Kinetics of D/H isotope fractionation between molecular hydrogen and water

At equilibrium, the D/H isotope fractionation factor between H2 and H2O (αH2O-H2(eq)) is a sensitive indicator of temperature, and has been used as a geothermometer for natural springs and gas discharges. However, δDH2 measured in spring waters may underestimate subsurface temperatures of origin due to partial isotopic re-equilibration during ascent and cooling. We present new experimental data on the kinetics of D–H exchange for H2 dissolved in liquid water at temperatures below 100 °C. Comparing these results with published exchange rates obtained from gas phase experiments (100–400 °C), we derive a consistent activation energy of 52 kJ/mol, and the following rate expressions;lnk=9.186-6298/Tandk1=9764.61[H2O]e-6298/Twhere T is absolute temperature (K), k is the universal rate constant ([L/mol]/hr), and k1 is a pseudo-first-order constant (hr−1) applicable to water-dominated terrestrial systems by constraining [H2O] as the density of H2O (in mol/L) at the P-T of interest. The density-dependent rate constant accounts for the kinetic disparity of D–H exchange with H2 when dissolved in liquid H2O relative to a gas/steam phase, exemplifed by 1/k1 at 100 °C of ∼2 days in liquid, versus ∼7 yrs in saturated steam. This difference may explain the high variability of δDH2 observed in fumarolic gases. Fluids convecting in the crust frequently reach T > 225 °C, where isotopic equilibrium is rapidly attained (<1 hr). We compare fractionation factors measured in natural fluids (αOBS) with values expected for equilibrium at the T of acquisition. Where these values differ, we use kinetic models to estimate cooling rates during upward advection that account for the observed disequilibrium. Models fit to fluids from Yellowstone Park and the Lost City (deep-sea) vent field, both recovered at ∼90 °C, require respective transit times of ∼7 hrs and ∼11 days between higher temperature reaction zones and the surface. Using estimates of subsurface depths of origin, however, suggests similar mean fluid flow rates (10 s of meters/hr). Additional complications must be considered when interpreting the δDH2 of lower-temperature effluent. When applied to data from deep-sea hydrothermal systems, our kinetic models indicate microbial catalysis accelerates D–H exchange once fluids cool below ∼60 °C. The H2 measured in both continental alkaline springs and fracture fluids from Precambrian shield rock is likely produced at T < 100 °C, through processes such as serpentinization. In these settings, δDH2 values appear closer to equilibrium with H2O than those from geothermal systems. Considering kinetic isotope effects may yield H2 that is out of equilibrium when generated at lower temperatures, we calculate maximum (isothermal) times to apparent isotopic equilibrium of 1.3 yrs at 50 °C, 9 yrs at 25 °C, and 35 yrs at 10 °C. A similar calculation applied to Antarctic brines (−13 °C), where measured δDH2 is far from equilibrium, yields ∼350 yrs. This time is shorter than the fluids have been isolated (2.8 ka), suggesting kinetic isotope effects associated with H2 destruction or loss via diffusion may also be possible.