## 3 Results and Discussions
### Pore Structures
#### 3.2.2 LP-NA and LP-CA Tests Results  
The SSA and TPV determined by the LP-NA test varied in the ranges 0.913-1.559 m\({}^{2}\)/g and 0.0015-0.0025 cm\({}^{3}\)/g, with averages of 1.161 m\({}^{2}\)/g and 0.002 cm\({}^{3}\)/g, respectively (Table 2). The average  
Figure 3: Curves of (**A**) cumulative mercury quantity and (**B**) incremental pore volume vs. pore diameter according to MIP data. pore diameter (APD) in the LP-NA test ranged between 6.47 and 9.66 nm. This indicates that the pores' sizes were mainly below 10 nm. The LP-NA adsorption-desorption isotherms can be adapted to identify the pore types [45]. According to their isotherm curves, the samples could be classified into two types [33]: Type A and Type B (Figure 4). The A3, A4, and A5 isotherms, which were parallel to the desorption isotherms (\(P/P_{0}<0.2\)), belonged to Type A. At this relative pressure range, the isotherms were reversible and corresponded to semi-closed pores. The isotherms exhibited moderate hysteresis loops when the relative pressure was higher, implying the existence of slit or cylindrical pores. On the contrary, the isotherms of Type B (A1 and A2) demonstrates a significant change in hysteresis loops (\(P/P_{0}\approx 0.5\)). This revealed the presence of spherical or ink-bottle pores. The maximum adsorption volume of CO\({}_{2}\) was between 22.88 and 34.29 cm\({}^{3}\)/g (mean: 28.42 cm\({}^{3}\)/g). The super-micropore diameters were mainly distributed in the range 0.4-0.9 nm. Three peaks at pore diameters of 0.48, 0.55, and 0.82 nm are shown in Figure 5. The SSA and TPV of LP-CA tests varied in the ranges 241.67-357.96 m\({}^{2}\)/g and 0.074-0.106 cm\({}^{3}\)/g, with averages of 298.65 m\({}^{2}\)/g and 0.0898 cm\({}^{3}\)/g, respectively. These values are considerably greater than those of the MIP and LP-NA tests. Comprehensive Characterization of Pore Fractals  
The fractal dimension is generally from 2 to 3. On account of the fractal theory, there are evident positive correlations in the scatter plots of Figure 6 between lg(\(dV_{p}\)/dP) and lg\(P\). The slope, \(k\), can be \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{2}{c}{**MIP**} & \multicolumn{2}{c}{**LP-NA**} & \multicolumn{3}{c}{**LP-CA**} & \multicolumn{3}{c}{**CH\({}_{4}\) Adsorption**} \\ \cline{2-10}  & \(V_{\text{M}}\) & \(S_{\text{M}}\) & \(V_{\text{BIH}}\) & \(S_{\text{BET}}\) & APD & \(V_{\text{CO2}}\) & \(V_{\text{DFT}}\) & \(S_{\text{DFT}}\) & \(V_{\text{L}}\) & \(P_{\text{L}}\) \\  & **(cm\({}^{3}\)/g)** & **(m\({}^{2}\)/g)** & **(cm\({}^{3}\)/g)** & **(m\({}^{2}\)/g)** & **(nm)** & **(cm\({}^{3}\)/g)** & **(cm\({}^{3}\)/g)** & **(m\({}^{2}\)/g)** & **cm\({}^{3}\)/g** & **MPa** \\ \hline A1 & 0.0277 & 7.5 & 0.0023 & 1.496 & 9.656 & 22.88 & 0.074 & 241.67 & 31.55 & 1.07 \\ A2 & 0.0301 & 11.55 & 0.0016 & 0.922 & 8.571 & 26.31 & 0.084 & 277.16 & 37.08 & 1.03 \\ A3 & 0.0275 & 10.62 & 0.0021 & 0.915 & 8.761 & 28.36 & 0.089 & 297.20 & 37.41 & 0.96 \\ A4 & 0.0338 & 12.16 & 0.0015 & 0.913 & 7.891 & 30.24 & 0.096 & 319.26 & 37.87 & 0.7 \\ A5 & 0.0298 & 12.67 & 0.0025 & 1.559 & 6.470 & 34.29 & 0.106 & 357.96 & 38.63 & 1.29 \\ Average & 0.0298 & 10.90 & 0.0020 & 1.161 & 8.270 & 28.42 & 0.090 & 298.65 & 36.51 & 1.01 \\ \hline \hline \end{tabular} Note: LP-NA = low-pressure N\({}_{2}\) adsorption; LP-CA = low-pressure CO\({}_{2}\) adsorption; \(V_{\text{M}}\) = Volume of MIP; \(S_{\text{M}}\) = Specific surface area of MIP; \(V_{\text{BIH}}\) = Volume of LP-NA; \(S_{\text{BET}}\) = Specific surface area of LP-NA; APD = Average pore diameter; \(V_{\text{CO2}}\) = Adsorption volume of CO\({}_{2}\); \(V_{\text{DFT}}\) = Volume of LP-CA; \(S_{\text{DFT}}\) = Specific surface area of LP-CA; \(V_{\text{L}}\) = Langmuir adsorption volume; \(P_{\text{L}}\) = Langmuir pressure.  
\end{table} 
Table 2: Characteristics of pore structure and methane adsorption. Figure 4: Adsorption isothermal curves obtained from the (**A**) LP-NA and (**B**) LP-CA tests.