# Analysis and Characterization of Micro-Nano Pores in Coal Reservoirs of Different Coal Ranks
## 3 Results and Discussion  
### Research on Representative Elementary Volume  
The 2D slices obtained using nano-CT scanning exhibited high-resolution and accurate data. Coal is an anisotropic material, and its pore structure exhibits an obvious size effect. However, due to the limitations imposed by the current computer hardware performance, it is difficult to fully characterize the pore structures of coal samples [28]. To realize the quantitative analysis of coal sample pores, it was necessary to introduce the concept of representative elementary volume (REV). The characterization unit is the smallest unit to describe the porosity and permeability of continuous porous media. Furthermore, when the volume of the coal is less than the REV, the coal porosity fluctuates significantly with volume changes. However, when the coal volume exceeds the REV, the porosity of coal tends to be stable with the volume change, making the REV model representative of coal [29]. Subsequently, the 3D pore modeling analysis was conducted using the determined \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multirow{2}{*}{**\(\mathbf{R_{Q}}\)/\%**} & \multirow{2}{*}{**Porosity/\%**} & \multicolumn{6}{c}{**Industrial Analysis**} & \multicolumn{6}{c}{**Elemental Analysis**} \\ \cline{3-10}  & & & \(\mathbf{M_{ad}}\)/\% & \(\mathbf{A_{ad}}\)/\% & \(\mathbf{V_{ad}}\)/\% & \(\mathbf{F_{ad}}\)/\% & \(\mathbf{C}\)/\% & \(\mathbf{H}\)/\% & \(\mathbf{O}\)/\% & \(\mathbf{N}\)/\% \\ \hline XJ & 0.64 & 5.1787 & 3.24 & 1.92 & 28.42 & 66.42 & 79.55 & 4.13 & 10.09 & 0.80 \\ LL & 1.52 & 9.3114 & 0.95 & 18.93 & 10.35 & 69.77 & 79.43 & 3.28 & 2.89 & 1.54 \\ ZZ & 3.46 & 7.8654 & 1.14 & 8.48 & 10.91 & 79.47 & 71.65 & 3.16 & 3.97 & 1.50 \\ \hline \hline \end{tabular} Note: \(M_{ad}\)—air-dried moisture; \(A_{ad}\)—air-dried ash; \(V_{ad}\)—air-dried volatile; \(F_{cd}\)—air-dried base-fixed carbon.  
\end{table} 
Table 1: Results of industrial analysis and elemental analysis of coal samples. REV model to study the overall characteristics of the coal sample pores, thereby saving computing resources. The size of the REV model can be calculated by selecting the region of interest (ROI), but it is biased to analyze the coal body directly according to the ROI. In this study, the box-counting method was employed to determine the characterization unit (REV). According to the local porosity distribution theory, the representativeness of the determined REV model was evaluated, indicating that the local structure was similar to the whole, and there was self-similarity among local areas [30]. The center point of the binary image obtained through the threshold segmentation of different-scale images was employed as the starting point of the box-counting method. To eliminate the influence of different starting point positions on the REV model, several other different positions in the binary image were also selected as the starting points of the box-counting method, and the 3D image was the center position of the six faces of the box, as shown in Figure 2.  
Subsequently, a cube box with an initial side length of 20 pixels was placed at nine different starting points (eight vertices and one center point) determined in the binary image (Figure 3). Upon calculating the ratio of the number of pore point pixels to the total number of pixels in the box at nine different positions, the local porosity values at different positions under the specific box size were obtained. Subsequently, the side length of the box gradually increased by 20 pixels. Finally, the relationship between the porosity of binary images with different sizes and the size of the box was obtained, and the specific change trend is shown in Figure 4. Furthermore, when the box size was small, the porosity values at different positions fluctuated significantly, owing to the uneven distribution of the pores inside the smaller-sized boxes at different positions.