## 3 Results and Discussions
### Pore Structures
#### 3.2.2 LP-NA and LP-CA Tests Results
obtained by fitting the scatters and the fractal \(D=4+k\). Figure 6A shows and Table 3 summarizes the calculation process and results, respectively. The adsorption mechanism transforms with changes in \(P/P_{0}\). The van der Waals forces are dominant when \(P/P_{0}\) is less than 0.5; however, the adsorption mechanism transforms to capillary condensations when \(P/P_{0}\) is larger than 0.5. [PERSON] and [PERSON] used \(\delta\) to discriminate the dominant adsorption mechanism. In general, if \(\delta>0\), then the relationship between \(A\) and \(D_{S}\) is as follows:  
\[Ds=3\times A+3 \tag{5}\]  
if \(\delta<0\), then it changes to:  
\[Ds=A+3 \tag{6}\]  
Figure 5: (**A**) Pore volume and (**B**) specific surface area (SSA) distributions for different pore sizes determined by LP-CA tests. Figure 6: Calculation process of the fractal dimension, (**A**) by MIP; (**B**) by LP-NA. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Samples** & \(k\) & \(D\) & \(A_{1}\) & \(\delta_{1}\) & \(D_{81}\) & \(A_{2}\) & \(\delta_{2}\) & \(D_{82}\) & \(D_{e}\), \(10^{-5}\) s\({}^{-1}\) \\ \hline A1 & \(-1.45\) & 2.55 & \(-0.57\) & \(-0.71\) & 2.43 & \(-0.27\) & 0.19 & 2.19 & 2.88 \\ A2 & \(-1.50\) & 2.5 & \(-0.92\) & \(-1.76\) & 2.08 & \(-0.28\) & 0.16 & 2.16 & 2.05 \\ A3 & \(-1.64\) & 2.36 & \(-1.15\) & \(-2.45\) & 1.85 & \(-0.30\) & 0.10 & 2.10 & 1.93 \\ A4 & \(-1.62\) & 2.38 & \(-1.31\) & \(-2.93\) & 1.69 & \(-0.30\) & 0.10 & 2.10 & 2.16 \\ A5 & \(-1.40\) & 2.60 & \(-1.27\) & \(-2.81\) & 1.73 & \(-0.21\) & 0.37 & 2.37 & 1.42 \\ Average & \(-1.52\) & 2.48 & \(-1.04\) & \(-2.13\) & 1.96 & \(-0.27\) & 0.18 & 2.18 & 2.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristics of fractal dimensions from MIP data and low-pressure adsorption data. where \(Ds_{1}\) and \(Ds_{2}\) represent the fractal dimensions when \(P/P_{0}\) is in the 0-0.5 and 0.5-1.0 intervals, respectively. The calculation process and results are shown in Figure 6B and summarized in Table 3, respectively. The macro-mesopore fractal dimensions (\(D\)), pore surface fractal dimensions (\(Ds_{1}\)), and pore structure fractal dimensions (\(Ds_{2}\)) varied in the ranges 2.36-2.60, 1.69-2.43, and 2.10-2.37, with averages of 2.48, 1.96, and 2.18, respectively. The factor \(Ds_{1}\) is not discussed in subsequent sections of this paper because it has distinct anomalies. Comprehensive Characterization of Pore Structures  
To comprehensively describe the PSD characteristics of anthracite reservoirs, the results of MIP, LP-NA, and LP-CA tests were superimposed. The LP-NA and LP-CA tests caused inconsiderable destruction to the sample. The data of the two experiments did not overlap; hence, the direct superposition method was selected. The MIP and LP-NA, however, characterized the macro-mesopore and micro-transitional pore systems, respectively. The test data overlapped and therefore were cut and combined. With regard to the coal matrix compressibility [46], a significant increase in mercury volume can be observed when the test pressure of MIP is higher than the critical value that can introduce errors to the fractal study of the pore structure. Relative to this, previous researchers have proposed a method for correcting MIP data based on the LP-NA test [47]. In this study, the fractal theory was used to analyze the compressibility of the coal matrix. By considering the fractal characteristics of MIP, it can be seen that fractal D distinctly changed at lgP = 1.16 (pore diameter = 100 nm in Figure 6A). It shows that when the mercury injection pressure was greater than 14.45 MPa, the coal matrix compressibility was considerable and would severely distort the pore volume test results. When the pressure was less than 14.45 MPa, however, the pore filling effect was dominant, and the mercury intrusion data were accurate. The MIP, LP-NA, and LP-CA data were therefore used to characterize macro-mesopores (larger than 100 nm), micro-transitional pores (2-100 nm), and super-micropores (less than 2 nm).