## 3 Numerical Simulation Results and Analysis  
Simulation Analysis of Radial Seepage Pressure Field of Coal Bed Water Injection borehole under Different Pore Water Pressure  
A numerical simulation was conducted on a unidirectional injection borehole with a length of 85 m. A cross-section was set at a radial distance of 1.5 m from the injection borehole to analyze the temporal variation of the seepage pressure around the borehole under different injection pressures. The simulation results are presented in Figure 3.  
The pressure around the injection wellbore changes over time, as shown in Figure 4. Under injection pressures of 4 Mpa and 10 Mpa, the pressure distribution around the wellbore remains relatively stable for the first 36 h, with a small range of influence. When the injection pressure reaches 15 Mpa, the pressure distribution around the wellbore becomes noticeably wider and more uniform after 36 h. As the pressure continues to rise, the injection pressure increases to 20 Mpa and the pressure distribution around the wellbore continues to widen and become more uniform after 36 h. As the pressure increases further, the injection pressure increases to 25 Mpa, and through the color width of the pressure distribution around the wellbore, the range of influence changes relatively little. Through numerical simulation, it can be found that during the coal seam injection process, the changes in coal seam permeability are not continuous with increasing injection pressure, but rather depend on a specific threshold. Only when the injection pressure exceeds this threshold does the coal seam's permeability exhibit a significant increase. Based on the numerical simulation results, the threshold pressure for increasing permeability in this coal seam is found to be between 15 Mpa and 20 Mpa. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Indicator** & **Parameter Value** & **Parameter Unit** \\ \hline Water viscosity coefficient & 1.04 \(\times\) 10\({}^{-3}\) & Pa-s \\ Water density & 1.0 \(\times\) 10\({}^{3}\) & kg/m\({}^{3}\) \\ Absolute permeability of coal seam & 7.526 \(\times\) 10\({}^{-18}\) & m\({}^{2}\) \\ Initial porosity of coal bed & 6.3586 & \% \\ Density of coal seam & 1.43 \(\times\) 10\({}^{3}\) & kg/m\({}^{3}\) \\ Poisson’s ratio & 0.32 & / \\ Modulus of elasticity of coal seam & 2.6 \(\times\) 10\({}^{3}\) & MPa \\ Tensile strength & 1.0 \(\times\) 10\({}^{4}\) & Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial parameter setting for numerical simulation of coal bed water injection. Analysis of Radial Seepage Velocity Field of Coal Bed Water Injection Borehole under Different Pore Water Pressure  
A numerical simulation was conducted on a unidirectional injection borehole with a length of 85 m. A cross-section was set at a radial distance of 1.5 m from the injection borehole to analyze the temporal variation of seepage velocity around the borehole under different injection pressures. The simulation results are presented in Figure 5. The data regarding the temporal variation of seepage velocity around the borehole were then compiled and plotted as a curve graph, as shown in Figure 6.  
Figure 4: Borehole radial pressure versus time plot. Figure 3: Cloud diagram of pressure changes with time around the radial direction of the borehole under different injection pressures. Based on an analysis of the contour plots depicting the temporal variation of seepage velocity around the borehole under different injection pressures, it is evident that the moisture migration range expands radially around the borehole within the first 36 h, accompanied by a decrease in average seepage velocity. During the initial stage of water injection, the seepage range of moisture within the coal seam is relatively limited, but the seepage velocity under high water pressure is significantly higher. At an injection pressure of 25 Mpa, the average seepage velocity around the borehole is approximately 22.55 m/s, whereas under a low injection pressure of 4 Mpa, it is approximately 1.64 m/s.