## 3 Results
### Fractal Characteristics  
Based on MIP data, the fractal model of seepage pores is established. The fractal dimension obtained by the Menger sponge model is shown in Table 2. The high-pressure mercury intrusion fractal model of porous media can generally be divided into two stages--the pores are deformed or damaged in the high-pressure stage (corresponding D\({}_{2}\) value, generally \(>\)3), and the low-pressure stage generally has significant fractal characteristics (D\({}_{1}\) represents its fractal dimension) [33]. The fractal dimension D\({}_{1}\) of the pore (mainly corresponding to macro- and mesopore) in the low-pressure stage of the test sample is shown in Table 3. The fractal dimensions of coal samples C-1-C-5 fluctuates greatly, ranging from 2.7335 to 3.1366. The variance of D\({}_{1}\) value of the coal sample is 0.0188283464. The D\({}_{1}\) value of the shale sample is between 2.9164 and 2.9829, with a variance of 0.000526418. The D\({}_{1}\) value of tight sandstone samples also fluctuates significantly, between 2.8722 and 3.1820, with a variance of 0.011885722. From the D\({}_{1}\) parameter value and its variance, it can be seen that the complexity of macroporous and mesoporous pore structures of different shale samples is similar, with the smallest change, so the structure is the most stable. However, coal samples and tight sandstone samples have significant changes, reflecting the significant differences in pore structure between samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **D\({}_{1}\)** & **Sample** & **D\({}_{1}\)** & **Sample** & **D\({}_{1}\)** \\ \hline C-1 & 2.8521 & S-1 & 2.9829 & T-1 & 2.9022 \\ \hline C-2 & 3.1366 & S-2 & 2.9650 & T-2 & 2.8722 \\ \hline C-3 & 2.8114 & S-3 & 2.9164 & T-3 & 3.0203 \\ \hline C-4 & 2.8416 & S-4 & 2.9622 & T-4 & 3.1820 \\ \hline C-5 & 2.7335 & S-5 & 2.9733 & T-5 & 2.9814 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The fractal dimension of seepage pores of Munger sponge model. Figure 12: N\({}_{2}\) adsorption–desorption curves of high-rank coal samples of C-1, C-2, and C-4. (**a**) N\({}_{2}\) adsorption–desorption curve of sample C-2. (**b**) N\({}_{2}\) adsorption–desorption curves of sample C-1 and C-4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sample** & **Fitting Formula** & **g\  
The MIP method is not accurate when measuring nanoscale pores. Thus, the data of gas absorption was used to measure the fractal characteristics of micropores. The Frenkel-Halsey-Hill (FHH) fractal model [48], which has been proven to be effective in the fractal analysis of dense porous geologic materials, was used in this research. Gas adsorption data of relative pressure p/p\({}_{0}\)?0.45 with a loop formed by the uncoincidence of adsorption and desorption curves were selected to build the FHH fractal model. The data of LP-N\({}_{2}\)GA were treated according to Equation (1), with ln (ln (p\({}_{0}\)/p)) being the \(x\)-axis and lnV being the \(y\)-axis. The curve and slope (R\({}^{2}\)) of each sample were obtained by using the principle of least squares (Figure 13) and the fractal dimension value D\({}_{3}\) of each sample was calculated according to Equation (2) (Table 3). Figure 12a shows the FHH plots of shale samples. The correlation coefficients of shale samples are all \(>\)0.95, and the S-2, S-4, and S-5 samples are larger than 0.98 (Table 3). All shale samples show a good linear relationship indicating that shale samples have obvious fractal characteristics. The D\({}_{3}\) values of shale samples calculated using Equation (2) range from 2.7545 to 2.8601. The FHH plots of high-rank coal samples are shown in Figure 12b, with correlation coefficients ranging from 0.9314 to 0.9945 and D\({}_{3}\) values from 2.3016 to 2.9192 (Table 3). Tight sandstone samples show a good linear relationship in FHH plots, with correlation coefficients ranging from 0.984 to 0.9993 and D\({}_{3}\) values from 2.6328 to 2.751 (Table 3).