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United States Patent Application 20170370152
Kind Code A1
Samuel; Robello ;   et al. December 28, 2017

Dogleg Severity Estimator for Point-The-Bit Rotary Steerable Systems

Abstract

An illustrative dogleg severity (DLS) estimation method includes: retrieving dimensions of steering assembly; determining an initial DLS estimate; using the DLS estimate in combination with the steering assembly dimensions to determine node displacements for a shaft portion of the steering assembly; deriving a bit side force from the node displacements while accounting for elastic bending in a housing portion of the steering assembly; performing a DLS calculation based in part on the bit side force; adjusting the DLS estimate if the DLS calculation does not match; repeating said using, deriving, performing, and adjusting until a match is achieved; and storing the DLS estimate on a nontransient information storage medium.


Inventors: Samuel; Robello; (Cypress, TX) ; Zhang; Yuan; (Missouri City, US)
Applicant:
Name City State Country Type

Halliburton Energy Services, Inc.

Houston

TX

US
Assignee: Halliburton Energy Services, Inc.
Houston
TX

Family ID: 1000002861272
Appl. No.: 15/525313
Filed: December 14, 2015
PCT Filed: December 14, 2015
PCT NO: PCT/US2015/065566
371 Date: May 9, 2017


Current U.S. Class: 1/1
Current CPC Class: E21B 47/0002 20130101; E21B 7/06 20130101; E21B 47/12 20130101
International Class: E21B 7/06 20060101 E21B007/06; E21B 47/00 20120101 E21B047/00

Claims



1. A dogleg severity (DLS) estimation method that comprises: retrieving dimensions of a steering assembly; determining an initial DLS estimate; using the DLS estimate in combination with the steering assembly dimensions to determine node displacements for a shaft portion of the steering assembly; deriving a bit side force from the node displacements while accounting for elastic bending in a housing portion of the steering assembly; performing a DLS calculation based in part on the bit side force; adjusting the DLS estimate if the DLS calculation does not match; repeating said using, deriving, performing, and adjusting until a match is achieved; and storing the DLS estimate on a nontransient information storage medium.

2. The method of claim 1, further comprising: obtaining measurements of formation parameters as a function of position along a borehole, wherein said DLS calculation is further based on said measurements, and wherein said determining, using, deriving, performing, adjusting, repeating, and storing operations are performed for multiple positions along the borehole to produce a log of DLS versus position.

3. The method of claim 2, wherein the calculation accounts for a rock strength.

4. The method of claim 2, wherein the determination of node displacements accounts for an axial force along the shaft portion of the steering assembly.

5. The method of claim 2, further comprising displaying a visual representation of said log.

6. The method of claim 1, wherein the dimensions include a setting for an eccentricity mechanism within the housing portion of the steering assembly, and wherein the method further comprises changing the setting to keep the DLS estimate within a desired range.

7. The method of claim 6, wherein said changing is performed to achieve a desired value for the DLS estimate.

8. The method of claim 6, wherein said mechanism is an eccentricity ring.

9. The method of claim 1, further comprising: determining initial housing deflection estimates when determining the initial DLS estimate, wherein said using accounts for said housing deflection estimates, wherein said deriving includes: obtaining internal side forces on the shaft portion; making a housing deflection calculation based on the internal side forces; refining the housing deflection estimate if the housing deflection calculation differs, and wherein said using and deriving are repeated until the housing deflection estimate and housing deflection calculation no longer differ.

10. The method of claim 9, wherein said deriving further includes computing shaft orientation angles from the node displacements, and computing the internal side forces based at least in part on the shaft orientation angles.

11. A dogleg severity (DLS) estimation system that comprises: a nontransient information storage medium having DLS estimation software; at least one processor that retrieves and executes said tendency predictor software, the software causing the at least one processor to implement a method comprising: retrieving dimensions of steering assembly; determining an initial DLS estimate; using the DLS estimate in combination with the steering assembly dimensions to determine node displacements for a shaft portion of the steering assembly; deriving a bit side force from the node displacements while accounting for elastic bending in a housing portion of the steering assembly; performing a DLS calculation based in part on the bit side force; adjusting the DLS estimate if the DLS calculation does not match; and repeating said using, deriving, performing, and adjusting until a match is achieved; and a display coupled to the at least one processor to provide a visual representation of the DLS estimate.

12. The system of claim 11, wherein the method further comprises: obtaining measurements of formation parameters as a function of position along a borehole, wherein said DLS calculation is further based on said measurements, and wherein said determining, using, deriving, performing, adjusting, repeating, and storing operations are performed for multiple positions along the borehole to produce a log of DLS versus position.

13. The system of claim 12, wherein the calculation accounts for a rock strength.

14. The system of claim 12, wherein the determination of node displacements accounts for an axial force along the shaft portion of the steering assembly.

15. The system of claim 12, wherein the method further comprises storing said log on the nontransient information storage medium.

16. The system of claim 11, wherein the dimensions include a setting for an eccentricity mechanism within the housing portion of the steering assembly, and wherein the method further comprises changing the setting to keep the DLS estimate within a desired range.

17. The system of claim 16, wherein said changing is performed to achieve a desired value for the DLS estimate.

18. The system of claim 16, wherein said mechanism is an eccentricity ring.

19. The system of claim 11, wherein the method further comprises: determining initial housing deflection estimates when determining the initial DLS estimate, wherein said using accounts for said housing deflection estimates, wherein said deriving includes: obtaining internal side forces on the shaft portion; making a housing deflection calculation based on the internal side forces; refining the housing deflection estimate if the housing deflection calculation differs, and wherein said using and deriving are repeated until the housing deflection estimate and housing deflection calculation no longer differ.

20. The system of claim 19, wherein said deriving further includes computing shaft orientation angles from the node displacements, and computing the internal side forces based at least in part on the shaft orientation angles.
Description



BACKGROUND

[0001] Directional drilling is the process of directing the borehole along a defined trajectory. Deviation control during drilling is the process of keeping the borehole trajectory contained within specified limits, e.g., limits on the inclination angle or distance from the defined trajectory, or both. Both have become important to developers of unconventional hydrocarbon resources.

[0002] Various drill string steering mechanisms exist to provide directional drilling and deviation control: whipstocks, mud motors with bent-housings, jetting bits, adjustable gauge stabilizers, and the increasingly popular rotary steering systems (RSS). These techniques each employ side force, bit tilt angle, or some combination thereof, to steer the drill string's forward and rotary motion. However, the resulting borehole's actual curvature is not determined by these parameters alone, and it is generally difficult to predict, necessitating slow drilling, and frequent survey measurements.

[0003] Among the most important trajectory parameters that need to be monitored and controlled is the wellbore dogleg, i.e., the sections along which the trajectory changes direction faster than anticipated or desired. The severity of such direction changes can be expressed in terms of degrees per unit length or alternatively in terms of the radius of curvature. Decreasing the curvature radius corresponds to increasing the degrees of directional change per unit length, both of which correspond to increasing the dogleg severity. Severe doglegs create a number of difficulties including casing insertion difficulty, increased friction, increased casing wear, and increased likelihood of bottomhole component trapping.

[0004] One method for measuring borehole curvature and, more specifically, dogleg severity, is to measure the bending of a bottomhole assembly as it passes along the borehole. A subtle yet important shortcoming of this method arises from the erroneous assumption that the bottomhole assembly bends in the same fashion as the borehole.

BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Accordingly, there are disclosed herein dogleg severity estimators that account for housing deflections in point-the-bit rotary steerable systems. In the drawings:

[0006] FIG. 1 is a schematic view of an illustrative directional drilling environment.

[0007] FIG. 2 is a block diagram of an illustrative directional drilling system.

[0008] FIGS. 3A-3C are schematic views of illustrative point-the-bit steering mechanism components.

[0009] FIG. 4 is a schematic illustration of force and moment parameters for one segment of the shaft.

[0010] FIGS. 5a-5c are line drawings illustrating certain geometric parameters of a steering mechanism in a curved borehole.

[0011] FIG. 6 is a flow diagram of an illustrative dogleg severity estimator method.

[0012] It should be understood, however, that the specific embodiments given in the drawings and detailed description thereto do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and modifications that are encompassed together with one or more of the given embodiments in the scope of the appended claims.

DETAILED DESCRIPTION

[0013] To provide context for the ensuing dogleg severity (DLS) estimator discussion, an illustrative directional drilling environment is shown in FIG. 1. A drilling platform 102 supports a derrick 104 having a traveling block 106 for raising and lowering a drill string 108. A top drive 110 supports and rotates the drill string 108 as it is lowered into a borehole 112. The rotating drill string 108 and/or a downhole motor in bottomhole assembly 114 rotates a drill bit 116. As the drill bit 116 rotates, it extends the borehole 112 in a directed manner through various subsurface formations. The bottomhole assembly 114 includes a point-the-bit rotary steerable system (RSS) 118 which enables the drilling crew to steer the borehole along a desired path. A pump 122 circulates drilling fluid through a feed pipe to the top drive 110, downhole through the interior of drill string 108, through orifices in drill bit 116, back to the surface via the annulus around drill string 108, and into a retention pit 124. The drilling fluid transports cuttings from the borehole into the retention pit 124 and aids in maintaining the borehole integrity.

[0014] The BHA 114 may further include one or more drill collars (i.e., thick-walled steel pipe) to provide weight and rigidity to aid the drilling process. Some of these drill collars typically include built-in logging instruments to gather measurements of various drilling parameters such as position, orientation, weight-on-bit, torque, vibration, borehole diameter, downhole temperature, pressure, etc. The tool orientation may be specified in terms of a tool face angle (rotational orientation), an inclination angle (the slope), and compass direction, each of which can be derived from measurements by magnetometers, inclinometers, and/or accelerometers, though other sensor types such as gyroscopes may alternatively be used. In one specific embodiment, the tool includes a 3-axis fluxgate magnetometer and a 3-axis accelerometer. As is known in the art, the combination of those two sensor systems enables the measurement of the tool face angle, inclination angle, and compass direction. Such orientation measurements can be combined with gyroscopic or inertial measurements to accurately track tool position.

[0015] One or more logging while drilling (LWD) tools may also be integrated into the BHA 114 for measuring parameters of the formations being drilled through. As the drill bit 116 extends the borehole 112 through the subsurface formations, the LWD tools rotate and collect measurements of such parameters as resistivity, density, porosity, acoustic wave speed, radioactivity, neutron or gamma ray attenuation, magnetic resonance decay rates, and indeed any physical parameter for which a measurement tool exists. A downhole controller associates the measurements with time and tool position and orientation to map the time and space dependence of the measurements. The measurements can be stored in internal memory and/or communicated to the surface.

[0016] A telemetry sub may be included in the BHA 114 to maintain a communications link with the surface. Mud pulse telemetry is one common telemetry technique for transferring tool measurements to a surface interface 126 and to receive commands from the surface interface, but other telemetry techniques can also be used. Typical telemetry data rates may vary from less than one bit per minute to several bits per second, usually far below the necessary bandwidth to communicate all of the raw measurement data to the surface. Much of the data obtained by the control sub may be stored in memory for later retrieval, e.g., when the BHA 114 is recovered at the surface.

[0017] The surface interface 126 is further coupled to various sensors on and around the drilling platform 102 to obtain measurements of drilling parameters from the surface equipment, parameters such as hook load, rate of penetration, torque, and rotations per minute (RPM) of the drill string. A processing unit, shown in FIG. 1 in the form of a tablet computer 128, communicates with surface interface 126 via a wired or wireless network communications link 130, and provides a graphical user interface (GUI) or other form of interactive interface that enables a user to provide commands and to receive (and optionally interact with) a visual representation of the acquired measurements. The measurements may be in log form, e.g., a graph of the borehole trajectory and/or measured parameters as a function of time and/or position along the borehole. The processing unit can take alternative forms, including a desktop computer, a laptop computer, an embedded processor, a cloud computer, a central processing center accessible via the internet, and combinations of the foregoing.

[0018] Among the various types of measurement data that may be acquired by the BHA 114 are multi-component measurements of the earth's magnetic field and gravitational field at each of a series of survey points (or "stations") along the length of the borehole. The survey points are typically those positions where the navigation tool is at rest, e.g., where drilling has been halted to add lengths of drill pipe to the drill string. The gravitational and magnetic field measurements reveal the slope ("inclination") and compass direction ("azimuth") of the borehole at each survey point. When combined with the length of the borehole between survey points (as measureable from the length added to the drill string), these measurements enable the location of each survey point to be determined using known techniques such as, e.g., the tangential method, the balanced tangential method, the equal angle method, the cylindrical radius of curvature method, or the minimum radius of curvature method, to model intermediate trajectories between survey points. When combined together, these intermediate trajectories form an overall borehole trajectory.

[0019] Also among the various types of measurement data that may be acquired by the BHA 116 are caliper measurements, i.e., measurements of the borehole's diameter, optionally including the borehole's cross-sectional shape and orientation, as a function of position along the borehole.

[0020] FIG. 2 is a function-block diagram of an illustrative directional drilling system. One or more downhole tool controllers 202 collect measurements from a set of downhole sensors 204, preferably but not necessarily including both drilling parameter sensors and formation parameter sensors, to be digitized and stored, with optional downhole processing to compress the data, improve the signal to noise ratio, and/or to derive parameters of interest from the measurements.

[0021] A telemetry system 208 conveys at least some of the measurements or derived parameters to a processing system 210 at the surface, the uphole system 210 collecting, recording, and processing measurements from sensors 212 on and around the rig in addition to the telemetry information from downhole. Processing system 210 generates a display on interactive user interface 214 of the relevant information, e.g., measurement logs, borehole trajectory, drill string trajectory, or recommended drilling parameters to optimize a trajectory to limit estimated dogleg severity. The processing system 210 may further accept user inputs and commands and operate in response to such inputs to, e.g., transmit commands and configuration information via telemetry system 208 to the tool controllers 202. Such commands may alter the settings of the steering mechanism 206.

[0022] FIG. 3A shows an illustrative RSS of the point-the-bit type, which employs a non-rotating housing 300 that introduces an adjustable bend in the drill string shaft 302, resulting in a controllable bit tilt angle. The housing includes a set of bearings 304, 306, 308, and an eccentricity ring 310 that cooperate to provide the adjustable bend while permitting the shaft 302 to rotate relative to the housing 300. The RSS assembly contacts the borehole wall with the bit 116 (there experiencing a first external side force F.sub.E1) and with both ends of the non-rotating housing 300 (there experiencing side forces F.sub.E2 and F.sub.E3). A baseline 312 is defined to extend from the borehole axis at the top of the steering mechanism to the borehole axis at the tip of the bit. (The top of the steering mechanism may be taken as the upper-most component from which a side force can affect the walk angle.)

[0023] To analyze the external and internal forces acting on the RSS assembly, we divide it into the shaft portion of the assembly (FIG. 3B) and the housing portion of the assembly (FIG. 3C). Note that in FIGS. 3B and 3C, the baseline 312 acts as a horizontal axis, and the side forces are taken as acting perpendicular to the baseline. In FIG. 3B, the shaft portion is treated as five segments of a stiff, continuous pipe, each segment parameterized as described further below with respect to FIG. 4.

[0024] Bit 116 is the first segment, having a length L.sub.S1 and experiencing a side force F.sub.S1 (same as the first external side force F.sub.E1) at its tip. The second segment, having a length L.sub.S2, extends from the base of bit 116 to bearing 308, which exerts a side force F.sub.S3 on the shaft. The third segment, having length L.sub.S3, extends from bearing 308 to eccentricity ring 310, which exerts a side force F.sub.S4 on the shaft. The fourth segment, having length L.sub.S4, extends from the eccentricity ring 310 to bearing 306, which exerts a side force F.sub.S5 on the shaft. The fifth segment, having length L.sub.S5, extends from bearing 306 to bearing 308, which exerts a side force F.sub.S6 on the shaft.

[0025] In FIG. 3C, the housing portion is treated as five segments of a stiff beam spanning the distance between the two housing ends, which are modeled as being fixed in place. Each of the bearings exerts a side force on the housing in reaction to the side forces they exert on the shaft. Thus, bearing 308, at a distance L.sub.H1 from the bit-end of the housing 300, exerts a side force F.sub.H2 on the housing 300. Eccentricity ring 310, at a distance L.sub.H2 from bearing 308, exerts a side force F.sub.H3 on the housing 300. Bearing 306, at a distance L.sub.H3 from eccentricity ring 310, exerts a side force F.sub.H4 on the housing 300. Bearing 304, at a distance L.sub.H4 from bearing 306, exerts a side force F.sub.H5 on the housing 300.

[0026] As shown in FIG. 4, each segment j of the shaft or housing is modeled as a smoothly-deformable stiff element extending from a node j to a node (j+1), the node index at the tip of the bit being j=1 and increasing towards the top of the BHA. When considering the segment j in isolation, nodes j and j+1 are also referenced as nodes jR and jL, respectively. Segment j experiences an axial force N, a shear force Q.sub.jL, and a bending moment M.sub.jL at node jL, and further experiences axial force N, a shear force Q.sub.jR, and a bending moment M.sub.jR at node jR. The axial force N may be taken as equal to the weight on bit. The shear forces at a given node j combine to equal the side force from the shaft (F.sub.Hj=Q.sub.(j-1)L+Q.sub.jR). Note that .theta..sub.(j+1)R=.theta..sub.jL, but M.sub.(j+1)R=-M.sub.jL.

[0027] At node jL, the axis of the segment j is displaced from the baseline by a signed displacement e.sub.jL and oriented at an angle .theta..sub.jL. Similarly, at node jR, the axis of the segment j is displaced from the baseline by a signed displacement e.sub.jR and oriented at an angle .theta..sub.jR. Note that e.sub.(j+1)R=e.sub.jL and .theta..sub.(j+1)R=.theta..sub.jL. The stiffness of the element is represented by the product of its elastic modulus E and its area moment of inertia I. The length of segment j is represented L.sub.j. Moments and angles are positive when directed clockwise; vertical forces and deflections are positive when directed downward; axial force is positive when it is compressive.

[0028] We note that at each point k, the deflection of the housing (relative to the housing's axis) can be estimated using the energy method to relate the moment caused a virtual unit force at point k, M(k) to the moments from the side forces from the shaft, yielding the following expression:

.delta. k = 1 EI .intg. M ( k ) _ Mds = 1 6 EI j = 1 5 [ M jL ( k ) _ ( 2 M jL - M jR ) + M jR ( k ) _ ( 2 M jR - M jL ) ] L j . ( 1 ) ##EQU00001##

A geometric analysis enables the housing node displacements relative to the baseline 312 to be readily derived from the deflection values. Other techniques for calculating displacement of the housing from the side forces from the shaft can be found in the open literature, including using a finite element analysis of the housing.

[0029] Turning the focus now to the shaft, the force and bending moments on a given shaft segment j are derivable from the displacement and orientation of the nodes using the following matrix equation:

[ ( 12 i j L j 2 - N L j ) 6 i j L j ( - 12 i j L j 2 + N L j ) 6 i j L j 6 i j L j 4 i j - 6 i j L j 2 i j ( - 12 i j L j 2 + N L j ) - 6 i j L j ( 12 i j L j 2 - N L j ) - 6 i j L j 6 i j L j 2 i j - 6 i j L j 4 i j ] { e jL .theta. jL e jR .theta. jR } = { Q jL M jL Q jR M jR } ( 2 ) ##EQU00002##

where i.sub.j is the stiffness factor and L.sub.j is the length of segment j; e.sub.jL and e.sub.jR are the displacements at the left and right ends of segment j; and .theta..sub.jL and .theta..sub.jR are the orientations at the left and right ends of segment j. The stiffness factor can be calculated as i=EI/L for each segment.

[0030] When force balancing is applied along the shaft, the equilibrium equation for the whole shaft becomes:

[ ( 4 i 2 - NL 1 + 12 i 2 L 1 2 L 2 2 - NL 1 L 2 + 12 i 2 L 1 L 2 ) ( 2 i 2 + 6 i 2 L 1 L 2 ) 0 0 ( 2 i 2 + 6 i 2 L 1 L 2 ) 4 ( i 2 + i 3 ) 2 i 3 0 0 2 i 3 4 ( i 3 + i 4 ) 2 i 4 0 0 2 i 4 ( 4 i 4 + 3 i 5 ) ] { .theta. 2 .theta. 3 .theta. 4 .theta. 5 } = { ( 6 i 2 L 2 + 12 i 2 L 1 L 2 2 - NL 1 L 2 ) ( e 1 - e 3 ) 6 i 2 L 2 e 1 - 6 ( i 2 L 2 - i 3 L 3 ) e 3 - 6 i 3 L 3 e 4 6 i 3 L 3 e 3 - 6 ( i 3 L 3 - i 4 L 4 ) e 4 - 6 i 4 L 4 e 5 6 i 4 L 4 e 4 - ( 6 i 4 L 4 - 3 i 5 L 5 ) e 5 - 3 i 5 L 5 e 6 } ( 3 ) ##EQU00003##

If the shaft node displacements e.sub.j are known (or estimated as discussed further below), equation (3) enables the axis orientations to be determined at each node. The bit is modeled as a rigid body, meaning that the bit tilt angle .theta..sub.1 (also referenced elsewhere herein as .theta..sub.t) is equal to the orientation at node 2, i.e., .theta..sub.1=.theta..sub.2. The displacements and orientations can then be used in equation (2) to derive the side forces on the shaft, including the side force on the bit.

[0031] FIGS. 5A-5C introduce certain additional geometrical parameters that are useful for deriving dogleg severity (DLS), which is defined to be the change in direction per unit length. Where the drilling configuration is in equilibrium, the borehole forms a circular arc. At the two defining points 502, 504, on the baseline 312, the borehole tangent forms an angle, hereafter termed the walk angle .theta..sub.w, with the baseline. Thus in the time it takes for the BHA to drill its own length L, the borehole tangent undergoes a directional change of 2.theta..sub.w with respect to the baseline, leading to the equation:

DLS = 2 .theta. W L ( 4 ) ##EQU00004##

[0032] However, the walk angle .theta..sub.w has multiple causes, one of which is the lateral cutting rate due to the side force exerted on the bit. FIG. 5B illustrates the side-cutting angle .theta..sub.s which is expressible as:

.theta. s = arctan ( ROS ROP ) .apprxeq. ROS ROP ( 5 ) ##EQU00005##

where ROS stands for rate of side-cutting, and ROP stands for rate of penetration. In 1986, J. F. Brett observed that the lateral penetration rate (i.e., ROS) can be expressed as

ROS = - A F S 1 ( F S 1 ) 2 S r ( 6 ) ##EQU00006##

where ROS is the side cutting rate in ft/hr, F.sub.s1 is the total side force at the bit in lbs, S.sub.r is a dimensionless rock strength, and A is an empirically determined factor for directional response of building, dropping and holding assemblies. Shortly thereafter, Onyia (1987) and Warren (1987) introduced a method to calculate Sr. The side-cutting angle is accordingly expressible as

.theta. S = - A F S 1 ( F S 1 ) 2 ROP S r ( 7 ) ##EQU00007##

[0033] The other contributor to the walk angle is the orientation of the bit. FIG. 5C shows the baseline 312 extending between the two defining points, i.e., the borehole axis 502 at the top of the BHA (point 504) and the borehole axis at the tip of the bit (point 506). Also shown in FIG. 5C is the BHA axis 508. Baseline 312, borehole axis 502, and BHA axis 508 all intersect at the tip of the bit (point 506) to define three angles. The angle between the baseline 312 and the BHA axis 508 is the bit tilt angle .theta..sub.t. The angle between the BHA axis 508 and the borehole axis 502 is the side-cutting angle .theta..sub.s. Note that .theta..sub.t and .theta..sub.s need not have the same sign. When added together, they yield the walk angle .theta..sub.w, which is also the angle between the baseline 312 and the borehole axis 502.

[0034] Given the foregoing, the analysis may proceed as shown in the illustrative method of FIG. 6. The method may be implemented in the form of software stored on a non-transitory information storage medium and loaded into fast memory or cache for execution by a processor, with user input accepted via a user interface and results provided to the user via the user interface. The information storage, memory, processor, and user interface may be all included in a single computer (e.g., tablet computer 128 of FIG. 1) or various computers and components may be networked together to perform the method in a distributed fashion.

[0035] In block 602, the system obtains the design parameters for the borehole and BHA, such as borehole diameter, bit diameter, bit length, housing diameter, housing length, and positioning of the bearings and eccentricity ring relative to the housing and bit. In block 604, the system obtains measurements of the rock properties of the subject formation, preferably sufficient to enable determination of the A and Sr coefficients for use in equation (7). The system may further obtain a measurement of the current eccentricity ring position, the weight on bit, and optional measurements of bending strain in the housing. In block 606, the system sets an initial estimate of borehole DLS. Where a value is available from a previous iteration of the loop, it may serve as the initial estimate in block 606. Alternatively, the estimate may be set at an arbitrary value, e.g., zero.

[0036] In block 607, the system estimates the housing deflections .delta..sub.k at each bearing and at the position of the eccentricity ring. Where values are available from a previous loop iteration, they may serve as the initial estimate in block 607. Alternatively, the estimated deflections may be set at an arbitrary value, e.g., zero.

[0037] In block 608, the system derives tentative shaft node displacements from the geometry of BHA dimensions, borehole diameter, estimated DLS, estimated housing deflections, and the current eccentricity ring setting. In block 610, the system employs equation (3) to obtain the shaft node orientation angles from the displacements. The system then uses the orientation angles and displacements in equation (2) to obtain the side forces on the shaft nodes.

[0038] In block 612, the system takes the side forces exerted by the bearings and eccentricity ring as acting on the housing 300 to calculate the deflections, e.g., using equation (1) or a finite-element analysis of the housing. In block 614, the system compares the calculated deflections with the previously estimated deflections. If the error exceeds a threshold, the estimated deflections are updated in block 615 and blocks 608-615 are repeated until the deflections converge.

[0039] Once deflection convergence has been achieved, the system determines the tilt angle and side force on the bit in block 616. As previously described with respect to block 610, the orientation and side force on the bit can be calculated using equations (3) and (2). In block 618, the system employs the side force on the bit in equation (7) to calculate the side-cutting angle .theta..sub.s, which when added to the bit tilt angle .theta..sub.t, yields the walk angle .theta..sub.w. Equation (4) then enables the DLS to be calculated. In block 620, the system compares the calculated DLS to the estimated DLS. If the error exceeds a predetermined threshold, the estimated DLS is updated in block 622 and blocks 607-622 are repeated until the calculated DLS matches the estimated DLS.

[0040] Once a match is achieved, the system, in block 624, stores the DLS for the current position of the BHA and updates the log of DLS versus position on a display. In block 626, the system determines whether the BHA is still moving, i.e., whether there are other positions for which the DLS should be determined. If so, blocks 604-626 are repeated until the DLS has been determined for each position along the borehole. Where the system is operating concurrently with the drilling process, the estimated DLS may be monitored and used for feedback control of the steering mechanism and other drilling parameters.

[0041] In summary, the embodiments disclosed herein include:

[0042] Embodiment A: A dogleg severity (DLS) estimation method that comprises: retrieving dimensions of steering assembly; determining an initial DLS estimate; using the DLS estimate in combination with the steering assembly dimensions to determine node displacements for a shaft portion of the steering assembly; deriving a bit side force from the node displacements while accounting for elastic bending in a housing portion of the steering assembly; performing a DLS calculation based in part on the bit side force; adjusting the DLS estimate if the DLS calculation does not match; repeating said using, deriving, performing, and adjusting until a match is achieved; and storing the DLS estimate on a nontransient information storage medium.

[0043] Embodiment B: A dogleg severity (DLS) estimation system that comprises: a nontransient information storage medium having DLS estimation software; at least one processor that retrieves and executes said tendency predictor software; and a display coupled to the at least one processor to provide a visual representation of a DLS estimate. The software causes the at least one processor to implement a method comprising: retrieving dimensions of steering assembly; determining the initial DLS estimate; using the DLS estimate in combination with the steering assembly dimensions to determine node displacements for a shaft portion of the steering assembly; deriving a bit side force from the node displacements while accounting for elastic bending in a housing portion of the steering assembly; performing a DLS calculation based in part on the bit side force; adjusting the DLS estimate if the DLS calculation does not match; and repeating said using, deriving, performing, and adjusting until a match is achieved.

[0044] Each of foregoing embodiments may have any one of the following additional elements alone or in any suitable combination: (1) the method further comprises: obtaining measurements of formation parameters as a function of position along a borehole, wherein said DLS calculation is further based on said measurements, and wherein said determining, using, deriving, performing, adjusting, repeating, and storing operations are performed for multiple positions along the borehole to produce a log of DLS versus position. (2) the DLS calculation accounts for a rock strength. (3) the node displacement determination accounts for an axial force along the shaft portion of the steering assembly. (4) the method further comprises displaying a visual representation of said log. (5) the method further comprises storing said log on a nontransient information storage medium. (6) the dimensions include a setting for an eccentricity mechanism within the housing portion of the steering assembly. (7) the method further comprises changing the setting to keep the DLS estimate within a desired range. (8) said changing is performed to achieve a desired value for the DLS estimate. (9) said mechanism is an eccentricity ring. (10) the method further comprises: determining initial housing deflection estimates when determining the initial DLS estimate, wherein said using accounts for said housing deflection estimates, wherein said deriving includes: obtaining internal side forces on the shaft portion; making a housing deflection calculation based on the internal side forces; refining the housing deflection estimate if the housing deflection calculation differs, and wherein said using and deriving are repeated until the housing deflection estimate and housing deflection calculation no longer differ. (11) said deriving further includes computing shaft orientation angles from the node displacements, and computing the internal side forces based at least in part on the shaft orientation angles.

[0045] Numerous other modifications, equivalents, and alternatives, will become apparent to those skilled in the art once the above disclosure is fully appreciated. For example, it may be applied to other point-the-bit steering mechanisms, including those that employ pistons or other displacement mechanism in place of the eccentricity ring. It is intended that the following claims be interpreted to embrace all such modifications, equivalents, and alternatives where applicable.

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