Experimental and theoretical determinations of hydrogen isotopic equilibrium in the system CH4–H2–H2O from 3 to 200 °C

The stable isotopic composition of methane (CH4) is commonly used to fingerprint natural gas origins. Over the past 50 years, there have been numerous proposals that both microbial and thermogenic CH4 can form in or later attain hydrogen isotopic equilibrium with water (H2O) and carbon isotopic equilibrium with carbon dioxide (CO2). Evaluation of such proposals requires knowledge of the equilibrium fractionation factors between CH4 and H2O or CO2 at the temperatures where microbial and thermogenic CH4 form in or are found in the environment, which is generally less than 200 °C. Experimental determinations of these fractionation factors are only available above 200 °C, requiring extrapolation of these results beyond the calibrated range or the use of theoretical calculations at lower temperatures. Here, we provide a calibration of the equilibrium hydrogen isotopic fractionation factor for CH4 and hydrogen gas (H2) (DαCH4(g)–H2(g)) based on experiments using γ-Al2O3 and Ni catalysts from 3 to 200 °C. Results were regressed as a 2nd order polynomial of 1000 × lnDαCH4(g)–H2(g) vs. 1/T (K−1) yielding: 1000×lnDαCH4(g)-H2(g)=[Formula presented]+[Formula presented]-179.48 We combine this calibration with previous experimental determinations of hydrogen isotope equilibrium between H2, H2O(g), and H2O(l) and we provide an interpolatable experimental calibration of 1000 × lnDαCH4(g)–H2O(l) from 3 to 200 °C. Our resulting 4th order polynomial is the following equation: 1000×lnDαCH4(g)-H2Ol=-[Formula presented]+[Formula presented]-[Formula presented]+[Formula presented]-382.05 At 3 °C, the value from our calibration differs by 93‰ relative to what would be calculated based on the extrapolation of the only experimental calibration currently available to temperatures below its calibrated range (lowest temperature of 200 °C; Horibe and Craig, 1995). We additionally provide new theoretical estimates of hydrogen isotopic equilibrium between CH4(g), H2(g), and H2O(g) and carbon isotopic equilibrium between CH4(g) and CO2(g) using Path Integral Monte Carlo (PIMC) calculations. Our PIMC calculations for hydrogen isotopic equilibrium between CH4 and H2 agree 1:1 with our experiments. Finally, we compile carbon and hydrogen isotopic measurements of CH4, CO2, and H2O from various environmental systems and compare observed differences between carbon and hydrogen isotopes to those expected based on isotopic equilibrium. We find that isotopic compositions of some microbial gases from marine sedimentary, coalbed, and shale environments are consistent with those expected for CH4–H2O(l) hydrogen and CH4–CO2 carbon isotopic equilibrium. In contrast, microbial terrestrial and pure culture gases are not consistent with both CH4–H2O(l) hydrogen and CH4–CO2 carbon isotopic equilibrium. These results are explained qualitatively using previously developed conceptual models that link free energy gradients available to microorganisms to the degree that their enzymes can promote isotope-exchange reactions between CH4, CO2, and H2O