Abstract
The shape of the hydraulic flushing hole is an important basis to determine the effective pumping radius. In the design and evaluation of the drilling hole, it is usually equivalent to a cylinder. However, the formation of the shape of the hole is affected by the gravity of coal and rock bulk, the friction of coal and rock, water force, stress, and other factors, so the scientific nature that is equivalent to a cylinder remains to be discussed. In this paper, based on the analysis of the whole process of hydraulic flushing and the formation of the pore shape, gravity, friction, water force, and ground stress of coal and rock bulk are selected as important factors affecting the pore shape, and the parallel Bergmark-Roos equation and PKN model are introduced to establish the BR-PKN equation of the pore shape of hydraulic flushing. MATLAB is used to reproduce the shape of the hydraulic flushing hole, which is a kind of ellipsoid with three different axes. In order to verify the accuracy of the hole shape, the YZD18.5 video imaging logging tool for mine lateral resistivity is used to collect and analyze the shape data of the hydraulic flushing hole, and the hole section is drawn, which is basically consistent with the theoretical derivation of the hydraulic flushing hole shape. COMSOL is used to simulate the hydraulic flushing equivalent of the ellipsoid hole compared with the cylinder hole under the same coal output and extraction time of 90 days. The extraction radius, desorption surface area, and effective extraction volume are 0.95, 0.79, and 1.14 times, respectively, providing a basis for the optimal design of hydraulic flushing.
1. Introduction
More than 95% of high-gas mines and outburst mines in China belong to low-permeability coal seams, with large gas content, small single-hole drainage range, fast attenuation, and great difficulty. Coal seam pressure relief and fracture making is an effective way to solve the extraction of the low-permeability coal seam [1–3]. Hydraulic flushing technology is a widely used outburst prevention technology in recent years. It uses high-pressure water jet technology to break the coal seam. A large amount of coal rushes out in a short time and forms a hole with a large diameter near the borehole, which destroys the original stress balance state of the coal seam, forms a pressure relief zone in a certain range around the hole, and greatly improves the permeability of the coal seam in this area, so as to achieve the purpose of gas drainage [4, 5]. However, when the coal body is not filled with creep, the hydraulic flushing hole easily forms high-concentration gas accumulation, resulting in crack communication between adjacent holes and holes, and the high-concentration gas directly flows into the adjacent heading face, resulting in a gas overrun accident [6]. Some scholars also put forward that the holes formed by hydraulic flushing and the pressure relief and fracturing effect on the coal seam cause the coal to be soft. Under the action of mining stress, in situ stress, and residual gas pressure, the surrounding rock of the coal roadway is prone to deformation and collapse, even gas outbursts [7–11]. Based on this, it is urgent to study the hole shape of hydraulic flushing.
The borehole extraction radius is an important parameter to determine the borehole spacing and hole layout, which directly affects the methane predrainage parameter layout, drainage time, and drainage effect [12–16]. In order to study the relationship between the effective extraction radius of hydraulic flushing and the coal washing volume, Wang et al. regarded the formed borehole cavity as a uniform cylinder and then investigated the effective extraction radius of hydraulic flushing [17]. It was found that the effective extraction radius increased exponentially with the increase of coal production; Tao et al. arranged several groups of extraction holes and pressure relief holes on site to evaluate the effect of hydraulic flushing and antireflection, defined the distance between the corresponding extraction holes and the pressure relief holes as the effective extraction radius, and achieved good results [18]. In order to determine the parameters such as the hydraulic flushing pressure relief radius, Wang et al. used the independently studied stress monitoring system to divide the coal around the hydraulic flushing hole into the stress relief area, stress transition area, and stress concentration area [19]. It was found that the radius of the relief area is more than 10 times the equivalent radius of the flushing hole. However, the process of hydraulic flushing is not uniform hole expansion, and the hole shape is not regularly cylindrical, which has a great impact on the pressure relief range and effective radius of flushing in the later research, and may even produce a goaf white belt, resulting in the islanding effect of the coal extraction pillar [20]. Based on the analysis of the whole process of hydraulic flushing and the formation of the hole shape, this paper introduces and establishes the Bergmark-Roos equation and PKN model, establishes the BR-PKN equation of the hydraulic flushing hole shape, reproduces the hydraulic flushing hole shape with MATLAB, and verifies it with field test data. It shows that the equation has high accuracy and has guiding significance for determining the effective extraction radius of the borehole.
2. Methods
2.1. Establishment of the Hole Shape Equation for Hydraulic Flushing
2.1.1. Basic Principles of the Bergmark-Roos and PKN Model
The Bergmark-Roos ore drawing theory establishes the mathematical model of loose ore and rock flow from the point of view of mechanics. It assumes that the ore and rock particles move continuously from the initial position to the ore drawing opening at the shortest distance. From the force in the movement of particles, it analyzes the relationship between the gravity of ore and rock and the direct friction force of surrounding particles and expounds on the formation principle of ore drawing ellipsoid, which is a major development in the research of the ore drawing theory [21–24]. The Bergmark-Roos equation is as follows: where is the moving distance of particles, m; is the height of the ore body, m; is the angle between the particle moving trace and the vertical direction, °; and is the maximum angle of dispersion movement, which is determined by the following formula: where is the internal friction angle of particles, which changes with particle size and particle roughness. The coarser the particles, the greater the value.
On the horizontal section of the hole after hydraulic flushing, the coal and rock are regarded as elastic and brittle materials, the hole height is fixed, and the force of water is a constant, which is highly consistent with the PKN model [25–29]. Therefore, the Bergmark-Roos equation and PKN model are combined to establish the BR-PKN equation suitable for the characteristics of hydraulic flushing holes. The basic assumptions are as follows: (1)The coal seam is homogeneous(2)The coal body is broken by hydraulic flushing and high-pressure water, which destroys the coal body structure, and the coal body is regarded as a discrete body within the flushing range(3)Assuming that the hydraulic flushing hole is the ore drawing window, the influence of the hole diameter is ignored(4)The coal cinder production process is assumed to move continuously, and the trajectory is a straight line(5)The coal cinder is affected by many forces in the production process, namely, gravity, flushing water force, and friction of surrounding coal, and the direction of flushing water flow is consistent with the direction of coal cinder migration, and the force on the coal cinder is constant(6)Coal and rock are elastic and brittle materials(7)The hole height is certain
2.1.2. Establishment of the Hole Shape Characteristic Equation of Hydraulic Flushing Based on the BR-PKN Model
The stress analysis of the hydraulic flushing cinder is shown in Figure 1. The stress of coal and rock in the process from crushing to output includes flushing water force, self-gravity, and friction. The resultant force of each component along the direction of the cinder output track is is the force of flushing water on coal slag, N, fixed value; and is the friction between ore and rock, N.
Then, the acceleration during coal slag transportation is
According to equation (3) and , the relationship between the distance from the initial state of the coal cinder to the coal point of flushing and drilling and the time can be calculated as
Since is a constant value, is a constant. Let , and is a constant. When is the maximum movement angle , the cinder is in a stable state, so the acceleration ; then,
When , the moving distance of coal slag is the coal section length of the borehole; then,
Equations (6) and (7) can eliminate and obtain the output equation applicable to the hydraulic flushing cinder:
According to the stress analysis of the horizontal section of the hole, the horizontal section is not regularly round and has a long axis and a short axis. Its short semiaxis is
The hole height is
Because the height of the PKN model is certain, the high in the formula is equivalent to the high of the hydraulic flushing hole, and in the formula is regarded as the minor axis of the horizontal section, i.e.,
In order to solve the value of the long half-axis in the horizontal direction of the hole, the Carter formula is introduced: where is the change of the hole volume, m3/min; is the area of the horizontal section of the hole, m2; is the coefficient, taken as 1; and is the error compensation function of .
The long half-axis of the horizontal section can be obtained by the following formula:
Simultaneously, using (11)–(13), we have
According to the characteristics of the deduced BR-PKN equation, the horizontal section of hydraulic punching is quasi-ellipsoid, and the pore shape of hydraulic punching is quasi-ellipsoid.
2.2. Determination of Morphological Characteristic Parameters of Hydraulic Flushing Holes
The morphological characteristic parameters of hydraulic flushing holes include borehole inclination, coal output, coal section length , short semiaxis , and long semiaxis . The specific data of coal section length , actual coal output volume , and borehole inclination can be obtained through actual measurement after drilling construction, while the short semiaxis , long semiaxis , and calculated coal volume are difficult to obtain through field measurement. The calculation formulas of coal volume , short half-axis , and long half-axis are derived from the hydraulic flushing cinder production equation.
2.2.1. Determination of the Parameters of the Long Half-Axis and Short Half-Axis of the Hydraulic Flushing Hole
At a given angle, according to equation (9), in the case of , the long half-axis and short half-axis of the hydraulic flushing hole can be obtained, and the derivative of equation (9) can be obtained:
Let to obtain , the short half-axis gets the maximum value , and the maximum value of the short half-axis of the hydraulic flushing hole can be obtained from equation (9):
At this time, the maximum value of the long half-axis is :
2.2.2. Determination of the Hole Volume in Hydraulic Flushing
Because the shape of the hydraulic flushing hole is ellipsoid, it can be simplified as an ellipsoid to calculate its volume :
Simultaneously, we use formulas (7), (9), (14), and (18) to obtain the hydraulic flushing hole volume :
2.3. Drawing of the Hole Shape Equation Based on MATLAB
According to the field hydraulic flushing test parameters, and , substituted into formulas (9), (10), and (14), the length of the hydraulic flushing coal section is 4.1 m. The deduced BR-PKN equation applicable to the production of the hydraulic flushing cinder is drawn in three dimensions by MATLAB. As shown in Figure 2, the section of the hydraulic flushing hole shape is expressed. It is found that the shape of the hydraulic flushing hole is an ellipsoid with the top slightly larger than the bottom, and the horizontal section ( section) of the hole is an approximate ellipse.
(a) Hydraulic flushing hole shape
(b) section ()
(c) section ()
(d) section ()
3. Results
The shape test of the hydraulic flushing hole was carried out in the 14250 working face of the Xin’an mine. The coal rock occurrence of the 14250 working face is generally as follows: strike 45°, dip 135°, dip angle of the No. 21 coal seam 6~9°, coal seam thickness 0.3~13.1 m, average coal thickness 4.1 m, and density . The original gas content of the working face is 4.0~14.0 m3/t, the original gas pressure is 0.4~1.2 MPa, the development of the geological structure is simple, the whole layer of soft coal in coal seam 21 has a firmness coefficient of and strong homogeneity, and the stratum histogram of the Xin’an coal mine is shown in Figure 3.
3.1. Test Method
3.1.1. Test Equipment
The YZD18.5 mine lateral resistivity video imaging logging tool is mainly composed of a probe, host control box, host control panel, and push rod.
The working principle is as follows: select the appropriate detection method according to the demand, then carry out on-site layout and construction, and select the corresponding detection method according to the construction method. The instrument can analyze the rock stratum structure of the borehole through video (layered lithology, rock hole fracture development, water outlet point characteristics, roof separation, etc.) and automatically generate the borehole orientation profile, borehole plane trajectory, and borehole histogram according to the scale through the detection data. And there is a camera ahead, which can realize automatic continuous measurement. With the continuous deepening of the push rod in the hole, the instrument can collect parameters such as different hole section diameters and shapes along the hole direction of hydraulic flushing.
Instrument parameters are as follows: the video resolution is , the probe angle of view is 120°, and the effective sight distance is 300 mm; the data acquisition frequency is 15 points/second; the measurement range of borehole inclination is -90°~90°, and the measurement accuracy is +0.1°; the detection depth is 0~200 m, and the hole depth error is less than 0.5%. Figure 4 shows the YZD18.5 mine lateral resistivity video imaging logging tool.
3.1.2. Test Procedure
(1)Select the drill hole after hydraulic flushing and blow out the coal and rock slag in the hole with compressed air to minimize the residue, ensure the smooth drilling, and maintain the drilling shape after hydraulic flushing to the greatest extent(2)The YZD18.5 mine lateral resistivity video imaging logging tool is used for borehole peeping, the collected video files are analyzed, and the standards including acquisition frequency, frequency, and image definition are formulated after many tests(3)The collected image information is summarized and processed in CAD, the section diagram of the hydraulic flushing hole shape is drawn, and the hydraulic flushing hole shape is analyzed
3.1.3. Data Acquisition and Analysis
When the probe of the YZD18.5 mine lateral resistivity video imaging logging tool enters the borehole, it is necessary to install the centralizer of the corresponding model to ensure that the probe remains in the center of the borehole. The borehole diameter is 113 mm, and the centralizer with a diameter of 93 mm is selected. After the probe enters the borehole, it will collect the hole information on the path. When the probe rod reaches the hole bottom and saves the data, the data acquisition is completed.
Analyze the video files obtained after data acquisition; consider the observation angle of the probe, the effective detection distance of the probe, the forward speed of the probe, the data acquisition frequency, and other factors; and use the intercepting frame function on the premise of ensuring the clarity and high accuracy of the image according to the actual test on the site. It plans to collect images every 0.15 m along the hole axis and every 90° along the hole circumference. The gray value of the collected image information is analyzed by the schlieren method, the spatial position information contained in the hole section is obtained, and the hole shape section is drawn and shown in Figures 5 and 6 [30].
3.2. Data Processing
Draw 68-08#, 9-03#, and 7-09# (3 hole shapes). Among them, the 68-08# hole has no hydraulic flushing, while the 9-03# hole and 7-09# hole are hydraulic flushing holes. The hole patterns are shown in Figures 7–9, respectively.
In Figures 8 and 9, the and sections show ellipsoid-like spheres whose upper part is slightly larger than the lower part, and the right side is slightly larger than the left side, and the maximum values of the long semiaxis and short semiaxis are obtained at about . The section shows an approximate ellipse, and the values of and are close to a fixed value. The cross-sectional view of the hole shape is roughly the same as the three-dimensional display of the BR-PKN equation deduced in MATLAB; that is, the hole shape after flushing is an ellipsoid with a slightly larger top than the bottom.
4. Discussion
The hole shape of hydraulic flushing is restricted by many factors such as coal rock bulk gravity, coal rock friction, water force, and stress. Through theoretical derivation, it is found that the hole shape is ellipsoid-like. In order to verify the feasibility of the BR-PKN equation and verify that the hole shape is ellipsoid, the hydraulic flushing test was carried out in the cutting bottom plate roadway of the 14250 working face in the Xin’an mine. Using the COMSOL Multiphysics simulation software, the effective extraction radius and effective extraction range of the holes that are equivalent to an ellipsoid and the holes that are equivalent to a cylinder are studied under the conditions of setting the extraction time as 90 days and the same coal yield [31–35].
4.1. Test Data Analysis
After the test, the holes with different coal thicknesses in the bottom slab roadway of the 14250 working face are selected to collect the drilling parameters of hydraulic flushing. See Table 1 for specific drilling parameters.
In Table 1, coal extraction volume is composed of coal extraction volume from hydraulic flushing and coal extraction volume from drilling. By substituting test data into equation (17), parameters and are fitted. Figure 10 shows the comparison between the actual coal output and the calculated coal output.
As can be seen from Figure 10, with the increase of coal thickness from the borehole, coal output presents a rising trend, and the average coal output per meter increases with the increase of coal thickness. The coal thickness of hole 9-03# is 2.60 m, and the actual average coal output is 0.54 t/m. The coal thickness of hole 11-09# is 7.60 m, and the actual average coal yield is 1.46 t/m; that is, the average coal yield from hole 11-09# increases with the increase of coal thickness. The calculated maximum short axis and long axis of the hole also increased, and the ratio of to remained roughly at about 1.20.
4.2. Comparison of the Extraction Radius
The extraction radii of the holes that are equivalent to an ellipsoid derived from the BR-PKN equation and the holes that are equivalent to a cylinder are simulated by the COMSOL Multiphysics software. The area where the gas pressure is reduced to less than 0.74 MPa is considered the influence range of the effective extraction radius. The COMSOL Multiphysics software is adopted, the coal output is set to be 1.00 t/m, the extraction time is 3 months, the drilling spacing is 8.30 m, the hole depth is 4.00 m, and the radius in the horizontal section of the holes that are equivalent to a cylinder is 0.48 m; the drilling sections of the holes that are equivalent to an ellipsoid are different. Here, only the maximum horizontal section and the minimum horizontal section are analyzed. The minimum horizontal section is obtained when it is close to the roof and floor of the coal seam; through the analysis of the drilling section diagram, it is found that the value of the maximum long axis and short axis is about half of the maximum horizontal section. The short semiaxis and long semiaxis of the maximum horizontal section are 0.81 m and 0.96 m, respectively, and the short semiaxis and long semiaxis of the minimum section are 0.41 m and 0.48 m, respectively. The gas pressure distribution around the borehole after 90 days of drainage is shown in Figures 11–13.
Figures 11–13 are, respectively, used to draw the gas pressure contour after 90 days of extraction. The area below 0.74 MPa of the contour is regarded as the effective extraction range. After 90 days of pumping, the effective pumping radius of the holes that are equivalent to a cylinder is greater than 4.15 m, the desorption surface area is 406.28 m2, and the volume of the effective pumping area is 458.92 m3. At this time, there is no pumping blank area between the two boreholes. The maximum section effective extraction radius of the holes that are equivalent to an ellipsoid is greater than 4.15 m, and the effective extraction radius in the long semiaxis direction is 5.70 m. The minimum section effective extraction radius is shorter than 4.15 m, the long semiaxis effective extraction radius is 3.95 m, the desorption surface area is 322.40 m2, and the effective extraction area volume is 524.63 m3.
It is found that the effective extraction radius of the holes that are equivalent to an ellipsoid is 0.95 times that of the holes that are equivalent to a cylinder, the desorption surface area is 0.79 times that of the holes that are equivalent to a cylinder, and the effective extraction volume is 1.14 times that of the holes that are equivalent to a cylinder. Under the condition that the actual hole shape is ellipsoid-like, the hole layout method of the holes that are equivalent to a cylinder is unreasonable, and it is easy to meet the drainage standard, but there is a drainage blank zone in the drainage evaluation. Arranging boreholes based on the minimum cross-section of the holes that are equivalent to an ellipsoid can effectively avoid the generation of the drainage blank area, improve the gas drainage effect, and ensure the safe production of the mine.
4.3. Enlightenments
(1)The derived BR-PKN equation suitable for describing the characteristics of hydraulic flushing holes and field tests show that the shape of hydraulic flushing holes is an ellipsoid with the top slightly larger than the bottom, rather than the holes that are equivalent to a cylinder(2)The test shows that under the same coal production and extraction time, the minimum short semiaxis of the holes that are equivalent to an ellipsoid is 0.95 times that of the equivalent radius, the desorption surface area of the holes that are equivalent to an ellipsoid is 0.79 times that of the holes that are equivalent to a cylinder, and the extraction volume is 1.14 times that of the holes that are equivalent to a cylinder. If the holes are arranged according to the holes that are equivalent to a cylinder, there is a goaf white belt in the short axis direction of the holes that are equivalent to a cylinder(3)The BR-PKN equation shows that the hole shape is ellipsoid-like, while the effective extraction range of the drilling design based on the holes that are equivalent to a cylinder is too large, which is easy to produce goaf, so it is no longer applicable. Dense drilling should be arranged during the drilling layout to ensure the extraction effect(4)At present, the hydraulic flushing process generally arranges extraction drilling holes according to the holes that are equivalent to a cylinder, which may produce problems such as empty belt extraction and uneven antireflection transformation, which restricts the safe and efficient production of the mine. To solve these problems, on the one hand, optimize the hydraulic flushing drilling layout parameters, and on the other hand, improve the existing hydraulic flushing method and process and learn from the protective layer mining theory. A certain layer of the coal seam is selected for pressure relief of the water jet out of coal to realize the purpose of pressure relief, permeability enhancement, and gas extraction of the whole layer
5. Conclusions
(1)Based on the Bergmark-Roos ore drawing theory and PKN model, the BR-PKN equation suitable for describing the hydraulic flushing hole shape is established. The hole shape map after hydraulic flushing in three-dimensional space is drawn in the MATLAB software, and the characteristic parameters of the hydraulic flushing hole shape are determined(2)In the Xin’an mine, the imaging video in the punched hole is obtained by using the YZD18.5 mine lateral resistivity video imaging logging tool, and the hole shape section is drawn. The results show that the three sections of the hole after flushing are approximately oval. The field test data are verified with the theoretical data calculated by the BR-PKN equation, which shows that the BR-PKN equation has high accuracy(3)The COMSOL software is used to study the effective extraction radius of the holes that are equivalent to a cylinder and the holes that are equivalent to an ellipsoid. The research shows that under the condition of the same coal yield, after 90 days of extraction, the current effective extraction radius and effective extraction range calculated based on the holes that are equivalent to a cylinder are greater than those calculated based on the minimum section of the holes that are equivalent to an ellipsoid. This shows that the effective extraction radius and extraction range obtained by the current holes that are equivalent to a cylinder model are actually too large, which has the risk of producing the extraction blank zone(4)The current research is on the basis of vertical coal seam bedding drilling, but in the field practice, more hydraulic flushing hole forms are also affected by coal seam inclination, drilling inclination, and other factors. It is necessary to further study the hole shape characteristics under the condition of multifactor coupling in order to provide a theoretical basis for optimizing the design and evaluation of extraction drilling
Data Availability
All data generated or analyzed during this study are included in this published article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Authors’ Contributions
Tianxiang Jing and Sen Xu contributed to the writing of the manuscript. Dequan Xuan, Shixiong Hu, and Yong Li made a contribution to the fieldwork, and Xiao Liu revised the manuscript. All authors have read and agreed to the published version of the manuscript.
Acknowledgments
This study was supported by the Youth Project of the National Natural Science Foundation of China (51804100), the Scientific and Technological Research Project in Henan Province (No. 202102310289), and the 2015 Henan Science and Technology Breakthrough Project (152102310095).