We developed a grain-based pore-scale model that tracks capillary-stable positions offl uid-fl uid interfaces (menisci) between grains of arbitrary wett ability. The model explicitlycalculates the stable menisci positions between two-dimensional disks at particular capillarypressures. With changing capillary pressure, the menisci are tracked and conditionsfor menisci stability in a pore throat (Haines condition) or menisci merging in a pore body(Melrose condition) are elucidated. When a meniscus becomes unstable, a pore-fillingevent occurs, and an invasion percolation routine is used to fi nd the next stable position ofthe meniscus (or menisci). We tested the method on networks extracted from two-dimensionalporous media consisting of randomly distributed oil-wet and water-wet disks. Themodel is robust in that it handles both fi lling mechanisms simultaneously and seamlesslyeven across changes in capillary pressure from positive to negative values. We comparedthe results of the two-dimensional model as a function of fractional wett ability to experimentsin fractionally wet packs. We found good qualitative agreement between the modeland the experiments for a water-oil system on both imbibition and drainage.
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