Detecting organic molecules synthesised via biological processes and distinguishing them from those synthesised via abiotic processes is critical to the search for life elsewhere in the universe1,2,3. Hydrocarbons have been detected on Mars4, Enceladus5, and certain meteorites6, although their origins remain a matter of debate. On Earth, natural hydrocarbons are mainly biotic in origin, produced either by thermal decomposition of sedimentary organic matter or microbial production including methanogenesis7,8. Contrastingly, some abiotic hydrocarbons are produced by a variety of reactions (including free-radical, the Sabatier, and Fischer–Tropsch-type reactions9,10,11,12) in both deep crustal fluids, hydrothermal systems, and sites of low-temperature water–rock reaction such as serpentinization.

Stable isotopes of carbon and hydrogen have long been used to discriminate hydrocarbon sources7,8. Thermogenic and abiotic hydrocarbons can sometimes be distinguished using compound-specific isotopic analysis (CSIA)10,13; namely, the relationship between the 13C/12C and 2H/1H ratios of individual hydrocarbons (methane, ethane, propane, and n-butane) (Fig. 1b). However, isotopic identification of abiotic hydrocarbons is often challenging (see ref. 11 and references therein), partly because the CSIA requires a set of molecules, all of which are not always available to sample. The recent development of the clumped-isotope analysis allows the collation of information preserved within a single molecule without a need for analysing other related molecules14,15,16. For example, the abundance of clumped isotopes of methane (13CH3D and CH2D2) is now routinely used as a geothermometer17, although the C-H bonding is susceptible to isotopic exchange which can lead, in some cases, to the reset of 13CH3D and CH2D2 abundances18. More robust information may come from 13C-13C clumping in organic molecules, because carbon in ethane is less readily exchanged than hydrogen, which is exchanged with surrounding water18.

Fig. 1: Results of ∆13C13C and compound-specific isotopic analysis (CSIA) of hydrocarbons (δ13C).
figure 1

a Relationship between ∆13C13CEthane and δ13CEthane value normalised against Vienna Pee Dee Belemnite (VPDB). Symbols are the same as shown in the legend of panel b. Grey circles denote bio-ethanol from three plants: the C3-type, the C4-type, and the Crassulacean Acid Metabolism (CAM)19. Light blue triangles represent ethene (C2H4) produced by propane pyrolysis (see Methods). Blue symbols represent proposed thermogenic gases, and orange represent proposed abiotic gases. The error bars are the standard error of the mean. The analytical uncertainty for the δ13C value is within the symbol. b Inverse of carbon number (nc) of individual hydrocarbon versus its carbon isotope composition relative to methane (δ13CCH4). The analytical uncertainty for the δ13C value is within the symbol.

We have developed a method to determine the relative abundances of the three isotopologues in ethane (12CH312CH3, 12CH313CH3, and 13CH313CH3) reported as ∆13C13C values19,20 (see Methods). Here, we show that this tool can be used to distinguish between abiotic and biotic hydrocarbons. We have examined natural gas ethane from various geological settings and compared them with abiotic ethane synthesised from methane in the laboratory. Based on experimental results and observations, we present a mechanistic understanding of 13C-13C abundances in hydrocarbons to account for the results found on abiotic and thermogenic ethane.

Results and discussion

General trends

Results of our clumped-isotope analysis show that thermogenic natural gas exhibits relatively high ∆13C13C values (Fig. 1a and Supplementary Table 1) and have a typical δ13C distribution pattern classically observed for thermogenic gas13,21, in which each longer-chain alkane is more enriched in 13C than the previous alkane (Fig. 1b and Supplementary Table 2). In contrast, abiotic ethane synthesised from CH4 exhibit distinctively low ∆13C13C values irrespective of the energy source used (i.e., ultraviolet [UV] light, spark discharge, and gamma-ray irradiation: see Methods). The low ∆13C13C values are also seen in hydrocarbons from deep fracture fluids in Kidd Creek (Canada) and the Dingo gas field in the Amadeus Basin (Australia) (see Methods for geologic settings), also proposed to have an abiotic origin.

A previous study using high-resolution mass spectrometry exhibited 4‰ variation of Δ13C13C values of thermogenic ethane22. This variation has been suggested to arise from the pyrolysis of ethane, which leads to a decrease in Δ13C13C values22,23. The present study using a conventional isotope ratio mass spectrometry after conversion of C2H6 to C2F6 shows a narrower range of the Δ13C13C values (0.57‰). Our pyrolysis experiment conducted at the same temperature as in ref. 22 (600 °C) and using a similar quartz vessel showed no change in the Δ13C13C values in contrast to ref. 22 (Supplementary Fig. 1 and Supplementary Table 3). These observations point to a potential discrepancy between the two methods for isotopologues analysis. Further interlaboratory comparisons will be necessary to calibrate the data from the two methods. The data presented here will be obtained solely by the method presented in ref. 19 that gives reproducible Δ13C13C values with no scale compression20 (see Methods).

Thermogenic ethane

The Δ13C13C value of thermogenic ethane could be attributed to C-C bonding in precursor molecules and the kinetic isotope effect during thermal cracking, as discussed in previous studies22,23 (Fig. 2a). In an ideal case where ethane is produced by breaking at least one C-C bond in an organic precursor, the kinetic isotope effect is relevant only to one carbon in ethane resulting in preferential 13C enrichment in one of the two carbons. In this case, the intramolecular bias in 13C lowers the Δ13C13C value owing to the combinatorial effect24,25, even though the two carbons in ethane are symmetrically equivalent. Combinatorial isotope effects are statistical clumped-isotope anomalies that occur when two atoms at two different positions in a single molecule isotopically differ24,25. In other words, when 13C is not evenly distributed at the two positions in an ethane molecule, the abundances of 13C-13C are lower than the stochastic (random) distribution. This does not apply to molecules with non-equivalent atomic sites, typically ethanol, for which an accurate stochastic distribution can be calculated based on the 13C/12C ratio of both sites.

Fig. 2: ∆13C13C vs. slope of compound-specific isotopic analysis (CSIA) trend.
figure 2

The horizontal axis shows the slope of the relationship between δ13C and 1/nc (derived from Fig. 1b), which also assumed to be an intrinsic δ13C bias between the two positions of carbon in a molecule (see text). The ∆13C13C scale to the stochastic distribution was estimated by assuming that the C-C bonds of biological glucose are under homogeneous isotopic equilibrium (see Methods). The error bars are the standard error of the mean. a The curved black line shows the predicted ∆13C13C value of ethane produced by C-C bond cleavage from an organic precursor (denoted as ‘P’) at each temperature, considering the combinatorial effect (see Methods). The CSIA slope at each temperature is also calculated using the same thermal cracking model21,22,23,26 (see Methods). The grey shaded area shows the uncertainty of the calculation, mainly derived from the possible range in ∆13C13C and differences in δ13C values between two adjacent positions of precursor molecules for the thermogenic hydrocarbons (see Methods). The dotted arrow shows the expected change due to microbial oxidation of ethane for Tokamachi mud volcano (Supplementary Fig. 2). b The curved black line shows the theoretically calculated ∆13C13C value of ethane at each temperature (Supplementary Fig. 3 and Supplementary Table 5) and δ13C values of hydrocarbons67,68 (see Methods). The dotted arrows show the notional changes due to isotope exchange among hydrocarbons after formation.

We estimated the intramolecular bias of thermogenic ethane based on a simple model in which hydrocarbons are formed by the cleavage of at least one C-C bond in an n-alkyl chain, as the simplest case considered in previous model21,22,23. For ethane, the δ13C (=[(13C/12C)sample/(13C/12C)standard] – 1) of one C-atom (C1) is that of the original precursor, whereas that of the other C-atom (C2) is altered by the cracking process. This creates an intramolecular bias within the ethane molecule, denoted as ∆13CEthane (= δ13CC1 – δ13CC2). The ∆13CEthane value can be obtained through the slope of the relationship between the δ13C values of individual hydrocarbons and the inverse of their carbon number (i.e., 1/nc) (see Methods) (Fig. 1b)21,22,23. The combinatorial effect (∆13C13CComb) can therefore be calculated as follows (see Methods for detailed calculation):

$${\varDelta }^{13}{{{{{{\rm{C}}}}}}}^{13}{{{{{{\rm{C}}}}}}}_{{{{{{\rm{Comb}}}}}}}=-{({\varDelta }^{13}{{{{{{\rm{C}}}}}}}_{{{{{{\rm{Ethane}}}}}}}/2({\delta }^{13}{{{{{{\rm{C}}}}}}}_{{{{{{\rm{Ethane}}}}}}}+1000))}^{2}\times 1000,$$

where δ13CEthane represents the carbon isotope composition of ethane. Assuming a typical δ13CEthane value of –40‰ and a kinetic isotope effect (13k/12k) from 0.958 to 0.986 (i.e., δ13CC1 >  δ13CC2), corresponding to temperatures ranging from 25 to 300 °C26, the ∆13C13CComb is predicted to range from –0.04 to –0.45‰ (Fig. 2a). Assuming a cracking temperature of 100 °C, the Δ13C13C value of ethane would be lower than –0.25‰ relative to the Δ13C13C value of precursor hydrocarbons. Estimating the Δ13C13C value of the original precursors is difficult, since measurement of 13C-13C clumped isotopes has not been applied to natural gas precursors, such as alkanes and kerogen. The only available data for biological molecules to date are derived from bio-ethanol (Fig. 1a)19. Despite the different types of photosynthetic pathway (the C3-type, the C4-type, and the Crassulacean Acid Metabolism [CAM]), the bio-ethanol show a narrow range of Δ13C13C values from +0.90 to +0.98‰, suggesting bio-ethanol is a good representative of biological molecules19. Using the Δ13C13C value of the ethanol as a starting estimate for an organic precursor (denoted as ‘P’ in Fig. 2a), the Δ13C13C value of thermogenic ethane can be calculated (Fig. 2a). Remarkably, the observed ∆13C13C values of the majority of the thermogenic natural gas ethanes in this study fall within the range predicted by this model at about 150 °C (Fig. 2a). The thermogenic ethane seems aligned perpendicular to the equilibrium temperature curve (Fig. 2b), which may potentially reflect the variation of ∆13C13C of the organic precursor, though, at present, the available ∆13C13C data of the organic precursor is only limited to bio-ethanol. Future studies should pursue ∆13C13C of organic molecules such as n-alkanes, fatty acids, and lignin to evaluate the ∆13C13C variations in the organic precursor.

Microbial oxidation of ethane

Three natural gas samples from Tokamachi show Δ13C13C values exceeding the predicted range of thermogenic ethane from this model (Fig. 2a). The high Δ13C13C in these samples could be due to microbial oxidation of ethane. Microbial strains capable of metabolising non-methane hydrocarbons (NMHCs) reportedly inhabit various geological settings under anoxic conditions27,28,29. The samples showing the high Δ13C13C values also have high C1/(C2 + C3) ratios, consistent with the anaerobic oxidation of NMHCs (Supplementary Fig. 2)30. Furthermore, at each of these localities, the high Δ13C13C in ethane correlated with the 13C enrichment of the central carbon in propane, strongly indicating microbial degradation of NMHCs (Supplementary Fig. 2 and Supplementary Table 4)31. Microbial oxidation of NMHCs is known to yield increased 13C enrichment in higher hydrocarbons31 (i.e., the steeper slope of the CSIA trend seen in Fig. 1b), consistent with the higher Δ13C13C values of ethane indicative of anaerobic oxidation origin.

Although the Δ13C13C analysis of pure culture anaerobic oxidation remains unreported, a conjecture can nevertheless be made based on recent findings on the anaerobic oxidation of ethane by archaea28,29. Previous culture experiments on ethane-oxidising archaea have shown that the enzymatic steps from ethane to CO2 by the archaea ‘Candidatus Ethanoperedens’ can be reversible within the cell29. In such case, a reverse reaction in which some CO2 is converted back into ethane may yield isotopic bond re-ordering towards thermodynamic equilibrium. Note that a similar mechanism has been proposed for the anaerobic oxidation of methane and is believed to promote isotopic re-equilibration in the residual methane32. Accordingly, it is conceivable that residual ethane undergoing microbial oxidation would approach isotopic equilibrium (Δ13C13C ≥ + 0.10‰ relative to the stochastic distribution of ethane; Fig. 2b, Supplementary Fig. 3 and Supplementary Table 5) at the microbiologically functional temperature range (<122 °C33) based on the assumption of stochastic reference frame (see Methods). A more precise estimate of the ∆13C13C change in microbial degradation is not possible at this stage, owing to the uncertainty in the growth temperature and degree of reversibility in natural populations. Nonetheless, the observed ∆13C13C increase seen in the three samples here is consistent with microbial degradation of ethane (Fig. 2b). Future studies should pursue Δ13C13C analysis to evaluate microbial activity pertaining to the anaerobic oxidation of ethane. Because the anaerobic oxidation of ethane increases ∆13C13C and its direction of the trend is away from those of abiotic ethane, the ability of Δ13C13C to distinguish between abiotic and thermogenic ethane is not impaired. Other processes potentially alter the ∆13C13C value in ethane and are compatible with the observed variation of thermogenic ethane. These include diffusion (an increase of ∆13C13C value by 0.3‰ in the case where molecular collision is important), mixing with different sources (an increase of ∆13C13C value by up to 0.13‰ in the case of mixing samples with the same ∆13C13C values but with different δ13C values of –20‰ and –45‰) and secondary cracking of ethane itself (no ∆13C13C variations at 600 °C in this study; see Supplementary Fig. 1)22,23. However, again, the discrimination potential of the Δ13C13C value of ethane is not weakened, because all these factors tend to increase the ∆13C13C value.

Abiotic hydrocarbon synthesis

In the stochastic reference frame assumed here (see Methods), the observed negative ∆13C13C values (i.e., anti-clumping25) of abiotic ethane can be explained by kinetic isotope effects governed by collision frequency between CH3 radicals (Fig. 2b). A radical–radical combination such as CH3 + CH3 is typically a barrierless reaction34, associated with mild kinetic isotope effects, depending on the ratio of collision frequencies35. These collision frequencies are scaled exactly by the inverse square root of the reduced mass (μ) of the collision pair (m1 and m2, respectively), i.e., μ = 1/m1 + 1/m2. Thus, the kinetic isotope effect due to the difference in collision frequency can be obtained from the relative reaction rate, calculated from the reduced mass ratio. In the case of a collision between CH3 radicals, the kinetic isotope effects are calculated to be k’/k = 0.9842 and k”/k = 0.9682, where the prime and double prime refers to singly and doubly substituted isotopologues, respectively. If kinetic isotope effects follow a stochastic distribution, (k”/k)/(k’/k)2 must be equal to 1 (see Supplementary Note 1). Any deviation from unity leads to Δ13C13C values different from 0. The intrinsic kinetic clumped-isotope effect calculated from the reduced mass of methyl radicals corresponds to a ∆13C13C value of –0.52‰. A more accurate quantitative estimate requires calculations that include a configurational effect, as isotopic substitutions can affect the minimum energy configuration of the transition state by changing its centre of mass36. However, the simple collision frequency calculation shows that ∆13C13C should be negative (anti-clumping) compared to a stochastic distribution during the methyl radical recombination reaction. Notably, a combinatorial isotope effect is not expected in the case of a methyl radical recombination since the two methyl radicals arise from the same reservoir. However, if one considers surface reactions such as Fischer–Tropsch-type reactions, the mechanism itself may lead to an intramolecular bias in ethane37, resulting in even lower Δ13C13C values. The data presented here provide, for the first time, a strong indicator of abiogenecity for ethane, based on the observed pattern of 13C-13C anti-clumping.

Isotope exchange in abiotic synthesis

After hydrocarbons are produced, their destruction enhances carbon exchange among individual hydrocarbons, which may potentially lead partial isotopic equilibrium through repeated production and destruction cycling. In our UV irradiation experiments of methane, C2H6 was produced from the combination of CH3 radicals (CH3 being generated through the reaction of CH4 with OH radicals derived from the photodissociation of water38) by the following reaction39:

$${{{{{{\rm{CH}}}}}}}_{3}+{{{{{{\rm{CH}}}}}}}_{3}+{{{{{\rm{M}}}}}}\to {{{{{{\rm{C}}}}}}}_{2}{{{{{{\rm{H}}}}}}}_{6}+{{{{{\rm{M}}}}}}$$

where M represents any third-body collision partner. In the wavelength range of UV light used in this study, neither CH4, C2H6, nor C3H8 photodissociates38. In addition, the C-C bonds in C2H6 and C3H8 are not decomposed by reactions with OH, H, O, and CH3 radicals, all of which should be present during UV experiments38. Hence, the C2H6 and C3H8 produced by UV irradiation of methane are unlikely to undergo C-C bond decomposition because of the lack of high-energy photon below 150 nm in our experimental setting. Conversely, for spark discharge and gamma-rays experiment, the C-C bonds of C2+ hydrocarbons frequently cleave after their formation as follows40 (Supplementary Table 6):

$${{{{{{\rm{C}}}}}}}_{2}{{{{{{\rm{H}}}}}}}_{6}\to 2{{{{{{\rm{CH}}}}}}}_{3}$$
$${{{{{{\rm{C}}}}}}}_{3}{{{{{{\rm{H}}}}}}}_{8}\to {{{{{{\rm{CH}}}}}}}_{3}+{{{{{{\rm{C}}}}}}}_{2}{{{{{{\rm{H}}}}}}}_{5}$$
$${{{{{{\rm{C}}}}}}}_{3}{{{{{{\rm{H}}}}}}}_{8}\to {{{{{{\rm{CH}}}}}}}_{4}+{{{{{{\rm{C}}}}}}}_{2}{{{{{{\rm{H}}}}}}}_{4}$$

In the case of gamma-ray irradiation of methane, the calculated dosage was sufficient to decompose the C2+ hydrocarbons formed from methane, although C2H4 was not detected12. Ethane in the spark discharge and gamma-ray irradiation experiments is produced not only by the CH3 radical polymerisation but also by the C3+ hydrocarbon decomposition. After production, ethane decomposes to CH3, implying that the C1 polymerisation is not unidirectional. The C-C chain elongation and shortening may alter the Δ13C13C values of ethane to an extent depending on the degree of reversibility. Fully reversible reactions may yield equilibrium isotope composition (the curved black line in Fig. 2b), whereas irreversible reactions tend to be governed by kinetic isotope effect as represented in the ethane synthesised by UV experiment (Fig. 2b). We suggest that cleavage of C-C bonds in hydrocarbons may enhance the reversibility and leads to an isotopic exchange, where ∆13C13C of abiotic ethane shifts toward the homogeneous isotopic equilibrium (∆13C13C = + 0.22‰ at 25 °C; Supplementary Fig. 3) (Fig. 2b).

13C13C systematics of abiotic hydrocarbons

In summary, the observed low ∆13C13C values in abiotic ethane can be explained by anti-clumping due to the kinetic isotope effect at the C-C bond formation (negative ∆13C13C). Subsequent isotope exchange facilitated through the backreaction from the higher hydrocarbons during the polymerisation sequence may cause the increase in ∆13C13C value (Fig. 2b). The two processes likely occur naturally and seem applicable to the abiotic hydrocarbons from Kidd Creek fracture fluids and the Dingo gas field (see Methods), both of which exhibit low ∆13C13C values within the expected abiotic range (Fig. 2b). The similarity of ethane from the gamma radiolysis experiments to the Kidd Creek samples is notable given the proposed role of radiolysis in producing acetate and formate at that site41. If isotope exchange continues, leading to homogeneous isotopic equilibrium, the ∆13C13C of abiotic ethane may eventually become indistinguishable from that of thermogenic hydrocarbons. However, the 13C-13C anti-clumping observed in the natural gases from the two sites (Kidd Creek and the Dingo gas field) demonstrates that the distinctively low abiotic ∆13C13C signature survives in nature. Based on these findings, 13C-13C anti-clumping in ethane can be a valuable approach to distinguish abiotic hydrocarbons from thermogenic, and potentially from microbial sources. The 13C-13C signature may thus be applied in investigations of the origin of ethane in terrestrial and extra-terrestrial settings. Moreover, not only ethane but a variety of organic molecules containing C-C bonds can be subjected to this analytical approach to distinguish abiotic formation pathways, in geological and even extra-terrestrial settings, such as Mars, Titan, and Enceladaus2,5,42.


13C13C notation

The abundance of 13C-13C isotopologues was conventionally reported as a deviation from the stochastic abundance of the isotopologues:

$${\varDelta }^{13}{{{{{{\rm{C}}}}}}}^{13}{{{{{\rm{C}}}}}}\equiv {}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{sample}}}}}}}/{}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{stochastic}}}}}}}-1$$

where 1313R is defined as the abundance of 13C-13C isotopologues compared to 12C-12C isotopologues, and Rstochastic refers to the abundance ratio in a random distribution. The stochastic distribution of C2 isotopologues is calculated as follows:

$${}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{stochastic}}}}}}}={}^{13}{{{{{\rm{R}}}}}}\times {}^{13}{{{{{\rm{R}}}}}}$$

where 13R indicates the 13C/12C ratio in all C2 molecules. In this study, we report ∆13C13C’ as the natural logarithm of α:

$${\varDelta }^{13}{{{{{{\rm{C}}}}}}}^{13}{{{{{\rm{C}}}}}}^{\prime} \equiv \,{{{{\mathrm{ln}}}}}(\alpha )\; \approx \;(\alpha -1);({{{{{\rm{since}}}}}}\,\alpha \; \approx \;1)$$

where α represents the equilibrium constant of the homogeneous isotope exchange reaction:

$$2{\,\!}^{12}{{{{{\rm{C}}}}}}{\,\!}^{13}{{{{{\rm{C}}}}}}\; \leftrightarrows \;{}^{12}{{{{{\rm{C}}}}}}{\,\!}^{12}{{{{{\rm{C}}}}}}+{\,\!}^{13}{{{{{\rm{C}}}}}}{\,\!}^{13}{{{{{\rm{C}}}}}}$$
$${{{{{\rm{\alpha }}}}}}\equiv [{\,\!}^{12}{{{{{\rm{C}}}}}}{\,\!}^{12}{{{{{\rm{C}}}}}}][{\,\!}^{13}{{{{{\rm{C}}}}}}{\,\!}^{13}{{{{{\rm{C}}}}}}]/{[{\,\!}^{12}{{{{{\rm{C}}}}}}{\,\!}^{13}{{{{{\rm{C}}}}}}]}^{2}\; \approx \;{\,\!}^{1313}{{{{{\rm{R}}}}}}/{(2\;\times {\,\!}^{13}{{{{{\rm{R}}}}}})}^{2}$$

where 13R is calculated from the isotopologue ratio of [12C13C]/[12C12C] divided by 2, reflecting the symmetry of two carbon atoms in ethane. The ∆13C13C’ value is approximately equal to that of the conventional ∆13C13C (Eq. (6)). In the case of C2 compounds, however, it is difficult to determine the 1313Rstochastic accurately because C-C bond breaking and recombination do not usually occur reversibly. Thus, calibrating the value with experiments at different temperatures is not feasible. Therefore, ∆13C13C’* value is calculated as follows:

$$\begin{array}{c}\varDelta {\,}^{13}{{{{{\rm{C}}}}}}{\,}^{13}{{{{{\rm{C}}}}}}^{\prime}*\equiv \varDelta {\,}^{13}{{{{{\rm{C}}}}}}{\,}^{13}{{{{{\rm{C}}}}}}^{\prime} _{{{{{{\rm{sample}}}}}}}-\varDelta {\,}^{13}{{{{{\rm{C}}}}}}{\,}^{13}{{{{{\rm{C}}}}}}^{\prime} _{{{{{{\rm{reference}}}}}}}\\=\,{{{{\mathrm{ln}}}}}({\,}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{sample}}}}}}}/{\,}^{13}{{{{{\rm{R}}}}}}_{{{{{{\rm{sample}}}}}}}^{2})-\,{{{{\mathrm{ln}}}}}({\,}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{reference}}}}}}}/{\,}^{13}{{{{{\rm{R}}}}}}_{{{{{{\rm{reference}}}}}}}^{2})\\=\,{{{{\mathrm{ln}}}}}({\,}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{sample}}}}}}}/{\,}^{1313}{{{{{\rm{R}}}}}}_{{{{{{\rm{reference}}}}}}})-2\times \,{{{{\mathrm{ln}}}}}({\,}^{13}{{{{{\rm{R}}}}}}_{{{{{{\rm{sample}}}}}}}/{\,}^{13}{{{{{\rm{R}}}}}}_{{{{{{\rm{reference}}}}}}})\\=\delta {\,}^{13}{{{{{\rm{C}}}}}}{\,}^{13}{{{{{\rm{C}}}}}}^{\prime} -2\times {\delta }^{13}{{{{{\rm{C}}}}}}^{\prime} \end{array}$$

where δ13C13C’ and δ13C’ represent the ratio of 1313R and 13R among sample and reference gases as the natural logarithm. Note that all isotope values (∆13C13C’*, δ13C13C’ and δ13C’) are expressed in ‰.

Measurement of ∆13C13C

We used a fluorination method for the measurement of 13C-13C species19,20, which is based on the fluorination of C2 compounds to hexafluoroethane (C2F6) and subsequent measurement of its 13C isotopologues with a conventional isotope ratio mass spectrometer. The purified C2F6 was introduced into a mass spectrometer (Thermo Fischer MAT253), used in the conventional dual inlet mode. The typical standard deviation of the mean for δ13C’, δ13C13C’, and ∆13C13C’* values was ±0.01‰, ±0.09‰, and ±0.09‰, respectively (n = 6).

Consequently, we define the empirical transfer function as follows:

$$\varDelta {}^{13}{{{{{\rm{C}}}}}}{}^{13}{{{{{\rm{C}}}}}}^{\prime} {\ast }_{{{{{\mathrm{CSC}}}}}}=\lambda \times \varDelta {}^{13}{{{{{\rm{C}}}}}}{}^{13}{{{{{\rm{C}}}}}}^{\prime} \ast$$

where ∆13C13C’*CSC value refers to the ‘true scale’ value, corrected for scale compression. The λ value is 1.2541 ± 0.0101 for ethanol and ethene, whereas 1 for ethane since the latter is not prone to scrambling which may have occurred during the fluorination of ethene but not in the ion source of the mass spectrometer20. For simplicity, we will describe the corrected ∆13C13C’*CSC as ∆13C13C in the following and main text.

Reference frame for ∆13C13C measurement

The ∆13C13C values obtained as described above are relative and are not referred to against the stochastic distribution but a working standard (C2F6)19,20. To obtain values reported against a stochastic distribution, we constructed a reference frame for 13C-13C isotopologues analysis by estimating that C-C bonds in biological glucose could be under thermodynamic isotope equilibrium. The ∆13C13C of ethanol produced by the fermentation of sugars from different plants (C3, C4, and CAM) is reportedly uniform, whereas the 13C/12C ratio and position-specific isotope composition vary19. The latter has been explained by differences in CO2 assimilation43 and internal metabolic fluxes44; the narrow range of ∆13C13C values can be explained by the metabolic origin of sugars, i.e., the Calvin–Benson–Bassham (CBB) cycle19. The C-C bonds of glucose are derived from the carboxylation, aldolisation, and transketolisation reactions in the CBB cycle. Enzymes facilitate these reactions, and while it is known that the carboxylation reaction is irreversible, the aldolisation and ketolisation reactions are at equilibrium45. The measured ethanol19 is derived from the carbons in the C1-C2 and C5-C6 positions of glucose which are produced in an aldolisation reaction45. In this scenario, the ∆13C13C values of ethanol could be controlled by thermodynamic equilibrium, which enriches the doubly substituted isotopologue, leading to a positive ∆13C13C value compared to the stochastic distribution.

Because glucose is a complex molecule, we performed theoretical calculations to estimate equilibrium distributions of isotopologues of CH2=CH2, CH3-CH3, CH3-CH2OH, and CH2OH-CH2OH as model molecules with C-C bonds (Supplementary Fig. 3 and Supplementary Table 5). The clumped-isotope signature at an isotopic equilibrium was calculated by applying the Bigeleisen–Mayer equation46,47. The molecular constants within the Bigeleisen–Mayer equation were obtained through quantum chemical calculations. We used B3LYP/6-311+G (d, p) level48,49,50 for geometry optimisations, single-point energy calculations, and harmonic frequency generations. All calculations were performed using the Gaussian 09 package51. ‘Very tight’ geometry convergence criteria and ‘superfine’ grids built in Gaussian 09 were applied for geometry optimisation procedures and further computations.

The calculated ∆13C13C values for ethane were in good agreement with the previous studies52. The obtained ∆13C13C differed by up to 0.02‰ among CH3-CH3, CH3-CH2OH, and CH2OH-CH2OH molecules; this difference is sufficiently low compared to the analytical accuracy of ∆13C13C (Supplementary Fig. 3 and Supplementary Table 5). Thus, we used data obtained from CH2OH-CH2OH to predict ∆13C13C of the C1-C2 and C5-C6 bonds in glucose under thermodynamic equilibrium, because the carbons in the C1-C2 and C5-C6 positions of glucose are composed as CH2OH-CHOH- and CHO-CHOH-, respectively. The ∆13C13C of the used C2F6 standard gas in this study was –0.72‰ compared to the stochastic distribution by assuming that the average of ∆13C13C of bio-ethanol (+0.93‰) is in thermodynamic equilibrium and using the results of the theoretical calculations for CH2OH-CH2OH (+0.2‰ at 25 °C). In natural ethanol, the δ13C values in positions CH3 and CH2OH can be different by up to 11.4‰, which would result in lower ∆13C13C values compared with the stochastic distribution owing to combinatorial effects25. However, the combinatorial effect in ethanol measured in this study is up to –0.03‰ considering a site-specific 13C distribution in ethanol of 11.4‰ at maximum53. The combinatorial effects calculated here are much lower than the analytical precision of ±0.09‰ and can thus be quantitatively neglected here.

Measurement of δ13C values of hydrocarbons

The δ 13C values were determined using gas chromatography coupled with isotope ratio mass spectrometry (DeltaplusXP, Thermo Fisher Scientific K.K., Tokyo, Japan) via a combustion furnace and a conflow interface (GC Combustion III, Thermo Fisher Scientific K.K., Tokyo, Japan) (GC-C-IRMS). The gas chromatography column used was HP-PLOT-Q (30 m × 0.32 mm i.d., 10 µm film thickness; GL Sciences Inc., Tokyo, Japan), and the carrier gas was high-purity helium (99.999%; Fujii Co.). The conditions of the GC oven were as follows: injector temperature 250 °C; split mode (variable split ratio); flow rate 1.5 mL/min; oven temperature programme 50 °C (maintained for 5 min) raised to 200 °C (maintained for 10 min) at a rate of 10 °C/min. The combustion furnace consisted of a ceramic tube packed with CuO, NiO, and Pt wires, operating at 960 °C. Isotopic standardisation was made by CO2 injections calibrated against the natural gas standard NGS-2 provided by the National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA.

Measurement of intramolecular δ13C composition in propane

Intramolecular δ13C bias of propane was determined by an online pyrolysis system coupled with GC-C-IRMS54. Isotopic standardisation was made by CO2 injections calibrated against the NIST natural gas standard NGS-2. The relative 13C enrichment in a given position is defined as the difference in isotopic composition between central and terminal carbon positions. Three fragments are used for its calculation: CH4, C2H4, and C2H6. CH4 and C2H6 arise from the terminal position only, while C2H4 arises from an equal contribution of terminal and central positions. The relative 13C enrichment in the central position (=Δ13Cpropane, expressed in ‰) is defined as follows:

$$\varDelta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{propane}}}}}}}=\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{central}}}}}}}-\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{terminal}}}}}}}$$

where δ13Ccentral and δ13Cterminal refer to the carbon isotope composition of central and terminal positions, respectively.

Purification of ethane and ethene

Ethene and ethane must be purified before the fluorination reaction19,20. These gases were purified using a gas chromatograph GC-4000 plus (GL Sciences Inc., Tokyo, Japan) equipped with Hayesep Q column (1/8” od., 60/80 mesh, 4 m; GL Sciences Inc., Tokyo, Japan) connected to a vacuum line. The sample was directly introduced into the system using a gas-tight syringe through a rubber septum. In both cases, condensable products were trapped at –196 °C (liquid nitrogen), and the remaining non-condensable gases were evacuated under a vacuum. The condensed products were then released with a water bath at room temperature (25 °C) before being introduced into the gas chromatograph. High-purity helium (99.999%; Fujii Co.) was used as the carrier gas. Ethane and ethene could be separated and collected through the 6-port switching valve due to their different retention times. Other impurities were discarded. The conditions of the GC oven were as follows: injector temperature 120 °C; column pressure1 200 kPa column; pressure2 160 kPa at 80 °C; oven temperature programme 35 °C (maintained for 15 min) raised to 200 °C (maintained for 16 min) at a rate of 60 °C/min.

UV irradiation experiment

UV irradiation of methane was conducted in a glass flask (457 mL) used in a previous study38. The top of the flask is made of UV-grade synthetic quartz window, which is transparent for >175 nm photon. A high-pressure xenon arc lamp (Xe lamp: Cermax, CX-04E, output setting 20 A) was used as the UV source, with a solar-like UV spectrum used in a previous report38. Before UV irradiation, 50 mL of doubly distilled water was injected through a syringe port. The water was frozen using liquid nitrogen, and the remaining gas was evacuated from the vacuum line to remove the CO2 or O2 trapped in the water. Then, methane (purity 99.9%, GL Science Inc.) was introduced without purification into the flask from the vacuum line at 25 °C to a pressure of about 12 kPa. After introducing methane gas, the flask was kept at 25 °C using a water bath (MC-1, ASONE). An aliquot of gas phase was sampled from the vacuum line to measure the chemical and carbon isotope composition before the UV irradiation (0 h). In this experiment, UV light was irradiated vertically from the top to the liquid water surface. Methane was exposed under UV light for 3 and 16 h. After the irradiation, the gas sample was collected from the vacuum line to a stainless-steel finger.

Spark discharge experiment

C2+ hydrocarbons were produced by spark discharge of methane gas. This experiment was conducted in a glass flask (457 mL) previously evacuated through a vacuum line. Methane (purity 99.9%, GL Science Inc.) was introduced without purification into the flask using a gas-tight syringe to a pressure of 12 kPa. The glass flask was connected with a tungsten pole through Swagelok, and the pole was connected with a spark discharger (BD-50E Heavy Duty Generator). Spark discharge of methane was conducted cyclically for 15 min and then stopped for 15 min to avoid elevating the temperature of the reaction vessel. The two experiments were conducted at room temperature (25 °C) with a total duration of 15 min and 5 h. Output adjustment of spark discharger was controlled at eight levels. After exposing methane under spark discharge, gas samples were collected through the vacuum line to a stainless-steel finger.

Gamma-ray irradiation experiment

The gamma-ray irradiation experiment was undertaken at ANSTO, Australia12,55, where C2-C5 light hydrocarbons were synthesised via the 60Co gamma-ray radiolysis of methane. The sample used in this study was irradiated for 650 h, and the temperature was maintained at 21 °C.

Ethane pyrolysis

Ethane (purity 99.9%, GL Science Inc.) was decomposed by heating at 600 °C in a muffle furnace. Ethane was introduced into quartz tubes through a vacuum line using liquid nitrogen. Once sealed with a gas burner supplied with oxygen, the tubes were heated at 600 °C in a muffle furnace. The remaining ethane in the tubes was isolated from the other reaction products and measured by manometry to calculate the percentage of gas remaining and measured for its carbon isotope and clumped-isotope composition (Supplementary Fig. 1 and Supplementary Table 3).

Pyrolysis of propane

Propane pyrolysis was conducted to produce hydrocarbons. Propane gas (purity 99.9%, GL Science Inc.) was introduced into empty Pyrex tubes through a vacuum line using liquid nitrogen. Once sealed with a gas burner, the tubes were heated at 500 °C in a muffle furnace. The chemical and isotopic compositions of the reaction products were characterised and measured using the methods presented above (Supplementary Table 7). Then, the produced ethene in the tubes was purified from the other reaction products to measure the ∆13C13C. Ethene was measured instead of ethane because the latter potentially arises from the recombination of CH3 fragments (2 CH3 → C2H6), not directly from propane cracking, contrary to ethene54.

Natural gas samples

We analysed samples from different natural gas reservoirs: Southwest Ontario Basin (Canada)31, Appalachian Basin (United States)56,57, and Arkoma Basin (United States)58. Based on isotope composition, hydrocarbons in these basins are suggested to be mainly of thermogenic origin (Fig. 1b). We also analysed gases from the Kidd Creek and the Dingo gas field (Amadeus Basin). CSIA suggests that these hydrocarbons are of abiotic origin (Fig. 1b). In addition, we collected natural gas samples from the Tokamachi mud volcano, which is situated in the Tertiary sedimentary basin in Niigata Prefecture, Central Japan. Niigata Basin is part of the wider Green Tuff belt of Honshu, one of the most important petroleum (oil and gas) producing areas in Japan59.

Southwest Ontario Basin

The sedimentary strata of Southwestern Ontario consist of Late Cambrian to Devonian sediments. The samples analysed in this study are of Silurian to Middle Ordovician age and were collected between June 2012 and December 2013. For more details on the basin and sampling method, please refer to a previous study31.

Appalachian Basin

Samples from the Appalachian Basin are gas seeps collected south of Lake Erie in upstate New York in June 2018. In this region, natural gas seeps are abundant and generally found bubbling in small water ponds or riverbeds on fractured shales of Ordovician and Devonian ages56,57. Specifically, samples collected and measured here are those defined in ref. 56 as: Amherst State Park, Barcelona Gas Spring, Chestnut Ridge Eternal Flame, Gasport, and from Pipe Creek. These samples all have signatures of thermogenic generation with methane δ13C ranging between –42 and –52‰, low C1/C2+ ranging from 1.5 to 10, and ethane concentrations of 7–24 vol.%. The samples were collected by setting on the gas seeps an inverted funnel connected to Tygon tubing and a flow-through gas chamber to avoid air contamination. Gases are then sampled from the gas chamber with a gas-tight syringe and added to a pre-evacuated 60 cc serum vial pre-poisoned with HgCl2.

Arkoma Basin, Oklahoma, USA

Hydrocarbons, the main material for shale gas, have been developed from late Devonian and early Mississippian formations, such as the Woodford Shale in Oklahoma and the Chattanooga Shale in Arkansas. Gas was collected from gas wells using standard well-sampling techniques58.

Tokamachi mud volcano, Niigata, Japan

Tokamachi area consists of two active mud volcanoes, Murono and Gamo, located 10 km west of Tokamachi village. At Murono, groundwater, mud, and gases erupt at the bubbling crater; natural gas also seeps from cracks formed in the asphalt pavement along the road of a car test track built around the mud volcano; the crack-seepage mainly occurs in at least two sites. At Gamo, only two small mud craters were found during the survey performed in this study. The gas samples were sampled using the water-displacement method and stored in a glass vial sealed with a butyl rubber septum.

Kidd Creek, Timmins, Ontario, Canada

Sampling and characterisation of fracture fluids located at 2.4 km below the surface in a mine operating to 3 km depth in the 2.7-billion-year-old rocks of the Canadian Shield in a Cu-Ag-Zn deposit (stratiform volcanogenic massive sulfide) hosted in interlayered felsic, mafic, ultramafic and metasedimentary deposits that form part of Abitibi greenstone belt as described in previous studies10,41,60,61,62,63,64. We analysed ethane samples from a borehole at 7850’ level in 2014 and at 9500’ level in 2012 (Supplementary Table 2). These samples were stored in a glass vial sealed with a butyl rubber septum. Evidence from bulk carbon, hydrogen isotope signatures, and clumped methane has demonstrated that hydrocarbons of abiotic origin are predominant in Kidd Creek10,41,62.

Amadeus Basin, Australia

Gas samples from Dingo gas field in Amadeus Basin were collected as described in previous study65. Both carbon and hydrogen signatures imply that hydrocarbons from Dingo gas field are derived from abiotic origins12.

Evaluation of the combinatorial effect of thermogenic ethane

We used the theoretical model to account for the carbon isotope composition of natural hydrocarbon gases produced by thermal cracking21,22,23. Various alkyl groups attached to a large kerogen molecule are assumed to produce hydrocarbon gases. In this model, the carbon atoms of any individual natural gas hydrocarbon molecule are defined as ‘Cn’. The carbon atom arising from the C-C bond breaking of the alkyl chain is defined as ‘Cm’. The remaining C-atoms in the hydrocarbons are defined as ‘Cp’. Considering only primary isotope effects, the carbon atom of Cm is enriched in 12C because of the C-C bond breaking. However, the C-atoms (Cp) are unaffected by any isotope fractionation, thus recording the original isotope composition of the alkyl chain in kerogen. A given hydrocarbon with n atoms has one Cm atom and (n – 1) Cp atoms. Therefore, its carbon isotope composition is:

$$\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{n}}}}}}}=-{\varDelta }_{{{{{{\rm{q}}}}}}}/n+\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{p}}}}}}}$$

If the δ13Cn values are plotted as a function of 1/n (‘natural gas plot’ of ref. 21), the slope and the intercept of this plot represent the ∆q (= δ13Cp – δ13Cm) and the δ13Cp values, respectively, based on Eq. (14). The slope of the plot represents the isotope fractionation associated with C-C bond breaking, leading to the difference in the carbon isotope composition between two carbon atoms of ethane (‘intramolecular bias’). Based on this model, the ethane produced contains two symmetrically equivalent carbon atoms, but they originate from precursor sites with different kinetic isotope effects during ethane production. The 13C/12C ratio of ethane (RAVE) is the average of the two carbon positions, and because of the symmetry of ethane, the probability of 13C2H6 formation is expected to be proportional to the square of that average ratio (Rstochastic). In practice, however, the probability of the formation of 13C2H6 (R26/24) is proportional to the product of the 13C/12C ratio of the two different carbon positions. The deviation of the 13C-13C isotopologues abundance ratio of ethane from stochastic (∆13C13CComb) is expressed as follows:

$$\varDelta {}^{13}{{{{{\rm{C}}}}}}{}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Comb}}}}}}}=1000({{{{{{\rm{R}}}}}}}_{26/24}/{{{{{{\rm{R}}}}}}}_{{{{{{\rm{AVE}}}}}}}^{2}-1)$$
$${{{{{{\rm{R}}}}}}}_{26/24}={{{{{{\rm{R}}}}}}}_{{{{{{\rm{A}}}}}}}\times {{{{{{\rm{R}}}}}}}_{B}$$

where RA and RB represent the 13C/12C ratio for the two carbon positions CA and CB of ethane, respectively. The solution to the simultaneous equations of Eqs. (16) and (17) can be expressed as:


Therefore, the difference in the 13C/12C ratio between the two carbon positions of ethane can be expressed as:


Converting Eq. (20) to δ values with respect to the standard (Rstd) is expressed as:

$$\varDelta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Ethane}}}}}}}=2\times (\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Ethane}}}}}}}+1000)\times {(-\varDelta {}^{13}{{{{{\rm{C}}}}}}{}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Comb}}}}}}}/1000)}^{0.5}$$

where ∆13CEthane and δ13CEthane represent the difference and average of the two carbon positions in δ13C between the two carbon positions of ethane. Equation (21) can be rearranged as:

$$\varDelta {}^{13}{{{{{\rm{C}}}}}}{}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Comb}}}}}}}=-{(\varDelta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Ethane}}}}}}}/2(\delta {}^{13}{{{{{\rm{C}}}}}}_{{{{{{\rm{Ethane}}}}}}}+1000))}^{2}\times 1000$$

Combinatorial isotope effects associated with intramolecular bias in the organic precursor can be estimated through the position-specific isotope composition of long-chain alkanes measured by nuclear magnetic resonance66. The latter shows differences in δ13C values between two adjacent positions (=δ13CCH3 – δ13CCH2) of ca. –3.9‰ (the C16-C31 range with odd carbon number), 10.4‰ (the C16-C31 range with even carbon number), and –12.5‰ (the C11-C15 range with odd and even carbon number)66, which corresponds to depletion of ∆13C13C values of –0.004‰, –0.03‰, and –0.04‰, respectively. The combinatorial effects calculated here are much lower than the analytical precision of ±0.09‰ and can thus be quantitatively neglected.