Adjusted Fick's law for gas diffusion in soils contaminated with petroleum hydrocarbons

In bioremediation, hydrocarbon biodegradation rates can be estimated from measured O₂ and CO₂ profiles in situ. Although Fick's law is typically used in calculating the respiration rates, its theoretical base is weak. We propose an adjusted Fick's law with a correction term for the advective flux. We evaluated the applicability of this model to simulate gas diffusion associated with passive degradation of petroleum hydrocarbons in a biopile by comparing the results of this model with the results of Fick's law and the Stefan–Maxwell equations. The deviations from the use of Fick's law depended strongly on the consumption rate of oxygen, the respiration quotient, the mineralization quotient and the volatility of the hydrocarbon. In the whole range of calculated CO₂ concentration versus depth profiles, production rates of CO₂ could be estimated by Fick's law with a maximum deviation of 6%. For the consumption rate of O₂ the maximum deviation is 19%. However, when we used the adjusted Fick's law, the deviations from the results obtained with the Stefan–Maxwell equations were much smaller. The deviations amounted up to only 4%, when the respiration rate r was 1.5 or a hydrocarbon with volatility similar to benzene was present. If the presence of a hydrocarbon was neglected in the calculations, the deviations of the adjusted Fick's law from the results obtained with the Stefan–Maxwell equations were substantial for a hydrocarbon with volatility similar to benzene or toluene.