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

Abstract At equilibrium, the D/H isotope fractionation factor between H 2 and H 2 O (α H2O-H2(eq) ) is a sensitive indicator of temperature, and has been used as a geothermometer for natural springs and gas discharges. However, δD H2 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 H 2 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; ln k = 9.186 - 6298 / T and k 1 = 9764.61 [ H 2 O ] e - 6298 / T where T is absolute temperature (K), k is the universal rate constant ([L/mol]/hr), and k 1 is a pseudo-first-order constant (hr −1 ) applicable to water-dominated terrestrial systems by constraining [H 2 O] as the density of H 2 O (in mol/L) at the P - T of interest. The density-dependent rate constant accounts for the kinetic disparity of D–H exchange with H 2 when dissolved in liquid H 2 O relative to a gas/steam phase, exemplifed by 1/ k 1 at 100 °C of ∼2 days in liquid, versus ∼7 yrs in saturated steam. This difference may explain the high variability of δD H2 observed in fumarolic gases. Fluids convecting in the crust frequently reach T  > 225 °C, where isotopic equilibrium is rapidly attained ( OBS ) 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 δD H2 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 H 2 measured in both continental alkaline springs and fracture fluids from Precambrian shield rock is likely produced at T H2 values appear closer to equilibrium with H 2 O than those from geothermal systems. Considering kinetic isotope effects may yield H 2 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 δD H2 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 H 2 destruction or loss via diffusion may also be possible.