Homogenization of two fluid flow in porous media
Homogenization of two fluid flow in porous media
The macroscopic behavior of air and water in porous media is often approximated using Richards’ equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e., constant gas pressure, this model is shown to reduce to the simpler form of Richards’ equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media to the underlying geometrical and material properties.
porousmedia, richards’ equation, homogenization
1-20
Daly, K. R.
64f85c2e-2562-44df-9cb8-1be7fbc7e74c
Roose, T.
3581ab5b-71e1-4897-8d88-59f13f3bccfe
8 April 2015
Daly, K. R.
64f85c2e-2562-44df-9cb8-1be7fbc7e74c
Roose, T.
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Daly, K. R. and Roose, T.
(2015)
Homogenization of two fluid flow in porous media.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (2176), , [20140907].
(doi:10.1098/rspa.2014.0564).
Abstract
The macroscopic behavior of air and water in porous media is often approximated using Richards’ equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e., constant gas pressure, this model is shown to reduce to the simpler form of Richards’ equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media to the underlying geometrical and material properties.
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PRSA-submitted version.pdf
- Accepted Manuscript
Available under License Other.
More information
Accepted/In Press date: 29 January 2015
e-pub ahead of print date: 25 February 2015
Published date: 8 April 2015
Keywords:
porousmedia, richards’ equation, homogenization
Organisations:
Bioengineering Group
Identifiers
Local EPrints ID: 373487
URI: http://eprints.soton.ac.uk/id/eprint/373487
ISSN: 1364-5021
PURE UUID: 8df7d77e-5b72-4f49-ba04-15c9de123550
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Date deposited: 22 Jan 2015 14:34
Last modified: 15 Mar 2024 03:31
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Author:
K. R. Daly
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