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 instru-
ment 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?
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
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
2.
Shocks
along
the borehole
axis
(sensor package axis):
b. Now if the braking force is supplied with a coil spring of
5,000
lb/in.
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 (inde-
pendent
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