# Analysis of Application Parameters of Hydraulic Slotting Technology in Jointed Coal Reservoirs
## 2 Optimization of Borehole Angles
### Simulation Results and Analysis  
According to the axial tensile stress cloud diagram shown in Figure 2, under the action of a high-pressure water jet, the stress concentration area and maximum stress of the cleat with different included angles occurred at the cleat tip. In the simulation, the stress at the cleat tip was obtained. The maximum values of the different stresses are shown in Figure 3. The values of the axial tensile  
\begin{table}
\begin{tabular}{c c} \hline
**Properties** & **Values** \\ \hline Young’s Modulus (MPa) & 1750 \\ Poisson’s ratio & 0.3 \\ Density (kg.m\({}^{-3}\)) & 1400 \\ Internal friction angle (\({}^{\circ}\)) & 23 \\ Uniaxial compressive strength (MPa) & 13 \\ Fracture toughness (MPa\(\cdot\)m\({}^{1/2}\)) & 0.11 \\ Initial porosity & 0.0186 \\ \hline \end{tabular}
\end{table}
Table 1: Basic parameters.  
Figure 2: Numerical simulation diagram: **(a–e)** cloud diagram of axial tensile stress with different included angles; **(f–g)** diagram of numerical simulation model.  
stress were maximum; that is, under the same water jet pressure, the axial tensile stress was the first to reach the tensile strength of the material. Additionally, the cleat in the coal seam was initiated by tensile failure. Moreover, according to [PERSON]'s theory, the cleat expanded along the axial tensile stress direction, which was the vertical direction of the natural cleat.  
To further investigate the cleat initiation, the K\({}_{\text{I}}\) values at different points close to the cleat tip were calculated using Equation (2). The K\({}_{\text{I}}\) values of the cleat tip at different included angles were obtained using the least squares method to fit K\({}_{\text{I}}\) and obtain the regression line. The K\({}_{\text{I}}\) fitting results for the cleats tips with different included angles are presented in Figure 4, and the K\({}_{\text{I}}\) values at the tips are shown in Figure 5. As can be seen, the K\({}_{\text{I}}\) values at both tips of the 0\({}^{\circ}\), 15\({}^{\circ}\), and 30\({}^{\circ}\) models exceeded the fracture toughness of the coal, and cleats were initiated from both cleat tips. In the 45\({}^{\circ}\) model, only the K\({}_{\text{I}}\) value of the right tip exceeded the fracture toughness, and the cleat initiated from the right tip. Because the K\({}_{\text{I}}\) values at both tips of the 60\({}^{\circ}\) model did not exceed the fracture toughness of coal, the cleat did not initiate.  
Figure 4: Fitted K\({}_{\text{I}}\) curves of different models.  
Figure 3: Stress of cleat tips in different models.  
As shown in Figure 5, under water jet action, the cleats at a small included angle to the normal direction of the high-pressure water jet were easier to initiate. The stress intensity factor \(\rm K_{I}\) was larger at the cleat tip of 20-45\({}^{\circ}\). Both cleat tips were more prone to initiate at 30\({}^{\circ}\). Additionally, the cracks extended along the axial tensile stress direction. To make the slot and cleats inside the coal seam connect with each other, the slotting borehole should be drilled at a small angle to the cleats. The beddings and cleats in the coal seam were perpendicular to each other. Therefore, the optimal arrangement parameter was the inclination of 30\({}^{\circ}\) for the included angles between the borehole and the coal seam strike. Thus, the water jet impact was beneficial to the development of cleats and beddings.