Study, exploration and development of coal-derived gas have promoted the rapid development of China’s natural gas industry. China’s natural gas is dominated by coal-derived gas in terms of the number of the discovered large-scale gas fields, total proven gas reserves and gas production^[1,2,3]. In recent years, more and more attention has been paid to unconventional gas exploration. In particular, the tight sandstone gas, as one type of unconventional gas, is also dominated by coal- derived gas^[4]. Thus, the study of coal-derived gas takes an important position in the study of natural gas in China.

The most common relations to determine the maturity of natural gas with geochemical parameters are the relations between δ¹³C₁ and R_o put forward by researchers. The most representative ones are proposed by Stahl^[5], Dai Jinxing^[6], and Liu Wenhui^[7] etc. All of these equations show clearly that the maturity increases gradually with the δ¹³C₁. Thus, they were broadly applied in the case where there is no way to determine the gas source rock or maturity of the gas source rock. Although subordinate oil field companies of PetroChina, in general, are capable of analyzing natural gas compositions, they usually don’t have the instrument for measuring carbon isotopes of natural gas, and it would take a long time if samples are sent to some institutions to be analyzed, bringing inconvenience to the study and production.

Researchers have long tried to seek a parameter from gas composition to reflect the maturity of gas. Recently, Dai Jinxing, based on the good correlation between the heavy hydrocarbon content in the coal-derived gas and the corrected R_o, has worked out the relation between the humidity coefficient (C_2—5/C_1—5) and maturity of the coal-derived gas^[8]. In addition, it is possible to track the migration of the natural gas by studying the gas composition^[9,10].

With the renewal of the instrument, natural gas composition analysis becomes much higher in precision, especially the measurement of the low-content butane and pentane isomers, making it possible to test the heavy hydrocarbon components in natural gas and compute the related parameters.

The iC₄/nC₄ and iC₅/nC₅ ratios of the natural gas are often neglected by researchers. The iso-alkane always exhibits higher diffusion coefficient than n-alkane with the same carbon number because of its low boiling point, high saturated vapor pressure and lower intermolecular force^[11]. Thus, the migration rate of iC₄ and iC₅ are higher than that of nC₄ and nC₅. When measuring the gas composition by means of gas chromatography, the time the iso-alkane peak appears is earlier than that of n-alkane with the same carbon number. Accordingly, it is inferred that, the iC₄/nC₄ and iC₅/nC₅ ratios may increase with the migration distance of natural gas. We tried to track the migration of the natural gas in the foreland basin in the western part of the Sichuan Basin with these parameters. It is found that, indeed, these ratios increase with the migration distance of the natural gas^[9]. Some researchers studied the relationship between the iC₄/nC₄ and iC₅/nC₅ ratios with the maturity of source rock, and reached the conclusion these ratios would decrease with the increase of maturity^[12,13]. However, lack of research examples and evidences, this conclusion hasn’t been fully proved. We, based on a study, believed that, the iC₄/nC₄ and iC₅/nC₅ ratios would not decrease as the maturity increases. In order to reveal the relationship between the ratios with maturity, natural gas samples from the Triassic Xujiahe Formation (T₃x) primary gas reservoirs of the gas fields located in the central part of the Sichuan Basin (hereinafter referred to as the Central Sichuan Basin), including the Guangan, Anyue, Longgang, Hechuan, Longnüsi, Moxi, Nanchong and Tongnan gas fields, were examined. In the Central Sichuan Basin, the Xujiahe Formation tight gas reservoirs are widely distributed, with multiple gas layers superimposing vertically. The gas went through hardly any lateral or vertical migration^[14], so the migration fractional distillation of gas composition is limited. This provides an ideal example for studying the variation of the composition of the coal-derived gas with maturity, and lays a solid foundation for introducing a potential maturity parameter.

The Xujiahe Formation, the target layer for our study, is in the Upper Triassic, underlying it is the Middle Triassic Leikoupo Formation (T₂l) and overlying it is the Lower Jurassic strata (J₁). This formation consists of multiple interbeds of coal-measure source rock and sandstone, and can be divided into six members. The Xu-1 (T₃x₁), Xu-3 (T₃x₃) and Xu-5 (T₃x₅) members are dominated by coal-measure intercalated with thin sandstone and act as the gas source rock. The Xu-2 (T₃x₂), Xu-4 (T₃x₄) and Xu-6 (T₃x₆) members are dominated by grey white to grey, fine- to moderate-grained sandstone interbedded with thin dark mudstone and act as good reservoir layers (Fig. 1). The Leikoupo Formation composed mainly of dolomite intercalated with gypsum and thin grey black shale is a good sealing over the whole study area. The Lower Jurassic black lacustrine shale overlying the Xujiahe Formation is not only a high-quality source rock that supplied the Jurassic oil & gas reservoirs in the Central Sichuan Basin, but a regional high-quality caprock for the underlying Xujiahe Formation gas.

In the Central Sichuan Basin, the Xujiahe Formation reser-voir layers are broadly distributed and vertically superimposed and gas-bearing over a broad area. In most of the areas, the structure is gentle and flat, and the gas reservoirs are dominated by combination structural-lithologic type^[15,16]. The reservoirs are poor in physical properties, as with a porosity from 4% to 8% and permeability from 0.01 to 1.00×10^-3 μm², representing low porosity & low permeability and extreme- low porosity & extreme-low permeability types^[17,18]. Although the Central Sichuan Basin was uplifted as a whole during the Himalayan movement, no large fault system was formed, which is very favorable for preservation of primary gas reservoirs.

From the perspective of carbon isotope composition feature of alkane gas, its ethane carbon isotope composition exceeds -28‰, which suggests that it is typical coal-derived gas according to the criterion for identifying the origin of the natural gas in China’s petroliferous basins^[19]. It is necessary to point out that, the Xujiahe Formation gas in the Central Sichuan Basin is the typical thermal gas generated by the coal-measure source rock, since its dryness coefficient (C₁/C₁₊) ranges from 0.84 to 0.96, averaging 0.91 (Table 1). If the dryness coefficient of 0.95 is taken as the boundary between the dry and wet gas^[20]; that is, gas with dryness coefficient of less than 0.95 is wet gas, otherwise, dry gas, clearly, the Xujiahe Formation gas is wet gas.

The Xujiahe Formation gas samples from the Central Sichuan Basin fall in the thermogenic gas zone on the Whitcar graph (Fig. 2). This suggests that this gas was not thermally cracked, thereby providing good geological and geochemical conditions for studying the geochemical features of the heavy hydrocarbon gas generated by the coal-measure source rock.

It is previously unnoticed that, natural gas sample from different layers of the Xujiahe Formation in the Central Sichuan Basin are widely different in iC₄/nC₄ and iC₅/nC₅ ratios. The general trend is that the ratio is higher in the lower layer than in the upper layer. For example, the gas samples from T₃x₆, T₃x₄ and T₃x₂ have an iC₄/nC₄ ratio of 1.04, 1.22 and 1.26, and the iC₅/nC₅ ratio of 1.89, 2.15 and 2.27, respectively. This phenomenon is hard to explain with the migration fractionation theory, since the natural gas trapped in the upper section is unlikely to migrate into the lower reservoir layer by passing through the underlying source rock. For example, it is unlikely that the T₃x₆ gas would pass through the T₃x₅ source rock and migrate into the T₃x₄ reservoir layer. Since the Xujiahe Formation gas in the Central Sichuan Basin is accumulated in the primary gas reservoir, with no large-scale vertical or lateral migration^[14], it is inferred that, the iC₄/nC₄ and iC₅/nC₅ ratios in the coal-derived gas are related to its maturity.

The R_o of the T₃x₅, T₃x₃ and T₃x₁ source rocks of the Xujiahe Formation increases with depth. For example, the R_o is 1.28% for the T₃x₅ member at 1 840 m and 1.53% for the T₃x₃ member at 2 043 m in Well Guang100 of the Guangan gas field; and the R_o is 1.30% for the T₃x₅ member at 1 895 m and 1.52% for the T₃x₃ member at 2 090 m in Well Nü107 of the Longnüsi gas field^[21]. In the same well, the heavy hydrocarbon content increases and the dryness coefficient decreases successively from T₃x₂ to T₃x₄ and then to T₃x₆, which is consistent with the gradual decrease in the maturity of the T₃x₁, T₃x₃ and T₃x₅ source rocks.

The authors selected a batch of natural gas samples from the T₃x₄ and T₃x₆ gas reservoirs to study the difference between the gas in the upper and lower reservoirs. The results show that, the T₃x₄ gas has higher dryness coefficient and lower heavy hydrocarbon content than the T₃x₆ gas.

By comparing some geochemical features of natural gas in reservoirs of different depths collected from wells penetrating the entire Xujiahe Formation in the Guangan and other gas fields, it is found that, the natural gas samples increase in density and decrease in methane content gradually from the lower to the upper sections (Table 1); that is, from T₃x₂ to T₃x₄ and then to T₃x₆, consistent with the gradual decrease in the maturity of the T₃x₁, T₃x₃ and T₃x₅ source rocks. This also suggests that, the natural gases in the upper and lower gas reservoirs are not mixed and accumulate in-situ with no evident migration.

There are several producing layers in the Guangan gas field, of which the major ones include T₃x₄ and T₃x₆. Natural gas in different layers are most likely from the underlying T₃x₃ and T₃x₅ coal-measure source rocks. The T₃x₃ source rock is thermally more mature than the T₃x₅ source rock, since it is buried deeper. In the Guangan gas field, as shown by Fig. 3, the T₃x₄ gas has higher dryness coefficient and iC₄/nC₄ ratio than the T₃x₆ gas. It is unlikely that the T₃x₆ gas would migrate downward into the T₃x₄ reservoir by passing through the T₃x₅ source rock to cause the increase in the dryness coefficient and iC₄/nC₄ ratio of the T₃x₄ gas. Similarly, it is unlikely that the natural gas would migrate from the T₃x₄ reservoir into the T₃x₆ reservoir, considering the gas composition characteristics. If this migration is possible, the T₃x₆ gas would have higher dryness coefficient and iC₄/nC₄ and iC₅/nC₅ ratios than the T₃x₄ gas as per the migration fractionation effect, which is in fact not the truth. It is possible to explain these phenomena using the difference in maturity of source rocks: with the increase in maturity, the dryness coefficient and iC₄/nC₄ ratio of the gas increases and the methane carbon isotope composition becomes increasingly less negative.

The iC₄/nC₄ and iC₅/nC₅ ratios for all the samples in Table 1 were plotted in a correlation diagram (Fig. 4). It can be seen from the figure that the iC₅/nC₅ ratio increases as the iC₅/nC₅ ratio increases, and they show the same variation trend and good correlation with a multiple correlation coefficient (R²) of up to 0.8185. In addition, the lowest iC₄/nC₄ and iC₅/nC₅ ra-tios are recorded in samples recovered from the Nanchong gas field, and the highest ratios are reported in some samples recovered from the Guangan gas field and the Hechuan gas field. Gas samples from the Guangan gas field are collected from the T₃x₄ and T₃x₆ reservoirs, and the corresponding source rocks are the T₃x₃ and T₃x₅ which differ more widely in maturity, this possibly leads to the higher iC₄/nC₄ and iC₅/nC₅ ratios.

With the increase in the maturity (R_o), the dryness coefficient and methane carbon isotope composition of the natural gas generated by the coal-measure source rock increase gradually. Thus, the dryness coefficient and methane carbon isotope composition of natural gas, to some extent, can reflect the maturity of the source rock. The relationship graph and equation of the iC₄/nC₄ and iC₅/nC₅ ratios with the dryness coefficient, methane carbon isotope composition and corrected R_o were built in the study for easy comparison.

According to the study of the relationship between the humidity coefficient with maturity of coal-derived gas made by Dai Jinxing et al., the humidity coefficient decreases as the maturity increases^[8]. Since the humidity coefficient is in negative correlation with dryness coefficient, the dryness coefficient of the natural gas would increase as the maturity increases. In this study, both the iC₄/nC₄ and iC₅/nC₅ ratios of the natural gas are in positive correlation with dryness coefficient; that is, the iC₄/nC₄ and iC₅/nC₅ ratios increase as the dryness coefficient increases (Fig. 5). Fig. 5 also shows that, the multiple correlation coefficients between the iC₄/nC₄ ratio and dryness coefficient and between iC₅/nC₅ ratios and dryness coefficient are 0.7480 and 0.5935, clearly the former is higher. This is possibly because the error in measurement induced by a variety of factors may have larger influence on pentane than butane, leading to the slight drop of the correlation coefficient between the iC₅/nC₅ ratio and dryness coefficient.

No matter it is coal-derived gas or oil-type gas, the methane carbon isotope composition has a good correlation with maturity; that is, the carbon isotope composition becomes heavier as the maturity increases. Accordingly, many relations of R_o andδ¹³C₁ were proposed by predecessors. For the coal-derived gas of the Xujiahe Formation in Central Sichuan Basin, iC₄/nC₄ and iC₅/nC₅ ratios are in positive correlation with the methane carbon isotope composition; that is, the ratios increase as the dryness coefficient increases (Fig. 6). Similarly, the iC₄/nC₄ ratio has higher correlation with methane carbon isotope composition than iC₅/nC₅ ratio, as evidenced by the multiple correlation coefficient of 0.7864 for the iC₄/nC₄ ratio against 0.5720 for the iC₅/nC₅.

The R_o was calculated using the equation δ¹³C₁ ≈ 14.12lgR_o- 34.39^[6]. The measured R_o from some wells in the Central Sichuan Basin was used to correct the calculated R_o. Fitting chart of the iC₄/nC₄ and iC₅/nC₅ ratios with the corrected R_o was prepared. Fig. 7 shows that, with the increase in the maturity of the source rock, the iC₄/nC₄ and iC₅/nC₅ ratios of the Xujiahe Formation coal-derived gas in the Central Sichuan Basin have a good positive correlation with the R_o. Similarly, the iC₄/nC₄ ratio shows a higher correlation with the R_o than iC₅/nC₅ ratio, as evidenced by the multiple correlation coefficient of 0.7742 for the iC₄/nC₄ ratio against 0.5990 for the iC₅/nC₅.

Some Chinese researchers believe that, the n-alkane and iso-alkane were generated by different mechanisms during the maturation process of organic matter. N-alkane originated mainly from the breaking of free radical, and iso-alkane is largely the product of the carbocation reaction. Free radical breaking is predominant during the relatively highly mature stage, while the carbocation reaction is predominant during the relatively less mature stage. Therefore, the iC₄/nC₄ ratio decreases as the maturity increases^{[12-13, 26]}. Through the thermal simulation test by adding water into humic coal, researchers found that the iC₄/nC₄ and iC₅/nC₅ ratios of the natural gas generated at the temperature range of 300 °C to 360 °C decreased gradually, and concluded that the thermal interaction may enable the breaking of the branched chain of alkane to generate the n-alkane with lower carbon number, resulting in the decrease in the iso-alkane/n-alkane ratio^[27]. Usually, the simulation tests utilize short-time and high-temperature process to offset the evolution characteristics of organic matter under the lengthy, low-temperature state in the geologic history. However, hydrocarbons are readily cracked under high-temperature, thereby making the reliability of the variation law of the iC₄/nC₄ and iC₅/nC₅ ratios with the maturity doubtful.

Some foreigner researchers, based on detailed studies of the composition of the shale gas and conventional natural gas from the Barnett and Fayetteville Formations in the Mississippian Basin, suggested that, the iC₄/nC₄ ratio decreases rapidly as the humidity decreases (maturity increases) in the case where the gas humidity is less than 5%, which indicates a relatively high maturity; and the ratio increases slowly as the humidity decreases (maturity increases) in the case where the gas humidity is above 5%^[28]. If the gas humidity is less than 5%, wet gas would be cracked, the iso-butane is less stable than the n-butane, and the rate of decrease of the iso-butane is higher than that of the n-butane^[29], leading to the rapid decrease of the iC₄/nC₄ ratio. However, no explanation is given to the phenomenon that the iC₄/nC₄ ratio increases orderly as the maturity increases when the gas humidity is above 5%.

Wet gas is produced from the Xujiahe Formation in the Central Sichuan Basin, along with a small proportion of condensate oil. The gas humidity is above 5% (Fig. 1), suggesting that the wet gas cracking stage has not yet been reached. The iC₄/nC₄ and iC₅/nC₅ ratios increase gradually as the maturity increases. In general, the Xujiahe Formation in the Central Sichuan Basin shares the similar variation trend of the iC₄/nC₄ ratio with the Mississippian Basin. Why the iC₄/nC₄ and iC₅/nC₅ ratios increase as the maturity increases? The possible reason is that the branched chain alkane requires more energy to break from kerogen than the straight chain alkane. When the maturity is relatively high but the wet gas cracking stage has not yet been reached, relatively more iso-alkanes would be generated. Thus, the data used in this study is from the coal-derived wet gas with no large-scale migration and trapped in the primary gas reservoir. In addition, the wet gas has not yet cracked, and the butane and pentane in natural gas originate mainly from the cracking of kerogen. Therefore, it is reliable to use the iC₄/nC₄ and iC₅/nC₅ ratios as the index for determining the maturity of the coal-derived gas, which is applicable to the coal-derived gas with the humidity coefficient of above 5% and no long-term migration and other coal-derived gas basins.

The iC₄/nC₄ and iC₅/nC₅ ratios in the natural gas are influenced by a variety of factors, such as the source type, maturity, migration, and biodegradation or oxidation. These factors, theoretically, may reflect many geological phenomena. However, they also have multiple explanations, which have limited their application for a long period of time. Thus, it is necessary to determine the variation law of these ratios with maturity during the generation of the natural gas. The variation law of the iC₄/nC₄ and iC₅/nC₅ ratios, in combination with the geological setting, may provide the solution to many geological issues. For example, these ratios can be used to roughly tell the maturity of the source rock in the primary gas reservoir. If the maturity of the source rock is known, it is possible to use these ratios to reveal the migration and accumulation process of the natural gas and, in the absence of large-scale migration, the variation of these ratios may reflect the occurrence of biodegradation and oxidization.

The Xujiahe Formation gas in the Central Sichuan Basin is essentially thermal wet gas generated by the moderately mature coal-measure source rock that has not yet reached the cracking gas stage. With no large-scale migration and alteration, the gas accumulated to form the primary gas reservoir, which provides ideal geological conditions for studying the variation law of the iC₄/nC₄ and iC₅/nC₅ ratios of the coal-derived gas. There is a good positive correlation between the iC₄/nC₄ and iC₅/nC₅ ratios of the coal-derived gas. At the low-moderate mature stage, the gas humidity is less than 5%, and the iC₄/nC₄ and iC₅/nC₅ ratios of the coal-derived gas increase linearly as the gas dryness coefficient increases and the methane carbon isotope becomes heavier. In other words, these ratios increase as the maturity gets higher. As the maturity goes up, more iso-alkanes would be formed and the iC₄/nC₄ and iC₅/nC₅ ratios rise, since the branched chain alkane requires more energy to break from the kerogen than the straight chain alkane. This study reveals the variation law of the iC₄/nC₄ and iC₅/nC₅ ratios of the coal-derived gas with the thermal evolution degree, introduces a new regression equation for calculating the maturity index of the coal-derived gas, and provides an important reference for studying the geochemical features and accumulation of the coal-derived hydrocarbons.