# US 10,865,634 B2 · Noise robust algorithm for measuring gravitational tool-face

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- Number: US 10,865,634 B2
- Document ID: US10865634B2
- Status: Granted
- Kind: B2
- Application number: 16/348,545
- Filed: 2018-11-29
- Published: 2020-09-24
- Granted: 2020-12-15
- Earliest claimed: 2017-12-14
- Assignees: Halliburton Energy Services, Inc.
- Applicants: Halliburton Energy Services, Inc.
- Inventors: Rashobh Rajan Sobhana
- Web page: https://patentgrep.com/patent/US10865634B2

## CPC

- E21B 47/024: of devices in the borehole (determining slope or direction of the borehole E21B47/022)
- E21B 47/022: of the borehole, e.g. using geomagnetism
- E21B 47/09: Locating or determining the position of objects in boreholes or wells {, e.g. the position of an extending arm}; Identifying the free or blocked portions of pipes
- G01C 21/1654: {with electromagnetic compass}
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)

## Abstract

A method may comprise penetrating a subterranean formation with a bottom hole assembly, determining a revolutions-per-minute (RPM) measurement based on a zero crossing of sinusoidal magnetometer data, determining a gyroscope bias from gyroscope data using the determined RPM measurement, determining bias compensated gyroscope data by subtracting the determined gyroscope bias from the gyroscope data, determining an angular displacement measurement using the bias compensated gyroscope data, determining a selected tool-face measurement, computing a weighted sum of the selected tool-face measurement with the determined bias compensated gyroscope data, and determining a gravitational tool-face measurement from the computed weighted sum. A system may comprise a drilling rig, a pipe string attached to the drilling rig, a bottom hole assembly attached to the pipe string, wherein the bottom hole assembly comprises at least one sensor, a drill bit, and a computing subsystem connected to the at least one sensor.

## Claims

### Claim 1

A method, comprising:
penetrating a subterranean formation with a bottom hole assembly, wherein the bottom hole assembly comprises a drill bit;
determining a revolutions-per-minute (RPM) measurement based on a zero crossing of sinusoidal magnetometer data;
determining a gyroscope bias from gyroscope data using the determined RPM measurement;
determining bias compensated gyroscope data by subtracting the determined gyroscope bias from the gyroscope data;
determining a gyro-based angular displacement measurement using the bias compensated gyroscope data;
computing a first tool-face measurement using the determined RPM measurement;
computing a second tool-face measurement using accelerometer data;
determining a selected tool-face measurement based on a selection between the first tool-face measurement and the second tool-face measurement using a predetermined selection criterion;
computing a weighted sum of the selected tool-face measurement and a gyro-based tool-face measurement;
determining a gravitational tool-face measurement from the computed weighted sum; and
further comprising altering a path of the bottom hole assembly based at least in part on the gravitational tool-face measurement.

### Claim 2 (depends on 1)

The method of claim 1, wherein the gyroscope bias is determined from N gyroscope data samples of the gyroscope data, where N is a positive integer.

### Claim 3 (depends on 2)

The method of claim 2, wherein the gyroscope bias, b′(n), is found with
b
′
⁡
(
n
)
=
1
N
⁢
∑
i
=
n
-
N
+
1
N
⁢
D
⁡
(
i
)
-
6
*
R
⁡
(
n
)
,
wherein D(i) is the gyroscope data, R(n) is the RPM, n is a sample index, N is the positive integer, and i is a summation index.

### Claim 4 (depends on 3)

The method of claim 3, further comprising averaging the gyroscope bias.

### Claim 5 (depends on 1)

The method of claim 1, wherein the angular displacement measurement is determined by computing an integral operation on a previous calculated bias compensated gyroscope data.

### Claim 6 (depends on 1)

The method of claim 1, wherein the gyroscope bias is determined by estimating the RPM measurement from a magnetic tool-face measurement.

### Claim 7 (depends on 1)

The method of claim 1, wherein the gyro-based angular displacement measurement, Δθgyro, is found with
Δ
⁢
θ
gyro
=
D
′
⁡
(
n
)
f
s
,
where D′(n) is the bias compensated gyroscope data, fs is sampling rate, and n a sample index.

### Claim 8 (depends on 1)

The method of claim 1, wherein the first tool-face measurement θRPM(n), using the determined RPM measurement is found with θRPM(n)={circumflex over (θ)}(n−1)+ΔθRPM(n) where {circumflex over (θ)}(n) is the gravitational tool-face measurement,
Δθ
RPM
⁡
(
n
)
=
R
⁡
(
n
)
*
6
f
s
,
where R(n) is the RPM, fs is sampling rate, and n is a sample index.

### Claim 9 (depends on 1)

The method of claim 1, wherein the second tool-face measurement, θconv(n), using accelerometer data is found with θconv(n)=a tan(Gy(n), −Gx(n)), where Gx and Gy are data from, respectively, X and Z-axis accelerometers, and n is a sample index.

### Claim 10

A system, comprising:
a drilling rig;
a pipe string attached to the drilling rig;
a bottom hole assembly attached to the pipe string, wherein the bottom hole assembly comprises at least one sensor;
a drill bit, wherein the at least one sensor measures a revolutions-per-minute (RPM) of the drill bit; and
a computing subsystem connected to the at least one sensor and configured to:
determine a revolutions-per-minute (RPM) measurement based on a zero crossing of sinusoidal magnetometer data;
determine a gyroscope bias from gyroscope data using the determined RPM measurement;
determine bias compensated gyroscope data by subtracting the determined gyroscope bias from the gyroscope data;
determine a gyro-based angular displacement measurement using the bias compensated gyroscope data;
compute a first tool-face measurement using the determined RPM measurement;
compute a second tool-face measurement using accelerometer data;
determine a selected tool-face measurement based on a selection between the first tool-face measurement and the second tool-face measurement using a predetermined selection criterion;
compute a weighted sum of the selected tool-face measurement and the gyro-based tool-face measurement; and
determine a gravitational tool-face measurement from the computed weighted sum.

### Claim 11 (depends on 10)

The system of claim 10, wherein the at least one sensor is an accelerometer.

### Claim 12 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to alter a path of the bottom hole assembly.

### Claim 13 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to determine the gyroscope bias from N gyroscope data samples of the gyroscope data, where N is a positive integer.

### Claim 14 (depends on 13)

The system of claim 13, wherein the computing subsystem is further configured to compute the gyroscope bias, b′(n), with
b
′
⁡
(
n
)
=
1
N
⁢
∑
i
=
n
-
N
+
1
N
⁢
D
⁡
(
i
)
-
6
*
R
⁡
(
n
)
,
wherein D(i) is the gyroscope data, R(n) is the RPM, n is a sample index, N is the positive integer, and i is a summation index.

### Claim 15 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to compute the angular displacement measurement with an integral operation on a previous calculated bias compensated gyroscope data.

### Claim 16 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to determine the gyroscope bias by estimating the RPM measurement from a magnetic tool-face measurement.

### Claim 17 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to compute the gyro-based angular displacement measurement, Δθgyro, with
Δ
⁢
θ
gyro
=
D
′
⁡
(
n
)
f
s
,
where D′(n) is the bias compensated gyroscope data, fs is sampling rate, and n is a sample index.

### Claim 18 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to compute the first tool-face measurement, θRPM(n), using the determined RPM measurement with θRPM(n)={circumflex over (θ)}(n−1)+ΔθRPM(n), where {circumflex over (θ)}(n) is the gravitational tool-face measurement,
Δ
⁢
θ
RPM
⁡
(
n
)
=
R
⁡
(
n
)
*
6
f
s
,
where R(n) is the RPM, fs is sampling rate, and n is a sample index.

### Claim 19 (depends on 10)

The system of claim 10, wherein the computing subsystem is further configured to compute the second tool-face measurement, θconv(n), using accelerometer data with θconv(n)=a tan(Gy(n), −Gx(n)), where Gx and Gy are data from, respectively, X and Y axis accelerometers, and n is a sample index.