Adapted Fick's Law Applied to Soil Respiration

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Abstract
In soil respiration studies the diffusive gas fluxes are often calculated using Fick's law. However, results obtained with Fick's law deviate from those obtained with the theoretically sound Stefan‐Maxwell equations. In the present study a numerical model based on an adapted form of Fick's law is applied to soil respiration. A pressure adjustment flux to maintain isobaric equilibrium in the system is employed to correct errors related to the usage of Fick's law. The results of the above‐mentioned model are compared with those of analytical solutions of Fick's law and the Stefan‐Maxwell equations to check the model's accuracy. The analytical solutions are derived for steady state transport at constant respiration rates in a hypothetical ternary system with N2, O2, and CO2. Calculations are performed at various constant rates of CO2 production and O2 consumption throughout the soil. Differences between the mole fraction gradients calculated with Fick's law and the Stefan‐Maxwell equations are substantial. If Fick's law is combined with the isobaric equilibrium correction procedure, the similarity with the Stefan‐Maxwell equations is much better. The numerical model employing the adapted Fick's law is subsequently tested against field measurements. Field measurements were carried out in large outdoor lysimeters filled with oil‐contaminated soil containing nonvolatile hydrocarbons. Nonsteady gas transport due to dynamic soil respiration during biodegradation of the hydrocarbons in the lysimeters is modeled at known boundary conditions. The result of the model agree with measurements of CO2 fluxes and O2 and CO2 concentration profiles in the lysimeters.