Abstract
Reactive transport in saturated/unsaturated porous media is numerically upscaled to the spacetime scale of a hypothetical measurement through coarse grained space-time (CGST) averages. The one-dimensional reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local scale balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous systems or in case of observations of reactive transport in heterogeneous aquifers made at large times or far away from the contaminant source, the differences between the two averages are negligible. Instead, the differences are significant if the averages are computed close to thesource at early times, in case of aquifer simulations, and can be extremely large in simulations of biodegradation in soils. In the latter case, the volume average is totally inappropriate as model for experimental measurements, leading for instance to overestimations by 100% of the CGST average.
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Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space–time scale of a hypothetical measurement through coarse-grained space–time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both variably saturated soils and saturated aquifers.
Authors
Nicolae Suciu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Florin A. Radu
Department of Mathematics, University of Bergen, Allegaten 41, 5007 Bergen, Norway
Iuliu Sorin Pop
Data Science Institute, Hasselt University, Campus Diepenbeek, 3590 Diepenbeek, Belgium
Keywords
Space-time upscaling, Global random walk, Reactive transport, Richards equation MSC: 76S05, 35K57, 86A05, 65C35
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Cite this paper as:
N. Suciu, F.A. Radu, I.S. Pop, Space-time upscaling of reactive transport in porous media, Advances in Water Resources Volume 176, June 2023, 104443, https://doi.org/10.1016/j.advwatres.2023.104443
N. Suciu, F.A. Radu, I.S. Pop, Space-time upscaling of reactive transport in porous media, Arxiv: https://doi.org/10.48550/arXiv.2112.10692
About this paper
Journal
Advances in Water Resources
Publisher Name
Elsevier Ltd.
Print ISSN
0309-1708
Online ISSN
Not available yet.
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