STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

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922 Drilling and Well Completions
between vector G and new vector Z. The new vector Z should also be used to
compute the new azimuth.
Vibrations and Shocks
Measurements while drilling are made with sensors and downhole electronics
that must operate in an environment where vibrations and shocks are sometimes
extremely severe. A brief study of vibrations and shocks will be made to
understand better the meaning of the specifications mentioned earlier.
The vibration frequencies encountered during drilling are well known. They
correspond to the rotation of the drill bit, to the passing of the bit rollers over the
same hard spot on the cutting face, and to the impact of the teeth. Figure 4235
gives the order of magnitude for frequencies in hertz (60 rpm = 1 Hz). In each
type the lowest frequencies correspond to rotary drilling and the highest ones
correspond to turbodrilling. Three vibrational modes are encountered:
1. axial vibrations due to the bouncing of the drill bit on the bottom
2. transverse vibrations generally stemming from axial vibrations by buckling
or mechanical resonance
3. angular vibrations due to the momentary catching of the rollers or stabilizers
In vertical rotary drilling, the drillpipes are almost axially and angularly free.
Therefore, the highest level of axial and angular vibration is encountered for
this type of drilling. In deviated rotary drilling, the rubbing of the drill string
on the well wall reduces axial vibrations, but the stabilizers increase angular
vibrations. In drilling with a downhole motor, the rubbing of the bent sub on
the well wall reduces the amplitude of all vibrations.
Vibrations are characterized by their peak-to-peak amplitude at low frequencies
or by their acceleration at high frequencies. Assuming that vibration is sinusoidal,
the equation for motion is
A .
x = -sin2af
2
x t
(4-1 77)
Rotation
30
Ro I le rs
L
3
25(
Teeth
r
I
15
100 1
Frequencies 1 10 .
Hz
Figure 4-235. Main vibration frequencies encountered while drilling.