# Study on the Effect of Pore Evolution on the Coal Spontaneous Combustion Characteristics in Goaf

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations for Goaf CSC

#### 2.1. Momentum Conservation Equation

^{4}; F is the volumetric force, N/m

^{3}; and $\left|u\right|$ is the velocity modulus of the gas transport in goaf, m/s. ${\beta}_{F}$ Mainly related to the structure of porous medium and the properties of fluid [21]:

^{3}; and ${C}_{f}$ is the friction coefficient of the goaf gas, ${C}_{f}=\frac{1.75}{\sqrt{150{\epsilon}_{p}^{3}}}$.

#### 2.2. Mass Conservation Equation

_{4}, O

_{2}, CO and CO

_{2}, etc.; ${c}_{\Theta}$ is the concentration, mol/m

^{3}; W is the source term, mol/(m

^{3}·s); c is the concentration of the mixed gas components in goaf, mol/m

^{3}, c = p/RT

_{g}; R is the universal gas constant, J/(mol·K); v

_{g}is the velocity vector, m/s; T

_{g}is the gas temperature, K; t is the time, s; ${D}_{\Theta}$ is the diffusion coefficient tensor, m

^{2}/s, which can be expressed as [22]:

_{gx}and v

_{gy}are the gas flow velocity components in the x and y directions, m/s, respectively; ${\alpha}_{L}$ and ${\alpha}_{T}$ are the longitudinal and transverse dispersion of the gas, m, respectively; ${\tau}_{1}$ is the tortuosity of the porous medium, dimensionless; and ${D}_{\Theta a}$ is the molecular diffusion coefficient, m

^{2}/s. The chemical composition of coal exhibits considerable variation with respect to its rank and source. It is challenging to ascertain the precise correlation between the rate of gas production and oxygen consumption. During the initial stages of coal oxidation, the chemical reaction equation can be expressed as follows:

_{a}is the activation energy, kJ/mol; T

_{s}is the solid temperature, K; and ${C}_{{O}_{2}}$ is the oxygen concentration, mol/m

^{3}.

#### 2.3. Energy Conservation Equation

_{p}is the specific heat capacity, J/(kg·K); k is the thermal conductivity, J/(m·s·K); T is the temperature, K; Q

_{T}is the heat source term in goaf, J/(m

^{3}·s); a

_{sg}is the specific surface area of the porous medium in goaf, m

^{−1}; and h

_{sg}is the heat transfer coefficient at the gas–solid interface, J/(m

^{2}·s·K).

_{T}is mainly the result of the combined effect of the heat released from the oxidation of the coal body and the heat exchange of the top and bottom plates, thus the heat accumulated in goaf can be expressed as [11,22]:

_{w}is the temperature of the top or bottom plate, K.

_{sg}and h

_{sg}can be expressed respectively as:

#### 2.4. Cross-Coupling Relationship

## 3. Model Construction and Validation

#### 3.1. Engineering Overview

^{3}/min from the working face, and the natural ignition period of the coal seam is from March to June [26]. During mining, an open fire was discovered in the upper corner of the working face. This was mainly caused by the spontaneous combustion of a large amount of residual coal inside the goaf, which then spread to the working face. Air leakage is a significant factor in the development of goaf CSC, and porosity plays a crucial role in air leakage in goaf [27]. Consequently, we conducted an investigation into the impact of porosity on the characteristics of the goaf CSC, with a focus on the change in porosity resulting from the CSC.

#### 3.2. Assumptions and Physical Modelling

- (1)
- The gas movement in goaf conforms to the non-Darcy Forchheimer’s law, and the oxygen consumption for coal oxidation is determined using the Arrhenius equation.
- (2)
- The gas in the goaf is considered an ideal gas, and the impact of temperature on its kinetic viscosity is disregarded.
- (3)
- Disregarding the gas outflow from the goaf and other gases (CO, CO
_{2}, CH_{4}, SO_{2}and NO_{X}, etc.) produced during CSC, the gases in the goaf are mainly air. - (4)
- The goaf is simplified to a two-dimensional non-homogeneous porous medium flow field.
- (5)
- Using the 1302 working face as an example, a physical model was established, as shown in Figure 2. The inlet and return airway measure 4 m in width and 8 m in length, the working face measures 7 m in width and 132 m in length, and the goaf measures 140 m in width and 150 m in length. The simulation boundaries and parameters for goaf CSC are shown in Table 1 and Table 2.

#### 3.3. Permeability Evolution of Goaf

_{P}(x,y) is the expansion coefficient, dimensionless; ${K}_{p,\mathrm{max}}$ is the initial value of the K

_{P}(x,y), dimensionless; ${K}_{p,\mathrm{min}}$ is the compaction expansion coefficient, dimensionless; a is the decay rate of expansion coefficient, m

^{−1}; d is the distance from any point to a specific location in goaf, m; and ${\xi}_{1}$ is the adjustment factor for the “O” ring shape.

_{P}(x,y) in the goaf [31]:

_{p}is the particle diameter of the porous medium in the goaf, m.

_{0}= 0.0368, a

_{1}= 0.268, and d

_{p}= 0.04 m, the spatial distribution of the expansion coefficient, porosity and permeability of the goaf is obtained, as shown in Figure 3.

#### 3.4. Parameter Setting

#### 3.5. Model Validation

## 4. Results and Discussion

#### 4.1. Spatial Distribution of Porosity and Permeability

^{−7}m

^{2}/s), and then it decreases with increasing goaf depth, reaching a minimum of 1.33 × 10

^{−8}m

^{2}/s. The goaf highest permeability corresponding to the highest porosity of 30%, 35%, and 40% is 1.09 × 10

^{−6}m

^{2}/s, 2.00 × 10

^{−6}m

^{2}/s, and 5.48 × 10

^{−7}m

^{2}/s, respectively, and the corresponding lowest permeability is 2.38 × 10

^{−8}m

^{2}/s, 3.95 × 10

^{−8}m

^{2}/s, and 6.08 × 10

^{−6}m

^{2}/s, respectively. In addition, the goaf permeability at different porosity varies near the working face (<60 m), indicating that the wind flow variations are more significant in this region.

#### 4.2. Spatial Distribution of Oxygen Concentration and Airflow Velocity

#### 4.3. Spatial Distribution of Temperature

#### 4.4. Spatial Distribution of CSC Three Zones

^{2}and 3928.24 m

^{2}to 1200.41 m

^{2}and 1951.11 m

^{2}, respectively. In contrast, the asphyxiation zone’s area increases with time from 12,951.10 m

^{2}to 17,817.64 m

^{2}. The oxidation zone is the region where CSC occurs frequently and is the focus of much scholarly attention. When the goaf porosity is 25%, the variation in the oxidation zone area with time ranges from 1951.11 m

^{2}to 3928.24 m

^{2}only, whereas when the goaf porosity is 40%, the variation in the oxidation zone area with time ranges from 3699.07 m

^{2}to 6156.88 m

^{2}. It can be seen that the higher the goaf porosity, the higher the oxidation zone area and the higher the CSC risk.

## 5. Conclusions

- (1)
- Both porosity and permeability decrease with increasing goaf depth. The goaf porosity is positively correlated with the permeability. When the goaf maximum porosity was increased from 25 to 40%, the average flow velocity increased by about 6 times. This demonstrates that porosity has a significant impact on air leakage in the goaf.
- (2)
- The oxygen concentration in the extraction zone increases as the porosity increases and exhibits a trend of initially increasing and then decreasing over time. Similarly, the temperature trend varies with different goaf porosities, increasing over time. As porosity increases, the high temperature zone gradually expands along the goaf depth.
- (3)
- Over time, the CSC three zones in the goaf exhibit a tendency to decrease in the radiator and oxidation zones, while increasing in the asphyxiation zone. The range of the CSC three zones is positively correlated with the goaf porosity. Specifically, the higher the goaf porosity, the greater the area of the oxidation zone and, consequently, the higher the CSC risk.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Variations of average flow rate and average oxygen concentration with different goaf porosity.

Coal Sample | Number | M_{ad} (%) | V_{ad} (%) | FC_{d} (%) | A_{d} (%) |
---|---|---|---|---|---|

Lignite coal | S1 | 16 | 33.5 | 31.7 | 34.8 |

Boundary | Pressure | Concentration | Temperature |
---|---|---|---|

AD | p = p_{0} + R·Q^{2}·(L − y) | ${C}_{{O}_{2}}={C}_{{O}_{2}}^{0}$ | T = T_{0} |

AB/BC/CD | $\phi \xb7\frac{k}{\mu}\nabla p=0$ | ${C}_{{O}_{2}}=0$ | $-\phi \xb7\left(k\nabla T\right)=0$ |

Parameters | Value | Unit | Parameters | Value | Unit |
---|---|---|---|---|---|

Initial expansion coefficient, ${K}_{p,\mathrm{max}}$ | 1.5 | - | particle diameter, d_{p} | 0.04 | m |

Compaction expansion coefficient, ${K}_{p,\mathrm{min}}$ | 1.12 | - | Initial pressure, p_{0} | 1 | atm |

Attenuation rate, a_{0} | 0.0368 | - | Adjustable parameters, ${\xi}_{1}$ | 0.233 | - |

Attenuation rate, a_{1} | 0.0268 | - | Initial O_{2} concentration,
${C}_{{O}_{2}}^{0}$ | 9.375 | mol/m^{3} |

Initial temperature, T_{0} | 27 | °C | solid density, ${\rho}_{s}$ | 1250 | Kg/m^{3} |

Activation energy, E_{a} | 45.5 | KJ/mol | Gas density, ${\rho}_{g}$ | 1.1 | Kg/m^{3} |

Indexing factor, A | 180 | 1/s | Solid specific heat capacity, C_{ps} | 1200 | J/(kg·K) |

Ideal gas constant, R | 8.314 | J/(mol·K) | Gases specific heat capacity, C_{pg} | 1012 | J/(kg·K) |

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**MDPI and ACS Style**

Li, J.; Xu, H.; Wu, G.
Study on the Effect of Pore Evolution on the Coal Spontaneous Combustion Characteristics in Goaf. *Fire* **2024**, *7*, 164.
https://doi.org/10.3390/fire7050164

**AMA Style**

Li J, Xu H, Wu G.
Study on the Effect of Pore Evolution on the Coal Spontaneous Combustion Characteristics in Goaf. *Fire*. 2024; 7(5):164.
https://doi.org/10.3390/fire7050164

**Chicago/Turabian Style**

Li, Jinglei, Hao Xu, and Genshui Wu.
2024. "Study on the Effect of Pore Evolution on the Coal Spontaneous Combustion Characteristics in Goaf" *Fire* 7, no. 5: 164.
https://doi.org/10.3390/fire7050164