# The Influence of the Permeability of the Fractures Zone Around the Heading on the Concentration and Distribution of Methane

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Area of Research

#### Description of the Excavated Dog Heading under Analysis

^{3}/min. of fresh air was supplied to the heading via the forcing air duct. The flow of methane to the heading area amounted to approx. 4.5 m

^{3}CH4/min. The scheme of the heading and air distribution, indicating the measurement points where methane sensors were located, is presented in Figure 3. The cross-section area of the excavated heading amounted to 14.8 m

^{2}. The numerical analysis was conducted for a heading with a length of 70 m.

#### 2.2. Methods

#### 2.2.1. Mathematical Models

#### Governing Equations

^{3}),

**U**is the gas velocity (m/s), p is pressure (Pa),

**τ**is the viscous stress tensor (Pa),

**g**is gravity acceleration (m∙s

^{−2}), c

_{p}is the heat of the gas, k

_{eff}is the effective gas thermal conductivity, T is the temperature (K), ω

_{i}is the mass fraction N

_{2,}O

_{2}and CH

_{4}, μ

_{t}is turbulent viscosity (Pa·s), D

_{i,eff}is the effective diffusivity of N

_{2,}O

_{2}and CH

_{4}(m

^{2}/s), Sc

_{t}is the turbulent Schmidt number (0.7), Pr

_{t}is the Prandtl number.

#### Model of Turbulence

_{k}, σ

_{ε}are turbulent Prandtl numbers for k and ε, G

_{b}is the generation of turbulence kinetic energy, C

_{1ε}, C

_{2ερ}, C

_{3ε}are constant, G

_{k}is the generation of turbulence kinetic energy, Y

_{M}is contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, S

_{k}, S

_{ε}are user-defined source terms.

#### Constitutive Equations

_{i}is the molar mass of oxygen, methane, water vapor or nitrogen.

_{i}, and x

_{j,}are the mole fraction of species i and j, respectively, and [39]:

_{4}is equal to ωCH

_{4}× 100%).

#### 2.3. Demarcation of the Fractures Zone Around the Excavated Dog Heading

^{−8}m

^{2}. The permeability of this zone was determined from the equations thoroughly described in the paper [61].

#### 2.4. Model of Undeground Dog Heading

## 3. Results

^{−8}m

^{2}. This variant reflects the parameters present in the actual heading.

#### 3.1. The Results of the Analysis of Methane Distribution and Concentration in the Excavated Dog Heading for the Volumetric Flow Rate of Fresh Air Amounting to 301.44 m^{3}/min

#### 3.2. The Results of the Analysis of Methane Distribution and Concentration in the Excavated Dog Heading for the Volumetric Flow rate of Fresh Air Amounting to 361.73 m^{3}/min

^{3}/min.

^{3}/min. (i.e., approx. 20%) reduced the value of methane concentration by approx. 0.2% for variants 1 and 2, and by approx. 0.4% for variants 3 and 4.

#### 3.3. Comparison of the Simulation Results and Measurement in Actual Conditions

## 4. Discussion

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**A scheme of the heading indicating the distribution of air and the measurement points where methane sensors were located (own study).

**Figure 4.**The geometric model of the heading under analysis, along with the fractures zone and the heading equipment [own study].

**Figure 7.**The distribution of methane emission into the excavated dog heading from the fractures zone.

**Figure 8.**The concentration and distribution of methane in the vertical planes of the excavated dog heading for different permeability values of the fractures (desorption) zones ((

**a**)—permeability equal to 3.55308·10

^{−8}m

^{2}; (

**b**)—permeability equal to 6.37053·10

^{−8}m

^{2}; (

**c**)—permeability equal to 1.05197·10

^{−7}m

^{2}; (

**d**)—permeability equal to 1.32935·10

^{−7}m

^{2}).

**Figure 9.**The concentration and distribution of methane in the horizontal plane at the height of 2.0 m from the floor of the excavated dog heading for different permeability values of the desorption zone ((

**a**)—permeability equal to 3.55308·10

^{−8}m

^{2}; (

**b**)—permeability equal to 6.37053·10

^{−8}m

^{2}; (

**c**)—permeability equal to 1.05197·10

^{−7}m

^{2}; (

**d**)—permeability equal to 1.32935·10

^{−7}m

^{2}).

**Figure 11.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 3.55308·10

^{−8}m

^{2}.

**Figure 12.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 6.37053·10

^{−8}m

^{2}.

**Figure 13.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 1.05197·10

^{−7}m

^{2}.

**Figure 14.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 1.32935·10

^{−7}m

^{2}.

**Figure 15.**The concentration and distribution of methane in the vertical planes of the excavated dog heading for different permeability values of the fractures (desorption) zones ((

**a**)—permeability equal to 3.55308·10

^{−8}m

^{2}; (

**b**)—permeability equal to 6.37053·10

^{−8}m

^{2}; (

**c**)—permeability equal to 1.05197·10

^{−7}m

^{2}; (

**d**)—permeability equal to 1.32935·10

^{−7}m

^{2}).

**Figure 16.**The concentration and distribution of methane in the horizontal plane at the height of 2.0 m from the floor of the excavated dog heading for different permeability values of the desorption zone ((

**a**)—permeability equal to 3.55308·10

^{−8}m

^{2}; (

**b**)—permeability equal to 6.37053·10

^{−8}m

^{2}; (

**c**)—permeability equal to 1.05197·10

^{−7}m

^{2}; (

**d**)—permeability equal to 1.32935·10

^{−7}m

^{2}).

**Figure 17.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 3.55308·10

^{−8}m

^{2}.

**Figure 18.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 6.37053·10

^{−8}m

^{2}.

**Figure 19.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 1.05197·10

^{−7}m

^{2}.

**Figure 20.**The concentration and distribution of methane along the measurement lines in the heading with a fractures zone with permeability of 1.32935·10

^{−7}m

^{2}.

Coal Thickness, m | The Compressive Strength of Coal, MPa | Depth of the Coal Seam, m | |||
---|---|---|---|---|---|

800.0 | 900.0 | 1000.0 | 1100.0 | ||

3.5 | 5.0 | 2.61 | 2.72 | 2.83 | 2.94 |

10.0 | 2.03 | 2.14 | 2.25 | 2.36 | |

15.0 | 1.76 | 1.87 | 1.98 | 2.09 | |

20.0 | 1.55 | 1.67 | 1.79 | 1.91 | |

6.5 | 5.0 | 2.55 | 2.66 | 2.77 | 2.88 |

10.0 | 1.92 | 2.03 | 2.14 | 2.25 | |

15.0 | 1.65 | 1.76 | 1.87 | 1.98 | |

20.0 | 1.43 | 1.55 | 1.67 | 1.79 |

Mining Parameters | Values |
---|---|

Air emission rate supplied to the dog face, m^{3}/min | 301.44 |

Methane emission rate (absolute methane content), kg/min | 4.5 |

The height of dog heading, m | 3.0 |

The lenght of dog heading, m | 60.0 |

The width of dog heading, m | 5.0 |

The location of the outlet from the air duct in relation to the heading face, m | 3.0 |

Diameter of air duct, m | 0.8 |

Case | The Permeability Values of the Fractures Zone, m^{2} |
---|---|

1 | 3.55308·10^{−8} |

2 | 6.37053·10^{−8} |

3 | 1.05197·10^{−7} |

4 | 1.32935·10^{−7} |

**Table 4.**The comparison of the methane concentration values obtained from the measurements points in underground conditions and those determined from numerical analysis, for the permeability of the fractures zone equal 3.55308·10

^{−8}m

^{2}.

Measurement Points (Figure 10) | Model (Case 1) | Real System | Error, % |
---|---|---|---|

P1 | 0.37 | 0.4 | 8.11 |

P2 | 0.39 | 0.4 | 2.56 |

P3 | 0.53 | 0.6 | 13.21 |

P4 | 1.08 | 1.2 | 11.11 |

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**MDPI and ACS Style**

Tutak, M.
The Influence of the Permeability of the Fractures Zone Around the Heading on the Concentration and Distribution of Methane. *Sustainability* **2020**, *12*, 16.
https://doi.org/10.3390/su12010016

**AMA Style**

Tutak M.
The Influence of the Permeability of the Fractures Zone Around the Heading on the Concentration and Distribution of Methane. *Sustainability*. 2020; 12(1):16.
https://doi.org/10.3390/su12010016

**Chicago/Turabian Style**

Tutak, Magdalena.
2020. "The Influence of the Permeability of the Fractures Zone Around the Heading on the Concentration and Distribution of Methane" *Sustainability* 12, no. 1: 16.
https://doi.org/10.3390/su12010016