Detection of downhole vibrations using surface data from drilling rigs

1. A method for estimating downhole lateral vibrations of a drill tubular disposed in a first borehole penetrating the earth or a component coupled to the drill tubular, the method comprising:

rotating the drill tubular to drill the first borehole;

performing a plurality of measurements in a series of time windows of one or more parameters of the drill tubular at or above a surface of the earth during the rotating using a sensor; and

estimating a series of downhole lateral vibrations corresponding to the series of time windows using a processor that receives the plurality of measurements;

wherein the series of time windows comprises a first time window and a second time window and one or more measurements in the plurality of measurements in the second time window include one or more measurements in the plurality of measurements in the first time window and one or more new measurements.

2. The method according to claim 1 , wherein each time window exceeds a time period of a fundamental torsional vibration mode.

3. The method according to claim 1 , wherein the one or more parameters comprise at least one of a minimum torque (T min ) of the drill tubular measured in the time window, a torque variation (ΔT) of the drill tubular measured in the time window, an average torque (L ave ) of the drill tubular measured in the time window, and a rate of penetration (ROP) of the drill tubular into the earth measured in the time window.

4. The method according to claim 3 , wherein the torque variation comprises a difference between a maximum torque and a minimum torque measured in the time window.

5. The method according to claim 3 , wherein estimating comprises solving for each time window an equation that is a function of one or more elements in a group consisting of the minimum torque (T min ), the average torque (T ave ), the torque variation (ΔT), the rate of penetration (ROP), and a scale factor (SF).

6. The method according to claim 5 , wherein estimating comprises calculating the following equation:

Lateral

⁢

⁢

Acceleration

⁢

⁢

Estimate

=

(

T

ave

)

a

⁢

(

T

min

)

b

⁢

(

SF

)

(

Δ

⁢

⁢

T

)

c

⁢

(

ROP

+

D

)

d

where a, b, c, and d are exponents and D is a constant.

7. The method according to claim 6 , wherein:

a=½; b=1; c=½; and D=14.

8. The method according to claim 6 , wherein:

d=0.

9. The method according to claim 8 , wherein:

a=0.

10. The method according to claim 5 , further comprising drilling a second borehole prior to the first borehole with a downhole sensor coupled to the drill tubular or the component and configured to sense acceleration in a plane perpendicular to a longitudinal axis of the borehole and determining the equation using data from the downhole sensor.

11. The method of claim 10 , wherein the downhole lateral vibrations are estimated without input from the downhole sensor.

12. The method according to claim 1 , wherein the component comprises a bottom hole assembly, a logging tool, or a drill bit.

13. An apparatus for estimating downhole lateral vibrations of a drill tubular disposed in a borehole penetrating the earth or a component coupled to the drill tubular, the apparatus comprising:

a sensor configured to perform a plurality of measurements in a series of time windows of one or more parameters of the drill tubular at or above a surface of the earth during rotating of the drill tubular to further drill the borehole; and

a processor configured to receive the plurality of measurements and to estimate a series of downhole lateral vibrations corresponding to the series of time windows using the plurality of measurements;

wherein the series of time windows comprises a first time window and a second time window and one or more measurements in the plurality of measurements in the second time window include one or more measurements in the plurality of measurements in the first time window and one or more new measurements.

14. The apparatus according to claim 13 , wherein the sensor is configured to measure at least one of a torque of the drill tubular and rate of penetration of the drill tubular into the earth.

15. The apparatus according to claim 14 , wherein the processor is further configured to calculate at least one of a minimum torque (T min ) of the drill tubular measured in each time window, a torque variation (ΔT) of the drill tubular measured in each time window, an average torque (T ave ) of the drill tubular measured in each time window, and a rate of penetration (ROP) of the drill tubular into the earth measured in each time window.

16. The apparatus according to claim 15 , wherein the processor estimates the downhole lateral vibrations without input from a downhole sensor configured to measure the downhole lateral vibrations while the borehole is being drilled.

17. A non-transitory computer-readable medium comprising computer-executable instructions for estimating downhole lateral vibrations of a drill tubular disposed in a borehole penetrating the earth or a component coupled to the drill tubular by implementing a method comprising:

receiving a plurality of measurements of one or more parameters of the drill tubular at or above a surface of the earth while the drill tubular is rotating to drill the borehole, the plurality of measurements being performed in a series of time windows; and

estimating a series of downhole lateral vibrations corresponding to the series of time windows using the plurality of measurements;

wherein the series of time windows comprises a first time window and a second time window and one or more measurements in the plurality of measurements in the second time window include one or more measurements in the plurality of measurements in the first time window and one or more new measurements.