# Analysis and Characterization of Micro-Nano Pores in Coal Reservoirs of Different Coal Ranks
## 3 Results and Discussion
### Fractal Dimension  
Pore fractal dimension, a parameter used to measure the physical characteristics of pores, was employed to measure the spatial distribution of the pores, representing the pore system complexity. Generally, the greater the fractal dimension of the pore, the higher the complexity of the pore system, and, the more complex the spatial distribution of the pores, the higher the degree of fracture development. Thus, the rougher the pores, the greater the lack of uniformity [34].  
Given the Avizo software, the fractal dimension command was based on the above formula for pores' fractal dimension statistics. The command was employed after the 3D reconstruction and threshold segmentation of the imported 2D slices. In this study, the pore model of the characterization unit after the threshold segmentation of each sample was obtained in the above process. The fractal dimension command was employed to calculate the fractal dimension of the pore body and surface of each xy slice. The statistical results are presented in Table 4 and Figure 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CT Type**} & **Sample** & **Fractal** & \multicolumn{3}{c}{**Surface Fractal Dimension D**} \\  & **Name** & **Dimension D\({}_{\mathbf{v}}\)** & **D\({}_{\mathbf{min}}\)** & **D\({}_{\mathbf{avg}}\)** & **D\({}_{\mathbf{max}}\)** \\ \hline \multirow{3}{*}{Micro-CT} & LL & 2.57 & 1.14 & 1.47 & 1.74 \\  & XJ & 2.36 & 0.94 & 1.17 & 1.79 \\  & ZZ & 2.49 & 1.23 & 1.42 & 1.77 \\ \hline \multirow{3}{*}{Nano-CT} & LL & 2.51 & 1.38 & 1.43 & 1.50 \\  & XJ & 2.30 & 0.87 & 1.08 & 1.41 \\ \cline{1-1}  & ZZ & 2.33 & 1.10 & 1.28 & 1.39 \\ \hline \hline \end{tabular} Note: “LL” means medium-rank coal sample name; “XJ” means low-rank coal sample name; “ZZ” means high-rank coal sample name; “D\({}_{\mathbf{v}}\)” means average value of surface fractal dimension.  
\end{table}
Table 4: Statistics of fractal dimensions for each characterization unit sample.  
In Table 4, it was observed that the volume fractal dimension of each sample under micro-nano-CT scanning was around 2.5, and the uniformity was poor. Among these, under the micro-CT scanning, the fractal dimension of XJ was the smallest, the fractal dimension of LL was the largest, and the volume fractal dimension of the sample scanned under nano-CT remained constant. However, the homogeneity of XJ and ZZ was relatively superior compared with LL.  
Given Table 4 and Figure 8, the fractal dimension of each sample surface was analyzed. It was observed that the surface fractal dimension of each sample exhibited characteristics of oscillation and fluctuation. Among these, under micro-CT scanning, ZZ displayed the least fluctuation, ranging between 1.14 and 1.74, whereas XJ exhibited the largest fluctuation, ranging between 0.94 and 1.79. Conversely, under nano-CT scanning, LL exhibited the least fluctuation, ranging between 1.38 and 1.50, while XJ exhibited the largest, ranging between 0.87 and 1.41. Given the average surface fractal dimension under micro-CT scanning, LL exhibited the largest at 1.47, while XJ exhibited the smallest at 1.17. Similarly, under nano-CT scanning, LL again exhibited the largest surface average fractal dimension, reaching 1.43, with XJ recording the smallest at 1.08. This analysis indicated that XJ exhibited the smallest fractal dimension with the best uniformity, while LL exhibited the largest fractal dimension, indicating rougher pores and poorer uniformity.  
Figure 9: Statistics of fractal dimensions for the xy slice surface of each sample.