The influence of mixing on stable isotope ratios in porous media: A revised Rayleigh model

Abstract

AbstractFor an irreversible reaction, the Rayleigh or distillation‐type relationship between stable isotope enrichment and reactant concentration is compromised if fluid samples are characterized by a range of water ages or different extents of reaction progress. Such mixed samples are rarely avoided in the standard methods of sampling fluid from natural porous media. As a result, application of a Rayleigh model to stable isotope ratios measured in aquifers commonly requires a diminished or effective fractionation factor relative to the intrinsic value obtained in the absence of transport effects. Thus, quantitative application of intrinsic parameter values to a fractionating reaction occurring in porous media flow requires revision to the functional form of the relationship between reactant concentration and isotope fractionation. Here we derive a series of analytical solutions for the relationship between fractionation and flow subject to nonuniform fluid travel time distributions. These solutions are unique from previous approaches in that they avoid the use of a dispersion coefficient. The results are demonstrated against multicomponent reactive transport simulations of stable isotope fractionation in homogeneous and spatially correlated heterogeneous flow fields, and applied to a data set of stable chromium (Cr) isotope enrichment obtained from a contaminated aquifer. We show that the flux‐weighted isotope ratio of a solute is more sensitive to the effects of physical heterogeneity than solute concentrations. Our results support an updated functional form of the traditional Rayleigh model that describes the relationship between reactant concentration and isotope fractionation and is valid for a mixed‐fluid sample.