Fluid flow in porous media using image-based modelling to parametrize Richards' equation

L.J. Cooper, K.R. Daly, P.D. Hallett, M. Naveed, N. Koebernick, A.G. Bengough, T.S. George, T. Roose

Research output: Contribution to journalArticle

Abstract

The parameters in Richards’ equation are usually calculated from experimentally measured values of the soil–water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards’ equation from these indirect measurements, image-based modelling is used to investigate the relationship between
the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6μm has been used to create a computational mesh. The Cahn–Hilliard–Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL MULTIPHYSICS. The upscaled parameters in Richards’ equation are then obtained via homogenization. The effect on the soil–water retention curve due to three different contact angles, 0◦, 20◦ and 60◦, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards’ equation.
Original languageEnglish
Article number20170178
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2207
DOIs
Publication statusPublished - 22 Nov 2017
Externally publishedYes

Fingerprint

Richards Equation
Flow in Porous Media
Pore structure
fluid flow
Fluid Flow
Porous materials
Flow of fluids
Contact angle
Modeling
Contact Angle
porosity
Hydraulic conductivity
mesh
Tomography
Hysteresis
Wetting
Mesh
Drying
Hydraulic Conductivity
X-ray Tomography

Cite this

Cooper, L.J. ; Daly, K.R. ; Hallett, P.D. ; Naveed, M. ; Koebernick, N. ; Bengough, A.G. ; George, T.S. ; Roose, T. / Fluid flow in porous media using image-based modelling to parametrize Richards' equation. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2017 ; Vol. 473, No. 2207.
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Fluid flow in porous media using image-based modelling to parametrize Richards' equation. / Cooper, L.J. ; Daly, K.R.; Hallett, P.D. ; Naveed, M.; Koebernick, N. ; Bengough, A.G. ; George, T.S. ; Roose, T.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, No. 2207, 20170178, 22.11.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Fluid flow in porous media using image-based modelling to parametrize Richards' equation

AU - Cooper, L.J.

AU - Daly, K.R.

AU - Hallett, P.D.

AU - Naveed, M.

AU - Koebernick, N.

AU - Bengough, A.G.

AU - George, T.S.

AU - Roose, T.

PY - 2017/11/22

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N2 - The parameters in Richards’ equation are usually calculated from experimentally measured values of the soil–water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards’ equation from these indirect measurements, image-based modelling is used to investigate the relationship betweenthe pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6μm has been used to create a computational mesh. The Cahn–Hilliard–Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL MULTIPHYSICS. The upscaled parameters in Richards’ equation are then obtained via homogenization. The effect on the soil–water retention curve due to three different contact angles, 0◦, 20◦ and 60◦, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards’ equation.

AB - The parameters in Richards’ equation are usually calculated from experimentally measured values of the soil–water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards’ equation from these indirect measurements, image-based modelling is used to investigate the relationship betweenthe pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6μm has been used to create a computational mesh. The Cahn–Hilliard–Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL MULTIPHYSICS. The upscaled parameters in Richards’ equation are then obtained via homogenization. The effect on the soil–water retention curve due to three different contact angles, 0◦, 20◦ and 60◦, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards’ equation.

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