Complex hydro-mechanical couplings with multiple fluid phases is a great challenge for the discrete element methods (DEM). We propose to use for this problem the same pore space decomposition that was used previously for one-phase flow, based on reguar triangulation of the sphere packing. The decomposition lead to a discretization of the pore space as a set of connected throats and the Lattice Boltzman method (LBM) is employed to obtain hydrostatic properties of each throat, which leads to a hybrid Pore Network-LBM framework. An application to the primary drainage of a random packing of spheres is presented and compared to the results of the same problem fully resolved by the Lattice Boltzman method (LBM). The invasion pattern shows a strong fingering effect, correctly reproduced by the hybrid method. The capillary forces estimated with the hybrid method are in semi-quantitative agreement with the reference values.
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