U.S. patent application number 13/865033 was filed with the patent office on 2013-11-07 for downhole drilling utilizing measurements from multiple sensors.
The applicant listed for this patent is GYRODATA, Incorporated. Invention is credited to Roger Ekseth, John Lionel Weston.
Application Number | 20130292176 13/865033 |
Document ID | / |
Family ID | 43033145 |
Filed Date | 2013-11-07 |
United States Patent
Application |
20130292176 |
Kind Code |
A1 |
Ekseth; Roger ; et
al. |
November 7, 2013 |
DOWNHOLE DRILLING UTILIZING MEASUREMENTS FROM MULTIPLE SENSORS
Abstract
A system and method for controlling a downhole portion of a
drill string is provided. The method includes receiving signals
from a first sensor package mounted at a first position to the
downhole portion, the signals indicative of an orientation of the
first sensor package. The method also includes receiving signals
from a second sensor package mounted at a second position to the
downhole portion, the signals indicative of an orientation of the
second sensor package. The method further includes calculating a
first amount of bend between the first and second sensor packages
in response to the signals and transmitting control signals to an
actuator which responds by adjusting the downhole portion to have a
second amount of bend between the first and second sensor
packages.
Inventors: |
Ekseth; Roger; (Trondheim,
NO) ; Weston; John Lionel; (Christchurch,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
GYRODATA, Incorporated |
Houston |
TX |
US |
|
|
Family ID: |
43033145 |
Appl. No.: |
13/865033 |
Filed: |
April 17, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13449191 |
Apr 17, 2012 |
8428879 |
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13865033 |
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12607927 |
Oct 28, 2009 |
8185312 |
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13449191 |
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12256410 |
Oct 22, 2008 |
8095317 |
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12607927 |
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Current U.S.
Class: |
175/24 |
Current CPC
Class: |
E21B 44/005 20130101;
E21B 7/067 20130101; E21B 7/10 20130101; E21B 47/022 20130101; E21B
47/024 20130101 |
Class at
Publication: |
175/24 |
International
Class: |
E21B 44/00 20060101
E21B044/00 |
Claims
1. A method of controlling a downhole portion of a drill string,
the method comprising: receiving one or more first signals from a
first sensor package mounted at a first position to the downhole
portion within a wellbore, the one or more first signals indicative
of an orientation of the first sensor package; receiving one or
more second signals from a second sensor package mounted at a
second position to the downhole portion within the wellbore, the
one or more second signals indicative of an orientation of the
second sensor package; calculating a first amount of bend of the
downhole portion between the first sensor package and the second
sensor package in response to the one or more first signals and the
one or more second signals; and transmitting control signals to an
actuator of the downhole portion in response to the first amount of
bend, wherein the actuator is responsive to the control signals by
adjusting the downhole portion to have a second amount of bend
between the first sensor package and the second sensor package, the
second amount of bend different from the first amount of bend.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/449,191, filed on Apr. 17, 2012 and
incorporated in its entirety by reference herein, which is a
continuation of U.S. patent application Ser. No. 12/607,927, filed
Oct. 28, 2009 and incorporated in its entirety by reference herein,
which is a continuation-in-part of U.S. patent application Ser. No.
12/256,410, filed on Oct. 22, 2008, now U.S. Pat. No. 8,095,317,
the entire contents of which is hereby incorporated by
reference.
BACKGROUND
[0002] 1. Field of the Invention
[0003] The present application relates generally to systems and
methods for utilizing measurements from multiple sensors on a
drilling tool within a wellbore to correct for measurement errors,
determine the curvature of a wellbore, and/or determine the
position of the wellbore in relation to another wellbore.
[0004] 2. Description of the Related Art
[0005] Rotary steerable drilling tools can be equipped with survey
instrumentation, such as measurement while drilling (MWD)
instrumentation, which provides information regarding the
orientation of the survey tool, and hence, the orientation of the
well at the tool location. Survey instrumentation can make use of
various measured quantities such as one or more of acceleration,
magnetic field, and angular rate to determine the orientation of
the tool and the associated wellbore with respect to a reference
vector such as the Earth's gravitational field, magnetic field, or
rotation vector. The determination of such directional information
at generally regular intervals along the path of the well can be
combined with measurements of well depth to allow the trajectory of
the well to be determined. However, measurements used in this
process can be subject to errors. For example, the errors may be
the result of imperfections internal to the instrumentation itself
or external disturbances that can affect the output of the
instrumentation and its associated sensors. Internal errors can
generally be accounted for using calibration techniques and other
methods. However, external errors, such as errors resulting from
misalignments of the sensors within the wellbore, or errors caused
by disturbances affecting the relevant reference vector (e.g., the
Earth's magnetic field) can be more difficult to correct.
[0006] In addition, when a wellbore is drilled in an area in which
one or more existing wellbores are present it is useful to
determine the relative position of the wellbore and downhole
portion of the drilling tool in relation to the existing wellbore.
For example, this information can be useful to avoid collisions
with existing wellbores or to drill a relief well to intercept an
existing well. Furthermore, there are situations in which it is
useful to drill a well alongside an existing well to implement a
process known as steam assisted gravity drainage (SAGD) to
facilitate the retrieval of heavy oil deposits in certain parts of
the world. In this case, existing methods involve inserting
equipment, such as a solenoid, into the existing wellbores. The
equipment gives rise to magnetic field disturbances, which can be
detected by sensors in the new well and used to determine the
position of the drilling tool and wellbore in relation to the
existing wellbore. Such techniques can be costly, in part because
of the additional equipment involved and because such operations
are time consuming.
SUMMARY
[0007] According to certain embodiments, a method of generating
information indicative of an orientation of a drill string relative
to the Earth while in a wellbore is provided. The method includes
receiving one or more first signals from a first sensor package
mounted in a first portion of the drill string at a first position
within a wellbore, the first signals indicative of an orientation
of the first portion of the drill string relative to the Earth. The
method further includes receiving one or more second signals from a
second sensor package mounted in a second portion of the drill
string at a second position within the wellbore, the second signals
indicative of an orientation of the second portion of the drill
string relative to the Earth. The method according to certain
embodiments also includes calculating a difference between the
orientation of the first portion and the second portion in response
to the first signals and the second signals.
[0008] A drill string is provided in certain embodiments,
comprising a downhole portion adapted to move within a wellbore.
The downhole portion having a first portion at a first position
within the wellbore and a second portion at a second position
within the wellbore. The drill string further includes a first
sensor package mounted within the first portion, the first sensor
package sensor adapted to generate a first measurement indicative
of an orientation of the first portion. In certain embodiments, the
drill string also includes a second sensor package mounted within
the second portion, the second sensor package adapted to generate a
second measurement indicative of an orientation of the second
portion. The drill string further includes a controller configured
to calculate a difference between the orientations of the first
portion and the second portion in response to the first measurement
and the second measurement.
[0009] In certain embodiments, a method of controlling a drill
string is provided. The method comprises receiving one or more
first signals from a first sensor package mounted in a first
portion of the drill string at a first position within a wellbore.
The first signals may be indicative of an orientation of the first
portion of the drill string relative to the Earth. The method also
includes receiving one or more second signals from a second sensor
package mounted in a second portion of the drill string at a second
position within the wellbore. In certain embodiments, the second
signals indicative of an orientation of the second portion of the
drill string relative to the Earth. The drill string may be adapted
to bend between the first portion and the second portion. The
method of certain embodiments includes calculating a first amount
of bend between the first portion and the second portion in
response to the first signals and the second signals.
[0010] A drill string is provided in certain embodiments comprising
a downhole portion adapted to move within a wellbore. The downhole
portion may have a first portion at a first position within the
wellbore and a second portion at a second position within the
wellbore. In certain embodiments, the downhole portion is adapted
to bend between the first portion and the second portion. The drill
string may include a first sensor package mounted within the first
portion which can be adapted to generate a first measurement
indicative of an orientation of the first portion relative to the
Earth. The drill string may further include a second sensor package
mounted within the second portion which can be adapted to generate
a second measurement indicative of an orientation of the second
portion relative to the Earth. The drill string of certain
embodiments includes a controller configured to calculate an amount
of bend between the first portion and the second portion in
response to the first measurement and the second measurement.
[0011] In certain embodiments, a drill string is provided which
includes a downhole portion adapted to move within a wellbore, the
downhole portion having a first portion at a first position within
the wellbore and oriented at a first angle relative to the wellbore
at the first position and a second portion at a second position
within the wellbore and oriented at a second angle relative to the
wellbore at the second position, wherein at least one of the first
and second angles is non-zero. The drill string of certain
embodiments includes a first acceleration sensor mounted within the
first portion, the first acceleration sensor adapted to generate a
first signal indicative of an acceleration of the first
acceleration sensor. The drill string of certain embodiments also
includes a second acceleration sensor mounted within the second
portion, the second acceleration sensor adapted to generate a
second signal indicative of an acceleration of the second
acceleration sensor.
[0012] In certain embodiments, a method for generating information
indicative of misalignment between first and second acceleration
sensors mounted within the downhole portion of a drill string is
provided. The method of certain embodiments includes providing a
drill string comprising. The drill string of certain embodiments
includes a downhole portion adapted to move within a wellbore, the
downhole portion having a first portion at a first position within
the wellbore and oriented at a first angle relative to the wellbore
at the first position and a second portion at a second position
within the wellbore and oriented at a second angle relative to the
wellbore at the second position wherein at least one of the first
and second angles is non-zero. The drill string can also include a
first acceleration sensor mounted within the first portion, the
first acceleration sensor adapted to generate a first signal
indicative of an acceleration of the first acceleration sensor and
a second acceleration sensor mounted within the second portion, the
second acceleration sensor adapted to generate a second signal
indicative of an acceleration of the second acceleration sensor.
The method of certain embodiments further includes generating the
first signal and the second signal while the downhole portion of
the drill string is within the wellbore.
[0013] In certain embodiments, a method of determining the
misalignment between first and second acceleration sensors mounted
within a drill string is provided. The method of certain
embodiments includes receiving one or more acceleration
measurements from a first acceleration sensor in a first portion of
the drill string at a first position within a wellbore, the first
portion oriented at a first angle relative the wellbore at the
first position. The method further includes receiving one or more
acceleration measurements from a second acceleration sensor in a
second portion of the drill string at a second position within the
wellbore, the second portion oriented at a second angle relative to
the wellbore at the second position, wherein at least one of the
first and second angles is non-zero. The method further includes
calculating the difference between the first angle and the second
angle in response to the one or more acceleration measurements from
the first acceleration sensor and the one or more measurements from
the second acceleration sensor.
[0014] In certain embodiments, a drilling system is provided which
includes a downhole portion adapted to move along a first wellbore,
the downhole portion comprising one or more magnetic regions and
one or more non-magnetic regions. The drilling system of certain
embodiments includes at least two magnetic sensors within at least
one non-magnetic region of the downhole portion, the at least two
magnetic sensors comprising a first magnetic sensor and a second
magnetic sensor spaced apart from one another by a non-zero
distance, the first magnetic sensor adapted to generate a first
signal in response to magnetic fields of the Earth and of the one
or more magnetic regions, the second magnetic sensor adapted to
generate a second signal in response to magnetic fields of the
Earth and of the one or more magnetic regions. The drilling system
can include a controller configured to receive the first signal and
the second signal and to calculate the magnetic field of the one or
more magnetic regions.
[0015] In certain embodiments, a method for generating information
indicative of the magnetic field in a first wellbore is provided.
The method includes providing a drilling system comprising a
downhole portion adapted to move along a first wellbore, the
downhole portion comprising one or more magnetic regions and one or
more non-magnetic regions. The drilling system of certain
embodiments further includes at least two magnetic sensors within
at least one non-magnetic region of the downhole portion, the at
least two magnetic sensors comprising a first magnetic sensor and a
second magnetic sensor spaced apart from one another by a non-zero
distance, the first magnetic sensor adapted to generate a first
signal in response to magnetic fields of the Earth and of the one
or more magnetic regions, the second magnetic sensor adapted to
generate a second signal in response to magnetic fields of the
Earth and of the one or more magnetic regions. The method further
includes generating the first signal and the second signal while
the downhole portion of the drilling system is at a first location
within the first wellbore and calculating the magnetic field in the
first wellbore in response to the first and second signals.
[0016] In certain embodiments, a method for determining the
magnetic field in a wellbore is provided. The method includes
receiving one or more magnetic measurements from at least two
magnetic sensors within at least one non-magnetic region of a
downhole portion of a drilling system, the at least two magnetic
sensors comprising a first magnetic sensor and a second magnetic
sensor spaced apart from one another by a non-zero distance, the
first magnetic sensor generating a first signal in response to
magnetic fields of the Earth and of one or more magnetic regions of
the downhole portion, the second magnetic sensor generating a
second signal in response to magnetic fields of the Earth and of
the one or more magnetic regions. The method of certain embodiments
further includes calculating the magnetic field in response to the
one or more magnetic measurements from the at least two magnetic
sensors.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] FIG. 1 schematically illustrates an example drill string for
use in a wellbore and having first and second acceleration sensors
that are misaligned in accordance with certain embodiments
described herein.
[0018] FIG. 2 schematically illustrates an example drill string for
use in a wellbore and having first and second acceleration sensors
that are misaligned and where the drill string is in a portion of
the wellbore having a curvature in accordance with certain
embodiments described herein.
[0019] FIG. 3 is a flowchart of an example method of generating
information indicative of misalignment between first and second
acceleration sensors mounted in the downhole portion of a drill
string in accordance with certain embodiments described herein.
[0020] FIG. 4 is a flowchart of an example method of determining
the misalignment between first and second acceleration sensors
mounted on the downhole portion of a drill string in accordance
with certain embodiments described herein.
[0021] FIG. 5 schematically illustrates an example drilling system
including a downhole portion moving along a first wellbore and
including at least two magnetic sensors in accordance with certain
embodiments described herein.
[0022] FIG. 6 schematically illustrates the example drilling system
of FIG. 5 wherein the downhole portion is moving along a first
wellbore and is positioned relative to a second wellbore spaced
from the first wellbore in accordance with certain embodiments
described herein.
[0023] FIG. 7 is a flowchart of an example method of generating
information indicative of the magnetic field in a wellbore in
accordance with certain embodiments described herein.
[0024] FIG. 8 is a flowchart of an example method of determining
the magnetic field in a wellbore in accordance with certain
embodiments described herein.
[0025] FIG. 9 schematically illustrates an example drill string for
use in a wellbore and having first and second sensor packages in a
portion of the wellbore having a curvature in accordance with
certain embodiments described herein.
[0026] FIG. 10 schematically illustrates an example control loop
for calculating and adjusting the curvature between first and
second portions an example drill string having first and second
sensor packages in a portion of the wellbore having a curvature in
accordance with certain embodiments described herein.
[0027] FIG. 11 is a directional diagram illustrating the relative
orientation between a first position in the wellbore and a second
position in the wellbore in a portion of the wellbore having a
curvature in accordance with embodiments described herein.
[0028] FIG. 12 is a flowchart of an example method of controlling a
drill string according to a calculated amount of bend in accordance
with certain embodiments described herein.
DETAILED DESCRIPTION
[0029] Certain embodiments described herein provide a
downhole-based system for utilizing measurements from multiple
sensors on a drilling tool within a wellbore to correct for
measurement errors and so allow the trajectory of the well to be
determined with greater accuracy than could be achieved using a
single set of sensors. The application of multiple sensors also
facilitates the determination of the position of the wellbore in
relation to another wellbore. In certain embodiments, the system is
generally used in logging and drilling applications. Additionally,
embodiments described herein utilize multiple sensor measurements
to detect an amount of well curvature and adjust the drilling tool
to achieve a desired curvature.
[0030] In certain embodiments described herein, measurements from
multiple sensors on a drill string provide improved measurement
accuracy. For example, certain embodiments described herein correct
for external sensor errors utilizing multiple sensors. Sensors may
be included in, for example, a measurement while drilling (MWD)
instrumentation pack. Additional sensors may be located on a rotary
steerable tool in accordance with certain embodiments described
herein, and can provide enhanced accuracy of, for example, the
measurement of the direction in which the well is progressing and
can provide more immediate information regarding changes in well
direction. Certain embodiments described herein disclose a drill
string including a MWD survey instrument and a rotary steerable
tool, where both the MWD survey instrument and the rotary steerable
tool include acceleration sensors, magnetic field sensors, or
both.
[0031] A measurement of a quantity (x.sub.M) may be expressed as
the sum of the true value of that quantity (x) summed with a
disturbance error term (.epsilon.), where the error may be a
function of the well path, its attitude or its heading at the
measurement location, and the position of the sensing means with
respect to a source of disturbance (d.sub.D). For example, d.sub.D
may be the position of a magnetic field sensor with respect to a
local magnetic disturbance field that may distort the components of
the Earth's magnetic field which the magnetic field sensor is
configured to measure.
x.sub.M1=x+.epsilon..sub.1(I,A,d.sub.D1, . . . ); (Eq. 1)
where x.sub.M1 is magnetic field measured by a first magnetic field
sensor, x is the magnetic field of the Earth at the location of the
first magnetic field sensor, and .epsilon..sub.1 is the disturbance
error which can be a function of tool azimuth angle (A),
inclination (I), and the distance (d.sub.D1) of the magnetic sensor
from a local magnetic disturbance field.
[0032] A second measurement of the quantity (x.sub.M) at another
location along the tool string may be expressed as:
x.sub.M2X+.epsilon..sub.2(I,A,d.sub.D2, . . . ). (Eq. 2)
where x.sub.M2 is magnetic field measured by a second magnetic
field sensor, x is the magnetic field of the Earth at the second
magnetic field sensor location, and .epsilon..sub.2 is the
disturbance error which can also be a function of azimuth (A),
inclination (I) and the distance (d.sub.D2) of the magnetic sensor
with respect to a local magnetic disturbance field.
[0033] Taking the difference between the two measurements
yields:
.DELTA..sub.x=x.sub.M1-x.sub.M2.epsilon..sub.1(I,A,d.sub.D1, . . .
)-.epsilon..sub.2(I,A,d.sub.D2, . . . ). (Eq. 3)
[0034] Thus, where the parameters affecting error terms are known,
the measurements may be generally used to estimate and correct for
the error. Certain embodiments described herein make use of
measurements from multiple acceleration sensors, multiple magnetic
field sensors, or both to correct for measurement errors. For
example, acceleration sensors mounted on the downhole portion of a
drill string can be used to determine the inclination of the drill
string. According to certain embodiments described herein, the use
of measurements from multiple acceleration sensors may be used to
determine inclination measurement errors owing to the misalignment
of the corresponding portions of the drill string in which the
sensors are mounted.
[0035] In certain embodiments, magnetic sensors included in a drill
string can provide measurements of the orientation of a downhole
portion of the drill string with respect to the magnetic field of
the Earth. However, magnetized portions of the drill string can
interfere with the orientation measurements causing measurement
errors. In certain embodiments disclosed herein, data from multiple
magnetic sensors may be used to determine the amount of magnetic
interference caused by the magnetized portions of the drill string.
In certain embodiments, the magnetic sensors may also be used to
determine the proximity of the drill string or a portion of the
drill string to an existing well.
[0036] The present application relates generally to systems and
methods for utilizing measurements from multiple sensors on a
drilling tool within a wellbore to correct for measurement errors
and/or determine the position of the wellbore in relation to
another wellbore.
[0037] Additionally, certain Embodiments described herein provide
two or more directional survey measurements from multiple sensors
at a known separation distance(s) along the tool string.
Additionally, certain embodiments described herein generate a
measure of the curvature of the well between two or more survey
system locations by differencing the survey system estimates of
orientation (e.g., inclination and azimuth angle) provided at each
location.
A. Comparison of Multiple Acceleration Measurements to Determine
Sensor Misalignment
[0038] FIG. 1 and FIG. 2 schematically illustrate an example
downhole portion 102 of a drill string 100 within a wellbore 104
having a first acceleration sensor 106 and a second acceleration
sensor 108 that are misaligned relative to one another. In FIG. 1,
the downhole portion 102 is in a generally straight section of the
wellbore 104, and in FIG. 2, the downhole portion 102 is in a
curved or angled section of the wellbore 104. In certain
embodiments, the drill string 100 may include an elongate portion
110, comprising sections of drill pipe and drill collars, and a
rotary steerable tool 112. In certain embodiments, the drill string
comprises a downhole portion 102 adapted to move within the
wellbore 104. In certain embodiments, the downhole portion 102
includes a first portion 114 at a first position 116 within the
wellbore 104. In certain embodiments, the first portion 114 of the
downhole portion 102 is oriented at a first angle 121 relative to
the wellbore 104 at the first position 116. The downhole portion
102 may further comprise a second portion 118 at a second position
120 within the wellbore 104 and oriented at a second angle 122
relative to the wellbore 104 at the second position 120. At least
one of the first angle 121 and the second angle 122 is
non-zero.
[0039] The drill string 100 may, in certain embodiments, be a
measurement-while-drilling string. In certain embodiments, the
drill string 100 can include a MWD instrumentation pack. In certain
embodiments, the first acceleration sensor 106 is mounted within
the first portion 114 (e.g., on the rotary steerable tool 112) and
is adapted to generate a first signal indicative of the specific
force acceleration to which the first acceleration sensor 106 is
subjected. In certain embodiments, the second acceleration sensor
108 is mounted within the second portion 118 (e.g., on the elongate
portion 110 of the drill string 100) and is adapted to generate a
second signal indicative of the specific force acceleration sensed
by the second acceleration sensor 108. In certain other
embodiments, the first and second acceleration sensors 106, 108 may
be mounted on the downhole portion 102 in other configurations
compatible with embodiments described herein. For example, in some
embodiments, both of the first and second acceleration sensors 106,
108 are mounted on the elongate portion 110 (e.g., in two MWD
instrumentation packs spaced apart from one another or alongside
one another). In other embodiments, both of the first and second
acceleration sensors 106, 108 are mounted on the rotary steerable
tool 112. In certain embodiments, one or more additional sensors
(not shown) are located near the first sensor 106, the second
sensor 108, or both. For example, in some embodiments, a third
sensor is located near the first sensor 106 and a fourth sensor is
located near the second sensor 108. In such an example, the fourth
sensor may be mounted in a separate MWD pack located alongside the
MWD pack on which the second sensor 108 is mounted.
[0040] In certain embodiments, the second position 120 can be
spaced from the first position 116 by a non-zero distance B along
the axis 130. In certain embodiments, the distance B is about 40
feet. The distance B in certain other embodiments is about 70 feet.
In certain embodiments, the second position 120 and the first
position 116 are spaced apart from one another by a distance B in a
range between about 40 feet to about 70 feet. Other values of B are
also compatible with certain embodiments described herein. In
certain embodiments, the drill string 100 or the logging string
includes a sufficient number of sensors and adequate spacings
between the first acceleration sensor 106 and the second
acceleration sensor 108 to perform the methods described
herein.
[0041] In certain embodiments, the rotary steerable tool 112
comprises a housing 126 containing at least one of the acceleration
sensors 106, 108. As schematically illustrated by FIG. 1, the
housing 126 of certain embodiments contains the first acceleration
sensor 106 while the second acceleration sensor 108 is attached on
or within the elongate portion 110. The rotary steerable tool 112
of certain embodiments further comprises a drill bit 113 providing
a drilling function. In certain embodiments, the downhole portion
102 further comprises portions such as collars or extensions 128,
which contact an inner surface of the wellbore 104 to position the
housing 126 substantially collinearly with the wellbore 104. In
certain embodiments, the drill bit 113 of the rotary steerable tool
112 is adapted to change direction, thereby creating a curvature in
the wellbore 104 (FIG. 2) as the rotary steerable tool 112
advances. Examples of such rotary steerable tools 112 are described
in UK Patent Application Publication No. GB2172324, entitled
"Drilling Apparatus," and UK Patent Application Publication No.
GB2177738, entitled "Control of Drilling Courses in the Drilling of
Bore Holes," each of which is incorporated in its entirety by
reference herein.
[0042] In certain embodiments, the first acceleration sensor 106
and the second acceleration sensor 108 comprise accelerometers
currently used in conventional wellbore survey tools. For example,
in certain embodiments, one or both of the first and second
acceleration sensors 106, 108 comprise one or more cross-axial
accelerometers that can be used to provide measurements for the
determination of the inclination, the high-side tool face angle, or
both, of the downhole instrumentation at intervals along the well
path trajectory. In certain embodiments, one or both of the first
acceleration sensor 106 and the second acceleration sensor 108
comprise multiple (e.g., 2 or 3) single-axis accelerometers, each
of which is sensitive to accelerations along a single sensing
direction. In certain such embodiments, one single-axis
accelerometer of the multiple single-axis accelerometers is
advantageously mounted so that its sensing direction is
substantially parallel with the axis 130 of the downhole portion
102. In certain embodiments, one or both of the first acceleration
sensor 106 and the second acceleration sensor 108 comprise an
accelerometer sensitive to accelerations in multiple directions
(e.g., a multiple-axis accelerometer). For example, a three-axis
acceleration sensor can be used which is capable of measuring
accelerations along the axis 130 of the downhole portion 102 and in
two generally orthogonal directions in a plane (e.g., a cross-axial
plane) that is generally perpendicular to the axis of the downhole
portion 102. In certain embodiments, the x and y axes of the
three-axis accelerometer sensor are defined to lie in the
cross-axial plane while the z axis of the three-axis accelerometer
sensor is coincident with the axis of the wellbore 104 or the
downhole portion 102. In certain such embodiments, the
multiple-axis accelerometer is advantageously mounted so that it is
sensitive to accelerations along at least one direction parallel to
the axis 130 of the downhole portion 102.
[0043] In certain embodiments, the first acceleration sensor 106
and the second acceleration sensor 108 are substantially identical.
Example accelerometers include, but are not limited to, quartz
flexure suspension accelerometers available from a variety of
vendors. Other types of acceleration sensors are also compatible
with certain embodiments described herein. In certain embodiments,
more than two acceleration sensors may be included in the drill
string 100. The first acceleration sensor 106 is also referred to
as the "lower acceleration sensor" and the second acceleration
sensor 108 is also referred to as the "upper acceleration sensor"
herein. The terms "upper" and "lower" are used herein merely to
distinguish the two acceleration sensors according to their
relative positions along the wellbore 104, and are not to be
interpreted as limiting.
[0044] The drill string 100 in some embodiments includes a
controller 124 which can be configured to calculate the difference
between the first angle 121 and the second angle 122. In the
embodiment schematically illustrated by FIG. 1, the controller 124
is at the surface and is coupled to the downhole portion 102 by the
elongate portion 110. In certain embodiments, the controller 124
comprises a microprocessor adapted to perform the method described
herein for determining the sag misalignment of the tool. In certain
embodiments, the controller 124 is further adapted to determine the
inclination and highside/toolface angle of the tool or the
trajectory of the downhole portion 102 within the wellbore 104. In
certain embodiments, the controller 124 further comprises a memory
subsystem adapted to store at least a portion of the data obtained
from the various sensors. The controller 124 can comprise hardware,
software, or a combination of both hardware and software. In
certain embodiments, the controller 124 comprises a standard
personal computer.
[0045] In certain embodiments, at least a portion of the controller
124 is located within the downhole portion 102. In certain other
embodiments, at least a portion of the controller 124 is located at
the surface and is communicatively coupled to the downhole portion
102 within the wellbore 104. In certain embodiments in which the
downhole portion 102 is part of a wellbore drilling system capable
of measurement while drilling (MWD) or logging while drilling
(LWD), signals from the downhole portion 102 are transmitted by mud
pulse telemetry or electromagnetic (EM) telemetry. In certain
embodiments where at least a portion of the controller 124 is
located at the surface, the controller 124 is coupled to the
downhole portion 102 within the wellbore 104 by a wire or cable
extending along the elongate portion 110. In certain such
embodiments, the elongate portion 110 may comprise signal conduits
through which signals are transmitted from the various sensors
within the downhole portion 102 to the controller 124. In certain
embodiments in which the controller 124 is adapted to generate
control signals for the various components of the downhole portion
102, the elongate portion 110 is adapted to transmit the control
signals from the controller 124 to the downhole portion 102.
[0046] In certain embodiments, the controller 124 is adapted to
perform a post-processing analysis of the data obtained from the
various sensors of the downhole portion 102. In certain such
post-processing embodiments, data is obtained and saved from the
various sensors of the drill string 100 as the downhole portion 102
travels within the wellbore 104, and the saved data are later
analyzed to determine information regarding the downhole portion
102. The saved data obtained from the various sensors
advantageously may include time reference information (e.g., time
tagging).
[0047] In certain other embodiments, the controller 124 provides a
real-time processing analysis of the signals or data obtained from
the various sensors of the downhole portion 102. In certain such
real-time processing embodiments, data obtained from the various
sensors of the downhole portion 102 are analyzed while the downhole
portion 102 travels within the wellbore 104. In certain
embodiments, at least a portion of the data obtained from the
various sensors is saved in memory for analysis by the controller
124. The controller 124 of certain such embodiments comprises
sufficient data processing and data storage capacity to perform the
real-time analysis.
[0048] One or more of the first angle 121 and the second angle 122
may be zero degrees in certain embodiments. For example, as
illustrated with respect to FIG. 1 and FIG. 2, the first portion
114 may be oriented at an angle of zero degrees with respect to the
wellbore 104 at the first position 106. In certain embodiments, at
least one of the first angle 121 and the second angle 122 is
non-zero. For example, as schematically illustrated in FIGS. 1 and
2, the second portion 118 may be oriented at a non-zero angle with
respect to the wellbore 104 at the second position 108. In various
embodiments, one or both of the first angle 121 and the second
angle 122 may change during operation of the drill string 100. In
certain embodiments, the first angle 121 may be much smaller than
angle 122 or the second angle 122 may be much smaller than the
first angle 121. The difference between the first angle 121 and the
second angle 122 may also be referred to as misalignment or
vertical misalignment. In certain embodiments, the difference
between the first angle 121 and the second angle 122 is less than
about one degree. In certain embodiments, the difference between
the first angle 121 and the second angle 122 is less than about 0.6
degrees. Other values of the difference between the first angle 121
and the second angle 122 are compatible with certain embodiments
described herein. In certain embodiments, the difference between
the first angle 121 and the second angle 122 may be caused by
gravity-induced misalignment, commonly referred to as sag, of one
part of the drill string 100 relative to another part of the drill
string 100. In some embodiments, the misalignment is caused by
forces internal to the wellbore 104 such as compression of the
drill string 100 within the wellbore 104, or by physical mounting
misalignment of one of or both of the first and second sensors 106,
108 on the drill string 100. Other causes of the difference between
the first angle 121 and the second angle 122 are also compatible
with certain embodiments described herein.
[0049] The size of the gravity-induced misalignment, the sag, is
generally proportional to the component of gravity perpendicular to
the well path in the vertical plane. In general, the inclination
error (.DELTA.I) attributable to sag is therefore assumed to be
proportional to the sine of inclination (I). Thus, the inclination
error of a segment of the drill string 100 can be expressed as:
.DELTA.I=Ssin I; (Eq. 4)
where S is the sag/inclination error that is present at the segment
of the drill string 100 when the wellbore 104 is horizontal.
[0050] Where there is a lower (first) sensor 106 and an upper
(second) sensor 108 mounted on the downhole portion 102 of the
drill string 100 such as described with respect to certain
embodiments herein, and where the rotary steerable tool 112 is
assumed to be supported within the wellbore 104 so that the lower
sensor 106 aligned with the wellbore 104 (e.g., the first angle 121
is zero), the sag of the upper sensor 108 can be determined using
the following equations:
I.sub.UM=I.sub.U+Ssin I.sub.U; (Eq. 5)
I.sub.LM=I.sub.L; (Eq. 6)
where I.sub.U and I.sub.L are the true inclinations of the upper
sensor 108 and the lower sensor 106 respectively. I.sub.UM and
I.sub.LM are measurements of these quantities obtained using the x,
y and z (e.g., along wellbore 104) measurements G.sub.X, G.sub.Y,
G.sub.Z provided by an orthogonal triad of accelerometers mounted
at each sensor location. For example, the measured inclination can
be calculated using the following equation:
I M = arctan [ G x 2 + G y 2 G z ] ; ( Eq . 7 ) ##EQU00001##
[0051] For a tangent well section, where the upper and lower
sensors 108, 106 are in alignment:
I.sub.U=I.sub.L=I. (Eq. 8)
Hence,
.DELTA.I.sub.M=I.sub.UM-I.sub.UM=Ssin I; (Eq. 9)
and an estimate of the horizontal sag may be obtained using:
S = .DELTA. I M sin I . ( Eq . 10 ) ##EQU00002##
[0052] In the more general situation in which sag is present at the
locations of both the upper sensor 108 and the lower sensor 106,
the process outlined above can provide an estimate of the
difference in sag between the first and second portions 114, 118 of
the downhole portion 102.
[0053] FIG. 2 schematically illustrates an example drill string 100
having a first acceleration sensor 106 and a second acceleration
sensor 108 that are misaligned and where the drill string is in a
portion of the wellbore 104 having a curvature (e.g., a bend or
dogleg). The curvature shown in FIG. 2 is such that the direction
of the wellbore 104 changes by a non-zero angle .theta.. Where the
drill string 100 is in a portion of the wellbore 104 having the
curvature, the measured difference in inclination between the upper
and lower sensors 108, 106 comprises an inclination difference
indicative of the amount of curvature in addition to any
inclination difference due to sag. In certain embodiments,
information indicative of well curvature between the upper sensor
108 and the lower sensor 106 can be used to determine an improved
calculation of the sag. In order to provide information relating to
the amount of curvature or bend, the drill string 100 may in
certain embodiments include a bend sensor adapted to generate a
third signal indicative of an amount of bend between the wellbore
104 at the first position 116 and the wellbore 104 at the second
position 120. In certain embodiments, the controller 124 is further
configured to calculate the difference between the first angle 121
and the second angle 122 in response to the first, second, and
third signals. Various types of bend sensors are compatible with
certain embodiments described herein. For example, the bend sensor
may be similar to the bend sensors described in U.S. patent
application Ser. No. 11/866,213, entitled "System and Method For
Measuring Depth and Velocity of Instrumentation Within a Wellbore
Using a Bendable Tool," which is incorporated in its entirety by
reference herein. For example, the bend sensor of certain
embodiments comprises an optical system comprising a light source
and a light detector separated from the light source by a non-zero
distance along the wellbore 104. The light source can be configured
to direct light towards the light detector such that light impinges
upon a first portion of the light detector when the downhole
portion 102 is in an unbent state and upon a second portion of the
light detector when the downhole portion 102 is in a bent
state.
[0054] In certain embodiments, the drill string 100 can be
configured to calculate the amount of bend between the wellbore 104
at the first position 116 and the wellbore 104 at the second
position 120. For example, such a calculation may be made using one
or more of the sensors mounted on the drill string 100. In certain
embodiments, the controller 124 may be configured to calculate the
amount of bend between the wellbore 104 at the first position 116
and the wellbore 104 at the second position 120 in response to the
first and second signals using a predictive filtering technique.
The predictive filtering technique, for example, may be a Kalman
filtering technique, examples of which described herein. In various
embodiments, the filtering technique may be used instead of or in
addition to using a bend sensor to calculate the amount of bend.
Further embodiments of a drill string 100 configured to calculate
the amount of bend between the wellbore 104 at the first position
116 and the wellbore 104 at the second position 120 are described
herein (e.g., with respect to FIGS. 9-11).
[0055] A calculation of the sag which takes into account the bend,
which may be measured by a bend sensor, can be made as follows. As
described above:
I.sub.UM=I.sub.U+Ssin I.sub.U; (Eq. 11)
I.sub.LM=I.sub.L. (Eq. 12)
For a curved wellbore section,
.DELTA.I=I.sub.L-I.sub.U=.delta.L; (Eq. 13)
where .delta. is the dogleg curvature (bend) of the wellbore
between the upper sensor 108 and the lower sensor 106 and where L
is the separation between the upper sensor 108 and the lower sensor
106. Hence,
.DELTA.I.sub.M=I.sub.UM-I.sub.UM=Ssin I-.delta.L; (Eq. 14)
and an estimate of the horizontal sag may now be obtained
using:
S = .DELTA. I M + .delta. L sin I . ( Eq . 15 ) ##EQU00003##
[0056] FIG. 3 is a flowchart of an example method 300 of generating
information indicative of misalignment between the first and second
acceleration sensors 106, 108 mounted within the downhole portion
102 of a drill string 100 in accordance with certain embodiments
described herein. While the method 300 is described herein by
reference to the drill string 100 schematically illustrated by FIG.
1 and by FIG. 2, other drill strings are also compatible with
certain embodiments described herein.
[0057] In certain embodiments, the method 300 comprises providing a
drill string 100 comprising a downhole portion 102 adapted to move
within a wellbore 104 in an operational block 302. The downhole
portion 102 comprises a first portion 114 at a first position 116
within the wellbore 104 and oriented at a first angle 121 relative
to the wellbore 104 at the first position 116. The downhole portion
102 also comprises a second portion 118 at a second position 120
within the wellbore 104 and oriented at a second angle 122 relative
to the wellbore 104 at the second position 120 wherein at least one
of the first and second angles 121, 122 is non-zero. The drill
string 100 further comprises a first acceleration sensor 106
mounted within the first portion 114. The first acceleration sensor
106 is adapted to generate a first signal indicative of an
acceleration of the first acceleration sensor 106. The drill string
100 further comprises a second acceleration sensor 108 mounted
within the second portion 118, the second acceleration sensor 108
adapted to generate a second signal indicative of an acceleration
of the second acceleration sensor 108.
[0058] In certain embodiments, the method 300 further comprises
generating the first signal and the second signal while the
downhole portion 102 of the drill string 100 is within the wellbore
104 in an operational block 304. In certain embodiments, the first
and second signals are generated while the downhole portion 102 is
moving within the wellbore 104.
[0059] In certain embodiments, the method 300 further comprises
calculating the difference between the first angle 121 and the
second angle 122 in an operational block 306. In certain
embodiments, the method 300 comprises storing the difference
between the first angle 121 and the second angle 122 in an
operational block 308. In certain embodiments, the method 300
further comprises displaying the difference between the first angle
121 and the second angle 122 in an operational block 310. For
example, the first and second angles 121, 122 may be displayed on a
monitor of a personal computer outside the wellbore 104 at the
surface in certain embodiments. In certain embodiments, the method
300 further comprises modifying a direction of drilling of the
drill string 100 with respect to the wellbore 104 based on the
difference between the first angle 121 and the second angle 122 in
an operational block 312. In certain embodiments, the direction can
be changed automatically (e.g., by the controller in response to
the calculated difference between the first angle 121 and the
second angle 122. In certain other embodiments, the direction is
changed by a user responding to the displayed difference.
[0060] FIG. 4 is a flowchart of an example method 400 of
determining the misalignment between first and second acceleration
sensors 106, 108 mounted within a drill string 100 in accordance
with certain embodiments described herein. While the method 400 is
described herein by reference to the drill string 100 schematically
illustrated by FIGS. 1-2, other drill strings are also compatible
with certain embodiments described herein.
[0061] In certain embodiments, the method 400 comprises receiving
one or more acceleration measurements from a first acceleration
sensor 106 in a first portion 114 of the drill string 100 at a
first position 116 within a wellbore 104 in an operational block
402. The first portion 114 is oriented at a first angle 121
relative the wellbore 104 at the first position 116. In certain
embodiments, the method 400 further comprises receiving one or more
acceleration measurements from a second acceleration sensor 108 in
a second portion 118 of the drill string 100 at a second position
120 within the wellbore 104 in an operational block 404. The second
portion 118 is oriented at a second angle 122 relative to the
wellbore 104 at the second position 120, wherein at least one of
the first and second angles 121, 122 is non-zero.
[0062] In certain embodiments, the method 400 further comprises
calculating the difference between the first angle 121 and the
second angle 122 in response to the one or more acceleration
measurements from the first acceleration sensor 106 and the one or
more measurements from the second acceleration sensor 108 in the
operational block 406. In certain embodiments, the method 400
further comprises storing the difference between the first angle
121 and the second angle 122. The method 400 of certain embodiments
further comprises displaying the difference between the first angle
121 and the second angle 122. For example, the first and second
angles 121, 122 may be displayed on a monitor of a personal
computer outside the wellbore 104 at the surface in certain
embodiments. In certain embodiments, the method 400 further
comprises modifying a direction of drilling of the drill string 100
with respect to the wellbore 104 based on the difference between
the first angle 121 and the second angle 122.
[0063] An example calculation method for determining the
misalignment between first and second acceleration sensors 106, 108
mounted within a downhole portion 102 of a drill string 100
utilizing a first acceleration sensor 106 and a second acceleration
sensor 108 is described herein. While the example method described
below utilizes a minimum number of variables, other embodiments are
not limited to only these variables.
[0064] In the example method described below, the periodicity of
the measurements from the two accelerometer sensors define time
periods or "epochs" whereby one set of accelerometer measurements
are taken at every epoch k. In certain embodiments, the upper and
lower sensors 106, 108 may be located in sensor packages which may
be mounted on the downhole portion 102 of the wellbore 104. Other
embodiments distinguish the two acceleration sensors from one
another using other terms.
[0065] 1. Example Method Utilizing Multiple Measurements to Correct
For Misalignment Due to Sag
[0066] In the example method described below, measurements of well
path inclination at the locations of the upper and lower
accelerometer sensors 108, 106 in a drill string 100 are compared
with estimates of those quantities derived from a mathematical
model of the system. In certain embodiments, these quantities are
combined in a recursive filtering process which minimizes the
variance of errors in the system error model and provide improved
estimates of various system characteristics including inclination,
dogleg curvature (bend) of the wellbore 104, and sag of the upper
and lower sensors 108, 106.
System Model
[0067] The example embodiment utilizes a state vector. The state
vector x.sub.k at time t.sub.k, for epoch k, may be expressed as
follows:
x.sub.k[I.sub.k.delta..sub.kS.sub.LS.sub.U].sup.T; (Eq. 16)
where,
[0068] I.sub.k=the inclination mid-way between the two sensors 106,
108;
[0069] .delta..sub.k=the average dogleg curvature between the two
sensors 106, 108;
[0070] S.sub.L=horizontal sag for the lower sensor 106; and
[0071] S.sub.U=horizontal sag for the upper sensor 108.
In certain embodiments, I.sub.k and .delta..sub.k are time
dependent states while S.sub.L and S.sub.U are independent of time.
Inclination predictions from one epoch to the next may be expressed
by the equation:
I.sub.k=I.sub.k-1+.DELTA.D.sub.k.delta..sub.k-1; (Eq. 17)
where .DELTA.D.sub.k is the along-hole depth difference between
epochs k-1 and k. The dogleg curvature is assumed to be nominally
constant, which is true in certain embodiments described herein.
The state covariance matrix at epoch k may be expressed as
follows:
P k = [ .sigma. I , k 2 .sigma. I .delta. , k .sigma. IS L , k
.sigma. IS U , k .sigma. .delta. L , k .sigma. .delta. , k 2
.sigma. .delta. S L , k .sigma. .delta. S U , k .sigma. S L I , k
.sigma. S L .delta. , k .sigma. S L , k 2 .sigma. S L S U , k
.sigma. S U I , k .sigma. S U .delta. , k .sigma. S U S L , k
.sigma. S U , k 2 ] ; ( Eq . 18 ) ##EQU00004##
where .sigma..sup.2.sub.i,k is the variance of parameter i in state
vector x.sub.k, and .sigma..sub.ij,k is the covariance between
parameters i and j in state vector x.sub.k.
[0072] Initial values are assigned to the inclination and dogleg
states in accordance with the initial inclination measurements
taken at the upper sensor 108 and lower sensor 106 locations,
I.sub.U0 and I.sub.L0 respectively. Hence, the initial state at
epoch 0 can be express as follows:
x.sub.k=[(I.sub.L0+I.sub.U0)/2(I.sub.L0-I.sub.U0)/L00].sup.T; (Eq.
19)
where L is the fixed distance between the two sensors 106, 108.
[0073] The covariance matrix P.sub.0 for the initial state at epoch
0 can be expressed as follows:
P 0 = [ .sigma. I 2 .sigma. I 2 / ( B 2 ) 0 0 .sigma. I 2 / ( B 2 )
.sigma. I 2 / L 2 0 0 0 0 .sigma. S L 2 0 0 0 0 .sigma. S U 2 ] ; (
Eq . 20 ) ##EQU00005##
where .sigma..sub.1 is the uncertainty in the initial inclination
mid-way between the two accelerometer packages, and
.sigma..sub.S.sub.L and .sigma..sub.S.sub.U are the uncertainties
in the initial estimates of sag at the sensor locations.
[0074] The state vector x.sub.k-1 at epoch k-1 can be used to
predict the state vector x.sub.k at epoch k using the following
equation:
x k = .PHI. k x k - 1 ; where ( Eq . 21 ) .PHI. k = [ 1 .DELTA. D k
0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] . ( Eq . 22 ) ##EQU00006##
[0075] The covariance matrix Q for the predicted state vector may
be expressed by the following diagonal matrix:
Q = [ ( p I / .alpha. ) 2 0 0 0 0 ( p .delta. / .alpha. ) 2 0 0 0 0
0 0 0 0 0 0 ] ; ( Eq . 23 ) ##EQU00007##
where p.sub.I is the maximum change in inclination over the
measurement update interval and p.sub..delta. is the maximum change
in apparent dogleg over the same time period. The elements of the
matrix associated with the sag may be set to zero owing to the fact
that the horizontal sag for a given tool string will be constant.
The parameter .alpha. is a multiplication factor between the
standard deviation of a state vector element (.sigma.) and the
maximum change of the state vector element, such that the maximum
change in the state vector element can be expressed as
p=.alpha..sigma.. In certain embodiments, this factor can vary from
approximately 2 to approximately 5. In other embodiments, this
factor can vary within another range compatible with certain
embodiments described herein.
Measurement Equations
[0076] Measurements of well path inclination at the upper and lower
sensor locations 116, 120 in the drill string 100 may be extracted
at regular intervals of time from the respective accelerometer
measurements from the upper sensor 108 and the lower sensor 106, as
described above. The inclination measurements obtained at epoch k
may be expressed as:
z k = [ I Lk I Uk ] ; ( Eq . 24 ) ##EQU00008##
where
I.sub.Lk=an inclination measurement derived from the lower
acceleration sensor 106 at epoch k; and (Eq. 25)
I.sub.Uk=an inclination measurement derived from the upper
acceleration sensor 108 package at epoch k; (Eq. 26)
[0077] Estimates of the inclination at the locations of the upper
and lower acceleration sensor 108, 106 at the upper and lower
sensor locations 120, 116 may be expressed in terms of the states
of the model as follows:
z ^ k = [ I k + .delta. K L / 2 + S L sin ( I k + .delta. K L / 2 )
I k - .delta. K L / 2 + S U sin ( I k - .delta. K L / 2 ) ] . ( Eq
. 27 ) ##EQU00009##
The differences between the inclination measurements and the
estimates of these quantities, denoted .DELTA.z.sub.k, can form the
inputs to a Kalman filter, where:
.DELTA. z k = z k - z ^ k = [ I Lk - { I k + .delta. K L / 2 + S L
sin ( I k + .delta. K L / 2 ) } I Uk - { I k - .delta. K L / 2 + S
U sin ( I k - .delta. K L / 2 ) } ] . ( Eq . 28 ) ##EQU00010##
The measurement differences may be expressed in terms of the system
error states,
.DELTA.x.sub.k=[.DELTA.I.sub.k.DELTA..delta..sub.k.DELTA.S.sub.L.-
DELTA.S.sub.U].sup.T, via the following linear matrix equation:
.DELTA.z.sub.k=H.sub.k.DELTA.x.sub.k+v.sub.k; (Eq. 29)
where H.sub.k is a 2.times.4 matrix in which the elements
correspond to the partial derivatives of the theoretical
measurement equations:
H 11 k = 1 + S L cos ( I k + .delta. k L / 2 ) ; ( Eq . 30 ) H 12 k
= L 2 { 1 + S L cos ( I k + .delta. k L / 2 ) } ; ( Eq . 31 ) H 13
k = sin ( I k + .delta. k L / 2 ) ; ( Eq . 32 ) H 14 k = 0 ; ( Eq .
33 ) H 21 k = 1 + S U cos ( I k - .delta. k L / 2 ) ; ( Eq . 34 ) H
22 k = - L 2 { 1 + S U cos ( I k - .delta. k L / 2 ) } ; ( Eq . 35
) H 23 k = 0 ; ( Eq . 36 ) H 24 k = sin ( I k - .delta. k L / 2 ) ;
( Eq . 37 ) ##EQU00011##
and where v.sub.k represents the noise in the inclination
measurements. The covariance of the measurement noise process at
epoch k can be expressed by the following diagonal matrix:
R k = [ .sigma. I L k 2 0 0 .sigma. I U k 2 ] ; ( Eq . 38 )
##EQU00012##
where .sigma..sub.1.sub.U.sub.k and .sigma..sub.1.sub.L.sub.k are
the uncertainties in the upper and lower inclination measurements,
respectively.
Filter Prediction Step
[0078] The covariance matrix corresponding to the uncertainty in
the predicted state vector may be expressed as follows:
P.sub.k/k-1=.PHI..sub.k-1P.sub.k-1/k-1.PHI..sub.k-1.sup.T+Q.sub.k-1;
(Eq. 39)
where P.sub.k/k-1 is the covariance matrix at epoch k predicted at
epoch k-1, or the covariance matrix prior to the update which can
be determined using the inclination measurements at epoch k. Since
the system states may be corrected following each measurement
update, a good estimate of the state error following each
measurement update can be zero. The predicted error state can also
be zero in certain embodiments.
Filter Measurement Update
[0079] The covariance matrix and the state vector can, in certain
embodiments, be updated following a measurement at epoch k using
the following equations:
P.sub.k/k=P.sub.k/k-1-G.sub.kH.sub.kP.sub.k/k-1; (Eq. 40)
X.sub.k/k=x.sub.k/k-1+G.sub.k.DELTA.z.sub.k; (Eq. 41)
where P.sub.k/k is the covariance matrix following the measurement
update at epoch k, x.sub.k/k-1 is the predicted state vector and
x.sub.k/k is the state vector following the measurement update.
[0080] The gain matrix G.sub.k can be expressed as:
G.sub.k=P.sub.k/k-1H.sub.k.sup.T[H.sub.kP.sub.k/k-1H.sub.m.sup.T+R.sub.k-
].sup.-1. (Eq. 42)
B. The Use of Multiple Magnetic Field Measurements to Determine
Magnetic Interference
[0081] A drilling system 200 of certain embodiments comprises
magnetic components, such as ferromagnetic materials. The magnetic
components can be magnetized by one or more magnetic fields, such
as, for example, the magnetic field of the Earth. In certain cases,
some residual magnetization will remain even after attempts to
de-magnetize these components of the drilling system 200. FIG. 5
schematically illustrates an example drilling system 200 including
a downhole portion 202 comprising one or more magnetic regions 210
and one or more non-magnetic regions 212. The downhole portion 202
moves along a first wellbore 204. The drilling system 200 of
certain embodiments further comprises at least two magnetic sensors
206, 208 within at least one non-magnetic region 212 of the
downhole portion 202. The at least two magnetic sensors 206, 208
comprise a first magnetic sensor 206 and a second magnetic sensor
208 spaced apart from one another by a non-zero distance L. In
certain embodiments, the first magnetic sensor 206 is adapted to
generate a first signal in response to magnetic fields of the Earth
and of the one or more magnetic regions 210 of the tool string. The
second magnetic sensor 208 is adapted to generate a second signal
in response to magnetic fields of the Earth and of the one or more
magnetic regions 210 of the tool string.
[0082] The downhole portion 202 of certain embodiments comprises a
drill string. The downhole portion 202 may include a
measurement-while-drilling string, for example. In certain
embodiments, the drilling system 200 can include a MWD
instrumentation pack. In certain embodiments, one or more of the
first and second magnetic sensors 206, 208 is located within or
mounted on the MWD instrumentation pack which may be mounted on an
elongate portion 217 of the drill string. In certain embodiments,
one or more of the first and second magnetic sensors 206, 208 is
mounted on a rotary steerable tool 218. For example, in the
illustrated embodiment, the first magnetic sensor 206 is mounted on
rotary steerable tool 218 and the second magnetic sensor 208 is
mounted on the elongate portion 217 of the drill string. In certain
other embodiments, the first and second magnetic sensors 206, 208
may be mounted on the downhole portion 202 in various
configurations compatible with embodiments described herein. For
example, in some embodiments, both of the first and second magnetic
sensors 206, 208 are mounted on the elongate portion 217 (e.g., in
two MWD instrumentation packs spaced from one another or alongside
one another). In other embodiments, both of the first and second
magnetic sensors 206, 208 are mounted on the rotary steerable tool
218. In certain embodiments, the drilling system 200 includes a
sufficient number of sensors and adequate spacings between the
first magnetic sensor 206 and the second magnetic sensor 208 to
perform the methods described herein.
[0083] In certain embodiments, the rotary steerable tool 218
comprises a housing 220 containing at least one of the magnetic
sensors 206, 208. As schematically illustrated by FIG. 5, the
housing 220 of certain embodiments contains the first magnetic
sensor 206 while the second magnetic sensor 208 is attached on or
within the elongate portion 217. The rotary steerable tool 218 of
certain embodiments further comprises a drill bit 207. In certain
embodiments, the downhole portion 202 is substantially collinear
with the wellbore 204.
[0084] In certain embodiments, the first and second magnetic
sensors 206, 208 may comprise an orthogonal triad of magnetometers
which detect the magnetic field in the x, y, and z directions. In
certain embodiments, the axial interference can be detected by the
z-magnetometer while the cross-axial interference can be detected
by the x and y magnetometers. The magnetometers may be of various
types including flux gate sensors, solid state devices, or some
other type of magnetometer. In certain embodiments, the first and
second magnetic sensors 206, 208 are spaced apart from one another
by a distance L. In some embodiments, the distance L is about 40
feet. The distance L in certain other embodiments is about 70 feet.
In certain embodiments, the second magnetic sensor 208 and the
first magnetic sensor 206 are spaced apart from one another by a
distance L in a range between about 40 feet to about 70 feet. In
other embodiments the distance L is another value compatible with
certain embodiments described. In certain embodiments, more than
two magnetic sensors may be included in the drill string 100. The
first magnetic sensor 206 is also referred to as the "lower
magnetic sensor" and the second magnetic sensor 208 is also
referred to as the "upper magnetic sensor" herein. The terms
"upper" and "lower" are used herein merely to distinguish the two
magnetic sensors 206, 208 according to their relative positions
along the wellbore 204, and are not to be interpreted as
limiting.
[0085] The drilling system 200 of certain embodiments further
comprises a controller 214 configured to receive the first signal
and the second signal and to calculate the magnetic field of the
one or more magnetic regions 210. In the embodiment schematically
illustrated by FIG. 5, the controller 214 is at the surface and is
coupled to the downhole portion 202 by the elongate portion 217. In
certain embodiments, the controller 214 comprises a microprocessor
adapted to determine an estimate of magnetic interference from the
drill string and corrected magnetic interference measurements which
can be used to determine tool azimuth with respect to magnetic
north. In certain embodiments, the controller 214 further comprises
a memory subsystem adapted to store at least a portion of the data
obtained from the various sensors. The controller 214 can comprise
hardware, software, or a combination of both hardware and software.
In certain embodiments, the controller 214 comprises a standard
personal computer.
[0086] In certain embodiments, at least a portion of the controller
214 is located within the downhole portion 202. In certain other
embodiments, at least a portion of the controller 214 is located
outside the wellbore 104 at the surface and is communicatively
coupled to the downhole portion 202 within the wellbore 204. In
certain embodiments in which the downhole portion 202 is part of a
wellbore drilling system capable of measurement while drilling
(MWD) or logging while drilling (LWD), signals from the downhole
portion 202 are transmitted by mud pulse telemetry or
electromagnetic (EM) telemetry. In embodiments where at least a
portion of the controller 214 is located outside the wellbore 104
at the surface, the controller 214 is communicatively coupled to
the downhole portion 202 within the wellbore 204 by a wire or cable
of the elongate portion 217. In certain such embodiments, the
elongate portion 217 comprises signal conduits through which
signals are transmitted from the various sensors within the
downhole portion 202 to the controller 214. In certain embodiments
in which the controller 214 is adapted to generate control signals
for the various components of the downhole portion 202, the
elongate portion 217 is adapted to transmit the control signals
from the controller 214 to the downhole portion 202.
[0087] In certain embodiments, the controller 214 is adapted to
perform a post-processing analysis of the data obtained from the
various sensors of the downhole portion 202. In certain such
post-processing embodiments, data is obtained and saved from the
various sensors of the drilling system 200 as the downhole portion
202 travels within the wellbore 204, and the saved data are later
analyzed to determine information regarding the downhole portion
202. The saved data obtained from the various sensors
advantageously may include time reference information (e.g., time
tagging).
[0088] In certain other embodiments, the controller 214 provides a
real-time processing analysis of the signals or data obtained from
the various sensors of the downhole portion 202. In certain such
real-time processing embodiments, data obtained from the various
sensors of the downhole portion 202 are analyzed while the downhole
portion 202 travels within the wellbore 204. In certain
embodiments, at least a portion of the data obtained from the
various sensors is saved in memory for analysis by the controller
214. The controller 214 of certain such embodiments comprises
sufficient data processing and data storage capacity to perform the
real-time analysis.
[0089] In certain embodiments, the controller 214 is configured to
calculate an axial interference and hence to calculate an improved
estimate of an azimuthal orientation of the downhole portion 202
with respect to the magnetic field of the Earth. In addition, and
as described herein with respect to FIG. 6, the controller 214 of
certain embodiments is further configured to calculate an estimate
of a relative location of a second wellbore 230 spaced from the
first wellbore 204.
[0090] In certain embodiments, the one or more non-magnetic regions
212 are not completely non-magnetic. For example, in some
embodiments, the non-magnetic regions 212 are less magnetic
relative to the magnetic regions 210 but may have some magnetic
field associated with them. The non-magnetic regions 212 of certain
embodiments comprise non-magnetic drill collars ("NMDCs").
[0091] In certain embodiments, the downhole portion 202 of the
drill string includes one or more collars 215 and the magnetic
regions 210 of the downhole portion 202 comprise two generally
equal magnetic poles with opposite signs located near the ends 216
of the collars 215. The magnetic regions 210 of certain embodiments
generally comprise axial components which are due to the magnetic
poles and are substantially aligned with the wellbore 204 in the
direction of drilling. Because the poles of certain embodiments may
not be precisely aligned with respect to the drill string axis,
cross-axial components may also be present. However, because the
misalignment of the poles may generally be relatively small in
comparison to the axial distance between the poles and the first
and second magnetic sensors 206, 208, the cross-axial components
are generally small in comparison to the axial components. The
axial and/or cross-axial components of certain embodiments can
interfere with measurements of the azimuthal orientation of the
downhole portion with respect to the magnetic field of the
Earth.
[0092] In general, the magnetic regions (e.g., drill pipes or
collars) nearest the magnetic sensors 206, 208 can exhibit a
significant effect on the magnetic measurements. The axial field
strength at the magnetic sensors (dB.sub.a) caused by the closest
magnetic collar 215 can be given by:
d B a = P D 4 .pi. ( 1 L N 2 - 1 ( L N + L P ) 2 ) ; ( Eq . 43 )
##EQU00013##
where P.sub.D is the magnetic pole strength of the drill pipe,
L.sub.P is distance between complementary poles (usually the length
of a single drill pipe or collar) and L.sub.N is the length of the
NMDC between the magnetic sensors and the nearest magnetic
pole.
[0093] An axial field strength at the magnetic sensors resulting
from the effects of the magnetic drill pipes and collars 215
further up the drill string can be given by the following
approximate equation:
d B a .apprxeq. P D 4 .pi. L N 2 ( Eq . 44 ) ##EQU00014##
[0094] The magnetic field sensed by a magnetic sensor can be the
combined effect of the Earth's magnetic field and the axial drill
string magnetization (dB.sub.a). The combined field generally may
only differ from the Earth's field in the axial (z-axis) direction,
and can therefore have the same effect as a z-magnetometer bias.
The azimuth error can therefore given by:
dA = - sin I sin A B cos .theta. d B a ; ( Eq . 45 )
##EQU00015##
where B is the Earth's magnetic field strength, .theta. is the
magnetic angle of dip and A is the magnetic azimuth angle.
[0095] In a straight section of a wellbore, a measured magnetic
azimuth at the upper and lower measurement locations (A.sub.UM and
A.sub.LM) (i.e., the locations of the upper and lower magnetic
sensors 208, 206) may be expressed in terms of the true azimuth (A)
and the axial magnetic interference at the two locations (dB.sub.aU
and dB.sub.aL), as follows:
A UM = A - sin I sin A B cos .theta. dB aU ; ( Eq . 46 ) A LM = A -
sin I sin A B cos .theta. dB aL ; where ( Eq . 47 ) dB aU = P D 4
.pi. L N 2 , ( Eq . 48 ) dB aL = P D 4 .pi. ( L + L N ) 2 , ( Eq .
49 ) ##EQU00016##
L is the distance between the two magnetic sensors, and L.sub.N is
the length of the non-magnetic section above the upper magnetometer
sensor 208. Calculating the difference between the two azimuth
measurements yields:
.DELTA. A M = A UM - A LM = - sin I sin A B cos .theta. .DELTA. dB
; where ( Eq . 50 ) .DELTA. dB = dB aU - dB aL = P D 4 .pi. ( 1 L N
2 - 1 ( L + L N ) 2 ) . ( Eq . 51 ) ##EQU00017##
Hence, the disturbance pole strength may be determined using:
P D = B cos .theta. 4 .pi. .DELTA. A M sin I sin A ( 1 L N 2 - 1 (
L + L N ) 2 ) ( Eq . 52 ) ##EQU00018##
[0096] Given knowledge of the axial interference through the
example equations outlined above, it is possible to compensate for
the interference using embodiments of the disclosure provided
herein.
[0097] FIG. 6 schematically illustrates a configuration in which
the downhole portion 202 of the drilling system 200 is moving along
a first wellbore 204 and is positioned relative to a second
wellbore 230 spaced from the first wellbore 204. In certain
embodiments, the controller 214 is further configured to calculate
an estimate of a relative location of the second wellbore 230
spaced from the first wellbore 204. Estimating the location of a
second wellbore 230 may be useful to help avoid collisions between,
for example, a new wellbore 230 under construction and an existing
wellbore 204. The first wellbore 204 may also be described as a new
wellbore 104 and the second wellbore 230 may be also described as
an existing wellbore 104 throughout the disclosure. The terms new
wellbore 104 and existing wellbore 104 are not intended to be
limiting.
[0098] In addition, detecting the location of the second wellbore
230 may also be beneficial when it is desirable to intercept a
second wellbore 230 such as, for example, to drill a relief to
intercept the second wellbore 230. In general, as the downhole
portion 202 approaches a second wellbore 230, the presence of the
second wellbore 230 can be detected using measurements from the
first and second magnetic sensors 206, 208 of the drilling system.
For example, the first and second sensors 206, 208 may be used to
detect the azimuthal orientation of the drilling system 200 with
respect to the magnetic field of the Earth. The estimated azimuthal
orientation may then be used to steer the drilling system 200. In
accordance with certain embodiments described herein, the magnetic
field resulting from the magnetized material in the second wellbore
230 (e.g., in the casing string of an existing wellbore) may be
detected by the first and second sensors 206, 208 and extracted
from measurements indicating the magnetic field of the Earth. These
extracted values may then be used to determine the location of the
second wellbore 230 in certain embodiments.
[0099] Referring to FIG. 6, the angular separation between the two
well paths can be denoted by .psi.. An axial field strength
uncertainty at the lower magnetic 206 can be caused by magnetized
material in the second wellbore 230 (e.g., in the casing string)
and can be given by the following approximate equation:
dB la .apprxeq. 0.8 L c ( 4 x 2 + L C 2 ) 3 / 2 P C cos .psi. + 0.9
x ( 4 x 2 + L C 2 ) 3 / 2 P C sin .psi. ; ( Eq . 53 )
##EQU00019##
The cross-axial interference sensed at the lower magnetic sensor
206 can be given by:
dB lc .apprxeq. 0.8 L c ( 4 x 2 + L C 2 ) 3 / 2 P C sin .psi. + 0.9
x ( 4 x 2 + L C 2 ) 3 / 2 P C cos .psi. ; ( Eq . 54 )
##EQU00020##
where P.sub.C represents the casing magnetic pole strength, L.sub.C
represents the average length of the casing sections, and x
represents the separation between the casing string and the lower
magnetic sensor 206 in the new wellbore 204.
[0100] The upper magnetic sensor 208 in the new wellbore 204 may
also be subject to interference from the magnetic portions 210 of
the casing in the second wellbore 230. In certain embodiments, the
magnetic interference will be lower for the situation shown in FIG.
6 where the new wellbore 230 is approaching the existing wellbore
204 because the upper magnetic sensor is further from the source of
magnetic interference (e.g., the casing of the existing wellbore).
The axial field strength uncertainty at the upper magnetic sensor
208 caused by casing interference can be given by the following
approximate equation:
dB ua .apprxeq. 0.8 L C ( 4 ( x + L sin .psi. ) 2 + L C 2 ) 3 / 2 P
C cos .psi. + 0.9 ( x + L sin .psi. ) ( 4 ( x + L sin .psi. ) 2 + L
C 2 ) 3 / 2 P C sin .psi. ; ( Eq . 55 ) ##EQU00021##
[0101] while the cross-axial interference at this location can be
given by:
dB uc .apprxeq. - 0.8 L C ( 4 ( x + L sin .psi. ) 2 + L C 2 ) 3 / 2
P C sin .psi. + 0.9 ( x + L sin .psi. ) ( 4 ( x + L sin .psi. ) 2 +
L C 2 ) 3 / 2 P C cos .psi. ; ( Eq . 56 ) ##EQU00022##
where L is the separation of the two magnetic instruments along the
tool string. Based on these two sets of magnetic readings, four
equations having three unknowns (P, x and .psi.) may be generated.
Therefore, it is possible in certain embodiments to determine the
unknown parameters by solving the equations. For example, in one
embodiment, a least squares adjustment procedure may be used to
compute these values.
[0102] Using certain embodiments described herein, the difference
between two upper and lower measurements generally increases as the
new wellbore 204 approaches the existing wellbore 230. In general,
when the new wellbore 204 approaches the existing wellbore 230
along a perpendicular path, the difference in the field
measurements between the upper and lower magnetic sensors 208, 206
will be the greatest. As will be appreciated by skilled artisans
from the disclosure provided herein, certain embodiments described
herein can use the calculated difference in the magnetic fields
sensed by the upper and lower magnetic sensors 208, 206 to
determine the changing separation distance between the new well 204
and an existing well 230 and to use this information either to
avoid a collision between the new well 204 and an existing wellbore
230, or to cause the new well 204 to intercept an existing wellbore
230. For example, where a new wellbore 204 approaches an existing
wellbore 230 along a path perpendicular to the existing wellbore
230, the magnetization resulting from the second wellbore 230 and
detected by the first and second magnetic sensors 206, 208 in the
new wellbore 204 are generally influenced by the same sets of poles
in the existing wellbore 230. However, when the new wellbore 204 is
approaching the existing wellbore 230 along a non-perpendicular
angle, as shown in FIG. 4, the group of magnetic poles from the
second wellbore 230 influencing the magnetic field measured by the
first magnetic sensor 206 may be different from the group of
magnetic poles influencing the magnetic field measured by the
second magnetic sensor 208. Whether different sets of magnetic
poles are detected by the first and second sensors 206, 208 can
depend, for example, on relative separation and can also vary with
time as the drilling system 200 moves with respect to the second
wellbore 230.
[0103] In certain embodiments, the first and second magnetic
sensors 206, 208 can also be used during the construction of a new
wellbore 204 in close proximity to an existing wellbore 230. For
example, when a drilling system 200 in a new wellbore 204 is moving
parallel to an existing wellbore, the magnetic field measurements
from the first and second magnetic sensors 206, 208 may generally
be represented by signals having similar magnitude but varying
phase. The relative phase of the two signals can depend, for
example, on the spacing between the two magnetic sensors 206, 208
and the length of the casing in the existing well. In certain
embodiments, the drilling system 200 can detect a difference
between the measurements of the first and second magnetic sensors
206, 208 which indicates that the new wellbore 204 is becoming
closer to or is diverging from the existing well 230. In certain
embodiments, this indication can be used to direct the drilling
system 200 to drill the new wellbore 104 in a direction
substantially parallel to the existing wellbore.
[0104] FIG. 7 is a flowchart of an example method 700 of generating
information indicative of the magnetic field in a first wellbore
204 in accordance with certain embodiments described herein. In
certain embodiments, the method 700 comprises providing a drilling
system 200 in an operational block 702. The drilling system 200 of
some embodiments comprises a downhole portion 202 adapted to move
along a first wellbore 204. The downhole portion 202 can include
one or more magnetic regions 210 and one or more non-magnetic
regions 212. The drilling system 200 further comprises at least two
magnetic sensors 206, 208 within at least one non-magnetic region
212 of the downhole portion 202. The at least two magnetic sensors
206, 208 comprise a first magnetic sensor 206 and a second magnetic
sensor 208 spaced apart from one another by a non-zero distance L
in certain embodiments. The first magnetic sensor 206 in certain
embodiments is adapted to generate a first signal in response to
magnetic fields of the Earth and of the one or more magnetic
regions 210 of the drill string. In some embodiments, the second
magnetic sensor 208 is adapted to generate a second signal in
response to magnetic fields of the Earth and of the one or more
magnetic regions 210 of the drill string.
[0105] In an operational block 704, the method 700 of some
embodiments further comprises generating the first signal and the
second signal while the downhole portion 202 of the drilling system
200 is at a first location within the first wellbore 204. In
certain embodiments, the method 700 further includes calculating
the magnetic field in the first wellbore 204 in response to the
first and second signals in an operational block 706. In certain
embodiments, the method 700 further comprises using the calculated
magnetic field to calculate an axial interference and hence to
calculate an improved estimate of an azimuthal orientation of the
downhole portion 202 with respect to the magnetic field of the
Earth at operational block 708. The method 700 of some embodiments
comprises using the calculated magnetic field to calculate an
estimate of a relative location of a second wellbore 230 spaced
from the first wellbore 204.
[0106] FIG. 8 is a flowchart of an example method 800 for
determining the magnetic field in a wellbore 204 in accordance with
certain embodiments described herein. In certain embodiments, the
method 800 comprises receiving one or more magnetic measurements
from at least two magnetic sensors 206, 208 within at least one
non-magnetic region 212 of the downhole portion 202 of a drilling
system 200 in an operational block 802. In certain embodiments, the
at least two magnetic sensors 206, 208 comprise a first magnetic
sensor 206 and a second magnetic sensor 208 spaced apart from one
another by a non-zero distance L. In certain embodiments, the first
magnetic sensor 206 generates a first signal in response to
magnetic fields from the Earth and from one or more magnetic
regions 210 of the downhole portion 202. In certain embodiments,
the second magnetic sensor 208 generates a second signal in
response to magnetic fields from the Earth and from the one or more
magnetic regions 210.
[0107] In an operational block 804, the method 800 of some
embodiments further comprises calculating the magnetic field in
response to the one or more magnetic measurements from the at least
two magnetic sensors 206, 208. In certain embodiments, in an
operational block 806, the method 800 further comprises using the
calculated magnetic field to calculate an axial interference and
hence to calculate an improved estimate of an azimuthal orientation
of the downhole portion 202 with respect to the magnetic field of
the Earth. In some embodiments, the method 800 further comprises
using the calculated magnetic field to calculate an estimate of a
relative location of a second wellbore 230 spaced from the wellbore
204.
[0108] An example calculation method for determining and correcting
for axial magnetization compatible with embodiments of the
disclosure is described below. While the example method has a
minimum number of variables, other embodiments are not limited to
only these variables. Additional variables may also be used,
including, but not limited to, velocities and/or depths of the
downhole portion of the wellbore 204. In certain embodiments, the
units of the parameters and variables below are in
meters-kilogram-second (MKS) units.
[0109] In the example method described below, the periodicity of
the measurements from the two magnetic sensors 206, 208 define time
periods or "epochs" whereby one set of magnetic measurements are
taken at every epoch k. In certain embodiments, the upper and lower
magnetic sensors 208, 206 may be located in sensor packages which
may be mounted on the downhole portion 202 of the wellbore 204.
Other embodiments distinguish the two magnetic sensors from one
another using other terms.
[0110] 1. Example Method Utilizing Multiple Measurements to Correct
For Axial Magnetization
[0111] In the example method described below, measurement of
magnetic azimuth based on measurements from the upper and lower
magnetic sensors 208, 206 in a drilling system 200 are compared
with estimates of those quantities derived from a mathematical
model of the system to provide a determination and correction of
axial magnetic interference. In certain embodiments, these
quantities are combined in a recursive filtering process which
minimizes the variance of errors in the system error model and
provide improved estimates of various system characteristics
including magnetic azimuth (A) and drill string pole strength
(P.sub.D).
System Model
[0112] A state vector x.sub.k at epoch k, can be expressed as
follows:
x.sub.k=[A.sub.kP.sub.D].sup.T; (Eq. 57)
where
A.sub.k=magnetic azimuth mid-way between the two magnetic sensors
(e.g., two magnetometer packages); and (Eq. 58)
P.sub.D=drill string pole strength. (Eq. 59)
A.sub.k is time dependent while P.sub.D is independent of time.
Azimuth doglegs are assumed to be small in the example method and
are therefore ignored.
[0113] The initial value assigned to the azimuth state may be the
mean of the azimuth readings obtained for the upper and lower
magnetometer locations, A.sub.U0 and A.sub.L0, respectively,
assuming any small dogleg curvature that does exist is fixed
between these two drill pipe locations. Hence, the initial state at
epoch 0 can be given by the following equation:
x.sub.k=[(A.sub.L0+A.sub.U0)/20].sup.T; (Eq. 60)
The covariance matrix P.sub.0 for the initial state at epoch 0 can
be expressed as follows:
P 0 = [ .sigma. A 2 0 0 .sigma. P D 2 ] ; ( Eq . 61 )
##EQU00023##
where .sigma..sub.A is the uncertainty in the initial azimuth
approximately mid-way between the two magnetic sensors 206, 208 and
.sigma..sub.P.sub.D is the uncertainty in the initial estimate of
the pole strength.
[0114] The state vector x.sub.k-1 at epoch k-1 can be used to
predict the state vector x.sub.k at epoch k using the following
equation:
x.sub.k=x.sub.k-1; (Eq. 62)
The covariance matrix Q for the predicted state vector can be given
by the following diagonal matrix:
Q = [ ( p A / .alpha. ) 2 0 0 0 ] ; ( Eq . 63 ) ##EQU00024##
where p.sub.A is the maximum change in azimuth over the measurement
update interval. The drill-string pole strength can be assumed to
be constant and the matrix element associated with this state can
therefore be set to zero. The parameter .alpha. is a multiplication
factor between the standard deviation of a state vector element
(.sigma.) and the maximum change of the state vector element such
that the maximum change in the state vector element can be
expressed as p=.alpha..sigma.. In certain embodiments, this factor
can vary from approximately 2 to approximately 5 in one embodiment.
In other embodiments, this factor can vary within another range
compatible with certain embodiments described herein.
Measurement Equations
[0115] Measurements of the well path azimuth based on the
respective magnetic sensor measurements at the upper and lower
locations of the magnetic sensors 206, 208 in the drill string may
be extracted at generally regular intervals of time. The
inclination measurements obtained at epoch k may be expressed
as:
z k = [ A Lk A Uk ] ; ( Eq . 64 ) ##EQU00025##
where
A.sub.Lk=the azimuth measurement derived from the lower
magnetometer package at epoch k; (Eq. 65)
A.sub.Uk=the azimuth measurement derived from the upper
magnetometer package at epoch k; (Eq. 66)
[0116] Estimates of the azimuth at the upper and lower
magnetometer/accelerometer package locations based on the model may
be expressed in terms of the states of the model as follows:
z ^ k = [ A k + sin I Lk sin A k P D / ( 4 .pi. B H ( L + L N ) 2 )
A k + sin I Uk sin A k P D / ( 4 .pi. B H L N 2 ) ] ; ( Eq . 67 )
##EQU00026##
Differences between the azimuth measurements and the estimates of
these quantities, denoted .DELTA.z.sub.k, form the inputs to a
Kalman filter, where:
.DELTA. z k = z k - z ^ k = [ A Lk - { A k + sin I Lk sin A k P D /
( 4 .pi. B H ( L + L N ) 2 ) } A Uk - { A k + sin I Uk sin A k P D
/ ( 4 .pi. B H L N 2 ) } ] ; ##EQU00027##
The measurement differences may be expressed in terms of the system
error states, via the following linear matrix equation:
.DELTA.z.sub.k=H.sub.k.DELTA.x.sub.k+v.sub.k; (Eq. 68)
where H.sub.k comprises a 2.times.2 matrix in which the elements
correspond to the partial derivatives of the theoretical
measurement equations:
H.sub.11k+1+sin I.sub.Lkcos
A.sub.kP.sub.D/(4.pi.B.sub.H(L+L.sub.N).sup.2); (Eq. 69)
H.sub.12k=sin I.sub.Lkcos A.sub.k/(4.pi.B.sub.H(L+L.sub.N).sup.2);
(Eq. 70)
H.sub.21k=1+sin I.sub.Ukcos
A.sub.kP.sub.D/(4.pi.B.sub.hL.sub.N.sup.2); and (Eq. 71)
H.sub.22k=sin I.sub.Ukcos A.sub.k/(4.pi.B.sub.HL.sub.n.sup.2); (Eq.
72)
and where v.sub.k represents noise in the azimuth measurements. The
covariance of the measurement noise process at epoch k can be given
by the following diagonal matrix:
R k = [ .sigma. A L k 2 0 0 .sigma. A U k 2 ] ; ( Eq . 73 )
##EQU00028##
where .sigma..sub.A.sub.U.sub.k and .sigma..sub.A.sub.L.sub.k
comprise the uncertainties in the upper and lower azimuth
measurements, respectively.
[0117] In certain embodiments, the above system and measurement
equations can be used to implement the filtering process as
follows.
Filter Prediction Step
[0118] The covariance matrix corresponding to the uncertainty in
the predicted state vector can be given by:
P.sub.k/k-1=P.sub.k-1/k-1+Q.sub.k-1; (Eq. 74)
Filter Measurement Update
[0119] The covariance matrix and the state vector are updated
following a measurement at epoch k using the following
equations:
P.sub.k/k=P.sub.k/k-1-G.sub.kH.sub.kP.sub.k/k-1; (Eq. 75)
x.sub.k/k=x.sub.k/k-1+G.sub.k.about..DELTA.z.sub.k; and (Eq.
76)
G.sub.k=P.sub.k/k-1H.sub.k.sup.T[H.sub.kP.sub.k/k-1H.sub.k.sup.T+R.sub.k-
].sup.-1. (Eq. 77)
C. The Use of Multiple Directional Survey Measurements to Determine
a Measure of the Curvature of the Wellbore
[0120] As discussed, certain embodiments described herein provide
two or more directional survey measurements from the multiple
sensors at a known separation distance(s) along the tool string.
Additionally, certain embodiments described herein generate a
measure of the curvature of the wellbore between two or more survey
system locations by comparing (e.g., differencing) the survey
system estimates of orientation (e.g., inclination and azimuth
angle) provided at each location. The terms bend, curvature, and
dog-leg are generally used interchangeably herein.
[0121] For example, where a rotary steerable tool is used to drill
a well, two sets of survey measurements may be generated, one by
survey sensors mounted within the rotary steerable tool and a
second set of measurements using a measurement while drilling (MWD)
instrumentation pack or a gyro survey tool mounted above the
drilling tool. The rotary steerable tool can attempt to create
curvature of the well being drilled (a dog-leg section) by bending
the drill shaft passing through it in the desired direction, for
example. By comparing (e.g., differencing) the two sets of
directional data provided by the two sets of survey sensors (e.g.,
from the rotary steerable tool and the MWD instrumentation pack),
an independent measure of the amount of dog-leg curvature created
by the rotary steerable tool over the separation distance between
the two sets of sensors can be obtained according to certain
embodiments described herein. Differences between the target or
desired well curvature and the measured well curvature can then be
used adjust the shaft bending and so correct the curvature in
accordance with the desired trajectory.
[0122] FIG. 9 schematically illustrates an example drill string 900
for use in a wellbore 904 and having first and second sensor
packages 906, 908 in a portion of the wellbore 904 having a
curvature .beta. in accordance with certain embodiments described
herein. The drill string 900 comprises a downhole portion 902
adapted to move within the wellbore 904. The downhole portion 902
includes a first portion 914 at a first position 916 within the
wellbore 904 and a second portion 918 at a second position 920
within the wellbore 904. The downhole portion 902 is adapted to
bend between the first portion 914 and the second portion 918.
[0123] The first sensor package 906 of certain embodiments is
mounted within the first portion 914 and adapted to generate a
first measurement indicative of an orientation of the first portion
914 relative to the Earth. Additionally, the second sensor package
908 of certain embodiments is mounted within the second portion 918
and is adapted to generate a second measurement indicative of an
orientation of the second portion 918 relative to the Earth. The
drill string 900 may further comprise a controller (not shown)
configured to calculate a first amount of bend .beta. between the
first portion 914 and the second portion 918 in response to the
first measurement and the second measurement.
[0124] The drill string 900 may, in certain embodiments, be a
measurement-while drilling (MWD) string. In certain embodiments,
the drill string 900 includes a MWD instrumentation pack. In
certain embodiments, the first portion 914 comprises a rotary
steerable portion 912 and the first sensor package 906 is mounted
on the rotary steerable portion 912. The second sensor package 908
of some embodiments is part of a MWD instrumentation pack mounted
on the second portion 918 (e.g., on the elongate portion 910 of the
drill string 900). In some embodiments, the second sensor package
908 comprises a gyroscopic survey tool. In other embodiments, the
first and second sensor packages 906, 908 are mounted on the
downhole portion 902 in other configurations compatible with
certain embodiments described herein. For example, in some
embodiments, both of the first and second sensor packages 906, 908
are mounted on the elongate portion 910 (e.g., in two MWD
instrumentation packs spaced apart from one another or alongside
one another). In other embodiments, both of the first and second
sensor packages 906, 908 are mounted on the rotary steerable tool
912. In certain embodiments, one or more additional sensor packages
(not shown) are located on the drill string 900, e.g., near the
first sensor package 906, the second sensor package 908, or both.
For example, in some embodiments, a third sensor package is located
near the first sensor package 906 and a fourth sensor package is
located near the second sensor package 908. In such an example, the
fourth sensor package may be mounted in a separate MWD pack located
alongside the MWD pack on which the second sensor package 108 is
mounted.
[0125] The first and second sensor packages of certain embodiments
906, 908 include sensors capable of generating directional survey
measurements such as inclination, azimuth angle, and tool-face
angle. For example, in certain embodiments, the first sensor
package 906 and the second sensor package 908 comprise
accelerometers currently used in conventional wellbore survey
tools. The first sensor package 906 and the second sensor package
908 may comprise any of the accelerometers described herein (e.g.,
with respect to FIGS. 1-4). Such accelerometer sensors may be
capable of measuring the inclination, the high-side tool face
angle, or both, of the downhole instrumentation at intervals along
the well path trajectory, for example. The first and second sensor
packages 906, 908 may comprise gyroscopic sensors. One or more of
the first and second sensor packages 906, 908 may be part of a
gyroscopic survey system, for example. Such gyroscopic sensors may
be capable of measuring the azimuth angle of the downhole
instrumentation at intervals along the well path trajectory. Other
types of sensors may be included in the first and second sensor
packages 906, 908. For example, one or more magnetic sensors such
as any of the magnetic sensors described herein (e.g., with respect
to FIGS. 5-8) may be included. Generally, the first and second
sensor packages 906, 908 may comprise any sensor packages capable
of providing directional measurements such as inclination, azimuth,
tool face angle or other parameters for determining the orientation
of the drill string 900, components thereof, and/or the wellbore
904.
[0126] In some embodiments, the drill string 900 may further
include one or more bend sensors such as any of the bend sensors
described herein (e.g., the optical and mechanical bend sensors
described with respect to FIG. 2) may be included. Such bend
sensors may be used to in conjunction with the bend calculation
made using the measurements from the first and second sensor
packages, for example. In some embodiments, the calculation from a
separate bend sensor may be combined or compared with the bend
calculation made using the measurements from the first and second
sensor packages to provide a more accurate determination of the
bend. As such, the additional data provided by the bend calculation
can provide measurement redundancy which can be used to improve
and/or provide a quality check on the estimate of the bend.
[0127] In certain embodiments, the first and second sensor packages
906, 908 are spaced apart from one another by a non-zero distance
.DELTA. along an axis 930. The distance .DELTA. is about 40 feet in
certain embodiments. The distance .DELTA. in other embodiments is
about 70 feet. In certain embodiments, the second sensor package
908 and the first sensor package 906 are spaced apart from one
another by a distance .DELTA. in a range between about 40 feet to
about 70 feet. Other values of .DELTA. are also compatible with
embodiments described herein. In some embodiments, the drill string
900 or the logging string includes a sufficient number of sensors
and adequate spacings between the first acceleration sensor 906 and
the second acceleration sensor 908 to perform the methods described
herein.
[0128] In certain embodiments, the rotary steerable tool 912
comprises a housing 926 containing at least one of the first and
second sensor packages 906, 908 or upon which at least one of the
first and second sensor packages 906, 908 is mounted. As
schematically illustrated by FIG. 9, the housing 926 of certain
embodiments contains the first sensor package 906 while the second
acceleration sensor package 908 is attached on or within the
elongate portion 910. The rotary steerable tool 912 of certain
embodiments further comprises a drill bit 913 providing a drilling
function. In certain embodiments, the downhole portion 902 further
comprises portions such as collars or extensions 928, which contact
an inner surface of the wellbore 904 to position the housing 926
substantially collinearly with the wellbore 904.
[0129] The controller (not shown) of certain embodiments is
configured to calculate an amount of bend .beta. between the first
portion 914 and the second portion 918 in response to the first
measurement from the first sensor package 906 and the second
measurement from the second sensor package 908. While not shown
with respect to FIG. 9, the downhole portion 902 may further
comprise an actuator configured to generate an amount of bend of
the downhole portion 902 at least between the first portion 914 and
the second portion 918. In certain embodiments, for example, the
actuator is configured to bend a shaft passing through the rotary
steerable portion 912 so as to_change the direction of the drill
bit 913 of the rotary steerable tool 912, thereby creating a
curvature in the wellbore 904 as the rotary steerable tool 912
advances. The controller may be further configured to compare the
calculated amount of bend .beta. to a target amount of bend and to
calculate a bend adjustment amount. For example, the dotted lines
905 in FIG. 9 show an example desired trajectory for the wellbore
904 having a desired or target well curvature or bend .beta..sub.t.
In such embodiments, the actuator can be configured to adjust the
generated amount of bend between the first portion 914 and the
second portion 918 by the bend adjustment amount. Additionally,
according to certain embodiments, the generated amount of bend
between the first portion 914 and the second portion 918 following
adjustment by the actuator is substantially equal to the target
amount of bend .beta..sub.t. As a result, drill strings described
herein can generally detect an amount of bend and adjust course to
generate a desired amount of bend.
[0130] FIG. 10 schematically illustrates an example control loop
931 for implementing the calculating and adjusting of the curvature
.beta. between first and second portions 914, 918 of a drill string
900. The control loop 931 of certain embodiments comprises one or
more modules which provide various functions for the control loop
931. These modules can be constructed using hardware, software, or
both. For example, one or more of the modules may be software
modules implemented in the controller in certain embodiments. In
some embodiments, one or more of the modules may be physically
implemented in the downhole portion 902. In other embodiments, the
one or more modules may be positioned above ground and be in
communication with the downhole portion. FIG. 10 further
schematically illustrates an example drill string 900 in accordance
with certain embodiments described herein. As shown, module 932
also receives, from the first sensor package 906, signals 936
indicative of a first measurement of an orientation of the first
portion 914 of the drill string 900 relative to the Earth. Module
932 also receives, from the second sensor package 908, signals 934
indicative of a second measurement of an orientation of the second
portion 918 of the drill string 900 relative to the Earth.
[0131] Module 932 can further be configured to calculate an amount
of bend 938 between the first portion 914 and the second portion
918 in response to the first measurement and the second
measurement. The calculated amount of bend 938 can be compared by
module 942 to a target amount of bend 940. In one embodiment, the
modules of the control loop 931 are implemented in the downhole
portion 902 and the target amount of bend 940 is received from the
surface. For example, in some embodiments, the calculated amount of
bend 938 may be subtracted from the target amount of bend 940 by
module 942. A bend adjustment amount 944 (e.g., the difference
between the target amount of bend 940 and the calculated amount of
bend 938) may be generated by module 942 in response to the
comparison.
[0132] The bend adjustment amount 944 may be received by module
946, and module 946 may generate an actuator command 948. The
actuator command 948 is received by the actuator 950 and is
configured to cause the actuator 950 to adjust the generated amount
of bend between the first portion 914 and the second portion 918 by
the bend adjustment amount 944. For example, the actuator 950 may
bend the shaft of the rotary steerable portion 912 so as to steer
the drill bit 913, thereby adjust the generated amount of wellbore
904 curvature as the drill string 900 progresses during drilling.
In one embodiment, the actuator 950 comprises a hydraulic actuator
and the actuator command 948 comprises an electrical signal which
causes the hydraulic actuation mechanism in the actuator 950 to
activate. According to certain embodiments, the generated amount of
bend between the first portion 914 and the second portion 918
following adjustment by the actuator 950 is substantially equal to
the target amount of bend 940. As a result, in certain embodiments,
the drill string 910 described herein can generally detect an
amount of bend and adjust course to generate a desired amount of
bend 940. In certain embodiments, one or more of the modules (e.g.,
the modules 932, 942, 946) of the control loop 931, either
individually or in combination, include components such as a
filtering network, components configured amplify and/or attenuate
the signals (e.g., the signals 934, 936, 938, 940, 944) in the
control loop 931, etc. Additionally, one or more of the modules,
either individually or in combination, can include a control
mechanism, such as some form of an adaptive control mechanism
configured to control the drilling process and help maintain a
generally stable control loop 931.
[0133] In general, the controller may be configured to programmed
or otherwise capable of performing the functions of one or more of
the modules (e.g., the modules 932, 942, 946). Additionally, in
certain embodiments, one or more of the calculated amount of bend
938, target amount of bend 940, bend adjustment amount 944, and
actuator command 948 comprise electrical signals representative of
the respective values or commands.
[0134] The controller (not shown) may be at the surface and coupled
to the downhole portion 902 by the elongate portion 910. In certain
other embodiments, the controller comprises a microprocessor
adapted to perform the method described herein for determining the
bend. In certain embodiments, the controller is further adapted to
determine the inclination, azimuth, and/or highside/toolface angle
of the tool or the trajectory of the downhole portion 102 within
the wellbore 904. In certain embodiments, the controller further
comprises a memory subsystem adapted to store at least a portion of
the data obtained from the various sensors. The controller can
comprise hardware, software, or a combination of both hardware and
software. In certain embodiments, the controller comprises a
standard personal computer.
[0135] In certain embodiments, at least a portion of the controller
is located within the downhole portion 902. In certain other
embodiments, at least a portion of the controller is located at the
surface and is communicatively coupled to the downhole portion 102
within the wellbore 904. In certain embodiments in which the
downhole portion 902 is part of a wellbore drilling system capable
of measurement while drilling (MWD) or logging while drilling
(LWD), signals from the downhole portion 902 are transmitted by mud
pulse telemetry or electromagnetic (EM) telemetry. In certain
embodiments where at least a portion of the controller is located
at the surface, the controller is coupled to the downhole portion
902 within the wellbore 904 by a wire or cable extending along the
elongate portion 910. In certain such embodiments, the elongate
portion 910 may comprise signal conduits through which signals are
transmitted from the various sensors within the downhole portion
902 to the controller. In certain embodiments in which the
controller is adapted to generate control signals for the various
components of the downhole portion 902, the elongate portion 910 is
adapted to transmit the control signals from the controller to the
downhole portion 902. For example, the controller may generate
control signals for the actuator so as to generate an amount of
bend of the downhole portion 902 at least between the first portion
914 and the second portion 918 as described herein.
[0136] In certain embodiments, the controller is adapted to perform
a post-processing analysis of the data obtained from the various
sensors of the downhole portion 902. In certain such
post-processing embodiments, data is obtained and saved from the
various sensors of the drill string 900 as the downhole portion 902
travels within the wellbore 904, and the saved data are later
analyzed to determine information regarding the downhole portion
902. The saved data obtained from the various sensors
advantageously may include time reference information (e.g., time
tagging).
[0137] In certain other embodiments, the controller provides a
real-time processing analysis of the signals or data obtained from
the various sensors of the downhole portion 902. In certain such
real-time processing embodiments, data obtained from the various
sensors of the downhole portion 902 are analyzed while the downhole
portion 902 travels within the wellbore 904. In certain
embodiments, at least a portion of the data obtained from the
various sensors is saved in memory for analysis by the controller.
The controller of certain such embodiments comprises sufficient
data processing and data storage capacity to perform the real-time
analysis.
[0138] 1. Example Method Utilizing Multiple Measurements to
Calculate Bend
[0139] FIG. 11 is a directional diagram illustrating the relative
orientation between a first position 916 in the wellbore 904 and a
second position 920 in the wellbore 904 in a portion of the
wellbore having a curvature in accordance with certain embodiments
described herein. For clarity of illustration, a drill string is
not shown with respect to FIG. 11. However, the wellbore 904 shown
in FIG. 11 and associated curvature may have been generated by one
of the drill strings described herein. For example, the rotary
steerable portion 912 of the drill string 900 may be used to create
the curvature of the well (or dog-leg section) in generally any
direction (e.g., a combination of inclination and azimuth change).
One position (also referred to herein as a "station") in the drill
string 900 and a next position in the drill string 900 (e.g., the
first position 916 and the second position 920) are denoted in FIG.
11 as Station k and Station k+1, respectively. The relative
orientation of Station k and Station k+1 may be defined by two
direction vectors, denoted t.sub.k and t.sub.k+1. FIG. 11 shows the
inclination and azimuth angle A.sub.k, I.sub.k at Station k and
A.sub.k+1, I.sub.k+1, at Station k+1, respectively. The vectors may
be given by the following equations:
t _ k = [ sin I k cos A k sin I k sin A k cos I k ] ( Eq . 78 ) t _
k + 1 = [ sin I k + 1 cos A k + 1 sin I k + 1 sin A k + 1 cos I k +
1 ] , ( Eq . 79 ) ##EQU00029##
where I.sub.k, I.sub.k+1 and A.sub.k, A.sub.k+1 represent the
inclination and azimuth angles at locations k and k+1
respectively.
[0140] A measure of the bend in the well trajectory between these
two locations may be determined by taking the dot product of the
two vectors t.sub.k and t.sub.k+1, yielding the following equation
for the well curvature .beta. between these two locations:
cos .beta.=cos I.sub.k cos I.sub.k+1+sin I.sub.k sin I.sub.k+1
cos(A.sub.k+1-A.sub.k). (Eq. 80)
[0141] For relatively small angles, as encountered typically during
the drilling process, an estimate of the bend in the well
trajectory (.beta.) between successive locations k and k+1 can be
given by the following equation:
.beta. = 2 sin - 1 { [ sin 2 ( I k + 1 - I k 2 ) + sin I k sin I k
+ 1 sin 2 ( A k + 1 - A k 2 ) ] 1 2 } ( Eq . 81 ) ##EQU00030##
Equation 81, which may be derived directly from Equation 80, is
disclosed in S. J. Sawaryn and J. L. Thorogood, "A compendium of
directional calculations based on the minimum curvature method",
SPE Drilling & Completion, March 2005.
[0142] This information provides feedback between the achieved and
desired well curvature and may be used to correct the trajectory to
the desired path as the well is being created. The estimates of
tool-face, inclination and azimuth obtained using the first and
second sensor packages 906, 908 (e.g., from first sensor package
906 located on or within a rotary steerable system 912 and a second
sensor package 908 located on or within an MWD instrumentation pack
located on the elongate portion 910 of the drill string 900) are
received by a controller or processor in which the achieved
curvature of the well .beta. (the dog-leg angle) is calculated
using the equations described above. A comparison (e.g., the
difference) between the target (which can also be referred to as
"demanded") and achieved dog-leg trajectory can be calculated. A
control signal may be generated as a function of the dog-leg
difference and passed to the actuator of the drill string 900
(e.g., an actuator 950 of the rotary steerable system 912) to
generate the target bend in the shaft passing through the rotary
steerable system 912. Examples of such a process are further
described herein with respect to the drill string 900 of FIG. 9,
the control loop 931 of FIG. 10, and the method 1200 of FIG. 12,
for example.
[0143] FIG. 12 is a flowchart of an example method 1200 of
controlling a drill string 900 according to a calculated amount of
bend in accordance with certain embodiments described herein. While
the method 1200 is described herein by reference to the drill
string 900 schematically illustrated by FIG. 9 and by FIG. 10,
other drill strings are also compatible with embodiments described
herein.
[0144] In certain embodiments, the method 1200 at operational block
1202 comprises receiving one or more first signals from a first
sensor package 906 mounted in a first portion 914 of the drill
string 900 at a first position 916 within a wellbore 904. The first
signals of certain embodiments are indicative of an orientation of
the first portion 914 of the drill string 900 relative to the
Earth. The method 1200 at operational block 1204 further comprises
receiving one or more second signals from a second sensor package
908 mounted in a second portion 918 of the drill string 900 at a
second position 920 within the wellbore 904. The second signals of
certain embodiments are indicative of an orientation of the second
portion 918 of the drill string 900 relative to the Earth, and the
drill string 900 can be adapted to bend between the first portion
914 and the second portion 18.
[0145] At operational block 1206, the method 1200 further comprises
calculating a first amount of bend between the first portion 914
and the second portion 918 in response to the first signals and the
second signals. In certain embodiments, the method 1200 further
comprises comparing the first amount of bend to a target amount of
bend. The comparing comprises calculating a difference between the
first amount of bend and the target amount of bend in some
embodiments. The method 1200 may further include calculating a bend
adjustment amount in response to the comparison.
[0146] In certain embodiments, the method 1200 may further
comprising adjusting the first amount of bend between the first
portion 914 and the second portion 918 by the bend adjustment
amount, resulting in a second amount of bend between the first
portion 914 and the second portion 918. The second amount of bend
between the first portion and the second portion can be
substantially equal to the target amount of bend, for example.
[0147] In certain embodiments, the first signals are indicative of
one or more of the inclination, azimuth and high-side tool-face
angle of the first portion 914 of the downhole portion 902 and the
second signals are indicative of the inclination, azimuth and
high-side tool-face angle of the second portion 918 of the downhole
portion 902.
[0148] The first sensor package 906 of certain embodiments
comprises at least one accelerometer sensor and at least one
magnetic sensor. Likewise, the second sensor package 908 can
comprise at least one accelerometer sensor and at least one
magnetic sensor. In some embodiments, the first sensor package 906
comprises at least one accelerometer sensor and at least one
gyroscopic sensor and the second sensor package 908 comprises at
least one accelerometer sensor and at least one gyroscopic sensor.
In some embodiments, the first and second sensor packages are
spaced apart from one another by a non-zero distance. The non-zero
distance of certain embodiments is in a range between about 40 feet
to about 70 feet.
[0149] Certain embodiments described herein provide a measure of
the misalignment of multiple acceleration sensors mounted in the
downhole portion of a drill string. In certain embodiments, the
measure of the misalignment corresponds to a measure of sag which
can be used to provide an improved estimate of the inclination of
the downhole portion of the drill string and/or the wellbore. In
certain embodiments, the measurements are based entirely on the use
of down-hole sensors, and are independent of any surface
measurement devices which are subject to error in the detection of
true down-hole location and movement. In order to provide an
improved determination of the trajectory and position of the
downhole portion of the drill string, certain embodiments described
herein may be used in combination with a system capable of
determining the depth, velocity, or both, of the downhole portion.
Examples of such systems are described in U.S. Pat. No. 7,350,410,
entitled "System and Method for Measurements of Depth and Velocity
of Instrumentation Within a Wellbore," and U.S. patent application
Ser. No. 11/866,213, entitled "System and Method For Measuring
Depth and Velocity of Instrumentation Within a Wellbore Using a
Bendable Tool," each of which is incorporated in its entirety by
reference herein.
[0150] In certain embodiments, a processing algorithm based on a
mathematical model of wellbore curvature (dogleg), inclination, and
misalignment of sensors mounted in the wellbore is used to provide
an improved estimate of the inclination of the downhole portion of
a drill string and/or wellbore. The measurements generated by the
multiple accelerometers in certain embodiments can be compared with
estimates of the same quantities derived from the states of the
model. These measurement differences can form the inputs to the
processing algorithm which effectively cause the outputs of the
model to be driven into coincidence with the measurements, thus
correcting the outputs of the model. In certain embodiments,
estimates of the misalignment error are based on measurements from
each location as the drill string traverses the path of the
wellbore. The measurement accuracy in certain such embodiments is
enhanced by the use of the independent measurements of well
curvature or inclination, obtained in the vicinity of the sensor
locations, thereby increasing the accuracy and reliability of the
estimation algorithm.
[0151] Certain embodiments described herein provide an estimate of
the magnetic interference incident upon multiple magnetic sensors
mounted within a non-magnetic region of the downhole portion of a
drilling system. In certain such embodiments, the interference
components result from magnetic fields incident upon the sensors
which are not from the magnetic field of the Earth. Certain
embodiments utilize the magnetic measurements to determine an axial
interference resulting from one or more magnetic portions of the
downhole portion and to provide an improved estimate of the
azimuthal orientation of the downhole portion with respect to the
magnetic field of the Earth. Certain embodiments utilize a
processing algorithm based on a mathematical model of magnetic
azimuth mid-way between two magnetic sensors and drill string pole
strength. The measurements generated by the two magnetic sensors in
certain embodiments can be compared with estimates of the same
quantities derived from the states of the model. These measurement
differences can form the inputs to the processing algorithm which
effectively cause the outputs of the model to be driven into
coincidence with the measurements, thus correcting the outputs of
the model.
[0152] In certain embodiments, the magnetic measurements are used
to detect magnetic fields from sources other than magnetic regions
in the downhole portion of the drill string, such as, for example,
from magnetic regions in a second wellbore. In certain such
embodiments, the magnetic measurements are used to detect the
location of the second wellbore relative to the first wellbore.
[0153] Various embodiments have been described above. Although
described with reference to these specific embodiments, the
descriptions are intended to be illustrative and are not intended
to be limiting. Various modifications and applications may occur to
those skilled in the art without departing from the true spirit and
scope of the invention as defined in the appended claims.
* * * * *