Downhole dynamics measurements using rotating navigation sensors
View Patent ↗A method for making downhole dynamics measurements using rotating navigational sensors includes rotating navigational accelerometers in a subterranean borehole to obtain a string of accelerometer measurements while rotating. The measurements are differentiated to obtain a string of differentiated accelerometer measurements and may then be further processed to obtain a drill string vibration parameter. Substantially simultaneous magnetometer measurements may be obtained and utilized to compute a corrected vibration parameter in which at least one of a gravitational acceleration component, a tangential acceleration component, and a centripetal acceleration component is removed from the vibration parameter.
1. A method for making downhole dynamics measurements in a drill string, the method comprising:
(a) rotating a downhole navigational sensor set in a borehole, the navigational sensor set deployed in the drill string and including at least first, second, and third tri-axial accelerometers;
(b) causing the navigational sensor set to obtain a string of accelerometer measurements, the string of accelerometer measurements including a plurality of tri-axial accelerometer measurements made at a predetermined measurement interval;
(c) differentiating the string of accelerometer measurements obtained in (b) to obtain a corresponding string of differentiated accelerometer measurements;
(d) causing a downhole processor to process the differentiated accelerometer measurements obtained in (c) to obtain a drill string vibration parameter;
(e) causing the downhole processor to further process the drill string vibration parameter obtained in (d) so as to remove at least one of a gravitational acceleration component, a tangential acceleration component, and a centripetal acceleration component to obtain a corrected drill string vibration parameter; and
(f) implementing one or more corrective measures based on the corrected drill string vibration parameter, wherein the corrective measures comprise the step of adjusting a dynamic drilling condition, the dynamic drilling condition comprising axial vibration, lateral shock, lateral vibration, torsional vibration and/or stick/slip.
2. The method of claim 1 , wherein the corrected drill string vibration parameter is obtained in (e) by subtracting a gravitational acceleration component from the drill string vibration parameter obtained in (d).
3. The method of claim 2 , wherein the gravitational acceleration component is proportional to a borehole inclination and a rotation rate of the navigational sensor set in the borehole.
4. The method of claim 2 , wherein the gravitational acceleration component is computed according to one of the following equations:
Gi
Δ
=
π
15
Rtg
sin
(
Inc
)
Gz
Δ
=
π
15
Rtg
cos
(
Inc
)
wherein Gi Δ represents a cross-axial component of the gravitational acceleration component, Gz Δ represents an axial component of the gravitational acceleration component, R represents a rotation rate of the sensor set, t represents the predetermined measurement interval, g represents a gravitational acceleration of the earth, and Inc represents a borehole inclination.
5. The method of claim 1 , wherein the corrected drill string vibration parameter is obtained in (e) by subtracting a tangential acceleration component from the drill string vibration parameter obtained in (d).
6. The method of claim 5 , wherein the tangential acceleration component is computed using magnetic field measurements made substantially simultaneously with the accelerometer measurements.
7. The method of claim 5 , wherein the tangential acceleration component is computed according to one of the following equations:
Ti Δ =max Ti −min Ti
Ti Δ =2max Ti
wherein Ti Δ represents the tangential acceleration component, Ti represents a substantially instantaneous tangential acceleration, maxTi and minTi represent the maximum and minimum instantaneous tangential accelerations within a set of measurements, and i represents the x- or y-axis.
8. The method of claim 7 , wherein the instantaneous tangential acceleration is computed according to the following equation:
Ti
=
r
α
=
r
[
ω
(
n
)
-
ω
(
n
-
1
)
t
]
wherein Ti represents the instantaneous tangential acceleration component, r represents a radial distance between the corresponding accelerometer and an axis about which the accelerometer rotates, α represents an angular acceleration of the accelerometer, ω represents an angular velocity of the accelerometer, t represents the predetermined measurement interval, and n represents an array index such that ω(n−1) and ω(n) represent sequential angular velocity measurements.
9. The method of claim 1 , wherein the corrected drill string vibration parameter is obtained in (e) by subtracting a centripetal acceleration component from the drill string vibration parameter obtained in (d).
10. The method of claim 9 , wherein the centripetal acceleration component is computed using magnetic field measurements made substantially simultaneously with the accelerometer measurements.
11. The method of claim 9 , wherein the centripetal acceleration component is computed according to the following equation:
Ci Δ =max Ci −min Ci
wherein Ci Δ represents the centripetal acceleration component, Ci represents a substantially instantaneous centripetal acceleration, maxCi and minCi represent the maximum and minimum tangential accelerations within a set of measurements, and i represents the x- or y-axis.
12. The method of claim 11 , wherein the instantaneous centripetal acceleration is computed according to the following equation:
Ci
=
r
ω
2
=
r
[
θ
m
(
n
)
-
θ
m
(
n
-
1
)
t
]
2
wherein Ci represents the instantaneous centripetal acceleration component, r represents a radial distance between the corresponding accelerometer and an axis about which the accelerometer rotates, α represents an angular acceleration of the accelerometer, ω represents an angular velocity of the accelerometer, t represents the predetermined measurement interval, and n represents the array index such that θ(n−1) and θ(n) represent sequential magnetic toolface measurements.