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ORIGINAL RESEARCH

Comparison of a Lattice-Boltzmann Model, a Full-Morphology Model, and a Pore Network Model for Determining Capillary Pressure–Saturation Relationships

^a Institute of Environmental Physics, Univ. of Heidelberg, INF 229, 69120 Heidelberg, Germany
^b Institute for Computer Applications in Civil Engineering, TU Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany
^* Corresponding author (hjvogel{at}iup.uni-heidelberg.de)

Received 5 August 2004.

Effective hydraulic properties of porous media such as the capillary pressure–saturation relation and the hydraulic conductivity function are a direct manifestation of the underlying pore geometry. The porous structure of a macroscopically homogeneous porous medium (sintered glass) was measured in detail using X-ray microtomography. We investigated the possibility of deriving the water characteristic on the basis of structure analysis. We compared three approaches differing in the amount of required input data, the effort of data processing, and their predictive potential. With increasing complexity, these were (i) a simple pore network model based on a few structural parameters and a simplified process model, (ii) a direct simulation of the pressure–saturation relation based on the full morphology of the porous structure together with a simplified process model, and (iii) Lattice-Boltzmann (LB) simulations based on the full morphology of the porous structure and modeling the complete multiphase fluid dynamics. We found that the network model, the most simple approach, may be sufficient for estimating the main drainage curve, thus suggesting that the complex pore structure can be reduced to a small set of geometric properties. If dynamic effects are considered, the LB approach provides a reliable representation, but at the cost of substantial computational efforts. Since very thin water films exist in the dry range, the continuity of the water phase cannot be described correctly with the LB approach, which presently uses uniform grids.

Abbreviations: D3Q19, three-dimensional 19 velocity LB model • FE, free energy [model] • FM, full-morphology [model] • LB, Lattice-Boltzmann [model] • NW, network [model] • NWP, nonwetting phase • REV, representative elementary volume • RK, Rothman–Keller • SC, Shan–Chen