Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone

Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion. The equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment. The comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporisation, diffusion and biodegradation. The net effect can lead to an enrichment or depletion of the heavy isotope in the remaining organic phase, depending on the compound and element considered. Finally, the isotope evolution of molecules migrating away from the source and undergoing degradation is governed by a combined degradation and diffusion isotope effect. This suggests that, in the unsaturated zone, the interpretation of biodegradation of VOC based on isotopic data must always be based on a model combining gas phase diffusion and degradation.