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

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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 6 μm 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
Pages (from-to)1-20
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences
Issue number2207
Early online date22 Nov 2017
Publication statusPublished - Nov 2017

Bibliographical note

Electronic supplementary material is available
online at https://dx.doi.org/10.6084/m9.figshare.c.3925807.

Funding. L.J.C. and N.K. are funded by BBSRC SARISA BB/L025620/1. K.R.D. is funded by ERC 646809DIMR. M.N., P.D.H. and T.S.G. are funded by BBSRC BB/J00868/1 and A.G.B. is funded by BB/L025825/1. The James Hutton Institute receives funding from the Scottish Government. T.R. is funded by BBSRC SARISA BB/L025620/1, EPSRC EP/M020355/1, ERC 646809DIMR, BBSRC SARIC BB/P004180/1 and NERC NE/L00237/1.

Acknowledgements. The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services, in particular Ivan Wolton, at the University of Southampton, and the μ-VIS Centre at the University of Southampton for the provision of necessary software and high-performance computer support in the completion of the work. The authors also acknowledge S. D. Keyes, University of Southampton, for providing the images used for this work. The authors would like to thank Prof. Ian Sinclair and members of the ‘Rooty Team’ at the University of Southampton for helpful discussions related to this work. T.R. would like to acknowledge useful discussions with Prof. David Smith and Floyd Woodrow DCM MBE.


  • Journal Article
  • image-based modelling
  • porous media
  • Richards' equation


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