## 3 Results and Discussions
### Effects of PSD and Macerals on Adsorption Capacity and Adsorption Kinetics  
The coal composition has a substantial influence on the adsorption capacity of methane. Methane is primarily present in the adsorbed state on the inner surface of coal. As the vitrinite content increases, \(V_{\rm L}\) distinctly increases. The effective diffusion coefficient, \(D_{\rm e}\), however, exhibits a negative correlation with the vitrinite content. The reason is that both the TPV and the SSA have significant linear correlations with the vitrinite content (Figure 10G), and both correlation coefficients (\(R^{2}\)) are higher than 0.96. The higher the vitrinite content, the larger the adsorption surface area. Our results are in contrast to those obtained by [PERSON] [49], whose research showed that the Langmuir volume decreased with the increase of vitrinite content in anthracite, but are consistent with the results of [PERSON] [50] and [PERSON] [51]. The potential reason is that vitrinite is characterized by higher SSA and TPV of super-micropores [52], which supply more adsorption sites [53]. As shown in Figure 10B, \(V_{\rm L}\) is negatively associated with mineral matter contents (\(R^{2}\) = 0.9031), indicating that the mineral matters may mainly develop macro-mesopores. It is therefore beneficial to diffusion (Figure 10B). The correlation coefficient between mineral matter contents and \(D_{\rm e}\) was 0.8548.  
Figure 9: Adsorption isothermal curves of CH\({}_{4}\) (**A**) absolute adsorption volume and (**B**) characterization of adsorption kinetics.  
Figure 10: Relationships between macal compositions, structural parameters, and adsorption and diffusion properties (**A**, vitrinite content; **B**, mineral matter content; **C**, \(S_{3}\)+\(S_{4}\); **D**, \(S_{5}\); **E**, APD of LP-NA; **F**, Fractal \(D_{\rm S2}\); **G**, Relationship between TPV, SSA and vitrinite content).  
Previous studies have shown a positive correlation between pore SSA and CH\({}_{4}\) adsorption capacity [54; 55]. As shown in Figure 10D, \(V_{L}\) positively correlated with SSA in super-micropores (\(R^{2}=0.7282\)), but there was a discrete relationship between \(V_{L}\) and SSA in micro-transitional pores (Figure 10C). By comparing the graphs in Figure 10A,D, it can be clearly observed that the controlling factors in materials with different compositions are the vitrinite content and the SSA of super-micropores.  
Generally, the higher the vitrinite content, the larger the SSA of super-micropores, the stronger the adsorption capacity, the stronger the Knudsen diffusion, and the weaker the Fick diffusion. Research has shown that the Fick diffusion is considerably larger than the Knudsen diffusion [56]. The effective diffusion coefficient, therefore, negatively correlates with the SSA of super-micropores.  
Figure 10D shows that as the APD of micro-transitional pores increased, \(V_{L}\) decreased, and \(D_{\rm e}\) increased. This indicates that \(D_{\rm e}\) is controlled by the APD of micro-transitional pores (\(R^{2}=0.6005\)). The larger the APD, the shorter the length of the diffusion channel, which is more conducive to diffusion.  
Previous studies have also shown that the larger the fractal dimension, the stronger the adsorption capacity. Fractal \(Ds_{2}\), however, showed a weak negative relationship to \(V_{L}\), and the relationship between fractal parameters and \(D_{\rm e}\) was dispersed (Figure 10F). This may be ascribed to differences in composition, measurement medium, measurement method, etc.