## 3 Results
### Embedding an Artificial Micro-fracture with Different Aperture
Once the micro-fracture aperture exceeds 10 \(\upmu\)m, the influence of the micro-fracture on permeability outweighs the impact of the initial model on permeability. The evaluation of the impact of pore and throat permeability is currently limited to theoretical analysis. One approach to calculating the porosity and permeability of various models involves the utilization of pore network modeling methods. The effect of the micro-fracture aperture on the permeability of the tight sandstone reservoir in different directions is shown in Table 1. The time needed for each pore network model is 0.1 h. The porosity of a rock can increase as micro-fractures within the rock become more open. This is due to the fact that micro-fractures can greatly enhance the connectivity between pores within the rock, allowing fluids to flow more freely, see Figure 5. As the fractures widen, the volume of open space within the digital rock also increases, increasing overall porosity. It is important to note that the relationship between fracture opening and porosity can be complex and depends on various factors. Analyzing the permeability in different directions can provide valuable insights into how micro-fractures affect fluid flow. It is easy to find that with the increase in micro-fracture aperture, the permeability increases significantly in the X and Y directions, and the permeability in the Z direction also increases, but the magnitude is significantly smaller than that in the X and Y directions. As a general trend, when a micro-fracture is parallel to the flow direction, it can significantly increase the permeability in that direction. This is because the micro-fracture provides a clear and unobstructed pathway for fluid flow. On the other hand, when a micro-fracture is perpendicular to the flow direction, the increase in permeability may not be as noticeable. This is because the micro-fracture does not provide as direct a pathway for fluid flow in that direction. To further examine the influence of micro-fracture on fluid flow, capillary pressure curves in different directions which were presented in Figure 8. The data reveals that, compared to the original model, the capillary pressure curves in the X and Y directions shift towards the left as the micro-fracture opening widens. Furthermore, the capillary pressure curves in these directions exhibit significant changes when the micro-fracture opening exceeds 10 \(\upmu\)m. However, as observed in the permeability at different directions, the capillary pressure curves in the Z direction display minimal changes. This phenomenon is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Different Aperture** & **Porosity/\%** & \multicolumn{3}{c}{
\begin{tabular}{c} **Permeability/10\({}^{-3}\)\(\upmu\)m** \\ **X Direction** \\ \end{tabular} } \\  & & **Y Direction** & **Z Direction** \\ \hline Initial & 3.21 & 0.17 & 0.01 & 0.10 \\ Ap = 2 \(\upmu\)m & 7.99 & 1.33 & 2.80 & 1.67 \\ Ap = 10 \(\upmu\)m & 8.55 & 18.33 & 21.92 & 2.87 \\ Ap = 30 \(\upmu\)m & 16.17 & 2625.91 & 2968.03 & 2.98 \\ Ap = 50 \(\upmu\)m & 23.76 & 6356.13 & 7066.84 & 2.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The porosity and permeability of the embedding an artificial fracture with different aperture. Figure 7: The contribution for permeability of embedding an artificial fracture with different apertures. The pore’s contribution to permeability is (**a**) while the throat’s contribution to permeability is (**b**). attributed to micro-fractures that run parallel to the XY plane. Capillary pressure curves are frequently utilized to assess the pore structure characteristics of rocks and can be beneficial for predicting fluid flow behavior in porous media. By comparing the capillary pressure curves in different directions, it is possible to establish the relationship between the curves and the direction of fluid flow. It is essential to consider the orientation of micro-fractures when analyzing the pore structure of cores that contain such micro-fractures indirectly through capillary force curves.