### Building a numerical model

This study utilizes COMSOL numerical simulation software based on the specific conditions of the site to determine the influence of parameters such as elevation angle, azimuth angle (angle with respect to the tunnel wall), and borehole length on the gas drainage effect. doing. A coupled model is constructed by considering the coal seam generation conditions and extraction parameters. Changes in gas concentration are used as an indicator for optimal borehole placement. By studying various influencing factors, the optimal layout parameters of high-level boreholes are determined.

Based on the actual parameters of high-rise boreholes in 24,130 working faces of Pingdingshan Coal Mine, the following parameters were selected in this study: the slope length of the working face is 186 meters, the gof length is 200 meters, the intake and Dimensions of the return airway are 3 × 4 m, the height of the working face is 3 m, the width is 5 m, the height of the cave zone is 15 m, the height of the crushing zone is 45 m, the mined area behind the working face is The length of the unsolid coal is 80 m, and the thickness of the coal in the solid coal area is 11.5 m. The strata above the coal seams in unmined areas are considered rock strata. The geometric model is shown in Figure 1. The model mesh is shown in Figure 2. The elevation angle of the borehole is expressed as: *be*_{1}the angle between the borehole and the coal seam is expressed as: *be*_{2}, the length of the borehole is L. Due to the high computational load of the three-dimensional model, this study only simulates individual boreholes and does not consider interactions between boreholes. The main focus is to optimize the elevation, azimuth, and length of the borehole as the main technical indicators through simulation.

### Numerical model parameters and boundary conditions

The numerical simulation in this paper is based on the relevant physical parameters of Pingdingshan coal mine. The inlet velocity is controlled at 2.5 m/s and the air volume is 1800 m.^{3}/min, the return air outlet is controlled by a pressure difference of 110 Pa between the ends, a high-level borehole is set as the mass outflow boundary, and the extraction flow rate is *q*_{ch4}, the solid coal is set according to the original gas content, and the goaf is set according to the proportion of residual gas. The height of the fracture zone is 45 m, and the height of the collapse zone is 15 m. The relevant parameters are shown in Table 1.

### Analysis of simulation results of the influence of high-level borehole parameters on extraction effectiveness

#### Effect of borehole elevation angle

The elevation angle of a single borehole is set as follows: *be*_{1} = 6°, 9°, 12° and 15°, length of the borehole L = 150 m, angle between the borehole and the coal wall *be*_{1}= 30°, extraction flow rate *q*_{ch4} = 3 meters^{3}/min, extraction time is 240 hours. Figure 3 shows the changes in gas concentration at monitoring points 1#(93,50,30), 2#(93,100,30), and 3#(93,150,30) inside the goaf.

Figure 3 shows that the gas concentration of 1# starts to decrease significantly after 12 h of extraction, and the gas extraction is completed after 50 h. Among the elevation angles tested, the lowest residual gas concentration is found at an elevation angle of 100 °C. *be*_{1} = 12°, which is approximately equivalent to the angle at that time. *be*_{1}= 9°. The highest residual gas concentrations are observed in *be*_{1}= 6°, then *be*_{1}= 15°. The gas concentration of 2# starts to decrease noticeably after 40 hours of extraction, and the gas extraction is completed after 140 hours. Among the elevation angles tested, the lowest residual gas concentration was found at: *be*_{1}= 9°, the highest concentration is observed at *be*_{1}= 6°, and *be*_{1}= 15° gives the second highest concentration. The gas concentration of 3# starts to decrease significantly after 100 hours of extraction, but a certain concentration of residual gas remains even after 240 hours. Among the elevation angles tested, the lowest residual gas concentration was found at: *be*_{1}= 9°, then *be*_{1}= 12°, the highest concentration is observed at *be*_{1}= 6°.

Figure 4 shows that the gas concentration is relatively high. *be*_{1}= 6°, 15°, best case *be*_{1}= 6°, second highest if *be*_{1}= 15°.concentration is relatively low *be*_{1}= 9° or 12°, lowest *be*_{1}= 9°, and for the second lowest *be*_{1}= 12°. This suggests an optimal range of elevation angles.* be*_{1}To increase gas extraction efficiency, the angle should be greater than 6° and maintained between 9° and 12°.

#### Effect of borehole azimuth

Set the azimuth of each borehole to 20°, 30°, 45°, 60°, and the length of the borehole. *L*= 150 m, elevation angle of the borehole *be*_{1}= 9°, extraction time is 240 hours. Figure 5 shows the changes in gas concentration at three monitoring points from 1# to 3# inside the goaf. Figure 5 shows that the gas concentration at 1# starts to decrease significantly after 6 h of extraction, and the gas extraction is completed after 80 h. At this time, the residual gas concentration is lowest when the azimuth is 0.5. *be*_{2}= 30° and 45°, best case *be*_{2}= 20°, and when the second *be*_{2}= 60°. The gas concentration of 2# started to decrease significantly at 42 h after extraction and completely decreased at 180 h after extraction. The minimum concentration of residual gas is: *be*_{2}= 30°, the highest concentration is found at: *be*_{2}= 20°, then *be*_{2}= 45 and 60°. After 100 hours of extraction, the gas concentration of 3# starts to decrease significantly, and a constant concentration of gas remains after 240 hours of extraction. The highest residual gas concentration occurs when: *be*_{2}= 20°, the lowest concentration is found when: *be*_{2}= 30°, then *be*_{2}= 45 and 60°. This indicates that azimuth angles between 30° and 45° are most effective.

Figure 6 shows the gas concentration distribution during 240 h extraction under different conditions. *be*_{2.}This figure shows that the amount of residual gas is small on the intake side and large on the return side.Furthermore, when *be*_{2}When the angle is between 30° and 45°, the residual gas content of the whole goaf is relatively low, indicating a more pronounced gas extraction effect and better gas extraction efficiency.

#### Effect of borehole length

For each individual borehole, the length is set as follows: *L*= 120 m, 140 m, 160 m, 180 m, the elevation angle is *be*_{1}= 9°, azimuth *be*_{2}= 30°, gas extraction flow rate *q*_{ch4}= 3m^{3}/min, total extraction time is 240 hours. Figure 7 shows the changes in gas concentration at the three monitoring points.

Figure 7 shows that the correlation between the residual gas content in the shallow part of the gof and the borehole length is low, as changing the borehole length does not result in a significant difference in the residual gas content. . 2# has the highest residual gas content in the goaf. *L*= 180 m, the residual gas content gradually decreases. *L*= 140 meters, 160 meters, 120 meters. Deeper parts of the goaf show minimal variation in the trend of residual gas content. *L*= 120 meters, 140 meters, 180 meters, 120 meters. In conclusion, if conditions remain unchanged, the borehole should not be too short and should be at least 120 m to ensure a large horizontal influence area. Controlling the length within the range of 140–160 m reduces the residual gas content in the goaf and relatively improves the gas extraction efficiency.

Figure 8 shows the gas concentration distribution in the goaf after 240 h of extraction at different borehole lengths. This figure shows that as the length of the borehole increases, the residual gas content in the goaf decreases. However, when the length reaches 180 m, the decrease in the residual gas content in the goaf becomes less significant.