STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

MWD and LWD 923
where x = elongation in m
A = peak-to-peak amplitude in m
f = frequency in Hz
t = time in s
By deriving twice, acceleration becomes
A
a = --(2nf)'sin2nf x t (4-178)
2
Maximum acceleration is thus am = 2An2P. For example, peak-to-peak 12 mm at
10 Hz corresponds to am = 11.8 m/s2 = 1.2 g. Acceleration of gravity is expressed
as g.
Very few vibration measurements are described in the literature, but the
figures in Figure 4-236 can be proposed for vertical rotary drilling. The lower
limits correspond to soft sandy formations and the upper limits to heterogeneous
formations with hard zones. Table 4-120 gives the specifications that the
manufacturers propose for several tools.
The shocks that measuring devices are subjected to are generally characterized
by an acceleration (or deceleration) and a time span. For example, a device is
said to withstand 500 g (5,000 m/s') for 10 ms. This refers to a "half-sine." Shock
testing machines produce a deceleration impulse having the form shown in
Figure 4-237.
In the preceding example, a, = 500 g, t, - t, = 10 ms. The impulse represented
as a solid line is approximately equivalent to the rectangular amplitude impulse
0.66 a,. This impulse can be used for calculating the deceleration distance,
which is
1
d = Jjt:adt = -0.66a,t2
2
Axial
Vibrations
Transverse
Vibrations
Angular
Vibrations
2 - 100 MM-CC
I 30 I 250
I
I
1 - 50 MM-CC
I
///I/////
I
I
I
Frequencies 1
Hz
10 100 300
Figure 4-236. Order of magnitude of the vibration amplitudes encountered
during drilling.