## 3 Results
### Embedding an Artificial Micro-Fracture with Different Dip Angle  
The direction of fluid flow in tight sandstone reservoirs with micro-fracture can significantly impact their permeability. To investigate this, we added a single micro-fracture to a digital rock of tight sandstone reservoir with an aperture of 10 voxels, a length of 500 voxels, and a dip angle ranging from 0 to 40 degrees. This produced a multi-scale digital rock of the tight sandstone reservoir which is illustrated in Figure 13. The pore network model of the multi-scale digital rock was extracted using the maximal balls method with 0.6 h, as shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Different Aperture** & **Porosity/\%** & \multicolumn{3}{c}{**Permeability/10\({}^{-3}\)\(\upmu\)m\({}^{2}\)**} \\  & & **X Direction** & **Y Direction** & **Z Direction** \\ \hline Initial & 3.21 & 0.17 & 0.01 & 0.10 \\ Le = 50 \(\upmu\)m & 4.60 & 0.56 & 1.46 & 0.57 \\ Le = 200 \(\upmu\)m & 5.89 & 3.77 & 14.63 & 1.77 \\ Le = 300 \(\upmu\)m & 7.66 & 5.65 & 572.53 & 2.82 \\ Le = 450 \(\upmu\)m & 10.70 & 298.63 & 1136.91 & 2.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The porosity and permeability of the embedding an artificial fracture with different length. The impact of the fracture dip angle on the pore throat structure can be observed in Figure 14. The figure clearly indicates that as the fracture dip angle increases, the pore radius distribution remains relatively stable. In contrast, the distribution of throat radius changes from a simple, single-peaked Gaussian distribution to a more complex, double-peaked, or multi-peaked distribution. By examining the values of pore structure contribution to permeability, as depicted in Figure 15, it can be concluded that the intervals with higher contributions to permeability for pore and throat radius are not significantly different from the original core intervals. However, there are more noticeable changes in the intervals with higher contributions to permeability for throat radius. Figure 12: The capillary pressure curve of the embedding is an artificial fracture with different lengths in different directions. (**a**) is for X direction, (**b**) is for Y direction, (**c**) is for Z direction. Figure 13: The digital rocks embedding an artificial fracture with a different dip angle and pore networks extracted using the maximal balls method. (**a**) shows the digital rock and pore network with the micro-fracture whose dip angle is \(10^{\circ}\), (**b**) is the digital rock and pore network with the micro-fracture whose dip angle is \(20^{\circ}\), (**c**) represents the digital rock and pore network with the micro-fracture whose dip angle is \(30^{\circ}\), and (**d**) displays the digital rock and pore network with the micro-fracture whose dip angle is \(40^{\circ}\). Table 3 summarizes the effects of micro-fracture dip angle on the permeability of a tight sandstone reservoir in different directions. The time needed for each pore network model is 0.1 h. As the dip angle of the micro-fracture increases, the permeability in both the X and Y directions initially increases before eventually decreasing. This results from the fact that when the micro-dip fracture's angle grows so does the dip angle between it and the flow directions along the X and Y axes which impacts the permeability in those directions. The permeability in the Z direction remains constant regardless of the dip angle of the micro-fracture. The impact of micro-fracture dip angle on fluid flow was investigated by analyzing capillary pressure curves in various directions, as depicted in Figure 16. The figure indicated that, with increasing micro-fracture dip angle, the capillary pressure curves shifted to the  
Figure 14: The pore structure distribution of the embedding an artificial fracture with different dip angles. (**a**) pore radius distribution and (**b**) throat radius distribution. Figure 15: The contribution for permeability of embedding an artificial fracture with different dip angles.