Abstract
To accurately determine the effective extraction radius of directional long drilling, the influence of the negative pressure of the hole mouth, the drilling diameter, and the drilling length of the hole on the effective extraction radius of a directional long drilling hole is simulated by establishing a coal-to-gas gas-structure coupling model considering the Klinkenberg effect. Finally, the reliability of the numerical simulation is verified through field testing in Yuxi Coal Mine. The results reveal that the attenuation of negative pressure in a directional long borehole along a long hole has a significant influence on the gas extraction effect. The radial gas pressure of the extraction drilling hole is distributed in a “V” shape when the negative pressure of the extraction decays along the direction of the hole length. The higher the negative pressure and the longer the diameter of the drilling hole, the higher is the gas extraction effect. The effective extraction radius is exponentially related to the drilled hole depth when the negative pressure of extraction is attenuated along the long hole direction. The negative pressure of the hole and the diameter of the borehole are linearly related to the effective extraction radius at the depth of drilling hole of 430 m. Through field tests, while extracting for 180 days based on the stubble pressing effect, the effective extraction radius of the directional long borehole of the No. 3 coal seam of Yuxi Coal Mine is 5.7 m, and the absolute error between the numerical simulation is 0.1 m. In addition, the gas pressure obtained from different sampling points is consistent with the numerical simulation. The relative error is 0.3–4.1%. The results provide a theoretical basis for the rational layout of directional drilling.
1. Introduction
Presently, China’s main energy supply is coal. It is estimated that the total coal consumption would account for 43% by 2030. Therefore, coal would continue to be an important energy source in China. However, the mining of deep coal resources is imminent because shallow coal seams are being exhausted gradually. In the process of coal mine production, particularly for deep coal seams, the increase in coal seam gas content and gas pressure with the increase in mining depth would increase the demand for coal seam gas extraction technology.
Gas extraction is the main measure to prevent coal and gas prominence. It has been widely promoted and used in high-gas and protruding mines.1,2 In the early days of the founding of the People’s Republic of China, ordinary drilling rigs were mainly used for gas extraction. It was convenient in terms of transportation, rapid installation, efficient construction, and cost savings. Recently, the coverage of extraction drilling holes has been nonuniform owing to the problems of inaccurate positioning, frequent shifting of rigs, large working intensity, small control range, and low efficiency of gas extraction in extracting drilling holes of ordinary drilling rigs. Furthermore, coal and gas protrusion accidents are likely to occur. For example, a major coal and gas accident occurred in the Hancheng Mine of the Shaanxi Liaoyuan Coal Industry on June 10, 2020. It resulted in seven deaths. One of its main causes was the extraction blank belt produced by the drift of the borehole.
Compared with conventional drilling, directional long drilling can accurately control the inclination and azimuth angle of drilling bits in real time (thereby effectively solving the technical problems of large mining surface tendencies and lengths), improve the drilling depth, increase the range and efficiency of gas extraction (thereby effectively solving the problem of mining succession tension), and have the advantages of long extraction times and large control areas. Directional long-borehole gas extraction has been widely used with the development of directional drilling technology.3−5 However, the effective extraction radius of the borehole deep in the coal seam cannot be determined conveniently owing to the gradual decrease in negative pressure in the directional long borehole along the borehole length. If the drilling spacing is excessively small, it would produce a string of holes. This would result in engineering wastage. If the spacing is excessively large, a blank strip of extraction would occur. This would increase the risk involved in coal mine production.6−8 The effective extraction radius of directional long drilling holes is an important basis for the design of extraction drilling holes.9 Therefore, determining a reasonably effective extraction radius for directional long boreholes is highly significant for the design of gas extraction and safe production of coal mines.
Considering the problem of measuring the effective extraction radius of boreholes, scholars have studied these through theoretical analysis,10,11 numerical simulation,12,13 and field experiments.14,15 In terms of numerical simulation, various scholars worldwide have studied the gas-structure interaction model of gas-containing coal and the factors affecting the effective extraction radius. Liang16 established a gas-structure coupling model based on the deformation characteristics of the coal skeleton and the adsorption and desorption characteristics of gas. Hao17 established a coupled model of the creep effect of coal and obtained the effective extraction radius of boreholes at different depths. Yin18 obtained the effective extraction radius of a borehole under mining conditions based on a compressible gas-structure interaction model. Guo19 simulated the effects of the hole negative pressure, extraction time, and drilling diameter on the effective extraction radius. Wang20,21 performed a numerical simulation of directional long drilling holes and analyzed the effects of drilling length and drilling spacing on the gas extraction effect. In terms of field tests, the methods used by scholars worldwide to determine the effective extraction radius of boreholes can be divided into various methods such as the extraction statistics,22 gas content determination,23 and SF6 gas tracing methods.24 For directional long drilling, Liu25 obtained an exponential relationship between the negative pressure in the extraction drilling hole and the drilling length, using a pressure test device in the extraction drilling hole. Duan26 designed a directional long-drilling pre-extraction hole. It substantially improved the efficiency of gas extraction. Wang3 calculated the number of directional long drilling holes and concluded that directional long drilling can improve the efficiency of gas extraction.
It is evident from the above research that in terms of numerical simulation, the predecessors primarily studied the negative pressure in the extraction drilling hole as a constant value. Furthermore, in terms of field tests, they primarily conducted qualitative research on the gas extraction effect of directional long drilling. The effective extraction radius and its influencing factors under the attenuation of negative pressure in directionally long drilled holes along the long direction of holes have been studied insufficiently. Therefore, this study constructs a coal-gas-structure interaction model considering the Klinkenberg effect, with Yuxi Coal Mine as the engineering background. In addition, it uses COMSOL software to simulate and analyze the influence of hole negative pressure, borehole diameter, drilling length, etc., on the effective extraction radius of directional long drilling. Finally, fixed-point sampling is carried out through field tests, the effective extraction radius of directional long boreholes is obtained based on the stubble pressure effect, and the reliability of the numerical simulation is verified. A theoretical basis for directional long-drilling arrangements is provided to improve the efficiency of gas extraction in coal mines.
2. Numerical Simulation of Directional Long Bore Gas
2.1. Mathematical Model of Extraction Drilling
2.1.1. Control Equation for Deformation of a Gas Coal Body
The deformation control equation of a gas-bearing coal body is composed of three parts: the geometric equation, the equilibrium equation, and the constitutive equation. These are combined with the effective stress law of the dual medium. The deformation control equation of the gas-bearing coal body considering the pore pressure is obtained as follows27
 |
1 |
where G is the shear modulus (MPa), ν is the Poisson ratio, λ is the Lame constant, ks is the coal skeleton modulus (MPa), Fi (i = 1, 2, 3) is the volumetric force (MPa), and ui, uj (j = 1, 2, 3) are the displacement components (m).
2.1.2. Coal-Permeability Model
The Klinkenberg effect during the gas seepage process significantly promotes the permeability of the coal body as follows28
 |
2 |
where kg is the gas permeability (m2), k0 is the initial permeability of the coal seam (m2), εv is the volumetric strain, φ0 is the initial porosity of the coal body (%), Δp is the differential pressure (Pa), and bb is the Klinkenberg coefficient (MPa).
2.1.3. Coal-Porosity Model
The porosity of coal represents the ratio of the pore volume of coal to the total volume as follows29
 |
3 |
where φ is the porosity of coal (%).
2.1.4. Gas Seepage Control Equation
The amount of variation in gas in the fracture is equal to the mass of the gas that diffuses into the fracture in the matrix minus the mass of the gas flowing into the borehole by the fracture. The seepage of the gas in the coal seam conforms to the law of conservation of mass. That is, the control equation for the variation in the gas pressure in the fracture of the coal body over time is30
 |
4 |
where α is the equivalent pressure coefficient, a is the maximum adsorption capacity of the coal saturation state (m3/kg), b is the coal body adsorption constant (MPa–1), c is the coal body correction parameter (kg/m3), pn is the atmospheric pressure (kPa), and μ is the dynamic viscosity of gas (Pa·s).
To summarize, joint vertical formulas 1–4 constitute a coal-gas-structure interaction model considering the Klinkenberg effect. COMSOL software can be used to simulate gas extraction to study and verify the gas extraction effect of directional drilling.
2.2. Physical Model of Extraction Drilling
A physical model with a coal body size of 400 m × 600 m (axial length × radial length) is established according to the actual situation of the 1304 working surface of Yuxi Coal Mine. Furthermore, five cross sections perpendicular to the drilling hole are set in the model. The borehole openings are 0, 140, 360, 430, and 500 m. The length of the five sections is 30 m. Simultaneously, a cross section parallel to the extraction drilling hole is set up at a distance of 5 m from the extraction drilling hole, and its length is 500 m (see Figure 1). The physical parameters of the model are listed in Table 1.
Figure 1.
Physical model of a directional long borehole.
Table 1. Model Physical Parameters.
| symbol | parameter name | value | unit | symbol | parameter name | value | unit |
|---|---|---|---|---|---|---|---|
| d | drilling diameter | 113 | mm | ks | Coal skeleton modulus | 4068 | MPa |
| pn | standard atmospheric pressure | 101.3 | kPa | α | Equivalent pressure coefficient | 0.667 | |
| bb | Klinkenberg coefficient | 0.11 | MPa | ρgs | Gas density in the standard state | 0.716 | kg/m3 |
| p0 | coal seam raw gas pressure | 2.6 | MPa | a | Maximum adsorption capacity of coal saturation state | 0.015 | m3/kg |
| μ | dynamic viscosity of gas | 1.1 × 10–5 | Pa·s | b | Coal body adsorption constant | 6.019 | MPa–1 |
| k0 | initial penetration rate | 8.7 × 10–15 | m2 | φ | Initial porosity | 0.2 | |
| c | coal body correction parameters | 1580 | kg/m3 | pc | Negative pressure at the orifice | 27 | kPa |
2.3. Initial and Edge Conditions
Initial conditions: At t = 0, the original gas pressure is 2.6 MPa. According to a previous study,25 the initial permeability of the coal seam is 4 × 10–15 m2, the negative pressure of the orifice is 27 kPa, the drilling diameter is 113 mm, and the negative pressure in the directional long borehole is attenuated gradually along the direction of the hole length as follows
 |
5 |
Stress boundary conditions: The initial displacement
of the stress field is 
, the stress on the top boundary of the
coal seam is 8 MPa, and the lower boundary of the coal seam and the
boundary on both sides are fixed constraints.
2.4. Study on the Effect of Gas Extraction with Negative Pressure Change in Directional Long Boreholes
When the extraction time is 180 days, the negative pressure in the hole is attenuated along the hole length according to the variation law of formula 5. The pressure distribution of the extraction drilling gas is shown in Figure 2.
Figure 2.
Effect of negative pressure distribution in the extraction borehole on the gas extraction effect.
As shown in Figure 2, the gas in the coal seam is extracted continuously by the borehole. This forms a contour line of the gas pressure similar to a concentric circle with the drilled hole as the axis. At the bottom of the extraction drilling hole, the gas pressure contour distribution is the densest, and the gas extraction effect is the worst. At the location of the borehole hole, the gas pressure contour is the most sparsely distributed, and the gas extraction effect is the best. The effect of gas drainage at the hole bottom is mainly affected by the large amount of gas gushing from the hole bottom.
It is established that the daily coal production of Yuxi Coal Mine is 7116 t. According to Article 27 of the Interim Regulations on Coal Mine Extraction Standards (2011), the amount of desorbed gas of the coal before coal mining on the working surface should be ≤5 m3/t. According to the index of deducible gas content required by the working surface and the measured nondesorbed gas content of the No. 3 coal seam in Yuxi Coal Mine (2.6 m3/t), the gas content ≤ 7.6 m3/t should be satisfied to achieve the gas extraction standard of the coal mining work surface. The pressure of the coal seam gas is calculated using Langmuir’s equation and the industrial analysis data of the No. 3 coal seam of Yuxi Coal Mine as follows
 |
6 |
where W is the gas content of the coal seam (m3/t), a1, b1 are the adsorption constants, p is the absolute gas pressure of the coal seam (MPa), Ad is the ash content of coal (%), Mad is the moisture of coal (%), n is the porosity of coal (m3/m3), and ρs is the apparent density (t/m3).
The gas content of formula 6 (i.e., 7.6 m3/t) corresponds to a gas pressure of 0.29 MPa. This satisfies the requirements of the “Detailed Rules for the Prevention and Control of Coal and Methane.” That is, the radius of this concentric circle is called the effective extraction radius when the gas pressure of the concentric circle around the extraction drill hole is less than 0.29 MPa.
The gas pressure variation curve parallel to sections 6-6 of the extraction drilling hole is drawn (see Figure 3) to study the gas extraction effect of directional long drilling along the hole length.
Figure 3.
Change law of gas pressure at cross sections 6-6.
As shown in Figure 3, the residual gas pressure parallel to the location of the extraction drilling hole is distributed in a “V” shape when the negative pressure in the hole is exponentially attenuated. After extraction for 180 days, the residual gas pressure from the borehole mouth of 5 m and the hole depth of 0–430 m is a diagonal line. It increases from 0.24 to 0.27 MPa. The residual gas pressure with a hole depth of 430–500 m is affected by the gas flowing out of the bottom of the borehole hole, and the maximum gas pressure at the bottom of the drilling hole is 0.63 MPa. Therefore, to prevent the extraction of blank belts along the length of the drilled hole in the directional long drilling hole, the negative pressure in the directional long drilled hole should be considered when gas extraction is attenuated gradually along the drilling length.
2.5. Effective Extraction Radius Analysis of Directional Long Drilling
The gas pressures of 1-1, 2-2, 3-3, 4-4, and 5-5 at cross sections of 0, 140, 360, 430, and 500 m of the borehole are extracted to obtain the effective extraction radius at different locations of the directional long drilling hole under an equal extraction time. Furthermore, a gas pressure of 0.29 MPa is considered the critical value. The effective extraction radius of the hole negative pressure is 27 kPa, the drilling diameter is 113 mm, and the drilling length is 500 m. The effective extraction radius of the directionally long drilled hole at different locations is drawn as shown in Figure 4.
Figure 4.
Effective extraction radii at different cross-section locations.
As shown in Figure 4, at the same location, the effective extraction radius increases gradually with the increase in extraction time. In addition, the farther away one is from the drilled hole, the smaller is the effective extraction radius of the directional long drilling hole at an equal extraction time. Because of the large amount of gas at the bottom of the borehole, the effective extraction radius is reduced substantially at the depth of 430 m under different extraction times, and the effective extraction radius after 180 days at the bottom of the borehole is 0.6 m. If the effective radius is 0.6 m cloth hole, it would cause considerable engineering wastage. Therefore, an effective extraction radius of 5.6 m after extraction for 180 days at a hole depth of 430 m is selected as the design basis. A borehole with a hole depth of 430–500 m is used as a stubble drilling hole. The gas extraction effect is not tested. This can reduce the amount of construction required and improve the efficiency of gas extraction.
By fitting the effective extraction radius at different cross-sectional locations in Figure 4, the drilling depth after extraction at 30, 60, 120, and 180 days under a negative pressure of 27 kPa, drilling diameter of 113 mm, and borehole length of 500 m is exponentially related to the effective extraction radius. The minimum fitting degree is 0.954, as shown in Table 2.
Table 2. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times.
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.4–6.9) × 10–5 e0.02x | 0.975 |
| 60 | R = 3.7–0.001 e0.016x | 0.954 |
| 120 | R = (5.0–1.1) × 10–6 e0.03x | 0.975 |
| 180 | R = (6.8–7.8) × 10–5 e0.02x | 0.995 |
3. Analysis of Influencing Factors of Effective Extraction Radius of Directional Drilling
3.1. Analysis of the Influence of Pore Negative Pressure on the Effective Extraction Radius
To study the effect of negative pressure of the orifice on the extraction effect of the directional long borehole gas, the gas pressure field distribution after 180 days of extraction is plotted (see Figure 5) by maintaining the coal seam gas pressure at 2.6 MPa, maintaining the borehole diameter at 113 mm, and setting the negative pressure of the orifice to 33 and 40 kPa; the distribution of negative pressure is as follows: px1 = 33 × e–0.0005x and px2 = 40 × e–0.0004x (kPa).
Figure 5.
Gas pressure field under 33 and 40 kPa orifice negative pressure.
As shown in Figure 5, as the negative pressure of the orifice increases, the value of the gas pressure contour line decreases at the same position. Under an equal extraction time, the higher the negative pressure of the orifice, the better is the gas extraction effect. Under an equal extraction time and negative hole pressure, the gas extraction effect deteriorates as the drilling depth increases.
To obtain the relationship between the drilling depth and the effective extraction radius under the negative pressure of different holes, the gas pressures of 1-1, 2-2, 3-3, 4-4, and 5-5 at the cross sections of 0, 140, 360, 430, and 500 m of the borehole are extracted. The effective extraction radii of the hole negative pressure are 33 and 40 kPa. The effective extraction radius of the directionally long drilled hole at different locations when the hole negative pressure is 33 kPa is shown in Figure 6. The effective extraction radius of the directionally long drilled hole is determined at different locations with a negative pressure of 40 kPa (see Figure 7).
Figure 6.
Effective extraction radius at different cross-section locations (33 kPa negative pressure at the aperture).
Figure 7.
Effective extraction radius at different cross-section locations (40 kPa negative pressure at the aperture).
The relationship between the effective extraction radius and the drilling depth of the hole with the negative pressures of the hole mouth of 33 and 40 kPa at different extraction times is obtained by fitting the effective extraction radius at different cross-sectional locations in Figures 6 and 7. The fitting degree is higher than 0.960, as shown in Tables 3 and 4.
Table 3. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Hole Negative Pressure Is 33 kPa).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.5–8.7) × 10–7 e0.03x | 0.980 |
| 60 | R = (4.0–2.1) × 10–4 e0.02x | 0.960 |
| 120 | R = (5.3–1.1) × 10–5 e0.03x | 0.980 |
| 180 | R = (7.0–7) × 10–5 e0.02x | 0.992 |
Table 4. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Hole Negative Pressure Is 40 kPa).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.7–2.1) × 10–6 e0.03x | 0.994 |
| 60 | R = (4.3–3.0) × 10–5 e0.02x | 0.998 |
| 120 | R = (5.8–1.2) × 10–4 e0.02x | 0.993 |
| 180 | R = (7.3–9.6) × 10–7 e0.03x | 0.998 |
When the negative pressure of the hole mouth is 33 kPa, the effective extraction radius of the directional long borehole extraction of 180 days is 7.2 m, the effective extraction radius of 180 days at the hole depth of 430 m is 5.8 m, and the effective extraction radius of the bottom of the hole extraction of 180 days is 0.7 m. When the negative pressure of the hole is 40 kPa, the effective extraction radius of the directional long borehole extraction of 180 days is 7.4 m, the effective extraction radius of 180 days at the hole depth of 430 m is 6.6 m, and the effective extraction radius of 180 days at the bottom of the hole is 7.3 m. To summarize, the higher the negative pressure of the orifice, the higher is the effective extraction radius of the borehole. This primarily occurs because the higher the negative pressure in the pore, the higher is the pressure gradient formed with the pressure of the coal seam methane, and the more conducive it is to gas extraction.
The effective extraction radius at the hole depth of 430 m decreases sharply under different negative pressures. Owing to the influence of the drilling stubble compression effect, the effective extraction radius of the borehole depth of 430 m under an equal extraction time and different hole negative pressures is plotted (see Figure 8) to obtain the relationship between the effective extraction radius and the negative pressure of the borehole at a depth of 430 m.
Figure 8.
Negative pressure of the hole and the effective extraction radius at the bottom of the drilled hole.
As is evident from Figure 8, under the negative pressures of orifice of 27, 33, and 40 kPa, with the increase in extraction time, (1) the increase in the effective extraction radius increases with an increase in the negative pressure of the orifice, and (2) the negative pressure of the orifice and the effective extraction radius of the borehole depth of 430 m are in line with the linear relationship. The fitting degree is greater than 0.950, the slope is the largest at 180 days, and the maximum slope is 0.15 (see Table 5).
Table 5. Relationship between the Negative Pressure at the Orifice and the Effective Pumping Radius at the Hole Depth of 430 m.
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = 0.89 + 0.04pc | 0.950 |
| 60 | R = 1.15 + 0.06pc | 0.996 |
| 120 | R = 1.48 + 0.09pc | 0.961 |
| 180 | R = 0.57 +0.15pc | 0.950 |
The gas pressure in the intercept 6-6 parallel to the extraction drilling hole and 5 m from the drilled hole is extracted (see Figure 9) to obtain the gas extraction effect along the drilling length under the negative pressure of different holes.
Figure 9.
Gas pressure change rule of the lower sections 6-6 with the borehole diameters of 89 and 94 mm.
As shown in Figure 9, under the condition of negative pressure at different orifices, the gas pressure is a diagonal line that does not parallel the extraction of the drilled holes. When the negative pressure of the orifice is 33 kPa, after extracting for 180 days, the residual gas pressure at the hole depth of 0–393 m is a diagonal line. It increases from 0.23 to 0.25 MPa. When the negative pressure of the orifice is 40 kPa, after extracting for 180 days, the residual gas pressure at the hole depth of 0–419 m is a diagonal line. It increases from 0.22 to 0.25 MPa. Thereby, as the drilling depth increases, the negative pressure of the hole increases, and the coal seam gas pressure increases at a lower rate along the drilling length.
3.2. Analysis of the Influence of Borehole Diameter on the Effective Extraction Radius
To study the effect of borehole diameter on the extraction effect of directional long borehole gas, the gas pressure field distribution after 180 days of extraction is plotted (see Figure 10) by maintaining the coal seam gas pressure at 2.6 MPa and the negative pressure of the hole mouth at 27 kPa, and setting the drilling diameters to 89 and 94 mm; the distribution of negative pressure follows px3 = 27 × e–0.0008x and px4 = 27 × e–0.0006x (kPa).
Figure 10.
Gas pressure field with borehole diameters of 89 and 94 mm.
As shown in Figure 10, as the diameter of the borehole decreases, the gas pressure contour increases at the same location. At an equal extraction time, the larger the drilling diameter, the better is the gas extraction effect. For equal extraction time and drill diameter, the gas extraction effect deteriorates as the drilling depth increases.
To determine the relationship between the drilling depth and the effective extraction radius under different drilling diameters, the gas pressures of 1-1, 2-2, 3-3, 4-4, and 5-5 at the cross sections of 0, 140, 360, 430, and 500 m of the borehole are extracted. Furthermore, a gas pressure of 0.29 MPa is considered the critical value. The effective extraction radii of the drilling hole diameter are 89 and 94 mm, and the effective extraction radius of the directionally long drilling hole at different locations is plotted when the drilling diameter is 89 mm (see Figure 11). The effective extraction radius of the directionally long drill hole is drawn at different locations with a drill diameter of 94 mm (see Figure 12).
Figure 11.
Effective extraction radius at different cross-section locations (drilling diameter of 89 mm).
Figure 12.
Effective extraction radius at different cross-section locations (drilling diameter of 94 mm).
By fitting the effective extraction radius at different cross sections in Figures 11 and 12, it is observed that the drilling depth and effective extraction radius are exponentially related to the drilling hole diameters of 89 and 94 mm at different extraction times. Moreover, the fitting degree is higher than 0.906 (see Tables 6 and 7).
Table 6. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Drilling Diameter of 89 mm).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.1–3.2) × 10–4 e0.02x | 0.995 |
| 60 | R = (3.1–1.5) × 10–4 e0.02x | 0.997 |
| 120 | R = (4.6–2.7) × 10–4 e0.02x | 0.946 |
| 180 | R = (6.2–3.3) × 10–5 e0.02x | 0.906 |
Table 7. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Drilling Diameter of 94 mm).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.2–6.0) × 10–5 e0.02x | 0.998 |
| 60 | R = (3.3–1.5) × 10–4 e0.02x | 0.997 |
| 120 | R = (4.8–2.0) × 10–4 e0.02x | 0.954 |
| 180 | R = (5.5–3.4) × 10–5 e0.02x | 0.943 |
When the borehole diameter is 89 mm, the effective extraction radius of 180 days of the directional long drilling hole is 6.4 m, the effective extraction radius of 180 days at a hole depth of 430 m is 5.2 m, and the effective extraction radius of 180 days of hole bottom extraction is 0.5 m. When the borehole diameter is 94 mm, the effective extraction radius of 180 days of the directional long drilling hole is 6.6 m, the effective extraction radius of 180 days at the hole depth of 430 m is 5.3 m, and the effective extraction radius of 180 days at the bottom of the hole is 0.5 m. To summarize, the larger the diameter of the drilled hole, the larger is the effective extraction radius of the drilled hole. This is primarily owing to the decrease in the diameter of the borehole, increase in the flow rate in the hole, increase in the loss of momentum exchange, increase in the negative pressure loss of 100 m, and decrease in the effective extraction radius.
The effective extraction radius at the hole depth of 430 m decreases sharply under different drilling diameters. Owing to the influence of the drilling stubble compression effect, the effective extraction radius of the borehole depth of 430 m under an equal extraction time and different borehole diameters is plotted (see Figure 13) to obtain the relationship between the effective extraction radius and the diameter of the borehole at a depth of 430 m.
Figure 13.
Diameter of the borehole and the effective extraction radius of the bottom of the borehole.
As can be observed from Figure 13, for drilling diameters of 89, 94, and 113 mm, with the increase in extraction time, (1) the increase in the effective extraction radius increases with the increase in the drilling diameter, and (2) the drilling diameter and the effective extraction radius at the depth of the borehole at 430 m are in line with the linear relationship. The fit is higher than 0.964, the slope is the largest at 180 days, and the maximum slope is 0.02 (see Table 8).
Table 8. Relationship between the Borehole Diameter and the Effective Extraction Radius at the Hole Depth of 430 m.
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = 3.7 + 0.02d | 0.996 |
| 60 | R = 2.0 + 0.02d | 0.996 |
| 120 | R = 0.4 + 0.02d | 0.999 |
| 180 | R = 0.6 + 0.01d | 0.964 |
To obtain the gas extraction effect along the drilling length for different drilling diameters, we extract the gas pressure in sections 5-5 parallel to the extraction drilling hole and 5 m from the drilled hole (see Figure 14).
Figure 14.
Gas pressure change rule of the lower sections 6-6 with the borehole diameters of 89 and 94 mm.
As shown in Figure 14, under different drilling diameter conditions, the gas pressure is a diagonal line that does not parallel the extraction of the borehole. When the borehole diameter is 89 mm, the residual gas pressure at the hole depth of 0–339 m is a diagonal line after extraction of 180 days. It increases from 0.24 to 0.25 MPa. When the negative pressure of the orifice is 94 mm, the residual gas pressure at the hole depth of 0–342 m is a diagonal line after extraction of 180 days. It increases from 0.24 to 0.25 MPa. Thereby, as the drilling depth increases, a larger drilling diameter results in a slower increase in the seam gas pressure along the drilling length.
3.3. Analysis of the Influence of Drilling Hole Length on the Effective Extraction Radius
To study the influence of the drilling length on the extraction effect of the directional long borehole gas, the gas pressure of the coal seam gas is maintained at 2.6 MPa, the negative pressure of the orifice is 27 kPa, the drilling diameter is 113 mm, the drilling length is set to 300 and 800 m, and the gas pressure field distribution after extraction for 180 days is plotted (see Figure 15). The distribution of negative pressure follows px5 = 27 × e–0.001x and px6 = 27 × e–0.0005x (kPa).
Figure 15.
Gas pressure field under the borehole length of 300 and 800 m.
As shown in Figure 15, the gas pressure contour lines remain essentially unaltered at the same location as the length of the borehole decreases. At equal extraction time and drill length, the gas extraction effect deteriorates as the drilling depth increases.
To obtain the relationship between the drilling depth and the effective extraction radius under different drilling lengths, the gas pressures of 1-1, 2-2, 3-3, 4-4, and 5-5 of the truncated line from the drilling port 0, 100, 200, 250, and 300 m are extracted under the condition that the drilling hole length is 300 m. The gas pressures of 1-1, 2-2, 3-3, 4-4, and 5-5 of the truncated line from the drilling port 0, 140, 360, 500, and 800 m are extracted under the condition that the drilling hole length is 800 m. Furthermore, the gas pressure of 0.29 MPa is considered the critical value to obtain the effective extraction radius under the condition that the drilling lengths are 300 and 800 m. The effective extraction radius of the directionally oriented long drill hole is drawn at different locations with a drill diameter of 300 m (see Figure 16) and a drill length of 800 m (see Figure 17).
Figure 16.
Effective extraction radius at different cross-section locations (drill length of 300 mm).
Figure 17.
Effective extraction radius at different cross-section locations (drill length of 800 mm).
By fitting the effective extraction radius at different cross-sectional locations in Figures 16 and 17, it is observed that the drilling depth and effective extraction radius are exponentially related to the drilling hole lengths of 300 and 800 m under different extraction times. Furthermore, the fitting degree is higher than 0.953 (see Tables 9 and 10).
Table 9. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Drilling Length of 300 m).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = (2.3–3.3) × 10–5 e0.04x | 0.994 |
| 60 | R = 3.7–0.006 e0.02x | 0.953 |
| 120 | R = (5.1–6.8) × 10–4 e0.03x | 0.990 |
| 180 | R = (6.5–1.1) × 10–4 e0.04x | 0.994 |
Table 10. Relationship between Drilling Depth and Effective Extraction Radius at Different Extraction Times (Drilling Length of 800 m).
| extraction time (days) | valid extraction radius fitting formula | degree of fit |
|---|---|---|
| 30 | R = 2.4–0.04 e0.005x | 0.998 |
| 60 | R = 4.2–0.4 e0.003x | 0.978 |
| 120 | R = 5.2–0.13 e0.005x | 0.999 |
| 180 | R = 6.7–0.07 e0.006x | 0.999 |
When the drilling length is 300 m, the effective extraction radius of 180 days of directional long drilling hole extraction is 6.6 m, the effective extraction radius of 180 days at a depth of 187 m is 5.6 m, and the effective extraction radius of 180 days of hole bottom extraction is 0.5 m. When the drilling length is 800 m, the effective extraction radius of 180 days of directional long drilling hole extraction is 25.7 m, the effective extraction radius of 180 days at a depth of 500 m is 5.5 m, and the effective extraction radius of 180 days of hole bottom extraction is 5.6 m. To summarize, the length of the borehole exerts a negligible influence on the gas extraction effect of an equal depth of the borehole. This is mainly owing to the fact that the flow of drilled holes of different lengths at an equal hole depth decreases with the increase in the drilling length. The smaller the flow rate in the hole, the smaller is the momentum exchange loss, and the smaller is the negative pressure loss of 100 m in the hole. Furthermore, the negative pressure at the bottom of the hole with different drilling lengths is equal. That is, the gas extraction effect at the bottom of the drilled hole is identical.
4. Results and Discussion
4.1. Test Location
The working surface of Yuxi Coal Mine 1304 is located in the south of Yuxi Wellfield. On the west side of the central lane, the working surface is stable at the cut eye coal seam, the inclination angle is 0–2°, the average thickness of the coal seam is 5.85 m, the thickness of the coal seam is approximately 0–0.5 m above the bottom plate of 0.93 m, the 0.1–0.5 m clamp is developed below the top plate of the coal seam, and the raw coal gas content is 17–23 m3/t.
Drilling is performed from the 1302 return wind three lanes to the 1304 working surface 26# drilling yard 5# drilling hole fixed-point, and the coal seam gas pressure at different distances from the directional drilling hole after 180 days of extraction is determined. The original seam gas pressure in this control area is 2.6 MPa, the total length of the 5# drilling hole is 500 m, the negative pressure of the hole is 33 kPa, and the drilling diameter is 113 mm.
4.2. Test Principle
Under the condition of the given borehole diameter and negative pressure of drainage, original coal samples around different borehole depths are collected underground, and the residual gas content of coal samples is measured. Then, the gas pressure is calculated using the Langmuir formula. Finally, with 0.29 MPa gas pressure as the critical value, the effective extraction radius at different drill hole depths is obtained.
4.3. Test Steps
Figure 18 shows the layout trajectory of the drilling hole and test hole layout of 26# drill field 5#. As is evident from this figure, the fixed-point coal samples of test holes 1, 2, 3, 4, and 5 are acquired when hole 26# drilling field 5# is extracted for 180 days. Among these, test hole 1 is located at the drilling hole, the sampling point 1-1 is 6 m from the drilled hole, 1-2 is 7 m from the drilled hole, and 1-3 is 8 m from the drilled hole. The construction point of test hole 2 is 140 m away from the borehole orifice, the sampling point 2-1 is 6 m from the extraction drilling hole, 2-2 is 7 m from the extraction drilling hole, and 2-3 is 8 m from the extraction drilling hole. The construction point of test hole 3 is 360 m away from the borehole orifice, the sampling point 3-1 is 6 m from the extraction drilling hole, 3-2 is 7 m from the extraction drilling hole, and 3-3 is 8 m from the extraction drilling hole. The construction point of test hole 4 is 430 m away from the borehole orifice, the sampling point 4-1 is 5 m from the extraction drilling hole, 4-2 is 6 m from the extraction drilling hole, and 4-3 is 7 m from the extraction drilling hole. The construction point of test hole 5 is 500 m away from the borehole orifice, the sampling point 5-1 is 0.5 m from the extraction drilling hole, 5-2 is 1.0 m from the extraction drilling hole, and 5-3 is 1.5 m from the extraction drilling hole.
Figure 18.
26# drill yard 5# directional drilling and test hole construction trajectory.
4.4. Test Results
The residual gas content and gas pressure are determined by sequentially sampling the sampling points described in Section 3.2, after the acquisition is completed. The results of this assay are presented in Table 11.
Table 11. Results of Determination of Residual Gas Content.
| sampling number | 1-1 | 1-2 | 1-3 | 2-1 | 2-2 | 2-3 | 3-1 | 3-2 | 3-3 | 4-1 | 4-2 | 4-3 | 5-1 | 5-2 | 5-3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| residual gas content (m3/t) | 6.88 | 7.47 | 7.85 | 7.08 | 7.66 | 7.85 | 7.28 | 7.85 | 8.22 | 7.08 | 7.66 | 8.04 | 7.28 | 7.85 | 8.22 |
| gas pressure (MPa) | 0.26 | 0.29 | 0.31 | 0.27 | 0.30 | 0.31 | 0.28 | 0.31 | 0.33 | 0.27 | 0.30 | 0.32 | 0.28 | 0.31 | 0.33 |
As shown in Table 11, after extraction for 180 days, the effective extraction radius from the location of the directional long borehole is 7.0 m, and the effective extraction radius at the hole depth of 140 m is 6.8 m. The effective extraction radii at hole depths of 360 m, 430 m, and 500 m are 6.3 m, 5.7 m, and 0.8 m, respectively. Furthermore, the absolute error of the effective extraction radius obtained from Figure 8 in the numerical simulation is 0.1, 0.1, 0.2, 0.1, and 0.1 m. The effective extraction radius vs. drill depth at different locations of the directional long drilling hole after 180 days of extraction is plotted (see Figure 19).
Figure 19.
Effective extraction radius at different hole depth locations of the drilled hole.
As shown in Figure 19, the effective extraction radius decreases gradually with an increase in the drilling depth at an equal extraction time. This is consistent with the results obtained from the numerical simulation. That is, the effective extraction radius at the hole depth of 430 m is reduced abruptly. Considering the influence of the stubble pressure effect on gas extraction, the effective extraction radius of 5.7 m after extraction at the hole depth of 430 m is used as the basis for the directional long drilling hole. The absolute error between the two is 0.1 m compared with the effective extraction radius obtained from the simulation results. For safety purposes, the smallest effective extraction radius of the two is selected as the final result. That is, the effective extraction radius of 180 days in the directional long borehole of the No. 3 coal seam of Yuxi Coal Mine is 5.7 m.
By comparing the gas pressure in Table 11 and Figure 6 with the simulation results, it is concluded that the field measured results are basically consistent with the simulation results, and the relative error is 0.3–4.1%, that is, the simulation results are reliable. At the same time, the data in Figure 19 are fitted, and the relationship between the actual drilling depth and the effective extraction radius of the site is obtained, which is distributed exponentially with a fit of 0.991, namely,
 |
7 |
where R is the effective extraction radius (m) and x is the length from the borehole orifice (m).
5. Conclusions
By constructing a gas-structure interaction model considering the Klinkenberg effect, the gas extraction effect of the negative pressure of a directional long borehole decaying along the hole length direction is simulated using COMSOL software. The following main conclusions are obtained at the site:
-
(1)
The attenuation of the negative pressure in the directional long borehole along the long hole has a higher impact on the gas extraction effect. The radial gas pressure of the extraction drilling hole is distributed in a V shape when the negative pressure of the extraction decays along the direction of the hole length.
-
(2)
The influence of the hole negative pressure, drilling diameter, and drilling hole length on the extraction effect of directional long drilling gas is analyzed. It is concluded that the larger the hole negative pressure and drilling diameter, the better is the gas extraction effect. Furthermore, the drilling length does not affect the gas extraction effect.
-
(3)
The effective extraction radius is exponentially related to the distance from the borehole opening when the negative pressure of the extraction is attenuated along the direction of the hole length. The negative pressure of the hole and diameter of the borehole are linearly related to the effective extraction radius at the depth of drilling hole of 430 m. When the borehole diameter is 113 mm and the negative pressures at the orifice are 27, 33, and 40 kPa, the effective extraction radii of the directional long borehole for 180 days are 5.6, 5.8, and 6.6 m, respectively. When the negative pressure at the orifice is 27 kPa and the diameter of the borehole is 89 and 94 mm, the effective extraction radius of the directional long borehole for 180 days is 5.2 and 5.3 m.
-
(4)
After on-site testing, when extracting for 180 days based on the stubble pressing effect, the effective extraction radius of the directional long borehole of the No. 3 coal seam of Yuxi Coal Mine is 5.7 m. Moreover, the absolute error between the results obtained from the numerical simulation is 0.1 m. In addition, the gas pressure obtained from different sampling points is consistent with the results of the numerical simulation. The relative error is 0.3–4.1%. The results provide a theoretical basis for a rational layout of directional long boreholes in Yuxi Coal Mine.
6. Discussion
Based on the stubble effect, this paper obtains the effective extraction radius of the directional long hole in Yuxi Coal Mine through COMSOL numerical simulation and field test, analyzes the influence mechanism of the gas extraction effect of the directional long hole, and the research results provide theoretical support for the optimal design of the directional long hole.
In this paper, the effective extraction radius of the directional long borehole is studied to guide the layout of extraction. For extraction boreholes, especially directional long boreholes, an effective extraction length can be determined according to the research conclusions.
Acknowledgments
The authors want to thank the anonymous reviewers for their valuable suggestions. The authors express their appreciation of the funding provided by the National Natural Science Foundation of China (Nos. 51874122 and 52074104) and the Key R&D and Extension Projects of Henan Province (222102320050).
The authors declare no competing financial interest.
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