A Local-Effective-Viscosity Multirelaxation-Time Lattice Boltzmann Pore-Network Coupling Model For Gas Transport In Complex Nanoporous Media

Gas transport in nanoporous media is controlled by both the nanoscale mechanisms and complex pore structure, details of which can accurately capture the detailed gas-transport behavior. However, direct-simulation methods in large digitized samples are not feasible because of high memory and computational-time demands. Furthermore, our previous work (Landry et al. 2016) shows that when resolution of the digitized sample is not ample, the sample has to be further magnified up to five times along each linear dimension to achieve the desired accuracy. Here we propose a local-effective-viscosity multirelaxation-time lattice Boltzmann pore-network coupling model (LEV-LBM-PNM) to tackle these problems. We ran a large number of LEV-LBM simulations in high-resolution geometries with simple cross sections that had surface roughness added to them in a controlled manner. Such carefully selected geometries were run at a large number of pressure conditions to establish gas-flux correlations that depend on shape, Knudsen number, and surface roughness and can be directly used in PNM to account for all of those properties. The semianalytical gas-transport models for a single pore with various cross-sectional shapes and surface roughness were established using the LEV-LBM simulation results. The established semianalytical gas-transport model is then implemented into a 3D pore-network model to investigate the gas-transport behavior at various conditions. In an example application, the pore-network model was extracted from a Marcellus Shale focused-ion-beam scanning-electron-microscopy (FIB-SEM) image using the maximum inscribed sphere method. We found that the proposed LEV-LBM-PNM accurately predicts gas apparent permeability by accounting for gas slip in irregular pore shape and surface roughness.