Low inclination magnetometer bias compensation for dynamic surveying
A method for drilling includes rotating a BHA in a wellbore. Triaxial accelerometer and triaxial magnetometer measurements are made while rotating the BHA using corresponding triaxial accelerometer and triaxial magnetometer sets that are deployed in a roll-stabilized housing. Magnetic dip angles are computed from the accelerometer and magnetometer measurements using an inclination independent model. The computed dip angles are compared with a reference magnetic dip angle and a magnetometer bias is selected that minimizes a difference between the computed magnetic dip angles and the reference magnetic dip angle.
1 . A method for drilling a subterranean wellbore, the method comprising:
rotating a bottom hole assembly (BHA) in the subterranean wellbore to drill, the BHA including a drill collar, a drill bit, a roll-stabilized housing deployed in the drill collar and configured to rotate with respect to the drill collar, and a triaxial accelerometer set and a triaxial magnetometer set deployed in the roll-stabilized housing;
using the triaxial accelerometer set and the triaxial magnetometer set to make corresponding triaxial accelerometer measurements and triaxial magnetometer measurements while rotating the BHA;
computing magnetic dip angles from the triaxial accelerometer measurements and triaxial magnetometer measurements using an inclination independent model that includes an unknown magnetometer bias;
comparing the computed magnetic dip angles with a reference magnetic dip angle; and
selecting a magnetometer bias that minimizes a difference between the computed magnetic dip angles and the reference magnetic dip angle.
2 . The method of claim 1 , further comprising computing a wellbore azimuth from the accelerometer measurements, the magnetometer measurements, and the selected magnetometer bias.
3 . The method of claim 2 , wherein:
the BHA further comprises a rotary steerable drilling tool deployed uphole from the drill bit, the roll-stabilized housing deployed in the rotary steerable drilling tool; and
the method further comprises changing a direction of drilling the subterranean wellbore in response to the computed azimuth via actuating a steering element on the rotary steerable drilling tool.
4 . The method of claim 1 , wherein the inclination independent model is azimuth independent and toolface independent.
5 . The method of claim 1 , wherein the inclination independent model is expressed mathematically as follows:
D
i
=
sin
-
1
(
G
i
T
(
B
i
-
b
)
❘
"\[LeftBracketingBar]"
G
i
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
B
i
-
b
❘
"\[RightBracketingBar]"
)
wherein D i represent the computed magnetic dip angles, G i represent the accelerometer measurements, B i represent the magnetometer measurements, and b represents the magnetometer bias.
6 . The method of claim 1 , further comprising:
measuring a change in a rotation rate of the drill collar while rotating the BHA;
computing an eddy current compensation term from the change in the measured rotation rate and the triaxial magnetometer measurements; and
wherein the computing the magnetic dip angles comprises computing magnetic dip angles from the triaxial accelerometer measurements, the triaxial magnetometer measurements, and the eddy current compensation term using an inclination independent model that includes an unknown magnetometer bias.
7 . The method of claim 6 , wherein the eddy current compensation term is computed as being equal to a derivative of angle X with respect to the rotation rate of the drill collar, wherein angle X is an angle between gravity and magnetic field vectors in a cross axial plane of the drill collar.
8 . The method of claim 6 , wherein the inclination independent model is expressed mathematically as follows:
D
i
=
sin
-
1
(
G
i
T
(
R
e
d
d
y
(
B
i
-
b
)
)
❘
"\[LeftBracketingBar]"
G
i
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
R
e
d
d
y
(
B
i
-
b
)
❘
"\[RightBracketingBar]"
)
wherein
R
e
d
d
y
=
(
1
0
0
0
f
a
f
b
0
-
f
b
f
a
)
wherein D i represent the computed magnetic dip angles, G i represent the accelerometer measurements, B i represent the magnetometer measurements, b represent the magnetometer bias, and ƒ a and ƒ b are mathematical relations of the eddy current compensation term such that ƒ a compensates an amplitude of an eddy current interference and ƒ b compensates a phase of the eddy current interference.
9 . The method of claim 1 , wherein the difference between the computed magnetic dip angles and the reference magnetic dip angle is a root mean square error expressed mathematically as follows:
ϵ
(
b
)
=
(
D
(
b
)
-
D
r
e
f
)
T
(
D
(
b
)
-
D
r
e
f
)
wherein ϵ represents the root mean square error, D represents a matrix of computed magnetic dip angles, and D ref represents a matrix of reference magnetic dip angles.
10 . The method of claim 1 , further comprising:
computing a total magnetic field strength from the magnetometer measurements and the selected magnetometer bias;
comparing the computed total magnetic field strength with a reference total magnetic field strength;
accepting the selected magnetometer bias when a difference between the computed total magnetic field strength and the reference total magnetic field strength is less than a threshold; and
rejecting the selected magnetometer bias when a difference between the computed total magnetic field strength and the reference total magnetic field strength is greater than the threshold.
11 . A rotary steerable system for drilling a subterranean wellbore, the system comprising:
a roll-stabilized housing deployed in a drill collar, the drill collar configured to rotate with a drill string, the roll-stabilized housing configured to rotate independent of the drill collar while drilling;
a triaxial accelerometer set and a triaxial magnetometer set deployed in the roll-stabilized housing; and
a controller deployed in the roll-stabilized housing, the controller configured to:
cause the triaxial accelerometer set and the triaxial magnetometer set to make corresponding triaxial accelerometer measurements and triaxial magnetometer measurements;
compute magnetic dip angles from the triaxial accelerometer measurements and the triaxial magnetometer measurements using an inclination independent model that includes an unknown magnetometer bias;
compare the computed magnetic dip angles with a reference magnetic dip angle; and
select a magnetometer bias that minimizes a difference between the computed magnetic dip angles and the reference magnetic dip angle.
12 . The rotary steerable system of claim 11 , wherein the controller is further configured to:
compute a wellbore azimuth from the accelerometer measurements, the magnetometer measurements, and the selected magnetometer bias; and
actuate a steering element on the rotary steerable system to change a direction of drilling in response to the computed wellbore azimuth.
13 . The rotary steerable system of claim 11 , wherein the inclination independent model is expressed mathematically as follows:
D
i
=
sin
-
1
(
G
i
T
(
B
i
-
b
)
❘
"\[LeftBracketingBar]"
G
i
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
B
i
-
b
❘
"\[RightBracketingBar]"
)
wherein D i represent the computed magnetic dip angles, G i represent the accelerometer measurements, B i represent the magnetometer measurements, and b represents the magnetometer bias.
14 . The rotary steerable system of claim 11 , wherein the controller is further configured to:
measure a change in a rotation rate of the drill collar while rotating the drill collar; and
compute an eddy current compensation term from the change in the measured rotation rate and the triaxial magnetometer measurements;
wherein the compute the magnetic dip angles comprises compute magnetic dip angles from the triaxial accelerometer measurements, the triaxial magnetometer measurements, and the eddy current compensation term using an inclination independent model that is expressed mathematically as follows:
D
i
=
sin
-
1
(
G
i
T
(
R
e
d
d
y
(
B
i
-
b
)
)
❘
"\[LeftBracketingBar]"
G
i
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
R
e
d
d
y
(
B
i
-
b
)
❘
"\[RightBracketingBar]"
)
wherein
R
e
d
d
y
=
(
1
0
0
0
f
a
f
b
0
-
f
b
f
a
)
wherein D i represent the computed magnetic dip angles, G i represent the accelerometer measurements, B i represent the magnetometer measurements, b represent the magnetometer bias, and ƒ a and ƒ b are mathematical relations of the eddy current compensation term such that ƒ a compensates an amplitude of an eddy current interference and ƒ b compensates a phase of the eddy current interference.
15 . The rotary steerable system of claim 11 , wherein the controller is further configured to:
compute a total magnetic field strength from the magnetometer measurements and the selected magnetometer bias;
compare the computed total magnetic field strength with a reference total magnetic field strength;
accept the selected magnetometer bias when a difference between the computed total magnetic field strength and the reference total magnetic field strength is less than a threshold; and
reject the selected magnetometer bias when a difference between the computed total magnetic field strength and the reference total magnetic field strength is greater than the threshold.