## 4 Discussion
### Influence of Metamorphic Degree on Fractal Characteristics  
When coal is heated to a specific temperature, some organic and mineral substances in the coal decompose, and the volatile components of coal, namely, the combustible gases, are released. Volatile matter is an important indicator of the degree of coal metamorphism. The smaller the amount of volatile matter, the higher the degree of coal metamorphism and the stronger the ability of the coal to adsorb gas [36]. Studying the relationship between the volatile matter and fractal dimension is crucial for understanding the influence of metamorphic degree on coal structure. The fractal dimension of the test data of each group of samples was calculated using common fractal models, and the calculation results are presented in Figures 7-9 and Table 3.  
Figure 7: Fractal calculation of sponge models with different coal ranks. (**a**) XJE, (**b**) PML, (**c**) HYS, and (**d**) LXK. Figure 8: Fractal calculation of FHH models for different coal ranks. (**a**) XJE, (**b**) PML, (**c**) HYS, and (**d**) LXX. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample Number** & **Fitting Equation** & \begin{tabular}{c} **Fitting Degree** \\ **R\({}^{2}\)** \\ \end{tabular} & \
\begin{tabular}{c} **Equation Slope** \\ **K** \\ \end{tabular} &
\begin{tabular}{c} **Fractal Dimension** \\ **D\({}_{\text{i (i = 1,2,3)}}\)** \\ \end{tabular} & **Fractal Model** \\ \hline \multirow{3}{*}{XJE} & y = \(-1.1282\text{x}-2.2951\) & 0.9647 & \(-1.1282\) & 2.8718 & Sponge \\  & y = \(-0.9395\text{x}-4.2986\) & 0.9869 & \(-0.9395\) & 2.0605 & FHH \\  & y = \(-0.5538\text{x}-0.9519\) & 0.9773 & \(-0.5538\) & 2.5538 & Density function \\ \hline \multirow{3}{*}{PML} & y = \(-1.2147\text{x}-2.1529\) & 0.9684 & \(-1.2147\) & 2.7853 & Sponge \\  & y = \(-0.6352\text{x}-2.3135\) & 0.9991 & \(-0.6352\) & 2.3648 & FHH \\  & y = \(-0.4252\text{x}-0.9551\) & 0.9640 & \(-0.4252\) & 2.4252 & Density function \\ \hline \multirow{3}{*}{HYS} & y = \(-1.3565\text{x}-2.0425\) & 0.9458 & \(-1.3565\) & 2.6435 & Sponge \\  & y = \(-0.3762\text{x}-0.0550\) & 0.9997 & \(-0.3762\) & 2.6238 & FHH \\  & y = \(-0.2977\text{x}-1.0409\) & 0.9567 & \(-0.2977\) & 2.2977 & Density function \\ \hline \multirow{3}{*}{LXX} & y = \(-1.0609\text{x}-2.4156\) & 0.9493 & \(-1.0609\) & 2.9391 & Sponge \\  & y = \(-0.5589\text{x}-1.8691\) & 0.9805 & \(-0.5589\) & 2.4411 & FHH \\ \cline{1-1}  & y = \(-0.4596\text{x}-1.2133\) & 0.9934 & \(-0.4596\) & 2.4596 & Density function \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of calculation results of full aperture fractal dimension. The full aperture fractal results reveal that the HYS sample (lean coal) with the highest degree of metamorphism had the smallest fractal dimension D\({}_{1}\) (sponge model), the largest D\({}_{2}\) (FHH model), and the smallest D\({}_{3}\) (density function model), among which the complexity of pores was the highest. The XJE sample (gas coal) with the lowest degree of metamorphism had the highest fractal dimension D\({}_{1}\), the lowest D\({}_{2}\), and the highest D\({}_{3}\). Moreover, the distribution of mesopores and throats was relatively regular. The relationship between volatile matter and fractal dimension (Figure 10) reveals that the fractal dimension D\({}_{1}\) value based on the sponge model exhibits an inverted U-shaped trend with the increase in volatile matter, first increasing and then decreasing. The fractal dimension D\({}_{2}\) value based on the FHH model decreased nonlinearly with the increase in volatile matter, and the higher the degree of metamorphism, the more complex the mesoporous structure becomes and the larger the fractal dimension. The fractal dimension D\({}_{3}\) value based on the density function model increased nonlinearly with the increase in volatile matter, and the degree of metamorphism intensified, resulting in the development of a more regular microporous structure.