DETERMINING CONTINUOUS INCLINATION ANGLE

Abstract

A method for determining an inclination of a wellbore can include receiving sensor data at a rig controller, wherein the sensor data comprises sensor data from a radial magnetometer, a tangential magnetometer, a radial accelerometer, and a tangential accelerometer, determining, via the rig controller, a magnetic toolface angle of a BHA based on the sensor data from the radial magnetometer and the tangential magnetometer, converting, via the rig controller, the magnetic toolface angle to a gravity toolface of the BHA based on the sensor data from the radial accelerometer and the tangential accelerometer; and determining, via the rig controller, an inclination angle based on the gravity toolface, and the sensor data from the radial magnetometer and the tangential magnetometer and determining an azimuth angle based on mapping of the earth's magnetic field vector, the inclination angle, and a high side offset angle.

Description

FIELD OF THE DISCLOSURE

The present invention relates, in general, to the field of drilling and processing of wells. More particularly, present embodiments relate to a system and method for calculating a continuous inclination of a bottom hole assembly (BHA) or other downhole tool in a wellbore during or after subterranean operations.

BACKGROUND

At periodic intervals (e.g., 50′, 100′, or 150′ intervals) along drilled portions of a wellbore, the drilling system may perform surveys of the wellbore to establish the actual measured depth of the wellbore, a true vertical depth of the wellbore, an inclination of the wellbore, and various other measurements or sensor readings at each survey point. The survey data at each of the survey points along the wellbore is normally collected using precisely calibrated instrumentation that minimizes errors in the collected survey data.

However, the precisely calibrated instrumentation tends to be expensive and the process of collecting survey data at a survey point also can require a significant amount of rig time. This is normally why the survey data is collected at the periodic intervals (e.g., 50′ [50 feet], 100′, or 150′ intervals) along the drilled portions of a wellbore and not continuously along the wellbore.

The survey tools provide survey data from high-grade accelerometer, gyroscope, and magnetometer sensors that have been pre calibrated for a wide range of temperatures. To make a continuous well trajectory available, the found values can be interpolated using a minimum quadrature method or similar approach. This approach assumes the same trajectory curvature at all intermediate points between two successive stations, but this underlying assumption is not necessarily accurate. On the other hand, due to the high cost of such high-grade sensors and their all-temperature calibration, the common M/LWD tools operate low-grade (usually micro electro-mechanical systems MEMS) accelerometers, gyroscopes, and magnetometers that have not been pre-calibrated for various temperatures.

As used herein, “continuous” refers to periodic intervals that are less than the periodic intervals for the survey points. Such as, “continuous” may refer to measurements or calculations that may be performed for 20′ intervals, 15′ intervals, 14′ intervals, 13′ intervals, 12′ intervals, 11′ intervals, 10′ intervals, 9′ intervals, 8′ intervals, 7′ intervals, 6′ intervals, 5′ intervals, 4′ intervals, 3′ intervals, 2′ intervals, 1′ intervals, or less than 1′ intervals. “Continuous” is not required to be the same interval since it can refer to a varied interval distance.

The standard continuous inclination (CI) log detection can require readings from a couple of magnetometers (m_r and m_t) and radial, tangential, and axial accelerometers a_r, a_τ, a_τ, all mounted on the same tool. The magnetometers are used to detect a magnetic toolface φ_m, then the ‘horizontal’ accelerometers (a_r, a_τ) can be used to convert the magnetic toolface φ_m into a gravity toolface φ_g, and since the well is gravity oriented, the axial accelerometer a_τ can be used to establish an estimated inclination angle φ^ci(md_j) between the survey points.

However, at vertical and subvertical wells this approach can fail to give accurate CI log detection due to a significant impact of axial accelerometer noise. As way of illustration, the inclination angle detection error δφ^ci can be shown as

${\mathrm{\delta \phi }}^{ci}\approx \frac{\delta a_z}{\sin \left({\phi }^{ci}\right)},$

where δα_τ is the axial accelerometer noise and φ^ci is the inclination angle. As can be seen, the detection error δφ^ci increases when the inclination angle φ^ci approaches zero degree (e.g., a substantially vertical wellbore portion).

Logging-while-drilling (LWD) or Measuring-while-drilling (MWD) tools are widely used to collect measurements or sensor readings along the wellbore, even between the survey points. However, the sensors in the LWD and MWD tools may not be as precisely calibrated as the survey tools used to collect the survey data at the periodic survey points. The sensor data from these sensors may be less precise or noisier than the survey tools but this sensor data may be collected at shorter intervals along the wellbore than the survey points. Therefore, improvements in calculating continuous inclination are continually needed.

SUMMARY

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

A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. One general aspect includes a method for determining an inclination of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ); determining, via the rig controller, a magnetic toolface angle (φ_m) of the logging tool based on the data from the radial magnetometer (b_r) and the tangential magnetometer (b_τ); converting, via the rig controller, the magnetic toolface angle (φ_m) to a gravity toolface (φ_g) of the logging tool based on the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ); and determining, via the rig controller, an inclination angle based on the gravity toolface, and the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ). Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

One general aspect includes a method for determining an inclination of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ); determining, via the rig controller, an inclination angle profile based on a gravity toolface of the BHA, and the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ), wherein the inclination angle profile is for a portion of the wellbore with an inclination angle of less than or equal to 10 degrees; and determining, via the rig controller, a dogleg severity profile based on the inclination angle profile, wherein the dogleg severity of the dogleg severity profile is between +10 degrees/100 feet and −10 degrees/100 feet for the portion of the wellbore.

One general aspect includes determining. The method also includes a method for determining an azimuth angle of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ); determining, via the rig controller, a magnetic toolface angle (φ_m) of the logging tool based on the data from the radial magnetometer (b_r) and the tangential magnetometer (b_τ); converting, via the rig controller, the magnetic toolface angle (φ_m) to a gravity toolface angle (φ_g) of the logging tool based on the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ) or the data from the axial accelerometer (a_ζ); determining, via the rig controller, an inclination angle (φ^ci) and a high side offset angle (φ^hs) based on the gravity toolface angle (φ_g), and the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ); and determining, via the rig controller, an azimuth angle (φ^ca) based on mapping of the earth's magnetic field vector (m_x, m_y, m_z), the inclination angle (φ^ci) and a high side offset angle (φ^hs). Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of present embodiments will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

FIG. 1A is a representative simplified front view of a rig being utilized for a subterranean operation, in accordance with certain embodiments;

FIG. 1B is a representative partial cross-sectional view of a wellbore being drilled by a BHA that is inclined from vertical, in accordance with certain embodiments;

FIG. 2A is representative plot of an estimated true vertical depth of a wellbore along a portion of the wellbore versus a measured depth, in accordance with certain embodiments;

FIG. 2B is representative plot of two estimated continuous inclination profiles along a portion of the wellbore, in accordance with certain embodiments;

FIG. 2C is representative plot of two estimated build dogleg severity profiles along a portion of the wellbore, in accordance with certain embodiments;

FIGS. 3 and 4 are representative partial cross-sectional views along line 3-3, as indicated in FIG. 1A, of a logging tool in a wellbore, in accordance with certain embodiments;

FIG. 5 is a representative functional block diagram of a rig controller including some peripherals, in accordance with certain embodiments;

FIG. 6 is a representative flow diagram of a method for determining a continuous inclination of a wellbore, in accordance with certain embodiments;

FIG. 7 is a spacial representative of the well trajectory vector e_ζ and the Earth's magnetic vector field m in the geographic/gravity coordinate system (X, Y, Z), in accordance with certain embodiments;

FIG. 8 is a spacial representative of the derivative vectors e_⊥, m_⊥ in the tool coordinate system (Tx, Ty, Tz), in accordance with certain embodiments;

FIGS. 9A-9D are representative of three axial rotations from an original orientation used to transform a geographic/gravity coordinate system (X, Y, Z) to a tool coordinate system (Tr, Tτ, Tz), with axis Z aligned with gravity and axis Tz aligned with a longitudinal tool axis, in accordance with certain embodiments.

DETAILED DESCRIPTION

The following description in combination with the figures is provided to assist in understanding the teachings disclosed herein. The following discussion will focus on specific implementations and embodiments of the teachings. This focus is provided to assist in describing the teachings and should not be interpreted as a limitation on the scope or applicability of the teachings.

As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of features is not necessarily limited only to those features but may include other features not expressly listed or inherent to such process, method, article, or apparatus. Further, unless expressly stated to the contrary, “or” refers to an inclusive-or and not to an exclusive-or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

The use of “a” or “an” is employed to describe elements and components described herein. This is done merely for convenience and to give a general sense of the scope of the invention. This description should be read to include one or at least one and the singular also includes the plural, or vice versa, unless it is clear that it is meant otherwise.

The use of the word “about”, “approximately”, “generally”, or “substantially” is intended to mean that a value of a parameter is close to a stated value or position. However, minor differences may prevent the values or positions from being exactly as stated. Thus, differences of up to ten percent (10%) for the value are reasonable differences from the ideal goal of exactly as described. A significant difference can be when the difference is greater than ten percent (10%).

As used herein, “tubular” refers to an elongated cylindrical tube and can include any of the tubulars manipulated around a rig, such as tubular segments, tubular stands, tubulars, and tubular string. Therefore, in this disclosure, “tubular” is synonymous with “tubular segment,” “tubular stand,” and “tubular string,” as well as “pipe,” “pipe segment,” “pipe stand,” “pipe string,” “casing,” “casing segment,” or “casing string.”

It should be noted that a geographic/gravity coordinate system X-Y-Z is indicated in FIG. 1A, where the X-Y-Z coordinate axes are relative to the rig floor 16. The rig floor 16 forms an X-Y plane with the Z axis being substantially perpendicular with the rig floor 16. As used herein, “horizontal,” “horizontal position,” or “horizontal orientation” refers to a position that is substantially parallel with the X-Y plane. As used herein, “vertical,” “vertical position,” or “vertical orientation” refers to a position that is substantially perpendicular relative to the X-Y plane or substantially parallel with the Z axis where the Z-axis is parallel to the direction of gravity. In particular, the X-axis is aligned with geographic North, the Y-axis is aligned with geographic East, and the Z-axis is aligned with a gravity force vector.

It should be noted that a tool coordinate system Tx-Ty-Tz is indicated in FIGS. 3, 4, and 8, where the Tx-Ty-Tz coordinate axes are relative to the logging tool 100. The Tz axis is a center longitudinal axis of the logging tool 100 with the axes Tx and Ty forming a Tx-Ty plane with the Tz axis being substantially perpendicular with the Tx-Ty plane. The Tx and Ty axes are substantially perpendicular to each other.

FIG. 1A is a representative partial cross-sectional view of a rig 10 that can be used to drill a wellbore 15 in an earthen formation 8. FIG. 1A shows a land-based rig, but the principles of this disclosure can equally apply to off-shore rigs, as well, where “off-shore” refers to a rig with water between the rig floor and the earth surface 6. The rig 10 can include a top drive 18 with a drawworks 44, sheaves 19, traveling block 28, anchor 47, and reel 48 used to raise or lower the top drive 18. A derrick 14 extending from the rig floor 16, can provide the structural support of the rig equipment for performing subterranean operations (e.g., drilling, treating, completing, producing, testing, etc.). The rig 10 can be used to extend a wellbore 15 through the earthen formation 8 by using a tubular string 58 having a Bottom Hole Assembly (BHA) 60 at its lower end. The BHA 60 can include a drill bit 68 and multiple drill collars 62, with one or more of the drill collars including a logging tool 100 for Logging While Drilling (LWD) or Measuring While Drilling (MWD) operations. During drilling operations, drilling mud can be pumped from the surface 6 into the tubular string 58 (e.g., via pumps 84 supplying mud to the top drive 18) to cool and lubricate the drill bit 68 and to transport cuttings to the surface via an annulus 17 between the tubular string 58 and the wellbore 15.

The returned mud can be directed to the mud pit 88 through the flow line 81 and the shaker 80. A fluid treatment 82 can inject additives as desired to the mud to condition the mud appropriately for the current well activities and possibly future well activities as the mud is being pumped to the mud pit 88. The pump 84 can pull mud from the mud pit 88 and drive it to the top drive 18 to continue circulation of the mud through the tubular string 58.

The tubular string 58 can extend into the wellbore 15, with the wellbore 15 extending through the surface 6 into the subterranean formation 8. With a segmented tubular string 58, when tripping the tubular string 58 into the wellbore 15, tubulars 54 are sequentially added to the tubular string 58 to extend the length of the tubular string 58 into the earthen formation 8. With the tubular string 58 is a wireline or coiled tubing, the tubular string 58 can be uncoiled from a spool and extended into the wellbore 15. With the segmented tubular string 58, when tripping the tubular string 58 out of the wellbore 15, tubulars 54 are sequentially removed from the tubular string 58 to reduce the length of the tubular string 58 extending into the earthen formation 8. With a wireline or coiled tubing tubular string 58, the tubular string 58 can be coiled onto a spool when being pulled out of the wellbore 15.

The wellbore 15 can have casing string 70 installed in the wellbore 15 and extending down to the casing shoe 72. The portion of the wellbore 15 with the casing string 70 installed, can be referred to as a cased wellbore. The portion of the wellbore 15 below the shoe 72, without casing, can be referred to as an “uncased” or “open hole” wellbore.

A rig controller 250 can be used to control the rig 10 operations including controlling various rig equipment, such as a pipe handle, the top drive 18, an iron roughneck, fingerboard equipment, imaging systems, or rig power systems 26. The rig controller 250 can control the rig equipment autonomously (e.g., without periodic operator interaction), semi-autonomously (e.g., with limited operator interaction such as initiating a subterranean operation, adjusting parameters during the operation, etc.), or manually (e.g., with the operator interactively controlling the rig equipment via remote control interfaces to perform the subterranean operation).

The rig controller 250 can include one or more processors with one or more of the processors distributed about the rig 10, such as in an operator's control hut, in pipe handler, in an iron roughneck, at various locations on the rig floor 16 or the derrick 14 or the platform 12, at a remote location off of the rig 10, at downhole locations, etc. It should be understood that any of these processors can perform control or calculations locally or can communicate to a remotely located processor for performing the control or calculations. Each of the processors can be communicatively coupled to a non-transitory memory, which can include instructions for the respective processor to read and execute to implement the desired control functions or other methods described in this disclosure. These processors can be coupled via a wired or wireless network.

The rig controller 250 can collect data from various data sources around the rig and downhole (e.g., sensors, user input, local rig reports, etc.) and from remote data sources (e.g., suppliers, manufacturers, transporters, company men, remote rig reports, etc.) to monitor and facilitate the execution of the subterranean operation.

During the subterranean operation, such as drilling, various logging operations are generally performed to collect and store sensor data for later processing to provide visualization to parameters and characteristics of the wellbore and its surroundings. The processing can be performed by the rig controller 250 during the subterranean operation or after the subterranean operation is complete. A logging tool 100 can be included in the BHA 60 (or otherwise included in the tubular string 58) for performing logging or measuring operations at various times during the operation, or during the operation. The logging tool 100 can have a center longitudinal axis Tz, which can also correspond to a longitudinal axis of the BHA 60.

As used herein, “gravity toolface” refers to the high side of the logging tool 100 or the tubular string 58 or the BHA 60. As used herein, “gravity toolface azimuth” refers to an azimuth (or angle) that the gravity toolface is rotated from a top center of the wellbore 15 relative to gravity. As used herein, “magnetic toolface angle” is the angle, or azimuth, of the logging tool in the wellbore 15 measured clockwise relative to magnetic north and in the plane perpendicular to the wellbore axis; the north, east, south and west directions relative to the wellbore axis have magnetic toolface angles of 0°, 90°, 180° and 270°, respectively.

The current disclosure provides one or more solutions for supplying sensor data from within the wellbore 15 (such as during drilling of the wellbore 15 or after the wellbore 15 is drilled) and calculating a continuous inclination angle along at least a portion of the wellbore 15 from a first measured depth to a second measured depth. The wellbore 15 is shown with a plurality of segments (e.g., segments 170 through 186) along the length of the wellbore 15. These segments progress through the wellbore 15 from a vertically oriented segment 170, through a sequence of segments 172 through 184 with increasing inclination from the vertical portion, to the substantially horizontally oriented segment 186.

The methods and systems described in this disclosure can be used to determine the continuous inclination along any (or all) portions of the wellbore 15. However, the methods and systems described in this disclosure are particularly adept at determining the continuous inclination along portions of the wellbore 15 that are near vertical inclination, such as with an inclination angle from a vertical axis 50 of the rig 10 of less than 15 degrees. The vertical axis 50 can generally be seen as being substantially parallel with the direction of gravity. Therefore, the inclination angle can be seen as the angle between the longitudinal axis Tz of the logging tool 100 at a measured depth of the wellbore 15 and the vertical axis 50.

FIG. 1B is a representative partial cross-sectional view of a wellbore 15 being drilled by a BHA 60 that is inclined from vertical, in accordance with certain embodiments. Rotating the drill bit 68 (arrows 90) can extend the bottom 74 of the wellbore 15 further into the subterranean formation 8. The well plan for the wellbore 15 establishes a desired trajectory of the wellbore 15 to reach the desired production zones. Sensor data (e.g., from magnetometers, accelerometers, gyroscopes, etc.) can be collected along the wellbore 15 via a logging tool 100 in addition to survey data collected at periodic intervals along the wellbore. The sensor data from the logging tool 100 can be used to determine the actual wellbore trajectory (e.g., between the survey points) by calculating the continuous inclination from the logging tool 100 sensor data collected between the survey points.

In FIG. 1B, the drill bit has advanced to a measured depth MD of the wellbore bottom 74. The sensor data collected from the logging tool 100 (or other sensors 40) can be used to calculate the inclination angle A2 for the measured depth MD, where the inclination angle A2 is the angle between the longitudinal axis Tz of the logging tool 100 at a measured depth MD and the vertical axis 50.

FIG. 2A is a representative plot of an estimated true vertical depth of a wellbore 15 along a portion of the wellbore versus a measured depth, in accordance with certain embodiments. The plot 130 shows survey points 136 and an estimated true vertical depth profile 134 plotted as true vertical depth (TVD) 132 versus measured depth (MD) 133. It can be desirable that the estimated true vertical depth profile 134 intersects each of the survey points 136. However, this is not necessarily the case for most wellbores. For example, the actual locations of each survey point 136 can deviate from the estimated inclination profile 134.

FIG. 2B is a representative plot of two estimated continuous inclination profiles 154, 155 along a portion of the wellbore 15, in accordance with certain embodiments. The plot 150 shows survey points 156 and two estimated continuous inclination profiles 154, 155 plotted as inclination angle (degrees) 152 versus measured depth (MD) 153. The profiles 154, 155 show an inclination ranging from substantially “0” zero degrees at around MD of 10600 feet to substantially 25 degrees. Of particular interest is the portion 151 of the wellbore 15 extending from a measured depth (MD) 153 of approximately 10600 feet to 10800 feet.

The inclination angle simulation that produces the profile 154 utilizes logging tool 100 sensor data from an axial accelerometer (a_τ) and a gravity toolface value to determine the inclination angle at the desired measure depth (MD). By running the simulation along the portion 151, the simulation can plot the profile 154 calculated based on the axial accelerometer (a_τ) sensor data. As can be seen, the profile 154 is noisy from “0” zero degrees inclination angle A2 at around a MD of 10600 feet to substantially 10 degrees inclination angle A2 at around a MD of 10800 feet.

The inclination angle simulation that produces the profile 155 utilizes sensor data from radial and tangential accelerometers a_r, a_τ, and a gravity toolface value to determine the inclination angle at the desired measure depth (MD). By running the simulation along the portion 151, the simulation can plot the profile 155 calculated based on the radial and tangential accelerometer a_r, a_τ, sensor data. As can be seen, the profile 155 is less noisy when compared to the profile 154 from “0” zero degrees inclination angle A2 at around a MD of 10600 feet to substantially 10 degrees inclination angle A2 at around a MD of 10800 feet. Unlike the profile 155, the profile 154 deviates substantially from an estimated inclination profile between survey points at the lower inclination angles.

FIG. 2C is representative plot of two estimated build dogleg severity profiles 164, 165 along a portion of the wellbore 15, in accordance with certain embodiments. The profiles 164, 165 are generally derivatives of the profiles 154, 155, respectively, with the profiles 164, 165 plotting a rate of change of the inclination per a length of the wellbore 15.

The build dogleg severity simulation that produces the profile 164 can perform a derivation of the inclination profile 154 to understand the calculated rate of change 162 of the inclination of the BHA (or the wellbore 15) per the measured depth (MD) 163. By running the simulation along the portion 161 (which can be synonymous to portion 151), the simulation can plot the profile 164 calculated by the derivation of the inclination angle of the profile 154. As can be seen, the profile 164 is significantly noisier when compared to the profile 165 from “0” zero degrees inclination angle A2 at around a MD of 10600 feet to substantially 10 degrees inclination angle A2 at around a MD of 10800 feet.

The build dogleg severity simulation that produces the profile 165 can perform a derivation of the inclination profile 155 to understand the calculated rate of change 162 of the inclination of the BHA (or the wellbore 15) per the measured depth (MD) 163. By running the simulation along the portion 161 (which can be synonymous to portion 151), the simulation can plot the profile 165 calculated by the derivation of the inclination angle of the profile 155. As can be seen, the profile 165 is significantly less noisy when compared to the profile 164 from “0” zero degrees inclination angle A2 at around a MD of 10600 feet to substantially 10 degrees inclination angle A2 at around a MD of 10800 feet. Unlike the profile 165, the profile 164 deviates substantially from a mean dogleg value of the profile 164 between survey points at the lower inclination angles.

The simulations that produce the profiles 155, 165 can use sensor data from the logging tool 100, which are not pre calibrated for a wide range of temperatures. The logging tool 100 sensor data can be calibrated by a method described in more detail below, where the simulation recalculates the coordinates of the sensor data from one coordinate system (e.g., geographic/gravity coordinate system X-Y-Z) to another coordinate system (e.g., tool coordinate system Tx-Ty-Tz). These recalculations can be used to establish (and calibrate) coefficients for calculating the inclination angle of the wellbore 15 as a function of depth.

In a non-limiting embodiment, FIG. 3 is a representative partial cross-sectional view along line 3-3, as indicated in FIG. 1A, of a logging tool 100 in a wellbore 15. The logging tool 100 is shown positioned inside the wellbore 15 with an annulus 17 between them and rotated (arrows 90) to an angle A1 from the top side 148 of the wellbore 15. The logging tool 100 can rotate (arrows 90) in either direction within the wellbore 15. The angle A1 can be seen as the gravity toolface azimuth A1 since it indicates the angle from the top side 148 (arrows 98) of the wellbore 15 to the high side 140 (or gravity toolface 140) of the logging tool 100, which has been rotated in the wellbore 15. The logging tool 100 can include a body 102 with a longitudinal flow passage 106 for the passage of mud through the logging tool 100, such as if the logging tool is assembled in a BHA 60. This longitudinal flow passage 106 can be positioned at other locations through the body 102 and it is not limited to the location shown. A longitudinal cavity 104 can also be formed in the body 102 to receive electronics for tool sensing and control.

As used herein, the Tx-Ty-Tz coordinate system used in the discussions below is relative to the high side 140, right side 142, low side 144, and left side 146 of the logging tool 100, as indicated by the Tx and Ty axes.

In a non-limiting embodiment, FIG. 4 is a representative partial cross-sectional view along line 3-3, as indicated in FIG. 1A, of a logging tool 100 in a wellbore 15. The logging tool 100 can include a body 102 with a longitudinal flow passage 106 for the passage of mud through the logging tool 100, such as if the logging tool is assembled in a BHA 60. This longitudinal flow passage 106 can be positioned at other locations through the body 102 and it is not limited to the location shown. A longitudinal cavity 104 can also be formed in the body 102 to receive electronics 108 mounted to a printed circuit board PCB 110. Appropriate structure (not shown for clarity) can be included to hold the electronics 108 in a desired position within the longitudinal cavity 104. The electronics can include one or more processors that are communicatively coupled to non-transitory memory device(s) for running software programs, whose instructions can be stored in the memory device(s) and retrieved as needed. The processors can receive data from sensors (e.g., 120, 122) mounted to the PCB and process the sensor data or transmit the sensor data to a controller that is remote from the logging tool 100.

The body 102 of the logging tool 100 can have a center axis Tz that intersects a Tx-axis and a Ty-axis at the intersection point 112. The center axis Tz can also be referred to as sigma g in the equations of this disclosure and the drawings. This forms a Tx-Ty-Tz tool coordinate system that will be used for discussion purposes to describe the current methods for calculating the gravity toolface azimuth A1 and the inclination angle A2. The high side 140 can be referred to as the gravity toolface 140, and the gravity toolface azimuth A1 can be seen as rotation of the high side 140 from the top side 148 of the wellbore 15.

The PCB 110 can include one or more accelerometers 120 that can detect acceleration in the radial, tangential, or axial directions (a_r, a_τ, a_ζ). The PCB 110 can also include one or more magnetometers 122 that can detect magnetic fields in the radial or tangential directions (m_r, m_τ). In this non-limiting embodiment, the accelerometer 120 and the magnetometers 122 can be used to collect sensor data while the logging tool 100 is rotated within the wellbore 15, where the sensor data can be used to calculate the gravity toolface azimuth A1 (or φ_g), the inclination angle A2 (or φ^ci), and a dogleg severity either by processors downhole, at the surface 6, on or near a rig 10, or remote from the rig 10.

As mentioned above, the gravity toolface azimuth A1 (or φ_g) can be calculated at periodic intervals of the measured depth MD based on the sensor data from the radial and tangential magnetometers 122 and from the radial and tangential accelerometers 120. With the gravity toolface azimuth A1 (or φ_g) calculated, the radial and tangential accelerometers 120 can be written as Equations (1) and (2) below:

$\begin{array}{cc}{a}_r=\mathrm{Acos}\left({\phi }_g\right)& \left(1\right)\end{array}$ $\begin{array}{cc}{a}_{\tau }=-A\sin \left({\phi }_g\right)& \left(2\right)\end{array}$

• • Where factor A=gsin(φ^ci) and

$g=9.81\frac{m}{s^2}.$

Applying a method, such as a quadrature detection method, to the sensor data from the radial and tangential accelerometers (a_r, a_τ), the equations (1) and (2) can yield the factor A as shown in Equation (3) below:

$\begin{array}{cc}A=g\sin \left({\phi }^{ci}\right)& \left(3\right)\end{array}$

Therefore, the inclination angle A2 (or φ^ci) can be seen as shown in Equation (4) below:

$\begin{array}{cc}{\phi }^{ci}=a\sin \left(\frac{A}{g}\right)& \left(4\right)\end{array}$

An example of the inclination angle A2 plotted (line 155) as a function of the measured depth MD 153 is shown in FIG. 2B. The dogleg severity can be determined by the derivation of the inclination angle A2. An example of the dogleg severity is plotted (line 165) as a function of the measured depth MD 163 in FIG. 2C.

FIG. 5 is a representative functional block diagram of a rig controller 250 that can control rig equipment of the rig 10 and perform methods of the current disclosure (e.g., determining the inclination angle and dogleg severity for a wellbore), in accordance with certain embodiments. The rig controller 250 can include one or more local or remote processing units 260 that can be locally or remotely positioned relative to the rig 10 or downhole. Each processing unit 260 can include one or more processors 262 (e.g., microprocessors, programmable logic arrays, programmable logic devices, etc.), non-transitory memory storage devices 264, peripheral interface 266, human machine interface (HMI) device(s) 268, and possibly a remote telemetry interface 265 for internet communication or satellite network communication. The HMI devices 268 can include a touchscreen, a laptop, a desktop computer, a workstation, or wearables (e.g., smart phone, smart watch, tablet, etc.). These components of the rig controller 250 can be communicatively coupled together via one or more networks 254, which can be wired or wireless networks.

The processors 262 can be configured to read instructions from one or more non-transitory memory storage devices 264 and execute those instructions to perform any of the operations described in this disclosure. A peripheral interface 266 can be used by the rig controller 250 to receive sensor data from around the rig 10 or downhole which can collect data on the rig operations being performed. The peripheral interface 266 can also be used by the rig controller 250 to send commands to personnel or rig equipment to control rig operations during a subterranean operation. The rig controller 250 can receive a well plan 263 via the network 254 (or peripheral interface 266) and can determine a rig state based on the well plan 263 and data from the sensors around the rig 10.

The rig controller 250 can include a sensor data database 269 that can store historical sensor data from previously drilled wells. This historical sensor data can be used by the rig controller 250 to determine the gravity toolface azimuth A1 (or φ_g), the inclination angle A2 (or φ^ci), and a dogleg severity. The rig controller 250 can also receive real-time sensor data from the sensors 120, 122, 40 to calculate the gravity toolface azimuth A1 (or φ_g), the inclination angle A2 (or φ^ci), and a dogleg severity.

FIG. 6 is a representative flow diagram of a method 200 for determining the inclination angle and dogleg severity for a wellbore, in accordance with certain embodiments. The method 200 can begin at operation 202, where the rig controller 250 (or a module of the rig controller 250) can receive sensor data from the radial and tangential accelerometers 120 and the radial and tangential magnetometers 122 (either in real-time or from the database 269). In operation 204, the rig controller 250 can use the sensor data from the radial and tangential magnetometers 122 to determine the magnetic toolface for the logging tool 100.

In operation 206, the rig controller 250 can convert the magnetic toolface to the gravity toolface azimuth A1 (or φ_g) based on the sensor data from the radial and tangential accelerometers 120. In operation 208, the rig controller 250 can determine the inclination angle A2 (or φ^ci) at a measured depth MD based on the gravity toolface azimuth A1 (or φ_g) and the sensor data from the radial and tangential accelerometers 120 for the measured depth MD. In operation 210, the operations 204 through 208 can be repeated to determine an inclination angle A2 (or φ^ci) profile (or continuous inclination) along the wellbore 15 from a first measured depth to a second measured depth at periodic (or random) intervals of the measured depth.

FIG. 7 is representative of a geographic coordinate system (X,Y,Z), with a gravity vector g=(0,0, g)^T and a well trajectory vector e_ζ. FIG. 8 is representative of a tool coordinate system (Tx, Ty, Tz) or (Tr, Tτ, Tz), with magnetic toolface angle φ_m, gravity toolface angle φ_g, and high side offset angle φ^hs defined. FIGS. 9A-9D are representative of three axial rotations (FIGS. 9B-9D) from an original orientation (FIG. 9A) used to transform a geographic/gravity coordinate system (X, Y, Z) to a tool coordinate system (Tr, Tτ, Tz), with axis Z aligned with gravity and axis Tz aligned with a longitudinal tool axis, in accordance with certain embodiments

Sensor data from radial, tangential and axial accelerometers a_r, a_τ, a_ζ(120) and magnetometers b_r, b_τ, b_ζ (122) mounted on a PCB board 110 of the logging tool 100 can be utilized to determine calibrated coefficients of the accelerometers and magnetometers to reduce or eliminate errors that can be caused by non-temperature compensated low-grade sensors. It is assumed that the sensors 120, 122 are the low-grade and not temperature compensated/calibrated sensors (e.g., micro electro-mechanical systems (MEMS) accelerometers or Fluxgate accelerometers, or Anisotropic Magneto-Resistive magnetometer sensors).

The following discussion describes a method for determining calibrated coefficients of the low-grade sensors 120, 122 and determining the continuous azimuth angle as a function of depth in the wellbore 15. The method assumes that the continuous inclination and continuous high side offset angles have already been determined as given above in this current disclosure. In order to determine the continuous azimuth angle, the method can utilize the previously determined continuous inclination and continuous high side angles, and the known Earth's magnetic field. The continuous build and dog leg severities can be calculated as a derivative of the continuous inclination and azimuth angles, respectively. The method also provides a way to calibrate, and temperature compensate, the low grade sensors 120, 122 of the logging tool 100.

Continuous inclination φ^ci and azimuth φ^ca angle logs are an improvement over the inclination and azimuth angle logs determined based on the standard MWD survey, which normally provides these values at each 50 or 100 or 150 ft (or other) interval of the measured depth, md_k⁰.

The magnetometer 122 readings (b_r and b_t) can be used to detect the magnetic toolface φ_m, then the accelerometer readings (a_r, and a_τ) can be used to convert the magnetic toolface φ_m into the gravity toolface φ_g, and establishing a gravity orientation for the wellbore 15. With the wellbore 15 gravity oriented, the axial accelerometer a_ζ (in sub horizontal wells) or ‘horizontal’ a_r, a_τ accelerometers (in subvertical wells) can be used to replenish the inclination angle [represented by: φ^ci(md_j)] and the high side offset angle [represented by: φ^hs(md_j)=φ_g−φ_m] between the rare MWD survey stations, md_k⁰, as discussed above.

The current disclosure also provides a method to determine the continuous azimuth angle, φ^ca. Through some algebra, the high side offset φ^hs can be alternatively found from the known Earth's magnetic field (m_x, m_y, m_z), and continuous inclination φ^ci and azimuth φ^ca angles [represented by: m_x, m_y, m_z, φ^ci, φ^ca→φ^hs] where axis X is aligned with the geographic North, axis Y is aligned with the geographic East, and axis Z is aligned with gravity. The details of such a calculation is described in more detail below. Resolving this mapping with respect to the continuous azimuth, φ^ca, can yield a desired mapping which can be represented by:

m _x ,m _y ,m _τ,φ^ci,φ^hs→φ^ca.

Due to the existence of a huge network of the magnetic observatories, the Earth's magnetic field [m=(m_x, m_y, m_z)^T] is well known at any point on, under and above the Earth's surface and at any moment in time. Therefore, the latter mapping allows for the continuous azimuth angle φ^ca (md_j) to be determined and allows calibration of the low grade sensors 120, 122.

Given the continuous inclination φ^ci and azimuth φ^ca angles (and the gravity toolface φ_g), the downhole magnetometer 120 readings can be expressed in the terms of the known Earth's magnetic field as [(b_ζ, b_τ, −b_r)^T=O₁(φ^ca)O₂(φ^ci)O₃(φ_g)(m_x, m_y, m_z)^T] via three known axial rotations (refer to FIGS. 9A-9D). The latter equation delivers a basis for downhole calibration of magnetometer 122 readings. Similarly, the accelerometer 120 readings can also be calibrated.

FIG. 9A represents an original orientation of the magnetic vector field m in a geographic coordinate system (X,Y,Z) aligned with gravity (also see FIG. 7). FIG. 9B is representative of a first axial rotation O₁ of the coordinate system (X,Y,Z) about the Z axis by an angle φ^a to coordinate positions (X′,Y′,Z′). The equation represents the magnetic vector field m transformed to the adjusted coordinate system (X′,Y′,Z′) as magnetic vector field m′. FIG. 9C is representative of a second axial rotation O₂ of the coordinate system (X′,Y′,Z′) about the Y′ axis by an angle φⁱ to coordinate positions (X″,Y″,Z″). The equation represents the magnetic vector field m′ transformed to the adjusted coordinate system (X″,Y″,Z″) as magnetic vector field m″. FIG. 9D is representative of a third axial rotation O₃ of the coordinate system (X″,Y″,Z″) about the X″ axis by an angle φ_g to coordinate positions (X′″,Y′″,Z′″). The equation represents the magnetic vector field m″ transformed to the adjusted coordinate system (X′″,Y′″,Z′″) as magnetic vector field m′″. In FIG. 9D, the resultant coordinate positions (X′″,Y′″,Z′″) correspond to the tool coordinate positions (Tr, Tτ, Tz), (also see FIG. 8).

To determine a continuous azimuth angle, φ^ca, with some continuous inclination φ^ci and azimuth φ^ca angles known (such as at MWD survey points), and given the Earth's magnetic vector field [m=(m_x, m_y, m_z)^T], we can detect the high side offset angle, φ^hs. In a geographic coordinate system (see FIG. 7), unity vectors e_τ=(0,0, −1)^T and e_ζ=(sin φ^ci cos φ^ca, sin φ ^ci sin φ^ca, cos φ^ci)^T can be established as well as derivative vectors e_⊥=e_τ−βe_ζ and m_⊥=m−αe_ζ, where the scalars are β=e_τ·e_ζ and α=m·e_ζ.

Referring to FIG. 8, a tool coordinate system (Tx, Ty, Tz) or (Tr, Tτ, Tz) is established that is relative to the logging tool 100. Both vectors e_⊥ and m_⊥ belong to the Tx-Ty plane which is perpendicular to the well trajectory (or Tz axis). After simple algebra, it can be seen from FIG. 8 that

$\sin {\phi }^{hs}=\frac{e_{ϛ}{e}_{\perp }\times m_{\perp }}{❘e_{\perp }❘❘m_{\perp }❘}$

and

$\cos {\phi }^{hs}=\frac{e_{\perp }·m_{\perp }}{❘e_{\perp }❘❘m_{\perp }❘},$

where the dot “.” and the cross “x” signs mean the inner and cross vector products, respectively.

These expressions readily give the high side offset angle as

${\phi }^{hs}={\tan }^{-1}\frac{e_{ϛ}·e_{\perp }\times m_{\perp }}{e_{\perp }·m_{\perp }}.$

This equation allows construction of a nonlinear mapping [m_x, m_y m_τ, φ^ci, φ^ca→φ^hs]. This mapping can be resolved with respect to the sought continuous azimuth angle φ^ca via the ‘inverse’ mapping [m_x, m_y, m_z, φ^ci, φ^hs→φ^ca] Therefore, this method can be used to determine the sought continuous azimuth angle φ^ca.

As stated above, the calibration of the low grade sensors 120, 122 can also be performed. Considering the geographic coordinate system (X, Y, Z) aligned with gravity (see FIG. 7) and the coordinate system (Tx, Ty, Tz) that is ‘frozen’ relative to the logging tool 100 (see FIG. 8). For any vector field, Equation (5) shown below allows recalculation of the vector field coordinates from one coordinate system to another, and back, if desired.

$\begin{array}{cc}{\left(m_x,m_y,m_z\right)}^T=\left(\begin{array}{ccc}\cos {\phi }^{\mathrm{ca}}& -\sin {\phi }^{\mathrm{ca}}& 0\\ \sin {\phi }^{\mathrm{ca}}& \cos {\phi }^{\mathrm{ca}}& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\sin {\phi }^{ci}& 0& -\cos {\phi }^{ci}\\ 0& 1& 0\\ \cos {\phi }^{ci}& 0& \sin {\phi }^{ci}\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {\phi }_g& -\sin {\phi }_g\\ 0& \sin {\phi }_g& \cos {\phi }_g\end{array}\right){\left(b_{ϛ},b_{\tau },-b_r\right)}^T& \left(5\right)\end{array}$

where

${\phi }^i=\frac{\pi }{2}-{\phi }^{\mathrm{ci}},$

and φ_g=φ_m+φ^hs.

Equation (5) can be used to calibrate coefficients of the low-grade downhole sensors such as accelerometer and magnetometer sensors 120, 122 of the logging tool 100. Regarding calibration of the magnetometer sensor 122, a vector field M can represent the known Earth's magnetic field [M=(m_x, m_y, m_z)^T], then for magnetometer sensor 122 readings (b_ζ, b_τ, b_r)^T the Equation (5) can be inverted and rewritten as Equation (6) below:

$\begin{array}{cc}{\left(b_{ϛ},b_{\tau },b_r\right)}^T=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {\phi }_g& \sin {\phi }_g\\ 0& -\sin {\phi }_g& \cos {\phi }_g\end{array}\right){\left({\mu }_x,{\mu }_y,{\mu }_z\right)}^T& \left(6\right)\end{array}$

where vector field μ=(μ_x, μ_y, μ_τ)^T depends on slow changing, and known, continuous inclination φ^ci and azimuth φ^ca angles, whereas the gravity toolface φ_g angle changes rapidly with the rate of the tool RPM, when the logging tool 100 is rotating in the gravity field.

Equation (6) allows separation of the magnetic field (b_ζ, b_τ, b_r)^T into slow and fast changing components. For low grade (and not compensated for temperature) magnetometer sensor readings (B_r, B^τ, B_ζ)^T, Equation (6) can be rewritten as Equation (7):

$\begin{array}{cc}\{\begin{array}{c}{k}_r{B}_r=-❘\mu ❘\cos \left({\phi }_g+{\phi }_{\mu }\right)+k_r^o\\ k_{\tau }{B}_{\tau }=❘\mu ❘\sin \left({\phi }_g+{\phi }_{\mu }\right)+k_{\tau }^o\\ k_{ϛ}{B}_{ϛ}={\mu }_x+k_{ϛ}^o\end{array}& \left(7\right)\end{array}$

where k_r, k_τ, k_ζ and k_r^o, k_τ^o, k_ζ^o are the gain and offset coefficients, respectively. We can assume that all six coefficients are unknown since the magnetometer sensors are low grade and not calibrated for common LWD tools.

In Equation (7), the |μ|=√{square root over (μ_y²+μ_τ²)} and φ_μ are known scalar functions of φ^ci and φ^ca angles. From the first pair of equations, since φ^ci and φ^ca are practically not changing during a few rotations of the logging tool 100, the gains k_r, k_τ and offsets k_r^o, k_τ^o can be determined. Now, when the calibrated values for B_r and B_τ are determined, the last of the above equations can be used to find gain k_ζ and offset k_ζ^o.

Equation (5) can be also written for the gravity vector g=(0,0, g)^T, where g=9.81 m/s{circumflex over ( )}2, as

$\begin{array}{cc}{\left(0,0,g\right)}^T=\left(\begin{array}{ccc}\cos {\phi }^{ca}& -\sin {\phi }^{ca}& 0\\ \sin {\phi }^{ca}& \cos {\phi }^{ca}& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\sin {\phi }^{ci}& 0& -\cos {\phi }^{ci}\\ 0& 1& 0\\ \cos {\phi }^{ci}& 0& \sin {\phi }^{ci}\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {\phi }_g& -\sin {\phi }_g\\ 0& \sin {\phi }_g& \cos {\phi }_g\end{array}\right){\left(a_{ϛ}^g,a_{\tau }^g,-a_r^g\right)}^T& \left(8\right)\end{array}$

where a_g=(a_r^g, a_τ^g, a_ζ^g)^T is the gravitational part of the accelerometer's readings. This part of the readings can be found, since the centripetal component

$\left(i.e.,\frac{1}{r}\frac{d{\phi }_g^2}{\mathrm{dt}}\right)$

and the Euler component

$\left(i.e.,r\frac{d^2{\phi }_g}{{\mathrm{dt}}^2}\right)$

of the logging tool 100 acceleration could be removed from the raw accelerometer readings [α=(a_r, a_τ, a_ζ)^T]. The RPM of the tool,

$\left(i.e.,\frac{d{\phi }_g}{\mathrm{dt}}\right),$

can be readily calculated from the magnetometer readings B_τ, B_r. Neglecting the acceleration of the tool as a whole or filtering it out if the tool RPM is reasonably slow (e.g., RPM<300), the a_g can be calculated and a calibration of the tool accelerometer low grade sensors 120 can be performed in the same manner as it is described above for the magnetometer sensors 122 calibration.

LISTING OF VARIABLES

The following identifies variables used in the above equations.

• • a_r radial accelerometer readings in the tool coordinate system, [m/s{circumflex over ( )}2]
  • a_τ tangential accelerometer readings in the tool coordinate system, [m/s{circumflex over ( )}2]
  • a_ζ axial accelerometer readings in the tool coordinate system, [m/s{circumflex over ( )}2]
  • b_r radial component of the true Earth's magnetic field in the tool coordinate system, [G]
  • b_τ tangential component of true Earth's magnetic field in the tool coordinate system, [G]
  • b_ζ axial component of the true Earth's magnetic field in the tool coordinate system, [G]
  • B_r radial magnetometer readings in the tool coordinate system, [G]
  • B_τ tangential magnetometer readings in the tool coordinate system, [G]
  • B_ζ axial magnetometer readings in the tool coordinate system, [G]
  • φ^ci continuous inclination angle, [rad]
  • φ^ca continuous azimuth angle, [rad]
  • φ_g gravity toolface angle, [rad]
  • φ_m magnetic toolface angle, [rad]
  • φ^hs high side offset angle, [rad]
  • e_ζ, e_τ unity vectors, [dimensionless]
  • e_⊥, m_⊥, α, β derivative vectors and scalars
  • g=9.81 gravity constant, [m/s{circumflex over ( )}2]
  • a_g '₂ (a_r^g, a_τ^g, a_ζ^g)^T gravitational part of the accelerometer readings, [m/s{circumflex over ( )}2]
  • k_r, k_τ, k_ζ gain correction coefficients, [dimensionless]
  • k_r^o, k_τ^o, k_ζ^o offset correction coefficients, [G]
  • md_j j-th measured depth point, [ft]
  • md_k⁰ k-th MWD survey station, [ft]
  • m_x North component of the Earth's magnetic field, [G]
  • m_y East component of the Earth's magnetic field, [G]
  • m_τ gravity (downward) component of the Earth's magnetic field, [G]
  • m=(m_x, m_y, m_z)^T Earth's magnetic vector field, [G]
  • O₁·O₂, O₃ abbreviations for three axial rotations of Equation 5, [rad]
  • μ=(μ_x, μ_y, μ_τ)^T part of the Earth's magnetic field, depending only on φ^ci and φ^ca [G]

$❘a❘=\sqrt[2]{a_x^2+a_y^2+a_z^2}$

norm of vector a=(a_x, a_y, a_z)^T,

• • a·b=a_xb_x+a_yb_y+a_τ b_τ inner product of two vectors,
  • a×b=(a_yb_τ−a_τ b_y, a_τ b_x−a_xb_τ, a_xb_y−a_yb_x)^T cross product of two vectors,

VARIOUS EMBODIMENTS

Embodiment 1. A method for determining an inclination of a wellbore, the method comprising receiving sensor data at a rig controller, wherein the sensor data comprises sensor data from a radial magnetometer (b_r), a tangential magnetometer (b_t), a radial accelerometer (a_r), and a tangential accelerometer (a_τ); determining, via the rig controller, a magnetic toolface angle (φ_m) of a bottom hole assembly (BHA) based on the sensor data from the radial magnetometer (b_r) and the tangential magnetometer (b_τ); converting, via the rig controller, the magnetic toolface angle (φ_m) to a gravity toolface (φ_g) of the BHA based on the sensor data from the radial accelerometer (a_r) and the tangential accelerometer (a_t); and determining, via the rig controller, an inclination angle based on the gravity toolface, and the sensor data from the radial accelerometer (a_r) and the tangential accelerometer (a_t).

Embodiment 2. The method of embodiment 1, wherein the radial magnetometer (b_r), the tangential magnetometer (b_τ), the radial accelerometer (a_r), the tangential accelerometer (a_τ) are disposed in a logging tool in the BHA.

Embodiment 3. The method of embodiment 1, wherein the sensor data from either one of the radial magnetometer (b_r), the tangential magnetometer (b_τ), the radial accelerometer (a_r), and the tangential accelerometer (a_τ) represent a plurality of sensor data readings from a respective one of the radial magnetometer (b_r), the tangential magnetometer (b_τ), the radial accelerometer (a_r), and the tangential accelerometer (a_τ).

Embodiment 4. The method of embodiment 3, wherein determining the magnetic toolface angle of the BHA is based on the plurality of the sensor data readings from the radial magnetometer (b_r) and the tangential magnetometer (b_τ).

Embodiment 5. The method of embodiment 4, wherein converting the magnetic toolface angle to the gravity toolface of the BHA is based on the plurality of the sensor data readings from the radial accelerometer (aτ) and the tangential accelerometer (aτ).

Embodiment 6. The method of embodiment 5, wherein determining the inclination angle is based on the gravity toolface, and the plurality of the sensor data readings from the radial accelerometer (aτ) and the tangential accelerometer (aτ).

Embodiment 7. The method of embodiment 6, further comprising determining the inclination angle of the wellbore at a measured depth of the wellbore.

Embodiment 8. The method of embodiment 6, further comprising determining the inclination angle of the wellbore at each of a plurality of incremental distances of a measured depth of the wellbore.

Embodiment 9. The method of embodiment 8, further comprising determining, via the rig controller, a continuous inclination angle profile of the wellbore from a first measured depth of the wellbore to a second measured depth of the wellbore.

Embodiment 10. The method of embodiment 9, wherein the continuous inclination angle is a profile of the inclination angle from the first measured depth of the wellbore to the second measured depth of the wellbore.

Embodiment 11. The method of embodiment 1, further comprising determining, via the rig controller, a dogleg severity for a first measured depth of the wellbore, wherein the dogleg severity indicates a rate of change of an inclination angle per an incremental distance along the wellbore.

Embodiment 12. The method of embodiment 1, further comprising determining, via the rig controller, a plurality of dogleg severities for a respective plurality of measured depths of the wellbore.

Embodiment 13. The method of embodiment 12, further comprising increasing an accuracy of ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 10 degrees when compared to an accuracy of the other ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of greater than 10 degrees.

Embodiment 14. The method of embodiment 12, further comprising increasing an accuracy of ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 8 degrees when compared to an accuracy of the other ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of greater than 8 degrees.

Embodiment 15. The method of embodiment 12, further comprising increasing an accuracy of ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 7 degrees when compared to an accuracy of the other ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of greater than 7 degrees.

Embodiment 16. The method of embodiment 12, further comprising increasing an accuracy of ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 5 degrees when compared to an accuracy of the other ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of greater than 5 degrees.

Embodiment 17. The method of embodiment 1, further comprising determining, via the rig controller, a plurality of inclination angles for a respective plurality of measured depths of the wellbore.

Embodiment 18. The method of embodiment 17, further comprising increasing an accuracy of ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 10 degrees when compared to an accuracy of the other ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of greater than 10 degrees.

Embodiment 19. The method of embodiment 17, further comprising increasing an accuracy of ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 8 degrees when compared to an accuracy of the other ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of greater than 8 degrees.

Embodiment 20. The method of embodiment 17, further comprising increasing an accuracy of ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 7 degrees when compared to an accuracy of the other ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of greater than 7 degrees.

Embodiment 21. The method of embodiment 17, further comprising increasing an accuracy of ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 5 degrees when compared to an accuracy of the other ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of greater than 5 degrees.

Embodiment 22. A method for determining an inclination of a wellbore, the method comprising receiving sensor data at a rig controller, wherein the sensor data comprises sensor data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ); determining, via the rig controller, an inclination angle profile based on a gravity toolface of a bottom hole assembly (BHA), and the sensor data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ), wherein the inclination angle profile is for a portion of the wellbore with an inclination angle of less than or equal to 10 degrees; determining, via the rig controller, a dogleg severity profile based on the inclination angle profile, wherein the dogleg severity of the dogleg severity profile is between +10 degrees/100 feet and −10 degrees/100 feet for the portion of the wellbore.

Embodiment 23. A method for determining an inclination of a wellbore, the method comprising:

• • receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ);
  • determining, via the rig controller, a magnetic toolface angle (φ_m) of the logging tool based on the data from the radial magnetometer (b_r) and the tangential magnetometer (b_τ); converting, via the rig controller, the magnetic toolface angle (φ_m) to a gravity toolface (φ_g) of the logging tool based on the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ); and
  • determining, via the rig controller, an inclination angle based on the gravity toolface, and the data from the radial accelerometer (a_r) and the tangential accelerometer (aτ).

Embodiment 24. A method for determining an inclination of a wellbore, the method comprising:

• • receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ);
  • determining, via the rig controller, an inclination angle profile based on a gravity toolface of the BHA, and the data from the radial accelerometer (a_r) and the tangential accelerometer (a_r), wherein the inclination angle profile is for a portion of the wellbore with an inclination angle of less than or equal to 10 degrees; and
  • determining, via the rig controller, a dogleg severity profile based on the inclination angle profile, wherein the dogleg severity of the dogleg severity profile is between +10 degrees/100 feet and −10 degrees/100 feet for the portion of the wellbore.

Embodiment 25. A method for determining an azimuth angle of a wellbore, the method comprising:

• • receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (b_r), a tangential magnetometer (b_τ), a radial accelerometer (a_r), and a tangential accelerometer (a_τ);
  • determining, via the rig controller, a magnetic toolface angle (φ_m) of the logging tool based on the data from the radial magnetometer (b_r) and the tangential magnetometer (b_τ); converting, via the rig controller, the magnetic toolface angle (φ_m) to a gravity toolface angle (φ_g) of the logging tool based on the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ) or the data from the axial accelerometer (a_ζ);
  • determining, via the rig controller, an inclination angle (φ^ci) and a high side offset angle (φ^hs) based on the gravity toolface angle (φ_g), and the data from the radial accelerometer (a_r) and the tangential accelerometer (a_τ); and
  • determining, via the rig controller, an azimuth angle (φ^ca) based on mapping of the earth's magnetic field vector (m_x, m_y, m_z), the inclination angle (φ^ci), and a high side offset angle (φ^hs).

Embodiment 26. The method of embodiment 25, further comprising: determining, via the rig controller, a plurality of azimuth angles based on mapping of the earth's magnetic field vector, a plurality of inclination angles, and a plurality of high side offset angles, wherein the plurality of azimuth angles correspond to a distance between a first measured depth of the wellbore to a second measured depth of the wellbore.

Embodiment 27. The method of embodiment 26, wherein a continuous azimuth angle is a profile of the plurality of azimuth angles from the first measured depth of the wellbore to the second measured depth of the wellbore.

Embodiment 28. The method of embodiment 25, further comprising:

• • determining, via the rig controller, a first azimuth angle at a first measured depth based on mapping of the earth's magnetic field vector, a first inclination angle at the first measured depth based on first sensor data from the logging tool, and first high side offset angle at the first measured depth based on the first sensor data;
  • determining, via the rig controller, a second azimuth angle at the first measured depth based on mapping of the earth's magnetic field vector, a second inclination angle at the first measured depth based on second sensor data from a measuring-while-drilling (MWD) survey, and a second high side offset angle at the first measured depth based on the second sensor data;
  • adjusting gain and offset coefficients for the radial magnetometer, the tangential magnetometer, the radial accelerometer, or the tangential accelerometer until the first azimuth angle substantially equals the second azimuth angle; and
  • storing the adjusted gain and offset coefficients as calibrated gain and offset coefficients for the radial magnetometer, the tangential magnetometer, the radial accelerometer, and the tangential accelerometer.

While the present disclosure may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and tables and have been described in detail herein. However, it should be understood that the embodiments are not intended to be limited to the particular forms disclosed. Rather, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosure as defined by the following appended claims. Further, although individual embodiments are discussed herein, the disclosure is intended to cover all combinations of these embodiments.

Claims

1. A method for determining an inclination of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (br), a tangential magnetometer (bτ), a radial accelerometer (ar), and a tangential accelerometer (aτ);determining, via the rig controller, a magnetic toolface angle (φm) of the logging tool based on the data from the radial magnetometer (br) and the tangential magnetometer (bτ);converting, via the rig controller, the magnetic toolface angle (φm) to a gravity toolface (φg) of the logging tool based on the data from the radial accelerometer (ar) and the tangential accelerometer (aτ); anddetermining, via the rig controller, an inclination angle based on the gravity toolface, and the data from the radial accelerometer (ar) and the tangential accelerometer (aτ).

2. The method of claim 1, wherein the sensor data from either one of the radial magnetometer (mr), the tangential magnetometer (bτ), the radial accelerometer (ar), and the tangential accelerometer (aτ) represent a plurality of sensor data readings from a respective one of the radial magnetometer (br), the tangential magnetometer (bτ), the radial accelerometer (ar), and the tangential accelerometer (aτ).

3. The method of claim 2, wherein determining the magnetic toolface angle of the BHA is based on the plurality of the sensor data readings from the radial magnetometer (br) and the tangential magnetometer (bτ).

4. The method of claim 3, wherein converting the magnetic toolface angle to the gravity toolface of the BHA is based on the plurality of the sensor data readings from the radial accelerometer (ar) and the tangential accelerometer (aτ).

5. The method of claim 4, wherein determining the inclination angle is based on the gravity toolface, and the plurality of the sensor data readings from the radial accelerometer (ar) and the tangential accelerometer (aτ).

6. The method of claim 5, further comprising determining the inclination angle of the wellbore at each of a plurality of incremental distances of a measured depth from a first measured depth of the wellbore to a second measured depth of the wellbore.

7. The method of claim 6, wherein a continuous inclination angle is a profile of the inclination angle from the first measured depth of the wellbore to the second measured depth of the wellbore.

8. The method of claim 1, further comprising: determining, via the rig controller, a dogleg severity for a first measured depth of the wellbore, wherein the dogleg severity indicates a rate of change of an inclination angle per an incremental distance along the wellbore.

9. The method of claim 1, further comprising: determining, via the rig controller, a plurality of dogleg severities for a respective plurality of measured depths of the wellbore; andincreasing an accuracy of ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 10 degrees when compared to an accuracy of other ones of the plurality of dogleg severities that are associated with a portion of the wellbore with an actual inclination angle of greater than 10 degrees.

10. The method of claim 1, further comprising: determining, via the rig controller, a plurality of inclination angles for a respective plurality of measured depths of the wellbore; andincreasing an accuracy of ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of less than or equal to 10 degrees when compared to an accuracy of other ones of the plurality of inclination angles that are associated with a portion of the wellbore with an actual inclination angle of greater than 10 degrees.

11. A method for determining an inclination of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (br), a tangential magnetometer (bτ), a radial accelerometer (ar), and a tangential accelerometer (aτ);determining, via the rig controller, an inclination angle profile based on a gravity toolface of the BHA, and the data from the radial accelerometer (ar) and the tangential accelerometer (aτ), wherein the inclination angle profile is for a portion of the wellbore with an inclination angle of less than or equal to 10 degrees; anddetermining, via the rig controller, a dogleg severity profile based on the inclination angle profile, wherein the dogleg severity of the dogleg severity profile is between +10 degrees/100 feet and −10 degrees/100 feet for the portion of the wellbore.

12. A method for determining an azimuth angle of a wellbore, the method comprising: receiving sensor data at a rig controller, wherein the sensor data was detected by sensors in a logging tool in a bottom hole assembly (BHA) in a wellbore, wherein the sensor data comprises data from a radial magnetometer (br), a tangential magnetometer (bτ), a radial accelerometer (ar), and a tangential accelerometer (aτ);determining, via the rig controller, a magnetic toolface angle (φm) of the logging tool based on the data from the radial magnetometer (br) and the tangential magnetometer (bτ);converting, via the rig controller, the magnetic toolface angle (φm) to a gravity toolface angle (φg) of the logging tool based on the data from the radial accelerometer (ar) and the tangential accelerometer (aτ) or the data from the axial accelerometer (aζ);determining, via the rig controller, an inclination angle (φca) and a high side offset angle (φhs) based on the gravity toolface angle (φ9), and the data from the radial accelerometer (ar) and the tangential accelerometer (aτ); anddetermining, via the rig controller, an azimuth angle (φca) based on mapping of the earth's magnetic field vector (mx, my, mz), the inclination angle (φci), and a high side offset angle (φhs).

13. The method of claim 12, further comprising: determining, via the rig controller, a plurality of azimuth angles based on mapping of the earth's magnetic field vector, a plurality of inclination angles, and a plurality of high side offset angles, wherein the plurality of azimuth angles correspond to a distance between a first measured depth of the wellbore to a second measured depth of the wellbore.

14. The method of claim 13, wherein a continuous azimuth angle is a profile of the plurality of azimuth angles from the first measured depth of the wellbore to the second measured depth of the wellbore.

15. The method of claim 12, further comprising: determining, via the rig controller, a first azimuth angle at a first measured depth based on mapping of the earth's magnetic field vector, a first inclination angle at the first measured depth based on first sensor data from the logging tool, and first high side offset angle at the first measured depth based on the first sensor data;determining, via the rig controller, a second azimuth angle at the first measured depth based on mapping of the earth's magnetic field vector, a second inclination angle at the first measured depth based on second sensor data from a measuring-while-drilling (MWD) survey, and a second high side offset angle at the first measured depth based on the second sensor data;adjusting gain and offset coefficients for the radial magnetometer, the tangential magnetometer, the radial accelerometer, or the tangential accelerometer until the first azimuth angle substantially equals the second azimuth angle; andstoring the adjusted gain and offset coefficients as calibrated gain and offset coefficients for the radial magnetometer, the tangential magnetometer, the radial accelerometer, and the tangential accelerometer.