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Space-time upscaling of reactive transport in porous media

Nicolae SuciuFlorin A. Radu
摘要
Reactive transport in saturated/unsaturated porous media is numericallyupscaled to the space-time scale of a hypothetical measurement through coarsegrained space-time (CGST) averages. The one-dimensional reactive transport ismodeled at the fine-grained Darcy scale by the actual number of moleculesinvolved in reactions which undergo advective and diffusive movements describedby global random walk (GRW) simulations. The CGST averages verify identitiessimilar to a local scale balance equation which allow us to derive expressionsfor the flow velocity and the intrinsic diffusion coefficient in terms ofaveraged microscopic quantities. The latter are further used to verify theCGST-GRW numerical approach. The upscaling approach is applied tobiodegradation processes in saturated aquifers and variably saturated soils andthe CGST averages are compared to classical volume averages. One finds that ifthe process is characterized by slow variations in time, as in homogeneoussystems or in case of observations of reactive transport in heterogeneousaquifers made at large times or far away from the contaminant source, thedifferences between the two averages are negligible. Instead, the differencesare significant if the averages are computed close to the source at earlytimes, in case of aquifer simulations, and can be extremely large insimulations of biodegradation in soils. In the latter case, the volume averageis totaly inappropriate as model for experimental measurements, leading, forinstance to overestimations by 100% of the CGST average.
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