*4.2. The Relationship between Coal Seam Gas Content W and K1*

The coal seam gas content *W* in Equation (1) and the drilling cuttings gas desorption index *K*<sup>1</sup> in Equation (2) are directly related to the gas pressure *p*, and as the gas pressure increases, *K*<sup>1</sup> and *W* increase. To find the relationship between *K*<sup>1</sup> and *W*, gas pressure *p* is set to 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 MPa. Equations (1) and (2) are used to calculate 7 *K*<sup>1</sup> and 7 *W* corresponding to 7 gas pressures, and then, the nonlinear fitting is carried out. The *W*–*K*<sup>1</sup> relationship model is obtained, and the correlation coefficient *R<sup>2</sup>* is greater than 0.9900. The results are summarized in Table 2. One coal sample each (limited to the length of the article) was selected from the Xiangshan Coal Mine, Xiayukou Coal Mine, Xinglong Coal Mine, Sangbei Coal Mine and Sangshuping Coal Mine for nonlinear fitting. The fitting relationship curve is shown in Figure 2.

**Figure 2.** The relationship between *W* and *K*1.

It can be seen from Figure 2 that there is a significant correlation between coal seam gas content *W* and drilling cuttings gas desorption index *K*1, which is characterized by logarithmic function. The *W*–*K*<sup>1</sup> relationship model can be expressed by Equation (3):

$$\mathcal{W} = \mathbb{C} \ln K\_1 + D \tag{3}$$

where *W* is the gas content of raw coal, m3/t. *K*<sup>1</sup> is the gas desorption index of drilling cuttings, mL·g−1·min<sup>−</sup>0.5. *<sup>C</sup>* is regression slope. *<sup>D</sup>* is regression constant.

In the process of adsorption and desorption of coal, the change of coal seam gas content *W* and drilling cuttings gas desorption index *K*<sup>1</sup> is caused by the change of coal seam gas pressure. This change eventually leads to the continuous change of diffusion coefficient in the process of coal desorption, which leads to the unique nonlinear relationship between *W* and *K*1. Figure 2 shows that when the gas desorption index *K*<sup>1</sup> of the five coal mines is the same, the coal seam gas content *W* of the Xiangshan Coal Mine is the largest, and the coal seam gas content *W* of the Xiayukou Coal Mine is the smallest. From Table 2, the *W*–*K*<sup>1</sup> relationship model coefficient *C* is 4.000~7.722, and *D* is 9.829~17.98.
