Fractal microstructure effects on effective gas diffusivity of a nanoporous medium based on pore-scale numerical simulations with lattice Boltzmann method

Abstract

The interaction between gas diffusion and complex microstructures of a nanoporous medium is important to gas diffusion in shale formation, but this interaction is complex and has not been fully understood. Those approaches based on fractal theory can well describe the fractal multiscale microstructure with simple boundaries. The lattice Boltzmann method (LBM) can consider the effects of complex microstructures at one scale. This study proposes a combination approach of fractal theory and LBM to simulate the gas diffusion process in fractal multiscale microstructures of a nanoporous medium. In this study, the gas diffusion in a complex microstructure at base scale is numerically simulated by the LBM and the gas diffusion in finer microstructures is described through a diffusion equation with a local gas diffusion coefficient. First, a microstructure of a nanoporous medium is reconstructed by a random reconstruction algorithm. Then, a local gas diffusion coefficient is proposed based on fractal theory to consider the effects of coupling molecular diffusion and Knudsen diffusion with the fractal structures of a nanoporous medium on the gas diffusion in finer microstructures. This local gas diffusion coefficient is validated by experimental data and introduced into the governing equation of gas diffusion. The LBM simulation is verified with experimental data and two other model results on the effective gas diffusivity of a nanoporous medium. Finally, key parameters for the effective gas diffusivity of a nanoporous medium are identified through sensitivity analysis. It is found that the effective gas diffusivity in a microstructure is higher for a smaller range of Knudsen number. Bigger pore diameter fractal dimension and smaller tortuosity fractal dimension represent lower gas diffusion resistance and have higher effective gas diffusivity. This combination approach provides a powerful tool to estimate the effective gas diffusivity in a complex nanoporous medium.