The generation of natural gas runs through the whole thermal maturation process of organic matter, and the depth and temperature ranges of gas generation are much wider than those of oil generation^{[1,2,3,4,5,6]}. Although after years of research, the theory of natural gas formation has made great progress, and the genetic identification has improved^{[7,8,9,10,11]}, new problems are emerging with the exploration targets gradually turning to deep, unconventional petroleum and complex tectonic hydrothermal activity areas^[12]. For example, abnormal geochemical characteristics often occur in natural gas at high to over mature stages, including inversion of carbon isotopic compositions of alkane gas, reversal of carbon isotopic series, and even occurrence of negative carbon isotopic series of thermogenic gas^{[13,14,15,16,17]}. Researchers have studied the "abnormal" geochemical phenomena of natural gas, and obtained a series of achievements. But there are still some controversies^{[15,16,17,18,19]}. Some researchers believed that the "abnormal" carbon isotopic compositions of alkane gas was caused by water rock reaction^{[15, 19]}, while others held that the "anomalies" of carbon isotopic compositions of alkane gas were caused by the mixing of natural gases from different sources^[15]. Since the gas reservoirs discovered all over the world are mostly formed by thermal maturation of organic matter, and thermal simulation experiment can dynamically investigate the whole process of gas generation in organic matter thermal maturation, in other words, it can reflect the isotopic composition characteristics in the process of natural gas generation. Therefore, thermal simulation experiment is considered as one of the most effective means to study isotopic fractionation mechanism in the process of natural gas generation^{[20,21,22,23,24,25,26,27,28]}. In this study, the thermal simulation gas experiment of coal was used to analyze the parameter characteristics of natural gas composition, yield and carbon isotopic composition. Combined with results of previous studies, the mechanisms of carbon isotopic fractionation in the process of natural gas generation are discussed to further understand the formation mechanisms of natural gas and provide theoretical basis for natural gas exploration.

Among many thermal simulation experimental instruments, gold capsule thermal simulation system can simulate the influence of temperature and pressure on the thermal maturation of organic matter at the same time. Chemically inert, gold can prevent the catalytic effect of reaction device on hydrocarbon generation. Gold also has good ductility at high temperature, so gold capsule pyrolysis system is considered to be one of the most suitable systems to simulate gas generation characteristics of organic matter^{[22,23,24,25,26,27,28]}. After comprehensive consideration, we select thermal simulation experiment of low mature coal in gold capsule to investigate the fractionation mechanism of carbon isotopic composition in the process of natural gas generation.

The sample was taken from the Lower Permian Shanxi Formation in the Shaping Coal Mine in the eastern Ordos Basin, NW China. The organic matter maturity of the sample was 0.55% (R_o%), the organic carbon content was 58.3%, the maximum pyrolysis temperature was 424 ºC, the free hydrocarbon content was 0.66 mg/g, the pyrolytic hydrocarbon content was 97.18 mg/g. The hydrogen index of the sample was 167 mg/g, which indicated that the organic matter of the sample was the gas-prone humic type. According to the standard of high quality gas source rock^[3], the coal sample with hydrocarbon generation potential index (S₁ + S₂) of more than 60 mg/g was high quality gas source rock, the low mature coal sample in this study had much higher hydrocarbon generation potential index than 60 mg/g, so it had high gas generation potential.

The simulation device is the gold capsule closed experimental system, and the specific experimental method is presented in the references [24-25, 29]. Considering that the petroleum system often has high pressure at the high to over mature stages, the designed pressure of experiment was high. The pressure of thermal simulation experiment system was maintained at 50 MPa by using pressure sensor. In order to investigate the gas generation process of coal more comprehensively, 16 temperature points were designed in the experiment, with 320 ºC as the first temperature point and 650 ºC as the highest temperature point. The heating program was set as two modes, rapid heating (20 ºC/h) and slow heating (2 ºC/h). The thermal simulation experiment and product analysis were both done in the Key Laboratory of Petroleum Geochemistry, Research Institute of Petroleum Exploration and Development PetroChina.

The parameters such as gas yield, component and carbon isotopic composition are shown in Tables 1 and 2.

Through calculation of geochemical parameters such as the relative content of each component, total gas content, weight of sample and total organic carbon content, the yields of gas components in the thermal simulation can be obtained. The calculated yields of gas components can help assess the gas generation potential of the coal sample and the source rock. Through calculation, the yields of gas components of the coal sample are shown in Table 1.

During the rapid and slow heating experiments, the maximum yields of CH₄ were 229.41 ml/g and 302.26 ml/g, respectively, and the maximum yields of alkane gas were 230.16 ml/g and 302.74 ml/g, respectively (Fig. 1 and Table 1). At the same temperature, the alkane gas yield of the slow heating system was significantly higher than that of the rapid heating process. Under the condition of slow heating, the reactant reaction might be more sufficient, which was conducive to the decomposition of organic macromolecules into small molecules, and the yield of CH₄ was significantly increased.

In the two groups of simulation experiments, the yields of heavy hydrocarbon gas were not high, the maximum values were 9.73 ml/g and 12.02 ml/g, and the corresponding temperatures were 460 °C and 500 °C respectively (Fig. 1 and Table 1). A small amount of H₂ was detected at higher temperature points, and the yield of H₂ increased with the increase of thermal simulation temperature (Fig. 1). In addition, a small amount of H₂S was also detected in the thermal simulation gas products. Due to the low content and poor analysis accuracy of the device to H₂S, the relationship between the H₂S yield and temperature was not obvious; the CO₂ yield generally increased with the increase of temperature, but its relative volume content gradually decreased with the increase of alkane gas (Table 1).

The components of hydrocarbon gases (CH₄, C₂H₆, C₃H₈, iC₄H₁₀, nC₄H₁₀, iC₅H₁₂, nC₅H₁₂) and non-hydrocarbon gases (CO₂, H₂S, H₂) in the simulated products at different temperatures were analyzed. The results are shown in Table 2.

In this study, there was no gas product data at 650 °C, which was caused by gas leakage after isotopic composition analysis. Because the integrity of the data was not affected, and the temperature point (650 °C) data was not supplemented. The relative content of CH₄ increased with the increase of temperature in both rapid and slow heating experiments. At the same temperature, the relative content of CH₄ in the condition of rapid heating was lower than that of slow heating. In the rapid and slow heating experiments, in which the highest contents of CH₄ were 81.64% and 89.72% respectively; and the corresponding temperature was 625 °C. The dryness coefficients (C₁/C_1-5) of gas products in the two groups of experiments also showed the same change trend, and the temperature of dryness coefficient at the inflection point of the slow heating experiment was lower than that of the rapid heating (Fig. 2).

The content of heavy hydrocarbon gas increased first and then decreased, which indicates that the heavy hydrocarbon gas was generated and cracked at the same time during the thermal maturation process of coal. In the early stage, generation took dominance, while in the late stage, cracking took dominance. At the point the two processes reached a balance, the relative content of heavy hydrocarbon gas reached the highest. The temperature corresponding to the highest content of heavy hydrocarbon gas was generally 400-500 °C. During the experiments, a small amount of nC₄H₁₀, iC₄H₁₀, nC₅H₁₂, iC₅H₁₂ (Table 2) were also produced. As heavy hydrocarbon content first increased and then decreased, the dryness coefficient of the gas product first decreased and then increased. In the early stage, the gas produced in the experiment showed features of dry gas or wet gas (in the slow heating experiment, the gas generated in the early stage showed features of dry gas, while in the rapid heating experiment, the gas showed features of wet gas in the early stage), and the gas produced in the late stage of both experiments showed dry gas characteristics (Fig. 2). In the thermal simulation experiments, a large amount of non-hydrocarbon gases, especially CO₂, were formed. And at lower temperatures, the relative content of CO₂ took absolute dominance. Under geological conditions, the relative content of CO₂ in gas reservoirs was generally low, which might be due to the high solubility of CO₂ in water^[6]. In addition, CO₂ might also participate in diagenesis and enter various diagenetic minerals^[30].

The carbon isotopic composition of natural gas is an important parameter to investigate the geochemical characteristics of natural gas^[11,12]. In this work, the carbon isotopic compositions of gas products in the experiments were tested. Because the yields of some gas components at some temperature points were lower than the precision range of the instrument analysis, there were no isotopic values at these temperature points. The detailed carbon isotopic values are shown in Table 2.In the experiments of rapid heating and slow heating, the variations of carbon isotopic composition generally had a similar maturation trend (Table 2). In the rapid heating and slow heating experiments, the δ¹³C₁ values were -34.8‰ to -23.6‰ and -35.5‰ to -24.0‰, δ¹³C₂ values were -28.0‰ to -9.0‰ and -28.9‰ to-8.3‰, δ¹³C₃ values were -25.8‰ to -14.7‰ and -28.9‰ to -8.3‰ respectively. These are similar to the results of previous studies^{[27, 31-32]}. It is worth noting that the inversion of δ¹³C₂ and δ¹³C₃ values in the high temperature stage was found in our experiment (the isotope value became lighter after the maximum value of δ¹³C₂ and δ¹³C₃ appeared in the high temperature stage). This phenomenon was not reported in previous studies. Recently, a few researchers found the inversion of δ¹³C₂ value at high temperature in simulation experiments^{[22, 26-27]}. Generally speaking, the fractionation effect of carbon isotopic composition of alkane gas in the slow heating experiment was stronger than that in the rapid heating experiment.

The hydrocarbon generation model during organic matter thermal maturation has been established through simulation experiments combined with reservoir examples^[5]. According to previous studies, there was non-monotonic variation of δ¹³C₁ value in the relatively low maturation stage of organic matter and "anomaly" of carbon isotopic composition of alkane gas at the high to over mature stages. The explanations of these two phenomena are still controversial in academic field. These two phenomena also appeared in our simulation experiments (Fig. 3 and Table 2), so we will focus on the discussion of them below.

In actual geological background, the rate of temperature rise of source rock is slower than that of any thermal simulation experiment. The isotopic fractionation lag of natural gas formed by thermal maturation of source rock in actual formation should be more obvious than that of thermal simulation experiment product. In our simulation experiments, the massive heavy hydrocarbon gas cracking corresponded to temperatures of about 440-480 ºC. The stage before massive heavy hydrocarbon gas cracking is defined as relatively low mature stage in this paper. In this stage, the yields of CH₄ and heavy hydrocarbon gas increased with the increase of source rock maturity. After reaching the cracking temperature of heavy hydrocarbon gas, the yield of heavy hydrocarbon gas began to decrease, but the yield of CH₄ increased constantly (Table 1).A large number of previous studies have shown that the value of δ¹³C₁ decreases first and then increases in alkane gas generated by either source rock, kerogen or crude oil at relatively low temperatures^{[22, 27, 31-32]}. In our thermal simulation products, the δ¹³C₁ value also decreased first and then increased. In the rapid temperature rise experiment, δ¹³C₁ reached the minimum value of -34.8‰ at 440 ºC, and then increased with the increase of experiment temperature. In the slow temperature rise experiment, δ¹³C₁ reached the minimum value of -35.5‰ at 400 ºC, and then increased with the increase of temperature (Fig. 3 and Table 2). The inversion of δ¹³C₁ corresponded to the temperatures of 400-440 ºC. In the thermal simulation experiments of marine kerogen and crude oil carried out by Tian et al.^[31], the inversion of δ¹³C₁ value at low temperature stage was also found. After the δ¹³C₁ value was higher than the inflection point, the difference of δ¹³C₁ of the same sample at different heating rates gradually decreased^[31].Many researchers put forward their own views on the phenomenon that the δ¹³C₁ value first decreased and then increased at the relatively low temperature stage. Shuai Yanhua et al.^[32] thought that the inversion of δ¹³C₁ value at relatively low temperature occurred in both closed system and open system thermal simulation experiments, and the structural complexity and heterogeneity of organic matter in reactants were the fundamental reasons of the inversion. Lorant et al.^[33] and Hill et al.^[34] considered that it was caused by complex precursors in immature or low mature kerogen. Galimov et al.^[35] suggested that the organic matter in all the experimental samples had previous transformation history, the residual organic matter from the previous stage was richer in ¹³C, and the new pyrolysis products were richer in ¹²C^[35]; at the beginning, the residual organic matter contributed a lot to CH₄; with the reaction going on, ¹³C enriched in the new pyrolysis products gradually, resulting in the inversion of δ¹³C₁ value^[35]. No matter it is humic organic matter or sapropelic organic matter, in the relatively low mature stage, due to the relatively weak thermal effect, the material generated first must be formed by break of branch chains with relatively lower activation energy and stability. He et al.^[29] analyzed the residual elements of lignite after thermal experiment, and found that the organic matter in the low mature stage lost a large amount of oxygen element, so they concluded that the products of early organic matter decomposition were mostly formed by the shedding of functional groups containing heteroatoms like oxygen. In the relatively low mature stage, the functional groups with oxygen and other heteroatoms first fell off, and ¹²C was likely to enrich in the heteroatom functional groups^[29], therefore, CH₄ generated at the beginning was richer in ¹²C, and had lighter δ¹³C₁, and with the thermal maturation going on, the δ¹³C₁ value gradually decreased in the initial stage^[29], when the heteroatom functional groups were consumed up, the δ¹³C₁ value gradually became heavier, which was due to the thermal effect of isotopic fractionation^[29]. It should be noted that the carbon isotopic inversion of CH₄ at low temperature also occurred in the thermal simulation experiments of some pure materials (with no heteroatom functional groups). Tang et al.^[36] and Zhang et al.^[37] carried out thermal simulation experiments of n-octadecane, and the δ¹³C₁ value in the simulated gas also inversed in the low temperature stage, indicating that the heteroatom functional group was not the necessary factor for the inversion of δ¹³C₁ value in the simulation experiment at low temperature. Tang et al.^[36] thought that the isotopic fractionation effect resulted from the activation energy difference between CH₄ richer in ¹²C and that richer in ¹³C caused the non-monotonic change of δ¹³C₁ value in the low mature stage. Through thermal simulation experiment of n-octadecane, Xiong Yongqiang et al.^[38] concluded that some unknown substances with light isotopic composition were formed in the disproportionation reaction during the thermal maturation process, and the decomposition of this new material caused the inversion of δ¹³C₁ value in the initial stage. In the thermal simulation experiment of n-octadecane, the δ¹³C₁ inversion was also found, which indicated that the shedding of heteroatom functional groups was not the essential factor for the early δ¹³C₁ inversion. Both the heterogeneity of organic matter and the isotopic fractionation effect of CH₄ richer in ¹³C and ¹²C were persuasive to some extent. In essence, the sources of CH₄ in the early stage of formation were different.In the relatively low mature stage, the inversion phenomenon might also occur in δ¹³C₂ and δ¹³C₃. However, due to the limited amount of heavy hydrocarbon gas in low maturation stage, it was difficult to accurately detect the carbon isotopic value of heavy hydrocarbon gas. In the relatively low mature stage, the simulated gas products were mainly CH₄, CO₂ and a small amount of heavy hydrocarbon gas (Table 1, Fig. 1 and Fig. 2). Because of the complexity of CH₄ source in the early stage, the carbon isotopic value of CH₄ was non-monotonic.

In our gold capsule thermal simulation experiments, there were two kinds of "anomalies" of carbon isotopic composition of alkane gas. One was the non-monotonic change of δ¹³C₁ value in the initial stage, the other was the inversion of carbon isotope value of heavy hydrocarbon gas at the high to over mature stages and the partial reversal of carbon isotopic series at a temperature point (550 ºC in rapid heating).Alkane gas from natural maturation of organic matter generally has positive carbon isotopic series (with the increase of carbon number, the carbon isotopic value of alkane gas increases gradually)^{[12, 17]}. However, in recent years, many cases of "abnormal" alkane gas isotopic composition were found in many gas reservoirs, such as partial reversal of isotopic series^[13,14], negative carbon isotopic series^[17], and the inversion of alkane gas isotopic composition^[13,14]. These "anomalies" of isotopic composition often occur at the high to over mature stages, which reflects the complex formation mechanisms of natural gas at the high to over mature stages.In our thermal simulation experiments, the carbon isotopic composition of alkane gases generally exhibited positive series, but when the temperature rose rapidly to 550 ºC, the carbon isotopic series of alkane gas was partially reversed (Figs. 3a and 4a). By reviewing the results of previous thermal simulation experiments, it could be found that the composition and yield characteristics of alkane gas were more deeply studied before^[39], but the formation mechanisms and isotopic values of natural gas at the high to over mature stages were relatively less studied. Most researches on the isotopic composition of alkane gas before were limited to δ¹³C₁^[36], and the research on heavy hydrocarbon was relatively weak^[40]. Some researchers studied the carbon isotopic composition of alkane gas, but the simulation experiments were at low temperatures (the maturation degree of organic matter was not high enough), and the alkane gas in most cases showed positive carbon isotopic composition series^[41]. A few researchers found negative carbon isotopic series or partial carbon isotopic composition reversal through thermal simulation experiments. For example, Du et al.^[21] carried out thermal simulation experiment on lignite in closed system at ultra-high pressure of 1-3 GPa and temperatures of 500-700 ºC, and found negative and partial reversal of carbon isotopic composition in alkane gas. However, the pressure of organic matter thermal maturation system was generally 20-60 MPa, so the pyrolysis in ultra-high pressure system couldn’t represent the actual process of thermal maturation of source rock. Zhang et al.^[23] carried out thermal simulation experiments with hydrogen and inorganic materials of three different carbon sources to simulate the Fischer-Tropsch synthesis reaction, and positive carbon isotope series, partial reversal carbon isotopic series and negative carbon isotopic series were found in the simulation products. However the actual thermal maturation of source rocks was mainly the conversion of complex organic macromolecules to small molecules, so the Fischer-Tropsch synthesis experiment might be quite different from the thermal maturation of organic matter in geological bodies. The simulation experiments designed by Du et al.^[21] and Zhang et al.^[23] couldn’t well represent the formation mechanism of alkane gas in actual gas reservoirs.In our thermal simulation experiment, partial carbon isotopic reversal only occurred at one temperature point (red line in Fig. 4a), but the carbon isotopic inversion of C₂H₆ and C₃H₈ occurred in the high temperature stage (Fig. 3). In recent years, Mao Rong et al.^[22], He et al.^[26], and Gao et al.^[27] observed the inversion of δ¹³C₂ value in the high temperature stage of pyrolysis experiments, but this paper was the first reporting δ¹³C₃ inversion at high temperature phase in thermal simulation experiment. It is worth noting that the reversal of isotopic series, negative isotopic series and carbon isotopic inversion of heavy hydrocarbon gas (C₂H₆ and C₃H₈) have been confirmed by researchers in several gas reservoirs^{[12,13,14,15,16,17]}. Based on previous studies^{[17, 42-48]}, we made the correlation diagrams of δ¹³C₁ and δ¹³C₂ values of coal-derived gas (Fig. 5a) and shale gas (oil-type gas) (Fig. 5b). It was found that the inversion and reversal of isotopic composition would occur in both coal-derived gas and oil-type gas at certain thermal maturation degree. Through the analysis of our experimental products, it is inferred that the inversion and reversal of carbon isotope may be a common phenomenon when organic matter reaches certain thermal maturation stage. Only the simulation experiment can dynamically study the formation process of natural gas, so this phenomenon can be well reflected in the experiment.

Before the discovery of shale gas with abnormal isotopic composition, there were four common views on the genetic interpretation of the abnormal isotopic series of natural gas^[49]: (a) mixing of organic gases from different sources or of different maturity from the same source; (b) mixing of organic gas and inorganic gas; (c) migration and fractionation of natural gas; and (d) microbial action. In recent years, with the discovery of a large number of cases of isotopic abnormal shale gas, many researchers have tried to find the causes of the inversion and reversal of isotopic series in shale gas. There are two types of views: (a) in over mature stage, water reacts with CH₄ to produce CO₂ with lighter carbon isotopic composition and H₂, and CO₂ and H₂ react again to produce heavy hydrocarbon gas with light carbon isotopic composition^{[14, 19]}, resulting in the inversion and reversal of isotopic composition^{[14, 19]}; and (b) the mixing of kerogen cracking gas and oil cracking gas results in these abnormalities^[15].The generated CO₂ and H₂ reacted again to form heavy hydrocarbon gas with light carbon isotopic composition, thus forming the abnormal isotopic composition. The reaction of CO₂ and H₂ at high temperature belonged to Fischer-Tropsch synthesis. We thought this was only a theoretical model or hypothesis. Considering the reactants (CO₂ and H₂) needed for Fischer-Tropsch reaction^[50,51], the reactants didn’t need to be formed by the oxidation-reduction reaction of CH₄. Both our thermal simulation experiment and previous studies showed that CO₂ had been formed in the maturation process of source rocks, and H₂ was also generated during the graphitization of organic matter. The question was whether this reaction could occur in the formation system. Generally, the Fischer-Tropsch reaction in the laboratory took place under the condition of transition metal as catalyst, and the reaction temperature of Fischer- Tropsch synthesis was not very high (200-400 ºC)^[50,51]. Compared with the laboratory conditions, there were less transition metals in the formation^[52]. Whether a very small amount of transition metals could make the Fischer-Tropsch synthesis reaction take place under the formation conditions needed more evidence to support. The main function of catalyst was to reduce the activation energy of the reaction. If there was not enough transition metal in the formation, the Fischer-Tropsch synthesis at relatively low temperature couldn’t occur smoothly. Although CO₂ could be generated in the whole maturation process of source rocks, the formation of H₂ mainly occurred in the graphitization process, i.e., high to over mature stages. Whether there were enough transition metals in source rocks to catalyze the Fischer-Tropsch synthesis also needed more evidences. Therefore, we thought that it was not convincing to explain the inversion or reversal of carbon isotopic composition by using the viewpoint that CO₂ and H₂ reacted to produce heavy hydrocarbon gas with light carbon isotope. In our thermal simulation experiments, there was no microbial, no water, no gas migration. And the simulated gas was typical organic gas generated by coal. The thermal simulation experiment of source rock in closed system showed a continuous accumulation of natural gas, and there was indeed a mixture of natural gas formed by thermal maturation of organic matter in different periods. In the high temperature stage, the heavy hydrocarbon gas had begun to crack gradually, and the secondary cracking of the retained hydrocarbon (mainly referred to chloroform asphalt "A") in the source rock should be earlier than that of the heavy hydrocarbon gas. Therefore, it might be improper to think that the secondary cracking of the retained hydrocarbon was the cause of "abnormal" geochemical characteristics of natural gas at the high to over mature stages.In our experiment, the inversion and partial reversal of carbon isotopic series occurred in the higher temperature stage. It is worth noting that the "abnormal" phenomena such as inversion and reversal of carbon isotope composition in actual gas reservoirs generally occurred at the high to over mature stages^[15,16,17], which indicated that natural gas at the high to over mature stages might be the key factor causing the "abnormal" geochemical characteristics, which also demonstrated the complexity of the formation mechanism of high-over mature natural gas. In our study, it was believed that the inversion of carbon isotopic value of heavy hydrocarbon gas at the high to over mature stages (the carbon isotopic value became lighter) might indicate that the source of heavy hydrocarbon gas had changed at the high to over mature stages, i.e., there was a new material source of heavy hydrocarbon gas at the high to over mature stages. This phenomenon might be similar to the inversion of δ¹³C₁ in the low mature stage. After the carbon isotopic composition of heavy hydrocarbon gas reached the maximum value, the carbon isotopic value of heavy hydrocarbon gas inversed and became lighter gradually (Fig. 3). To further analyze this phenomenon, it is necessary to analyze the thermal maturation structure of organic matter. With the thermal maturation of source rock, both sapropelic and humic organic matter would continuously enrich carbon and dehydrogenate, and aromatization or graphitization^{[25, 39]}. Therefore, the study on the structure of organic matter in high mature stage would help us understand the mechanisms of natural gas formation and isotopic fractionation. Mi et al.^[39] carried out nuclear magnetic resonance analysis on coal samples of different maturities. The structure analysis of coal samples showed that when R_o value was greater than 3.0%, coal mainly contained a large number of aromatic rings, and the side chains were mainly methyl^[39]. Therefore, at the high to over mature stages (especially the over mature stage), and demethylation of ring structures and aromatic nuclei should be the main way of gas generation of the source rock^{[25, 38, 53]}. It should be a good point to investigate the formation and isotopic fractionation mechanisms of natural gas at the high to over mature stages from the thermal simulation experiment of aromatic hydrocarbon. As humic organic matter contained more aromatic core structure, it may contribute more gas by aromatic hydrocarbon demethylation than sapropelic organic matter^{[25, 38, 53]}. No matter it is sapropelic or humic organic matter, at the high to over mature stages, the gas generated by dehydrogenation of methyl side chains should be CH₄. However, the actual results of exploration and thermal simulation have confirmed that the gas from the high to over mature stages of thermal simulation experiment (regardless of shale gas or coal-derived gas) contains a certain amount of heavy hydrocarbon gas^[46,47,48]. The heavy hydrocarbon gas may contain a part not fully cracked formed by the thermal maturation of organic matter in the early stage, but as the carbon isotopic composition of heavy hydrocarbon gas reverses, there should be lighter carbon isotope heavy hydrocarbon gas formed. Although obvious partial reversal of carbon isotopic series of alkane gas only occurred at one temperature point in our thermal simulation experiment (Fig. 4a), the reversal of carbon isotopic series at the high to over mature stages has been found in a few natural gas reservoirs^[48]. Fusetti et al.^[54] found that a large amount of CH₄ could be formed during the pyrolysis of 1,2,4-trimethylbenzene in the gold capsule simulation system. Gas generation by organic matter at the high to over mature stages may be mainly side chain shedding of aromatics. Unfortunately, Fusetti et al.^[55] did not conduct in-depth analysis on carbon isotopic composition of alkane gas.Aromatic hydrocarbon is one of the main products of organic matter at the high to over mature stages. In order to further explore the formation mechanisms of natural gas at the high to over mature stages, we took toluene as an example to discuss the characteristics of aromatic hydrocarbon cracking products, and then compared the geochemical characteristics of the products at the high to over mature stages. Toluene thermal simulation experiment was carried out at different temperature conditions. The carbon isotopic values of alkane gas in the experimental products are shown in Table 3.

The toluene thermal simulation in gold capsule was carried out. Due to the high stability of aromatic compounds, the temperature was rapidly raised to the target temperature at 20 ºC/h, and then kept constant for 72 h. It was found that not only CH₄ but also a small amount of heavy hydrocarbon gas were formed in the thermal simulation experiment of toluene, and partial reversal of carbon isotopic series of alkane gas occurred (Table 3). The initial temperature of this experiment was 325 ºC, but when the simulated temperature was lower than 450 ºC, there was little gas produced, ie., toluene hardly crack into gas before 450 ºC, and gas products were detected after 450 ºC. Combined with the structural characteristics of coal at the high to over mature stages and the toluene pyrolysis experiment, it could be concluded that the alkane gas formed at the high to over mature stages of organic matter might mainly come from the desorption of aromatic compounds (Fig. 6). It was considered that at the high to over mature stages, on the one hand, the dehydrogenation of the detached methyl could form CH₄; on the other hand, the linkage between methyl and methyl could form a small amount of C₂H₆; in addition, the polymerization of aromatic compounds could form ethyl, and ethyl could also form a small amount of ethane through hydrogen transfer (hydrogenation) (Fig. 6). At the high to over mature stages, CH₄ was mainly formed by demethylation of alkane gas. In the experiment of toluene pyrolysis at 550 ºC, it could be found that the C₃H₈ also showed carbon isotopic value inversion, and the partial inversion of carbon isotopic series did appear in the pyrolysis products of toluene (450 ºC, Table 3). With the increase of temperature, the carbon isotopic composition of toluene pyrolysis products also showed obvious fractionation effect. It was believed that the formation of CH₄ was due to the demethylation of aromatic rings in kerogen, and the heavy hydrocarbon gas mainly came from the polymerization of methyl (Fig. 6). Due to the stability of aromatic compounds, the short side chains of aromatic structures in kerogen fell off later^{[38, 53]}.

The isotopic fractionation effect of aromatic compounds lags behind that of kerogen cracking gas and retained hydrocarbon cracking gas. In the high temperature stage, the formation and cracking of heavy hydrocarbon gas were in a dynamic state. There were heavy hydrocarbon gases cracked at high temperature, and a very small amount of heavy hydrocarbon gas formed by the aromatics in kerogen under high temperature. The carbon isotopic fractionation effect of the early formed natural gas was inconsistent with that of the later formed natural gas, i.e., the carbon isotopic fractionation of the late formed natural gas was lagging behind.

When the organic matter evolved into its structure, which was mainly aryl methyl side chain, the carbon isotopic composition of the detached methyl carbon was usually heavier than that of the relatively low mature stage. However, this didn’t mean that all the methyl groups removed from the coal structure at this time were -¹³CH₃ and also contained a large amount of -¹²CH₃^[36], but there were more -¹³CH₃ in the methyl groups removed from the coal structure at lower maturity. That was to say, both -¹²CH₃ and -¹³CH₃ were separated from the parent structure. In the process of forming C₂H₆ and C₃H₈ (small amount) from coal structure, because -¹²CH₃ was lighter than -¹³CH₃, its energy and chemical activity were stronger, so the probability of -¹²CH₃ connecting with -¹²CH₃ was greater than that of -¹²CH₃ connecting -¹³CH₃ and-¹³CH₃ connecting -¹³CH₃, which might lead to the enrichment of more ¹²C in C₂H₆ and C₃H₈ generated by methyl linkage. Therefore, δ¹³C₂ value might be lighter than δ¹³C₁ (Table 3), and δ¹³C₃ value might be lighter than δ¹³C₂ (Table 2). A small amount of C₂H₆ and C₃H₈ formed in the over mature stage might cause abnormal isotopic composition, such as inversion of carbon isotopic composition (Table 2). If the isotopic composition is inverted to a certain extent, causing the δ¹³C₂ value higher than the δ¹³C₃ (Fig. 4a), then the partial reversal of carbon isotope composition of C₂H₆ and C₃H₈ was formed. If δ¹³C₁ value was higher than δ¹³C₂, then a partial reversal of carbon isotopic compositions of CH₄ and C₂H₆ was formed (Table 3). Therefore, the aromatic demethylation of organic matter and the carbon isotopic fractionation during the formation of heavy hydrocarbon gas by methyl linkage might be an important reason for the inversion or reversal of carbon isotopic composition of natural gas (including shale gas) at the high to over mature stages.

Organic matter thermal maturation and gas generation were very complex processes, and the source of natural gas was complex^{[5,32,35,38,53]}. The carbon isotopic compositions of natural gas formed by different materials in different periods had fractionation effect. Especially, the organic matter rich in aromatic structure in the late stage could form alkane gas with light carbon isotopic composition. Because the content of heavy hydrocarbon gas was low, even if the amount of heavy hydrocarbon gas formed in the late stage was very little, it might also have an important impact on the δ¹³C of heavy hydrocarbon gas. The fractionation effect of δ¹³C₁, δ¹³C₂ and δ¹³C₃ were different, which had an important relationship with the amount of alkane gas. The more the amount of alkane formed in the early stage, the more difficult it was for the later formed alkane gas to affect its isotopic composition. Therefore, the fractionation effect of δ¹³C₁ was slower than that of δ¹³C₂, and the fractionation effect of δ¹³C₂ was slower than that of δ¹³C₃. On the one hand, the lighter δ¹³C alkane gas formed in the late stage could form the δ¹³C inversion phenomenon of heavy hydrocarbon gas; on the other hand, the reversal phenomenon of δ¹³C series of alkane gas could be formed by aromatic structure dealkylation side chain.

Since natural gas geology and geochemistry became an independent discipline, the analysis of the characteristics of isotopic composition has become one of the most useful means to carry out natural gas research^[5,6]. In previous studies, it was generally believed that organic alkane gas had positive carbon isotopic series, while inorganic alkane gas had negative carbon isotopic series^[12]. With the deepening understanding of natural gas geology and geochemistry, the partial reversal and even negative carbon isotopic series of alkane gas were generally discovered in petroliferous basin all over the world^[16,17]. The negative carbon isotopic series of natural gas can also be organic origin, which is widely accepted now. However, the interpretation of inversion or anomaly of carbon isotopic series of alkane gas was mostly based on theoretical speculation^[17]. Thermal simulation experiment could explore the internal relationship of gas geochemical characteristics from the perspective of hydrocarbon formation, which was conducive to the study from the perspective of mechanism^[28]. Through the thermal simulation experiment of low mature coal and toluene, we tried to investigate the origin of "anomaly" of isotopic series from the formation mechanism of alkane gas. There were a series of abnormal carbon isotopic compositions of alkanes in both coal-derived gas and oil-type gas (Fig. 5), which were mainly manifested at the high to over mature stages. The main gas production of organic matter at the high to over mature stages was aromatic structure shedding side chain or methylation. We speculated that demethylation or side chain shedding of aromatic structure was an important reason for the formation of "anomaly" of carbon isotopic composition series of alkane gas at the high to over mature stages. This conjecture was not a complete negation of previous views, but an analysis from a new perspective. Li et al.^[56] found that there were four stages of δ¹³C₁ fractionation in shale gas production process, and proposed that the carbon isotopic fractionation of shale gas was mainly controlled by adsorption, desorption and diffusion, and the δ¹³C₁ value in each stage was mainly affected by the enrichment of ¹³C and ¹²C methane fractionation. Their viewpoint was further demonstrated by kinetic calculation. The viewpoint proposed by Li et al.^[56] was consistent with that obtained by our thermal simulation experiment. The gas formed in thermal simulation experiment only experienced hydrocarbon generation, and did not experience the accumulation process such as geological gas reservoir. Moreover, the heating rate of organic matter in the actual geological condition was extremely slow. The existing experimental technical conditions can not completely simulate the actual geological conditions, so the thermal simulation experiment has certain limitations. However, the limitations don’t affect the thermal simulation experiment to be one of the most effective methods to analyze hydrocarbon gas formation under present conditions.

The thermal simulation experiment of a low mature coal sample from the Lower Permian Shanxi Formation in the eastern Ordos Basin was carried out in a gold capsule closed pyrolysis system at slow and rapid heating rates. The maximum yields of alkane gas were 302.74 ml/g and 230.16 ml/g, respectively. In the slow heating process, the organic matter reaction was more sufficient and the δ¹³C fractionation effect more obvious. In the simulation experiments at slow and rapid heating rates, δ¹³C₁ values were -34.8‰ to -23.6‰ and -35.5‰ to -24.0‰, δ¹³C₂ values were -28.0‰ to -9.0‰ and -28.9‰ to -8.3‰, and δ¹³C₃ values were -25.8‰ to -14.7 ‰ and -26.4‰ to -13.2‰, respectively.

In both heating processes, δ¹³C₁ turned lighter first and then heavier. The non-monotonic change of δ¹³C₁ was caused by different sources of CH₄ formed in the early stage, and the cause of different sources of CH₄ was the heterogeneity of organic matter or the difference of activation energy between CH₄ rich in ¹²C and that rich in ¹³C.

The inversion of δ¹³C in heavy hydrocarbon gas can occur in highly mature shale gas (oil-type gas) or in coal-derived gas. The thermal simulation experiment further proved that heavy hydrocarbon gas can have inversion of δ¹³C at the high to over mature stages. The inversion of δ¹³C indicates that the sources of heavy hydrocarbon gas at the high to over mature stages are complex, and heavy hydrocarbon gases from different sources show fractionation effect in different times. Based on the thermal simulation experiment of toluene, it is concluded that the δ¹³C fractionation effect caused by demethylation of aromatic structure and methyl linkage may be an important reason for δ¹³C inversion and reversal of alkane gas at the high to over mature stages.