Intensity analysis of frictional heat source during core tube sampling and drilling

Currently, the heat generated during coal core tube sampling causes rapid gas desorption, leading to substantial measurement errors in laboratory gas content assessments. Reducing these errors requires studying frictional heat from core tube friction against the hole wall and coal core temperature rise. Combining the independently developed device to simulate the thermal effect of coring and the COMSOL finite element analysis software, the intensity of the frictional heat source during the core tube sampling and drilling process was analyzed under different coring depth and rotational speed conditions. The research results show that: At constant speed, frictional heat intensifies as the core depth increases. However, the rate of temperature rise decreases with increasing core depth; when the coring depth is constant, the frictional heat is proportional to the rotational speed. For example, at a depth of 140 m and a rotational speed of 120 r/min, the intensity of frictional heat generated by drilling is 2.21 ∗ 10E6J. Similarly, at 180 r/min, the strength is 2.28 ∗ 10E6J, and at 240 r/min, the strength reaches 3.65 ∗ 10E6J; Under certain conditions, core tube wall temperature will not rise indefinitely but will stabilize to a certain value.


| INTRODUCTION
According to the statistics of the State Bureau of Mine Safety Supervision, from 2002 to 2019, the death toll of coal mine gas accidents accounted for about one-third of all coal mine accident deaths, and coal bed methane (CBM) is known as the "number one killer" of coal mine safety production. 1 The primary cause of the aforementioned incident is uncertainty in Coalbed Methane Determination, therefore emphasizing the importance of precise measurement of coal seam gas concentration as a fundamental requirement for guaranteeing the safety of coal mine operations.
The effective management of coalbed methane is crucial in mitigating coalbed methane accidents.Achieving such management requires precise measurement of fundamental coalbed methane parameters, particularly the coalbed methane content.3][4] CBM content determination methodologies are classified as either direct or indirect. 5,6Nevertheless, as a result of the challenges posed by a protracted measurement cycle, a suboptimal success rate, and a substantial accumulative error, the indirect approach currently lacks efficacy.Consequently, China's coal mines have adopted the "Direct Determination Method of Coalbed Methane Content Underground" (AQ1066-2008) 7 to ascertain the coalbed methane content.][10][11] The quantity of desorption of underground coalbed methane and the amount of residual coalbed methane can be determined in the laboratory. 10,12,13However, the quantity of CBM loss is calculated based on the law of CBM desorption and the CBM loss time, and the error is relatively large, which significantly reduces the accuracy of the measured CBM content value, which leads to misevaluation of the degree of CBM risk.It is not uncommon for coalbed methane outburst risk area prediction and regional outburst prevention measures to be distorted. 14Therefore, the accuracy of the direct approach for determining the coalbed methane content is primarily dependent on the accuracy of the calculation of coalbed methane loss. 157][18] However, twist drill pipe sampling has the disadvantages of uncertain sampling location and inaccurate determination of desorption time.Compressed air sampling has the disadvantage that fixed-point sampling cannot be performed.The sampling depth is shallow, and the extracted coal sample particles are minute.Despite the fact that negative pressure injection sampling can accomplish fixed-point sampling, the coal sample is under negative pressure during the sampling procedure, which accelerates the desorption of coal bed gas from the coal sample.There is no suitable calculation method for the loss of coal bed gas under negative pressure conditions.Consequently, several flaws exist.Core tube sampling permits point-based sampling, and the coal sample is plentiful and more representative of its original state.Therefore, the direct measurement method of coalbed methane content in coal mines requires the use of core tube sampling or other effective verification fixed-point sampling methods, with core tube sampling being recommended. 19Core pipe sampling is divided into three processes: empty tank drilling, cutting sampling, and back drilling.Throughout the whole of the operation, there exist three distinct heat sources that have an influence on the coal core.These sources include the generation of frictional heat resulting from the friction that occurs between the core pipe wall and the wall of the hole.1][22][23][24][25][26] The example provided exhibits a deficiency in the clarity of the temperature field distribution of the collected coal samples, and the understanding of the desorption behavior of coalbed methane remains uncertain.Currently, the existing approaches for estimating coalbed methane loss rely only on gas desorption principles at standard temperature conditions.Hence, the crucial factor in precisely determining the coalbed methane concentration lies in acquiring the three intensities of heat sources that impact the temperature alteration of the coal core throughout the coring procedure.
Extensive scholarly study has been conducted on the thermal effects produced by drilling instruments in the course of drilling operations.In their study, Okamura and Sasahara 27 conducted experimental measurements of the temperature in the vicinity of the cutting edge.They used an implanted K-type thermocouple to accurately quantify the drilling temperature throughout both drilling and nondrilling phases of low-frequency vibration drilling.In their investigation, Wang et al. 28 used a device for measuring core tube wall temperature to investigate the impact of various core depths on said wall.The researchers' findings demonstrated a direct correlation between the highest recorded temperature of the core tube wall and the depth of sampling.Yan et al. 29 researched the changing rules of friction cone temperature and friction coefficient through experiments and simulations.Han et al. 30 established the FPS threedimensional thermal-mechanical coupling finite element model to obtain the strength and energy consumption of the bearing during operation.The scholars mentioned above have conducted extensive research on the temperature change of the drill bit during cutting operations and the generation of frictional heat.However, there has been limited attention given to the impact of frictional heat on the temperature of the coal core during the coring process.
To investigate the impact of frictional heat on the temperature of coal cores during the coring process, the research team has designed a device capable of simulating the thermal effects encountered during coring.This device enables the continuous monitoring of the temperature of both the core tube wall and the coal core in real time, allowing for data collection under various operational conditions.To replicate the temperature fluctuations in coal cores resulting from coring activities, with the aim of investigating the intensity of frictional heat generation during the sampling procedure.This research utilizes COMSOL Multiphysics in conjunction with a specific instrument to investigate and analyze the generation of frictional heat during the coring drilling process.The findings of this study provide a theoretical framework for quantitatively assessing the thermal impact of the following coring procedure and the precision of coalbed methane concentration measurement.

| EXPERIMENTAL SYSTEM AND EXPERIMENTAL METHOD 2.1 | Experiment system
This work presents the development of a series of thermal effect devices designed to simulate the coring process.The physical map of the system is shown in Figure 1.The equipment is divided into three parts: data processing unit, rotating acquisition unit, and power unit.The fundamental operational procedure of the device can be described as follows: The three-phase asynchronous motor impels the rotation of the core tube, resulting in the generation of heat through friction between the core tube wall and the friction plate located on its outer side.This heat generation simulates the friction occurring between the core tube wall and the hole wall.Additionally, the stepping motor is responsible for regulating the movement of the coal sample towards the cutting bit, ensuring its proximity.The operation of coring generates cutting heat, and the data processing unit simulates the desorption heat to determine the pressure change of the coalbed gas inside the coring tube and the corresponding temperature change of the coal core during the coring process.The temperature sensors on the wall of the core tube (T1, T2, and T3) and inside (T4, T5, T6, T7, T8, and T9) (the arrangement of the temperature sensors is shown in Figure 2) are transferred through the rotating collector during the whole sampling process.The data are transmitted to the data processing unit for data recording, so as to simulate the thermal effect in the coring process to achieve the purpose of studying the three heat sources in the coring process.

| Experimental program
The coal samples from Jiulishan Coal Mine 31 were carefully chosen in advance for the purpose of conducting studies.The drilling equipment used in Jiulishan Mine was the Tiefulai ZDY4500LXY, a crawler hydraulic drilling rig.The torque ranges from 1000 to 4500 N m, while the speed ranges from 60 to 255 r/min.Therefore, three sets of drilling rig speed parameters are selected as 120, 180, and 240 r/min, respectively.The drilling speed is 2 m/min, the coal sample cutting speed is 0.2 m/min, and the drilling speed is 2.5 m/min.The coring process is divided into drilling, cutting and sampling, and drilling back.According to the selected three sets of coring depth parameters of 60, 100, and 140 m, it can be obtained that the selected three sets of coring and drilling times are 30, 50, and 70 min, respectively.The specific experimental parameters are shown in Table 1.

| Sample preparation
The coal samples used in the experiment were chosen from the Jiulishan Coal Mine located in Jiaozuo City, Henan Province.The physical properties of the coal samples were afterwards measured.To assure the credibility of the experimental findings, the coal samples used in the experiment were obtained from the working face numbered 14,141.The coal core extracted from the lowermost section of the borehole using the coring tube consists mostly of fine powder particles, interspersed with a little proportion of larger particles.The coal samples collected from the sampling site were subjected to pulverization using a pulverizer.Subsequently, the coal samples with a particle size ranging from 60 to 80 mesh (0.17-0.25 mm) were selected using a screening process for the purpose of conducting sampling simulation studies.The coal samples underwent an industrial examination, whereby the true/ apparent density and porosity were determined following the guidelines set by Chinese norms.The obtained findings are shown in Table 2.

| Coal friction coefficient
The temperature increase of the coal core is influenced significantly by the friction heat created during the drilling process, resulting from the friction between the core tube and the coal body.The simulated coring heat device employs a friction plate to replicate the rotational friction occurring between the wall of the hole and the coring pipe.Therefore, it is essential to conduct a friction coefficient test between the Jiulishan coal sample and the coring pipe.
The experiment included the evaluation of the coefficient of friction between coal samples and steel using an Amsler friction and wear testing unit.The apparatus comprises a metallic circular disc characterized by an outside diameter of 22 cm and an inner diameter measuring 15 cm.This disc is affixed to a motor for operational purposes.The coal sample is placed in a metal holder connected to a pneumatic system that pushes the coal sample towards the rotating disk.Continuously record the speed of the disc, the normal load, torque, and temperature of the leave on the coal sample.
The coefficient of friction can be expressed as where μ c is the coefficient of friction, M is the torque (N m), F N is the load on the coal sample (N), and R ext and R int are the outer and inner radii of the friction zone, respectively (m).
Ultimately, it has been ascertained that the friction coefficient between Jiulishan coal and steel is 0.4.The core pipe, constructed in accordance with the standard, is composed of DZ40 medium carbon steel, possessing a density of 10.25 kg/m.Additionally, the friction coefficient between the core pipe and the friction plate is determined to be 0.15.Consequently, the force exerted between the friction plate and the core tube is equivalent to 0.15 kN after appropriate conversion.3 | SIMULATION RESEARCH ON TEMPERATURE FIELD OF CORING TUBE

| Model construction
The COMSOL program is used to construct a simulation model of the coring tube in three dimensions.This model consists of three main components: the core drill bit, the friction plate, and the core tube.On the basis of the specifications of the testing apparatus, the core tube has the following parameters: a length of 560 mm, an inner  diameter of 200 mm, and a wall thickness of 20 mm.The cutting drill bit is equipped with a total of six cutting teeth, while the friction plate exhibits a wall thickness of 5 mm.The simplified model and grid of the coring tube were established in the COMSO software, as shown in Figures 3 and 4.

| Heat transfer boundary condition setting
In the process of coring and drilling, three primary forms of heat transfer are observed: convection, conduction, and radiation. 32One of the mechanisms contributing to heat generation is the frictional heat resulting from the relative motion between the friction plate and the core tube wall.This heat is then conducted through the surface of the friction plate, the outer layer of the core tube, and the cutting edge of the core bit.The convective heat exchange occurring between the surface and the surrounding air during the rotation process, as well as the dissipation of heat through surface radiation, can be categorized as heat convection and heat radiation, respectively.
Thermal analysis adheres to the principle of energy conservation, which states that the total energy within a closed system remains constant: where Q is the heat, W is the energy produced, U Δ is the internal energy of the system, K Δ is the kinetic energy of the system, and P Δ is the potential energy of the system.
(1) Thermal convection Heat convection is a prominent mechanism for the transport of thermal energy, and it may be mathematically represented as where q is the heat flux (W/m 2 ), h is the convective heat transfer coefficient (W/(m 2 K)), T w is the solid temperature (K), and T f is the ambient temperature (K).When calculating heat convection, the heat transfer coefficient may be mathematically represented as where N μ is the Nusselt number, N = 0. 197 3 ; Pr is the Prandtl constant, Pr = 0.669; H and δ are the height and width of the finite empty space, respectively; g is the acceleration of gravity; υ a is the kinematic viscosity of air; T Δ is the temperature difference.(2) Heat conduction Heat conduction is the phenomenon by which thermal energy is transferred from an area characterized by greater temperature to a region characterized by lower temperature within a given system, or across systems that possess distinct temperature levels.The main way to transfer heat in solids is heat conduction; in nonsolid substances, heat transfer is often conducted jointly by heat conduction and heat convection.The basic law of heat conduction can be expressed by Fourier's law as where q is the heat flux (W/m 2 ), λ is the thermal conductivity of the material (W/(m K)), T is the material temperature (K), and n is the external normal direction of the heat transfer surface of the object.
(3) Heat radiation Thermal radiation refers to the ability of hightemperature objects to radiate energy outward.Although heat radiation belongs to heat transfer like heat conduction and heat convection, it is different from the latter two heat transfer methods.It can transfer heat without a medium.Thermal radiation mainly uses electromagnetic radiation to emit heat, and the intensity of thermal radiation is mainly related to the level of temperature.There is a positive correlation between temperature and the intensity of thermal radiation.Thermal radiation serves as the predominant mechanism for heat transfer over extensive distances.
The maximum thermal radiation density is given by Stefan-Boltzmann's law: Friction plate and coring tube dissipate the heat generated at the boundary of both by convection with air and radiation.This model simulates rotation as convection in the simulated coring heat.The velocity vector of the local coring tube is At the end of the calculation, the heat generated and dissipated can be recovered using the following relationship: The physical parameters of the core tube (DZ40) and the PDC (core drill bit) cutting bit are shown in Table 3.
Simultaneous formulas (2)-( 9) begin to establish a heat transfer analytical calculation model that fits the actual coring process.

| Influence of coring depth
Figures 5-7 show the temperature changes collected by three sensors on the coring pipe wall at different coring depths during the coring drilling process.It can be seen from the figure that among the three sensors, the T3 position has the fastest temperature rise, and its temperature amplitude is the largest as the coring depth increases.It can also be seen that during the core drilling process, there are two stages of temperature rise of the core tube wall, which are the rapid temperature rise stage and the steady temperature rise stage.With the increase of the coring depth, the temperature rise rate of the core tube wall gradually decreases.Assuming a constant ambient temperature, the temperature of the coring tube wall eventually reaches an upper limit with increasing depth.The specific peak temperature values collected by the three sensors during the drilling process are shown in Table 4.

| Influence of rotating speed
The relationship between the rotating speed of the core tube and the temperature rise efficiency of its wall can be shown in Figure 8.It is evident that as the rotational speed rises, the ultimate stable value of the core tube temperature also increases, when the core tube reaches the same coring depth.In the course of drilling, the rate at which the temperature of the core tube increases is inversely related to its proximity to the core bit.As the rotational velocity rises, there is an observed increase in the temperature differential between the core tube T3 and T1.heat effect device.This friction generates a certain amount of heat, which in turn affects core tube wall temperature.However, It is imperative to acknowledge that the thermal energy produced by the friction plate surpasses the thermal energy generated by bearing friction.Hence, the latter exerts a minimal influence on the accuracy of the model.

| Model data results
Figure 10 depicts a three-dimensional visualization of the variations in core tube wall temperature throughout the coring procedure at various velocities.In contrast, Figure 11 shows temperature contour plots of the core tube wall throughout the coring process.The provided graphic depicts a direct relationship between the velocity and the temperature of the inner wall of the core tube.Specifically, as the speed rises, core tube wall temperature also increases.At the 70-min mark, the core tube wall temperature reaches its peak.Notably, when the speed is set at 240 r/min, the extreme value of the core tube wall temperature is 43°C higher compared with when the speed is set at 120 r/min.The rise in temperature of the core tube during the drilling process is solely determined by the heat generated from friction between the core tube wall and the wall of the hole.Hence, it is evident that the temperature exhibits a progressive rise down the axis of the core tube.When the speed is 120 r/min, the temperature of the cutting teeth is 54.7°C lower than that of the coring tube at position T3 min, the temperature of the cutting tooth was 89.5°C lower than that of the coring tube wall at T3 position.On the basis of the findings, it can be inferred that there exists a direct relationship between the speed of the core bit and the temperature differential between the drill bit and the core tube.Furthermore, the simulation results demonstrate that the temperature of the core bit remains constant in relation to the ambient temperature.This suggests that the core drill bit does not exhibit any alteration in the core depth of 140 m.During the process, the frictional heat source affects the temperature of the cutting teeth in a small range.Figure 12 depicts the temperature distribution within the core tube in three dimensions.It illustrates the temperature distribution along the T1, T2, and T3 crosssection directions on the core tube wall, observed at various speeds.The illustration illustrates a progressive rise in temperature along the T1, T2, and T3 axes in the core tube.The curvature of the coring tube wall exhibits a constant reduction along the time axis, corresponding to an increase in coring depth.Consequently, the temperature rise rate of the coring tube wall also shows a continuous decrease.The correlation between the temperature discrepancy of the coring tube wall and the surrounding environment is directly proportional to the depth of coring.Convective heat transfer and radiation efficiency between tube wall and air.
To study how much of the generated heat is dissipated to the air, we study the surface integral that generates the heat that is well dissipated.These two integrals give the total heat rate (W) of the heat production Q prod and Q diss as a function of time during the drilling of the coring pipe.The time integral W prod and W diss of these two physical quantities, respectively, provide the total heat (J) generated and dissipated by the core pipe during the drilling process.Figure 13 shows the frictional heat source intensity and dissipated heat generated by the core pipe during the drilling process at different rotational speeds.
The data shown in Figure 13 illustrates a notable trend whereby the heat production rate of the frictional heat source gradually decreases with increasing coring depth.The observed phenomenon may be attributed to the positive correlation between the depth of coring and the temperature differential between the core and the surrounding environment, leading to an increase in convective heat transfer.The pace at which heat is dissipated by radiation is directly proportional to efficiency.Consequently, a slower rate of heat production is seen when there is difficulty in warming up.Furthermore, it can be seen that the dissipated heat rate exhibits a progressive rise as the coring depth increases.This observation suggests that the dissipated energy curve eventually converges towards the produced heat curve.It can be speculated that if the coring depth continues to increase, there is an upper limit for core tube wall temperature.
Table 5 shows the frictional heat source intensity and dissipated heat of the coring tube when the coring depth is 140 m.The analysis of the table reveals that as the rotational speed increases, there is an exponential growth in the intensity of the frictional heat source, as well as the energy wasted by convective heat exchange with air and heat radiation.

| CONCLUSION
Based on the simulation experiment of the thermal effect of core tube sampling and combined with the COMSOL Multiphysics finite element analysis software, this paper analyzes the friction heat source of the core tube during

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I G U R E 2 Schematic diagram of the layout of the core tube temperature sensor.

( 1 ) 21 F
Before the test starts, use the empty room temperature sensor to check whether the sensor is normal by comparing it with the indoor T A B L E 1 Experimental parameter settings.L E 2 Physical parameters of coal samples.Coal sample Moisture (%) Ash points (%) Volatile matter (%) True density (g/cm 3 ) Apparent density (g/cm 3 ) Φ (%) I G U R E 3 Simplified model of coring tube.F I G U R E 4 Grid layout of the model.temperatureand humidity meter, and restore the friction belt load to zero.(2) Turn on the load cell detector, calibrate the three friction belts, and keep the set value at a load of 0.15 kN.(3) Turn on the power of the equipment, adjust the working frequency of the asynchronous motor, set the speed to (120, 180, and 240 r/min), keep rotating for 70 min, and stop the motor.(4) After collecting the temperature data of T1, T2, and T3 in the whole process, complete this experiment.

5
Thermal fluctuation of the coring tube wall at different coring depths at 120 r/min speed.(A) 60 m, (B) 100 m, and (C) 140 m.
Thermal fluctuation of the coring tube wall at different coring depths at 180 r/min speed.(A) 60 m, (B) 100 m, and (C) 140 m.

7
Thermal fluctuation of the coring tube wall at different coring depths at 240 r/min speed.(A) 60 m, (B) 100 m, and (C) 140 m.T A B L E 4 Peak temperature of coring tube wall at different coring depths.

)F I G U R E 8
Temperature variation of coring pipe wall during coring and drilling at different speeds.(A) 120 r/min, (B) 180 r/min, and (C) 240 r/min.
Comparison of experimental data and simulated data of core tube wall temperature at different speeds.(A) 120 r/min, (B) 180 r/min, and (C) 240 r/min.

Figure 9
Figure9illustrates a comparative examination of the temperature variation in the core tube wall at different velocities, displaying both the empirical and simulated data.The illustration demonstrates that the evolution pattern of the simulated data closely matches the experimental data, with a maximum deviation of 8%.However, the simulated core tube temperature change amplitude is slightly smaller than the experimental data.This phenomenon occurs due to the presence of friction in the bearing during the rotation of the simulated coring

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I G U R E 11 Three-dimensional temperature isosurface of core pipe wall during drilling at different speeds.(A) 120 r/min, (B) 180 r/ min, and (C) 240 r/min.

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I G U R E 12 Three-dimensional temperature field of the core tube along the T1, T2, and T3 section lines on the core tube wall at different speeds.(A) 120 r/min, (B) 180 r/min, and (C) 240 r/min.

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I G U R E 13 Frictional heat source intensity and dissipated energy of the coring tube wall at different speeds.(A) 120 r/min, (B) 180 r/ min, and (C) 240 r/min.T A B L E 5 Frictional heat source intensity and dissipated heat of coring pipe when the coring depth is 140 m.Rotating speed (r/min) Energy (J)