## 4 Results and Discussion
### Analysis of Isotope Geochemistry  
Adopting the averaging method, the average values of volume fractions and carbon isotope values are shown in Table 2.  
The mean values of the volume fractions and carbon isotopes of CH\({}_{4}\) and CO\({}_{2}\) determined in Table 2 are substituted into Equation (9), and the calculation results of the extraction ratio from each coalbed are shown in Figure 10.  
It can be observed from Figure 10 that, when boreholes are adopted for CBM extraction from the 6u + 6m + 6l coalbeds, the extraction ratio from the 6m coalbed accounts for the largest, ranging from 57.81% to 69.58%, and the results of three samples are basically the same. The extraction ratios from the adjacent 6u and 6l coalbeds are in a secondary position, in which the extraction ratio from 6u coalbeds ranges from 10.82% to 24.54%, and that from 6l coalbeds ranged from 5.88% to 31.37%. The values during CBM extraction from 6u + 6m coalbeds are processed and converted. The extraction ratio from the 6m coalbed ranged from 73.92% to 84.23%, and the adjacent 6u coalbed ranged from 15.77%\(\sim\)-26.08%. This is largely consistent with the extraction ratio from the 6m coalbed and adjacent 6u coalbed, which are 74.05% and 25.95%, respectively, as calculated in actual practice. This indicates that the calculation results of extraction ratio from the three coalbeds are applicable to any two of the three coalbeds, and indirectly confirmed the scientific nature of this method. Some scholars have studied the correlation between the CBM carbon isotope and CBM content and believe that, with the increase in CBM content and pressure, the CBM carbon isotope also becomes heavier, reflecting that the factors controlling CBM content are consistent with those controlling CBM carbon isotope factors. The maximum original CBM contents of the 6u, 6m and 6l coalbeds in the Xiaotun Coal Mine are 9.23 m\({}^{3}\)/t, 12.47 m\({}^{3}\)/t and 9.56 m\({}^{3}\)/t, respectively, and no obvious correspondence is found with the CBM carbon isotope. However, the process of CBM extraction is accompanied by the desorption and diffusion of CBM, and the fractionation effect of the CBM carbon isotope also occurs in the process of desorption, diffusion and migration of CBM. In Figure 10, the 6m coalbed with a high CBM content is more prone to desorption and diffusion during the extraction process, and the extraction ratio occupies an absolute position, indicating that the factors controlling the CBM content are still consistent with those controlling the carbon isotope of CBM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Coalbed**} & \multicolumn{2}{c}{**Average Values of Volume**} & \multicolumn{2}{c}{**Average Values of Carbon**} \\  & \multicolumn{2}{c}{**Fraction (\%)**} & \multicolumn{2}{c}{**Isotope (\%)**} \\ \cline{2-5}  & \(\mathbf{CH_{4}}\) & \(\mathbf{CO_{2}}\) & \(\mathbf{CH_{4}}\) & \(\mathbf{CO_{2}}\) \\ \hline
6u & 33.54 & 0.19 & \(-\)35.49 & \(-\)8.37 \\
6m & 52.14 & 0.26 & \(-\)34.24 & \(-\)2.15 \\
6l & 65.75 & 0.21 & \(-\)33.58 & \(-\)4.75 \\
6u + 6m * & 81.51 & 0.29 & \(-\)34.47 & \(-\)4.88 \\
6u + 6m + 6l (1–1) * & 83.17 & 0.28 & \(-\)34.40 & \(-\)3.50 \\
6u + 6m + 6l (1–2) * & 83.17 & 0.28 & \(-\)34.86 & \(-\)3.93 \\
6u + 6m + 6l (1–3) * & 83.17 & 0.28 & \(-\)34.12 & \(-\)3.48 \\ \hline \hline \end{tabular}
* Note: Due to the abnormal values of the carbon isotope of CO\({}_{2}\) for samples No. 2–3 and No. 2–5, the average value of the CO\({}_{2}\) carbon isotope in CBM extraction of the 6u + 6m coalbeds was computed based on the test data of samples No. 2–2, No. 2–6 and No. 2–10–b2. Due to the abnormal values of samples No. 1–6 and No. 1–b8, the test data of samples No. 1–1, No. 1–2 and No. 1–3 were selected, respectively, for the CH\({}_{4}\) and CO\({}_{2}\) carbon isotope values in CBM extraction of the 6u + 6m + 6l coalbeds.  
\end{table} 
Table 2: The average values of volume fraction and carbon isotope. Figure 10: Calculation results of extraction ratio from each coalbed.