Coal breakage features and fragment size distribution in water jet drilling for coalbed methane development

Water jet drilling (WJD) technology has been widely used to extract coalbed methane. Coal breakage features and fragment size in WJD determine the drilling efﬁciency. The smaller the coal fragments, the easier the fragments are discharged from hydraulic boreholes. This study discloses the coal breakage features and size distributions of fragments, ﬁeld experiments under the original in-situ stress condition were conducted to obtain the coal fragments generated in WJD. The effects of the jet pressure and coal strength on fragment size distributions were investigated based on the Weibull distribution and fractal model. The results indicate that ﬁne particles dominate the coal fragments and its proportion increases with the increase of jet pressure and the decrease of coal strength. The fragment size distributions accord with the Weibull distribution. The breakage degree index of fragments decreases in the logarithmic form as the jet pressure increases. The coal fragments have the fractal characteristic, and the fractal dimension increases with the increasing jet pressure and decreases with the increasing coal strength. Additionally, the fractal dimension increases with the decreases in breakage degree index. This work could provide a guide for research on the coal fragments transportation and


INTRODUCTION
High-pressure water jets have been widely used for rock and coal fragmentation in the field applications of oil and gas exploration and development [1][2][3]. Due to the unique advantages, such as high efficiency, dust-free, heat-low and vibrationlow performance, the applications of water jets have become increasingly prominent in improving the permeability of coal seams in recent years [4]. For instance, hydraulic punching, water jet slotting and water jet drilling have been developed to improve the coalbed methane drainage in underground coal mines [5][6][7]. Among these techniques, water jet drilling (WJD) in coal seam is a highly efficient type of drilling method. Compared with the conventional drilling technology, it has many operational advantages of convenient power transmission, high rock-breaking efficiency, slight bit wear and no spark in drilling process and so forth [8]. impingement but also have a dramatic influence on slag discharge from boreholes. It is easy to cause sticking and serious friction resistance without a good slag-flushing ability. Therefore, it is very necessary to study the coal breakage features and size distribution of fragments impacted by high-pressure water jet in WJD. Many researches have focused on the distributions of rock fragments from various impact fragmentations. Hogan et al. analysed the dynamic fragmentation of granite for impact energies of 6-28 J [9]. The size distributions of coal and rock fragments (granite, slate and sandstone) were investigated by using the split Hopkinson pressure bar system, respectively; and the effects of impact stress on the fracture energy consumption were studied [10][11][12]. Different methods including scanning electron microscope (SEM) and 3D laser scan were used to obtain the information of fragments with different sizes for rockburst samples and to analyse the fragmentation degree and characteristics of energy conversion [13,14]. Based on the fractal theory, Liu et al. studied the distribution laws of coalcutting size and analysed the effects of coal strength and cutting parameters on the fractal dimension [15]. Jiang et al. adopted Weibull distribution to investigate the effects of impact velocity on the energy and size distribution of rock crushing and established the fracture energy consumption expression of rock impact crushing [16]. However, rock fragmentation via high-pressure water jet impact is a very complicated process, involving the fluid-solid coupling problem. This makes the rock breakage different from other impact failure patterns [17]. Moreover, there are few studies to discuss the size distribution of coal fragments under water jet impact. It is still unclear whether the existing analysis methods can be used to study the distribution characteristic of coal fragments generated by water jet impact in WJD. Therefore, in this study, numerous field experiments were carried out to obtain the coal fragments generated by water jet under the original in-situ stress condition. The breakage features of coal fragments for different particle sizes were discussed. Based on the Weibull distribution and fractal theory, the size distribution laws of coal fragments were investigated. Furthermore, the effects of coal strength and jet pressure on the size distributions were analysed. The obtained results would provide a guide for further research on the coal fragments transportation in hydraulic boreholes and selecting the hydraulic parameters in WJD.

SIZE DISTRIBUTION THEORY OF ROCK FRAGMENTS
Some methods have been proposed to describe the size distributions of coal and rock fragments, such as standard distribution, Poisson distribution, log-normal distribution, Weibull distribution and fractal theory and so forth. Among these size distribution models based on the data analysis of a large number of coal and rock fragmentation, the Weibull distribution model and fractal theory have been confirmed to be very suitable for fragments size distribution [16]. Therefore, in this study, the Weibull distribution and fractal theory will be introduced to investigate the size distribution of coal fragmentation under high-pressure water jet impact.

Weibull distribution model
Existing studies indicate that the Weibull distribution is one of the most effective methods for characterising the physical properties of rock fragmentation because it links the macroscopic mechanical behaviour and microscopic mechanical properties of rock [15,18,19]. For instance, Jiang et al. [16] and Liu et al. [15] adopted the Weibull distribution to investigate the size distribution of rock crushing; Cheong et al. [19] used the two-parameter Weibull distribution equation to characterise the fragment size distribution of fractured glass spheres. These experimental results were in good agreement with the Weibull distribution function. Therefore, in this study, the Weibull function was used to describe the particle-size distribution of coal fragments in WJD. Rosin and Rammler proposed the theoretical model of Weibull distribution by comparing many experimental results with the expression [20]. The Weibull distribution model can be described as follows [21]: where W is the mass ratio of rock fragments not larger than a certain size d to total mass%; d 0 is the fragment size that the cumulative mass of fragments sizing smaller than d 0 accounts for 63.2% of the total mass, indicating the breakage degree of rock (breakage degree index (BDI)), mm; m is the characteristic index of rock fragmentation (breakage characteristic index (BCI)), which depends on the rock properties and is usually 0.4-1.3. In order to better analyse the size distribution laws, a natural logarithmic transformation is taken for formula (1), and the equation can be described as where F(d) is the cumulative mass distribution function of rock fragments not larger than a certain size d.

Fractal theory
Fractal theory can be used to quantitatively describe the complex morphology, such as extremely irregular shapes and distribution characteristic of fragments [22,23]. Therefore, the fractal method has been adopted to analyse fragmentation characteristics of coal and rock fragments for rockburst, blasting, impact loading and uniaxial compression and so forth [11,13,24,25]. Based on the relationship between number and size in a statistically self-similar system, the fractal definition can be given and defined by the following equation: where N(x > x i ) is the cumulative number of fragments larger than a certain size x i , k is the number of elements at a unit length scale, and D is the fractal dimension. The greater the D, the more serious the fragmentation degree. However, it is very difficult to accurately obtain the number and sizes of fragments. To overcome this problem, the cumulative mass frequency is selected to estimate the fractal dimension of the fragments according to the following expression [14]: where M R is the cumulative mass of fragments smaller than R; M is the total mass of the fragments.

MATERIALS AND METHODS
As for rock fragmentation under high-pressure water jet impact, it is very difficult for a laboratory to restore the original in-situ stress in actual engineering coal seams, which causes the coal mass to split. This will lead to a huge difference between the split fragments and actual coal fragments of WJD in the coal seam. In this study, in order to obtain the actual coal fragments under in-situ stress environment, field experiments of WJD with different coal strengths and jet pressures were conducted by utilising the water-jet bit.

Experimental devices of WJD
As shown in Figure 1, the WJD system is mainly composed of a high-pressure pump, water tank, pressure control system, winch, flexible high-pressure hose, collection box of coal fragments and a water-jet bit. The main performance parameters of these devices are described below: 1. High-pressure pump. This is a five-plunger high-pressure pump with a rated pressure of 56 MPa and a rated flow of 200 L/min. 2. Pressure control system. It mainly includes a relief valve and a pressure gauge. The aim is to adjust the system pressure expediently. 3. Winch. Its aim is to twine orderly the flexible high-pressure hose. Furthermore, it can realise the high-pressure water transmission between the linear motion of high-pressure water pipe and the circumference roll of winch through the high-pressure sealing rotator. 4. Flexible high-pressure hose. It is used as the working pipe to convey high-pressure working fluid to break coal. It has an inner diameter of 10 mm, an outer diameter of 17 mm, a minimum bending radius of 90 mm, a working pressure of 60 MPa and a bursting pressure of 135 MPa.
5. Water-jet bit. As the most critical component of WJD, the self-propelled multi-nozzles bits are used in the experiments due to the compact structure, low energy consumption, and high rock-breaking efficiency [26,27]. The multi-nozzles bit has one centre nozzle, four forward lateral nozzles with an axial diffusion angle of 25 degrees, and eight backward nozzles with an axial diffusion angle of 30 degrees. The nozzle diameter is 0.8 mm as shown in Figure 2. The working principle of borehole formation for the multi-nozzles bit is as follows: The forward nozzles (including centre nozzle and lateral nozzles) generate the high-velocity jets to break up the coal in front of it and form a borehole. While the backward nozzles form backward jets to generate the self-propelled force to pull the hose moving forward and have the functions of further breaking coal to expand the borehole diameter and discharging slags. Thus, the coal fragments discharged from hydraulic boreholes are entirely caused by the high-pressure water jet impingement. Furthermore, they are collected through the integrated gas-water-fragment capture and separation device, of which the detailed introduction is given in [28].

Field experiments and WJD parameters
Jet pressure is the most important hydraulic parameter in WJD, which determines the jet impact energy. Coal strength is a key parameter used to assess the ability of the coal to resist destruction. Thus, this study mainly focuses on the effects of jet pressure and coal strength on size distributions of coal fragments in WJD. The WJD field trials are carried out at +300N1 rock crosscut of Fengchun coal mine in Songzao mining area (Figure 3(a)). The exposed coal seams are mainly M7 and M8 coal seams (Figure 3(b)). The occurrence conditions and properties of coal seams are as follows: The Protodyakonoy coefficients of M7 and M8 coal seams are 1.1 and 0.5, respectively. The M7 coal seam is hard and in a bulk, while M8 coal seam is soft and

Breakage features of coal induced by water jet
Coal fragments generated by water jet in WJD are classified into seven different degrees based on their sizes. The weight of each degree is taken using a high-precision electronic scale, and the fragment sieving results for the different coal sizes are given in Table 1. To better analyse the mass distribution of fragments in different degrees, the coal fragments are categorised as 'large', 'medium', 'small' and 'line' with respective particle-size ranges of > 12, 3-12, 0.5-3, and < 0.5 mm (Figure 4). Figure 5 shows their mass distribution.
As can be seen from Figure 6, the coal fragments generated by water jet are mainly concentrated in fine particles, including 'line', 'small' and 'medium' particles. The ratio of 'large' particles is very small and is less than 6%. This may be caused by the following reasons: The coal fragmentation and damage induced by water jet in WJD are mainly caused by impact stress wave [29,30]. When high-pressure water jet impacts coal, the following fracture patterns will be formed in coal, namely, the broken pit on the impact surface and the internal cracks surrounding the broken pit, respectively. As illustrated in Figure 6, the internal fractures include circumferential fractures, radial fractures and conical fractures. The former two types of fractures usually occur around the broken pit with a high density of small fractures, which will generate the fine particles. These fractures may be caused by the tensile and shear components of stress wave, respectively. Besides, the high-density fracture zone will expand deeply because the broken pit will move down after the coal fragments is washed away by water flow. As for the conical fractures, they initiate below the broken pit and expand outward. When fractures expand outwards to the free surface or interconnect with circumferential fractures, the macro-cracks will be formed. This behaviour will cause the volume fragmentation, forming the fragments with a large size as marked with ①, ② and ③ in the grey shaded areas. In WJD, the borehole formation in coal seam is the joint results of coal fragmentation impacted by multi high-pressure water jets. So, more cracks will be generated and interconnect with each other. Moreover, coal has abundant joints and fissures. Therefore, the fine particles dominate the coal fragments in WJD. However, due to the propagation of conical fractures and the 'water wedge' effect of high-pressure water, some coal bulks will be spelt off from the original coal mass to form coarse particles. It is difficult to discharge the large fragments from WJD boreholes. As a result, large fragments can easily accumulate in the borehole resulting in sticking and serious friction resistance. Therefore, fragments with large size should be avoided in WJD as much as possible.
It can be drawn from Figure 5 that the mass percentage of fine particles gradually increases with the increase of jet pressure. The mass percentages of 'line' and 'small' particles at the jet pressure of 36 MPa increase by 10.1% and 1.1% than those of 24 MPa, respectively. While the mass percentages of 'medium' and 'large' particles decrease by 7.2% and 3.8%, respectively. The reasons are as follows: The higher the jet pressure, the FIGURE 5 Mass distribution of coal fragments with different particle sizes FIGURE 6 Different fracture patterns inside the coal and rock under water jet impact, and the relationships between crack patterns and fragment sizes. Rock sample from the literature [31] greater the impact energy of coal fragmentation. Furthermore, the impact stress waves with higher energy propagate on the coal surface and inside coal in the form of Rayleigh and volume waves, respectively. The internal particles of coal mass will be subjected to the greater effective stress, such as shear and tensile stresses, causing more damage to coal. Thus, the fragmentation degree is much greater. In addition, it has been found that the number of cracks increased and the secant angle of conical fractures decreased with the increasing jet pressure, respectively [32], thus generating more coal fragments with small sizes.
The coal strength and structure have also important influences on the coal fragmentation degree under high-pressure water jet impact. A higher strength will decrease the breakage degree of coal mass, leading to the increase of the percentage of large fragments in WJD at the same jet pressure. This may be caused by the fact that the higher the coal strength, the fewer the joints and fissures inside coal. It will consume more energy to break the coal into the same size particles compared with the low strength coal mass. Therefore, the following phenomena can be observed that: (i) The particle sizes of WJD in M7 coal seam are much larger than those in the M8 coal seam; (ii) the coarse particles for M7 coal seam are shaped as lumps due to its bulk structure, while the majority of fragments for M8 coal seam become powders.

Weibull distribution laws of the fragments
According to the Weibull distribution model (Equation 2), the relationships between the cumulative mass and fragment sizes for the various jet pressures and coal strength are obtained. The fitting results are shown in Figure 7(a) and Table 2. The fitting correlation coefficients R 2 are 0.97-0.99. In addition, the same method is used to investigate the size distribution of coal fragments collected from WJD in the Wuyang coal mine in the Luan mining area [33]. The R 2 values of fitting curves (Figure 7(b)) reach 0.90-0.99. The fitting results indicate that the Weibull distribution model is very suitable for analysing the size distribution of coal fragments of WJD in coal seam. The BCI m and BDI d 0 of coal fragmentation are related to the coal properties and the hydraulic parameters of the water jet.
The BDI of M7 coal seam is about twice that of the M8 coal seam when the jet pressure is 36 MPa. For WJD in the Wuyang coal mine, the BDI is also larger compared with most BDI of the M8 coal seam in spite of jet pressure of 60-70 MPa. This is caused by coal strength and its structure difference. The coal structure in the Wuyang coal mine is stable and the Protodyakonov coefficient is 0.8-1.0. So, with respect to WJD in M7 and Wuyang coal mines, the fragmentation degree of coal will be less, leading to the increase of mass ratio of large size particles.
To better analyse the size distribution and fragmentation degree of coal impacted by water jet, the effects of the jet pressures on BCI and BDI are investigated. Figures 8 and 9 are the relationships of BCI and BDI versus jet pressures, respectively. It can be found that the BCI increases first and then decreases with the increasing jet pressure, and there is no single growth or decreasing trend. While the BDI decreases logarithmically with the increase of jet pressure, which indicates that the higher the jet pressure, the greater the fragmentation degree of coal under water jet impact. The relationship between  (5) where P is the jet pressure MPa. According to the Weibull distribution laws for different coal strengths and jet pressures, the coal fragmentation degree and characteristic indexes can be predicted by utilising Equations (2) and (5). It will be helpful for optimising the working pressure of water jets and water flow rate of discharging slags in WJD.

4.3
Fractal features of the fragments Figure 10 shows the diagrams of the relative mass versus the relative fragment size for coal fragments of WJD in the coal seam. Furthermore, the fitting results can reveal the fractal feature of coal fragments with different coal strengths and jet pressures. Moreover, the fractal dimensions are also calculated based on Equation (4). On the one hand, the most correlation coefficients of the fitting straight lines are over 0.90, which shows that coal fragments of WJD have the fractal characteristic. On the other hand, the fractal dimensions are determined by the coal strength and hydraulic parameters of the water jet. The fractal dimension of M7 coal seam is smaller than that of M8 coal seam under the same jet pressure due to its higher strength. As shown in Figure 11, the fractal dimension value increases logarithmically with the increasing jet pressure. As a result, the growth rate of fractal dimension gradually slows down with the increase of jet pressure. The relationship between fractal dimension and jet pressure is given in Equation (6). When the jet pressure is 24-36 MPa, the fractal dimension D of coal fragments in M8 coal seam is 2.58-2.69. In addition, Table 3 shows that the fractal dimensions have some relationship with the BDI. The fractal dimensions increase as the BDI decreases, and there is an

CONCLUSIONS
The size distributions of coal fragments generated in WJD were investigated by conducting numerous WJD field experiments under the original in-situ stress condition. Furthermore, the effects of jet pressure and coal strength on the size distributions were analysed. Moreover, the breakage features of coal fragments for different particle sizes were discussed. The main conclusions of this study are as follows: 1. Weibull distribution model is very suitable for studying the size distribution of coal fragments under water jet impingement, and coal fragments have the fractal characteristic and the fractal dimensions are 2.50-2.68. 2. Owing to the impact stress wave induced by high-pressure water jet, fine particles are formed by the circumferential fractures and radial fractures with a high density, whereas the conical fractures cause the volume fragmentation, forming the fragments with large size. The coal fragments in WJD are mainly composed of fine particles (>94%). Besides, the mass percentage of fine particles gradually increases with the increase of jet pressure and the decrease in coal strength.
3. The coal strength, structure and hydraulic parameters have significant influences on the size distribution of coal fragments. The coal fragmentation degree decreases with the increase of its strength and structural integrity. With the increase of jet pressure, there is no single growth or decreasing trend for the BCI, whereas the BDI and fractal dimension of coal fragments in WJD decrease and increases in the logarithmic form, respectively. The fractal dimension obviously increases with the decreasing BDI.