Calculation of hydrogen isotopic fractionations in biogeochemical systems

Hydrogen-isotopic data are often interpreted using mathematical approximations originally intended for other isotopes. One of the most common, apparent in literature over the last several decades, assumes that delta values of reactants and products are separated by a constant fractionation factor: δp = δr + εp/r. Because of the large fractionations that affect hydrogen isotopes, such approximations can lead to substantial errors. Here we review and develop general equations for isotopic mass balances that include the differential fractionation of each component in a mixture and discuss their use in three geochemical applications. For the fractionation of a single component, the reactant and product are related by δp = αp/rδr + εp/r, where α and ε refer to the same fractionation. Regression of δp on δr should give equivalent fractionations based on the intercept and slope, but this has not generally been recognized in studies of D/H fractionation. In a mixture of two components, each of which is fractionated during mixing, there is no unique solution for the three unknown variables (two fractionation factors and the elemental mixing ratio of the two hydrogen sources). The flow of H from CH4 and H2O to bacterial lipids in the metabolism of Methylococcus capsulatus provides an example of such a case. Data and conclusions from an earlier study of that system (Sessions et al., 2002) are reexamined here. Several constraints on the variables are available based on plausible ranges for fractionation factors. A possible refinement to current experimental procedures is the measurement of three different isotopes, which would allow unique determination of all variables.