## 3 Results and Discussion
### Adsorption Characteristics of Coal Samples  
Coal exhibits pronounced adsorption properties due to its intrinsic structural characteristics--abundant pore networks and well-developed microfractures. These fea \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Sample Size**} & \multicolumn{2}{c}{**Sample Forming**} & \multicolumn{2}{c}{**Cohesion Force \(c\)**} & \multicolumn{1}{c}{**Internal Friction**} \\ \cline{2-6}
**Coal Sample** & **Diameter (mm)** & **Height (mm)** & **Pressure \(\sigma_{m}\) (MPa)** & **(MPa)** & **Angle \(\varphi\) (\({}^{\circ}\))** \\ \hline BT-1 & 50.80 & 98.24 & 50 & 0.048 & 51.23 \\ BT-2 & 50.80 & 99.06 & 70 & 0.053 & 52.06 \\ BT-3 & 50.80 & 99.12 & 100 & 0.103 & 53.34 \\ BT-4 & 50.80 & 99.20 & 130 & 0.125 & 54.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of cohesion force and internal friction angle of briquette coal samples with different sample forming pressures under a fixed confining pressure of 2 MPa. Figure 4: Triaxial strength characteristics of raw coal and briquette coal samples. (**a**) Triaxial strength of raw coal samples under different confining pressures; (**b**) triaxial strength of briquette coal samples with different sample forming pressures under a fixed confining pressure of 2 MPa. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Sample Size**} & \multicolumn{2}{c}{**Confining**} & \multicolumn{2}{c}{**Cohesion**} & \multicolumn{1}{c}{**Mean Value of**} & \multicolumn{1}{c}{**Internal Value of**} \\ \cline{2-6}
**Coal Sample** & **Diameter** & **Height (mm)** & **Pressure \(\sigma_{2}\)=\(\sigma_{3}\) (MPa)** & **Force \(c\) (MPa)** & **\(c\) (MPa)** & **\(\varphi\) (\({}^{\circ}\))** \\ \hline RT-1 & 48.45 & 100.02 & 2 & 0.94 & & 60.94 \\ RT-2 & 48.52 & 100.14 & 4 & 1.27 & & 51.62 \\ RT-3 & 48.48 & 100.05 & 5 & 1.41 & 1.35 & 47.69 \\ RT-4 & 48.63 & 100.08 & 6 & 1.59 & & 42.84 \\ RT-5 & 48.59 & 100.11 & 8 & 1.54 & & 44.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of cohesion force and internal friction angle of raw coal samples under different confining pressures. tures provide numerous binding sites for gas molecules. When gas molecules enter the coal matrix, they are attracted by the adsorptive potential generated through van der Waals forces between the molecules and coal surface, adhering to pore walls. Desorption occurs when molecules acquire sufficient kinetic energy to overcome this potential. The dynamic equilibrium between adsorption and desorption arises from the stochastic motion of molecules and real-time variations in adsorption conditions, predominantly occurring in micropores. This process is typically described by the Langmuir (monolayer adsorption) [59] and BET (multilayer adsorption) theories [60]. The Langmuir theory posits that gas molecules form a single adsorbed layer on specific surface sites, aligning with Type I isotherms classified by the IUPAC [61]. It is widely used to derive critical adsorption constants. In contrast, the BET theory accounts for multilayer adsorption by considering the attraction between adsorbed and free-phase molecules, primarily applied for specific surface area determination [62]. In this study, the Langmuir theory was applied to analyze experimental data. Figure 5 illustrates the adsorption characteristics of N\({}_{2}\), CH\({}_{4}\), and CO\({}_{2}\) in coal. All three gases exhibited Type I isotherms, where adsorption volume increases with rising equilibrium pressure under constant temperature until reaching saturation. Adsorption capacity grows progressively as pressure escalates, with more molecules occupying available sites. At a critical pressure, adsorption equilibrium is established when adsorbed molecules dynamically balance with those escaping from sites. Notably, coal demonstrated distinct adsorption affinities for the three gases: CO\({}_{2}\) adsorption capacity was the highest, followed by CH\({}_{4}\), while N\({}_{2}\) adsorption was the weakest.