ADAPTIVE PARAMETER ESTIMATION FOR STATIC AND DYNAMIC WELLBORE SURVEYS

Description

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application No. 63/700,788, which was filed on Sep. 30, 2024 and is incorporated herein by reference in its entirety.

FIELD

Disclosed embodiments relate generally to wellbore surveying methods and more particularly to adaptive parameter estimation for static and dynamic wellbore surveys.

BACKGROUND

In conventional drilling and measurement while drilling (MWD) operations, wellbore inclination and wellbore azimuth are measured during the drilling operation. Static survey measurements have long been made at a discrete number of longitudinal points along the axis of the wellbore when drilling has temporarily stopped and the drill string has been lifted off the bottom of the wellbore. More recently, methods have been developed to make continuous (dynamic) survey measurements in real time while drilling. These definitive dynamic surveys (DDS) have been a break-through in the drilling industry in that they enable accurate surveys to be obtained while drilling and without stops to calculate the tool orientation and position.

One of the difficult challenges in making DDS measurements is the dynamic, high noise levels inherent in the drilling operation, for example, owing to the severe and constantly changing lateral and rotational tool vibrations. Accordingly, acquiring accurate DDS measurements may require extensive noise compensation. Moreover, the noise compensation needs to be accurate, efficient, and fast to provide accurate dynamic surveys and to minimize processing requirements on downhole processors. There is a need in the industry for improved noise compensation, particularly to improve the timeliness of noise compensation in rotating magnetometer measurements.

SUMMARY

An example wellbore surveying method comprises making dynamic surveying measurements while rotating a drill string in a wellbore to drill; making static surveying measurements when drilling has temporarily stopped and the drill string has been pulled off of a bottom of the wellbore; comparing the dynamic surveying measurements and the static surveying measurements to compute at least one dynamic surveying compensation term; applying the dynamic surveying compensation term to subsequent dynamic surveying measurements to obtain compensated dynamic surveying measurements; and computing at least one survey parameter from the compensated dynamic surveying measurements.

Another example wellbore surveying method comprises making dynamic surveying measurements while rotating a drill string in a wellbore to drill, the dynamic surveying measurements including at least cross-axial magnetometer measurements; fitting the cross-axial magnetometer measurements with a second-degree polynomial equation of an ellipse; evaluating the fit to determine a cross-axial magnetometer measurement compensation; and applying the cross-axial magnetometer measurement compensation to the cross-axial magnetometer measurements to compute a compensated transverse magnetic field measurement or compensated cross-axial magnetometer measurements.

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the disclosed subject matter, and advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

FIG. 1 depicts a drilling rig including a disclosed MWD tool.

FIG. 2 depicts the MWD tool on FIG. 1

FIG. 3 depicts a flow chart of one example method for compensating dynamic surveying measurements.

FIG. 4 depicts a flow chart of another method for compensating dynamic surveying measurements.

FIG. 5 schematically depicts cross-axial magnetic interference and a corresponding interference compensation.

FIG. 6 depicts a flow chart of one example method for compensating static surveying measurements.

DETAILED DESCRIPTION

Systems and methods for surveying a subterranean wellbore while drilling are disclosed. In one example embodiment a disclosed method includes making dynamic surveying measurements while rotating a drill string in a wellbore to drill and making static surveying measurements when drilling has temporarily stopped and the drill string has been pulled off of a bottom of the wellbore. The dynamic surveying measurements and the static surveying measurements are compared to compute at least one dynamic surveying compensation term which is applied to subsequent dynamic surveying measurements to obtain compensated dynamic surveying measurements.

In another example embodiment, a disclosed method includes making dynamic surveying measurements while rotating a drill string in a wellbore to drill. The dynamic surveying measurements include at least one cross-axial magnetometer measurement which are fit with a second-degree polynomial equation of an ellipse. The fit is evaluated to determine a cross-axial magnetometer measurement compensation, which is in turn applied to the cross-axial magnetometer measurements to compute a compensated transverse magnetic field measurement or compensated cross-axial magnetometer measurements.

Example embodiments disclosed herein may provide various technical advantages and improvements over the prior art. For example, the disclosed embodiments may provide for improved measurement compensation and may therefore enable dynamic surveying measurements to be made with increased accuracy and precision. The disclosed embodiments may therefore provide for improved dynamic surveying of subterranean wellbores.

FIG. 1 depicts a drilling rig 20 including a disclosed survey tool 80 deployed in the string 30 and disposed within a wellbore 40. The drilling rig 20 may be deployed onshore or offshore (an onshore application is depicted). As is known to those of ordinary skill, offshore rigs commonly include a platform deployed atop a riser that extends from the sea floor to the surface. The drill string extends downward from the platform, through the riser, and into the wellbore through a blowout preventer (BOP) located on the sea floor. The disclosed embodiments are not limited in these regards. In both onshore and offshore operations, the wellbore 40 may be drilled in the subterranean formations via rotary drilling, slide drilling, or power drilling in a manner that is well-known to those of ordinary skill in the art (e.g., via well-known directional drilling techniques).

In the depicted embodiment, the drilling rig 20 is positioned over a subterranean formation and may include a derrick and a hoisting apparatus (not shown) for raising and lowering a drill string 30, which, as shown, extends into wellbore 40 and includes a drill bit 32 and the surveying tool 80, which may include, for example, a measurement while drilling (MWD) tool 50 and/or a rotary steerable system (RSS) 60. As is known to those of ordinary skill in the art, the drill string 30 may further include other tools such as a downhole drilling motor, a downhole telemetry system (e.g., deployed in or adjacent to MWD tool 50), and one or more logging while drilling (LWD) tools including various sensors for measuring one or more properties of the formation through which the wellbore penetrates, for example, including resistivity, NMR relaxation times, density, porosity, sonic velocity, gamma ray counts, and the like. Moreover, the MWD tool 50 may be configured to measure one or more properties of the wellbore 40 as it is drilled or at any time thereafter. The physical properties may include, for example, pressure, temperature, wellbore caliper, wellbore trajectory (attitude), a toolface angle, and the like.

It will be understood by those of ordinary skill in the art that the deployment illustrated on FIG. 1 is merely an example and that the disclosed embodiments are expressly not limited in regards to the bottom hole assembly (BHA) configuration. Nor are they limited to any particular type of drilling operation. Moreover, it will be understood that wellbore surveying measurements (inclination and azimuth measurements) are commonly made in one or both of MWD tool 50 and RSS tool 60. While the disclosed embodiments are described in more detail below with respect to downhole survey measurements, it will be appreciated that such measurements may be MWD and/or RSS measurements.

FIG. 2 depicts one example embodiment of survey tool 80. Survey tool 80 may include substantially any suitable downhole tool or tool sub configured to make wellbore surveying measurements, for example, including an MWD tool and/or an RSS as described above. MWD tools are commonly deployed at an upper end of the bottom hole assembly (BHA) and are generally configured to rotate with the drill string. While the disclosed embodiments are not limited in this regard, MWD tools commonly further include a mud pulse telemetry transmitter or another telemetry system and an alternator for generating electrical power. An RSS is commonly deployed in the lower BHA and connected with the drill bit 32. RSSs generally includes steering elements that may be actuated to control and/or change the direction of drilling the wellbore 40. In embodiments employing an RSS, substantially any system configuration may be used. For example, the PowerDrive rotary steerable systems (available from SLB) fully rotate with the drill string (i.e., the outer housing rotates with the drill string). The PowerDrive Xceed makes use of an internal steering mechanism that does not require contact with the wellbore wall and enables the tool body to fully rotate with the drill string. The PowerDrive X5, X6, and Orbit rotary steerable systems make use of mud actuated blades (or pads) that contact the wellbore wall. The extension of the blades (or pads) is rapidly and continually adjusted as the system rotates in the wellbore. The disclosed embodiments are not limited to any particular RSS configuration.

Survey tool 80 further includes survey sensors including accelerometer and magnetometer sets 90 and 95 that may be deployed to rotate with the drill string or may be deployed in a roll stabilized housing that may be slowly rotated from time to time. The depicted sensor sets may include triaxial accelerometer and triaxial magnetometer navigation sensor sets, which could be any suitable commercially available devices. Suitable accelerometers for use in sensor set 90 may be chosen, for example, from among substantially any suitable commercially available devices known in the art. Suitable accelerometers may alternatively include micro-electro-mechanical systems (MEMS) solid-state accelerometers, which tend to be shock resistant, high temperature rated, and inexpensive. Suitable magnetic field sensors for use in sensor set 95 may include conventional ring core flux gate magnetometers or conventional magnetoresistive sensors.

FIG. 2 further includes a diagrammatic representation of the triaxial accelerometer set 90 and the triaxial magnetometer 95. By triaxial it is meant that each sensor set includes three mutually perpendicular sensors, the accelerometers being designated as G_x, G_y, and G_z and the magnetometers being designated as B_x, B_y, and B_z. By convention, a right-handed system is designated in which the x-axis accelerometer and magnetometer (G_x and B_x) are oriented substantially parallel with the tool axis (and therefore the wellbore axis) as indicated. Each of the accelerometer and magnetometer sets may therefore be considered as determining a cross-axial plane (the y- and z-axes) and an axial pole (the x-axis along the axis of the BHA) such that the y- and z-axis measurements may be referred to as cross-axial measurements and the x-axis measurements may be referred to as axial measurements. It will be appreciated that the disclosed embodiments are not limited to any particular coordinate convention and that another common convention used in the industry designates the tool axis as the z-axis.

By further nonlimiting convention, the gravitational field is taken to be positive pointing downward (i.e., toward the center of the earth) while the magnetic field is taken to be positive pointing towards magnetic north. Moreover, also by nonlimiting convention, the y-axis is taken to be the toolface reference axis (i.e., such that the gravity toolface GTF equals zero when the y-axis is uppermost and the magnetic toolface MTF equals zero when the y-axis is pointing towards the projection of magnetic north in the yz plane). The magnetic toolface MTF is projected in the yz plane and may be represented mathematically as the angle between the projections of the horizontal projection of the earth's magnetic field B_h on the y- and z-axes: tan(MTF)=−B_hz/B_hy. Likewise, the gravity toolface GTF may be represented mathematically as: tan(GTF)=G_z/−G_y. The negative sign in the gravity toolface expression arise owing to the nonlimiting convention that the gravity vector is positive in the downward direction while the toolface angle GTF is positive on the high side of the wellbore (the side facing upward).

It will be appreciated that the disclosed embodiments are, of course, not limited to the above-described conventions for defining wellbore coordinates. These conventions can affect the form of certain of the mathematical equations that follow in this disclosure. Those of ordinary skill in the art will be readily able to utilize other conventions and derive equivalent mathematical equations.

As also noted above, the disclosed embodiments are not limited to MWD deployments but may also include RSS deployments. Those of ordinary skill will readily recognize that RSS tools include steering elements that may be actuated to control and/or change the direction of drilling the wellbore 40. In embodiments employing a rotary steerable tool, substantially any suitable rotary steerable tool configuration may be used. Various rotary steerable tool configurations are known in the art. For example, various rotary steerable system includes a substantially non-rotating (or slowly rotating) outer housing employing blades that engage the wellbore wall. Engagement of the blades with the wellbore wall is intended to eccenter the tool body, thereby pointing or pushing the drill bit in a desired direction while drilling. A rotating shaft deployed in the outer housing transfers rotary power and axial weight-on-bit to the drill bit during drilling. Accelerometer and magnetometer sets may be deployed in the outer housing and therefore are non-rotating or rotate slowly with respect to the wellbore wall.

The PowerDrive rotary steerable systems (available from SLB) fully rotate with the drill string (i.e., the outer housing rotates with the drill string). The PowerDrive Xceed makes use of an internal steering mechanism that does not require contact with the wellbore wall and enables the tool body to fully rotate with the drill string. The PowerDrive X5, X6, and Orbit rotary steerable systems make use of mud actuated blades (or pads) that contact the wellbore wall. The extension of the blades (or pads) is rapidly and continually adjusted as the system rotates in the wellbore. Moreover, it will be appreciated that the RSS may include a steerable drill bit, such as the NeoSteer® at bit steerable system available from SLB, in which the steering pads extend outward from the drill bit body into contact with the wellbore wall.

The PowerDrive Archer® makes use of a lower steering section joined at a swivel with an upper section. The swivel is actively tilted via pistons so as to change the angle of the lower section with respect to the upper section and maintain a desired drilling direction as the bottom hole assembly rotates in the wellbore. Accelerometer and magnetometer sets may rotate with the drill string or may alternatively be deployed in an internal roll-stabilized housing such that they remain substantially stationary (in a bias phase) or rotate slowly with respect to the wellbore (in a neutral phase).

With reference again to FIG. 2, the accelerometer and magnetometer sets 90, 95 may be configured for making downhole navigational (surveying) measurements during a drilling operation. Such measurements are well known and commonly used to determine, for example, wellbore inclination, wellbore azimuth, gravity toolface, magnetic toolface, and dipping angle (dip). The accelerometers and magnetometers may be electronically coupled to a digital signal processor (or other digital controller) through corresponding analog signal conditioning circuits. The signal conditioning circuits may include low-pass filter elements that are intended to band-limit sensor noise and therefore tend to improve sensor resolution and surveying accuracy.

Recently, methods have been developed to make continuous (dynamic) survey measurements in real time while drilling (e.g., on the order of one independent survey measurement per second). Commonly assigned U.S. Pat. No. 11,692,432 discloses a surveying methodology in which the accelerometer measurements and magnetometer measurements are synchronized, for example, to compensate for temperature drift, phase shift and attenuation of the measurements, and/or distortion caused by magnetic interference. The '432 patent is incorporated by reference herein in its entirety. The corrected/synchronized measurements are then used to compute the desired wellbore survey parameters, such as wellbore inclination, wellbore azimuth, and/or dip angle. The '432 patent further discloses magnetic interference compensation. While such interference compensation is commercially serviceable, there is room for further improvement.

One aspect of the disclosed embodiments was the realization that static and dynamic surveying measurements can be complementary and therefore that static surveying measurements may be used to further compensate dynamic surveying measurements and that dynamic surveying measurements may be used to further compensate static surveying measurements. In particular, it was realized that in certain embodiments, static surveying measurements may be used to compensate dynamic axial magnetic field measurements, dynamic accelerometer measurements, and/or dynamic toolface offset measurements and that dynamic surveying measurements may be used to compensate static cross-axial magnetic field measurements.

With still further reference to FIG. 2, downhole tool 80 further includes an electronic controller 85. A suitable controller 85 may include, for example, a programmable processor, such as a digital signal processor or other microprocessor or microcontroller and processor-readable or computer-readable program code embodying logic. The controller may be utilized, for example, to automatically execute certain ones of the steps in the method embodiments described in more detail below with respect to FIGS. 3-6 and the accompanying equations. For example, the controller may be configured to cause the triaxial accelerometer set 90 and the triaxial magnetometer set 95 to make corresponding accelerometer and magnetometer measurements while the survey tool 80 rotates in the wellbore and to apply a compensation term to the measurements as described in more detail below.

A suitable controller 85 may also optionally include other controllable components, such as other sensors, data storage devices, power supplies, timers, and the like. The controller 85 is commonly disposed in electronic communication with the accelerometers 90 and magnetometers 95 and may also optionally communicate with other instruments in the drill string, such as, for example, telemetry systems that communicate with the surface. A suitable controller may further optionally include volatile or non-volatile memory or a data storage device.

FIG. 3 depicts a flow chart of one example method 100 for compensating dynamic surveying measurements using previously obtained static surveying measurements. Static surveying measurements may be made at 102. The static surveying measurements may be made, for example, when drilling has temporarily stopped and the drill string has been lifted off the bottom of the wellbore. The static measurements may include both triaxial accelerometer measurements and triaxial magnetometer measurements. Dynamic surveying measurements may be made while drilling at 104. The dynamic surveying measurements may be made when drilling/rotating has been restarted after making the static surveying measurements at 102 or before drilling/rotating has been stopped to make the static survey measurements at 102 and may also include both triaxial accelerometer measurements and triaxial magnetometer measurements. The disclosed embodiments are not limited in this regard; however, it will be appreciated that improved compensation may be achieved when the static surveying measurements and the dynamic surveying measurements are made at about the same measured depth in the wellbore (e.g., within 15 meters, within 10 meters, within 5 meters, within 3 meters, within 2 meters, or within 1 meter).

With continued reference to FIG. 3, the static surveying measurements and the dynamic surveying measurements made at 102 and 104 may be compared at 106 to compute at least one dynamic surveying compensation term. The dynamic surveying compensation term may include, for example, at least one of an axial magnetometer compensation term, a toolface offset (e.g., angle X) compensation term, and/or an accelerometer compensation term. The dynamic surveying compensation term(s) may then be subtracted (or otherwise removed) from subsequent dynamic surveying measurements at 108 to obtain compensated dynamic surveying measurements.

It will be appreciated that static surveys are commonly conducted when a new stand of drill pipe is being added to the drill string (e.g., at measured depth intervals ranging from about 10 meters to about 30 meters). In the absence of drilling vibrations and rotation, the static surveying measurements are generally made when the survey sensors (e.g., the triaxial accelerometers and triaxial magnetometers) are axially, laterally, and rotationally stationary. Moreover, downhole turbine alternators are inactive, which reduces or eliminates high voltage induced magnetic interference (e.g., axial magnetic interference).

With still further reference to FIG. 3, an axial magnetometer compensation term ΔB_x may be computed at 106, for example, as follows:

Δ ⁢ B x = B x D ⁢ S - B x S ⁢ S ( 1 )

where

B x D ⁢ S

represents the axial magnetic field measurement made during dynamic surveying at 104 and

B x SS

represents the axial magnetic field measurement made during static surveying at 102. The axial magnetometer compensation term ΔB_x may be applied to subsequent dynamic surveying measurements at 108 to obtain compensated axial magnetic field measurements

B x COM ,

for example, as follows:

B x COM = B x SDS - Δ ⁢ B x ( 2 )

where

B x SDS

represents the axial magnetic field measurements acquired during the subsequent dynamic surveying measurements made at 108.

A toolface offset compensation term ΔX may be computed at 106, for example, as follows:

Δ ⁢ X = X D ⁢ S - X S ⁢ S ( 3 )

where X^DS represents the toolface offset computed from the dynamic surveying measurements made at 104 and X^SS represents the toolface offset computed from the static surveying measurements made at 102. The toolface offset compensation term ΔX may be applied to subsequent dynamic surveying measurements at 108 to obtain a compensated toolface offset X^COM, for example, as follows:

X COM = X SDS - Δ ⁢ X ( 4 )

where X^SDS represents the toolface offset computed from the subsequent dynamic surveying measurements made at 108.

The toolface offset compensation term ΔX may also be used to compute a time shift offset Δγ, for example, as follows:

Δ ⁢ γ = f ⁡ ( Δ ⁢ X ) ( 5 )

where the time shift offset Δγ compensates the delay of the magnetometer measurements owing to rotation of the drill collar in the Earth's magnetic field.

Accelerometer compensation terms ΔG_x, ΔG_y, and/or ΔG_z may be computed at 106, for example, as follows:

Δ ⁢ G x = G x D ⁢ S - G x S ⁢ S ( 6 ) Δ ⁢ G y = G y D ⁢ S - G y S ⁢ S Δ ⁢ G z = G z D ⁢ S - G z S ⁢ S

where

G x D ⁢ S

represents the axial accelerometer measurement and

G y D ⁢ S ⁢ and ⁢ G z D ⁢ S

represent the cross-axial accelerometer measurements made during dynamic surveying at 104 and

G x SS

represents the axial accelerometer measurement and

G y D ⁢ S ⁢ and ⁢ G z D ⁢ S

represent the cross-axial accelerometer measurements made during static surveying at 102. The accelerometer compensation terms ΔG_x, ΔG_y, and/or ΔG_z may be applied to subsequent dynamic surveying measurements at 108 to obtain compensated accelerometer measurements

G x COM , G y COM , and / or ⁢ G z COM ,

for example, as follows:

G x COM = G x SDS - ΔG x ( 7 ) G y COM = G y SDS - Δ ⁢ G y G z COM = G z SDS - Δ ⁢ G z

where

G x SDS , G y SDS , and / or ⁢ G z SDS

represent the accelerometer measurements acquired during the subsequent dynamic surveying measurements at 108.

With further reference to FIG. 3, it will be appreciated that the compensated dynamic surveying measurements, such as the compensated axial magnetic field measurements, the compensated toolface offset, and/or the compensated accelerometer measurements may optionally be utilized to compute one or more dynamic survey parameters at 110. Such dynamic survey parameters may include, for example, a wellbore inclination, a wellbore azimuth, and/or a dip angle. Example computations may make use of Eqs. (12)-(14) in the '432 patent.

FIG. 4 depicts a flow chart of another method 120 for compensating dynamic surveying measurements for cross-axial magnetic interference (magnetic interference in the cross axial yz plane). Dynamic surveying measurements are made at 122 while rotating a drill string in the wellbore (e.g., while drilling). As described above, the dynamic surveying measurements may include triaxial magnetometer measurements, however, the compensation only requires cross-axial (y- and z-axis magnetometer measurements). A suitable number of measurements are collected and stored in a buffer at 124. For example, the buffer may include a predetermined number of measurements (e.g., collected over a predetermined time interval, such as from about one second to several seconds, or over a predetermined number of tool rotations, such as from about three to about ten tool rotations). The locus of buffered measurements may be fit with a second-degree polynomial equation of an ellipse at 126. Rotation, scaling (or attenuation), and offset parameters may be computed at 128 from the second-degree polynomial fit obtained in 126. These compensation parameters may then be used to compensate the cross-axial magnetometer measurements at 130, for example, to compute a compensated transverse magnetic field measurement (a compensated transverse or cross-axial component of the magnetic field). The compensated cross-axial magnetometer measurements may then optionally be used to compute one or more dynamic survey parameters, such as a wellbore azimuth and/or a dip angle.

With continued reference to FIG. 4, it will be appreciated that under the ideal conditions (e.g., in the absence of magnetic interference and phase shift), the rotating cross-axial magnetometer measurements measure only the earth's magnetic field as follows:

B y = B T ⁢ cos ⁢ T ⁢ θ ( 8 ) B z = B T ⁢ cos ⁡ ( T ⁢ θ + π / 2 )

where B_y and B_z represent the cross-axial (y- and z-axis) magnetometer measurements,

B T = B y 2 + B z 2

represents the transverse component of the magnetic field, θ represents the magnetic toolface angle, and T=2π/360. It will be further appreciated that these equations define a circle with radius B_T, centered at (0,0) in the cartesian coordinate system (B_y, B_z). Local magnetic disturbances that may emanate from electrical currents in the drill string and/or magnetic materials in the drill collar, drilling fluid, and/or the subterranean formation may distort the locus of rotating magnetometer measurements from being a centered circle to being an eccentered, rotated ellipse, for example, as depicted on FIG. 5. One example intent of the disclosed compensation is to remove the influence of the local magnetic disturbances such that the compensated measurements again define a centered circle with radius B_T.

As described above, the locus of buffered measurements may be fit with a second-degree polynomial equation of an ellipse, for example, as follows:

A ⁢ B y 2 + CB y ⁢ B z + D ⁢ B z 2 + EB y + FB z + G = 0 ( 9 )

where B_y and B_z represent the y- and z-axis magnetometer measurements and A, C, D, E, F, and G represent the polynomial coefficients (the fitting parameters) of the second-degree polynomial equation of the ellipse. After appropriate substitutions of variables in Eq. (9) (e.g., via rotation and linear translation), the ellipse may be transformed to canonic form, for example, as follows:

x 2 a 2 + y 2 b 2 = 1

where x and y represent the axes of the cross-axial plane (the measurement axes of B_y and B_z) and a and b represent the major and minor axes of the ellipse. Such transformation enables the buffered measurements to be compensated so that they lie on a circle, centered at (0,0) of B_y, B_z and having radius r=B_T=(a+b)/2. Note that the transformation includes at least a rotational transformation and a linear translational transformation from which B_T may be obtained. The transformation may further include a scaling (or gain) transformation to obtain compensated B_y and B_z measurements. It will be appreciated that use of the rotational transformation advantageously improves the accuracy of the compensation.

The disclosed embodiments may also be described with reference again to FIG. 5. A circle 152 is shown centered in the B_y, B_z plane having radius B_T. As noted above, this circle 152 represents the locus of cross-axial magnetometer measurements (B_y and B_z measurements) in the absence of magnetic interference or disturbances. Such disturbances 154 may cause the locus of cross-axial magnetometer measurements to be an eccentered and/or rotated ellipse as shown at 156. In the example depiction, the ellipse is eccentered (offset) by Oy and Oz and rotated by angle α. The compensation described above (shown at 158) may translate the ellipse (via a translational transformation) such that it is centered in the B_y, B_z cross axial plane and rotate the ellipse (via a rotational transformation) such that major axis is aligned with the B_y axis. The compensation may further optionally scale the ellipse (via a gain transformation) such that the major and minor ellipse axes are equal to one another and equal to the circle radius B_T. It will be appreciated that the depiction in FIG. 5 is merely schematic and is not drawn to scale. As such, the depiction is not intended to illustrate the scale of common magnetic interference or disturbances.

Turning now to FIG. 6, a flowchart of another disclosed compensation method 180 is depicted. Dynamic surveying measurements may be made while drilling a wellbore at 182. The measurements may include triaxial accelerometer and triaxial magnetometer measurements, for example, as described above. The dynamic surveying measurements may be compensated for cross-axial magnetic interference (magnetic interference in the cross-axial yz plane) at 184, for example, as described above with respect to FIGS. 4 and 5. As also described above, the compensation may include transforming an eccentered, rotated ellipse to a centered circle. The transformation may include a rotational transformation, a linear translational transformation, and/or a gain transformation. Static surveying measurements may be made at 186, for example, when drilling has temporarily stopped and the drill string has been lifted off the bottom of the wellbore. The cross-axial magnetic interference compensation determined for the dynamic surveying measurements may be applied to the cross-axial magnetometer measurements obtained during the static survey to compute compensated static, cross-axial magnetometer measurements at 188.

With continued reference to FIG. 6 (and further reference to FIG. 5), the compensation at 188 may include, for example, subtracting Oy and Oz from the static, cross-axial magnetometer measurements. The compensation at 188 may further include rotational and gain transformations that are applied to the static, cross-axial magnetometer measurements in combination with the magnetic toolface of the surveying tool during the static surveying measurements. The magnetic toolface may be obtained, for example, from the magnetometer measurements themselves or from the accelerometer-based gravity toolface and the angle X.

It will be appreciated that the disclosed embodiments may advantageously improve the accuracy of both static surveying measurements and the dynamic surveying measurements. The accuracy of the dynamic surveying measurements may be improved by applying compensation from previously obtained static surveying measurements. Likewise, the accuracy of the static surveying measurements may be improved by applying compensation from previously obtained dynamic surveying measurements.

It will be further appreciated that the methods described herein may be configured for implementation via one or more controllers deployed downhole (e.g., in the MWD tool or RSS tool). A suitable controller may include, for example, a programmable processor, such as a digital signal processor or other microprocessor or microcontroller and processor-readable or computer-readable program code embodying logic. A suitable processor may be utilized, for example, to execute the method embodiments (or various steps in the method embodiments) described above with respect to FIGS. 3-6 and the accompanying equations. A suitable controller may also optionally include other controllable components, such as other sensors, data storage devices, power supplies, timers, and the like. The controller may also be disposed to be in electronic communication with the accelerometers and magnetometers. A suitable controller may also optionally communicate with other instruments in the drill string, such as, for example, telemetry systems that communicate with the surface. A suitable controller may further optionally include volatile or non-volatile memory or a data storage device.

It will be further appreciated that the disclosed methods may be implemented automatically. For example, the disclosed compensation methods may be automatically implemented upon making the static and/or dynamic surveying measurements without input or even prompting from surface personnel. The disclosed embodiments may further include an automated system or tool (such as an MWD tool or an RSS tool) configured for making static and/or dynamic wellbore surveying measurements and for automatically compensating the measurements as described above. The system may include computer hardware and software configured to execute the automatic compensation routines. The hardware may include one or more processors (e.g., microprocessors) which may be connected to one data storage devices (e.g., hard drives or solid state memory) and user interfaces. The software may include processor executable instructions stored in the data storage device and or in firmware. The disclosed embodiments are, of course, not limited to the use of or the configuration of any particular computer hardware and/or software.

Although adaptive parameter estimation for static and dynamic wellbore surveys has been described in detail, it should be understood that various changes, substitutions and alternations can be made herein without departing from the spirit and scope of the disclosure as defined by the appended claims.