# The Method of Determining Layer in Bottom Drainage Roadway Taking Account of the Influence of Drilling Angle on Gas Extraction Effect

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## Abstract

**:**

## 1. Introduction

## 2. Influence of Drilling Angle on Area of Rock Loose Circle around Drilling

#### 2.1. Theoretical Analysis

_{ζ}eiθ = ρ

_{ζ}(cosθ + isinθ) into Equation (2), the ζ plane parameter represents the functional expression of the ellipse in the Z plane.

_{0}is the radius of mapping plane, its value is 1 m, ρ

_{ζ}is the corresponding polar coordinate polar radius of the junction line of the elastic zone and plastic zone in the ζ plane, θ is the polar angle, P is the ground stress, λ is the lateral pressure coefficient, φ and c are the friction angle and cohesion inside wall rock, respectively.

_{z}of loose circle in polar coordinates in the Z plane and the radius ρ

_{ζ}of loose circle in the ζ plane is:

_{1}is the area of the loose circle containing the elliptical orifice, according to the symmetry, ${S}_{1}=2\times {\displaystyle {\int}_{0}^{\frac{\pi}{2}}{\rho}_{z}{}^{2}}(\theta )d\theta $, S

_{2}is the area of elliptical orifice, S

_{2}= πab.

#### 2.2. Result Analysis

## 3. Influence Pattern of Drilling Angle on Gas Extraction Effect

^{3}/t, and the average absolute gas emission is 4.16 m

^{3}/min. The gas pressure is in the range of 0.9~1.0 MPa. It belongs to an area with high gas pressure and high gas content.

#### 3.1. Equation of Dynamic Change of Coal Permeability

_{0}is the initial porosity, k

_{∞}is the initial permeability, and ε

_{v}is the volumetric strain of coal generated during the deformation process.

#### 3.2. Determination of Fluid-Solid Coupling Equation

^{3}·Pa), p is the gas pressure in Pa, k

_{g}is the effective permeability, μ

_{g}is the dynamic viscosity coefficient of gas, φ is the dynamic varying porosity of coal, P

_{n}is the atmospheric pressure, ρ

_{c}is the density of coal, b

_{1}is the ultimate adsorption capacity of coal in m

^{3}/kg, b

_{2}is the Langmuir pressure parameter of coal, A and B are the ash and moisture in coal, E

_{s}is the modulus of volume elasticity of skeleton particles of gas-containing coal in Pa, Q

_{s}is the mass of gas generated or absorbed per unit time in the unit volume of gas-containing coal in kg/(m

^{3}·s), α is the equivalent pore pressure coefficient of coal, and ε

_{v}is the volumetric strain of coal. Where k

_{g}= k

_{∞}(1 + b/p), k

_{∞}is the initial permeability, φ = 1 − (1 − φ

_{0})/(1 + ε

_{v}), φ

_{0}is the initial porosity, u

_{i}is the displacement component of coal, F

_{i}is the force component applied to coal, and G is the shear modulus of coal.

#### 3.3. Model Establishment and Boundary Condition Setting

#### 3.4. Result Analysis

#### 3.4.1. Varying Pattern of Coal Permeability around Drilling with Inclination Angle

^{−16}along the far away from the orifice, indicating that the volumetric strain of coal around drilling increases with the reduction of drilling angle, the increase of fractures in the coal improves the permeability of coal.

#### 3.4.2. Varying Pattern of Gas Pressure around Drilling with Inclination Angle

## 4. Arrangement Optimization for BDR

_{θ}is the tangential stress around the borehole, θ is the polar angle of the borehole, P

_{0}is the ground stress, λ is the lateral pressure coefficient, k is the ratio of the major axis to minor axis, and k = b/a = 1/sinβ from Equation (1), β is the drilling angle (0° < β ≤ 90°), a is the minor axis of the ellipse, and b is the major axis of the ellipse.

_{t}, as shown in Figure 10, and the tangential stress around drilling be the largest as the polar angle of the borehole at 0°and 180°, which is the most prone to collapse. Therefore, only the tangential stress around drilling at 0° and 180° are considered, and Equation (13) is converted to:

_{t}is the maximum compression strength of rock in MP.

## 5. Engineering Applications

^{3}/min, 0.0040 m

^{3}/min and 0.0068 m

^{3}/min, respectively. In the original BDR with the spacing of 30 m from the coal seam, the gas drainage volume of group A, group B and group C are 0.0021 m

^{3}/min, 0.0014 m

^{3}/min and 0.0026 m

^{3}/min, respectively. The extraction rate of three groups of boreholes with the spacing of 10 m is about 60% higher than that with the spacing of 30 m. The above results show that the optimized BDR with the spacing of 10 m can significantly improve the gas drainage effect and further verify the reliability of the theoretical research.

## 6. Conclusions and Discussions

- (1)
- The complex function method is used to analyze the area of the loose circle around the elliptical borehole, which is similar to the field measured results, and is quite different from the calculated value of the area of the loose circle around the circular borehole;
- (2)
- With the increase in drilling angle, the area of the loose circle and permeability of coal around the borehole decays negatively and exponentially. It shows that with the decrease in drilling angle, the volumetric strain of coal around the borehole increases, the cracks in the coal increase, and the permeability of coal is improved. At the same time, with the decrease in drilling angle, the gas pressure of coal around the borehole decreases, and the area of gas pressure reduction expands, which is conducive to the drainage of gas in the coal seam;
- (3)
- Through theoretical calculation, it is found that the coal gas pre-drainage effect is better when the drilling angle of the 8406 longwall face of Yangmei Coal Mine is 29°, and the distance between the BDR and the coal seam is 10 m. Through field measurement, the maximum average single hole gas drainage volume is 0.0068 m
^{3}/min; the extraction rate of the boreholes with the spacing of 10 m is about 60% higher than those with the spacing of 30 m.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Arrangement with different drilling angle. (

**a**) Arrangement of borehole in BDR of the coal seam, (

**b**) Projection of horizontal section of borehole.

**Figure 4.**The change rule of loose circle area and drilling angle of the coal around the elliptic borehole.

**Figure 8.**Gas pressure distribution of gas pressure in coal seam with different drilling angles. (

**a**) b/a = 1, (

**b**) b/a = 2, (

**c**) b/a = 3, (

**d**) b/a = 4.

**Figure 9.**Gas pressure of coal around boreholes with different drilling angles. (

**a**) longitudinal secant, (

**b**) transverse secant.

**Figure 11.**The gas extraction amount of lane with different distance to coal seam: (

**a**) Boreholes of group A, (

**b**) Boreholes of group B, (

**c**) Boreholes of group C.

Parameter | Value |
---|---|

Shear modulus G/MPa | 90.3 |

Poisson ratio v | 0.16 |

Density ρ_{c}/(kg·m^{−3}) | 1400 |

Initial porosity φ_{0} | 0.0456 |

Gas dynamic viscosity coefficient μ_{g}/(Pa·s) | 1.9 × 10^{−6} |

Equivalent pore pressure coefficient α | 0.1604 |

Temperature T/°C | 20 |

Atmospheric pressure P_{n}/MPa | 0.101 |

Adsorption constant b_{1}/(m^{3}·kg^{−1}) | 36.492 × 10^{−3} |

Adsorption constant b_{2}/MPa | 1.48 |

Ash content A | 11.48% |

Moisture content B | 3.41% |

Bulk modulus of coal skeleton Es/MPa | 300 |

Initial permeability k_{∞}/m^{2} | 0.2748 × 10^{−16} |

Gas compression factor β/(k_{g}/(m^{3}·Pa)) | 0.987 |

Gas adsorbed per unit volume of coal Q_{s}/kg/(m^{3}·s) | 30.98 × 10^{−4} |

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**MDPI and ACS Style**

Yang, Y.; Han, P.; Zhao, Z.; Chen, W.
The Method of Determining Layer in Bottom Drainage Roadway Taking Account of the Influence of Drilling Angle on Gas Extraction Effect. *Sustainability* **2022**, *14*, 5449.
https://doi.org/10.3390/su14095449

**AMA Style**

Yang Y, Han P, Zhao Z, Chen W.
The Method of Determining Layer in Bottom Drainage Roadway Taking Account of the Influence of Drilling Angle on Gas Extraction Effect. *Sustainability*. 2022; 14(9):5449.
https://doi.org/10.3390/su14095449

**Chicago/Turabian Style**

Yang, Yuliang, Penghua Han, Zhining Zhao, and Wei Chen.
2022. "The Method of Determining Layer in Bottom Drainage Roadway Taking Account of the Influence of Drilling Angle on Gas Extraction Effect" *Sustainability* 14, no. 9: 5449.
https://doi.org/10.3390/su14095449