Hybrid multi-scale model for partially saturated media based on a pore network approach and lattice Boltzmann method

A model combining the efficiency of the pore-network (PN) models and the accuracy of the lattice Boltzmann Method (LBM) is proposed. We introduce a multi-scale approach based on a decomposition of the granular as sembly into small subsets. A tetrahedrization is considered to describe the pore space and extract the subsets. Hydrostatic properties such as entry capillary pressure, liquid morphology and capillary pressure - degree of saturation relationship are evaluated for each pore throat (subset) of the granular system. This information is incorporated into the pore-network model to reproduce the macro-scale effects during a primary drainage. The hybrid method is able to reproduce accurately the capillary pressure - volume relationship and the motion of the interface during the drainage process. The results obtained with the hybrid method evidence the capability of the method to investigate complex phenomena. Additionally, the combination of PN and LBM leads to a significant gain in terms of computation resources. Finally, the results obtained with a fully resolved LBM and the hybrid model help us validate the accuracy of pore-scale methods based on approximations (MS-P and Incircle methods).