Dispersive transport and symmetry of the dispersion tensor in porous media
Abstract
The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. Here, we show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Dij satisfies the flow-reversal symmetry Dij(+q)=Dji(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. Particularly, the numerical experimentsmore »
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Energy Geosciences Division
- Univ. of Oslo (Norway). Dept. of Physics
- Hebrew Univ. of Jerusalem (Israel)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1379801
- Alternate Identifier(s):
- OSTI ID: 1351051
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 4; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Pride, Steven R., Vasco, Donald W., Flekkoy, Eirik G., and Holtzman, Ran. Dispersive transport and symmetry of the dispersion tensor in porous media. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.95.043103.
Pride, Steven R., Vasco, Donald W., Flekkoy, Eirik G., & Holtzman, Ran. Dispersive transport and symmetry of the dispersion tensor in porous media. United States. https://doi.org/10.1103/PhysRevE.95.043103
Pride, Steven R., Vasco, Donald W., Flekkoy, Eirik G., and Holtzman, Ran. Mon .
"Dispersive transport and symmetry of the dispersion tensor in porous media". United States. https://doi.org/10.1103/PhysRevE.95.043103. https://www.osti.gov/servlets/purl/1379801.
@article{osti_1379801,
title = {Dispersive transport and symmetry of the dispersion tensor in porous media},
author = {Pride, Steven R. and Vasco, Donald W. and Flekkoy, Eirik G. and Holtzman, Ran},
abstractNote = {The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. Here, we show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Dij satisfies the flow-reversal symmetry Dij(+q)=Dji(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. Particularly, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.},
doi = {10.1103/PhysRevE.95.043103},
journal = {Physical Review E},
number = 4,
volume = 95,
place = {United States},
year = {Mon Apr 10 00:00:00 EDT 2017},
month = {Mon Apr 10 00:00:00 EDT 2017}
}
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Works referencing / citing this record:
Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations
journal, January 2019
- Kjelstrup, Signe; Bedeaux, Dick; Hansen, Alex
- Frontiers in Physics, Vol. 6