Simulation of quasi-static drainage displacement in porous media on pore-scale: Coupling lattice Boltzmann method and pore network model

Lattice Boltzmann method (LBM) and pore network model (PNM) are two types of simulation methods for modelling the fluid flow in porous media at the pore scale. LBM is accurate in representing the pore structures but is computationally expensive, while PNM is very efficient but cannot capture the details of pore structures. In this work, we propose to couple these two methods to simulate two-phase drainage flow in porous media. To describe the throat geometry more accurately, an improved pore network extraction method is proposed based on watershed method, where throat bonds with real throat cross sections are extracted. A multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate the flow properties for each throat bond, namely critical entry capillary pressure, capillary pressure – saturation relationship, single-phase conductance and relative conductance – saturation relationship for both phases, which are the input parameters for PNM simulations. To further improve the computational efficiency, five artificial neural network models are developed which relate the five flow properties to the actual shape of throat cross sections, where the shape is characterized by 9 parameters. The database consists of LBM simulations of the flow properties of 1421 throat cross sections extracted from 5 sandstone digital rocks. The trained artificial neural network models show much better performance than the conventional PNM when predicting the flow properties for each throat bond. Finally, the accuracy of the improved PNM coupled with LBM is validated by both the single-phase flow and two-phase drainage flow in a Berea sandstone.