**3.** *K***1–***p* **Relation Model**

The drilling cuttings gas desorption index *K*<sup>1</sup> characterizes the characteristic parameters of the coal gas desorption speed. It reflects the coal seam gas content and the size of the initial pressure relief gas desorption rate. Scholars at home and abroad have carried

out extensive and in-depth research on the law of gas desorption from drilling cuttings in the laboratory [27,28]. They mainly studied the influence of mathematical fitting of gas desorption law and gas pressure on the gas desorption index of drilling cuttings. The research results show that the gas desorption law of drilling cuttings is the law of gas desorption amount of drilling cuttings changing with time. It can not only reflect the gas adsorption pressure and desorption gas content in coal but also reflect the damage degree of coal; that is, it can be used for outburst prediction. It is also used to determine the gas pressure and tile content of a coal seam. According to Zhao's research results [29], there is a power function relationship between the gas desorption index of drilling cuttings and the gas pressure of adsorption equilibrium:

$$K\_1 = mp^n \tag{2}$$

where *<sup>K</sup>*<sup>1</sup> is the gas desorption index of drilling cuttings, mL·g−1·min−0.5. *<sup>p</sup>* is the adsorption equilibrium gas pressure, MPa. *m* and *n* are undetermined constants, 0 < *n* < 1.

The instrument used to determine *K*<sup>1</sup> in the underground field and laboratory is a WTC gas outburst parameter instrument. The underground site is measured according to the AQ/T 1065–2008 drilling cuttings gas desorption index determination method. The laboratory determination of the *K*1–*p* relationship model test process is based on the test method adopted by Lei [30]. According to Equation (2), the key to determine the gas desorption index of drilling cuttings is to determine the undetermined constants *m* and *n*. The essence of laboratory determination of the *K*1–*p* relationship model is to determine the undetermined constants *m* and *n*. The measured *K*1–*p* relationship model results of 24 coal samples, gas basic parameters such as gas initial velocity Δ*p*, coal firmness coefficient *f* and coal quality index measurement results are summarized in Table 2 below.



The variation ranges of each parameter of 24 coal samples measured in Table 2 are as follows: Δ*p* is 7~37 mmHg, *f* is 0.10~0.55, *K*1–*p* relationship model coefficient *m* is 0.217~0.9371, and index *n* is 0.4431~0.7740.

### **4. Test Result Analysis**
