  A pore-scale model is introduced for two-phase flow in dense packings of
polydisperse spheres. The model is developed as a component of a more general
hydromechanical coupling framework based on the discrete element method, which
will be elaborated in future papers. Here the emphasis is on the generation of
a network of pores mapping the void space between spherical grains, and the
definition of local criteria governing the primary drainage process. The pore
space is decomposed by Regular Triangulation, from which a set of pores
connected by throats are identified. A local entry capillary pressure is
evaluated for each throat, based on the balance of capillary pressure and
surface tension at equilibrium. The model reflects the possible entrapment of
disconnected patches of the receding wetting phase. It is validated by a
comparison with drainage experiments. A series of simulations are reported to
illustrate size and boundary effects, key questions when studying small samples
made of spherical particles be it in simulations or experiments. Repeated tests
on samples of different sizes give evolution of water content which are not
only scattered but also strongly biased for small sample sizes. More than
20,000 spheres are needed to reduce the bias on saturation below 0.02.
Additional statistics are generated by subsampling a large sample of 64,000
spheres. They suggest that the minimal sampling volume for evaluating
saturation is one hundred times greater that the sampling volume needed for
measuring porosity with the same accuracy. This requirement in terms of sample
size induces a need for efficient computer codes. The method described herein
has a low algorithmic complexity in order to satisfy this requirement. It will
be well suited to further developments toward coupled flow-deformation problems
in which evolution of the microstructure require frequent updates of the pore
network.
