Clumped methane isotopologues (¹³CH₃D and ¹²CH₂D₂) of natural samples measured using a high-resolution mass spectrometer with an improved pretreatment system

Abstract

Doubly-substituted methane isotopologues (¹³CH₃D and ¹²CH₂D₂) can provide unique information to resolve the origin, transport, and conversion of environmental methane. We used a high-resolution mass spectrometer (Thermo Fisher Scientific 253 Ultra) to precisely determine Δ¹³CH₃D and Δ¹²CH₂D₂ (precision and accuracy of ∼0.35‰ and ∼1.35‰ (1σ), respectively) in this study. The impacts of temperature, humidity, and slit quality are found to be critical for the reproducibility of the results, while the fragmentation rate and bellows effects on the clumped isotope results were negligible. A heating equilibrium experiment performed at 500 °C, 400 °C and 300 °C (n = 19) calibrates the results to an absolute reference. A pretreatment system that can extract methane having concentrations from ∼15% to ∼99.8% is proposed, while the fractionation produced throughout the pretreatment is negligible within precision (Δ¹³CH₃D = +0.16 ± 0.32‰ and Δ¹²CH₂D₂ = +0.14 ± 1.12‰ (n = 16)). Analyses of natural gases from shale basins and variable methane-rich gases emitted from artificial lakes validate the capability of the current pretreatment and spectrometer systems to determine methane clumped isotopes in a wide range of natural environmental samples.

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1. Introduction

Methane (CH₄) is the primary component of natural gas and hence a critical energy source, but also the most potent anthropogenic greenhouse gas emission.^1,2 The origin of environmental methane is usually classified into three types: thermogenic, biogenic, and abiotic.³ Methane bulk isotope compositions (δ¹³C-CH₄ and δD-CH₄) can be diagnostic,^4,5 and are used to trace the fate and source of methane in the carbon cycle.^6,7 However, there is partial overlap between CH₄ of different origins, and the subsequent migration and conversion processes also affect the stable isotopic compositions making conventional C and H isotope data inconclusive.⁸ The abundances of methane clumped (doubly substituted) isotopologues (¹³CH₃D and ¹²CH₂D₂) record the formational conditions and provide reliable apparent temperatures in the equilibrium state,^9–12 and trace the causes of disequilibrium characteristics caused by kinetic effects in the generation and/or post-generation process.^13–19

In practice, due to the low abundance (proportional relative abundance of 10⁻⁶ and 10⁻⁷, while the most abundant ¹²CH₄ is ∼9.88 × 10⁻¹) and similar masses (18.041 amu and 18.044 amu) of ¹³CH₃D and ¹²CH₂D₂, resolved measurements of abundance of doubly substituted methane isotopologues are challenging.¹² The recent development of high-resolution isotope ratio mass spectrometry has facilitated the measurement of doubly-substituted methane isotopologues.^10,16,20 However, detailed commissioning data and the influence of a variety of potential analytical factors (e.g., temperature, humidity, slit quality, fragmentation rate, and bellows effects) have not been widely reported.

The introduction of HR-IRMS also requires confirmation that sample pre-treatment methods are robust to the standards of the enhanced measurement capability. In the pre-treatment of natural samples, two alternative methods are generally used: (i) cryogenic purification (at 45 K) and 5 Å molecular sieve collection (at 70 K)^10,12 or (ii) gas chromatography (GC) purification and a silica gel collection method.^13,19 The Δ₁₈ (abundance of both ¹³CH₃D and ¹²CH₂D₂ relative to a random isotopic distribution) fractionation of 5 Å molecular sieve collection-release is ∼+0.49‰.^12,13 GC systems typically exhibit no fractionation, but are variably efficient in water removal,²¹ which becomes important in methane isotopologue measurements because the common ¹H₂¹⁶O (18.011 amu) molecule is approximately isobaric with doubly-substituted methane isotopologues. In particular, ¹³CH₅ might lead to CH₄ 18 amu isobaric interferences. The ¹H₂¹⁶O peak was used for the tailing correction procedure in ¹²CH₂D₂ measurement.²² Previously reported^10,23–26 pretreatment methods have been shown to be effective for methane-dominated samples of relatively high purity (e.g., natural gas) and a limited number of samples with relatively low methane purity (e.g., natural water emitted gases with a CH₄ concentration of <20%). Efficient purification and collection of methane from low concentration environmental samples is necessary for clumped isotope measurements in natural systems.

Here, we report a one-year dataset of high-resolution mass spectrometry measurements in our laboratory, including the δ¹³C-CH₄, δD-CH₄, δ¹³CH₃D, and δ¹²CH₂D₂ results. The precision, accuracy, and four potentially important factors which may influence measurements are discussed and compared to those of previous studies. Using the temperature scale from catalyzed equilibration experiments at 500 °C, 400 °C and 300 °C, the working gas results (δ¹³CH₃D and δ¹²CH₂D₂) can be calibrated and converted to an absolute reference frame (Δ¹³CH₃D and Δ¹²CH₂D₂). We present a cryogenic purification (at 50 K) and silica gel collection (at 75 K) pretreatment system with demonstrably negligible isotope fractionation. A series of synthetic and natural samples with large isotopic (bulk and clumped) differences have been successfully measured using this system.

2. Experimental section

2.1 Mass spectrometer commissioning

The high-resolution isotope ratio mass spectrometer (253 Ultra, Thermo Fisher Scientific, Germany), installed at the School of Earth System Science, Tianjin University, China, has a mass resolving power (MRP; 5% and 95% edge definition) of 45 000–50 000 with the HR+ mode (high-resolution slit with a width of 5 μm and an additional mechanical aperture for higher resolution combination²⁷). The spectrometer is equipped with nine Faraday cup (L4–L1, Center, H1–H4) detectors. Three of the Faraday cups (H2, H3, and H4) are co-mounted with miniature compact discrete dynode (CDD) electron multipliers designed to quantify low intensity signals.

L1 [¹³CH₄⁺], L4 [¹²CH₄⁺], H3 CDD [¹³CH₃D⁺], and H4 CDD [¹²CH₂D₂⁺] are used in methane clumped isotope measurement. The resulting mass scans for δ¹³C, δD, Δ¹³CH₃D, and Δ¹²CH₂D₂ are shown in Fig. 1.

Fig. 1 Mass scan results of ion intensity for δ¹³C (a), δD (b), Δ¹³CH₃D (c), and Δ¹²CH₂D₂ (d) measurements on April 29, 2022. Δ¹³CH₃D and δ¹³C are simultaneously analyzed (cps = counts per second).

Measurements are ordered as Δ¹³CH₃D and δ¹³C, δD, Δ¹²CH₂D_2, and peak tailing corrections, with a complete cycle measurement of about 30 h (complete 2 days of measurement is shown as a flow chart in Fig. S1†). The samples were thoroughly mixed over 20 cycles of bellows compression and relaxation (100–20% software settings) to ensure homogeneous isotope distribution before introduction to the mass analyser.^12,13

2.2 Methane bulk and clumped isotopes

The bulk isotope compositions of CH₄ are expressed as:

δ¹³C_VPDB = [(¹³C/¹²C)_sample/(¹³C/¹²C)_VPDB − 1] × 1000 (1)

δD_SMOW = [(D/H)_sample/(D/H)_VSMOW − 1] × 1000 (2)

The clumped isotope compositions of CH₄ are expressed below:

Δ¹³CH₃D = [(¹³CH₃D/¹²CH₄)_sample/(¹³CH₃D/¹²CH₄)_stochastic − 1] × 1000 (3)

Δ¹²CH₂D₂ = [(¹²CH₂D₂/¹²CH₄)_sample/(¹²CH₂D₂/¹²CH₄)_stochastic − 1] × 1000 (4)

To establish a temperature scale for our laboratory, the in-house standard was ascribed a Δ value of zero, and measurements are performed within the ‘working gas reference frame’. Then, by independent calibration of the internal standard gain from the heated equilibrium experiments, the measured results for samples are converted to an ‘absolute thermodynamic reference frame’ (details of the calculation process in ESI Text S1†).

(¹³CH₃D/¹²CH₄)_stochastic = 4 × (¹³C/¹²C)_sample × (D/H)_sample (5)

(¹²CH₂D₂/¹²CH₄)_stochastic = 6 × (D/H)_sample × (D/H)_sample (6)

2.3 Methane clumped isotope thermometer

Methane clumped isotope signatures (Δ¹²CH₂D₂ and Δ¹³CH₃D) are reliable independent intramolecular thermometers at thermodynamic equilibrium, based on the following thermodynamic equilibrium equations for methane isotopic exchange reactions:

¹³CH₄ + ¹²CH₃D ⇋ ¹²CH₄ + ¹³CH₃D (7)

2 ¹²CH₃D ⇋ ¹²CH₄ + ¹²CH₂D₂ (8)

The equilibrium constants K_¹³CH3D and K_¹²CH2D2 of reactions (7) and (8) are directly related to temperature (T). The relationship between T and Δ¹²CH₂D₂ and Δ¹³CH₃D can be theoretically calculated using previous studies adopting two distinct approaches. Young et al. used ab initio calculations¹³ to derive:

K_¹³CH3D = 1 + 0.0355502/T – 433.038/T² + 1270210.0/T³ − 5.9804 × 108/T⁴ + 1.196630 × 10¹¹/T⁵ − 9.07230 × 10¹²/T⁶ (9)

(8/3) K_¹²CH2D2 = 1 + 0.183798/T – 785.483/T² + 1056280.0/T³ + 9.37307 × 10⁷/T⁴ – 8.919480 × 10¹⁰/T⁵ + 9.901730 × 10¹²/T⁶ (10)

Subsequently, comparison of the Bigeleisen and Mayer/Urey (BMU) model and the path integral Monte Carlo (PIMC) model allowed Eldrige et al. to obtain the PIMC theoretical results:²²

2.4 Sample preparation

Instrument internal precisions (±1 s.e.) and external precision (±1 s.d.) were determined using commercially purchased pure methane used as working standard gases. The first (HL) was obtained from Tianjin Haolun Gas Co., Ltd (CH₄ purity 99.999%) and the second (JH) is from Suzhou Jinhong Gas Co., Ltd (CH₄ purity 99.999%). Both in-house methane working standards are stored in high-pressure cylinders (∼2 MPa) and connected directly to the spectrometer's inlet system via a 1/4 inch needle connection.

Samples for heated gas equilibration experiments used a Pyrex tube filled with silica gel (∼2–5 mm granules) and a nickel catalyst (65 wt% nickel dispersed on a silica/alumina support; Sigma Aldrich). The tube was packed with glass wool (Thermo Fisher) and pre-evacuated (<10⁻¹ Pa) in a vacuum line system. ∼300 torr methane cylinder gas was transferred into the Pyrex tube and subsequently flame sealed. Gas samples were heated in a muffle furnace (Yamato) at fixed temperatures (300 °C, 400 °C, and 500 °C) for a fixed period (1.5–90 h). We removed the samples at high temperatures and quenched them to room temperature. Then, the gas sample was collected in a Kimble glass bottle after purification.

Natural gas samples were collected from a natural gas well head in the Gaoshiti-Moxi (Gao-Mo) area, Sichuan Basin, and stored in high-pressure cylinders (∼3 MPa). The Gao-Mo methane samples exceed 95% purity and contain only trace amounts of H₂S, H_2, and other impurities. The lake emitted samples were collected from artificial lakes, Qingnian Lake (39°06′42.1′′N, 117°10′16.7′′E), Youyi Lake (39°06′27.6′′N, 117°10′10.4′′E), and Aiwan Lake (39°06′33.8′′N, 117°10′09.0′′E), on the Tianjin University campus (TJU), Tianjin. Samples were collected by submerged, umbrella-style gas bubble traps from surface water, with a methane purity of 15–30%.

2.5 Methane pretreatment system

Pure methane (purity > 99%) samples at 70–110 mbar were required for the dual-inlet isotopic measurement. A pretreatment system with stainless steel tubing joined with Swagelok valves was used for purification and collection (Fig. 2) using previously described methods.^10,12 Before starting sample processing, the whole system was evacuated to <10⁻¹ Pa. The gas sample was introduced using a gas-tight syringe or a one-quarter-inch needle directly into the vacuum line and then passed into a liquid N₂ trap to remove H₂O, CO₂, and H₂S (Fig. 2). The headspace gases, including CH₄, O₂, and N₂, were transferred into a 20 K liquid-helium cryostat trap (Lanhai Keyi Instrument Co., Ltd, Tianjin, China) for 10 minutes and residual He and H₂ in the headspace were pumped away for about 3 minutes. The cold trap was then heated to 80 K and cooled to 45 K, while pumping the headspace gas until the pressure was <2.67 Pa at 45 K, when the theoretical purity of CH₄ is >99.8%.¹⁰ After completing each sample pretreatment, the liquid-helium cryostat was heated to room temperature and the whole system was required to attain a vacuum level of <10⁻¹ Pa before the next sample pretreatment.

Fig. 2 Cryogenic vacuum line purification and silica-gel collection pretreatment systems. The black lines and blue switches represent stainless steel tubes and Swagelok valves, respectively.

Two methods were utilised for final gas collection. One used a conventional flame-seal tube technique in which a Pyrex break-seal tube containing silica-gel at liquid N₂ temperature was sealed using an oxy-hydrogen welding torch. The second method used a silica-gel-filled high-vacuum high-boron glass bottle (Kimble, America) or a stainless cold finger submerged in liquid N₂, which can directly collect methane gas to avoid flame sealing. Both collection methods required heating for 5 minutes with a heat gun or a 50 °C water bath before introduction to the sample bellows.

All heated gas, natural gas samples, and lake source point samples were measured within a half-day of the pre-treatment process. We note that in the pre-treatment of the source point samples, the purification pumping temperature was set to 50 K and the collection temperature was set to 75 K due to the low methane purity.

3. Results and discussion

3.1 Precision and accuracy

The optimization and commissioning of the spectrometer started in November 2020. δ¹³C and δ¹³CH₃D measurements achieved an internal precision of ±0.01‰ and ±0.36‰ (±1 s.e.), respectively after basic commissioning (Fig. S2†). δD has a higher requirement for the MRP; from December 2020 until April 2021, the HR+ mode of instrument operation reached a MRP of ∼45 000, with internal precision (±1 s.e.) for achieving δD ∼±0.1‰. The detail of δ¹²CH₂D₂ commissioning is shown in Text S2 and Fig. S3.† HR+ mode (high resolution slit with an aperture) has higher MRP but low sensitivity ([¹²CH₂D₂⁺] ∼ 55 cps). HR mode (high resolution slit but without the additional aperture) gave better sensitivity but the lower MRP necessitated a tailing correction procedure. Nonetheless, the tailing correction appears to be successful and facilitates improved analytical precision consistent with the increased sensitivity. Thus, HR mode with a tailing correction procedure was used for δ¹²CH₂D₂ giving an internal precision (±1 s.e.) for δ¹²CH₂D₂ of ∼±1.35‰. This illustrates the play-off between MRP and sensitivity that needs to be optimized to achieve the most precise measurements.

The in-house methane showed the instrument internal precisions (±1 s.e.) in complete 2 days of measurements to be: δD = ±0.08‰, δ¹³C = ±0.01‰, δ¹³CH₃D = ±0.31‰, and δ¹²CH₂D₂ = ±1.44‰ (±1 s.e.) (Table 1). However, this dataset includes the results obtained before the δ¹²CH₂D₂ commissioning was fully optimized and the precision of optimized δ¹²CH₂D₂ measurements is slightly lower, close to ∼±1.35‰ (Tables S1 and S2;† the 21 heated gas samples have a precision mean value of ∼±1.32‰).

Table 1 Summary of the in-house methane standards

Methane type	n	δD(wg) (‰)	1 s.e.	1 s.d.	δ^13C(wg) (‰)	1 s.e.	1 s.d.	Δ^13CH3D(wg) (‰)	1 s.e.	1 s.d.	Δ^12CH2D2(wg) (‰)	1 s.e.	1 s.d.
a All processed pure HL gases, including different types of purification and collection.
HL gas	14	0.0	0.06	0.07	0.06	0.02	0.07	−0.01	0.33	0.35	0.21	1.59	1.20
p-HL gas^a	11	0.68	0.07	0.24	−0.17	0.01	0.40	0.18	0.32	0.40	0.06	1.45	1.34
JH gas	4	−32.52	0.08	0.07	8.06	0.01	0.01	0.08	0.28	0.10	0.08	1.39	0.56

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The external precision (±1 s.d.) represents reproducibility between samples. The external precision for each indicator of “raw” HL gas (n = 14) was δD = ±0.07‰, δ¹³C = ±0.07‰, Δ¹³CH₃D = ±0.35‰, and Δ¹²CH₂D₂ = ±1.20‰. Processed HL gas (n = 11; including 5 variations of collecting and releasing procedures) gave external precisions of: δD = ±0.24‰, δ¹³C = ±0.40‰, Δ¹³CH₃D = ±0.40‰, and Δ¹²CH₂D₂ = ±1.34‰. JH gas, replicated 4 times, gave external precisions of: δD = ±0.07‰, δ¹³C = ±0.01‰, Δ¹³CH₃D = ±0.10‰, and Δ¹²CH₂D₂ = ±0.56‰ (Table 1).

The precision and accuracy results in this study are comparable to those reported at Caltech,¹⁰ UC Berkeley,²² and the Tokyo Institute of Technology¹⁹ using similar instruments. All individual replicate measurements are provided in Table S1† and the comparison results are shown in Table S2.†

3.2 Factors influencing the measurements of clumped methane isotopologues

3.2.1 Temperature & humidity. Ambient temperature and humidity are very important influencing factors for mass spectrometry measurement,^28,29 and their effect may be particularly critical for systems designed to achieve high resolution. During a period when the laboratory air-conditioning system was faulty (temperature change over 5 °C and humidity change over 40% within 6 h), we found a magnetic field offset of ∼0.004 amu within 6 h. This level of instability may be acceptable for bulk isotope measurement, but greater mass stability is required to perform methane clumped isotopologue measurements (details in Text S3, Fig. S4–S6†). We have also noticed in daily operation that the high-resolution mass spectrometer is exceptionally, though not unexpectedly, sensitive to temperature and humidity. Even though the 253 Ultra has some built-in features that are designed for stable operation, these can only work effectively within a controlled laboratory environment, where the specification from the manufacturer is a temperature range of 18–24 °C (fluctuations < ±2 °C h⁻¹) and humidity range of 40–70%. Here, we caution that a relatively stable experimental environment in which temperature fluctuations should be lower than ±1 °C and humidity ±5% within a measurement cycle is critical for optimal operation of the 253 Ultra instrument.

3.2.2 Slit quality. An important component of the spectrometer ion optics is the variable entrance slit width (250, 16, and 5 μm entrance slits for LR MR and HR modes respectively) which determines the ion beam width on the image plane of the mass spectrometer (i.e., detector array) to control the mass resolution.²⁷ The smaller slit rejects most of the ion fragments, which on the one hand leads to a decrease in sensitivity (see above) and on the other hand causes some of the ion fragments to block the slit. For the narrowest slit (HR mode; 5 μm slit) this effect is critical, and the most direct effect is the reduction of the signal size of [¹²CH₂D₂⁺]. Therefore, the quality of the slit needs to be maintained which is readily achieved by monitoring the intensity ratio (i.e., M/H) of [¹²CH₄⁺] from the L4 cup between the MR mode (16 μm slit) and the HR mode (5 μm slit) at the same source pressure. The theoretical value of M/H should be the ratio of medium and high resolution slit widths, i.e., 3.2. In practice, a new slit M/H is typically ∼3.4 whereupon the [¹²CH₂D₂⁺] signal can reach ∼150 cps, and the internal precision value of δ¹²CH₂D₂ is about ±1.25‰ (±1 s.e.) (Table 2). For the slit after a period of time, M/H can reach ∼7.9, when the [¹²CH₂D₂⁺] signal is only 60–70 cps, and the internal precision falls to about ±1.86‰ (Table 2). The long-term results show that as the M/H ratio increases, the δ¹²CH₂D₂ precision worsens, although this relationship is not linear (Fig. S7†). Thus, the slit quality should be regularly monitored and the slit should be replaced after a few months of measurements, to facilitate optimal measurements, especially for δ¹²CH₂D₂. We recommend that the acceptable working range of M/H should be between 3.2 and 6.

Table 2 Relationship of δ¹²CH₂D₂ analysis and slit quality

Data	M/H ratio^a	[^12CH2D2^+] intensity^b (cps)	1 s.e.^c (‰)	1 s.d.^d (‰)
a Estimated from the intensity ratio of [^12CH4^+] recorded by L4 in MR mode and HR mode. b Initial gas volume is 100–110 mbar and the ion source pressure is below 2 × 10^−7 mbar (cps = counts per second). c Represents the internal precision (±1 s.e.) of δ^12CH2D2 in 8 cycles × 30 blocks. d Represents the external precision (±1 s.d.) of Δ^12CH2D2 from 2022/2/22–2022/3/1 and 2022/4/13–2022/5/15. e The results were measured immediately after the slit was changed on 2022/4/21.
2022/2/25	4.5	110	1.44	1.04
2022/4/10	6.7	80–90	1.53	0.56
2022/4/19	7.9	60–70	1.86
2022/4/26^e	3.4	140–150	1.25

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3.2.3 Fragmentation rate (F). The spectrometer used in this study has an extended electron impact energy range of 25–150 eV, which reduces fragmentation of molecular ions,²⁷ but may induce artefacts that require investigation. Mass-16 includes [¹³CH₃⁺] and [¹²CH₂D⁺] (about 1% of the mass-16 signal), and when the F value is assumed as the rate of H and D removal during ionization and is the same for all isotopologues (¹²CH₄, ¹²CH₃D, and ¹³CH₄), [¹²CH₂D⁺] and [¹³CH₃⁺] fragments can be corrected accordingly, whereupon iteration of mass-17/16 and mass-18/16 is possible.¹² In this study, the F value was measured after a complete measurement using a 2 cycles × 3 blocks (with the integration time the same as that of sample measurement, 67.12 s for 1 cycle; this is an additional procedure to the sample measurement and, unlike the sample measurement procedure shown in Fig. S1,† is generally carried out during the instrument commissioning or routine testing) procedure maintaining the same source pressure as that in the previous measurement:^12,22

F = [¹²CH₃⁺]/[¹²CH₄⁺] = [¹³CH₃⁺]/[¹³CH₄⁺] (15)

In this study, the measured F value is ∼0.78 and range of six-month measurements’ external accuracy (±1 s.d.) was about ±0.03.

The introduction of the F value would change the calculation process to some extent and affect the results of δ¹³C_VPDB, δD_SMOW, Δ¹³CH₃D, and Δ¹²CH₂D₂ values (see details in Text S1†). The F values of this mass spectrometer are mostly in the range of 0.7 to 0.8 and comparable with those of previous studies using similar instruments.^12,22 To explore the effect of F on clumped isotope (Δ¹³CH₃D and Δ¹²CH₂D₂) calculations, we performed simulations of F values from 0 to 1 in increments of 0.01 (i.e., different F values were assigned during the calculations of the samples). The results of two sets of cylinder gases (HL and JH), a sample gas (GS8), and a mixed gas (MG) were considered. During this process, the other measurement factors and the calculation process remain unchanged. In the working gas reference frame, the HL, JH, and GS8 results show almost no change (<0.01‰), and the results of the MG Δ¹³CH₃D_(wg) changed by ∼0.04‰, and Δ¹²CH₂D_2(wg) changed ∼0.18‰ (Fig. S8†).

Compared with the internal precision (±1 s.e.) of Δ¹³CH₃D (±0.35‰) and Δ¹²CH₂D₂ (±1.35‰) measurements, this change is negligible and the process can be incorporated into the entire measurement and used as validation of the calculations and instrument performance stability.

3.2.4 Bellows effect: gas capillary leak. IRMS dual-inlet systems allow rapid matching between samples and standards, resulting in better accuracy by matching instrument conditions. Gas-leakage experiments reported by Yan et al. demonstrated pressure-dependent fractionation of the capillary due to one-side of the bellows leaking in an industry standard IRMS (MAT 253 Plus).³⁰ Theoretical calculations showed that even at pressures of tens of millibars, capillary leakage still falls within the range of the transitional flow regime.³¹ For measurements with the 253 Ultra with similar dual-inlet mode and capillary leakage (Fig. S9†), a large amount of sample gas is consumed for each sample measurement, and bellows can be compressed at a rate of 50% to 80%. Thus the effects of pressure-dependent fractionation that might be negligible in conventional stable isotope analysis could be significant in measurement of rare isotopologues and, therefore, need to be understood.

JH gas (sample, in the left bellows) and HL gas (reference, in the right bellows) were used to make a bellows effect comparison. We adjusted the initial gas volume (mbar) and compression (%) of the bellows, and ten blocks of measurements were performed to verify the possible effect of the bellows leaking process on the δD results (details of the gas leakage experiments are shown in Text S4†). The results show that measured δD_(wg) values do not correlate with the initial gas volume, compression ratio, or measured gas volume (Table S4†). All the results (including measurement on 2022/4/24 without compression) had an external precision (±1 s.d.) of ∼±0.08‰, which is acceptable, both for the subsequent calculation procedure involving δD and the internal precision (±1 s.e. ∼ ±0.1‰). This study showed that any pressure-dependent isotope fractionation during gas leakage can be effectively canceled by the Ultra 253 dual inlet. To avoid possible fractionation, it is recommended that the sample be released quickly and have a relatively high initial pressure (>100 mbar),³⁰ and that a uniform isotopic distribution of the gas be established prior to measurement by repeated compression and relaxation of the bellows.¹²

3.3 Pretreatment process: purity and fractionation

We have refined pretreatment procedures for methane clumped isotope analysis in two significant respects. (1) To analyze samples in the surface environment, we combined aspects of two previous pretreatment protocols^12,13 and used a new cryogenic purification and silica gel collection method (Fig. 2); (2) in previous studies purification and collection steps were performed at 45 K and 70 K, respectively.^10,12,32 Our method increased purification and collection temperatures by 5 K. In our method a large amount of headspace gas (N₂ and O₂) was pumped away at 50 K, leaving a level of sample purity (headspace pressure < 2.67 Pa and purity > 99.8%) achieved at 45 K in previous studies. The collection temperature of 75 K (compared to 70 K in previous studies) similarly does not appear to induce deleterious effects and facilitated the collection of copious quantities of gas from the cryostat quickly.

Methane clumped isotopes measurements require 3 ml pure (∼99%) sample,¹⁴ so removing impurity gases is the first step for pretreatment. It was verified that pumping at 45 K or 50 K and collecting at 70 K or 75 K does not change the purity of the final collected gas. The natural gas sample from Sichuan basin (GS8, initial methane content of ∼90%) and lake source point sample from Aiwan Lake (initial methane content of ∼15%) were measured after purification, collection, and release procedures. To determine the purity of the methane sample, we used three constraints: (i) the purity of methane samples in the pre-treatment process is generally considered to be greater than 99.8% at 45 K with a headspace pressure of <2.67 Pa.^10,12,32 In our sample pre-treatment process this pressure is usually <1 Pa; (ii) the intensity of mass-28 was compared to the intensity of mass-16 to indicate the air content.²⁷ After the samples were introduced into the 253 Ultra, a mass scan was carried out first, which verified an air (mass-28 content) content lower than ∼0.2% (Fig. S10†); (iii) the signal values of mass-16 of the purified samples and HL cylinder gases (CH₄ purity 99.999%) under the same pressure were compared; the ratios were >0.998, and finally the verified purity of the purified samples was obtained. These constraints mean that the methane purity was ∼99.8% and met the measurement requirements.

Clearly it is necessary to demonstrate that the pretreatment process is not responsible for artefactual isotopic fractionation. Overall, the cryogenic purification and silica gel collection method may have produced a slight shift in δD and δ¹³C, but this was negligible for both the conventional isotope analysis,¹⁹ and Δ¹³CH₃D (mean ± s.d. = +0.16 ± 0.32‰) and Δ¹²CH₂D₂ (mean ± s.d. = +0.14 ± 1.12‰) and did not vary significantly for pre-treated in-house methane samples (n = 16; Table S3†). A comparison of Fig. 3a and b shows that the presence or absence of the purification process had no significant effect on the isotope results. The results of the direct collection method show higher precision, and the flame-sealed collection method appeared to show an increased uncertainty (Fig. 3) that has not been reported in previous studies.^12,22 The additional uncertainty is thought to be operator-induced variability in the flame-sealing process. We suggest that the conventional flame-seal method is necessary for samples that require long-term storage which ensures the reliability of the sample preservation. However, direct collection is preferable if the samples can be measured promptly. After changing the purification and collection temperatures to 50 K & 75 K respectively, there is almost no significant difference in fractionation compared to fractionation at 45 K & 70 K (Fig. 3) supporting the contention that isotopic fractionation resulting from changes in the pre-treatment strategy is negligible.

Fig. 3 Clumped isotope fractionation for the pretreatment process. (a) Without purification, only the collection procedure, separated by the dotted line into two types: direct collection and flame-seal collection. (b) With purification and collection procedures, separated by the dotted line into three types: purification at 40 K and direct collection at 70 K, purification at 45 K and direct collection at 75 K, and purification at 40 K and flame-seal collection at 75 K. All of these categories are intended to validate the fractionation of improved pre-treatment. 40 K and 45 K represent the liquid-helium cryostat trap temperature during purification and 70 K and 75 K represent the liquid-helium cryostat trap temperature during sample collection. These two sets of temperatures (40 K purification – 70 K collection and 45 K purification – 75 K collection) were used for pre-treatment processes with high and low methane content samples respectively. The validation here is to explore the isotopic fractionation at different temperature intervals. The solid circles represent the mean values of the Δ¹³CH₃D and Δ¹²CH₂D₂ fractionation results, the error bars represent the external precision (±1 s.d.) obtained from repeated experiments, the blue shading represents the acceptable error range (±0.35‰) for Δ¹³CH₃D_(wg), and the orange shading represents the acceptable error range (±1.35‰) for Δ¹²CH₂D_2(wg).

3.4 Temperature scale calibration

Two independent theoretical predictions exist to describe the temperature dependence of isotopically equilibrated methane doubly substituted isotopologue abundances based upon ab initio and PIMC calculations respectively,^13,22 but they largely predict concordant relationships (Fig. 4). In the range of 0–1000 °C, the two sets of predictions are highly correlated (correlation analysis: P value (2 tailed) <0.001) and not significantly different (ANOVA: P value (2 tailed) ∼0.96) (Table S5†). In this study, all results were calculated using the ab initio model prediction.

Fig. 4 Experimental and theoretical values of equilibrium CH₄ clumped isotopologues as a function of temperature: (a). Δ¹³CH₃D values versus T (°C) and (b). Δ¹²CH₂D₂ values versus T (°C). Error bars for experimental data points here represent the internal precision (±1 s.e.) of replicates (i.e., experimental reproducibility). Data of CH₄ double substituted isotopologues heating experiments result from previous studies.^13,19,22

The results after heating both JH and HL gases at different temperatures (500 °C, 400 °C, and 300 °C; the reasons for selecting the three temperatures are shown in Text S5†) are summarized in Table 3 (see Fig. 4 and Table S6† for the individual results). The internal precision (±1 s.e.) for all heated gas samples was Δ¹³CH₃D ∼ ±0.35‰ and Δ¹²CH₂D₂ ∼ ±1.35‰. The external precision (±1 s.d.) for the samples at 500 °C (n = 11; heating durations from 1.5–24 h) was Δ¹³CH₃D = ±0.39‰ and Δ¹²CH₂D₂ = ±1.35‰. The external precision (±1 s.d.) of the sample heated at 400 °C (n = 4; heating durations from 5–20 h) was Δ¹³CH₃D = ±0.34‰ and Δ¹²CH₂D₂ = ±1.30‰. The external precision (±1 s.d.) of the samples heated at 300 °C (n = 4; heating durations from 40–90 h) was Δ¹³CH₃D = ±0.08‰ and Δ¹²CH₂D₂ = ±0.35‰. To establish a temperature scale, the results are indistinguishable at the same heating temperature, indicating that intramolecular equilibrium is comparable with the previous temperature scale data^13,19,22 (Fig. 4; a detailed discussion of the validation of isotopologues reaching intramolecular equilibrium after heating is given in Text S5, Table S7†).

Table 3 Summary of the heated gas experiment results

Heated temperature^a	Duration^b (h)	Δ^13CH3D(wg) (‰)	1 s.e.	1 s.d.	Δ^12CH2D2(wg) (‰)	1 s.e.	1 s.d.	n
a The 500 °C, 400 °C, and 300 °C represent the samples heated temperature of equilibrated gas experiments. b The duration time represents the heated gas experiment duration (hours) at a certain temperature.
500 °C	1.5–24	−1.34	0.33	0.39	−2.15	1.35	1.35	11
400 °C	5–20	−1.14	0.30	0.34	−1.31	1.23	1.30	4
300 °C	40–90	−0.62	0.30	0.08	−0.30	1.21	0.35	4

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The measured results (mean ± s.d.) were fitted linearly with the ab initio theoretical results at 500 °C, 400 °C, and 300 °C (Fig. S11†). A linear trend with a slope of 1 and an intercept of Δ¹³CH₃D ∼ −2.27 ± 0.019 (1σ; R² ∼ 0.98) and Δ¹²CH₂D₂ ∼ −3.51 ± 0.06 (1σ; R² ∼ 0.97) implied a ‘true’ Δ¹³CH₃D value of +2.27‰ and a Δ¹²CH₂D₂ value of +3.51‰ for the reference gas (HL working gas) in the SESS laboratory, relative to the random isotope distribution. A weighted least-squares regression of the data results in slopes for Δ¹³CH₃D ∼ 0.89 ± 0.08 (1σ; R² ∼ 0.99) and Δ¹²CH₂D₂ ∼ 0.86 ± 0.07 (1σ; R² ∼ 0.99), which are comparable with the previous temperature scaling results,^12,19 and at a 95% confidence interval are indistinguishable from the results for slope = 1. Theoretical calculations provide a reference frame that, when combined with the obtained results of heating gas to equilibrium at different temperatures, can help correct the CH₄ clumped isotope compositions (Δ¹³CH₃D and Δ¹²CH₂D₂) for the working gas in the ‘absolute thermodynamic reference frame’. Using the ‘true values’ of the working gas, the measured samples can be converted to the absolute reference frame (see Text S1† for details of the calculations). The accuracy of our temperature calibration results was tested by inter-laboratory comparisons of the same samples (STD-A and STD-C). Our results were comparable to those of TIT,¹⁹ further validating the accuracy of the entire method including the temperature scale results.

3.5 Natural environmental samples

The bulk and clumped isotope signatures of the laboratory in-house methanes (HL and JH), the heated equilibrium gas, and the two sets of natural samples (natural gases and lake emission gases) are shown in Fig. 4. HL and JH have different bulk isotope compositions of δ¹³C_VPDB = −45.16‰ and δD_SMOW = −162.81‰, and δ¹³C_VPDB = −37.41‰ and δD_SMOW = −190.04‰, respectively, but similar clumped isotope compositions of Δ¹³CH₃D = +2.27‰ and Δ¹²CH₂D₂ = +3.51‰ and Δ¹³CH₃D = +2.35‰ and Δ¹²CH₂D₂ = +3.59‰ (Table S1;† corrected by temperature scale), respectively. The industrial production processes of the two in-house methanes were close, and the clumped isotope signatures indicated that they formed at temperatures of ∼200–250 °C. The results of heated gas at 300 °C, 400 °C, and 500 °C are shown in Table 4. The process of heating methane using 65 wt% nickel dispersed on a silica/alumina support catalyst is essentially C–H bond activation and hydrogen isotope exchange.²² The high temperature and the presence of a catalyst can drive methane to intra-species equilibrium.¹³ As shown in Fig. 5, this process can be regarded as a re-equilibrium process that produced equilibrated clumped isotope signatures at a specific temperature.

Table 4 Results of natural environmental samples

Sample	δDVSMOW (‰)	1 s.e. (‰)	δ^13CVPDB (‰)	1 s.e. (‰)	Δ^13CH3D (‰)	1 s.e. (‰)	T-Δ^13CH3D^a (°C)	Δ^12CH2D2 (‰)	1 s.e. (‰)	T-Δ^12CH2D2^a (°C)
a Estimated temperatures were derived from Δ^13CH3D and Δ^12CH2D2 using the ab initio model prediction.
GS8-D4-DOWN	−143.45	0.12	−34.10	0.01	1.68	0.37	296.8	3.59	1.42	281.4
GS8-D4-UP	−138.76	0.07	−34.08	0.01	1.91	0.27	264.3	6.06	1.26	193.6
GS11-D2	−138.37	0.06	−29.54	0.01	2.01	0.28	252.5	4.45	1.30	244.5
MX17-D2	−143.67	0.07	−33.83	0.01	2.79	0.29	174.4	5.00	1.31	224.9
MX8-LWM	−132.00	0.10	−33.96	0.01	2.77	0.30	176.4	6.57	1.43	180.9
MX18-LWM	−131.22	0.09	−33.88	0.01	1.87	0.25	269.0	3.54	1.24	284.2
Qingnian lake	−349.70	0.06	−60.51	0.01	0.02	0.22	—	−33.33	0.94	—
Youyi lake	−303.96	0.06	−66.96	0.01	0.11	0.28		−24.60	1.01
Aiwan lake	−342.41	0.06	−67.81	0.01	−0.27	0.27		−35.69	0.92

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Fig. 5 Clumped isotope results of methane for natural gas (GS- and MX-), lake gas (Youyi, Aiwan, and Qingnian Lake), and heated gas (mean values of 500 °C, 400 °C and 300 °C) plotted as the Δ¹³CH₃D versus Δ¹²CH₂D₂ plot. Hydrogenotrophic and methylotrophic methanogenesis culturing experiment data from previous studies.^13,24,40

The Gao-Mo area is the main natural gas-producing area in the Sichuan Basin of southwestern China, having the Sinian Dengying Formation and the Cambrian Longwangmiao Formation (LWM) as important gas reservoirs.³³ The results show that δD_VSMOW of Dengying Fm (D2 and D4) was lighter relative to that of LWM Fm (Table 4). This might be related to the difference in aqueous medium conditions in the depositional environment.^34,35 Previous thermochemical sulfate reduction (TSR) studies in the Gao-Mo area suggest that the CH₄ bulk isotopes might be due to different degrees of TSR.³⁶ However, Δ¹³CH₃D and Δ¹²CH₂D₂ signatures fitted well with the equilibrium curve and do not show a distribution that varies with bulk isotope composition (Fig. 5). The paired clumped isotope results showed that GS8-D4-UP was located on the upper side of the equilibrium line, suggesting gas diffusion from the lower to upper formation when compared with the GS8-D4-DOWN results; MX17-D2 was located on the lower side of the equilibrium line, which might be influenced by exotic organisms or post-generation processes. However, overall, methane clumped isotopes indicate that formation (or re-equilibration) temperature of natural gas in the Gao-Mo area ranged from 174.6 to 296.3 °C (T-Δ¹³CH₃D = 174.6–296.3 °C and T-Δ¹²CH₂D₂ = 180.9–284.1 °C). The highest temperature experienced by the Sinian formations exceeded 240 °C (R_o ∼ 3.5‰).³⁷ Bulk isotope reversal of methane and ethane suggested that the natural gas in the study area originated from high-over maturity shale and is a mixture of two thermogenic gases.³⁴ Generally, the kinetic process controlled the thermogenic gases' bulk isotope compositions,³⁸ and the clumped isotope compositions reflect ¹³C–D and D–D clumping in the methyl precursor at the cracking temperature.³⁹ The methane-clumped isotope thermometer gives additional reliable temperature information at equilibrium. Combining the results of the methane bulk and clumped isotopes places new additional constraints on the formation and evolution of the thermogenic gas.

The results of doubly substituted isotopologues of methane released from natural water environments have not been extensively reported in previous studies. The samples released from the artificial lakes (Qingnian Lake, Youyi Lake, and Aiwan Lake in TJU) had δ¹³C_VPDB values from −60.51‰ to −67.81‰ and δD_SMOW values from −303.69‰ to −349.70‰. The bulk isotopes were consistent with the isotopic source signatures of microbial methyl-type fermentation on ‘Whiticar plots’.⁶ The lake samples’ clumped isotope results (Δ¹³CH₃D from −0.27‰ to +0.11‰ and Δ¹²CH₂D₂ from −24.60‰ to −35.69‰) showed a clear disequilibrium characteristic (Fig. 5). The results of the Youyi Lake sample lie between previously reported hydrogenotrophic and methylotrophic methanogenic culturing experimental results.^13,24,40 Qingnian and Aiwan Lake were closer to the methylotrophic methanogenic pathway and the results of their samples are similar to the results reported by Young et al. using Methanosarcina barkeri incubated at 30 °C (Δ¹³CH₃D = −1.11‰ and Δ¹²CH₂D₂ = −34.33‰).¹³ However, as the paired clumped isotope results for acetoclastic methanogenesis were not reported, only the Δ¹³CH₃D (from −1.70‰ to −3.10‰) can be compared.⁴¹ The data from the culture experiments need to be further refined, but the methane production pathway can be characterized by using clumped isotopes. In combination with other environmental parameters, the results can be used as a proxy to explore kinetic processes in methane release,²⁴e.g., biogeochemical processes and their connection with sediment components.²⁵

4. Conclusions

We present a new measurement protocol for methane clumped isotopes and bulk isotopes, with an MRP of 45 000–50 000. The following conclusions can be reached:

(1) The high-resolution mass spectrometer could separate adjacent methane peaks and achieved internal precision of δ¹³C = ±0.01‰, δD = ±0.08‰, δ¹³CH₃D = ±0.35‰, and δ¹²CH₂D₂ = ±1.35‰ (±1 s.e.). The external precision of the samples was δ¹³C = ±0.01‰, δD = ±0.10‰, Δ¹³CH₃D = ±0.35‰, and Δ¹²CH₂D₂ = ±1.35‰ (±1 s.d.).

(2) It is recommended to maintain relatively constant ambient laboratory temperature (±1 °C) and humidity (±5%) for the spectrometer. It was found that slit quality directly influenced signal intensity and further determined the stability of measurement, and a relatively minor impact on the clumped isotope results (Δ¹³CH₃D and Δ¹²CH₂D₂) was associated with the fragmentation rate. In addition, a gas leakage experiment showed that in the dual-inlet system, any bellows effect, previously observed in low resolution IRMS measurements, has a negligible impact on the measurement results.

(3) Cryogenic purification at 50 K and silica gel collection at 75 K remove impurity gases from low methane concentration samples, resulting in a methane purity of ∼99.8%, and both flame-sealed and direct collection are acceptable. The system does not produce isotopic fractionation during either purification collection or release, and no additional correction of the results is necessary.

(4) The heated equilibrium gas experiments at 500 °C, 400 °C and 300 °C provide a reliable temperature scale for correcting the relative equilibrium ¹³CH₃D and ¹²CH₂D₂ abundances of the working gas to convert the dataset to an absolute reference frame. The results from industrial tank gas (in-house methane), heated re-equilibrium gas, natural gas, and lake emission samples showed 150–500 °C equilibrium and microbially dominated disequilibrium clumped isotope signatures, which support the measurement possibilities for broad environmental samples. This study demonstrated an improved efficient purification, collection, and clumped isotope analysis method for natural methane with a wide range of concentrations.

Author contributions

Xinchu Wang: methodology, investigation, data curation, writing – original draft, review and editing. Cong-Qiang Liu: funding acquisition, supervision, project administration, and writing – review and editing. Naizhong Zhang: methodology, validation. Sheng Xu: supervision, writing – review and editing. Zhiyong Pang: methodology, visualization. Si-Liang Li: supervision, writing – review and editing. Hu Ding: supervision, conceptualization, resources. Jianfa Chen: supervision, validation Zengye Xie: validation. Rob M. Ellam: methodology, writing – review and editing.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This research was funded by the National Natural Science Foundation of China [grant number 41925002, 41971123, and 42150710532]; the National Science & Technology Fundamental Resources Investigation Program of China (Grant No. 2021FY101000); Tianjin Municipal Science and Technology Bureau [20ZLGCGX00030]; National Key R&D Program of China (Grant No. 2018YFC1800306). We thank Zhifeng Yan and Xueqi Niu for sampling. We also thank Hao Xie and Li Lu for the use of the instrument.

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Footnote

† Electronic supplementary information (ESI) available: Datasets include all measurement results; process of δ and Δ value calculations; experimental details; measurement flowcharts, schematic data results; additional figures and tables (PDF). See DOI: https://doi.org/10.1039/d2ja00315e

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