## 5 Discussion  
The coal samples were collected from coal seam No. 5 in the Panzhihua coal mine located in western Guizhou, China. The moisture, ash, and volatile matter of coal were determined according to GB/T 212-2008. Referring to GB/T 217-2008 and GB/T 23561-2009, the apparent density \(\rho\) and porosity \(\varphi\) of coal were determined. The adsorption constants \(a\) and \(b\) of coal were determined by the high-pressure volumetric method. The results are shown in Table 5.  
The cumulative gas desorption amount in unit mass coal \(Q_{t}\) is mainly determined by the total amount of gas adsorbed by coal in an adsorption equilibrium state and the effective diffusion coefficient of coal. The limit of diffusion is the difference between the initial gas content \(Q_{a}\) and the final gas content \(Q_{a0}\) at the same temperature and atmospheric pressure. It is \(Q_{\infty}=Q_{a}-Q_{a0}\).The gas content under experimental conditions is calculated according to the following Equation (35). \[ \begin{array}{l}Q=Q_{a}\ +\ Q_{f}\\ Q_{a}\ =\ \frac{abp}{\frac{1}{\Gamma+bp}}.\frac{100-A_{d}-W}{100}\frac{1}{1+0.31W} \\ Q_{f}=\frac{10p+273}{\rho(273+t_{\varphi})}\end{array}  \tag{35}\]  
Figure 9: Relationship between desorption rate ratio and distribution index of granularity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{5}{c}{**Analysis of Coal Industry**} & \multicolumn{1}{c}{\(\rho\)**/(g/cm\({}^{-3}\))**} & \(\varphi\)**/\%** & \multicolumn{1}{c}{**a/(cm\({}^{3}\)/g)**} & \multicolumn{1}{c}{**b/(1/MPa)**} \\ \hline
**Mad/\%** & **Aad/\%** & **Vad/\%** & **Fcad/\%** & & & & \\ \hline
1.1 & 15 & 17.28 & 66.62 & 1.425 & 5 & 30 & 1 \\ \hline \end{tabular}
\end{table} 
Table 5: Basic parameters of coal sample. where \(Q\) is the total gas content, cm\({}^{3}\)/g, \(a\) and \(b\) are adsorption constant of combustible base, \(p\) is adsorption equilibrium pressure, MPa, \(A_{d}\) is ash on a dry basis, \(W\) is water content. \(\rho\) is apparent density of coal, g/cm\({}^{3}\), \(\phi\) is porosity. \(t_{w}\) is equilibrium temperature, \({}^{\circ}\)C.  
When the adsorption equilibrium pressure is constant, the diffusion capacity of methane in coal can be characterized by the diffusivity at different times. The diffusivity is the ratio of the cumulative desorption amount to the limit desorption amount. It is:  
\[\frac{Q_{t}}{Q_{\infty}}=\frac{M_{t}}{M_{\infty}} \tag{36}\]  
where \(Q_{t}\) is cumulative gas desorption amount in unit mass coal; \(Q_{\infty}\) is limit gas desorption amount in unit mass coal. The amount of free gas released in a short period is:  
\[Q_{ft}=\frac{10p\phi\cdot 273}{\rho(273+t_{w})}-\frac{\phi\cdot 273}{\rho(273+t_ {w})} \tag{37}\]  
The amount of adsorption gas released in a short period is (for convenience of comparison, the time is set to 30 s). \[Q_{at}=g(D_{e}(R),t)\cdot\left(\frac{abp}{1+bp}-\frac{ab}{10+b}\right)\cdot \left(\frac{100-A_{d}-W}{100}\frac{1}{1+0.31W}\right) \tag{38}\]  
Put the values in Table 5 into Equations (37) and (38), and the amount of free gas and adsorbed gas released when the coal is broken into coal of different particle sizes after 30 s is calculated. The amount of gas released by coal with different particle sizes at different adsorption equilibrium pressures is shown in Figure 10.  
When the adsorption equilibrium pressure remains constant, such as at 1 MPa, the adsorption and free gas released amounts vary with particle size and time, as illustrated in Figure 11.  
Figure 10: The amount of gas released by coal with different particle sizes at different adsorption equilibrium pressures. Figures 10 and 11 illustrate that the desorption amount of adsorbed gas increases as the particle size decreases at a given adsorption equilibrium pressure. For coal in this study collected from Yangquan coal mine in Shanxi province, North China, when the coal is broken from the size range of 5-10 mm to the size less than 0.075 mm, the size ratio for coal particles before and after being broken is up to 100.