STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

926 Drilling and Well Completions
1. Vz’ibrations:
a. Compute the maximum acceleration that the instrument will accept at
2 and at 10 Hz.
b. Compute the peak to peak motion which can be applied to the instrument
at 10 and 200 Hz.
c. Compare the 10-Hz values. At what frequency will the peak to peak data
of the low frequency be consistent with the acceleration data of the high
frequency?
d. The package is held in a housing with several rubber rings laterally
assumed to behave like perfect springs. Two different ring stiffnesses
are available with total values of:
100 lb/in
10,000 lb/in
Compute the resonant frequencies for lateral vibrations. In the frequency
range usually encountered in drilling, which one should be used?
2. Shocks along the borehole axis (sensor package axis):
Assume that the shock specification refers to the maximum deceleration
(am,) of a half sine wave impact. The mean deceleration will be taken equal
to 0.66 amax.
a. Assuming a dampener in the tool housing exerting a constant force and
the housing stopping abruptly, compute according to the specifications:
the distance of deceleration
9 the velocity at the beginning of the deceleration
the braking force applied to the sensor package
b. Now if the braking force is supplied with a coil spring of 5,000 lb/in.
compute:
the braking length for the velocity calculated in a.
the maximum deceleration, is it acceptable?
will such a coil spring be suitable for the vertical vibrations generated
in rotary drilling?
Solution
1. a. 0.1 and 2.55 g
b. 3.91 and 0.039 in.
c. At 10-Hz amplitudes: 0.5 and 3.91 in.; 28 Hz
d. 22 and 221 Hz; lO,OOO-lb/in. ring more suitable since frequency further
from drilling frequencies
2. a. d = 0.03 in.; v = 10.6 ft/s; F = 1320 lb
b. x = 0.13 in.; a = 324 g (am = 491 g); acceptable; f = 156 Hz; acceptable
Example 6: Vibration and Shock Analysis-Mule
Shoe Engaging Shock
A steering tool sensor and electronic package is mounted in a housing in
Figure 4-238 with a shock absorber and a spring to decrease the value of
deceleration when engaging the mule shoe.
The package has a mass of 2 kg or a weight of 4.415 lb. Assume a downward
velocity of about 10 ft/s. The shock absorber develops a constant force (independent
of the relative velocity) of 10 lb (44.48 N). The spring stiffness is 57.10
lb/in. The potential energy due to gravity will be neglected.
1. Taking into account only the shock absorber, compute the distance x
traveled by the instrument package with respect to the housing when the