Simulation of Rock-Breaking Ability of Polycrystalline Diamond Compact Cutter Based on Rock Mechanics Experiment After Heat Treatment

The rising energy consumption globally has spotlighted deep oil, gas extraction, and geothermal development as key areas of interest, prompting numerous countries to embark on related projects [1,2]. These initiatives, however, encounter significant challenges, notably the high formation rock temperatures where bottom hole temperatures in high-temperature wells can exceed 177 °C with the geothermal sector aiming for temperatures around 300 °C for enhanced commercial viability. At such elevated temperatures, rocks exhibit complex behaviors, including elastoplastic strengthening and thermal fracture, which can diminish the lifespan of drilling bits [3].

Regarding rock properties post-high-temperature exposure, since direct experimental research on original high-temperature rock is impractical, studies employ indoor heating for mechanical tests [4]. These have revealed that heating rocks to temperatures between 60 °C and 70 °C can induce thermal cracking and acoustic emission (AE) phenomena [5,6], with the heating rate influencing the AE count rate but not the threshold temperature for acoustic emission. Additionally, rock heterogeneity significantly affects its mechanical properties [7].

Drilling efficiency suffers due to reduced cutter lithology breaking capability in high-temperature conditions, significantly impacting drilling operations' efficiency and cost. Notably, drilling costs can constitute 60–70% of the total investment for wells reaching depths of 4–6 km [8,9], underscoring the importance of studying rock-breaking mechanisms to enhance drilling efficiency in deep high-temperature formations. Polycrystalline diamond compact (PDC) bits, renowned for their high rock-breaking efficiency and longevity, dominate the drilling landscape, accounting for over 90% of the total drill bit footage worldwide [10]. The interaction between drill teeth and rock primarily involves cutting and intrusive rock breaking, with the latter consisting of plastic and brittle crushing [11]. Studies have shown that plastic crushing is less efficient and can cause premature bit failure, thus drilling strategies often aim for a penetration depth that ensures brittle rock breaking. The complex composition of rocks and their varying strengths at high temperatures necessitate further research to align traditional rock drill ability tests with the actual conditions in deep wells, aiding in the selection of drill bits and optimization of drilling parameters [12,13]. Historical research on rock breaking since 1985 has focused on the stress distribution during cutting by teeth of various geometrical shapes [14,15]. Although Johnson's theory addresses the initial contact phase, it does not fully explain stress changes during rock breaking, prompting further investigation into the impact of cutter shape and rock mechanical properties on stress field characteristics after contact [16]. Innovations such as NOV's Fuse Tek composite bit and Smith's ONYX360 deg Rotary PDC composite bit in 2013 have targeted friction heat buildup on PDC cutters to extend their lifespan, yet the performance of PDC cutters can still be significantly improved [17,18]. Research on conical cutters has indicated the cone tip angle's substantial effect on wear resistance and rock-breaking efficiency, suggesting advantages over traditional PDC bit cutters when the cone tip angle is minimized [2,19].

Although the physical properties of rock exposed to high temperature and the mechanism of PDC rock breaking have been extensively studied, few studies have been conducted to evaluate the rock-breaking efficiency of PDC cutters at high temperature by integrating these aspects, and the discussion of brittle rock-breaking, which is essential for efficient drilling, has been neglected in previous studies. This paper, therefore, utilizes parameters from triaxial compression tests on heat-treated rocks, based on the critical penetration depth theory of brittle broken rock, exploring through numerical simulation the impact of thermal stress, PDC tooth front rake angles, formation temperature, confining pressure, and rotational speed on rock fracture by PDC cutters, cooled by drilling fluid. This investigation aims to inform PDC rock fracture mechanisms, tooth placement parameters, and drilling rate selections for operations in high-temperature formation.

Due to the difficulty of obtaining original samples of high-temperature formation rocks, the sample of rock subjected to high temperature is obtained by heating the rock in an electric furnace. The appearance analysis and mechanical test of the rock after high-temperature treatment are carried out to study the physical property changes of the rock after high temperature.

Rock mechanics is studied by using Wujiaping Formation limestone. The limestone from different locations was precisely cut, polished, and ground to form seven standard cylindrical rock samples, each 100 mm in height and 50 mm in diameter. The rock sample is heat treated using the electric furnace shown in Fig. 1. According to American Society for Testing and Materials (ASTM) guidelines, a low heating rate of 55 °C/h was used to reduce cracking caused by heating, and the set temperature was maintained for 2 h before the sample was allowed to cool naturally.

The high-temperature-treated rock samples were placed into the pressure chamber of the main unit of the triaxial stress–strain tester shown in Fig. 2(a). The confining pressure is set by the servo oil source and auxiliary control mechanism shown in Fig. 2(b) to provide power for the test. The test results were collected and simply organized by the data acquisition and control system shown in Fig. 2(c). The experimental parameters and conditions are shown in Table 1.

The heat-treated rock samples are shown in Fig. 3. Although the cooling process of the rock after heat treatment is allowed to cool naturally in high-temperature heating furnaces in accordance with ASTM guidelines, the inherent joints, cracks, and defects normally present in natural rocks inevitably become more apparent after heat treatment (Figs. 3(a) and 3(b)).

The results of triaxial stress–strain tests on rock samples are shown in Fig. 4. The splitting of the rock samples is shown in the red boxed line in Fig. 4, the angle between most crack surfaces and the vertical axis was under 45 deg, demonstrating the intrinsic heterogeneity of the rock.

As shown in the image with magenta areas in Fig. 4, reveal that beyond 150 °C, the rock's low-temperature elasticity transitions to elastic–plastic strengthening at higher temperatures. At 400 °C, elastic strain represents a mere 15% of total strain, with the remaining 85% occurring during the elastic–plastic strengthening phase. The distinct stress–strain behaviors between these two phases underscore the importance of accounting for high-temperature-induced elastic–plastic strengthening in numerical simulations.

By analyzing the stress–strain curves from the compression tests at varied temperatures, the changes of elastic modulus and Poisson's ratio are shown in Fig.5. Rock samples Wx-60 and Wx-100 exhibited a lower elastic modulus and a higher Poisson's ratio, likely due to the pre-existing bedding and natural fissures, which were further exacerbated by the heat treatment. Considering the uncertainty of natural defects in rocks, in order to make this study more representative to the general rule, the data obtained from the experiments of samples Wx-60 and Wx-100 will not be used in the subsequent simulation. Combined with the fitted curves, it can be seen that the modulus of elasticity decreases with increasing temperature, while Poisson's ratio shows a fluctuating trend of decreasing and then increasing with increasing temperature. The modulus of elasticity decreased from 25.44 GPa at 20 °C to 9.70 GPa at 400 °C, a decrease of 61.9%, which highlights the significant effect of temperature on the mechanical properties of rocks.

$k1=1116⋅1sin2θ$⁠, $k2=1.015sinθ⋅1π$⁠, and $k3=2.03⋅cosθ⋅1π$⁠. d_c denotes the cutter's penetration depth, mm. A is the projected area of the drill teeth contact surface in the vertical direction, m², and f is the friction coefficient.

The linear Druker–Prager model degenerates to the classical Druker–Prager model when the $ψ=β$⁠, $k=1$⁠. The extended Druker–Prager model in the finite element software allows the yield surface to be enlarged (hardened) or reduced (softened). The variation of yield surface size is controlled by some equivalent stress. The user controls by giving the relationship between the deficit $σ¯$ and the equivalent plastic strain $εpl$⁠, where the equivalent plastic strain is $εpl=∫Δεpldt$ [25].

Only when PDC teeth are eaten deep enough can the PDC cutter achieve brittle rock breaking, which is highly efficient rock-breaking state pursued by drilling operations. During drilling, drilling fluid keeps cooling the rocks at the bottom of the well, and thermal stress caused by temperature differences cannot be ignored in rock breaking in high-temperature formation.

Post high-temperature treatment, triaxial compression tests have revealed changes in rock mechanical properties. However, during actual drilling, the drilling fluid imposes a cooling load, inducing thermal stress in the rock. Given the high rotational speed of drill bits, typically over 60 revolutions per minute (rpm), the heat transfer process duration does not exceed 1 s [26]. This process is simulated by abaqus software. The first second is dedicated to thermal coupling analysis to model the rock post-drilling fluid cooling, followed by simulation of the PDC cutter's rock-breaking process under defined motion parameters.

Drilling in the high-temperature formation needs to take into account the thermal stress changes caused by the drilling fluid temperature in the high-temperature formation (Fig. 8(a)). The bottom rock model is established to analyze the thermal stress of drilling fluid on high-temperature formation, and the formation is meshed as shown in Fig. 8(b). The drilling fluid temperature acts on the rock surface at the bottom of the borehole, and the result of encrypting the rock grid at the bottom of the borehole is shown in Fig. 8(c).

The PDC cutter rock-breaking calculation model is shown in Fig. 9(a). The PDC cutter rotation at the bottom of the well is converted into linear velocity, and the PDC cutter is set to move horizontally on the rock model. Encrypting the mesh in the area where the PDC cutter passes through. The entire rock model is divided into 40,000 grid cells. Figure 9(b) shows the setup of PDC cutting tooth intrusion depth and forward rake angle. The model's parameters are listed in Tables 2 and 3.

Based on the rock parameter of 200 °C, the temperature difference between drilling fluid and bottom hole temperature is set to 20 °C. Figure 10(a) shows that the thermal stresses due to the drilling fluid are distributed in a circular pattern, and by further analyzing the longitudinal profile of the rock, the high thermal stresses are more widely distributed at the periphery of the bottom hole (Fig. 10(b)).

Figure 11(a) shows that the cold drilling fluid causes the rock to shrink, and the distribution of the shrinkage displacement extends outward from the circumference of the wellbore, with a peak displacement of 0.0073 mm, which occurs at the outer boundary of the wellbore (Fig. 11(b)), and the shrinkage of the rock due to the thermal stresses may amplify the existing defects in the rock.

The longitudinal distribution of thermal stress and temperature at the outer circle of the wellbore after 1 s is shown in Fig. 12, and the effect of drilling fluid cooling spreads to about 6 mm to the surface of the rock that is in contact with the drilling fluid, which suggests that the depth of action of the drilling fluid's thermal stress on the rock at the bottom of the wellbore will exceed the depth of the draft of the PDC teeth, and that the cooling of the drilling fluid has a great influence on the PDC teeth to break up the rock in the high-temperature formation.

According to the Chinese energy industry standard (NB/T 10097-2018), hot dry rocks t with commercial value are defined as having no or only a small amount of fluid at temperatures above 180 °C [27]. The confining pressure of the model is set as 25 MPa, the rock strength parameter at 200 °C formation temperature and the corresponding critical penetration depth of brittle rock breakage are adopted, and the rotating speed during drilling is 50 rpm. The fractured rock mesh units in the PDC Cutter rock-breaking model are removed. Figure 13 shows the number of fractured rock units cut by PDC cutters with different front rake angles in the same simulation time. The simulation results show that with the increase of the front angle, the number of rock units deleted first increases and then decreases. When the front rake angle of the PDC cutter is 20 deg, the number of rock units deleted is the largest, which indicates that the rock-breaking efficiency of the PDC cutter is higher at the front rake angle of about 20 deg.

When the PDC cutter eats rock at the critical penetration depth of brittle rock breaking, the contact stress on the rock in contact with PDC cutter increases continuously with the advance of PDC cutter. When the stress exceeds the fracture strength of a certain rock, the rock will suddenly brittle fracture into debris, and then the stress between the rock and PDC cutter will decrease. The stress received by PDC teeth fluctuates continuously with the continuous process of rock contact, extrusion, crushing, and debris stripping. Based on the model parameters in Sec. 5.2, the initial forward rake angle of PDC cutter is set to 20 deg for simulation. The stress changes in this process are shown in Fig. 14.

On the one hand, when the PDC cutter front rake angle is too small or too large, it is not conducive to the PDC tooth pressing into the rock. On the other hand, the PDC cutter front rake angle is too large, the rock under the PDC tooth will be subjected to greater pressure, which is not conducive to the PDC cutter cutting rock.

The average stress and maximum stress required by PDC cutter to break rocks when the front rake angles from 5 deg to 25 deg are calculated as shown in Fig. 15. When the front rake angle of PDC cutter is 20 deg, the maximum stress value of PDC cutter during rock breaking is larger, which is 274.8 MPa, but the average stress under this condition is the smallest. This is because inefficient brittle rock breaking, the larger volume of rock debris removed from the formation requires higher stress. The fewer the cycles of PDC teeth and rock contact—extrusion—crushing—rock debris stripping in the same period of time, the shorter the time for PDC cutters to maintain high-stress contact with rock, i.e., the lower the average stress during rock breaking under the same rotational speed and rock strength conditions. The higher the brittle rock-breaking efficiency.

Based on the rock parameters obtained from the high-temperature rock mechanics test, PDC cutters with a front rake angles range of 10 deg, 20 deg, and 30 deg were selected to simulate the stress characteristics of PDC cutters crushing rocks at different temperatures. Due to the chance of the maximum stress value during the numerical simulation, the average stress maximum rock-breaking process during rock breaking was extracted for analysis, and the results are shown in Fig. 16. With the increase of temperature, the average stress required for rock breakage decreases first and then increases (because the natural defects of rock samples at 60 °C and 100 °C are amplified by heat treatment, the strength of rock is low, and the stress required for rock breakage is small), which is because the strength of rock decreases at high temperature. However, the critical cutting depth of PDC cutter for brittle rock breaking increases the volume of rock that PDC teeth need to be broken at one time, and the stress required in the rock-breaking process will increase.

It can also be seen from Fig. 16 that, based on the rock-breaking simulation of rock parameters under the same temperature condition, the average stress required for rock-breaking is the smallest when the front rake angle of PDC cutter is about 20 deg, indicating that the temperature change has little influence on the forward inclination arrangement of PDC cutter for efficient rock-breaking.

The in situ stress value of the high-temperature formation is generally high. After the borehole is opened, the original stress balance of the formation will be destroyed, and the in situ stress will concentrate on the rock at the bottom of the hole, and the rock at the bottom of the hole will be squeezed by the original in situ stress. Figure 17 shows the displacement distribution of rock under extrusion when the confining pressure is 25 MPa, 50 MPa, 75 MPa, and 100 MPa, respectively. According to the possible formation temperature at the depth corresponding to the effective ground stress, the selected rock parameters are samples, Wx-20, Wx-60, Wx-150, and Wx-200 respectively. When the confining pressure is 100 MPa, the maximum displacement reaches 0.119 mm (Fig. 17(d)).

When the rotational speed is 50 rpm (equivalent to the linear speed of PDC cutter movement is 554.73 mm/s), the simulation under different confining pressures and front rake inclination angles is shown in Fig. 18. As the confining pressure at the bottom of the hole increases from 25 MPa to 100 MPa, the average stress in the rock-breaking process of PDC cutters with the same front rake inclination angles first increases and then decreases. This is because the direction of confining pressure is opposite to the direction of the PDC cutter rock-breaking force. Under the condition of low confining pressure, the rock directly in contact with the PDC teeth is further compacted, and the strength of the rock increases. When the confining pressure further increases (75 MPa), the ratio of uniaxial compressive strength to tensile strength of the rock at the bottom of the hole increases due to the action of high stress, and the brittleness of the rock increases. In the case of changes in downhole confining pressure, the optimal forward rake angle of the PDC cutter is 20 deg.

The confining pressure of the model was set to 25 MPa and the front rake angles of PDC cutter were set to 25 deg. The speed setting of the model was changed to conduct rock-breaking simulation under the conditions of 50 rpm, 60 rpm, 70 rpm, 80 rpm, 90 rpm, and 100 rpm, and the calculated average rock-breaking stress and the number of grid deletion of the rock model were extracted, as shown in Fig. 19.

The increase of rotational speed increases the rock-breaking efficiency at the same time, and at the same time, the average stress required for rock-breaking increases. When the rotational speed increases from 70 rpm to 80 rpm, the growth rate of the number of rock mesh breaks is large, the growth rate of the average rock-breaking stress is small, and the rock-breaking effect is significantly improved. As the rotational speed increases from 80 rpm to 100 rpm, the improvement of rock-breaking effect slows down and the growth rate of average rock-breaking stress increases. This is because when the rotational speed is high, the cuttings will be repeatedly broken before they are removed from the rock bottom, which is not conducive to the extension of rock brittle cracking. Under the condition of high rotational speed, the stress growth rate increases, which has an adverse effect on the bit life. After the mechanical drilling rate can be significantly improved by increasing the rotational speed, attention should be paid to further accelerating the rotational speed to reduce the damage to PDC cutter caused by excessive stress during rock breaking.

Based on the rock samples after heat treatment, the rock triaxial stress–strain test was carried out, and the thermal stress at the bottom of the hole during drilling in the high-temperature formation was analyzed by numerical simulation. In addition, based on the brittle rock-breaking theory and combined with experimental parameters and conventional engineering parameters, the influences of front rake angles, rock confining pressure at the bottom of the hole, and rotational speed on rock breaking were analyzed. The main conclusions are as follows:

1. With the increase of temperature, the compressive strength and elastic modulus of rock decrease, and Poisson's ratio shows a fluctuating trend. At the same time, the inherent defects of rock (stratification and micro-fissures) can amplify the effect of temperature on rock strength. The critical depth required for PDC cutter to break rock efficiently is increased by the decrease in rock strength caused by the increase in temperature, and exceeds 1 mm at 150 °C.

2. The thermal stress caused by the temperature difference between drilling fluid and the bottom rock mainly affects the outer circumference of the bottom rock. After the transient heat transfer between drilling fluid and bottom hole for 1 s, the temperature disturbance can reach 6 mm, which exceeds the critical cutting depth of PDC cutter.

3. Across different temperatures, a front rake angle of approximately 20 deg proves optimal for rock breaking. In this study, the temperature and confining pressure have little influence on the front rake angles.

4. As the temperature increases, the strength of the rock decreases, but the critical depth of rock fragmentation increases, thereby expanding the contact area of the PDC teeth with the rock. As a result, the stress required for rock breaking decreases first and then increases with the increase of temperature.

5. Under the parameter conditions of this study, the increase of rotational speed will accelerate the rock-breaking speed, and lead to the increase of stress in the PDC cutter during the rock-breaking process. However, when the rotational speed is too high, it is not conducive to the brittle spalling of rock debris, resulting in the rapid increase of stress and slow growth of rock-breaking speed during PDC cutter rock breaking.

These insights underscore the delicate interplay between thermal effects, mechanical stresses, and cutter dynamics in rock-breaking processes at elevated temperatures and could inform future drilling operations to optimize efficiency and minimize costs. The rock mechanical parameters measured based on the high-temperature-treated rocks have certain limitations in describing the rocks in the high-temperature formation. In further study, the joint influence of stress environment and the real change of temperature with formation depth on rock breaking by PDC cutters will be considered.

• The National Key Research and Development Program (Grant No. 2022YFC2806501).

• The National Natural Science Foundation of China (NSFC: No. 52101340).

• The Science Foundation of China University of Petroleum, Beijing (Grant No. 2462021BJRC008).

There are no conflicts of interest.

The authors attest that all data for this study are included in the paper.

$A$ =

projected area of the drill teeth contact surface in the vertical direction

$d$ =

intercept of the yield surface on the axis t of the $p−t$ stress space

$f$ =

friction coefficient

$k$ =

ratio of triaxial tensile strength to triaxial compressive strength

$dc$ =

critical cutting depth of rock breaking

$k1$ =

horizontal contact pressure coefficient

$k2$ =

bow contact area contact pressure coefficient

$k3$ =

contact pressure coefficient for horizontal displacement of cutting teeth

$F1$ =

two-letter abbreviations should appear in italics

$F2$ =

three-letter abbreviations should not appear in italics

$E*$ =

Reynolds number and similar abbreviations do not use italics

$β$ =

inclination of the yield surface in the $p−t$ stress space

$β1$ =

use the “Tab” key to add more rows to this table

$β2$ =

horizontal shape factor of PDC teeth rubbing against rock

$εpl$ =

equivalent plastic strain

$σc$ =

compressive strength