Analysis of drillstring dynamics using angular and linear motion data from multiple accelerometer pairs

1. A downhole drilling vibration analysis method, comprising:

drilling with a drilling assembly by rotating the drilling assembly;

measuring acceleration with at least two accelerometer pairs oriented at a first orientation relative to one another on the drilling assembly, each of the at least two accelerometer pairs having at least two accelerometers oriented at a second orientation relative to one another;

compensating for angular bias associated with the measured acceleration by cancelling corresponding angular acceleration components of each of the accelerometers between the at least two accelerometer pairs;

determining motion of the drilling assembly with the compensated acceleration while drilling downhole, the determined motion at least including linear motion of the drilling assembly;

analyzing the determined motion; and

determining that detrimental vibration is occurring during drilling based on the analysis.

2. The method of claim 1 , wherein the determined motion further comprises angular motion of the drilling assembly.

3. The method of claim 1 , wherein the determined motion comprises one or more of displacement, velocity, and acceleration of the drilling assembly.

4. The method of claim 1 , wherein determining the motion of the drilling assembly further comprises measuring an angular rate with a gyroscope.

5. The method of claim 1 , wherein measuring the acceleration with the at least two accelerometer pairs oriented at the first orientation relative to one another and the at least two accelerometers oriented at the second orientation relative to one another comprises measuring the acceleration in orthogonal X and Y directions both radially and tangentially relative to the drilling assembly.

6. The method of claim 1 , wherein the first orientation comprises the at least two accelerometer pairs being oriented 90-degrees relative to one another on the drilling assembly.

7. The method of claim 6 , wherein the second orientation comprises the at least two accelerometers in a given one of the pairs being oriented 90-degrees relative to one another.

8. The method of claim 6 , wherein the second orientation comprises the at least two accelerometers in a given one of the pairs being oriented on a same side or on opposing sides of the drilling assembly.

9. The method of claim 1 , wherein measuring the acceleration with at least two accelerometer pairs comprises:

measuring the acceleration with a first of the at least two accelerometer pairs, the first accelerometer pair having first and second accelerometers disposed at the second orientation relative to one another at a first radius from a center axis of the tool.

10. The method of claim 9 , wherein the first and second accelerometers are disposed at substantially the same first radius from the center of the tool and are disposed on substantially a same axial plane.

11. The method of claim 9 , wherein measuring the acceleration with the first accelerometer pair comprises:

determining a first X-component of the acceleration with the first accelerometer, the first X-component being tangential to the rotation of the tool; and

determining a first Y-component of the acceleration with the second accelerometer, the first Y-component being orthogonal to the first X-component and being radial to the rotation of the tool.

12. The method of claim 11 , wherein measuring the acceleration with the at least two accelerometer pairs comprises:

measuring the acceleration with a second of the at least two accelerometer pairs, the second accelerometer pair having third and fourth accelerometers disposed at the second orientation relative to one another at a second radius from the center axis of the tool.

13. The method of claim 12 , wherein the second radius is substantially the same as the first radius.

14. The method of claim 12 , wherein measuring the acceleration with the second accelerometer pair comprises:

determining a second X-component of the acceleration with the third accelerometer, the second X-component being radial to the rotation of the tool and being parallel to the first X-component; and

determining a second Y-component of the acceleration with the fourth accelerometer, the second Y-component being orthogonal to the second X-component, being parallel to the first Y-component, and being tangential to the rotation of the tool.

15. The method of claim 1 , wherein determining the motion of the drilling assembly with the measured acceleration while drilling downhole comprises determining the motion with axially displaced sets of the at least two accelerometer pairs displaced from one another along the central axis while drilling with the drilling assembly.

16. The method of claim 15 , wherein determining that detrimental vibration is occurring during drilling based on the analysis comprises determining an aspect of at least one of bending or twisting of the drilling assembly by comparing the determined motion from the axially displaced sets of the at least two accelerometer pairs.

17. The method of claim 1 , further comprising changing one or more operating parameters of the drilling assembly based on the determined detrimental vibration.

18. The method of claim 17 , wherein changing the one or more operating parameters of the drilling assembly comprises:

changing one or more of weight on bit, rotational speed, torque, pump rate, mud flow rate, and mud motor operation; or

operating a drilling interrupting mechanism on the drilling assembly based on the determined detrimental vibration.

19. The method of claim 1 , wherein analyzing and determining comprises:

at least partially processing the determined motion downhole at the drilling assembly; and

communicating the at least partially processed motion from the drilling assembly to the surface.

20. The method of claim 1 ,

wherein analyzing the determined motion comprises determining a pattern of vibration per one or more revolutions of the drilling assembly from the determined motion; and

wherein determining that detrimental vibration is occurring during drilling based on the analysis comprises determining a severity measure of the detrimental vibration based on one or more aspects of the determined pattern.

21. The method of claim 1 ,

wherein analyzing the determined motion comprises determining one or more cycles of an increase in the determined motion per one or more revolutions of the drilling assembly; and

wherein determining that detrimental vibration is occurring during drilling based on the analysis comprises calculating a vibration measure, indicative of the detrimental vibration, based on a number of the one or more cycles or based on an amplitude of the one or more cycles.

22. The method of claim 1 ,

wherein analyzing the determined motion comprises determining vibration over revolutions over time of the drilling assembly; and

wherein determining that detrimental vibration is occurring during drilling based on the analysis comprises calculating a vibration measure, indicative of the detrimental vibration, based on a frequency of the vibration over the revolutions over time of the drilling assembly.

23. The method of claim 1 ,

wherein analyzing the determined angular data comprises determining maximum angular velocity over time, minimum angular velocity over time, and average angular velocity over time; and

wherein determining that detrimental vibration is occurring during drilling based on the analysis comprises calculating a measure relating the maximum angular velocity over time, the minimum angular velocity over time, and the average angular velocity over time.

24. A downhole drilling vibration analysis method, comprising:

drilling with a drilling assembly by rotating the drilling assembly;

measuring acceleration in orthogonal X and Y directions both radially and tangentially relative to the drilling assembly using a plurality of accelerometers disposed on the drilling assembly;

compensating for angular bias associated with the measured acceleration by cancelling corresponding angular acceleration components between pairs of the accelerometers;

determining motion of the drilling assembly with the compensated acceleration while drilling downhole, the determined motion at least including linear motion of the drilling assembly;

analyzing the determined motion; and

determining that detrimental vibration is occurring during drilling based on the analysis.

25. A downhole vibration analysis method, comprising:

obtaining acceleration measured downhole with at least two accelerometer pairs disposed on a downhole assembly, the at least two accelerometer pairs oriented at a first orientation relative to one another on the downhole assembly, each of the at least two accelerometer pairs having at least two accelerometers oriented at a second orientation relative to one another;

compensating for angular bias associated with the measured acceleration by cancelling corresponding angular acceleration components of each of the accelerometers between the at least two accelerometer pairs;

determining motion of the downhole assembly with the measured compensated acceleration, the determined motion at least including linear motion of the drilling assembly;

analyzing the determined motion; and

determining that detrimental vibration has occurred downhole based on the analysis.

26. A drilling assembly, comprising:

a drill collar disposed on a drill string;

at least two accelerometer pairs disposed on the drill collar and measuring acceleration downhole while drilling with the drilling assembly, the at least two accelerometer pairs oriented at a first orientation relative to one another on the drill collar, each of the at least two accelerometer pairs having at least two accelerometers oriented at a second orientation relative to one another; and

processing circuitry in communication with the at least two accelerometer pairs, the processing circuitry configured to:

cancel corresponding angular acceleration components of each of the accelerometers between the at least two accelerometer pairs to compensate for angular bias associated with the measured acceleration,

determine motion of the drilling assembly with the compensated acceleration while drilling downhole, the determined motion at least including linear motion of the drilling assembly,

analyze the determined motion, and

determine that detrimental vibration is occurring during drilling based on the analysis.

27. The assembly of claim 26 , wherein a first of the at least two accelerometer pairs comprises first and second accelerometers arranged at the second orientation relative to one another at a first radius from a central axis of the drill collar.

28. The assembly of claim 27 , wherein:

the first accelerometer provides acceleration data related to a first X-component of the acceleration, the first X-component being tangential to the rotation of the tool; and

the second accelerometer provides acceleration data related to a first Y-component of the acceleration, the first Y-component being orthogonal to the first X-component and being radial to the rotation of the tool.

29. The assembly of claim 28 , wherein a second of the at least two accelerometer pairs comprises third and fourth accelerometers arranged at the second orientation relative to one another at a second radius from the central axis of the drill collar.

30. The assembly of claim 29 , wherein:

the third accelerometer provides acceleration data related to a second X-component of the acceleration, the second X-component being radial to the rotation of the tool and being parallel to the first X-component; and

the fourth accelerometer provides acceleration data related to a second Y-component of the acceleration, the second Y-component being orthogonal to the second X-component, being parallel to the first Y-component, and being tangential to the rotation of the tool.

31. The assembly of claim 29 , wherein the second radius is substantially the same as the first radius.

32. The assembly of claim 26 , wherein the processing circuitry comprises first circuitry disposed on the drill collar.

33. The assembly of claim 26 , wherein the processing circuitry comprises second circuitry disposed at the surface.

34. The assembly of claim 26 , further comprising telemetry unit communicating information indicative of the detrimental vibration from the drill collar to the surface.

35. The assembly of claim 26 , further comprising a mechanism disposed on the drilling assembly and operable to interrupt drilling by the assembly.