assumes the drill collar section has a uniform cross section from the bit to the collar/drillpipe interface and contains no downhole tools. It can be shown that the natural frequencies of BHA's made up of different collar sizes can be reasonably approximated by assuming uniform drill collars. An exception to this simplification is heavy drillpipe in tandem with drill collars. The natural frequencies of nonuniform BHA'S, however, can be calculated from classical vibration equations.
In calculating natural frequencies for both axial and torsional modes, the drill collars are assumed fixed at the drillbit and free at the collar/drillpipe interface. The free constraint at the top of the collar section is based on relatively low dynamic force (or torque) applied to the top of the collars by drillpipe.
JPT
P. 637^