# US 12,006,813 B2 · Real-time curvature estimation for autonomous directional drilling

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- Number: US 12,006,813 B2
- Document ID: US12006813B2
- Status: Granted
- Kind: B2
- Application number: 17/587,991
- Filed: 2022-01-28
- Published: 2023-08-03
- Granted: 2024-06-11
- Earliest claimed: 2022-01-28
- Assignees: Halliburton Energy Services, Inc.
- Applicants: Halliburton Energy Services, Inc.
- Inventors: Khunsa Hisham; Shahin Tasoujian; Ketan C. Bhaidasna; Yuanyan Chen; Robert Darbe; Vy Pho
- Web page: https://patentgrep.com/patent/US12006813B2

## CPC

- E21B 44/02: Automatic control of the tool feed ({E21B44/005,} E21B44/10 take precedence)
- E21B 47/022: of the borehole, e.g. using geomagnetism
- E21B 7/04: Directional drilling
- E21B 47/024: of devices in the borehole (determining slope or direction of the borehole E21B47/022)
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

A method and system for estimating a wellbore curvature. The method may include disposing a rotary steerable system (RSS) into a borehole, storing a real-time curvature estimation for the borehole in an information handling system, wherein the information handling system is disposed on the RSS, taking a first attitude measurement at a first sensor, and taking a second attitude measurement at a second sensor. The method may further include applying a filter to at least the first attitude measurement and the second attitude measurement to form a filtered measurement set, performing a curvature estimation with the filtered measurement set to form an estimated curvature signal, comparing the estimated curvature signal to a curvature set point to find a difference, and adjusting at least one operating parameter of the RSS based on the difference.

## Claims

### Claim 1

A method for estimating a wellbore curvature comprising:
disposing a rotary steerable system (RSS) into a borehole;
storing a real-time curvature estimation for the borehole in an information handling system, wherein the information handling system is disposed on the RSS;
taking a first attitude measurement at a first sensor;
taking a second attitude measurement at a second sensor;
applying a filter to at least the first attitude measurement and the second attitude measurement to form a filtered measurement set using a first noise covariance, wherein the first noise covariance is a time-varying function;
performing a curvature estimation with the filtered measurement set to form an estimated curvature signal, wherein the curve estimation is a difference between a first filtered attitude measurement and a second attitude measurement that is divided by a length between the first sensor and the second sensor;
comparing the estimated curvature signal to a curvature set point to find a difference, wherein the curvature set point is from a stationary survey measurement; and
adjusting at least one operating parameter of the RSS based on the difference.

### Claim 2 (depends on 1)

The method of claim 1, wherein the first sensor is disposed proximal a drill bit that is at least a part of the RSS.

### Claim 3 (depends on 2)

The method of claim 2, wherein the second sensor is disposed on a bottom hole assembly (BHA) that is connected to the drill bit.

### Claim 4 (depends on 3)

The method of claim 3, wherein the length between the first sensor and the second sensor is known.

### Claim 5 (depends on 1)

The method of claim 1, further comprising calculating the wellbore curvature from the first attitude measurement and the second attitude measurement.

### Claim 6 (depends on 5)

The method of claim 5, further comprising applying an adaptive Kalman filter to the wellbore curvature to form the estimated curvature signal.

### Claim 7 (depends on 1)

The method of claim 1, further comprising applying an adaptive law to the first noise covariance of the first attitude measurement and a second noise covariance of the second attitude measurement.

### Claim 8 (depends on 7)

The method of claim 7, further comprising applying the first noise covariance and the second noise covariance to the filtered measurement set.

### Claim 9 (depends on 1)

The method of claim 1, wherein the RSS is adjusted to achieve the curvature set point.

### Claim 10 (depends on 1)

The method of claim 1, wherein the filter is a low pass filter.

### Claim 11 (depends on 1)

The method of claim 1, further comprising identifying if the first attitude measurement and the second attitude measurement are in a spatial window or a time window.

### Claim 12

A system for estimating a wellbore curvature comprising:
a rotary steerable system (RSS) comprising:
a drill bit;
a bottom hole assembly (BHA) connected to the drill bit;
a first sensor disposed proximal the drill bit and configured to take a first attitude measurement;
a second sensor disposed on the BHA and configured to take a second attitude measurement; and
an information handling system disposed on the RSS and configured to:
store a real-time curvature estimation for a borehole;
apply a filter to at least the first attitude measurement and the second attitude measurement to form a filtered measurement set using a first noise covariance, wherein the first noise covariance is a time-varying function;
perform a curvature estimation with the filtered measurement set to form an estimated curvature signal, wherein the curve estimation is a difference between a first filtered attitude measurement and a second attitude measurement that is divided by a length between the first sensor and the second sensor;
compare the estimating curvature signal to a curvature set point to find a difference, wherein the curvature set point is from a stationary survey measurement; and
adjust at least one operating parameter of the RSS based on the difference.

### Claim 13 (depends on 12)

The system of claim 12, wherein the length between the first sensor and the second sensor is known.

### Claim 14 (depends on 12)

The system of claim 12, wherein the information handling system is further configured to calculate the wellbore curvature from the first attitude measurement and the second attitude measurement.

### Claim 15 (depends on 14)

The system of claim 14, wherein the information handling system is further configured to apply an adaptive Kalman filter to the wellbore curvature to form the estimated curvature signal.

### Claim 16 (depends on 12)

The system of claim 12, wherein the information handling system is further configured to apply an adaptive law to the first noise covariance of the first attitude measurement and a second noise covariance of the second attitude measurement.

### Claim 17 (depends on 16)

The system of claim 16, wherein the information handling system is further configured to apply the first noise covariance and the second noise covariance to the filtered measurement set.

### Claim 18 (depends on 12)

The system of claim 12, wherein the RSS is adjusted to achieve the curvature set point.

### Claim 19 (depends on 12)

The system of claim 12, wherein the filter is a low pass filter.

### Claim 20 (depends on 12)

The system of claim 12, wherein the information handling system is further configured to identify if the first attitude measurement and the second attitude measurement are in a spatial window or a time window.