Polycrystalline Diamond Compact Drill Research Articles

Computational Fluid Dynamics Study on Bottom-Hole Multiphase Flow Fields Formed by Polycrystalline Diamond Compact Drill Bits in Foam Drilling

High-temperature geothermal wells frequently employ foam drilling fluids and Polycrystalline Diamond Compact (PDC) drill bits. Understanding the bottom-hole flow field of PDC drill bits in foam drilling is essential for accurately analyzing their hydraulic structure design. Based on computational fluid dynamics (CFD) and multiphase flow theory, this paper establishes a numerical simulation technique for gas-liquid-solid multiphase flow in foam drilling with PDC drill bits, combined with a qualitative and quantitative hydraulic structure evaluation method. This method is applied to simulate the bottom-hole flow field of a six-blade PDC drill bit. The results show that the flow velocity of the air phase in foam drilling fluid is generally higher than that of the water phase. Some blades’ cutting teeth exhibit poor cleaning and cooling effects, with individual cutting teeth showing signs of erosion damage and cuttings cross-flow between channels. To address these issues, optimizing the nozzle spray angle and channel design is necessary to improve hydraulic energy distribution, enhance drilling efficiency, and extend drill bit life. This study provides new ideas and methods for developing geothermal drilling technology in the numerical simulation of a gas-liquid-solid three-phase flow field. Additionally, the combined qualitative and quantitative evaluation method offers new insights and approaches for research and practice in drilling engineering.

Multi-objective optimization of Stinger PDC cutter breaking rock parameters under intrusion-cutting action using Taguchi-based gray relational analysis.

To enhance the efficiency of the Stinger Polycrystalline Diamond Compact (PDC) cutter in breaking hard rocks, this study focuses on optimizing the cutter intrusion-cutting rock breaking parameters. A numerical calculation model for the rotational breaking of granite by a Stinger PDC cutter was established. A comprehensive statistical examination was performed to assess the influence of various factors on intrusion ability (IA), tangential force (TF), and mechanical specific energy (MSE). The Taguchi method was used to determine the optimal settings for each factor, while analysis of variance was employed to assess the significance and relative impact of these factors on the target outcomes. In addition, the multi-objective function was optimized using the gray relational analysis method. The primary process parameters obtained for the various performance characteristics are the cone top angle (α), the cone top radius (r), the cutter diameter (d), the cutter back inclination angle (β), and weight on bit (P). The impact ratios of these parameters are 6.20%, 7.66%, 3.93%, 17.20%, and 65.02%, respectively. The optimal geometrical parameters are α = 60°, r = 2mm, and d = 15mm, while the optimal working parameters are β = 30° and P = 800 N. In the optimal case, IA and MSE were reduced by 55.335% and 15.809%, respectively, compared to the initial case. Despite a 15.706% increase in TF, the overall GRG increased for all three evaluation criteria, with an overall increase in efficiency of 18.229%. The results of this paper can provide guidance for the design of Stinger cutter PDC drill bits.

Numerical Investigations for Rock-Breaking Process and Cutter Layout Optimization of a PDC Drill Bit with Dual-Cutter

PDC (polycrystalline diamond compact) drill bits are widely employed for rock-breaking in many industries like underground engineering and building constructions. The cutter layout would directly affect the overall performance of the drill bits. Field applications show that the staggered cutter layout strategy of dual-cutter can increase the drilling efficiency of the PDC bit. In order to explore the rock breaking mechanism of this type of drill bit, a numerical model of a dual-cutter and rock breaking with damage evolution based on a hybrid finite and cohesive element method (FCEM) has been established in this work. The model is verified through Brazilian disk tests. The rock breaking processes of this type of bit have been analyzed, including crack initiation, propagation, and the formation of rock debris. Moreover, the effects of horizontal and vertical offset of the back cutter on the MSE (mechanical special energy) have been investigated. Results demonstrate that the dual-cutter can prominently reduce the MSE compared to a single-cutter. The vertical offset of the back cutter has a minor effect on the MSE, while the horizontal offset is of great significance on the MSE. On this basis, the relationships between the MSE and both the vertical and horizontal offset coefficients have been built based on the response surface methodology (RSM). Finally, an optimized layout solution, with optimal vertical and horizontal offset coefficients of 0.641 and 0.497, is determined via the Gray Wolf algorithm.

A novel experimental setup for axial-torsional coupled vibration impact-assisted PDC drill bit drilling.

The geological conditions of hot dry rock (HDR) reservoirs are complex. The geothermal mining of HDR faces major challenges in the drilling and construction of wells, fracturing to create storage, and flowing to extract heat. Vibration impacts help improve the rock-breaking efficiency, where the axial-torsional coupled vibration impact technology can increase the bit penetration depth and reduce the stick-slip effect. To study the feasibility and efficiency of the axial-torsional-coupled vibration impact-assisted Polycrystalline Diamond Compact (PDC) bit to break high-temperature and high-pressure rocks, a new experimental setup was designed. The system includes a drilling fluid circulation system, an axial-torsional coupled impact drilling system, a formation simulation system, and a data acquisition and control system. This setup can produce a rock-breaking torque of 2000 N·m, a drilling speed of 200rpm, a weight on bit of 100kN, an axial vibration frequency of 100Hz, and a torsional vibration frequency of 50Hz. It can simulate the formation pressure of 70 MPa and the rock temperature of 400 °C. A series of rock-breaking drilling experiments were successfully conducted using this setup. The results show that the axial-torsional coupled vibration-impact assisted PDC bit has a good performance in breaking high-temperature and hard rocks, which can accelerate the application of this new technology in deep formation drilling.

Application of Three-Dimensional Printing Technology to the Manufacture of Petroleum Drill Bits

Drill bits are the main rock-breaking tools in the petroleum and gas industry. Their performance directly affects the quality, efficiency, and cost of drilling. Drill bit manufacturing mainly employs traditional mold forming processes such as milling molding and press molding, which have low production efficiency and long processing cycles and are not conducive to rapid responses to field requirements. Inadequate production accuracy makes it difficult to produce drill bits with complex structures. Three-dimensional (3D) printing technology has fast molding speeds and high molding accuracy. In this paper, 3D printing was applied for the first time to the manufacture of molds for carcass polycrystalline diamond compact (PDC) drill bits and PDC–cone hybrid drill bits. In comparison with forging and milling molding, 3D printing improved production efficiency. The manufactured molds had higher machining accuracy. The ability of 3D printing to make molds with complex surfaces enables the development of drill bits with complex structures. A field experiment was conducted on a PDC drill bit produced by 3D printing, which had a higher rate of penetration and was more efficient in breaking rocks than bits manufactured by traditional processes. The ROP of the drill bit increased by 20.1–25.8%, and the drilling depth increased by 7.7–29.5%. It is therefore feasible to apply 3D printing to the manufacture of petroleum drill bits.

Numerical Simulation and Field Test of a PDC Bit with Mixed Cutter Arrangement to Break Non-Homogeneous Granite

As the depth of petroleum drilling increases, the strata environment becomes more complex. The efficiency and lifespan of Polycrystalline Diamond Compact (PDC) drill bits fail to meet current drilling demands. However, the structure and arrangement of PDC cutters are valuable determinants of drilling efficiency, although related research still has gaps and deficiencies. This study focuses on PDC cutters in axe, triangular prism, and circular forms. It establishes an inhomogeneous granite model based on the actual measurements of granite and verifies the accuracy of this model through uniaxial compression simulation. Finite element models of three types of cutters in various combination schemes are constructed to examine rock-breaking effects, with the best scheme optimized using Box-Behnken response surface methodology. The rock-breaking process of the optimal PDC drill bit layout has been compared to that of a single cutter bit. Field drilling has demonstrated the effectiveness of a mixed cutter arrangement. The results show that the inhomogeneous granite model can be trusted. The optimal arrangement involves axe cutters in the front row and an alternate arrangement of triangular prism cutters and axe cutters in the back row. The optimal lateral and longitudinal distances for the triangular cutters from the front row of axe cutters are 10 mm and 7 mm, respectively, while those for the back row of axe cutters from the front row are 10.06 mm and 7 mm, respectively. The ROP standard deviation in the drilling process of mixed cutter bits decreases by 53.06% and 43.08% compared to axe and triangular prism cutter bits, respectively. The drilling efficiency increases by 16.8% and 16.6%, respectively, demonstrating higher efficiency and stability. Field drilling results indicate that a mixed cutter bit increases efficiency by 23.5% compared to a bit with only triangular prism cutters. This study posits that research on the combination schemes and parameters of PDC cutters can significantly enhance drilling efficiency, thereby reducing the drilling cycle and costs.

CFD modeling of the flow behavior around a PDC drill bit: effects of nano-enhanced drilling fluids on cutting transport and cooling efficiency

ABSTRACT In the present study, hydraulic and thermal performances of nano-enhanced drilling muds have been studied across the complex geometry of a rotating polycrystalline diamond compact (PDC) drill bit using computational fluid dynamics techniques. Toward this goal, a robust converging procedure is applied to generate an advanced tetrahedral/prism grid structure using special techniques. We also utilize a combination of the realizable k-ԑ turbulence model with enhanced wall treatment and Eulerian-Lagrangian discrete phase model (DPM) to investigate the flow field and particles tracking across the bit. The results reveal that the rheological properties enhancement obtained by adding even a small quantity of nano-fluids leads to a remarkable increase in the cutting transport efficiency. According to our results, CuO and ZnO nano-enhanced muds show up to 127% and a 68% rise over the cutting transport ratio of the base fluid at the bit rotational speed of 30 rpm. Besides, the predicted temperature on tip of the bit cutters indicates that increasing the thermal conductivity of nano-enhanced muds can lead to effective cooling only in conjunction with improving rheological characteristics. CuO NWBMs show up to a 16.7% reduction in the temperature of the front surface of bit cutters over the base fluid.

An experimental study on steering response of PDC drill bits

This paper presents the findings from an experimental study conducted to understand the steering response of PDC (polycrystalline diamond compact) bits. Various tests are carried out by drilling large limestone blocks with an actual size PDC bit and a highly sophisticated drilling machine. High resolution data acquired during the drilling process and 3D laser scans of the drilled holes are analyzed to assess the effect of drilling parameters and bit dynamics on steering response. The hole deviations measured during experiments are compared to a quasi-static FE (finite element) model, which utilizes a simplified bit-rock interaction formulated via a single bit steerability parameter. It is shown that, although this approach has its merits due to its computational efficiency, it can produce inaccurate prediction when the bit dynamics change. The experiments showed that the WOB (weight on bit) is a crucial parameter in this regard, dictating the stability of the drilling process, which in return affects the influence of the remaining parameters such as RPM (revolutions per minute) and side force.

Dynamic trip point categorisation using manufacturing process for polycrystalline diamond compact bits as case study

Disruptions in the manufacturing process cast substantial impacts on the consumer's centric values, cost, and overall efficiency. The ripple effect of these disruptions is observed in the whole assembly line. The proper analysis and mitigation of disruptions is the key to the proficiency of the plant and resource utilisation. The research focuses on the quantitative analysis of the impact of disruptions of the manufacturing process, which is performed by analysing the disruptive workstation dynamically. The disruptive workstations have a significant impact on succeeding and preceding workstations, which have been analysed dynamically, and accordingly, the pre-set alarm trip points are elevated. The results show that lowering the number of starts and stops decreases the number of rejections of valuable process batches that finally improve efficiency. Finally, the developed model is implemented on a polycrystalline diamond compact drill bit manufacturing plant. The results are compared with the research work of other researchers, showing a 60% reduction in the number of start/stop events, 60% reduction in downtime, while a 75% reduction in the number of rejections is noted.

Influence of Heavy Weight Drill Pipe Material and Drill Bit Manufacturing Errors on Stress State of Steel Blades

Drilling volumes should be increased in order to increase hydrocarbon production, but this is impossible without the usage of high-quality drilling tools made of modern structural materials. The study has to analyze the design, technological and operational methods to increase the performance of drilling tools made of various materials and has highlighted prospects of technological method applications. The scientific novelty of the study consists in the development of a new analytical model of PDC drill bit–well interaction. The developed model takes into account the drill bit manufacturing errors in the form of bit body–nipple axes misalignment on the drill bit strength. This result makes it possible to determine the permissible manufacturing errors to provide safe operation of the drill bit. It is established that there is an additional transverse force that presses the drill bit to the well wall in the rock due to manufacturing errors. It is determined that the magnitude of this clamping force can be significant. The material effect has been analyzed on additional clamping force. It is established that geometric imperfection of the drill bit causes the minimal effect for the elastic system of the pipe string, which includes a calibrator and is composed of drill pipes based on composite carbon fiber material, and the maximal effect—for steel drill pipes. Polycrystalline diamond compact (PDC) drill bit and well wall contact interaction during operation in non-standard mode is considered. Non-standard stresses are determined, and the strength of the blades is estimated for different values of drilling bit manufacturing error.

Anti-balling Mechanism on the Non-smooth Surface of Bionic Polycrystalline diamond compact Drill Bits

Polycrystalline diamond compact (PDC) bit balling is one of the major factors that limits the penetration rate of drilling and causes bit failure in soft stratum. In order to solve the PDC bit balling problem, in this research we designs typical bionic non-smooth surfaces and analyzes the anti-adhesion mechanisms. Next, the non-smoothness characterization is extended from a two-dimensional to three-dimensional in which the area ratio and the width ratio are used to characterize lateral and longitudinal non-smoothness. Then, a comparative experiment between typical non-smooth surfaces and the smooth surface condition is carried out. The results show that the scale-like non-smooth surface has the best anti-adhesion effect and that longitudinal non-smoothness has a greater influence on mud block adhesion than lateral non-smoothness. The research results also show that after applying the principle of anti-adhesion and resistance reduction for the non-smooth surface of soil animals to the design of the flow channel of a PDC drill bit, the novel bionic anti-balling PDC bit can effectively avoid the problem of bit balling.

Effects of spherical WC powders on the erosion behavior of WC-Ni hardfacing used for steel body drill bit

Improving the erosion resistance of polycrystalline diamond compact (PDC) bit can prolong its service life. The influence of spherical WC powders on the erosion behavior of WC-Ni hardfacing used for steel body drill bit has not been reported. In this work, Ni-based hardfacing coatings reinforced with various content of spherical cast tungsten carbide (CTCS) and angular cast tungsten carbide (CTC-A) particles are fabricated by oxy-acetylene welding process. The erosion behavior of WC-Ni hardfacing used for steel body PDC drill bit is experimentally studied. Results show that, the coating's microstructure, microhardness, fracture toughness and corrosion resistance varies under different CTC-S content, which leads to the differences in erosion mechanisms. The erosion resistance of hardfacing coatings decreases first and then increases with the decrease in CTC-S content. Sample 1 with 60% CTC-S and 0% CTC-A has the best erosion resistance, while sample 3 with 30% CTC-S and 30% CTC-A has the worst erosion resistance. As CTC-S content decreases, the erosion wear mechanism of hardfacing coating transforms from brittle mechanism to ductile mechanism. At a high CTC-S content, hardfacing coatings present brittle erosion wear mechanisms, such as micro-fracture and precipitate removal. At a low CTC-S content, hardfacing coatings show ductile erosion wear mechanisms, such as plastic deformation and crater formation.

Experimental evaluation of rock disintegration detection in drilling by a new acoustic sensor method

A simple and reliable method for monitoring the rock properties in drilling is recognized as a global challenge, especially for cluster and infill development well drilling in oil and gas production. To improve the existing limitations in the detection of formation lithology in drilling systems, an acoustic sensor approach for rock disintegration in the drilling using a polycrystalline diamond compact (PDC) drill bit is developed and evaluated. In this paper, we report the application of a special acoustic sensor device to qualitatively survey rock disintegration by rotary drilling. In this work, an acoustic focusing component is designed to assist a condenser microphone in detecting signals emerging in the process of drilling as an integrating information resource. A time-frequency with zoom fast-Fourier-transform analysis method is presented to recognize the acoustic signal features in breaking different rocks. Additionally, principal component analysis and Support Vector Machine method are used to check the qualitative analysis results for the monitored rock information. An experimental investigation considered four types of rock broken by a PDC drill bit with drilling weights ranging from 5 to 12.5 kN and drilling rates ranging from 64 to 128 r/min. To verify the reliability and accuracy of our acoustic rock detection method, two sensors installed in the orthogonal direction are examined. Furthermore, the coherent analysis was used to reveal the correlation of the output auto-correlation spectrum for each measurement. The results show that there is a good average percentage of lithology calculated by the time-frequency analysis results between the acoustic signal features and different types of rock. Accordingly, the acoustic sensor approach can help enhance the detection of rock properties in drilling systems, laying the foundation for quantitative lithology identification in more complex drilling.

Vibration failure and anti-vibration analysis of an annular-grooved PDC bit

To extend the service life of drill bits through reducing various drilling vibrations, this paper presents a fundamental analysis of the root cause of failure for polycrystalline diamond compact (PDC) bits during the drill-based process of vortex generation. In this work we develop a new type of PDC drill bit, namely the annular-grooved PDC bit, which can form one or more annular convex rock ridges at the bottom of the hole, having a raised ring that can limit transverse vibration. Our experimental results confirm that the accelerations of the annular-grooved PDC bit in axial, tangential, and radial directions are smaller than that of a conventional PDC bit. More specifically, acceleration declines by 33.5%, 21.6%, and 25.9% in tangential, axial, and radial direction, respectively. Our experimental investigation also shows that, as the weight on bit and the rotation speed increase, bit vibration intensifies, and the impact load on bit increases which can worsen bit stability. However, as the height and the width of the rock ridge increase, the drilling vibrations in three directions can decline. Therefore, the developed annular-grooved PDC bit can reduce bit vibration and improve bit’s drilling stability.

Cuttability and drillability studies towards predicting performance of mechanical miners excavating in hyperbaric conditions of deep seafloor mining

The research program outlined in this paper starts with the assumption that if there is a significant relationship between drilling and cutting specific energies in atmospheric conditions, there would also be a significant relationship between these variables in hyperbaric conditions. Five “model rock samples” having uniaxial compressive strength varying from 9 to 160 MPa were subjected to full-scale laboratory drilling tests with polycrystalline diamond compact (PDC) drill bits and a core drill, as well as laboratory full- and small-scale linear cutting tests with a conical and chisel cutter in atmospheric conditions. As a result, significant correlations between drilling and cutting specific energies were found for atmospheric conditions of laboratory. PDC drill bits and core drill bit used in laboratory tests were also used in the subsea drilling operations under hyperbaric conditions in Bismarck Sea. The conical cutter used in the laboratory tests are intended to be used on mechanical miners for subsea metal production. Core samples taken from Bismarck undersea mineral deposits were also subjected to physical and mechanical property tests in the deck and separately in the laboratories of Istanbul Technical University; and small-scale linear cutting tests were also applied in the university. Significant correlations were also found between the results of small- and full-scale cutting test. It is concluded that the capabilities of in-situ measurements will permit to detect some physical and mechanical properties of undersea mineral deposits. These properties interpreted with laboratory drilling and cutting tests would serve a basis to predict performance of mechanical miners to be used in hyperbaric conditions.

Mathematical modelling of performance and wear prediction of PDC drill bits: Impact of bit profile, bit hydraulic, and rock strength

The estimation of Polycrystalline Diamond Compact (PDC) cutters wear has been an area of concern for the drilling industry for years now. The cutter's wear has been measured practically by pulling the bit out for evaluation at the surface. It is important to find the right time for tripping out as this helps to avoid the fishing job and reduces the operational cost significantly. The prediction of the drilling performance is based on the interaction of cutter and rock. Several authors focused on the cutter-rock interface but only a few researchers tried to model the wear of the PDC bit cutters. The aim of this research is to understand the relationships between the rate of penetration (ROP) and the drilling variables per each foot, and then determine the overall bit efficiency for the whole drilling operation. A new mathematical model is derived to predict the PDC bit performance by considering the factors that were already not taken into account. These factors include rock strength, bit design, and bit hydraulic. The model investigates the effect of these parameters to estimate the abrasive cutters wear on the inner and the outer bit cones by deriving modified equations to calculate the mechanical specific energy (MSE), torque, and depth of cut (DOC) as a function of effective blades (EB). The model is used to forecast the bit cutters wear conditions in four wells in the oil fields located in Libya, which were drilled with three different PDC's sizes. The model enables the results to be compared to the actual bit cutters wear measured for inner and outer cones. The results are found that are well in agreement with the actual field data obtained in bit records.

Research on the working mechanism of the PDC drill bit in compound drilling

A combined ground-driven and down-hole-driven motor significantly improves the penetration rate of polycrystalline 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.

Rock breaking mechanism in percussive drilling with the effect of high frequency torsional vibration

ABSTRACT High-frequency torsional vibration percussive drilling is considered a promising approach to improve drilling performance in deep hard formations, so studying its rock breaking mechanism and effect is the essential and basic issue. Compared with percussive-rotary drilling and high-pressure jet drilling, it can increase the service life of drilling tools and reduce drilling cost significantly. In this paper, based on elastic mechanics and principles of mechanical vibration, the cutting mechanism model of PDC (polycrystalline diamond compact) drill bit cutter and the amplitude–frequency characteristic model of steady-state vibration response of rock system are established, as well as the response characteristics of the rock system are also pointed out. Based on elastic–plastic mechanics and rock mechanics, Drucker–Prager criterion is adopted as the constitutive equation of rock, and plastic strain is used as the criterion of rock failure. Moreover, the model of rock damage failure is also established. The effect of exciting frequency on ROP (rate of penetration) has been studied by carrying out rock breaking test using high-frequency torsional vibration percussive drilling of PDC drill bit along with analyzing and handling test data. The study results show that when torsional vibration percussive frequency is approximately equal to inherent frequency of the rock, rock resonates with cutter, the plastic strain and ROP reach maximum, and drilling efficiency is the highest. The research results can help to deepen the understanding of the percussive drilling with high-frequency torsion vibration and provide useful insight into the design, application, and optimization of this new type of downhole tools in drilling engineering.

Development of a Cutting Force Model for a Single PDC Cutter Based on the Rock Stress State

Polycrystalline diamond compact (PDC) bits are currently the most widely used bits in the petroleum industry. However, the rock-breaking mechanisms of PDC bits are not well understood, especially in deep hard-rock drilling. By modifying the Nishimatsu model, a single PDC cutter force model based on in situ stress is developed in this study. By coupling the mechanical properties of rock and the technological measures of rock breaking, the model can accurately solve the cutting force and assess the rock drillability when applied to a PDC bit. The analysis of research findings shows that the vertical stress initially has a greater impact on the cutting force despite a larger horizontal stress relative to the vertical stress. Moreover, the optimal cutting angle of a PDC cutter is between 15° and 20°. The applicable conditions of the model are obtained experimentally. The model can predict cutting forces in non-expansive rocks well with 2% error. Furthermore, the mechanical-specific energy under low confining pressure has been theoretically demonstrated to increase more quickly than that under high confining pressure. The proposed model can analyse the influence of effective horizontal and vertical stresses and rock strength on the cutting force, which can lead to a better understanding of the rock-breaking mechanisms of PDC drill bits. The results of this work can be used to study PDC bit performance and provide guidelines for the application and design of PDC bits for specific rocks.

Evaluation of rock abrasiveness class based on the wear mechanisms of PDC cutters

To accurately predict the wearing of a polycrystalline diamond compact (PDC) drill bit and the abrasiveness class of the rocks in the drilled stratum, macroscopic stress conditions during drilling with a PDC drill bit were obtained based on the fracture conditions of the rocks. Next, the microscopic contact characteristics of the contact surface between the stratum and the PDC drill bit were analyzed to obtain the distribution of the micro-bulge contact points of the friction pairs of the two objects within an area and to reveal changes in the contact surface temperature. Based on these results, a model was built to calculate the actual contact area between the stratum and the PDC drill bit during the sliding-induced temperature increase. The wear equation for the PDC drill bits was established by correcting the Archard equation since the major wear mechanisms of PDC drill bits are abrasive wear and adhesive wear. This wear equation was examined and validated through laboratory experiments, and then the rock-related attribute parameters were extracted and used as a basis for evaluation indicators and grading methods of rock abrasiveness.