A Model Linking Stable Isotope Fractionation to Water Flux and Transit Times in Heterogeneous Porous Media

Hydrogeochemical processes governing the composition of groundwater are often inferred from water samples that are the flux-weighted average of a heterogeneous system. The stable isotope ratios of these samples are commonly employed to evaluate biogeochemical cycling or the intensity of weathering. However, these data are often interpreted using simplified relationships that assume the chemical composition and fluid residence times are homogeneous. This disparity results in part from the difficulty in obtaining appropriate observations needed to quantitatively link the effects of variable fluid residence time to stable isotope fractionation. Here, we present a synthetic dataset of steady state stable isotope ratios using the aqueous, irreversible reduction of hexavalent chromium (Cr(VI)) and precipitation of chromium hydroxide (Cr(OH)3(s)) in structurally correlated heterogeneous porous media using the CrunchTope reactive transport code. Our results demonstrate that flux-weighted average Cr(VI) values collected across a fixed control plane for multiple heterogeneous permeability fields consistently produce higher reactant concentrations and less enriched stable isotope ratios than a comparable homogeneous domain for average flow rates ranging across several orders of magnitude. This variability is thus directly attributable to the physical heterogeneity of the porous media. Furthermore, the isotopic signature of accumulated Cr(OH)3(s) is highly contingent upon the pH-dependent precipitation rate and the structure of the flow field, resulting in a wide range of bulk isotope ratios. These results provide a first step in the development of new frameworks for linking the effects of subsurface heterogeneity to the observed stable isotope ratios and fractionation factors in a wide variety of systems.