https://orcid.org/0000-0003-4934-7374
Figures
Abstract
Aimed at the technical problems of low drilling speed and difficult rock-breaking in deep-well and hard rock-stratum, particle waterjet coupled impact rock-breaking technology in rotary drilling is put forward in this paper. Firstly, the working principle of particle jet impact rock-breaking in rotary drilling was introduced, and the acceleration model of particle jet and the damage model of rock were established. The acceleration mechanism of particles and dynamic damage evolution process of rock under particle jet were studied, which showed that the broken pit and rock damage would increase with time gone on, and damage evolution of rock presented the radial expansion. Then, experimental device of particle jet coupled impact rock-breaking in rotary state was developed, and the effect of jet parameters on penetration depth and failure volume was analyzed with comparison of la experiment and numerical simulation. The results showed that drilling speed with particle jet impact is twice that of conventional drilling, and combination nozzles layout of impact angle with 8°and 20° can achieve rock-drilled rapidly, which also demonstrated the correctness of simulation method. The device development and the rock-breaking results analysis would be of great value for engineering application.
Citation: Fang T, Ren F, Wang B, Cheng J, Liu H (2021) Particle jet impact deep-rock in rotary drilling: Failure process and lab experiment. PLoS ONE 16(4): e0250588. https://doi.org/10.1371/journal.pone.0250588
Editor: Peitao Wang, University of Science and Technology Beijing, CHINA
Received: December 26, 2020; Accepted: April 11, 2021; Published: April 28, 2021
Copyright: © 2021 Fang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting information files.
Funding: The study was funded by National Natural Science Foundation of China (11972113; 11902072), the Guiding Innovation Fund Project of Northeast Petroleum University (2019YDL-07), and the Post-doctoral Research Start-up Fund Project of Heilongjiang Province (LBH-Q15018).
Competing interests: The authors have declared that no competing interests exist.
Introduction
With depletion of shallow oil resources and complexity of exploration geology, the drilling depth is greatly increasing, and the drilling conditions are becoming more complex, such as high temperature, high pressure and high hardness, and Fig 1 is shown the temperature and pressure distributions of some deep-well of oil and gas reservoirs at home and abroad [1]. At present, the rock-breaking technology of abrasion resistant formation in deep-well and ultra-deep-well would become an urgent technical research of China [2]. In drilling process of deep-well hard formation, the deeper the drilling depth, the more serious the bit wear, and the higher the drilling cost. Therefore, drilling speed and rock-breaking efficiency in abrasion resistant formation become the key technologies to restrict rapidly development of deep-well drilling [3]. In recent years, non-contact rock-breaking technology has developed rapidly and is becoming an important approach to achieve rapid drilling in deep-well.
Particle jet coupled impact rock-breaking technology is an efficient non-contact rock-breaking method, which mainly uses subsonic spherical particles to break rock, and high-velocity waterjet is used to act to remove debris and impact rock auxiliary. Then, hard rock is formed to well-bore with bit teeth cutting and grinding [4, 5]. Therefore, the rock-breaking mechanism is that fracture zones and damage areas of hard rock are impacted by particles, then the impact of waterjet can aggravate rock damage, and finally the rock released confining pressure is broken with action of bit rotary cutting. Compared with traditional drilling, the efficiency of particle waterjet impact drilling can be increased by about twice times, which is suitable for hard formation section of ultra-deep wells. However, the rock-breaking technology has complex ground equipment such as particle injection equipment and recovery equipment, and has certain challenges to the pressure and service life of pipelines. The technology has great development potential and gradually applied in fields of oil drilling, coal exploitation and underground engineering [6–8].
Recently, study on particle jet coupled impact rock-breaking technology was mainly carried by some research scholars with field application and laboratory test. PDTI, the particle impact drilling company in America, has conducted many laboratory simulation experiments and improved field tests, which proves the feasibility and advantage of drilling method [9]. Cui et al. studied the effect of jet, hydraulic and particle size on rock fragmentation through laboratory simulation test [10]. And particle classification device, and particle injection system were studied and the influence of different concentrations of particles on rock-breaking effect analyzed [11, 12]. The indoor experiment and field experiment of particle jet impact rock-breaking were carried out, which verified the feasibility of particle impact drilling technology [13, 14]. Kovalyov et al. used the method of high-speed camera to capture the movement state of metal particles in the flow channel, and proposed a structural scheme of metal particles recycling in the drill [15]. Besides, the mechanism of rock failure was studied, and the matching relationship between particle size, impact velocity, fluid velocity and rock-breaking volume is proposed [16, 17]. At present, these researches are mainly focused on fixed-point impact with single nozzle, and the researches on particle impact rock fracture in rotary drilling and cutting of bit are relatively lacking.
Based on the principle of particle jet coupled impact rock-breaking technology in rotary drilling, the numerical model of rock-breaking is established and the laboratory experimental device is developed respectively. The change of penetration depth and failure volume under different jet parameters are studied with verification of simulation and experiment. By compared with traditional drilling method, the advantages and engineering application significance of particle jet coupled impact rock-breaking technology are further clarified.
Working principle and rock-breaking mechanism
Working principle of rock-breaking technology
Particle jet coupled impact drilling technology was proposed based on projectile impact [9, 18], and its working principle is to add a certain proportion of steel particles into the drilling fluid, and then the two-phase fluid would accelerate through the special nozzle to form subsonic particle waterjet. The high-velocity particle waterjet would firstly impact and break rock to form the pressure-relief pit on rock surface, which would release compaction stress in deep-well and the crushing strength of damaged rock would reduce greatly [5, 16]. And then, the damaged rock would be formed to drilling hole under the action of rotary cutting and grinding by bit teeth. Meanwhile, the cutting debris and steel particles could be removed by drilling fluid. The rock-breaking process of particle jet coupled impact is shown in Fig 2.
Compared with conventional drilling technology, particle jet coupled impact rock-breaking technology mainly relies on high-frequency and high-velocity steel particles to break rock at the bottom of deep-well, which has the advantages of high rock-breaking efficiency, fast drilling speed and small deviation.
Modeling and simulation
Modeling and analysis of jet acceleration impact.
In particle jet coupled impact drilling technology, two phase flow would mainly be accelerated through nozzle. When waterjet carries steel particles from high-pressure pipeline into nozzle, the cross-sectional area of accelerating nozzle would change, so the particle jet velocity would also change [19, 20]. And the acceleration of nozzle can be divided into contraction acceleration and cylinder acceleration.
In the modeling process of particle jet acceleration, it is assumed that steel particles and water could be uniformly mixed. The coordinate system is established in the center of the nozzle inlet. The radial direction of nozzle is Y-axis, and the depth direction of nozzle is X-axis, as shown in Fig 3. Analyzed contraction section of accelerating nozzle, the acceleration model of particle and jet is obtained by the Bernoulli equation and second Newton’s law:
(1)
(2)
Where, vf0 is the jet velocity at nozzle inlet; vf is the velocity variable of waterjet; CD is the viscosity coefficient of jet [20]; d0 is the diameter of nozzle inlet; vp is particle velocity; Dp is particle diameter; ρp and ρf represent the density of particle and jet respectively.
Then, analyzed cylinder section of accelerating nozzle, the acceleration model of particle waterjet is:
(3)
(4)
Where, d1 is the diameter of nozzle outlet.
The flow state of the fluid is judged by the Reynolds coefficient. Because the two-phase flow of particle and water has high speed and great change in accelerating process, therefore, in the calculation of the flow field, the flow state of jet is turbulent, and its Reynolds number and turbulence intensity can be obtained [21]:
(5)
Where, Re is the Reynolds of fluid; I is the turbulence intensity. Generally speaking, when Reynolds number Re < 2300, the flow of fluid is laminar stage, and when Reynolds number Re > 40000, the flow of fluid is turbulent state. When the flow of fluid is transition state, the Reynolds number meets the requirement of Re = 2300 ~ 4000.
The RNG k − ε equation is used to describe the turbulent flow of particle jet when the computational fluid dynamics method is used to calculate the fluid flow:
(6)
(7)
Where, k is the turbulent kinetic energy; t is the time; ε is the dissipation rate of turbulence; Gk and Gb are the kinetic energy due to velocity gradient and buoyancy; xi and xj are the displacement component; YM is the compressibility of turbulent fluid, and its value is 0; G1ε, G2ε and G3ε are the turbulent constant; σε and σk are the Prandtl constant [22].
For the acceleration model of particle jet, calculation solution and simulation solution are obtained by MATLAB and FLUENT respectively, and the velocity obtained is compared and analyzed. In the process of simulation, the RNG k − ε turbulence equation is used for flow field, and the SIMPLE algorithm is used for discrete equation of computational fluid model. In calculation and simulation process, the parameters of particle and waterjet are shown in Table 1.
According to the established acceleration model, the velocity distribution and flow field of particle and waterjet is as shown in Fig 4. The acceleration process of waterjet is mainly concentrated in contraction section, and the velocity of waterjet in cylindrical section is basically unchanged, while the acceleration process of particles runs through the contraction and cylinder section. This is because the acceleration of particles lags behind jet, and the velocity of waterjet in cylindrical section is basically unchanged, while its velocity is obviously higher than that of particles, so particles will continue to accelerate with carried by high-speed waterjet. The jet core region would be formed outside area of nozzle, and the velocity of waterjet gradually decreases, while the velocity of particles would increase first and then decrease.
When steel particles and water jet flow through the long high-pressure pipeline to mix evenly, the velocity of particle and jet at nozzle inlet is basically the same. When the flow rate of power pump is different, the velocity at nozzle inlet will also be different. The effect of velocity change at nozzle inlet on the acceleration of nozzle is shown as Fig 5.
According to the calculation of established acceleration model, the velocity of particle and waterjet at nozzle outlet would increase linearly with that of at nozzle inlet. And for accelerating nozzle, jet velocity can be accelerated to about 13 times, and particle velocity can be accelerated to about 11 times. This model can provide support for the pump power selection of particle jet impact rock-breaking.
Rock damage model and mechanism analysis.
When impact velocity of particle jet reaches subsonic speed, fracture and internal damage would appear in rock. The rock-breaking mechanism under particle jet coupled impact is mainly due to powerful instantaneous impact stress on rock. When high-velocity metal particles impact on rock surface, the instantaneous impact stress would produce in a very small contact area and the stress value is very large. When particle size, impact velocity and other parameters reach the certain value, the instantaneous impact stress would exceed the compressive strength of hard rock, and tensile stress and shear stress will occur around the boundary of contact area. When tensile stress or shear stress exceeds the tensile or shear strength of rock respectively, many cracks or macroscopic failure will be formed inside rock [5, 23].
At present, the failure models applied to impact and collision field mainly include Holmquist-Johnson-Cook (HJC) model, Drucker-Prager (DP) model, Riedel-Hiermaier-Thoma (RHT) model, and Johnson-Holmquist (JH-2) model [16, 24, 25]. HJC model is mainly used for brittle elastic materials such as glass and ceramics; DP model is mainly used to simulate ideal elastic-plastic models such as cohesive soil; RHT model is suitable for concrete materials; JH-2 model is expressed as the functions of pressure, damage and strain, which can realize dynamical simulation and analysis of rock fragmentation. Therefore, JH-2 model is proposed to describe the rock-breaking phenomenon and damage evolution under particle waterjet impact.
The relationship between volume strain rate and static pressure can be expressed by the state equation. With the high-speed impact of particle waterjet, the high-pressure state equation is needed. Therefore, the cubic-state equation is:
(8)
Where, Pr is static pressure; K1 is volume model; K2 and K3 are constant; ψ is strain rate, ψ = ρ/ρr − 1; ρr is current density; ρ0 is initial density.
Introducing strain rate and damage factor to characterize the strength model of material [26], its normalized equivalent stress model can be expressed as:
(9)
Where,
is equivalent stress of undamaged material, and
; σHel is effective stress of elastic limit;
is equivalent stress at completely broken stage; D is damage factor.
JH-2 model is adopted for rock material in simulation process, which can well simulate the broken and damage accumulation of rock under coupled impact of particle waterjet [27, 28]. The cumulative expression of JH-2 model is as follows:
(10)
Where, Δεp is effective plastic strain in an integral period;
is elastic strain of equivalent fracture; D1 and D2 is damage constant.
To determine the parameters of rock, the shear modulus G and bulk modulus K1 are firstly determined through the tensile-compressive test and these basic physical parameters (such as, density ρr, Poisson’s ratio μ and elastic modulus E) [5, 29]:
(11)
(12)
Meanwhile, for the effective stress of elastic limit σHel:
(13)
Where, Fc is compressive strength, and it has been measured by rock compression test [16, 30].
The JH-2 model is used to simulate rock failure effect, and it is also coupled with the fracture softening model to simulate plastic compression and shear failure effects, and also crack propagation inside of rock target [27, 31]. To sum up, the model parameters in the simulation process of rock damage and failure under particle jet impact are summarized in Table 2.
Based on the above modeling method, the simulation model and rock-breaking effect under waterjet impact and single particle impact are established and simulated dynamically, as shown in Fig 6. For waterjet impact, only a small amount of fracture appears on rock surface at the edge of jet impact area, while the particle impact not only causes plastic damage at the impact point, but also causes some cracks inside of rock. Therefore, according to simulation analysis, the rock-breaking effect is mainly impacted by particles, and waterjet can aggravate damage with the auxiliary role in rock-breaking process.
Under multi-particles and jet impact, the dynamic simulation of rock-breaking is carried out, damage evolution and broken effect of rock under particle jet coupled impact is simulated. The failure effect and damage evolution status under multiple particles and waterjet impact on the same place (impact velocity is 200 m/s, particle size is 1 mm) is shown in Fig 7.
According to the figure of rock failure effect, rock-breaking depth increases with the impact times, but is not only simply superposition. The main reason is that it will be formed the small damage area under the first impact, and also produced pits and many dominant and hidden cracks. When the particle impact rock again, it is easier to realize the larger fracture area and be formed the deeper damage. Besides, the impact of jet can also remove debris and cause crack propagation. Under such cyclic impact of particles and waterjet, rock-breaking depth will be accumulated and intensified. Meanwhile, from the damage evolution, with the coupled impact of particles and waterjet, longitudinal damage expansion would be appeared firstly and accompanied by miniature broken pit. As time goes on, the broken pit and longitudinal damage of rock are increasing with increase of time. The broken pit section present shape of “cylindrical” and the damage section present shape of “Radial-shaped”.
Based on the above dynamical simulation model, the effect law of particle jet impact rock-breaking depth under different impact velocity (jet velocity within 100m/s~220m/s) is shown in Fig 8.
With increase of jet impact velocity, the rock-breaking velocity would also increase, and presents the trend of slowly growth at first and then approximately linear growth. The main reason is that when particle diameter is fixed, the greater the jet impact velocity, the larger the particle velocity with acceleration of waterjet, and the greater the rock-breaking kinetic energy under particle jet impact. Because jet velocity is mainly determined by the pressure and flow of power pump, the higher the jet impact velocity, the higher the requirement of surface equipment. Therefore, on the premise of ensuring the safety of surface equipment, the lager impact velocity should be adopted as far as possible to improve rock-breaking efficiency and drilling speed.
According to the analysis of acceleration model and impact rock breaking model of particle waterjet, it can be seen that, in the rock-breaking process under particle jet coupled impact, the impact times per minute of steel particles can reach more than four million times, and impact velocity of particle is more than 150 m/s (jet velocity is more than 160m/s). Under such high-frequency and high-velocity impact, rock-breaking speed would be multiplied.
Experiment results and discussion
Overall scheme and key technology
According to the working principle of particle jet coupled impact drilling technology in rotary drilling, the overall design scheme of laboratory experimental device is put forward, as shown in Fig 9. Laboratory experimental device of particle jet coupled impact rock-breaking mainly includes power system, particle mixing system, simulated top-drive system, simulated bottom-well system, PID (Particle Impact Drilling) bit, water circulation system, high-pressure pipeline system and control system. Among them, the key technologies include particle mixing system, PID bit, simulated top-drive system, simulation bottom-well system.
The power system is mainly composed of high-pressure plunger pump (GPB-90F) and control cabinet, which could ensure hydrodynamic force supply for rock-breaking experiment. It adopts step-down starting mode and is equipped with remote control device to realize remote control. The water circulation system can not only realize the recycling of drilling fluid, but also realize the separation of metal particles and cutting debris, so as to save resources. The high-pressure pipeline system and control system could realize the sealed connection and precise control of independent key devices. PLC and its supporting modules are used to realize the monitoring of motor speed, pressure signal and position signal. The diagram of control system is shown in Fig 10.
Device development and experimental sample
According to working principle and key technologies, a set of particle jet coupled impact rock-breaking device in rotary drilling was self-developed, as shown in Fig 11. The rock-breaking experimental materials mainly include steel particles, hard granite and clear water. Spherical particles are made of carbon steel [20]; clean water is instead of drilling fluid, and hard granite (Pingyi quarry, Shandong Province) is used for rock-breaking sample. The experimental parameters are shown in Table 3.
The merit of self-developed experiment equipment can be summarized as: (1) The simulated top drive is designed, which can realize the drilling pressure up to 0~70KN in rotary cutting state of bit; (2) It can realize the rock fracture under impact of particle waterjet with jet velocity of 0~280m/s, while the bit drills concurrently at a speed of 0~100r/min in rotary state. (3) It can realize the comprehensive rock-breaking experiments under impact of different objects, such as waterjet, particle and abrasive. (4) It can provide hydrodynamic power of 10.8m3/h and 32Mpa, and can realize rock-breaking effect under different impact velocity, particle size, angle and particle ratio.
With coupled impact of particle waterjet, rock sample is broken for irregular hole and ring, and the rock-broken effect is shown in Fig 12. The measurement method of rock failure volume and penetration depth is “equivalent water injection method” and “laser ranging method”. The “equivalent water injection method” is to immerse the rock in water to make it in state of water saturation, and then inject water into the broken hole, and the water-injected volume is crush volume of rock. The “laser ranging method” refers to use laser as the light source for ranging. In process of measurement, repeated measurements are made to take the average value to reduce manual error.
Result analysis and discussion
Based on the established numerical model and rock-breaking lab experiment results, the comparison and verification of penetration depth and failure volume under impact of particle waterjet are conducted to analyze the influence of jet parameters on rock-breaking effect and the similarities and differences between particle jet impact drilling and traditional drilling.
Comparative analysis with conventional drilling.
In deep-well hard formation drilling process, the constant-speed drilling technology is difficult to achieve in engineering, while the constant-pressure drilling technology is easier to achieve and operate. As long as the cutting speed of bit teeth is less than that of particle waterjet, particle jet coupled impact drilling technology can be satisfied the drilling process. Therefore, the comparative experiment of particle jet coupled impact and drilling bit cutting is carried out. During experiment, the mode of particle waterjet combined bit is adopted, while for conventional drilling, only bit is used to break rock. The experimental results with different drilling pressure are shown in Fig 13.
According to rock-breaking samples with particle waterjet impact and drilling bit cutting, the impact of particle waterjet mainly forms annular pressure-relief groove, and the rotary cutting of drilling bit mainly forms borehole. The drilling speed curve shows that the difference of drilling speed between conventional drilling and particle jet coupled impact drilling at low drilling pressure is not obvious; when drilling pressure continues to rise, the difference would be gradually obvious, and when pressure is 35KN, the difference of drilling speed is more than one time. The reasons is that: when drilling pressure is low, the pressure can’t reach rock failure strength, so the difference of drilling speed is not significant; with increasing of drilling pressure, a ring groove is broken on the bottom rock surface in advance by particle waterjet, the compaction effect is eliminated and rock failure strength is reduced, so drilling speed could be significantly increased. Therefore, the advantages of particle waterjet impact drilling technology can be highlighted to a greater extent when it is used to break the hard strata in deep-wells.
In addition, due to the complexity of rock-breaking, these parameters can also be adjusted by real-time monitoring of drilling pressure and the footage rate. When the footage speed is fast and the drilling pressure is small, particle ratio and jet velocity can be reduced properly; when particle ratio and jet velocity cannot be increased significantly, the drilling pressure can be increased properly to obtain the fast footage speed.
Effect of impact angle on rock-breaking.
The impact angle refers to the angle between the axis of water jet and the axis of bit. The rock breaking effect is obviously different under different impact angles. Based on the particle jet impact rock breaking experiment, the rock breaking effect is analyzed when the impact angle is 0°, 8° and 20°, and penetration depth under different impact angles was studied with numerical simulation. The experiment and simulation results with different angles are shown in Fig 14 (experiment time is 50s, particle size is 1.0mm, and jet velocity is 200m/s).
According to the results analysis, with increase of impact angle, penetration depth and failure volume would increase first and then decrease. And the maximum penetration depth is about 3~4 times of the minimum depth. Quantitative analysis shows, there is a critical value of impact angle (0°~10°), which can not only reach the maximum value of depth, but also achieve the purpose of removing rock debris. Because there would be collision and interference when impact angle is 0°, and also there would be more energy loss because the angle is too large. In process of engineering drilling, the impact angle and number of nozzles should be reasonably arranged according to experimental results, and it is suggested to use the combination layout of a nozzle with 8° and three or four nozzles with 20° for rapidly rock-breaking.
Because rock-breaking experiment volume contains the crushing effect of bit, the simulated volume is not verified. The penetration depth in simulation state is basically consistent with that in experiment state, which prove the correctness and applicability of simulation model.
Effect of jet velocity on rock-breaking.
The jet velocity determines impact kinetic energy and acceleration ability, so jet velocity plays an important role in rock-breaking process. In order to analyze the effect of jet velocity on failure volume and penetration depth, the rock-breaking experiment under particle waterjet coupled impact is carried out, and compared with dynamic simulation. The experimental and simulation results with different velocities are shown in Fig 15 (experiment time is 10s, impact angle is 8°, and particle size is 1.0mm).
According to the analysis of experimental results, when jet velocity is low, the penetration depth and failure volume are small. And when jet velocity exceeds 180m/s, failure volume and penetration depth would increase rapidly. Therefore, the higher the jet velocity, the greater the penetration depth and failure volume. Comparing the simulation results with experiment results, the change trend of penetration depth and failure volume is basically consistent in qualitative analysis, and the average error is within 5% in quantitative analysis. The research results prove the correctness and applicability of JH-2 model in particle impact rock-breaking simulation.
Conclusion
In this paper, the rock-breaking performance of particle jet coupled impact drilling technology is analyzed by studying penetration depth and failure volume with comparison of lab experiment and numerical simulation, and the main researches are as follows:
- The working principle of particle jet impact rock-breaking in rotary drilling was introduced, and the acceleration mechanism of particle waterjet is studied, which shows that waterjet velocity can be accelerated to about 13 times, and particle velocity can be accelerated to about 11 times. And damage evolution and broken effect at such high-velocity impact is simulated, which reveals that damage evolution under particle jet impact presents radiating expansion, and rock-breaking effect will be better when particle velocity exceeds 150m/s.
- Particle jet coupled impact experimental equipment in rotary drilling is self-developed, and the penetration depth and failure volume experiments were comparative verified with numerical simulation. Result showed that combination nozzles layout of impact angle with 8°and 20° are suggested to adopt to achieve rock-drilled rapidly, which also demonstrated the correctness and applicability of simulation model.
- Comparative analysis with conventional drilling, drilling speed with particle jet impact is twice that of conventional drilling, which demonstrates the advantages and engineering application significance of particle jet coupled impact rock-breaking technology in rotary drilling.
Supporting information
S1 Table. The parameters of particle and waterjet.
https://doi.org/10.1371/journal.pone.0250588.s002
(DOC)
S2 Table. The model parameters of rock damage simulation.
https://doi.org/10.1371/journal.pone.0250588.s003
(DOC)
References
- 1. Wang H, Ge Y, Shi L. Technologies in deep and ultra-deep well drilling: present status, challenges and future trend in the 13th Five-Year Plan period (2016–2020). Natural gas industry 2017; 037(004):1–8.
- 2. Su Y, Lu B, Liu Y. Current situation of drilling and completion technology of deep well and ultra deep well on land in china and relevant suggestions. Oil Drilling & Production Technology 2020;11:1–24.
- 3. Yao J, Huang Z, Liu W, Zhang Y, Zeng Q, Yan X. Key mechanical problems in the development of deep oil and gas reservoirs. Scientia Sinica (Physica, Mechanica & Astronomica) 2018; 48(04):5–31.
- 4. Zhu X, Tang L, Tong H. Effects of high-frequency torsional impacts on rock drilling. Rock Mechanics and Rock Engineering 2014; 47(4):1345–1354.
- 5. Ren F, Fang T, Cheng X. Study on rock damage and failure depth under particle water-jet coupling impact. International Journal of Impact Engineering 2020;139:103504.
- 6. Kuang YC, Zhu ZP, Jiang HJ, Wu KS. The experimental study and numerical simulation of single-particle impacting rock. Acta Petrolei Sinica 2012; 17(6):779–788.
- 7. Ma Y, Cai X, Zhao P. The support of petroleum engineering technologies in trends in oil and gas exploration and development: Case study on oil and gas exploration in sinopec. Petroleum drilling technology 2016; 44(2):1–9.
- 8. He J, Liang Y, Li L, Luo Y. Theoretical analysis and design of hydro-hammer with a jet actuator: An engineering application to improve the penetration rate of directional well drilling in hard rock formations. PLoS ONE 2018; 13(5): e0196234. pmid:29768421
- 9. Hardisty Thomas. Particle Drilling Pulverizes Hard Rocks. The American Oil & Gas Reporter 2007; 50(7):86–89.
- 10. Cui M, Zhai Y, Ji G. Experimental study of rock breaking effect of steel particles. Journal of Hydrodynamics 2011; 23(02):241–246.
- 11. Xu Y, Mao B, Zhao J. Research on principle and structure design of particle classification device for particle impact drilling. Drilling and production technology 2012; 35(03):18–21.
- 12. Xu Y, Liao K, Jin J, Liu Q, Sun Y. Design of dual ram particle impact drilling injection system. Petroleum machinery 2013; 41(3): 7–10.
- 13. Zhao J, Han L, Xu Y, Jin J, Liu F. Theory and field test of the particle impact drilling technology. Natural gas industry 2014; 034 (008):102–107.
- 14. Zhao J, Zhang G, Xu Y, Wang R, Zhou W, Han L. Mechanism and effect of jet parameters on particle waterjet rock breaking. Powder Technology 2017; 313: 231–244.
- 15. Kovalyov A V, Ryabchikov S Y, Isaev Y D, Aliev F R, Gorbenko M V, Baranova A V. Pellet impact drilling operational parameters: experimental research. IOP Conference Series: Earth and Environmental Science 2015; 24:012015.
- 16. Ren F, Fang T, Cheng X. Theoretical modeling and experimental study of rock-breaking depth in particle jet impact drilling process. Journal of Petroleum Science and Engineering 2019; 183:106419.
- 17. Ren F, Fang T, Cheng X, Chang Y. Rock-breaking stress analysis and rock-breaking region under particle jet impact. Acta petroleuca Sinica 2018; 39(9):1070–1080.
- 18. Tibbitts G A, Galloway G G. Particle drilling alters standard rock-cutting approach. World Oil, 2008; 229(6): 37–44.
- 19. Manzar MA, Shah SN. Particle Distribution and Erosion During Flow of Newtonian and Non-Newtonian Slurries in Straight and Coiled Pipes. Engineering Applications of Computational Fluid Mechanics 2009; 3:296–320.
- 20. Ren F S, Fang T C, Cheng X Z. Parameter optimization and experimental study of particle jet impact rock breaking nozzle. China Petroleum Machinery 2018; 46 (02):5–11.
- 21. Ge M, Fang L, Tian D. Influence of Reynolds Number on Multi-Objective Aerodynamic Design of a Wind Turbine Blade. PLoS ONE 2015;10(11): e0141848. pmid:26528815
- 22. Hayat T, Bibi S, Alsaadi F, Rafiq M. Peristaltic Transport of Prandtl-Eyring Liquid in a Convectively Heated Curved Channel. PLoS ONE 2016;11(6): e0156995. pmid:27304458
- 23. Zhang H, Wang D, Yu C, Wei J, Liu S, Fu J. Microcrack evolution and permeability enhancement due to thermal shocks in coal. PLoS ONE 2020;15(5): e0232182. pmid:32437359
- 24. Li S, Li X, Guo Y. Numerical simulation of projectile impacting target at high speed based on AUTODYN. Journal of System Simulation 2013;25(04):621–625.
- 25. Wang H, Shou L, Zhang J, Tian Z, Ou Z, Zhou G. Experimental and numerical analysis of failure effect of granite target impacted by projectile. Chinese Journal of Rock Mechanics and Engineering 2014;33(02):366–375.
- 26. Wang F, Wang R, Zhou W, Chen G. Numerical simulation and experimental verification of the rock damage field under particle water jet impacting. International Journal of Impact Engineering 2017; 102:169–179.
- 27. Jiang H, Liu Z, Gao K. Numerical simulation on rock fragmentation by discontinuous water jet using coupled SPH/FEA method. Powder Technology 2017; 312:248–259.
- 28. Papini M, Dhar S. Experimental verification of a model of erosion due to the impact of rigid single angular particles on fully plastic targets, International Journal of Mechanical Sciences 2006; 48(5):469–482.
- 29.
Richard A C, Colin J H, Iain R. Development and application of a Rankine plasticity model for improved prediction of tensile cracking in ceramic and concrete materials under impact, 14th DYMAT Technical Meeting, Sevilla, Spain, 2002.
- 30. Ren F, Fang T, Cheng X. Study on Rock-Breaking Depth and Damage Area under Particle Jet Impact, Shock and Vibration 2020; 2020:4140165.
- 31. Li X, Qi C. A micro-macro dynamic compressive-shear fracture model under static confining pressure in brittle rocks. International Journal of Impact Engineering 2018; 122:109–118.