Inclination Build Rate of a Point-The-Bit Rotary-Steerable Tool

The combination of a rotary-steerable system (RSS) and power screws has become the main drilling tool for the efficient exploration and development of unconventional oil and gas. However, the application of point-the-bit (POB) rotary-steerable tools in directional drilling subjects spindle bearings to continuous alternating stress, which can lead to fatigue failure. In this study, numerical analysis and simulation are employed to guide the engineering application of rotary-steerable tools, particularly in the field of oil and gas exploitation. The structural composition and steering principles of rotary-steerable tools are analyzed. The influence of the structural parameters of the spindle on the deflection capacity of the tool is analyzed, and the optimal structural parameters are selected. Based on the results, the recommended distances between the various components of the tool could be obtained. Moreover, the maximum deflection capacity increases with torque when the WOB (weight-on-bit) is constant. Similarly, at constant torque, the maximum deflection capacity increases with the WOB. Overall, the WOB has a greater influence on the maximum deflection capacity than torque. To ensure the safe operation of the spindle, the WOB and torque must be within 200 kN and 20 kN·m, respectively. The findings of this study provide valuable insights into the safe application of POB rotary-steerable tools.


Introduction
As a high-tech automatic drilling technology [1], rotary steering technology has the advantages of fast drilling speed, high wellbore quality, good ductility, and low drilling cost.It is a high-end drilling technology suitable for particularly harsh environments [2,3].
Previous research on rotary-steering tools analyzed the torsional vibrations of a lower bottom hole assembly (BHA).Various methods, including finite element simulation analysis, optimization of the stabilizer positions, and determination of the optimal BHA position, have been used to reduce the vibrations generated during the operation of steering tools [4][5][6][7][8][9].In addition, previous studies have analyzed the drill string mechanics of static push-the-bit rotary-steering tools [10][11][12].From a fieldapplication perspective, pointing tools exhibit several advantages over push-the-bit rotary-steering tools, such as improved borehole quality and independence from the wellbore during operation [13][14][15].However, when the spindle of a point-the-bit (POB) rotary-steerable tool rotates around the spindle axis in a curved state, the core bearing undergoes continuous alternating stress, which is prone to fatigue 2 failure, resulting in an increase in the error of the offset angle, which eventually leads to a large deviation between the actual wellbore and preset wellbore trajectory [16][17][18].In engineering applications, the drilling pressure and torque are usually increased to ensure the build-up rate, resulting in the fracture of the spindle [19].This can render the rotary steering tool unusable, or even cause downhole accidents such as sticking, which lead to economic losses [20].Therefore, the structure and deflection performance of a directional rotary-steerable system (RSS) must be analyzed [21].
In this study, the vertical and horizontal bending beam methods were used to derive a mathematical model suitable for obtaining the deflection ability of a POB rotary-steerable tool, analyze the influence of different parameters on its deflection ability, and optimize the structural parameters of the spindle.Simultaneously, finite element simulation software was used to establish a simulation model considering the influence of drilling parameters.Moreover, the dynamic characteristics of the spindle were studied to provide theoretical guidance for directional rotary-steerable tools in engineering applications.

Structure of the POB
The structure of the POB consists of a drill pipe, drive connector, spindle, upper seal, bearing assembly, cantilever bearing, non-rotating outer sleeve, eccentric ring assembly, transmission mechanism, selfaligning bearing, and lower seal (figure 1).The cantilever bearing supports the spindle and prevents the upper spindle from bending.The power of the spindle originates from the drill pipe and the torque is transmitted by the drive connector.The drilling pressure of the drill pipe is transmitted to the non-rotating outer sleeve through the bearing combination.The non-rotating outer sleeve passes the drilling pressure to the lower end of the spindle through the core-adjusting bearing, and then passes it to the drill bit.The core-adjusting bearing facilitates the rotation of the rotating spindle and transfers the drilling pressure.Therefore, the distance between the cantilever bearing and core-adjusting bearing on the spindle is only affected by the torque and not by the WOB.

Mechanical Model of the POB Trajectory Control
The spindle of the POB rotary-steerable tool is connected directly to the drill bit.The guidance of the system primarily depends on the deflection of the spindle to produce the lateral force and rotation angle of the drill bit.Therefore, this study adopted the stress-strain approach of the core axis to determine the force equilibrium state of the system.

Spindle Mechanical Analysis
During the mechanical analysis of the spindle, the drill bit and spindle were treated as a unified entity, whereas the outer sleeve acted as a radial displacement constraint for the spindle, with displacement constraints present at the bearing location.The basic assumptions of the spindle mechanical analysis model are as follows.The spindle mechanical analysis model assumes that the drill bit and spindle are analyzed as a single entity.The combination of the drill bit, spindle, and bearings results in a small elastic deformation body.The spindle materials have identical properties, and there is no coupling force interaction between the drill bit and formation.The mechanical model of the spindle of the POB rotarysteering system is shown in figure 2. Calculation of the moment at the center of the first bearing using ∑M′=0 yields: The lateral force of the bit    is equal to and opposite to    ′ in figure 2 Mechanical model of the spindle of the POB rotary-steering system: ( ) ( ) Substituting expression equation ( 5) into equation (4) yields: The lateral force of the drill bit and rotation angle of the drill bit caused by the deformation of the spindle can be obtained by substituting the solution for M1' obtained from equation (6) into equation ( 2):

Spindle Parameter Analysis
Different values of the structural parameters of the spindle have a certain impact on the deflection ability of the tool and enhance the deflection ability of the BHA to ensure the drilling trend of the drill bit.The basic structural parameters of the BHA were selected through experiments: 215.9 mm drill bit + Ф172 mm point-the-bit steering drilling tool (with Ф215.9 mm lower stabilizer) + Ф122 mm flexible sub + Ф172 mm drill collar + Ф210 mm upper stabilizer + Ф172 mm drill collar + Ф 127 mm drill pipe.The preset deviation angle was 15°.The curvature of the drilled hole in the BHA section was 8°/30 m; the WOB was 150 kN; the elastic modulus of the steel was 210 GPa; and the density of the steel was 7830

Spindle
kg/m 3 .The density of the drilling fluid was 1.25 g/cm 3 ; the structural parameters of the spindle were analyzed using the control variable method.The lateral force of the drill bit decreases significantly, and the rotation angle of the drill bit first increases and then decreases as the first span length (l1) of the spindle increases (figure 3 and figure 4).The deflection ability is the strongest when the first span length (l1) of the spindle is approximately 2 m.As the second span length (l2) of the spindle increases, the increasing trend of the lateral force, rotation angle of the drill bit and the increase of the tool deflection ability become slower.In theory, greater deformation of the spindle is preferable; however, excessive deformation may lead to fatigue failure and limit the size of the outer sleeve of the tool.Therefore, the recommended first and second span lengths of the spindle are 2 m and 3.5 m, respectively.

Dynamics Simulation of Deflection Ability
To clarify the deflection ability of the POB rotary-steerable tool under the influence of drilling parameters, a simulation model of the POB rotary-steerable tool was established using finite element software, and the influence of the drilling parameters on the deflection ability of the tool was analyzed.

Model of the Spindle
According to the aforementioned recommended structural parameters of the spindle, a threedimensional model of the pointing guide spindle was established using CAE software.The material of the spindle was P550, and its elastic modulus, Poisson's ratio, yield strength, and tensile strength were 2.1×105 MPa, 0.3, 965 MPa, and 1035 MPa, respectively.According to the data, the safety factor with an impact vibration load is generally in the range 1.2-3.5.In the analysis and calculations presented here, the safety factor and allowable stress of the spindle material were 1.74 and MPa, respectively.
Boundary conditions: A reference point was established at the center of the upper surface of the spindle and coupled with the upper surface, thereby assigning six degrees of freedom in the X, Y, and Z directions (figure 7).A reference point was established at the center of the spindle in the core-adjusting bearing, constraining four degrees of freedom in the X-and Y-directions.Drilling pressure and torque were applied to the lower surface of the drill bit, while a transverse displacement load was applied in the Z-direction at the eccentric ring position.

Simulation Result
To analyze the influence of different WOB and torques on the limit deflection ability of the tool and to determine whether its working condition was satisfactory, 16 sets of data of different WOB and torques were applied to the spindle while maintaining the maximum offset displacement of the eccentric ring.These were compared and summarized, as shown in table 1.The lateral displacement and stress distribution cloud diagrams of the drill bit under different working conditions were obtained by applying the working parameters of the spindle, as shown in table 1 Different operating parameters applied to the finite element model of the rotary-steerable spindle and the simulation results are shown in figure 8 to figure 11.When the eccentric ring is at the maximum offset position, the maximum displacement of the spindle is located at the eccentric ring, and the displacement of the constraint point is 0. The deflection displacement of the drill bit gradually increases with the WOB and torque.When the WOB is 50 kN, the deflection displacement of the drill bit increases from 3.16 mm to 3.84 mm as the torque increases (5-20 kN•m), and the drill bit is blue in the displacement distribution cloud diagram.The maximum stress in the spindle was located near the fixed end, eccentric ring, and bearings; they experienced high stress owing to the presence of maximum displacement, displacement constraints, and stress concentration.The stress from the drill bit to the bearing was the     The stress and displacement of the spindle increase with the drilling pressure and torque when the maximum offset of the spindle is considered.The maximum stress is shown in figure 11; the stress under a WOB of 200 kN and torque of 20 kN•m is 539.6 MPa.Within the allowable stress range of 554.6 MPa for the spindle material, 16 working conditions satisfied the working requirements.To ensure that the spindle does not experience fatigue damage, the drilling pressure and torque should be limited to within 200 kN and 20 kN•m, respectively.

Field Application
The Sichuan Basin region is one of China's major reservoirs for tight gas and shale gas development, where rotary steerable tools are extensively employed.The JQ 815 well, a tight gas well located in Mianyang City, Sichuan Province.Based on numerical analysis and dynamic simulation, a rotary steerable tool was utilized to achieve the desired well trajectory.Wellbore was drilled to a depth of 450m with a build angle of 48.12° and then continued drilling at an inclination angle of 10.08°.Upon reaching a depth of 752.00m, wellbore was stabilized in terms of inclination and azimuth.Wellbore was further steered to a depth of 2291.00m at an azimuth of 228.5° and an inclination of 52°.Upon reaching the target point A at 2581.00m, the wellbore inclination increased to 90.76°.Afterward, the wellbore was steered to target point B at a depth of 3786.00m and further drilled smoothly for an additional 40m.In figure 12, rotary steerable tool experienced an increasing build-up rate between 1600-2500 meters to meet the drilling requirements of limited WOB (≤200 kN) and torque (≤20 kN•m).Moreover, it is observed that WOB has a greater influence on the maximum achievable build rate of the rotary steerable tool.

Conclusion
This study establishes a mechanical model of a POB rotary-steerable tool spindle and analyzes its optimal structural parameters.The following conclusions were obtained from the dynamic simulations performed by combining the model with the CAE software: 1.The recommended lengths of the first (l1) and second (l2) spans of the spindle were 2 m and 3.5 m, respectively.The recommended positions of the first bearing (a) and eccentric ring (b) were 1.2 m and 2.5 m, respectively.
2. When the eccentric ring was in the maximum offset position, the pointing guidance exhibited the maximum deflection ability.When the WOB was constant, the limit build-up rate increased with the torque.When the torque was constant, the limit build-up rate increased with WOB.In general, the WOB had a greater impact on the final build-up rate.To ensure the safe working of the spindle, the WOB and torque should lie within 200 kN and 20 kN•m, respectively.

Figure 1 .
Figure 1.Schematic of the pointing rotary-steerable drilling tool structure.

Figure 2 .
Figure 2. Mechanical model of the spindle of the POB rotary-steering system.In the figure:   -WOB,N,   is transmitted to the outer sleeve through Z1 and only l1 is subjected to WOB;   =   ′ ;   ′ is the reaction force of the lateral force of the drill bit caused by the deformation of the spindle (N) ; M'1、M'2 are the internal bending moments of the bearings Z1, Z2 (N•m); and Q is the bias force of the eccentric ring assembly on the spindle (N).Calculation of the moment at the center of the first bearing using ∑M′=0 yields:

Figure 3 .
Figure 3. Influence of the first span length l1 on the deflection ability.

Figure 4 .
Figure 4. Influence of the second span length l2 on the deflection ability.

Figure 5
Figure 5 Influence of the first bearing position a on the deflection ability shows that the lateral force and the rotation angle of the drill bit are almost constant as the first bearing position a of the spindle increases.Thus, the first bearing position of the spindle has little effect on the deflection ability of the tool.Figure 6 Influence of eccentric ring position b on the deflection ability shows that the lateral force of the drilling tool increases considerably, and the rotation angle of the drill bit increases almost linearly as the distance (b) between the eccentric ring position of the spindle and first bearing increases.The core principle of controlling the wellbore trajectory for a steerable rotary drilling tool relies on the deformation of the spindle under applied forces; thus, increasing the (b) causes greater flexural deformation of the core axis and enhances the inclination-building capability of the tool.The recommended value of the position b of the eccentric ring is 2.5 m.According to the influence law of the structural parameters of the spindle on the slope, the recommended values of the first span length l1 of the spindle, second span length l2 of the spindle, first bearing position (a) of the spindle, and eccentric ring position (b) are 2 m, 3.5 m, 1.2 m, and 2.5 m, respectively, to ensure high deflection ability of the tool.

Figure 5 .
Figure 5. Influence of the first bearing position a on the deflection ability.

Figure 6 .
Figure 6.Influence of eccentric ring position b on the deflection ability.

Figure 7 .
Figure 7. Boundary conditions applied to the spindle.
largest; it gradually increased with the WOB and torque.The maximum Mises stress in the spindle increased from 212 MPa to 260.2 MPa, which was significantly lower than the yield strength of the spindle (965 MPa).The strength of the spindle completely satisfies this demand.The drill bit to the bearing part is denoted by yellow-green in the stress distribution cloud diagram.When the torque is 5 kN•m, the deflection displacement of the drill bit increases from 3.16 mm to 5.28 mm with increased drilling pressure (50-200 kN), and the drill bit changes from blue to blue-green in the displacement distribution cloud diagram.The stress gradually increases.The maximum Mises stress of the spindle increases from 215 MPa to 490.8 MPa, which is lower than the allowable stress of the spindle (554.6 MPa).The strength of the spindle completely satisfies the demand.The part from the drill bit to the bearing gradually changes from yellow-green to red from both ends to the middle in the stress distribution cloud diagram.The WOB played a major role in the deflection of the drill bit.

Figure 12 .
Figure 12.Actual build-up rate, WOB and torque of JQ815 well.

Table 1 .
Different operating parameters applied to the finite element model of the rotary-steerable spindle.