**4. Simulation Results and Analysis**

#### *4.1. Influence of Negative Pressure Extraction on Gas Migration*

The method of predicting whether it is an outburst danger zone stipulated in the "Coal and Gas Outburst Prevention Rules" is based on the coal seam gas pressure of 0.74 MPa and the content of 8 m3/t as the critical value. Reducing the gas pressure of coal seam to 0.74 MPa during the extraction process is an important discriminant index. In the twodimensional plane, the radius of the area where the gas pressure is lower than 0.74 MPa is the effective extraction radius. The area where gas pressure is less than 0.74 MPa is regarded as an effective extraction area. In the three-dimensional model, the area where the gas pressure in coal is less than 0.74 MPa is regarded as an effective extraction area.

A single borehole is set up to simulate the effective extraction radius considering coal fracture and gas pressure in matrix under different extraction time. As shown in Figure 2, taking the bottom of the coal seam as an example, the effective extraction radius considering gas pressure in the coal matrix is always smaller than that considering gas pressure in coal fracture. However, the difference of effective extraction radius decreases with the extension of extraction time. Combined with the three-dimensional effect diagram of the effective extraction area at different times obtained by simulation, it can also be understood that the effective extraction area with a smaller coal matrix gas pressure less than 0.74 MPa is contained in the effective extraction area where the coal fracture gas pressure is less than 0.74 MPa. Two days before the extraction, the effective extraction radius of coal fracture increased sharply, and then maintained a certain trend of continuous increase, but with the increase in extraction time, the increase gradually decreased. In the first 5 days of extraction, the increase in the effective extraction radius of the coal matrix was very small, and then increased significantly, but with the increase in extraction time, the increase was gradually reduced.

**Figure 2.** Change in effective extraction radius under different extraction time.

As shown in Figure 3a, points A (0,0.5,0), B (0,1,0), C (0,2,0), and D (0,4,0) are selected as simulation monitoring points to simulate the gas pressure of coal matrix pores and coal fractures under different extraction time monitored in the same plane and different radius. The result is shown in Figure 3b. It can be seen from Figure 3 that at the same extraction time, the gas pressure in coal matrix pores is always larger than that in the coal fractures. At 30 days before drainage, gas pressure in fracture of A and B coal bodies decreases greatly. In contrast, with the four monitoring points farther away from the borehole distance, C and D two-coal seam gas pressure in the fracture decreased slightly. The gas pressure of the coal matrix at the four monitoring points did not decrease significantly as the gas pressure of coal fracture. At the four monitoring points, the gas pressure of coal fracture and the gas pressure of the coal matrix decrease gradually with the continuous extraction and tend to be gentle. The difference between gas pressure in the coal fracture and coal matrix at the four monitoring points decreases gradually.

**Figure 3.** Coal matrix and fracture gas pressure under different extraction time.

In the initial stage of drilling drainage, the pressure difference between the gas pressure in the fracture and the negative pressure of the borehole is obvious, and the free gas in the fracture flows to the borehole, so the gas pressure in the coal fracture decreases sharply. The seepage of gas in the fracture to the borehole causes the obvious pressure difference between the coal matrix and the gas in the fracture. The gas in the coal matrix diffuses to the fracture, and the gas adsorbed by the coal matrix desorbs under the influence of the pressure difference, and then participates in the diffusion to the fracture. Gas diffusion and desorption diffusion in coal matrix produce gas pressure difference with surrounding coal

matrix, which will also absorb gas diffused by surrounding coal matrix. Under the same extraction time at the same position, the gas pressure in the coal fractures is always smaller than that in a negative pressure borehole, and the gas pressure in coal matrix pores is always larger than that in coal fractures. The influence scope of borehole negative pressure extraction expands gradually with the increase in extraction time. The fracture around borehole and matrix gas pressure decreases gradually with the increase in extraction time. However, the gas content in coal is constant, and there is a pressure difference between the negative pressure borehole and free gas in the fracture. The gas pressure between the fracture and the coal matrix, and the gas pressure between the coal matrix and the surrounding coal matrix gradually decrease with the extraction. The gas pressure in the effective extraction area, the coal matrix around the borehole, and the fracture will tend to be gentle and no longer change significantly after reaching a certain extraction time.

### *4.2. Drilling Engineering Optimization*

When studying the effective extraction radius, in order to avoid the possible interaction between multiple boreholes, the single borehole extraction used in Section 4.1 is adopted. The effective extraction radius increases with the increase in extraction time, but the increase gradually decreases until it tends to be gentle. With the increase in extraction time, the amount of gas extraction increases. However, more than a certain extraction time, even if the extraction time is longer, it has little effect on the pure amount of gas extraction. Since the adsorbed gas in the coal matrix occupies the vast majority of the total gas in the coal seam, the effective extraction radius r = 1.3 m, considering the gas pressure of the coal matrix, is selected as the reference for the arrangement of borehole spacing when the extraction is 140 d. According to the research of Chen Yuexia et al. [22,27] without considering the influence of superposition effect between boreholes, when four boreholes are used for extraction, through geometric derivation, it is concluded that when the spacing between boreholes is less than or equal to <sup>√</sup>2r, there will be no blank zone with pressure higher than the specified pressure in the borehole layout area. However, in fact, when multiple boreholes are extracted, due to the interaction between boreholes due to borehole spacing, the superposition effect is generated [28,29]. As shown in Figure 4, when the hole spacing of the three extraction boreholes is set to 2r, the three boreholes are surrounded by an equilateral triangle with a side length of 2r. In theory, if the superposition effect between boreholes is not considered, there will be a blank zone shown in the shadow part, where the gas pressure of the coal matrix is higher than 0.74 MPa. According to the Pythagorean theorem, the AO length can be obtained as <sup>2</sup> √3 <sup>3</sup> r = 1.5 m. When the borehole spacing is 2 √3 <sup>3</sup> r = 1.5 m, 2r = 2.6 m, 4 m, 5 m, and 6 m, the gas extraction simulation is carried out by three boreholes. Figure 5 shows the variation curve of the coal matrix gas pressure with time at the center points (0,0,0) of three boreholes during gas extraction. When the drill hole spacing changes, it is ensured that the point is always located in the center of the equilateral triangle surrounded by three boreholes. It can be seen that when the extraction spacing is 1.4 m and the extraction time is 0 d–70 d, the gas pressure of the coal matrix decreases obviously. After the extraction time was 70 days, the gas pressure in the coal matrix did not decrease significantly and finally stabilized. When the borehole spacing is different, the depressurization effect of the drilling area is less obvious with the increase in borehole spacing. The gas pressure in the coal matrix showed a rapid decrease trend at the initial stage, and then the downward trend slowed down. The gas pressure in the coal matrix decreases not obviously with the extension of extraction time, and gradually tends to be gentle. The decrease rate of coal matrix gas pressure in the area surrounded by boreholes becomes slower with the increase in borehole spacing. This is because the superposition effect between boreholes decreases with the increase in borehole spacing. In addition, with the continuation of the extraction process, the gas pressure gradient between coal fractures and boreholes, between coal fractures and coal matrix pores, and between coal matrix pores, gradually decreases, and the gas migration is not strong at the beginning of extraction.

**Figure 4.** Schematic diagram of borehole gas extraction influence area.

Figure 6 shows the distribution of the coal matrix gas pressure and effective extraction radius when the extraction time is 140 d and the borehole spacing is 1.5 m, 2.6 m, 4 m, 5 m, and 6 m, respectively. The light green surface in the figure is 0.74 MPa isosurface. It can be seen from Figure 6a that when the borehole spacing is 1.5 m, the effective extraction area of the three boreholes is approximately cylindrical, and the gas pressure of the coal matrix in the area surrounded by the three boreholes is obviously low. This is because the borehole spacing is small, the borehole superposition effect is obvious, and the gas extraction effect in the area surrounded by the borehole is obvious. It can be seen from Figure 6b–d that when the borehole spacing is 2.6 m, 4 m, and 5 m, the effective extraction area of the three boreholes is a rounded triangular prism. With the increase in borehole spacing, the higher the gas pressure in the area surrounded by the three boreholes, the more irregular the effective extraction area, and with the internal depression, there is an overall trend of division. This is because the superposition effect of boreholes decreases with the increase in borehole spacing, and the effect of gas extraction in the area surrounded by boreholes is weakened. It can be seen from Figure 6e that when the borehole spacing is 6 m, the effective extraction area of the three boreholes is distributed around the three boreholes in three irregular cylinders, and the blank zone appears in the area surrounded by the three boreholes. This is because the superposition effect weakens with the increase in borehole spacing until a certain distance between boreholes is no longer affected by the superposition effect. The borehole spacing is different. The gas pressure in the area around the borehole decreases continuously with the increase in the extraction time. The

smaller the borehole spacing, the greater the gas pressure drop and the faster the gas drop rate. However, the longer the extraction time, the slower the gas pressure decreases. When the borehole spacing increases to a certain distance, a blank zone appears in the area surrounded by boreholes. When the borehole spacing is small, the time required to achieve the expected extraction effect is shorter; but the more boreholes required, the higher the construction cost. When the borehole spacing is large, the extraction rate of gas slows down, and it takes a long time to achieve the expected extraction effect. However, the number of boreholes required is small, and the effective extraction area is large over time within a reasonable project budget.

**Figure 6.** Effective extraction area effect diagram under different hole spacing of 140 d extraction.

As shown in Figure 7a, (−15,0,0) and (15,0,0) points are selected to make the *X*-axis direction section. The gas pressure of the coal matrix on the section line is simulated at 140 days of extraction with different hole spacing, and the results are shown in Figure 7b. In the extraction of 140 d, under different borehole spacing: with the increase in borehole spacing, the effect of gas pressure reduction is more obvious. The smaller the borehole spacing is, the greater the gas pressure drop rate in the area around the borehole is, and

the more obvious the gas extraction effect is. The gas pressure drop rate around borehole decreases with the increase in borehole spacing, and the effect of gas extraction is worse. It shows that the drilling superposition effect is inversely proportional to the borehole spacing.

(**a**) monitoring line selection (**b**) distribution of gas pressure

**Figure 7.** Gas pressure distribution of coal matrix on the cut-off line under different extraction spacing at 140 d.

Figure 8 is the volume change curve of the effective extraction area with time and borehole spacing. It can be seen from the diagram that under the condition of five different borehole spacing, the volume of the effective extraction area increases from gentle to sharp and then to a large increase. When the borehole spacing is 1.5 m, 2.6 m, 4 m, 5 m, and 6 m, the effective extraction area volume increases sharply in about 10 d–15 d, 15 d–30 d, 45 d–65 d, 60 d–75 d, and 105 d–120 d, respectively. At the beginning of extraction, the bigger the superposition effect is, the smaller the borehole spacing is, and the bigger the effective extraction area is. Primarily, at about 25 d, the volume of the effective extraction area with a borehole spacing of 2.6 m expands sharply, exceeding the volume of the effective extraction area with a borehole spacing of 1.2 m. Next, with the increase in extraction time, the volume of effective extraction area with borehole spacing of 4 m expands sharply, which exceeds the volume of effective extraction area with borehole spacing of 1.5 m and 2.6 m, successively. Then, the volume of the effective extraction area with a borehole spacing of 5 m continues to expand, exceeding the volume of the effective extraction area with a borehole spacing of 1.5 m, 2.6 m, and 4 m. As the extraction continues, the volume of the effective extraction area with a borehole spacing of 6 m first expands sharply, and then the increase decreases and continues to expand, successively exceeding the effective extraction area with a borehole spacing of 1.5 m, 2.6 m, 4 m, and 5 m. The effective extraction area volume of different borehole spacing changes with the extraction time, as shown in Table 2.

**Table 2.** Table of parameters required for simulation.


**Figure 8.** The volume change in effective extraction area under different extraction spacing at 140 d.

After the extraction time is 135 d, although the effective extraction area with borehole spacing of 6 m has the largest volume, it can be seen from Figure 7b that when the extraction time is 140 d, there is a blank zone with gas pressure higher than 0.74 MPa in the area surrounded by boreholes, so the extraction effect is not ideal. As the extraction time becomes longer and longer, the internal blank zone is gradually eliminated. Considering that if the gas pressure in the internal area surrounded by the borehole already reached the standard, the long extraction time may lead to safety problems due to pressure imbalance. When the borehole spacing is small, the actual economic problems caused by the increase in the effective extraction area with the extraction time are no longer obvious, and the extraction time is allowed under the actual working conditions. The comprehensive analysis shows that when the extraction time of the mine is about 140 d and the borehole spacing is set to 5 m, the extraction effect is the best.

#### **5. Discussion**

In this paper, based on the porous model of pore-fracture dual medium, considering the influence of coal skeleton and coal matrix deformation when coal adsorbs and desorbs gas, considering coal fracture seepage, coal matrix adsorption, desorption and diffusion gas, gas diffusion between coal matrix, and the Klinkenberg effect, a gas-solid coupling model is established. The effective extraction radius is obtained according to the variation law of coal matrix gas content with extraction time. Extending from a two-dimensional plane to a three-dimensional space, the volume change in effective extraction area is studied, so as to more intuitively analyze and verify the migration of gas in borehole coal fracture coal matrix during negative pressure borehole extraction. In the three-dimensional visualization model, it can be clearly seen that under the same extraction time, the effective extraction area, considering the change in gas pressure in coal fracture, is different from the effective extraction area considering the change in gas pressure in the coal matrix. Compared with two-dimensional theoretical analysis, it is more intuitive and more conducive to explain the mechanism of gas migration. Through the three-dimensional visualization model, at a certain distance between boreholes, it can be clearly seen that the gas pressure in the area around the borehole decreases more obviously than that outside the borehole, which indicates that the boreholes are affected by the superposition effect. When multiple boreholes are used for gas extraction, the borehole spacing has a great influence on the extraction effect. The extraction time required to eliminate the blank zone in the area surrounded by the borehole is longer with the increase in the borehole spacing. As long as the spacing of boreholes is within a reasonable range, the blank zone can be eliminated by prolonging the extraction time in theory. If the borehole spacing is too large, in theory, it reduces the number of boreholes and needs to extend the extraction time to eliminate blank area. However, the pressure imbalance may be caused by excessive extraction, and

safety accidents may occur. Extending the extraction also requires the consumption of certain economic resources. If the borehole spacing is too small, the superposition effect between boreholes is strong, and the extraction time required to eliminate the blank zone time is short, but the increase in the number of boreholes may cause waste of resources. Therefore, the study of reasonable borehole spacing has a certain guiding significance for practical engineering.

This study has some inspiration and guiding significance for coal energy security and sustainable mining, but there are still deficiencies. According to different geological conditions, there are elastic–plastic changes in the actual coal, and the change in temperature will also affect the deformation of coal structure, so the coal deformation control equation remains to be improved. In the study of the optimal borehole spacing, the layout and spacing of boreholes need to be adjusted according to the actual coal mine conditions and engineering planning, and the selection method of the optimal borehole spacing needs to be improved.

#### **6. Conclusions**

(1) The gas-solid coupling model of negative pressure drilling gas extraction was established. The model is based on the coal pore-fracture porous media model, considering the coal deformation, gas diffusion seepage, gas adsorption, and desorption process. The change in gas pressure Pm in the coal matrix and gas pressure Pf in coal fracture is simulated, and the migration mechanism of gas between coal matrix, coal fracture, and borehole is verified.

(2) When gas is extracted by a negative pressure borehole, the gas in a coal fracture seeps into borehole driven by extraction negative pressure. After the gas in the fracture flows out, the coal matrix gas diffuses into the fracture under the pressure difference to participate in the seepage. The gas pressure of the coal matrix decreases, the gas adsorbed in the surrounding coal matrix desorbs, and the free gas contained diffuses to the coal matrix under the action of pressure difference. The gas pressure in the coal body near the borehole decreases obviously, and the farther away from the borehole, the weaker the influence of extraction. The pressure gradient decreases with the increase in extraction time, the effect of gas migration will gradually weaken, and the effective extraction range of the borehole is limited.

(3) During multi-borehole extraction, the gas pressure in the area around the borehole decreases obviously under the influence of the superposition effect. With the increase in borehole spacing, the extraction effect in the area around the borehole decreases. The effective extraction area formed by multi-borehole negative pressure gas extraction is related to extraction time and borehole spacing. When the three boreholes are extracted for 140 days, the effective extraction area is approximately cylindrical when the borehole spacing is 1.5 m. The effective extraction area is approximately a rounded triangular prism when the borehole spacing is 2.6 m, 4 m, and 5 m, but the longer the borehole spacing, the surrounding inward depression is split. The effective extraction area is divided into three near-cylindrical areas when the borehole spacing is 6 m, and a blank zone appears in the area surrounded by the borehole. Considering the shape, volume change, extraction effect, safety, and economic problems of the effective extraction area, the best effect is to select the hole spacing of 5 m when the three boreholes are used as the group extraction for 140 days.

**Author Contributions:** Investigation, W.C.; methodology, F.D.; supervision, K.W.; writing—original draft, F.D.; writing—review and editing, W.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 52004291 and 52130409.

**Data Availability Statement:** The data are available from the corresponding author on reasonable request.

**Acknowledgments:** We also would like to thank the anonymous reviewers for their valuable comments and suggestions that lead to a substantially improved manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
