Int. J. Materials and Product Technology, Vol. 50, Nos. 3/4, 2015 Kinematic and rock-breaking characteristics of new drill bit with swirling bottom-hole model Jialin Tian* School of Mechanical Engineering, Southwest Petroleum University, Chengdu, 610500, China and School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, China Email: tianjialin001@gmail.com *Corresponding author You Li, Lin Yang, Chuanhong Fu, Yonghao Zhu and Xiaolin Pang School of Mechanical Engineering, Southwest Petroleum University, Chengdu, 610500, China Email: 1272865015@qq.com Email: 370390928@qq.com Email: 358691787@qq.com Email: 519645776@qq.com Email: 512375458@qq.com Abstract: For the low rock-breaking efficiency at borehole centre of the current drill bit, this paper presents a new bit with swirling bottom-hole model (swirling-cutting bit) and analyses its kinematics and rock-breaking features. Using the cylindrical coordinate, the bit revolution and cone rotation motion behaviour are analysed. With the position and velocities equations establishment of cutting element, the contact section between different cutting elements ring and rock are given, including the velocities distribution results on the section. With the numerical calculation and experimental test, the results show that the elements on maximum elements ring pass through the borehole centre, and broke the rock with compression and cutting effect. With the start point at the bottom-hole and end point at the borehole wall, the contact force of element acting on rock contains effect of ‘digging’ from the inside out and from the bottom up. The conclusions provide reference for improving the bit rock-breaking efficiency, cutting element distribution and bit structure optimisation. Keywords: new drill bit; swirling; bottom-hole model; kinematics; rate of penetration; ROP; rock-breaking. Reference to this paper should be made as follows: Tian, J., Li, Y., Yang, L., Fu, C., Zhu, Y. and Pang, X. (2015) ‘Kinematic and rock-breaking characteristics of new drill bit with swirling bottom-hole model’, Int. J. Materials and Product Technology, Vol. 50, Nos. 3/4, pp.305–318. Copyright © 2015 Inderscience Enterprises Ltd. 305 306 J. Tian et al. Biographical notes: Jialin Tian received his PhD in Mechanical Engineering from Southwest Petroleum University in 2009. He is currently an Associate Professor at Southwest Petroleum University, School of Mechanical Engineering. His research interests include drill bit technology, downhole tools and drilling dynamics. He has years of experience in teaching and researching about mechanical design and drilling tools. He has been a reviewer for several journals. He has published over 20 refereed papers in journals and conferences. You Li received his Bachelor degree in Mechanical Engineering from Southwest Petroleum University in 2013. He is currently a postgraduate at the School of Mechanical Engineering, Southwest Petroleum University. His research interests include drill bit technology and drilling dynamics. Lin Yang received her PhD degree in Mechanical Engineering from Southwest Petroleum University in 2013. She continued her postdoctoral research at the School of Petroleum Engineering, Southwest Petroleum University. Her research interests include drilling dynamics and hydromechanics. Chuanhong Fu received his Bachelor degree in Mechanical Engineering from China University of Petroleum in 2013. He is currently a postgraduate at the School of Mechanical Engineering, Southwest Petroleum University. His research interests include downhole tools and drill bit technology. Yonghao Zhu received his Bachelor degree in Mechanical Engineering from Southwest University of Science and Technology in 2013. He is currently a postgraduate at the School of Mechanical Engineering, Southwest Petroleum University. His research interests include downhole tools and drilling dynamics. Xiaolin Pang received his Bachelor degree in Mechanical Engineering from Southwest Petroleum University in 2012. He is currently a postgraduate at the School of Mechanical Engineering, Southwest Petroleum University. His research interests include drill bit technology and drilling dynamics. 1 Introduction The rate of penetration (ROP) and service life are two important indicators to measure the drill bit performance and improving the ROP has been a key issue in drilling engineering. On the premise of guaranteed service life, high ROP is important for increasing bit total footage, reducing the drilling tripping number and production costs (Bahari et al., 2007). Based on the analysis of different types of drill bits (including the PDC and tricone bit), the field data indicated that the low borehole centre rock-breaking efficiency has become one of the main factors restricting the ROP. Franca (2010) analysed drilling action of roller-cone bits and Richard and Detournay (2006) discussed the influence of bit-rock interaction on stick-slip vibration of PDC bits. Moreover, the causes of low efficiency in centre rock-breaking is due to the downhole model of drill bit concentric shape, as shown in Figure 1, which resulted in the element cutting rock with low velocity and low efficiency. In fact, the low cutting element velocity caused the drill bit core portion resisted by rock. However, the borehole centre rock-breaking form was snapping rather than crushing (tricone bit) or cutting (PDC bit), which eventually became the major cause of borehole centre low rock-breaking efficiency and low drilling ROP. Kinematic and rock-breaking characteristics of new drill bit Figure 1 307 Current drill bit bottom-hole model (a) tricone bit bottom-hole model (b) PDC bit bottom-hole model (a) (b) Over the years, many related field researches were carried out to improve the ROP, including drill bit structure and bottom-hole assembly (BHA) (Elsayed and Raymond, 2002). For the drill bit structure design, many researchers developed optimisation methods, or the cutting element distribution (Iqbal, 2008). To the BHA, more involved efforts were also completed using BHA combined vibration effect to improve the drill ROP (Yigit and Christoforou, 2006; Wise et al., 2003). However, these methods did not solve the problem of borehole centre low rock-breaking efficiency and the cutting element motion with low speed at the borehole centre. Consequently, these methods could not change the status that the outer element wears early while the centre element has not been fully utilised. 308 Figure 2 J. Tian et al. Swirling bottom-hole model design (see online version for colours) 60 40 20 -60 -40 -20 20 40 60 -20 -40 -60 In response to these problems, this paper presented a new swirling-like bottom-hole model and designed the corresponding drill bit structure (hereinafter referred to as swirling-cutting drill bit) on this basis, as shown in Figure 2. During the rock-breaking process, the element on maximum cutting elements ring crossed the borehole centre and cut rock with high-speed movement (the maximum cutting elements ring shown in Figure 3). Therefore, it could effectively improve the bit centre rock-breaking efficiency. Moreover, in the contact sections between the element and rock, including from the borehole centre to the borehole wall, the contact force of element acting on rock has effect of ‘digging’ from the inside out and from the bottom up. The digging effect enhanced the drill bit bottom-hole cleaning ability and was favourable to improve ROP. Meanwhile, the swirling-cutting drill bit got all elements on different ring cutting the borehole wall and optimised the rock-breaking volume of each element. Figure 3 Swirling-cutting drill bit structure design and analysis coordinates (a) bit revolution coordinates and parameters (b) cone rotation coordinates and parameters (c) positional parameters of cone and bit body (see online version for colours) Z P( ρ P ,θ P , Z P ) ZP X O Maximum ring θP Minimum ring ρP (a) Kinematic and rock-breaking characteristics of new drill bit Figure 3 309 Swirling-cutting drill bit structure design and analysis coordinates (a) bit revolution coordinates and parameters (b) cone rotation coordinates and parameters (c) positional parameters of cone and bit body (continued) (see online version for colours) C0 Oi OiP ¦Á Hi P HP P ( rP , α P , hP ) Xi (b) D s Drill bit axis s β (c) According to the swirling-cutting bit structure parameters, this paper established the position and velocities equations with cylindrical coordinates. With the numerical example, it discussed the contact section of cutting element and rock. Based on experiment cone/bit speed ratio, the cutting element motion characteristics were analysed. The velocities distributions were given along the contact section of element and rock. Finally, using the experimental data verified the bottom-hole model results. The purpose is to study the element kinematics and provide basis for the study of swirling-cutting drill bit rock-breaking mechanism. 310 2 J. Tian et al. Analysis method and calculation model Based on the swirling bottom-hole model, the drill bit structure included cutting element, cone and bit body, shown in Figure 3. The cutting element is relatively static to the cone and the cone (including element) rotates around the bit body, with the definition of ‘cone rotation’. In addition, the bit body motions to the rock include rotation and axial direction movement, with the definition of ‘bit revolution’. Relative motion of the element and the rock can be analysed using the following method. With these definitions, VTooth -the absolute velocity of cutting element, VTooth − DrillBit -the relative velocity of element to bit, VDrillBit -the velocity of bit body to rock, and the calculation equation is given by equation (1): VTooth = VDrillBit + VTooth − DrillBit Z (1) Based the relationship definition of ‘cone rotation’ and ‘bit revolution’, the position equation can be established with cylindrical coordinate. To the point p coordinate P (ρP, θP, ZP), ρP is the radial distance, θP is angular coordinate, and ZP is height, as shown in Figure 3(a). To the cone rotation around the bit body, the same method is used with cylindrical coordinate and defined point p coordinate p(rp, αp, hp). Similarly, rp is the radial distance, αp is angular coordinate, and hp is height. Moreover, symbol s represents the axis distance between the cone and bit, and symbol β represents the axis angle of cone and bit. The symbol C0 is the distance of the cone centre to the bit axis, as shown in Figure 3. With the motion analysis method and parameters above, the cutting elements position equation can be established. The radial distance ρP, angular coordinate θP and height ZP can be calculated by the following equation (2) ~ equation (4): ρP = ( C0 − hP cos β + rP sin β cos α P )2 + ( rP sin α P − s )2 (2) rP sin α P − s ⎛ ⎞ θP = θ0 − θi − tan −1 ⎜ ⎟ − + cos sin cos C h r β β α P P ⎠ ⎝ 0 P (3) Z P = Z 0 − hP sin β − rP cos β cos α P (4) where θ0 is the bit initial position angle, θi is the angle between cone i and cone no. 1, and Z0 is the bit initial height value. The formulas below can convert equation (2) ~ equation (4) to Cartesian coordinates. ⎧ xP = ρP cos θP ⎪ ⎨ y P = ρP sin θP ⎪z = Z P ⎩ P (5) In the analysis of contact section of cutting element and rock, the start point is the first contact point of cutting element and rock at the bottom-hole centre, where ZP = min(ZPi), and the end point is the last point on the borehole wall, where ρP = max(ρPi). The discriminant can be described with: Kinematic and rock-breaking characteristics of new drill bit 311 ⎧Start point : z = min( Z Pi ) i = 1, 2,3… ⎨ ⎩End point : ρP = max( ρPi ) i = 1, 2,3… (6) During the rock-breaking process, the rotation speed ratio Ri of the cone and bit body is given by: ωi ωb Ri = (7) where ωi is the cutting element and the cone rotation angular velocity, and it can be calculated by the following equation (8). ωi is the bit body rotation angular velocity, and it be calculated by equation (9). ωi = dα P dt (8) dθ0 dt (9) ωb = After time derivation of equation (2) ~ equation (4), the cutting element velocities equations can be established. With the parameters definition of equation (7) ~ equation (9), the radial velocity vPρ of point p can be calculated by equation (10). dρP dt ⎛ rP 2 ⎜ 2 cos β sin 2α P − ( C0 − hP cos β ) sin β sin α P − s cos α P = rP ⎜ ⎜ ( C0 − hP cos β + rP sin β cos α P )2 + ( rP sin α P − s )2 ⎝ ⎛ rP 2 ⎜ 2 cos β sin 2α P − ( C0 − hP cos β ) sin β sin α P − s cos α P = rP ⎜ ⎜ ( C0 − hP cos β + rP sin β cos α P )2 + (rP sin α P − s)2 ⎝ v Pρ = ⎞ ⎟ dα P ⎟ ⎟ dt ⎠ (10) ⎞ ⎟ ⎟ ωi ⎟ ⎠ The tangential velocity vPt of point p is given by equation (11): vPt = ρP dθP dt ⎛ dθ ⎛ ( C0 − hP cos β ) cos α P + rP sin β − s sin β sin α P ⎞ dα P =ρP ⎜ 0 − rP ⎜ ⎜ ( C0 − hP cos β + rP sin β cos α P )2 + ( rP sin α P − s )2 ⎟⎟ dt ⎜ dt ⎝ ⎠ ⎝ ( C0 − hP cos β ) cos α P + rP sin β − s sin β sin α P = ρP ωb − ρP rP ωi ( C0 − hP cos β + rP sin β cos α P )2 + ( rP sin α P − s )2 ⎞ ⎟ (11) ⎟ ⎠ The axial velocity vPZ of point p is given by equation (12): dZ P dZ 0 dα P = + rP cos β sin α P dt dt dt = vbZ + rP ωi cos β sin α P vPZ = (12) J. Tian et al. 312 where vbZ is the axial velocity of bit body. With the definition of contact section in equation (6), the velocities can be analysed during the rock-breaking process. Compared with the concentric bottom-hole model, the swirling-cutting bit axial velocity vPρ of point p is in changing. 3 Numerical example With the kinematic analysis method established above, the numerical example and results were presented following. According to the given parameters, the cutting element trajectory was analysed. On the contact section of cutting element and rock, the velocities value were given below. The parameters shown in Table 1, it took the experimental result of rotation speed ratio Ri as input value for it was influenced by many factors. Numerical example parameters Table 1 Parameter Value The maximum ring radius rPmax (mm) 50 The minimum ring radius rPmin (mm) 20 The axis angle of cone and bit β (°) 30 The axis distance between the cone and bit s (mm) 8 The distance of the cone centre to the bit axis C0 (mm) –24.5 The height of maximum cutting elements ring in cone rotation coordinates hp (mm) 10.5 the rotation speed ratio of the cone and bit body Ri 0.46 According to the example parameters, kinematic analysis methods and calculation equations, the bottom-hole model of swirling-cutting bit was calculated as shown in Figure 4. The bottom-hole model calculation results (see online version for colours) 80 60 40 20 y/mm Figure 4 0 -20 -40 -60 -80 -100 -50 0 x/mm 50 100 Kinematic and rock-breaking characteristics of new drill bit 313 During the rock-breaking process, contrasting with concentric bottom-hole model, the swirling model ensures that the rock-breaking form at the hole centre is cutting, rather than snapping. Moreover, the bottom makes cutting elements have the effect of pushing lithic from the inside out and avoiding repeating broken. It is beneficial to improve rock-breaking efficiency and drill bit ROP. In addition, with observing rock-breaking process, the results show the cutting elements on maximum ring pass through the hole centre. Due to its high speed, it can improve the centre rock-breaking ability. Different rings involve in rock-breaking from the centre to the borehole wall and all rings contact with the wall position. Such motion characteristics can optimise effective rock-breaking volume of different ring cutting element and improve the bit service life. To analyse the contact section and its characteristics of cutting element and rock, it takes the maximum cutting elements ring as the research object. According to equation (6), the start point is at the bottom-hole centre where ZP = min(Zpi), and the end point is on the borehole wall where ρP = max(ρPi), as shown in Figure 5. Figure 5 Contact sections of rock and cutting element on maximum and minimum ring (see online version for colours) End point 0 -5 the maximum elements ring the minimum elements ring -10 -15 z/mm -20 -25 -30 -35 -40 -60 -45 -50 -30 -40 Start point -20 -10 0 y/mm 10 -20 0 20 30 40 x/mm 20 Comparing contact sections of rock with cutting element on maximum and minimum ring, it shows that the rock-breaking behaviours of new drill bit are different with current cone bit or PDC bit. The element breaks rock both with impact crushing and cutting effects. Meanwhile, the contact section shows that the element rock-breaking behaviour has characteristics of ‘digging’ from the inside out and from the bottom up which enhances lithic removal effect. Moreover, for the cutting element space spiral trajectory, there is no repeat cross line. For the long contact section corresponding to maximum ring and short to minimum ring, the maximum ring has more cutting elements than minimum ring and this contact section distribution makes the rock-breaking volume roughly equal of cutting element on different ring. It is beneficial to extend bit service life. 314 J. Tian et al. Based on the contact section results, the velocities results and its distribution can be obtained using the equation (10) ~ equation (12). According the example parameters, the velocities calculation results were given as shown in Figure 6 and the following conclusions could be obtained: Various velocities results of cutting element on minimum and maximum ring (a) various velocities on minimum ring (b) various velocities on maximum ring (see online version for colours) Radial velocity Tangential velocity 400 Axial velocity Velocity /(mm/s) 300 200 100 Start Point 0 -100 30 End Point 20 20 10 0 0 y/mm -20 -10 -20 x/mm -40 (a) 500 Radial velocity Tangential velocity Axial velocity 400 速度 v/(mm·s-1) Figure 6 300 Start Point 200 100 0 40 End Point 20 20 0 y/mm 0 -20 -20 -40 -40 -60 (b) x/mm Kinematic and rock-breaking characteristics of new drill bit 315 To the various direction velocities, comparing the distribution features of radial velocity vPρ, tangential velocity vpt and axial velocity vPz, the following conclusions can be obtained that the composite velocity of vPρ and vPt embodies the cutting effect of element breaking rock, while vPz means the extrusion or tension effect (Vz – ROP < 0 means extrusion, while Vz – ROP < 0 means tension). At the contact section beginning, the elements broke the rock with impact and cutting effect. The velocities distribution law is that radial velocity vPρ and tangential velocity vPt are small; the synthesis value of vPρ and vPt determined the effect of cutting rock. To the axial velocity vPz, if the relationship between vPz and ROP is Vz – ROP ≥ 0, it indicated that the cutting element breaks rock with tensile effect and it contained the behaviour of ‘digging’ from the bottom up. Comparing the similarities and differences of cutting element velocities on maximum and minimum ring, it shows the features of various direction velocities changing with different ring. From the numerical results, it can be obtained the contact section’s velocities distribution rule of cutting elements on maximum and minimum ring. From starting point to end point of the contact section, the radial velocity vPρ, tangential velocity vpt and axial velocity vPz have trends of first increases and then decreases. At the point of maximum synthesis value of vPρ and vPt, the element cutting rock behaviour is most obvious. At the maximum value of (Vzi – ROP), the element tensile behaviour on rock is most obvious. 4 Experimental analysis With parameters corresponding to the example, the experiment bit was manufactured and the bench test was completed. The experiment results included observing rock-breaking process, analysing the drill bit vibration, checking the cutting element trajectory and its characteristics, studying the bottom-hole model shape. The experimental rock size was 225 mm × 200 mm × 150 mm, the bit rotation speed was 90rpm, the WOB was 20,000 N and the ROP was 2.6 mph. The experimental results were shown in Figure 7. The following conclusions can be obtained from the experiment. Figure 7 Swirling-cutting drill bit experiment and results (a) swirling-cutting drill bit experiment (b) the bottom-hole model – 1 (c) the bottom-hole model – 2 (see online version for colours) (a) 316 Figure 7 J. Tian et al. Swirling-cutting drill bit experiment and results (a) swirling-cutting drill bit experiment (b) the bottom-hole model – 1 (c) the bottom-hole model – 2 (see online version for colours) (b) (c) The experimental bottom-hole model matched the example calculation result. With the swirling bottom-hole model and same trajectory distribution characteristics, the experimental results verified the calculation method correctness. Observing the experimental contact section of element and rock, it was consistent with the numerical example results. The contact section starts at the position of minimum vertical coordinate, while it ends at the maximum radial coordinate. The cutting elements on maximum ring cross through hole centre and all the elements contact the borehole wall with space spiral trajectory. The experimental test showed that the rock-breaking behaviour of element coincided with the numerical results. The element broke rock with obvious digging effect from inside out and from bottom up, with the radial velocity vPρ and tangential velocity vPt corresponding cutting effect and the axial velocity vPz corresponding extrusion or tension effect. With changing the bit structure or rock property parameters, the experimental results were different. Corresponding to the numerical model, it shows that the key factors of Kinematic and rock-breaking characteristics of new drill bit 317 rock-breaking features include the structural parameters such as cone and bit axis angle β and distance s, the motion parameters such as rotation speed ratio Ri, the mechanical parameters such as weight on bit (WOB) and lithology. Moreover, the rotation speed ratio Ri is influenced by many factors. Experiment results showed that the rock hardness influence on Ri is larger ratio corresponding to harder rock. In experiment condition, the ratio Ri was 0.46 ~ 0.55, which was different from the current tricone bit ratio (> 1). 5 Conclusions Comparing with the current drill bit, the swirling-cutting bit bottom-hole model is different with current drill bit. During the rock-breaking process, with the maximum cutting elements passing through the borehole centre, the new bit can effectively improve the centre rock-breaking efficiency. The swirling-cutting bit motion behaviour includes the cone rotation and the bit revolution. Taking advantage of cylindrical coordinate and establishing the position and velocities equations, it can analyse the cutting element motion behaviour and rock-breaking features, including the contact section and velocities distribution characteristics. The cutting elements break rock with crushing and cutting effect. The kinematic analysis results in this paper are the basis of rock-breaking mechanism research. Based on the analysis method and results, with the analysis of cutting element’s effective rock-breaking volume and its failure modes, it can provide theoretical support for cutting element distribution and the bit structure optimisation. Acknowledgements This work is supported by National Natural Science Foundation of China (11102173), Foundation of Key Laboratory of Oil and Gas Equipment of China Education Ministry and Major Cultivation Foundation of Sichuan Education Department (12ZZ003, No. 667). References Bahari, A. and Baradaran, S.A. (2007) ‘Drilling cost optimization in Iranianm Khangiran Gas Field’, SPE 108246 presented at International Oil Conference and Exhibition, Veracruz, Mexico. Elsayed, M.A. and Raymond, D.W. (2002) ‘Analysis of coupling between axial and torsional vibration in a compliant model of a drillstring equipped with a PDC bit’, Proceedings of ASME ETCE Conference, Houston, TX. Franca, L.F.P. (2010) ‘Drilling action of roller-cone bits: modeling and experimental validation’, Journal of Energy Resources Technology, Vol. 132, No. 4, p.043101-1-9. Iqbal, F. (2008) Drilling optimization technique-using real time parameters, SPE 114543, Moscow, Russia. Richard, T. and Detournay, E. (2006) ‘Influence of bit-rock interaction on stick-slip vibration of PDC bits’, SPE 77616, Vol. 30, No. 3, pp.50–54. 318 J. Tian et al. Wise, J.L., Finger, J.T., Mansure, A.J., Knudsen, S.D., Jacobson, R.D. and Grossman, J.W. (2003) ‘Hard-rock drilling performance of a conventional PDC drag bit operated with, and without, benefit of real-time downhole diagnostics’, Transactions, Geothermal Resources Council Annual Meeting, Morelia, Mexico. Yigit, A.S. and Christoforou, A.P. (2006) ‘Stick-slip and bit-bounce interaction in oil-well drillstrings’, J. Energy Resour. Technol., Vol. 128, No. 4, pp.268–274.