## 4 Results and Discussion
### Test Results of Volume Fraction and Carbon Isotope Value
increase in extraction time, the carbon isotope value of CH\({}_{4}\) becomes heavier linearly with CBM desorption time, while the carbon isotope value of CO\({}_{2}\) becomes lighter nonlinearly with CBM desorption time, and it is believed that fractionation effect may occur in the process of CBM extraction in coalbeds. Because the polarity of the \({}^{12}\)C-H bond in CBM is weaker than that of the \({}^{13}\)C-H bond, there is a phenomenon of \({}^{12}\)CH\({}_{4}\) preferential desorption and \({}^{13}\)CH\({}_{4}\) lagging desorption in the process of extraction, which is mainly due to the continuous conversion of \({}^{12}\)C to \({}^{13}\)C in CBM, which makes the \({}^{13}\)C accumulate gradually, and the extraction power may result in the fractionation of carbon isotopes. As the polarity of the \({}^{13}\)C-O bond in CO2 is weaker than that of \({}^{12}\)C-O bond, there exists the phenomenon of \({}^{13}\)CO2 preferential desorption and \({}^{12}\)CO2 lagging desorption in the extraction process, which is mainly due to the conversion of \({}^{13}\)C of CO\({}_{2}\) to \({}^{12}\)C, making \({}^{13}\)C gradually diluted, indicating that the difference of desorption dynamics between different molecules may result in fractionation of carbon isotopes. Due to the strong or weak ability of mutual exchange between \({}^{13}\)CH\({}_{4}\) or \({}^{12}\)CH\({}_{4}\) in methane molecules and \({}^{13}\)CO\({}_{2}\) or \({}^{12}\)CO\({}_{2}\) in carbon dioxide molecules, it leads to the fractionation difference characteristic of CBM carbon isotopes in the negative pressure extraction process. To summarize, the difference in the fractionation characteristics of gas carbon isotopes during negative-pressure extraction is due to the strong or weak ability of mutual exchange between \({}^{13}\)CH\({}_{4}\) or \({}^{12}\)CH\({}_{4}\) in methane molecules and \({}^{13}\)CO\({}_{2}\) or \({}^{12}\)CO\({}_{2}\) in carbon dioxide molecules. According to other studies, in terms of hydrocarbon isotopes, the carbon isotope values of the No. 6-1, No. 6-2, No. 6-3, No. 7-1, No. 8-2 and No. 9 coalbeds tend to become heavier with depth increase in the Qidong Coal Mine in Anhui Province [24]; the No. 2 coalbed at the top measures the same as to the No. 15 coalbed at the bottom in the Sihe Coal Mine in Shanxi Province [30]. However, the carbon isotope values of the No. 3, No. 9 and No. 15 coalbeds gradually become lighter with depth increase in the Fenghuangshan Coal Mine in Shanxi Province [27], and the same is for the M6-3, M7-2, M8 and M11 coalbeds in Fengchun Coal Mine in Chongqing [38]. Therefore, it can be found that, in different regions, CBM carbon isotope composition and burial depth show completely different change rules, and there is no good explanation for this phenomenon. However, for the purpose of this study, it is only necessary to understand that, even if there is a certain overlap area in the variation range of isotopes, the isotopes of different coalbeds are different overall, so isotope geochemistry can be applied to determine the extraction ratio of a target coalbed. In different coalbeds, since the volume fraction and carbon isotope of CH\({}_{4}\) and CO\({}_{2}\) have linear differences with depth, when CBM extraction is carried out by drilling through coalbeds of different depths, the target CBM extraction can be well distinguished from the adjacent CBM. According to the difference characteristics of CBM in isotope geochemistry, it is considered that it is possible to determine a target CBM extraction ratio.