On multi-block lattice Boltzmann method for high Knudsen number flows

This work introduces a new computational framework aimed at advancing the modeling of gas transport in confined porous media, particularly shale and tight geological formations that are characterized by their intricate network of meso-and micro-scale fractures and a broad distribution of organic pores. Accurate simulation of gas behavior in such media is challenging due to the complex interactions occurring at high Knudsen numbers, where conventional continuum-based methods fail and kinetic-theory approach becomes more suitable. To tackle these complexities, this work presents a lattice Boltzmann framework tailored for large computational domains with multi-scale pore structures from nano to micro scales. This framework incorporates slip boundary conditions and features an innovative multi-block approach to enable efficient simulations over a wide range of pore sizes, from nanometers to micrometers. The novel contributions of this work include: A scale-informed grid refinement strategy, the incorporation of shear stress terms, multi-block evolution algorithm, and a novel classification method for implementing specular reflection boundary conditions on irregular surfaces. Validation against Direct Simulation Monte Carlo and Molecular Dynamics data from the literature confirms the model's accuracy in predicting gas behavior. Simulations of methane transport in tight porous media with irregular geometries highlight the framework's effectiveness in modeling gas permeability across varying pressure conditions. Apparent permeability results across a range of Knudsen numbers demonstrate the versatility of this framework in capturing the physics of gas transport in confined porous media.