Effective Pore-Scale Dispersion Upscaling with the Correlated Continuous Time Random Walk Approach

Journal Article · Thu Dec 29 04:00:00 EST 2011 · Water Resources Research

DOI:https://doi.org/10.1029/2011WR010457· OSTI ID:1239512

Le Borgne, Tanguy; Bolster, Diogo; Dentz, Marco; de Anna, Pietro; Tartakovsky, Alexandre M.

We propose a general framework for upscaling dispersion in porous media. A key challenge of the upscaling procedure is to relate the temporal evolution of spreading to the small scale velocity field properties. The representation of the Lagrangian velocity transition process as a Markovian process in space provides a simple way to quantify complex correlation properties, i.e. non-Gaussian velocity distributions. The resulting effective transport model is a correlated CTRW. We use this framework to upscale pore scale dispersion for a periodic pore geometry. The correlated CTRW model is defined by the transit time distribution across one pore and the transition probability density quantifying the correlation between successive transit times. The latter is of central importance since it accounts for incomplete mixing at the pore throats. The predictions of the correlated CTRW model are in good agreement with the pore scale simulations over the pre-asymptotic and asymptotic regimes. We investigate the representation of this effective dispersion model in phase space (position, velocity) in a form similar to a Boltzmann transport equation.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1239512
• Report Number(s): PNNL-SA-78847; KJ0401000
• Journal Information: Water Resources Research, Journal Name: Water Resources Research Journal Issue: 12 Vol. 47; ISSN 0043-1397
• Publisher: American Geophysical Union (AGU)
• Country of Publication: United States
• Language: English

Related Subjects

multiscale modeling
dimension reduction
transport
CTRW