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Research on the working mechanism of the PDC drill bit in compound drilling
Journal of Petroleum Science and Engineering xxx (xxxx) xxx
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Journal of Petroleum Science and Engineering journal homepage: http://www.elsevier.com/locate/petrol
Research on the working mechanism of the PDC drill bit in compound drilling Yingxin Yang a, b, *, Yan Yang a, Haitao Ren a, b, Qingliang Qi a, Xinwei Chen a a b
School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
A R T I C L E I N F O
A B S T R A C T
Keywords: PDC drill bit Compound drilling Numerical simulation Rock-breaking mechanism Customized design
A combined ground-driven and down-hole-driven motor significantly improves the penetration rate of poly crystalline diamond compact (PDC) drill bits but greatly reduces bit life. By studying the mechanical behavior of the drill string in compound drilling, a kinematics model of a PDC drill bit under compound drilling was established, and the effects of transmission ratio, cutter layout, and drill string geometry on the cutting trajectory formed by the cutters were analyzed. Furthermore, a numerical drilling simulation of the PDC drill bit was developed and enhanced to research the kinematics and cutting regularities of the PDC drill bit in compound drilling. In addition to high rotation rate, nonparallel scraping of the PDC cutters and the unbalanced contact state between the cutters and the rock are the prime reasons for improvement of the penetration rate of the PDC bit in compound drilling. An error analysis comparing simulation and experimental results was performed and the two agree to within <20%. Based on the working mechanism of the PDC drill bit in compound drilling, technical ideas and implementation methods for customized designs of PDC drill bits are discussed.
1. Introduction With the advantages of good stability, high rate of penetration (ROP), and high design flexibility, polycrystalline diamond compact (PDC) bits are widely used in exploration for and exploitation of oil and gas (Dougherty et al., 2014; Zhu et al., 2015). Compound drilling is a drilling method in which the ground-driven and down-hole-driven motors are combined to drive the drill bit to break rock in oil and gas drilling engineering. Using compound drilling with a screw drilling tool combined with a PDC bit can relieve the back pressure on the drilling string and enable the cutters to effectively penetrate the formation, thereby improving rock-breaking efficiency (Azizov, 2011; Gaudin, 1991; Grindrod, 2002; Grandis, 2015; Warren and Lesso, 2005; Wang, 2015; Zhu et al., 2019). It is a very effective technique for speeding up and increasing efficiency in drilling. However, because of the super position of the two motion states and the introduction of the motor bending angle of the screw, eccentricity and deflection occur between the actual center of rotation of the PDC bit and the center of the well trace. Each of the cutters suffers from severe load distribution uneven ness and varying degrees of impact loading, which in turn can cause failure of an individual cutter. Presently, classical means arranging PDC
bit cutters entails equal cutting volume and full coverage. Accordingly, failure of individual cutters inevitably leads to a sharp increased working load on the adjacent cutters of the drill bit, causing serious failure modes such as balling, coring, and ring out (Clegg, 1992; Mor timer, 2010; Sinor and Warren, 1993). Under the constraints of a casing program, formation conditions, and bottom-hole assembly, identifying the rock-breaking mechanism for PDC bits in compound drilling is a design precondition. Numerical drilling simulation technology for PDC drill bits is a newly developed effective technical means to simulate the interaction between the bit and the formation rock, analyze the load distribution of cutters, and evaluate the performance of the drill bit in underground complex conditions (Zheng et al., 2016). By using this system, the influence of the casing program and the geometry of the down-drilling string on PDC drill bit cutters under the condition of compound drilling were studied, the corresponding kinematics analysis equation was established, and the simulation system was developed and improved. In addition, the effects of factors such as the rotation speed ratio between the rotation speed of the screw motor and the revolution speed of the rotary table, cutters arrangement design of the drill bit, and bend angle of the screw on the bottom-hole trajectory of the cutters were analyzed, analysis of the
* Corresponding author. School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China. E-mail address: [email protected] (Y. Yang). https://doi.org/10.1016/j.petrol.2019.106647 Received 26 June 2019; Received in revised form 18 October 2019; Accepted 3 November 2019 Available online 5 November 2019 0920-4105/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Yingxin Yang, Journal of Petroleum Science and Engineering, https://doi.org/10.1016/j.petrol.2019.106647
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bottom-hole morphology was performed, and corresponding conclu sions were obtained. These research results improve our understanding of the rock-breaking mechanism for PDC bits under the condition of compound drilling and provide a reference for customized drill bit de signs. In particular, the simulation system considered the influence of elastic deformation of the down-drilling string under the constraint of the borehole wall on the working state of the PDC bit, and the research results were close to the actual working conditions of the bit.
2.1. Research and development of numerical drilling simulation technology for PDC bits Based on MATLAB, an interaction model between the PDC bit and the formation rock under compound drilling was constructed in the simulation system. This model’s simulation strategy is based on processoriented weight on bit (WOB) equilibrium. In each simulation step, the dynamic rock-breaking process for the PDC bit was transformed into a static balance problem at every step, thus minimizing the calculation amount and optimizing calculation efficiency. Results such as the tra jectory of the drill bit, variation of loading, and bottom-hole morphology during the whole drilling process were thus obtained (Qi, 2015). Flow chart of the numerical simulation system is shown in Fig. 1.
2. Establishment of kinematics model of PDC bit in compound drilling The numerical drilling simulation system is an integrated analyzing tool for PDC bit. Based on the mechanical behavior analysis of downhole string and the kinematics model of PDC cutters, the kinematics laws of PDC cutters under compound drilling can be studied via the numerical drilling simulation system.
2.2. Mechanical behavior analysis of down-drilling string It was assumed that, in high-angle directional wells and horizontal wells, the drill string was tangent to the lower shaft lining owing to its weight, and the upper part of the drill string from the tangent point was attached to the lower shaft lining, which was far away from the drill bit,
Fig. 1. Flow chart of the numerical simulation system. 2
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so that the effect of elastic deformation on the drill bit can be ignored here. The down-drilling string from the tangent point to the drill bit was simplified as a double-span continuous beam subjected to self-weight and the lateral force of the bit under drilling fluid conditions (Su, 2001; Yang, 2017). As shown in Fig. 2(a), the dogleg severity was 90� γ, the initial bending angle of the screw was θm , the drill string was tangent to the lower shaft lining at point C, and the contact between the elbow point (point A) of the screw and the shaft lining was regarded as a fixed hinge support. The down-drilling string from the elbow point (point A) of the screw was disconnected, and the double-span beam was piecewise handled in accordance with a static balance problem. The line masses of the double-span beam were q1 and q2 , and the bit (point B) was sub jected to a lateral force FB from the shaft lining. Because the direction of the WOB was along the axial line of the drill bit, the rotation angle and flexibility of the drill string were less affected, so the effect of the WOB was not considered here. The double-span beam will generate elastic
deformation under the joint action of the forces mentioned and rotate and flex. Because the bending angle of the screw was small, the defor mation of the double-span beam conformed to the conditions of small deformation with linear elastic properties, so θ � sin θ � tan θ. Fig. 2(b) shows a simplified mechanical model of the first span beam. For the force analysis of the first span beam, the elbow point (point A) was regarded as the fixed end. According to static equilibrium of the beam, the fixed end was subjected to a bending moment MA and a supporting force FA and the drill bit was subjected to a lateral force FB. The AB segment beam was subjected to a uniform load and its line mass was q1 . Under the joint action of the these forces, the first span beam underwent elastic deformation with a rotation angle θ1 and a flex of wB1 . Fig. 2(c) shows a simplified mechanical model of the second span beam. For the force analysis of the second span beam, the elbow point (point A) was regarded as a fixed hinge support, and it was subjected to a bending moment MA and supporting forces FAW and FAX. Point C of the beam was the tangent point with the lower shaft lining, and it was
Fig. 2. Simplified model of a drill string under the condition of flexibility. 3
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subjected to a supporting force FC. The AC segment beam was subjected to a uniform load and its line mass was q2 . Under the joint action of these forces, the second span beam underwent elastic deformation with a rotation angle of θ2 . Therefore, the force deformation of the downdrilling string can be represented by Fig. 2(d). According to the material mechanics principle of the bending deflection of beam, the rotation angle θ and the flex w can be expressed as � Z EIdw dx ¼ EIθ ¼ MðxÞdx þ C Z Z f (1) EIw ¼ dx MðxÞdx þ Cx þ D According to the elastic mechanics principle of superposition, the rotation angles θ1 , θ2 , the flex wB1 and the bending angle θt of the screw under the flexible condition of the drill string (hereinafter referred to as the flexible bending angle) were q1 lm 3 cosðθm 6E1 I1
θ1 ¼
FB l m 2 2E1 I1
8FB lm 3 þ 3q1 lm 4 cosðθm 24E1 I1
wB1 ¼
θ2 ¼
γÞ
(2) γÞ
8FB lm a 4q1 lm 2 a cosðθm 24E2 I2
q2 a3 cos γ
(3) γÞ
Fig. 3. Absolute rotation speed of a bit in compound drilling.
(4)
The kinematics equation (Guo, 2010) of the PDC bit in compound drilling can be expressed as
(5)
θt ¼ θm þ θ1 =2 þ θ2
In this formula, θt is a negative value, which indicates that the sec tion was rotated clockwise. It can be obtained that the force deformation of the down-drilling string will reduce the bending angle of the screw. The deflection wB of the B section is the superposition of the deflection wB1 of the free end of the AB beam and the rigid-body displacement caused by the rotation of the AB beam from the rotation angle θ2 of the A section, namely,
½X; Y; Z; 1� ¼ ½x; y; z; 1� � T0 ð0; 0; vωtÞ �Tx ½ φm �
3. Kinematics analysis on PDC cutters in compound drilling
Therefore, in compound drilling, the reamed borehole diameter Dt and the wellbore expansion rate δ are Dt ¼ 2ðlm sinθm δ¼
Dt
Db Db
¼
2ðlm sinθm Db
From the relationship between geometry and kinematics, the threedimensional space state equation of PDC cutters at any time can be obtained (Ren et al., 2010) as
(7)
wB Þ þ Db wB Þ
(10)
In the numerical drilling simulation system, the above equations are used as the kinematics model of the PDC bit. Thus, analyses on the ki nematics and cutting mechanics of PDC cutters under compound drilling condition can be performed.
(6)
wB ¼ wB1 þ θ2 ⋅lm
cosðωtÞ þ 1 � � Tz ðωtÞ 2
(8)
x ¼ e cosω2 t þ r cosθt cos½ði þ 1Þω2 t� f y ¼ e sinω2 t þ r cosθt sin½ði þ 1Þω2 t� z ¼ e=tanθt r sinθt cos iω2 t þ vz t
In this formula, Db is the diameter of the PDC bit. 2.3. Establishment of kinematics model
(11)
where e ¼ ðlm þh0 Þsinθt is the distance from the location points of the cutters to the central axis of the wellbore, h0 and r are the location height and radius of the PDC cutters on the drill bit, and i is the ratio of the motor speed to the rotary table speed. From the above analysis, one can see that the cutter trajectories in compound drilling are affected by many factors, such as the position coordinates of the cutter (h0 and r), structural parameters of the screw (lm and θt ), and motor speed and rotary table speed i. Taking a PDC bit as an example, and the simulation parameters were taken as follows:
The geometric coordinate system for the PDC bit at the hole bottom was established according to the methods described in Chen (2016) and Yang (2003), and the kinematic model of the PDC bit under the condi tion of flexible drill string was studied. In compound drilling, the absolute rotation speed n of the drill bit is the vector synthesis of the screw motor speed n1 and the rotary table speed n2 , as shown in Fig. 3. This is one of the reasons why compound drilling has such a high rate of penetration. The feed rate of the drill bit was vz (m/h), the speed of the screw motor was n1 (rpm), the speed of the rotary table was n2 (rpm), the arm length was lm , and the azimuth of the arm deflection was ϕm . Then the absolute rotation speed n (rpm), absolute angular velocity ω (rad/min), and the drilling depth per radian of the drill bit are qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ¼ n1 2 þ n2 2 þ 2n1 n2 cosθt qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . f (9) ω ¼ nπ 30 ¼ ω1 2 þ ω2 2 þ 2ω1 ω2 cosθt v ¼ 8:3vz =nπ
(1) Drilling process parameters: speed of the rotary table speed is 30 rpm, speed of the screw motor speed is in the range of 90–180 rpm, the drilling pressure is 12 kN, the mud density is 1.4 g/cm3, the dogleg severity is 0� , the footage of each circle is 2 mm, the bending angles are respectively 0.5� and 1� and the arm length are respectively 1 m and 1.2 m. (2) Cutter parameters: the cutter diameter is 16 mm, the position coordinates of the three cutters are respectively (15.78 mm, 49.86 mm), (49.09 mm, 60.6 mm) and (80.08 mm, 59.42 mm) 4
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where the cutters are respectively in the cone, in the shoulder and in the gauge area of the PDC bit. (3) Rock sample parameters: the friction coefficient is 0.2, the in ternal friction angle is 22� and the shear strength is 11 MPa.
The three cutters are in the cone area, the shoulder area, and the gauge area of the drill bit, and the cutting tracks are shown in Fig. 6. According to the calculation results, cutter trajectories coincide with the cutter trajectory of the inner cone region when r < e=cosθt , and cutter trajectories are in accordance with the cutter trajectory of the outer shoulder area when r > e=cosθt .
3.1. Effect of rotation speed ratio
3.3. Effect of screw structural parameters
The rotation speed ratio i is equal to the ratio of the motor speed to the rotary table speed, namely, i ¼ n1 =n2 . The rotation speed ratio i is an important factor affecting the cutting tracks. Fig. 4(left) shows four tracks of one PDC cutter in the cone region of the drill bit when the rotation speed ratio i was taken as 3–6. From the above figure, two conclusions can be obtained:
The structural parameters of the screw are the flexible bending angle θt and the arm length lm . Fig. 7 shows trajectories of PDC cutters when the rotation speed ratio is i ¼ 4, the arm length is lm1 , and the flexible bending angle is θt2 , which is greater than θt1 in Fig. 6. When the arm length lm is a constant, as the flexible bending angle θt increases, the change in the direction of the cutter in the inner cone region of the PDC bit becomes sharper, and the radial fluctuation range of the trajectories becomes wider. Fig. 8 shows trajectories of PDC cutters when the rotation speed ratio is i ¼ 4, the flexible bending angle is θt1 , and the arm length is lm2 , which is longer than lm1 in Fig. 6. When the flexible bending angle θt is con stant, as the arm length lm increases, the radial fluctuation range of the trajectories becomes wider. From the above simulation results, we can conclude that the impact of the four factors on the trajectory of the cutter increases in the order of positioning height h0 , arm length lm , flexible bending angle θt of the screw, and positioning radius r of the PDC bit.
(1) The greater the rotation speed ratio i, the longer the cutter tra jectory. As the rotation speed ratio i increases, the number of changes of the cutter direction increases but the curvature of the cutter trajectory at the whirl becomes smaller. This indicates that, as the rotation speed ratio i increases, the rate of change of the direction of the cutter becomes slower. (2) It can be seen from Fig. 4(right) that the cutting track of the cutter in the cone area exhibits knotting. This indicates that, during the scraping process, the direction of cutter motion and the contact working face (curved face) of the cutter and the rock are constantly changing. In the figure, a semicylindrical cutter cut into the rock with an axial plane as the scraping face. During the scraping process, the cutter continuously rotates with respect to the rock, and the scraping face gradually transitions from the axial plane to the side and then continues to rotate to the cylin drical surface (the back of the axial plane) and cut out again. During the cutting and cutting out of the bottom hole, the scraping face of the cutter changes by ~180� , and the cutter is reversed with respect to the scraping direction of the rock. If the cutter cuts into the rock at the front face, then the back side will be reversely cut out.
4. Working mechanism analysis on the PDC drill bit in compound drilling The kinematics analysis results show that the PDC bit removes rock material more similar to “milling”. Taking the rock-breaking process of the PDC bit in compound drilling as “milling”, both the kinematics and cutting mechanics of the bit can be explained more reasonably. 4.1. Working principle of milling instead of drilling
This special movement of the cutters in the cone area of the PDC bit is the primary reason why the PDC bit is cored in compound drilling, as shown in Fig. 5 (Brett and Whirl, 1989; Rajabov et al., 2012).
In compound drilling, the “drilling” principle of PDC bits changes significantly. Some of the cutters on the bits will participate in cutting intermittently. Even if the cutters are not interrupted, at least their cutting state will change periodically, and the cutting depth of each cutter will change during the cutting process. Indeed, the combination of rotation and revolution-driven mode with a bending motor makes the PDC bit cut the rock more similar to milling instead of drilling. The rotation of the drill bit driven by a bending motor is the main motion of milling, while the revolution of the drill pipe becomes the feed motion. In this special “milling instead of drilling” mode, the working state of the cutters on the drill bit exhibits a certain degree of alternation, rather
3.2. Effect of position coordinates The position coordinates of the cutter are determined by two pa rameters: the positioning height h0 and the positioning radius r. Ac cording to the kinematics simulation results for the cutter, the influence of the positioning radius r on cutting tracks of different cutters is sig nificant, but the influence of the positioning height h0 is not obvious.
Fig. 4. Cutting tracks for different rotation speed ratios i and the knotting behavior of the cutter. 5
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Fig. 5. Failure mode for central cutters on a PDC bit.
Fig. 8. Cutting tracks for an arm length of lm2 .
Fig. 6. Cutting tracks for different position coordinates of the cutters.
the central region. The central region has a higher degree of irregularity than the outer region and has a multipeaked shape, which is signifi cantly different from that of the conventionally drilled bottom. This feature provides a direct basis for a rational interpretation of the bit cored failure phenomenon in compound drilling. 4.2. Penetration characteristics of cutters and nonparallel scraping status From the observation of the bottom-hole morphology in compound drilling, there are two main characteristics of PDC cutters: (1) The interaction between the PDC cutters and the rock is a nonparallel cutting process. (2) The nonparallel scraping creates a ragged rock ridge on the bottom hole, so that the cutters can naturally penetrate the rock. Because of the existence of the flexible bending angle of the screw, the center of the drill bit deviates from the center of the borehole. The eating depth on one side of the drill bit is larger than that on the other side. At the same time, PDC cutters are not completely involved in scraping and breaking rock (see Fig. 10). Therefore, the drill bit will form an uneven and intersecting rock ridge at the bottom hole, which will help the subsequent PDC cutters naturally penetrate the rock. Compared with the concentric circular cutting in ideal drilling, the nonparallel scraping in compound drilling is beneficial to the reduction of cohesion of the rock unit, the generation and diffusion of small cracks inside the rock, and the acceleration of the volume breaking of the rock, thereby improving the rock-breaking efficiency and working life of the PDC drill bit. In addition, the Drilling Institute of Southwest Petroleum University has found through nonparallel scarping experiments of PDC cutters (Zhang, 2018) (Fig. 11) that the rock-breaking method of nonparallel scraping is better than one-way concentric circular scraping, achieving
Fig. 7. Cutting tracks for an elastic bending angle of θt2 .
than continuous scraping under ideal drilling conditions, and the cutting tracks also change from concentric circles to helical trajectories (see Fig. 9 (left)). Fig. 9 (right) shows the numerical bottom-hole morphology obtained by simulating the compound drilling process of the drill bit in the PDC bit rock-breaking numerical simulation system. Obviously, the morphology is distinctly different from that of the conventional bottom. The nonparallel helical scraping trajectory by the cutters of the drill bit and the undulating geometry bottom surface indicate that the drill bit is indeed milling the rock. The unbalanced bearing of the drill bit and the changing cutting work state are not unimaginable. Another special morphological feature of the bottom hole is seen in 6
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Fig. 9. Helical trajectory of the cutters and the bottom-hole morphology.
number of actual working cutters is smaller than the total cutter number. The cutters periodically detach and enter in cutting, which makes the cutting area and cutting force of each cutter change periodically. Fig. 12 shows the actual number of PDC bit cutters in contact during the drilling process, which ranges from 8 to 15 during the working process. The total number of main cutting cutters on the drill bit is 26, while the average actual number of effective cutters involved in the cutting is 11.44, which is less than half of the total number of main cutters. Therefore, under the same drilling pressure, the average cutting load of the effective cutters of the drill bit during compound drilling is higher than that of conventional drilling. The axial force of the PDC cutters is one of the important indicators of the difficulty of penetrating the rock. From this point of view, the ROP of compound drilling should be higher. Fig. 13 shows the cutting area curves of three PDC cutters in the cone area, the shoulder area, and the gauge area, respectively. The cutting area changes with time, and the variation range is quite large, and the cutting area is often zero. The cutters periodically detach and enter in cutting, which is a typical working state of compound drilling of the cutters on the drill bit.
Fig. 10. Nonparallel scraping status of the cutters.
savings in both labor and energy. That is, under the condition of nonparallel scraping, the axial and tangential forces on the PDC cutters are both smaller than those in one-way concentric circular scraping. Especially when the spacing of PDC cutters reaches 16 mm, axial labor is reduced by up to 26.8%, and the tangential energy needed is reduced by up to 29.4%. Therefore, the nonparallel mesh bottom hole formed in compound drilling is conducive to the effective eating of PDC cutters on rocks, so that the ROP of the PDC drill bit can be effectively improved, thereby improving the rock-breaking efficiency.
4.4. Error analysis of simulation results Based on the above theories, to correct the numerical drilling simulation technology of a PDC drill, a laboratory test of a 600 PDC bit under eccentric working conditions was performed (see Fig. 14). The experimental rock selected was Wusheng sandstone. The main relationship among the lateral force, torque, and rock properties of the bit under eccentric working conditions was determined. The eccentricity was controlled to <1 mm in the experiment by adjusting the bolts on the drill stand to test the lateral force, torque, and lateral force of the drill bit
4.3. Working mechanics analysis of PDC drill bits Due to the existence of the angle in the screw motor, some cutters in the drill bit are out of contact with the rock in a short period, i.e. the
Fig. 11. Photographs of the nonparallel scraping experiment and the rock ridge. 7
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Fig. 15. Torque curve obtained in the simulation experiment.
analysis of the simulation system is reliable.
Fig. 12. Cutter number vs. rotation angle.
5. Customized design of PDC dill bits under compound drilling conditions From the above analysis, it can be seen that the amplitude of vari ation of the cutting angle of the PDC cutters under compound drilling conditions is large; especially, the cutters on the inner cone of the bit have sharply knotting trajectories. In addition, the radial fluctuation of the PDC cutter trajectories inevitably causes a large periodic variation of the lateral force of the bit, which easily causes lateral vibration of the bit. Therefore, the following design ideas are proposed: (1) The cutters arrangement contour should be designed with a shallow cone or a flat cone. By increasing the radius of curvature of the contour, each area of the cutters arrangement contour can smoothly transition, which can effectively relieve the backing pressure effect of the cone and reduce the cutting load of the PDC cutters on the cone area. At the same time, increasing the cutters density of the cone and using a single blade with a multi-cutter or interlaced cutters can improve the cutting ability of PDC cutters on the inner cone of the bit. (2) The cutters arrangement suitably introduces a negative bypass angle. Setting the negative bypass angle for cutters areas where the cutter trajectories change sharply can reduce the probability of the cutters being subjected to a reverse cutting force and avoid the occurrence of abnormal failure phenomena such as delami nation and breakage of the diamond layer. (3) A customized design of the PDC drill bit can improve its stability, enhance the ability of gauge protection, reduce the exposure height of the cutters, or set the feathers like a cushioning cutter, flat insert cutter, and reverse cutter. At the same time, all the methods such as reducing the length of the gauge protection section, enhancing the cutting ability of the gauge cutters, and
Fig. 13. Cutting area vs. rotation angle.
Fig. 14. Photographs of the PDC bit and the test laboratory.
(Yang, 2017). The average value of the torque received by the drill bit in the simulation calculation was 651.16 N m (see Fig. 15) and it changed periodically. At the same time, a corresponding numerical model was established in the simulation system, and the simulation parameters were controlled as follows: Φ152.4 mm (bit) � 0.3 m þ Φ114 mm (drill pipe) � 20 m, drilling pressure ¼ 16.2 kN, rotary table speed ¼ 30 rpm, mud density ¼ 1.7 g/cm3, and dogleg severity ¼ 0� . The error was analyzed by com parison to the experimental results. The average torque at the drill bit calculated by the experimental recorder (see Fig. 16) in the bench test was 798.51 N m. This value is within 20% of the simulation results, so it can be inferred that the
Fig. 16. Torque curve obtained in the laboratory test. 8
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improving the gauge cutters density can help the reduce the torque response and depress the possibility of lateral vibration of the drill bit.
Brett, J. Ford, Whirl, Bit, 1989. A New Theory of PDC Bit Failure. 19571-MS SPE Conference Paper. Clegg, J.M., 1992. An analysis of the field performance of antiwhirl PDC bits. In: SPE/ IADC Drilling Conference. Society of Petroleum Engineers. SPE 23868. Chen, X.W., 2016. Study on Rock-Breaking Mechanism of PDC Bit in Compound Drilling. Master’s Thesis. Southwest Petroleum University, Chengdu, Sichuan, China (in Chinese with English abstract). Grindrod, J., 2002. The introduction of new-generation positive displacement motor technology in combination with application-specific PDC bits. In: 74455-MS SPE Conference Paper,2002. Dougherty, Patrick, S.M., Pudioprawoto, Randyka, Fred Higgs, C., 2014. Bit cutter onrock tribometry: Analyzing friction and rate-of penetration for deep well drilling substrates. Tribol. Int. 77, 178–185. Gaudin, D.B., 1991. A Comparison of MWD and Wireline, Steering Tool Guidance Systems in Horizontal Drilling 22536-MS SPE Conference Paper. Guo, Q., 2010. Key to Personalized Design of PDC Bit for Shale Gas Drilling Technical Study. Master’s Thesis. Southwest Petroleum University, Chengdu, Sichuan, China (in Chinese with English abstract). Grandis, D., 2015. The Successful Application of a Hybrid Rotary Steerable System Allowed to Drill a Sidetrack Well with a Record Build-Up of 13 0/30m and a Tangent Section to Increase the Reservoir Exposure. Mortimer, L., 2010. Innovative Design Features on PDC Bit Result in Record Run in Orenburg Region, Russia. 135881-MS SPE Conference Paper. Qi, Q.L., 2015. Research and Development on PDC Bit Numerical Rock Drilling system. Master’s Thesis. Southwest Petroleum University, Chengdu, Sichuan, China (in Chinese with English abstract). Ren, H.T., Yang, Y.X., Chen, L., Yan, J., Zhou, C.X., 2010. Research on the numerical method of the PDC bit drilling progress simulation system. J. Southwest Pet. Inst. 32 (5), 150–154 (in Chinese with English abstract). Rajabov, V., Miska, S., Mortimer, L., 2012. The effects of back rake and side rake angles on mechanical specific energy of single PDC cutters with selected rocks at varying depth of cuts and confining pressures. In: IADC/SPE Drilling Conference and Exhibition. Society of Petroleum Engineers. SPE 151406. Sinor, L.A., Warren, T.M., 1993. Application of Anti-whirl PDC Bits Gains momentum. Middle East Oil Show. Society of Petroleum Engineers. SPE 25644. Su, Y.N., 2001. Research and Application of Screw Drilling Tool. Petroleum Industry Press, Beijing, pp. 142–158 (in Chinese). Warren, T., Lesso, B., 2005. Schlumberger Casing Drilling Directional Wells OTC 17453. Wang, N., 2015. Automated Slide Drilling System and Multi-Body Dynamics Aided Slide Drilling Simulation SPE-173396-MS. Yang, Y., 2017. Research on Drilling Mechanics of PDC Bits in Sliding Steering Drilling. Master’s Thesis. Southwest Petroleum University, Chengdu, Sichuan, China (in Chinese with English abstract). Yang, Y.X., 2003. Research on the Cutting Mechanics of PDC Bits. Ph.D. Dissertation. Southwest Petroleum Institute, Nanchong, Sichuan, China (in Chinese with English abstract). Zhang, C. L., 2018. Research on rock-breaking mechanism of cross-cutting PDC bit.J. Pet. Sci. Eng.. WOS:000419828800053. Zheng, J.W., Kuang, Y.C., Wang, X., Zou, Z.Y., Chen, Y.Z., Yang, Y.X., 2016. Simulation study on the drilling of PDC bit at compound drilling condition. Pet. Mach. 44 (1), 40–44 (in Chinese with English abstract). Zhu, H.Y., Deng, J.G., Jin, X.C., Hu, L.B., Luo, B., 2015. Hydraulic fracture initiation and propagation of oil and gas wellbore with oriented perforating technique. Rock Mech. Rock Eng. 48 (2), 585–601. Zhu, H.Y., Shen, J.D., Zhang, F.S., 2019. A fracture conductivity model for channel fracturing and its implementation with discrete element method. J. Pet. Sci. Eng. 172, 149–161.
6. Conclusions (1) Based on the mechanical behavior of the down-drilling sting, a numerical drilling simulation for a PDC drill bit was developed and perfected. Based on this technology, a kinematics model of a PDC drill bit under compound drilling was established, and the effects of transmission ratio, cutter layout, and drill string ge ometry on the cutting trajectory formed by the cutters were studied. (2) The cutting track of the cutter in the cone area exhibits knotting, and this special movement of the cutters in the cone area of the PDC bit is the primary reason why the PDC bit is cored in com pound drilling. (3) Under the condition of compound drilling, the PDC cutters break the bottom rock similarly to milling, and the cutters are in an unbalanced contact state. The number of effective working cut ters of the drill bit is less than the total number of cutters; the scraping motion track of the cutters is no longer concentric but follows a helical trajectory. (4) Customized design of the PDC drill bit under compound drilling conditions should be focused on preventing the abnormal failure, improving the stability, and thus extending the service life of the drill bit. Acknowledgement The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant No. 51504209, No. 51374176), and China Postdoctoral Science Foundation (2019M653479). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.petrol.2019.106647. References Azizov, A., 2011. In: Baker Hughes, Positive Displacement Motor Innovation Drives Increased Performance with Pdc Bits in Unconventional Plays 148262-MS SPE Conference Paper.
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Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: http://www.elsevier.com/locate/petrol
Research on the working mechanism of the PDC drill bit in compound drilling Yingxin Yang a, b, *, Yan Yang a, Haitao Ren a, b, Qingliang Qi a, Xinwei Chen a a b
School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
A R T I C L E I N F O
A B S T R A C T
Keywords: PDC drill bit Compound drilling Numerical simulation Rock-breaking mechanism Customized design
A combined ground-driven and down-hole-driven motor significantly improves the penetration rate of poly crystalline diamond compact (PDC) drill bits but greatly reduces bit life. By studying the mechanical behavior of the drill string in compound drilling, a kinematics model of a PDC drill bit under compound drilling was established, and the effects of transmission ratio, cutter layout, and drill string geometry on the cutting trajectory formed by the cutters were analyzed. Furthermore, a numerical drilling simulation of the PDC drill bit was developed and enhanced to research the kinematics and cutting regularities of the PDC drill bit in compound drilling. In addition to high rotation rate, nonparallel scraping of the PDC cutters and the unbalanced contact state between the cutters and the rock are the prime reasons for improvement of the penetration rate of the PDC bit in compound drilling. An error analysis comparing simulation and experimental results was performed and the two agree to within <20%. Based on the working mechanism of the PDC drill bit in compound drilling, technical ideas and implementation methods for customized designs of PDC drill bits are discussed.
1. Introduction With the advantages of good stability, high rate of penetration (ROP), and high design flexibility, polycrystalline diamond compact (PDC) bits are widely used in exploration for and exploitation of oil and gas (Dougherty et al., 2014; Zhu et al., 2015). Compound drilling is a drilling method in which the ground-driven and down-hole-driven motors are combined to drive the drill bit to break rock in oil and gas drilling engineering. Using compound drilling with a screw drilling tool combined with a PDC bit can relieve the back pressure on the drilling string and enable the cutters to effectively penetrate the formation, thereby improving rock-breaking efficiency (Azizov, 2011; Gaudin, 1991; Grindrod, 2002; Grandis, 2015; Warren and Lesso, 2005; Wang, 2015; Zhu et al., 2019). It is a very effective technique for speeding up and increasing efficiency in drilling. However, because of the super position of the two motion states and the introduction of the motor bending angle of the screw, eccentricity and deflection occur between the actual center of rotation of the PDC bit and the center of the well trace. Each of the cutters suffers from severe load distribution uneven ness and varying degrees of impact loading, which in turn can cause failure of an individual cutter. Presently, classical means arranging PDC
bit cutters entails equal cutting volume and full coverage. Accordingly, failure of individual cutters inevitably leads to a sharp increased working load on the adjacent cutters of the drill bit, causing serious failure modes such as balling, coring, and ring out (Clegg, 1992; Mor timer, 2010; Sinor and Warren, 1993). Under the constraints of a casing program, formation conditions, and bottom-hole assembly, identifying the rock-breaking mechanism for PDC bits in compound drilling is a design precondition. Numerical drilling simulation technology for PDC drill bits is a newly developed effective technical means to simulate the interaction between the bit and the formation rock, analyze the load distribution of cutters, and evaluate the performance of the drill bit in underground complex conditions (Zheng et al., 2016). By using this system, the influence of the casing program and the geometry of the down-drilling string on PDC drill bit cutters under the condition of compound drilling were studied, the corresponding kinematics analysis equation was established, and the simulation system was developed and improved. In addition, the effects of factors such as the rotation speed ratio between the rotation speed of the screw motor and the revolution speed of the rotary table, cutters arrangement design of the drill bit, and bend angle of the screw on the bottom-hole trajectory of the cutters were analyzed, analysis of the
* Corresponding author. School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China. E-mail address: [email protected] (Y. Yang). https://doi.org/10.1016/j.petrol.2019.106647 Received 26 June 2019; Received in revised form 18 October 2019; Accepted 3 November 2019 Available online 5 November 2019 0920-4105/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Yingxin Yang, Journal of Petroleum Science and Engineering, https://doi.org/10.1016/j.petrol.2019.106647
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bottom-hole morphology was performed, and corresponding conclu sions were obtained. These research results improve our understanding of the rock-breaking mechanism for PDC bits under the condition of compound drilling and provide a reference for customized drill bit de signs. In particular, the simulation system considered the influence of elastic deformation of the down-drilling string under the constraint of the borehole wall on the working state of the PDC bit, and the research results were close to the actual working conditions of the bit.
2.1. Research and development of numerical drilling simulation technology for PDC bits Based on MATLAB, an interaction model between the PDC bit and the formation rock under compound drilling was constructed in the simulation system. This model’s simulation strategy is based on processoriented weight on bit (WOB) equilibrium. In each simulation step, the dynamic rock-breaking process for the PDC bit was transformed into a static balance problem at every step, thus minimizing the calculation amount and optimizing calculation efficiency. Results such as the tra jectory of the drill bit, variation of loading, and bottom-hole morphology during the whole drilling process were thus obtained (Qi, 2015). Flow chart of the numerical simulation system is shown in Fig. 1.
2. Establishment of kinematics model of PDC bit in compound drilling The numerical drilling simulation system is an integrated analyzing tool for PDC bit. Based on the mechanical behavior analysis of downhole string and the kinematics model of PDC cutters, the kinematics laws of PDC cutters under compound drilling can be studied via the numerical drilling simulation system.
2.2. Mechanical behavior analysis of down-drilling string It was assumed that, in high-angle directional wells and horizontal wells, the drill string was tangent to the lower shaft lining owing to its weight, and the upper part of the drill string from the tangent point was attached to the lower shaft lining, which was far away from the drill bit,
Fig. 1. Flow chart of the numerical simulation system. 2
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so that the effect of elastic deformation on the drill bit can be ignored here. The down-drilling string from the tangent point to the drill bit was simplified as a double-span continuous beam subjected to self-weight and the lateral force of the bit under drilling fluid conditions (Su, 2001; Yang, 2017). As shown in Fig. 2(a), the dogleg severity was 90� γ, the initial bending angle of the screw was θm , the drill string was tangent to the lower shaft lining at point C, and the contact between the elbow point (point A) of the screw and the shaft lining was regarded as a fixed hinge support. The down-drilling string from the elbow point (point A) of the screw was disconnected, and the double-span beam was piecewise handled in accordance with a static balance problem. The line masses of the double-span beam were q1 and q2 , and the bit (point B) was sub jected to a lateral force FB from the shaft lining. Because the direction of the WOB was along the axial line of the drill bit, the rotation angle and flexibility of the drill string were less affected, so the effect of the WOB was not considered here. The double-span beam will generate elastic
deformation under the joint action of the forces mentioned and rotate and flex. Because the bending angle of the screw was small, the defor mation of the double-span beam conformed to the conditions of small deformation with linear elastic properties, so θ � sin θ � tan θ. Fig. 2(b) shows a simplified mechanical model of the first span beam. For the force analysis of the first span beam, the elbow point (point A) was regarded as the fixed end. According to static equilibrium of the beam, the fixed end was subjected to a bending moment MA and a supporting force FA and the drill bit was subjected to a lateral force FB. The AB segment beam was subjected to a uniform load and its line mass was q1 . Under the joint action of the these forces, the first span beam underwent elastic deformation with a rotation angle θ1 and a flex of wB1 . Fig. 2(c) shows a simplified mechanical model of the second span beam. For the force analysis of the second span beam, the elbow point (point A) was regarded as a fixed hinge support, and it was subjected to a bending moment MA and supporting forces FAW and FAX. Point C of the beam was the tangent point with the lower shaft lining, and it was
Fig. 2. Simplified model of a drill string under the condition of flexibility. 3
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subjected to a supporting force FC. The AC segment beam was subjected to a uniform load and its line mass was q2 . Under the joint action of these forces, the second span beam underwent elastic deformation with a rotation angle of θ2 . Therefore, the force deformation of the downdrilling string can be represented by Fig. 2(d). According to the material mechanics principle of the bending deflection of beam, the rotation angle θ and the flex w can be expressed as � Z EIdw dx ¼ EIθ ¼ MðxÞdx þ C Z Z f (1) EIw ¼ dx MðxÞdx þ Cx þ D According to the elastic mechanics principle of superposition, the rotation angles θ1 , θ2 , the flex wB1 and the bending angle θt of the screw under the flexible condition of the drill string (hereinafter referred to as the flexible bending angle) were q1 lm 3 cosðθm 6E1 I1
θ1 ¼
FB l m 2 2E1 I1
8FB lm 3 þ 3q1 lm 4 cosðθm 24E1 I1
wB1 ¼
θ2 ¼
γÞ
(2) γÞ
8FB lm a 4q1 lm 2 a cosðθm 24E2 I2
q2 a3 cos γ
(3) γÞ
Fig. 3. Absolute rotation speed of a bit in compound drilling.
(4)
The kinematics equation (Guo, 2010) of the PDC bit in compound drilling can be expressed as
(5)
θt ¼ θm þ θ1 =2 þ θ2
In this formula, θt is a negative value, which indicates that the sec tion was rotated clockwise. It can be obtained that the force deformation of the down-drilling string will reduce the bending angle of the screw. The deflection wB of the B section is the superposition of the deflection wB1 of the free end of the AB beam and the rigid-body displacement caused by the rotation of the AB beam from the rotation angle θ2 of the A section, namely,
½X; Y; Z; 1� ¼ ½x; y; z; 1� � T0 ð0; 0; vωtÞ �Tx ½ φm �
3. Kinematics analysis on PDC cutters in compound drilling
Therefore, in compound drilling, the reamed borehole diameter Dt and the wellbore expansion rate δ are Dt ¼ 2ðlm sinθm δ¼
Dt
Db Db
¼
2ðlm sinθm Db
From the relationship between geometry and kinematics, the threedimensional space state equation of PDC cutters at any time can be obtained (Ren et al., 2010) as
(7)
wB Þ þ Db wB Þ
(10)
In the numerical drilling simulation system, the above equations are used as the kinematics model of the PDC bit. Thus, analyses on the ki nematics and cutting mechanics of PDC cutters under compound drilling condition can be performed.
(6)
wB ¼ wB1 þ θ2 ⋅lm
cosðωtÞ þ 1 � � Tz ðωtÞ 2
(8)
x ¼ e cosω2 t þ r cosθt cos½ði þ 1Þω2 t� f y ¼ e sinω2 t þ r cosθt sin½ði þ 1Þω2 t� z ¼ e=tanθt r sinθt cos iω2 t þ vz t
In this formula, Db is the diameter of the PDC bit. 2.3. Establishment of kinematics model
(11)
where e ¼ ðlm þh0 Þsinθt is the distance from the location points of the cutters to the central axis of the wellbore, h0 and r are the location height and radius of the PDC cutters on the drill bit, and i is the ratio of the motor speed to the rotary table speed. From the above analysis, one can see that the cutter trajectories in compound drilling are affected by many factors, such as the position coordinates of the cutter (h0 and r), structural parameters of the screw (lm and θt ), and motor speed and rotary table speed i. Taking a PDC bit as an example, and the simulation parameters were taken as follows:
The geometric coordinate system for the PDC bit at the hole bottom was established according to the methods described in Chen (2016) and Yang (2003), and the kinematic model of the PDC bit under the condi tion of flexible drill string was studied. In compound drilling, the absolute rotation speed n of the drill bit is the vector synthesis of the screw motor speed n1 and the rotary table speed n2 , as shown in Fig. 3. This is one of the reasons why compound drilling has such a high rate of penetration. The feed rate of the drill bit was vz (m/h), the speed of the screw motor was n1 (rpm), the speed of the rotary table was n2 (rpm), the arm length was lm , and the azimuth of the arm deflection was ϕm . Then the absolute rotation speed n (rpm), absolute angular velocity ω (rad/min), and the drilling depth per radian of the drill bit are qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ¼ n1 2 þ n2 2 þ 2n1 n2 cosθt qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . f (9) ω ¼ nπ 30 ¼ ω1 2 þ ω2 2 þ 2ω1 ω2 cosθt v ¼ 8:3vz =nπ
(1) Drilling process parameters: speed of the rotary table speed is 30 rpm, speed of the screw motor speed is in the range of 90–180 rpm, the drilling pressure is 12 kN, the mud density is 1.4 g/cm3, the dogleg severity is 0� , the footage of each circle is 2 mm, the bending angles are respectively 0.5� and 1� and the arm length are respectively 1 m and 1.2 m. (2) Cutter parameters: the cutter diameter is 16 mm, the position coordinates of the three cutters are respectively (15.78 mm, 49.86 mm), (49.09 mm, 60.6 mm) and (80.08 mm, 59.42 mm) 4
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where the cutters are respectively in the cone, in the shoulder and in the gauge area of the PDC bit. (3) Rock sample parameters: the friction coefficient is 0.2, the in ternal friction angle is 22� and the shear strength is 11 MPa.
The three cutters are in the cone area, the shoulder area, and the gauge area of the drill bit, and the cutting tracks are shown in Fig. 6. According to the calculation results, cutter trajectories coincide with the cutter trajectory of the inner cone region when r < e=cosθt , and cutter trajectories are in accordance with the cutter trajectory of the outer shoulder area when r > e=cosθt .
3.1. Effect of rotation speed ratio
3.3. Effect of screw structural parameters
The rotation speed ratio i is equal to the ratio of the motor speed to the rotary table speed, namely, i ¼ n1 =n2 . The rotation speed ratio i is an important factor affecting the cutting tracks. Fig. 4(left) shows four tracks of one PDC cutter in the cone region of the drill bit when the rotation speed ratio i was taken as 3–6. From the above figure, two conclusions can be obtained:
The structural parameters of the screw are the flexible bending angle θt and the arm length lm . Fig. 7 shows trajectories of PDC cutters when the rotation speed ratio is i ¼ 4, the arm length is lm1 , and the flexible bending angle is θt2 , which is greater than θt1 in Fig. 6. When the arm length lm is a constant, as the flexible bending angle θt increases, the change in the direction of the cutter in the inner cone region of the PDC bit becomes sharper, and the radial fluctuation range of the trajectories becomes wider. Fig. 8 shows trajectories of PDC cutters when the rotation speed ratio is i ¼ 4, the flexible bending angle is θt1 , and the arm length is lm2 , which is longer than lm1 in Fig. 6. When the flexible bending angle θt is con stant, as the arm length lm increases, the radial fluctuation range of the trajectories becomes wider. From the above simulation results, we can conclude that the impact of the four factors on the trajectory of the cutter increases in the order of positioning height h0 , arm length lm , flexible bending angle θt of the screw, and positioning radius r of the PDC bit.
(1) The greater the rotation speed ratio i, the longer the cutter tra jectory. As the rotation speed ratio i increases, the number of changes of the cutter direction increases but the curvature of the cutter trajectory at the whirl becomes smaller. This indicates that, as the rotation speed ratio i increases, the rate of change of the direction of the cutter becomes slower. (2) It can be seen from Fig. 4(right) that the cutting track of the cutter in the cone area exhibits knotting. This indicates that, during the scraping process, the direction of cutter motion and the contact working face (curved face) of the cutter and the rock are constantly changing. In the figure, a semicylindrical cutter cut into the rock with an axial plane as the scraping face. During the scraping process, the cutter continuously rotates with respect to the rock, and the scraping face gradually transitions from the axial plane to the side and then continues to rotate to the cylin drical surface (the back of the axial plane) and cut out again. During the cutting and cutting out of the bottom hole, the scraping face of the cutter changes by ~180� , and the cutter is reversed with respect to the scraping direction of the rock. If the cutter cuts into the rock at the front face, then the back side will be reversely cut out.
4. Working mechanism analysis on the PDC drill bit in compound drilling The kinematics analysis results show that the PDC bit removes rock material more similar to “milling”. Taking the rock-breaking process of the PDC bit in compound drilling as “milling”, both the kinematics and cutting mechanics of the bit can be explained more reasonably. 4.1. Working principle of milling instead of drilling
This special movement of the cutters in the cone area of the PDC bit is the primary reason why the PDC bit is cored in compound drilling, as shown in Fig. 5 (Brett and Whirl, 1989; Rajabov et al., 2012).
In compound drilling, the “drilling” principle of PDC bits changes significantly. Some of the cutters on the bits will participate in cutting intermittently. Even if the cutters are not interrupted, at least their cutting state will change periodically, and the cutting depth of each cutter will change during the cutting process. Indeed, the combination of rotation and revolution-driven mode with a bending motor makes the PDC bit cut the rock more similar to milling instead of drilling. The rotation of the drill bit driven by a bending motor is the main motion of milling, while the revolution of the drill pipe becomes the feed motion. In this special “milling instead of drilling” mode, the working state of the cutters on the drill bit exhibits a certain degree of alternation, rather
3.2. Effect of position coordinates The position coordinates of the cutter are determined by two pa rameters: the positioning height h0 and the positioning radius r. Ac cording to the kinematics simulation results for the cutter, the influence of the positioning radius r on cutting tracks of different cutters is sig nificant, but the influence of the positioning height h0 is not obvious.
Fig. 4. Cutting tracks for different rotation speed ratios i and the knotting behavior of the cutter. 5
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Fig. 5. Failure mode for central cutters on a PDC bit.
Fig. 8. Cutting tracks for an arm length of lm2 .
Fig. 6. Cutting tracks for different position coordinates of the cutters.
the central region. The central region has a higher degree of irregularity than the outer region and has a multipeaked shape, which is signifi cantly different from that of the conventionally drilled bottom. This feature provides a direct basis for a rational interpretation of the bit cored failure phenomenon in compound drilling. 4.2. Penetration characteristics of cutters and nonparallel scraping status From the observation of the bottom-hole morphology in compound drilling, there are two main characteristics of PDC cutters: (1) The interaction between the PDC cutters and the rock is a nonparallel cutting process. (2) The nonparallel scraping creates a ragged rock ridge on the bottom hole, so that the cutters can naturally penetrate the rock. Because of the existence of the flexible bending angle of the screw, the center of the drill bit deviates from the center of the borehole. The eating depth on one side of the drill bit is larger than that on the other side. At the same time, PDC cutters are not completely involved in scraping and breaking rock (see Fig. 10). Therefore, the drill bit will form an uneven and intersecting rock ridge at the bottom hole, which will help the subsequent PDC cutters naturally penetrate the rock. Compared with the concentric circular cutting in ideal drilling, the nonparallel scraping in compound drilling is beneficial to the reduction of cohesion of the rock unit, the generation and diffusion of small cracks inside the rock, and the acceleration of the volume breaking of the rock, thereby improving the rock-breaking efficiency and working life of the PDC drill bit. In addition, the Drilling Institute of Southwest Petroleum University has found through nonparallel scarping experiments of PDC cutters (Zhang, 2018) (Fig. 11) that the rock-breaking method of nonparallel scraping is better than one-way concentric circular scraping, achieving
Fig. 7. Cutting tracks for an elastic bending angle of θt2 .
than continuous scraping under ideal drilling conditions, and the cutting tracks also change from concentric circles to helical trajectories (see Fig. 9 (left)). Fig. 9 (right) shows the numerical bottom-hole morphology obtained by simulating the compound drilling process of the drill bit in the PDC bit rock-breaking numerical simulation system. Obviously, the morphology is distinctly different from that of the conventional bottom. The nonparallel helical scraping trajectory by the cutters of the drill bit and the undulating geometry bottom surface indicate that the drill bit is indeed milling the rock. The unbalanced bearing of the drill bit and the changing cutting work state are not unimaginable. Another special morphological feature of the bottom hole is seen in 6
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Fig. 9. Helical trajectory of the cutters and the bottom-hole morphology.
number of actual working cutters is smaller than the total cutter number. The cutters periodically detach and enter in cutting, which makes the cutting area and cutting force of each cutter change periodically. Fig. 12 shows the actual number of PDC bit cutters in contact during the drilling process, which ranges from 8 to 15 during the working process. The total number of main cutting cutters on the drill bit is 26, while the average actual number of effective cutters involved in the cutting is 11.44, which is less than half of the total number of main cutters. Therefore, under the same drilling pressure, the average cutting load of the effective cutters of the drill bit during compound drilling is higher than that of conventional drilling. The axial force of the PDC cutters is one of the important indicators of the difficulty of penetrating the rock. From this point of view, the ROP of compound drilling should be higher. Fig. 13 shows the cutting area curves of three PDC cutters in the cone area, the shoulder area, and the gauge area, respectively. The cutting area changes with time, and the variation range is quite large, and the cutting area is often zero. The cutters periodically detach and enter in cutting, which is a typical working state of compound drilling of the cutters on the drill bit.
Fig. 10. Nonparallel scraping status of the cutters.
savings in both labor and energy. That is, under the condition of nonparallel scraping, the axial and tangential forces on the PDC cutters are both smaller than those in one-way concentric circular scraping. Especially when the spacing of PDC cutters reaches 16 mm, axial labor is reduced by up to 26.8%, and the tangential energy needed is reduced by up to 29.4%. Therefore, the nonparallel mesh bottom hole formed in compound drilling is conducive to the effective eating of PDC cutters on rocks, so that the ROP of the PDC drill bit can be effectively improved, thereby improving the rock-breaking efficiency.
4.4. Error analysis of simulation results Based on the above theories, to correct the numerical drilling simulation technology of a PDC drill, a laboratory test of a 600 PDC bit under eccentric working conditions was performed (see Fig. 14). The experimental rock selected was Wusheng sandstone. The main relationship among the lateral force, torque, and rock properties of the bit under eccentric working conditions was determined. The eccentricity was controlled to <1 mm in the experiment by adjusting the bolts on the drill stand to test the lateral force, torque, and lateral force of the drill bit
4.3. Working mechanics analysis of PDC drill bits Due to the existence of the angle in the screw motor, some cutters in the drill bit are out of contact with the rock in a short period, i.e. the
Fig. 11. Photographs of the nonparallel scraping experiment and the rock ridge. 7
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Fig. 15. Torque curve obtained in the simulation experiment.
analysis of the simulation system is reliable.
Fig. 12. Cutter number vs. rotation angle.
5. Customized design of PDC dill bits under compound drilling conditions From the above analysis, it can be seen that the amplitude of vari ation of the cutting angle of the PDC cutters under compound drilling conditions is large; especially, the cutters on the inner cone of the bit have sharply knotting trajectories. In addition, the radial fluctuation of the PDC cutter trajectories inevitably causes a large periodic variation of the lateral force of the bit, which easily causes lateral vibration of the bit. Therefore, the following design ideas are proposed: (1) The cutters arrangement contour should be designed with a shallow cone or a flat cone. By increasing the radius of curvature of the contour, each area of the cutters arrangement contour can smoothly transition, which can effectively relieve the backing pressure effect of the cone and reduce the cutting load of the PDC cutters on the cone area. At the same time, increasing the cutters density of the cone and using a single blade with a multi-cutter or interlaced cutters can improve the cutting ability of PDC cutters on the inner cone of the bit. (2) The cutters arrangement suitably introduces a negative bypass angle. Setting the negative bypass angle for cutters areas where the cutter trajectories change sharply can reduce the probability of the cutters being subjected to a reverse cutting force and avoid the occurrence of abnormal failure phenomena such as delami nation and breakage of the diamond layer. (3) A customized design of the PDC drill bit can improve its stability, enhance the ability of gauge protection, reduce the exposure height of the cutters, or set the feathers like a cushioning cutter, flat insert cutter, and reverse cutter. At the same time, all the methods such as reducing the length of the gauge protection section, enhancing the cutting ability of the gauge cutters, and
Fig. 13. Cutting area vs. rotation angle.
Fig. 14. Photographs of the PDC bit and the test laboratory.
(Yang, 2017). The average value of the torque received by the drill bit in the simulation calculation was 651.16 N m (see Fig. 15) and it changed periodically. At the same time, a corresponding numerical model was established in the simulation system, and the simulation parameters were controlled as follows: Φ152.4 mm (bit) � 0.3 m þ Φ114 mm (drill pipe) � 20 m, drilling pressure ¼ 16.2 kN, rotary table speed ¼ 30 rpm, mud density ¼ 1.7 g/cm3, and dogleg severity ¼ 0� . The error was analyzed by com parison to the experimental results. The average torque at the drill bit calculated by the experimental recorder (see Fig. 16) in the bench test was 798.51 N m. This value is within 20% of the simulation results, so it can be inferred that the
Fig. 16. Torque curve obtained in the laboratory test. 8
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improving the gauge cutters density can help the reduce the torque response and depress the possibility of lateral vibration of the drill bit.
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6. Conclusions (1) Based on the mechanical behavior of the down-drilling sting, a numerical drilling simulation for a PDC drill bit was developed and perfected. Based on this technology, a kinematics model of a PDC drill bit under compound drilling was established, and the effects of transmission ratio, cutter layout, and drill string ge ometry on the cutting trajectory formed by the cutters were studied. (2) The cutting track of the cutter in the cone area exhibits knotting, and this special movement of the cutters in the cone area of the PDC bit is the primary reason why the PDC bit is cored in com pound drilling. (3) Under the condition of compound drilling, the PDC cutters break the bottom rock similarly to milling, and the cutters are in an unbalanced contact state. The number of effective working cut ters of the drill bit is less than the total number of cutters; the scraping motion track of the cutters is no longer concentric but follows a helical trajectory. (4) Customized design of the PDC drill bit under compound drilling conditions should be focused on preventing the abnormal failure, improving the stability, and thus extending the service life of the drill bit. Acknowledgement The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant No. 51504209, No. 51374176), and China Postdoctoral Science Foundation (2019M653479). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.petrol.2019.106647. References Azizov, A., 2011. In: Baker Hughes, Positive Displacement Motor Innovation Drives Increased Performance with Pdc Bits in Unconventional Plays 148262-MS SPE Conference Paper.
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