### 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.

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 language | English |
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Article number | 20170178 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 473 |

Issue number | 2207 |

DOIs | |

Publication status | Published - 22 Nov 2017 |

Externally published | Yes |

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## Cite this

Cooper, L. J., Daly, K. R., Hallett, P. D., Naveed, M., Koebernick, N., Bengough, A. G., George, T. S., & Roose, T. (2017). Fluid flow in porous media using image-based modelling to parametrize Richards' equation.

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,*473*(2207), [20170178]. https://doi.org/10.1098/rspa.2017.0178