## 4 Gas Desorption Law of Different Water-Bearing Coal Bodies under Various Stress Paths
### Influencing Analysis of Gas Desorption by Water-Bearing Coal under Various Stress Paths  
The change in gas desorption by water-bearing coal under different stress conditions could be characterized using the accumulated gas desorption during the test. Specifically, the time-dependent variation trend of gas desorption was characterized through the Langmuir-type relational expression, and the accumulated gas desorption by different water-bearing coal bodies under various stress paths was further analyzed [33; 34].  
\[\mathrm{Q_{t}}=\frac{\mathrm{AB\sqrt{t}}}{1+\mathrm{B\sqrt{t}}} \tag{1}\]  
where Q is the accumulated gas desorption at time t, mL/g; t is desorption time, s; A represents the limiting gas desorption, mL/g; and B is the desorption rate constant.  
Figure 4: XRD patterns of AB and PE coal samples.  
Combining the test, the accumulated gas desorption of different water-bearing coal bodies under different stress paths was finally measured and fitted as per Formula (1). Then, the limiting accumulated gas desorption of AB and PE coal samples under different test conditions was acquired, and the gas desorption curves of different water-bearing coal bodies and the change curves of their limiting accumulated gas desorption under various stress paths were plotted as shown in Figures 5-8.  
Figure 5: Gas desorption curves of AB coal samples with moisture content of 2.65% under various stress path states.  
Figure 6: Gas desorption curves of PE coal samples with moisture content of 2.65% under various stress path states.  
Figure 7: Changes in limiting gas desorption of AB coal samples with moisture content of 2.65% under various stress path states.  
By analyzing Figures 5-8, it can be seen that: (1) AB and PE coal samples were subjected to different stress paths under a certain water-bearing state, and the corresponding gas desorption process was also different. Taking 12 min as the time node in the curve change of the figures, within 0-12 min in the initial stage, the stress borne by the two types of coal samples gradually increased and the gas desorption grew rapidly, but an overlapping gas desorption was observed in this initial stage. According to the gas desorption curves, it could be observed that the total gas desorption by coal samples was in direct proportion to the stress increase at the same time node. (2) AB and PE coal samples experienced the action of various stress paths under the water-bearing state, and they differed in gas desorption after each stress path exerted its action, but the variation trend of gas desorption was similar, where the gas desorption by AB coal samples was greater than that by PE coal samples under all stress paths.  
It can be observed from Figures 7 and 8 that when the stress borne by AB and PE water-bearing coal samples rose from 0 MPa to 16 MPa, the fitted limiting desorption of AB coal samples was about 16.931-22.131 mL/g, with an increase of 5.2 mL/g, and that of PE coal samples' fitted limiting desorption was about 12.331-15.223 mL/g, increasing by 2.892 mL/g. Axial stress exerted an obvious promoting effect on the gas desorption of two types of coal samples, but the effect varied. The increment of limiting desorption by AB coal samples was greater than that by PE coal samples.  
gas migration channels directly increased the pore pressure, which enlarged the pressure difference between gas channels and increased the gas accumulation.