Theoretical and experimental constraints on hydrogen isotope equilibrium in C1-C5 alkanes

Stable isotope ratios of C₁–C₅ alkanes, the major constituents of subsurface gaseous hydrocarbons, can provide valuable insights on their origins, transport, and fates. Equilibrium isotope effects are fundamental to interpreting stable isotope signatures, as recognition of them in natural materials indicates reversible processes and constrains the temperatures of equilibrated systems. Hydrogen isotope equilibrium of C₁–C₅ alkanes is of particular interest because evidence shows that alkyl H can undergo isotopic exchange with coexisting compounds under subsurface conditions. We present the results of a combined experimental and theoretical effort to determine equilibrium hydrogen isotope distributions in mixtures of these hydrocarbon compounds. We created two mixtures: one with C₁, C₂ and C₃ (where C1 indicates methane, C₂ ethane, etc., hereinafter called ‘C₁–C₃ mixture’) and another one with C₂, C₃, iC₄, nC₄, iC₅ and nC₅ (hereinafter called ‘C₂–C₅ mixture’); in both cases, the mixtures were created to start out of hydrogen isotope equilibrium prior to any subsequent experimental treatments. We tested the performance of several metal catalysts as aids to H isotopic exchange by exposing these mixtures to different metal catalysts at 100 or 200 ˚C and analyzing the compound-specific hydrogen isotope ratios of the product gases. The C₁–C₃ mixture exchanged hydrogen isotopes among the starting gas components rapidly in the presence of Ru/Al₂O₃ at 200 °C. The isotope ratios reach a steady-state (presumably equilibrium) after 72 h of heating (up to 120 h). The hydrogen isotopic ratios of alkanes in the C₂–C₅ mixture shifted significantly in the presence of Rh/Al₂O₃ at 100 °C and C₃-C₅ compounds approached steady state after 70 h, whereas C₂ had not yet reached a steady state D/H ratio after 216 h of heating. We evaluated the reaction progress of isotope exchange for each compound as a function of time with a reaction-network model informed by constraints on chemical kinetics. The model indicates that C₃, iC₄, nC₄, iC₅ and nC₅ in the C₂-C₅ mixture reached internal isotope equilibrium after 70 h, hence we used their values to calculate experimental equilibrium results. We also calculated equilibrium isotope fractionations with the Bigeleisen-Mayer theorem using vibrational frequencies computed from the density functional theory (B3LYP/aug-cc-pVTZ). We included torsional conformers and explicit H positions in the calculations. We found that the experimental results from both the 200 ˚C C₁–C₃ experiment and 100 ˚C C₂–C₅ experiment are consistent with theoretical equilibrium results within experimental uncertainty. Additionally, our reaction-network model for catalyzed hydrogen isotope exchange between alkanes succeeded in fitting our experimental results. This modeling framework can be adjusted to simulate exchange in natural settings for constraining temperature histories and sources of natural gases.