METHOD AND APPARATUS FOR DIRECTIONAL DRILLING USING WIRED DRILL PIPE

Abstract

A method for drilling a wellbore includes rotating a drill string having a steerable drilling motor proximate a distal end thereof in a wellbore to a selected tool face angle. A torque applied to the drill string and a rotational orientation of the drill string is measured at spaced apart positions along the drill string. The drill string is rotated in a first direction until rotation at one of the selected positions is measured. Rotation of the drill string is reversed to a second direction until rotation of the drill string at the one of the selected positions is measured. Rotation of the drill string is reversed to the first direction until a torque measured at at least one position along the drill string corresponds to a torque measured when drill string rotation was reversed from the first direction.

Claims

1. A method for drilling a wellbore, comprising: rotating a drill string having a steerable drilling motor proximate a distal end thereof in a wellbore to a selected tool face angle; measuring a torque applied to the drill string at a plurality of spaced apart positions along the drill string and a rotation of the drill string; rotating the drill string in a first direction until rotation of the drill string at one of the plurality of spaced apart positions is measured; reversing rotation of the drill string to a second direction until rotation of the drill string is detected at the one of the plurality of spaced apart positions is measured; and reversing rotation of the drill string to the first direction until a torque measured at at least one of the plurality of spaced apart positions along the drill string corresponds to a torque measured at the same one of the plurality of spaced apart positions when drill string rotation was reversed from the first direction.

2. The method of claim 1 further comprising measuring axial and torsional loading on the drill string at each of the plurality of spaced apart positions and determining a distribution along the drill string of force resisting rotation between the drill string and the wellbore.

3. The method of claim 1 wherein the measuring rotation comprises measuring a rotary orientation of the drill string.

4. The method of claim 3 wherein the measuring rotary orientation comprises at least one of measuring acceleration and measuring Earth's magnetic field direction.

5. The method of claim 1 further comprising determining a neutral point of torque along the drill string using the measurements of torque or rotary displacement at the plurality of spaced apart positions along the drill string, or both.

6. The method of claim 1 further comprising determining accumulation of drill cuttings in the wellbore using the measurements of torque or rotary displacement at the plurality of spaced apart positions, or both.

7. The method of claim 1 further comprising determining changes in force resisting rotational and resisting axial movement of the drill string instantaneously or over time.

8. The method of claim 1 further comprising determining changes in force resisting rotation and axial movement and relating the changes to accumulation of cuttings in the wellbore along the drill string instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

9. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to differential sticking between the drill string and the wellbore instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

10. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to well bore stability along the drill string instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

11. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to damage in the drill string along the drill string instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

12. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to inaccurate sensor reading at a repeater in the drill string instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

13. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to changes in properties of subsurface formations along the drill string instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

14. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to changes in drilling fluid properties instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

15. The method of claim 1 further comprising determining changes in force resisting rotation and resisting axial movement and relating the changes to changes in drilling fluid flow rate instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

16. The method of claim 1 further comprising determining neutral point changes resulting from changes in force resisting rotation and resisting axial movement and relating the changes to at least one of drill bit cutting efficiency, and steerable drilling motor efficiency instantaneously or over time using the measurements of torque and measurements of axial force at each of the plurality of spaced apart positions.

17. (canceled)

18. A wellbore drilling system, comprising: a plurality of torque sensors disposed at spaced apart locations along a drill string; a steerable drilling motor coupled to the drill string proximate a longitudinal end thereof; a tool face angle sensor disposed in the drill string proximate the steerable drilling motor; a drill string rotation controller functionally coupled to a means for rotating the drill string disposed at an upper end of the wellbore; and a processor in signal communication with the plurality of torque sensors and the tool face angle sensor, the processor in signal communication with the drill string rotation controller, the processor programmed to receive signals from the plurality of torque sensors and the tool face angle sensor, the processor programmed to operate the drill string rotation controller to rotate the drill string in a first direction until rotation of the drill string at one of the spaced apart locations is measured, the processor programmed to operate the drill string rotation controller to reverse rotation of the drill string to a second direction until rotation of the drill string is detected at the one of the selected locations is measured, the processor programmed to operate the drill string rotation controller to reverse rotation of the drill string to the first direction until a torque measured at at least one location along the drill string corresponds to a torque measured when drill string rotation was reversed from the first direction.

19. The wellbore drilling system of claim 18 further comprising a plurality of axial load sensors disposed on the drill string at the spaced apart positions, wherein the processor is programmed to determine a distribution along the drill string of coefficient of friction between the drill string and the wellbore using measurements from the torque sensors and the axial load sensors.

20. The wellbore drilling system of claim 18 further comprising a plurality of sensors for measuring a rotary orientation of the drill string disposed at spaced apart locations along the drill string.

21. The wellbore drilling system of claim 20 wherein the plurality of rotary orientation sensors comprises at least one of acceleration sensors and magnetic field sensors.

22.-34. (canceled)

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0004] FIG. 1 is a pictorial view of an example directional drilling system.

[0005] FIG. 2 is a block diagram of an example directional driller control system that may be used in some embodiments.

DETAILED DESCRIPTION

[0006] An example embodiment of a well drilling system including one possible embodiment of a directional drilling system is shown schematically in FIG. 1. A drilling unit or “rig” is designated generally by numeral 11. The drilling rig 11 in FIG. 1 is depicted as a land rig. However, as will be apparent to those skilled in the art, a method and apparatus according to the present disclosure will find equal application to marine drilling rigs, including without limitation, jack-up rigs, semisubmersible platforms and drill ships. The type of drilling rig used is not a limitation on the scope of the present disclosure.

[0007] The drilling rig 11 includes a derrick 13 that is supported on the ground surface above a rig floor 15. The drilling rig 11 includes lifting gear, which comprises a crown block 17 mounted to or suspended from the derrick 13, and a traveling block 19. The crown block 17 and the traveling block 19 are interconnected by a cable 21 that is driven by draw works 23 to control upward and downward movement of the traveling block 19 in the derrick 13. The traveling block 19 carries or has affixed thereto a hook 25 from which may be suspended a top drive 27. The top drive 27 supports a drill string, designated generally by reference numeral 31, in a wellbore 33. The top drive 27 may be operated to rotate the drill string 31 in either direction.

[0008] In some embodiments, a length of connected drill pipe segments having certain drilling tools at a longitudinal end thereof, collectively, the “drill string” 31, is coupled to the top drive 27. In the present embodiment such connection may be made through an instrumented top sub 29. As will be described in more detail, the instrumented top sub 29 may include sensors that measure torque and axial loading and may receive signals from a communication channel in the drill string 31. In the present example, the drill string 31 may comprise a “wired” drill pipe. Wired drill pipe may include a communication channel comprising at least one or more insulated electrical conductors extending along the lengths of each segment 35 (“joint”) of the drill pipe and electromagnetic couplings at the longitudinal ends of each segment 35 and thus between adjacent pipe segments 35 so that signals may be communicated from proximate the wellbore end of the drill string 31 to the surface, e.g., to the instrumented sub 29, and then to a processor 55 (explained in more detail with reference to FIG. 2). The processor 55 may be disposed in and/or form part of a signal recording and processing unit 32. An example of a wired drill pipe that may be used in some embodiments is described in U.S. Pat. No. 6,641,434 issued to Boyle et al.

[0009] A wired drill pipe as disclosed in the Boyle et al. '434 patent may include one or more signal repeaters 36 disposed at selected positions along the length of the drill string 31. A non-limiting example embodiment of a signal repeater usable with such a wired drill pipe is described in U.S. Pat. No. 7,064,676 issued to Hall et al. The signal repeater(s) 36 may amplify and retransmit signals communicated along the wired drill pipe such that there is sufficient signal amplitude both at the instrumented sub 29 for signals communicated to the surface and at a sensor system (51, described below) at the end of the drill string 31 for signals communicated from the surface. The signal repeater(s) 36 may include sensors therein, for example and without limitation, strain gauges to measure torsion on the drill string 31, strain gauges to measure axial loading on the drill string 31, accelerometers and magnetometers and/or gyroscopes to measure the geodetic (or geomagnetic) direction and inclination of the drill string 31 at any one or more of the repeaters 36, pressure sensors to measure pressure inside and/or outside the drill string 31 at each repeater position and temperature sensors to measure temperature in the wellbore 33 at each repeater 36 position. In other embodiments, the repeater(s) 36 may be substituted by sensor housings having one or more of the above described sensors, although the described types of sensors are not a limitation on the number of and types of sensors that may be used in any particular embodiment. In some embodiments, the instrumented top sub 29 may include a wireless signal transceiver 30 that can transmit the signals generated by each of the sensors in each of the repeaters 36 and a measurement while drilling (MWD) sensor forming part of the sensor system 51 (explained below) to the signal recording and processing unit 32 for further processing by the processor 55 as will be further explained with reference to FIG. 2.

[0010] The drill string 31 may include a bottom hole assembly (BHA) 37 at its end, which may include stabilizers, drill collars, and a set of (MWD) sensors forming part of the sensor system 51 including, without limitation a directional and inclination sensor, a pressure sensor, a torque sensor and an axial load sensor (not shown separately for clarity). As will be explained in more detail, the directional and inclination (D&I) sensor may generate a signal corresponding to the tool face angle orientation of a steerable drilling motor 41 coupled within the drill string 31.

[0011] Drilling fluid is delivered to the drill string 31 by mud pumps 43 through a mud hose 45. During “rotary” drilling, the drill string 31 is rotated within the wellbore 33 by operating the top drive 27 to rotate the drill string 31 connected thereto such that the drill string 31 imparts rotation to a drill bit 40 at the end of the drill string 31. The top drive 27 may be mounted on parallel, vertically extending rails (not shown) to couple reactive torque to the derrick 13 as torque is applied to the drill string 31 by the top drive 27. Rotary drilling is used to extend the length of a bore hole 33.

[0012] The bent housing (“steerable”) drilling motor 41 may be connected to the drill string 31 proximate the bottom of BHA 37 and may have the drill bit 40 functionally connected to a rotary output of the steerable drilling motor 41. As is known in the art, by controlling a “tool face angle” (i.e., the orientation of a plane intersecting the largest angle subtended by the bend in the housing) of the steerable motor 41 the trajectory (i.e., azimuth and/or inclination) of the wellbore 33 may be maintained, controlled or changed during “slide” directional drilling, that is, when the drill string (31 in FIG. 1) is not rotated by the top drive 27. During slide directional drilling, the drill string 31 may be held rotationally substantially stationary by the top drive 27 while the drill bit 40 is rotated by the steerable drilling motor 41. The steerable drilling motor 41 in some embodiments may be operated by flow of drilling fluid through the drill string 31 and thence through the steerable drilling motor 41.

[0013] The drilling rig operator (“driller”) may further operate the top drive 27 to move the tool face angle of the steerable drilling motor 41 to a selected rotational orientation and thereby change the trajectory of the wellbore 33 to a selected orientation. Although a drilling rig having a top drive is illustrated, those skilled in the art will recognize that the present example system may also be used in connection with drilling rigs in which a rotary table and kelly are used to rotate the drill string 31. Drill cuttings produced as the drill bit 40 drills into the formations to extend the wellbore 33 are carried out of wellbore 33 (through an annular space 39 between the wellbore wall and the drill string 31) by the drilling fluid supplied by the mud pumps 43.

[0014] FIG. 2 shows a block diagram of an example control apparatus according to the present disclosure. The MWD sensors, which may be part of sensor system 51 as explained with reference to FIG. 1, may include a directional an inclination (D&I) sensor (not shown separately), which produces a signal indicative of the steerable drilling motor (41 in FIG. 1) tool face angle, the gravitational inclination, and magnetic direction of the D&I sensor (and thereby the wellbore geomagnetic trajectory at the position of the MWD sensors). In the present example embodiment, the wired drill pipe communication channel may provide substantially instantaneous communication of tool face angle measurements and other measurements from the MWD sensors (e.g., at 51) to the processor 55.

[0015] Additionally, any one or more of the repeaters 36 may also provide an indication of its tool face position using similar D&I sensors disposed in or proximate to each repeater 36 or a subset thereof in order to detect whether or not any particular repeater 36 is rotating or is rotationally stationary with reference to the axial direction of the wellbore (33 in FIG. 1; i.e., along the wellbore).

[0016] The control apparatus may also include a surface drill string torque sensor 53, which provides a measurement corresponding to the torque applied to the drill string (31 in FIG. 1) at the surface. The surface drill string torque sensor 53 may be implemented, for example and without limitation, as a strain gage in the instrumented top sub (29 in FIG. 1). The surface drill string torque sensor 53 may also be implemented as a current measurement device for an electric rotary table or top drive motor, or as pressure sensor for an hydraulically operated top drive. Measurements corresponding to torque, pressure, axial loading, rotation, pressure and temperature at the locations of each of the repeaters 36 (or sensor housings if repeaters are not used) may also be provided using corresponding sensors located in or proximate to any one or more of the repeaters 36.

[0017] The output of the respective sensors 51, 36 and 53 may be received as input to the processor 55. The processor 55 may be programmed to process signals received from sensors 51, 36, 53 in a manner to be further explained below. The processor 55 may also receive user input from user input devices, such as a keyboard 57. Other user input devices such as touch screens, keypads, and the like may also be used. The processor 55 may provide signals to a display 59 wherein a visual representation of the various sensor measurements may be observed. The processor 55 also provides output to a drill string rotation controller 61 that operates the top drive (27 in FIG. 1) or rotary table to rotate the drill string (31 in FIG. 1). Secondary displays to computer systems or other processors that are networked or otherwise in signal communication with the processor 55 may also use any of the sensor data or data computed in the processor 55 to display for some other user on or off the location of the drilling rig (11 in FIG. 1).

[0018] In some embodiments, the steerable drilling motor 41 may be oriented at a tool face angle selected to attain a desired wellbore trajectory. As the steerable drilling motor 41 is advanced into the wellbore (33 in FIG. 1) while drilling with the drill bit (40 in FIG. 1) on the bottom of the wellbore, the processor 55 may operate the drill string rotation controller 61 to cause the top drive (27 in FIG. 1) rotate drill the string (31 in FIG. 1) in a first direction while monitoring drill string torque using the torque sensor 53, and the torque sensors in each of the repeaters 36 if so used, the tool face angle using measurements from the D&I sensor in the MWD instrument (see 51 in FIG. 1), as well as the tool face angle measured in any one or more of the repeaters 36. As long as the steerable motor (41 in FIG. 1) does not rotate, the rotation controller 61 (at surface) may cause the top drive (27 in FIG. 1) to continue to rotate the drill string (31 in FIG. 1) in the first direction.

[0019] As the drill string (31 in FIG. 1) is rotated, the D&I sensors in each repeater 36 may provide a measurement of the tool face angle at each repeater. The processor 55 may record the respective measured tool face angles along with the torque magnitude measured by the surface torque sensor 53, each of the torque sensors in any or all of the repeaters 36, as well as torque in sensors (not shown) that may be disposed near the steerable motor (41 in FIG. 1), e.g., in sensor system 51 in FIG. 1. The processor 55 may determine rotation along the drill string (31 in FIG. 1) by examining the time rate of change of the tool face angle measured by each repeater 36. Rotation at the surface may continue until rotation occurs at a repeater nearest to the steerable motor (41 in FIG. 1) or any other selected repeater. The processor 55 then actuates the drill string rotation controller 61 to reverse the direction of rotation of drill string (31 in FIG. 1). The drill string (31 in FIG. 1) is then rotated in the opposite direction until the opposite rotation is detected near the steerable motor (41 in FIG. 1), or at any other repeater 36. The processor 55 then operates the drill string rotation controller 61 to reverse drill string rotation and rotate the top drive (27 in FIG. 1) and thus the drill string (31 in FIG. 1) again in the first direction until the previously described rotation limit is reached.

[0020] As slide directional drilling progresses, the processor 55 continues to monitor measured drill string torque and rotation at the surface and along the drill string (31 in FIG. 1), e.g., using the surface torque sensor 53 in the instrumented sub (29 in FIG. 1) and the torque and tool face angle measured at each repeater 36, and actuates the rotation controller 61 to rotate the drill string (31 in FIG. 1) back and forth assuring that maximum torques in the forward and backward rotational direction are not exceeded. The back and forth rotation of the drill string caused by operating the top drive (27 in FIG. 1) at the surface may reduce or eliminate stick/slip friction between the drill string (31 in FIG. 1) and the wellbore (33 in FIG. 1), thereby making it easier for the driller to control axial force (weight) along the drill string (33 in FIG. 1) to the drill bit (40 in FIG. 1) as well as the tool face angle of the steerable motor (41 in FIG. 1). The latter is made possible by reducing variations in reactive torque exerted by the steerable drilling motor (41 in FIG. 1). In some embodiments, the torque sensor in each repeater 36 may be used to determine a torque distribution along the drill string (31 in FIG. 1), so that during drilling, changes in the forces and moments preventing rotation along the drill string may be used to detect and monitor remedial actions of detrimental drilling situations such as cuttings accumulation or drill string to wellbore wall sticking situations (differential sticking).

[0021] In some embodiments, the selected point along the drill string (31 in FIG. 1) for rotation to be transferred may be at a position along the drill string at which reactive torque from the steerable drilling motor (41 in FIG. 1) is fully absorbed by friction between the drill string (31 in FIG. 1) and the wellbore wall. The selected point may be calculated using “torque and drag” simulation computer programs well known in the art. Such programs calculate axial force and frictional/lateral force at each position along the drill string for any selected wellbore trajectory. One such program is sold under the trade name WELLPLAN by Landmark Graphics Corp., Houston, Tex. Generally, such simulations do not account for situations that can cause forces and moments that prevent rotation. By using the computed results under the assumed “problem free” drilling situation as the baseline for torque distribution along the drill string, deviations from modelled profiles can be attributed to some detrimental drilling situation.

[0022] It may also be possible in some embodiments to determine distribution of the reactive torque along the length of drill string by observing the measured torque at each repeater 36.

[0023] In some embodiments, the selected point (referred to as the “neutral point”) may be determined using measurements from the sensors in the repeaters 36. In some embodiments, measurements of rotary orientation of the drill string at each of the repeaters 36 may be made, and the selected point determined by determining which of the repeaters 36 is not rotated when the drill string is rotated at the surface. In some embodiments, measurements using the D&I sensors in each repeater 36 may be used to infer rotation of the drill string at each repeater 36. In some embodiments, the first torque magnitude may be determined by rotating the drill string in the first direction until slight rotation of the drill string is measured by the D&I sensor in any one of, or the deepest one of the repeaters 36 while measuring torque on at least the surface torque sensor 53. For purposes of the present example embodiment, it may be assumed that the drill string does not rotate below the deepest repeater 36 at which rotation is measured or determined. Rotation of the drill string may be inferred, for example by measurements of acceleration due to gravity along different directions, e.g., three orthogonal directions, indicating a change in the orientation of the drill string with respect to gravity when one or more of the acceleration measurements changes. In other embodiments, rotation may be inferred by measuring directional components of Earth's magnetic field, e.g., along three mutually orthogonal directions, wherein change in orientation may be inferred by changes in the relative magnitude of any one or more of the component measurements. The controller 55 may be programmed to then operate the drill string rotation controller 61 to reverse direction of rotation of the top drive and the drill string. The torque measured by at least the surface sensor may be measured and the drill string rotation stopped when the deepest one of the repeaters 36 detects slight rotation of the drill string.

[0024] In some embodiments, measurements of torque and/or rotation at each repeater 36 may be used as an indication that a detrimental drilling situation is occurring such as drill cuttings beginning to accumulate in the wellbore annulus (39 in FIG. 1). For example, an increase in the amount of torque measured at each repeater 36 without causing change in the measured tool face angle may be indicative of drill cuttings accumulation. Additionally by using a distributed set of sensors at various locations along the drill string using the described wired drill pipe, it may be possible to determine exactly how much of the drill string has rotated during sliding drilling while rotating the drill string in the first and second directions. The foregoing determination may be used to provide a feedback signal to the processor 55 and may be used to determine the actual amount of torque, displacement, or energy to be applied by the top drive (27 in FIG. 1) to ensure the proper transmission of drill string weight to the drill bit (40 in FIG. 1). In some embodiments, it may be possible to measure changes in force or torque resisting rotational movement and resisting axial movement of the drill string instantaneously or over time by the measurements of torque and/or axial force at each sensor (e.g., proximate the steerable drilling motor, proximate the drill bit and at each repeater or sensor housing). The foregoing measurements made over time may be used for determining any one or more of a number of different characteristics. For example, and without limitation the following example characteristics may be determined.

[0025] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and axial movement and to relate the changes to accumulation of cuttings in the wellbore along the drill string instantaneously or over time. This is especially relevant when the forces and torques are linked with hydraulic algorithms which can estimate wellbore annulus cleaning issues and cuttings bed movements.

[0026] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to differential sticking between the drill string and the wellbore instantaneously or over time.

[0027] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to well bore stability along the drill string instantaneously or over time.

[0028] In some embodiments the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to damage in the drill string along the drill string instantaneously or over time. This is especially the case when a hole is developing in the drill pipe due to a washout (fluid flow wearing away the interior of the drill pipe) or abrasion on the exterior. In either case, the torsional stiffness of the drill pipe between two repeaters will decrease, which can be estimated between repeaters using the rotational displacement and torque measurements at the repeaters.

[0029] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to inaccurate sensor reading at a repeater in the drill string instantaneously or over time. This can be performed by examining trends in displacement along the drill string and statistically determining if measurements on a repeater are outside of an acceptable range.

[0030] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to changes in properties of subsurface formations along the drill string instantaneously or over time.

[0031] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement to relate the changes to changes in drilling fluid properties instantaneously or over time.

[0032] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine changes in force or torque resisting rotation and resisting axial movement and to relate the changes to changes in drilling fluid flow rate instantaneously or over time.

[0033] In some embodiments, the processor (e.g., 55 in FIG. 2 or any other processor) may be programmed to determine neutral point changes resulting from changes in force or torques resisting rotation and resisting axial movement and to relate the changes to at least one of drill bit cutting efficiency, and steerable drilling motor efficiency instantaneously or over time.

[0034] By monitoring a distributed set of torque, rotation, and/or axial load sensors a wellbore “efficiency” may be computed that can indicate the amount of friction and torque loss that is being experienced along the wellbore. Determined distribution of friction losses along the length of the drill string may aid in computation of dynamic drill string behavior and in general estimating the drillability of the portion of the wellbore remaining to be drilled. Using distributed torque and axial loading measurements may also enable estimating the coefficients of friction along the length of the drill string and their changes due to dynamic environmental changes, for example and without limitation, cuttings accumulation and movement within the wellbore.

[0035] While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.