Numerical simulation of isotope fractionation in steady-state bioreactive transport controlled by transverse mixing

Compound-specific stable isotope analysis (CSIA) has increasingly been used as a tool to assess intrinsic biodegradation at contaminated field sites. Typically, the Rayleigh equation is used to estimate the extent of biodegradation from measured isotope ratios of the contaminant. However, if the rate-limiting step in overall degradation is not the microbial reaction itself, the Rayleigh equation may no more be applicable. In this study we simulate biodegradation of continuously emitted petroleum hydrocarbons in groundwater systems. These contaminants are effectively degraded at the plume fringe where transverse dispersion makes them mix with dissolved electron acceptors present in the ambient groundwater. We simulate reactive transport to study the coupled effects of transverse mixing and biodegradation on the spatial patterns of carbon isotope signatures and their interpretation based on depth-integrated sampling which represents the most common setup in the assessment of contaminated sites. We present scenarios mimicking a hydraulically uniform laboratory experiment and a field-scale application considering heterogeneous conductivity fields. We compare cases in which isotopologue-specific transverse dispersion is considered to those where this additional fractionation process is neglected. We show that these effects cause significant shifts in the isotopic signals and may lead to overestimation of biodegradation. Moreover, our results provide evidence that the rate-limiting effect of transverse mixing on the overall degradation spatially varies along the length of a steady-state contaminant plume. The control of biodegradation by transverse dispersion and the fractionating effect of dispersion modulate the fractionation caused by the microbial reaction alone. As a consequence, significantly nonlinear isotopic patterns are observed in a Rayleigh plot. Simulations in heterogeneous flow domains show that these effects persist at larger field scales and are sensitive to the degree of mixing enhancement, determined by the heterogeneity of the hydraulic conductivity fields, and to the groundwater flow velocity.