# Pressure-Relief Gas Cooperative Drainage Technology in a Short-Distance Coal Seam Group
## 2 Fracture Evolution Mechanism of the First Mining Layer in the Short-Distance Coal Seam Group
### Physical Model Establishment and Parameter Setting  
Taking the 1211 working face as the prototype, the gas flow in the goat was simplified into a steady-state flow field, ignoring the influence of personnel and supports. COMSOL was used to construct the goat data model. The calculation model simplified the working face, intake, and return air roadways as cuboids. The length of the working face was 170 m, and the height was 2.5 m. The distance from the rear boundary of the goat calculation area to the working face was set to 200 m, the width of the inlet and return air roadway was 4 m, and the height was 2.5 m. The model was divided into multiple regions according to the different permeabilities. The middle of the goat was the compaction zone, and the surrounding area was the \"O\" ring. The compaction zone and the \"O\" ring were divided into four regions from top to bottom; these included the upper part of the fracture zone. The lower part of the fracture zone, the upper part of the caving zone, and the bottom of the caving zone were investigated. The \"O\" ring was subdivided into 16 regions from front, back, left, and right. It was assumed that the permeability coefficients of each region were anisotropic and uniformly distributed. The grid was encrypted and divided into 410,000 units, as shown in Figure 5.  
Figure 4: Coal seam histogram.  
Three important parameters, permeability, porosity, and gas source term, were determined in the COMSOL simulation of the gas flow process in the mining fracture field. The permeability coefficient and porosity of the goaf are related to the coefficient of rock collapse and crushing expansion, and they follow the Blake-Kozeny formulas, Formulas (1) and (2):  
\[k=\frac{\varepsilon^{3}d_{m}^{2}}{150{(1-\varepsilon)}^{2}} \tag{1}\]  
\[\varepsilon =1-\frac{1}{K_{P}} \tag{2}\]  
\(k\)--permeability coefficient;  
\(\varepsilon\)--porosity;  
\(K_{P}\)--coefficient of dilatancy of crushed stone;  
\(dm\)--average particle diameter of porous media, m.  
The gas quality sources in the model are set as the gas source of the coal wall, the residual coal in the goaf, and the gas emission source of the adjacent seam. According to the field measurement, the gas emission from the coal wall of the 1211 working face was 5.3 m\({}^{3}\)/min, and the gas emission from the residual coal in the goaf and the upper and lower adjacent seams was 19.3 m\({}^{3}\)/min. The gas emission in the model was regarded as continuous; that is, the gas sources in each area were averaged to the unit volume of the calculation domain, and the gas emission source of each area was determined according to Formula (3):  
\[Q_{S}=\frac{Q_{g}\cdot\rho_{g}}{V} \tag{3}\]  
\(Q_{s}\)--model gas mass source term, kg/(m\({}^{3}\cdot\)s\({}^{-1}\));  
\(Q_{g}\)--gas emission, m\({}^{3}\)/s;  
\(\rho_{g}\)--gas density, 0.7167 kg/m\({}^{3}\);  
\(V\)--total volume of the gas mass source term, m\({}^{3}\).  
The position of the intake air roadway was set as the speed boundary; the wind speed was 2 m/s, and the gas concentration was 0. The return air roadway was the outlet boundary and was set to free outflow type; the remaining solid boundaries were set to the wall surface. The parameter values of this model are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Region** & **Natural** & **Load Influence** & **Recompaction** & **Coal wall** & **Compaction Stable Zone** \\  & **Accumulation Area** & **Zone** & **Zone** & **Influence Area** & **Compaction Stable Zone** \\ \hline Crushing expansion coefficient & 1.20 & 1.12 & 1.05 & 1.13 & 1.08 \\ Porosity/\% & 0.17 & 0.11 & 0.05 & 0.12 & 0.07 \\ Permeability/m\({}^{2}\) & \(1.45\times 10^{-11}\) & \(1.20\times 10^{-11}\) & \(0.03\times 10^{-11}\) & \(0.30\times 10^{-11}\) & \(0.14\times 10^{-11}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Relevant parameter values for different regions.  
Figure 5: Stope model diagram.