ABSTRACT
Isotope fractionation is a promising tool for quantifying methane oxidation in landfill cover soils. For good quantification an accurate determination of the isotope fractionation factor (alpha) of methane oxidation based on independent batch experiments with soil samples from the landfill cover is required. Most studies so far used data analysis methods based on approximations of the Rayleigh model to determine alpha. In this study, the two most common approximations were tested, the simplified Rayleigh approach and the Coleman method. To do this, the original model of Rayleigh was described in measurable variables, methane concentration and isotopic abundances, and fitted to batch oxidation data by means of a weighted non-linear errors-in-variables regression technique. The results of this technique were used as a benchmark to which the results of the two conventional approximations were compared. Three types of batch data were used: simulated data, data obtained from the literature, and data obtained from new batch experiments conducted in our laboratory. The Coleman approximation was shown to be acceptable but not recommended for carbon fractionation (error on alpha-1 up to 5%) and unacceptable for hydrogen fractionation (error up to 20%). The difference between the simplified Rayleigh approach and the exact Rayleigh model is much smaller for both carbon and hydrogen fractionation (error on alpha-1<0.05%). There is also a small difference when errors in both variables (methane concentration and isotope abundance) are accounted for instead of assuming an error-free independent variable. By means of theoretical calculations general criteria, not limited to methane, (13)C, or D, were developed for the validity of the simplified Rayleigh approach when using labelled compounds.