Pore-scale lattice Boltzmann simulation of CO2-CH4 displacement in shale matrix

This study couples the Navier-Stokes and multicomponent advection-diffusion equations within the lattice Boltzmann method (LBM) to innovatively simulate the CO2-CH4 displacement in nanoporous shale matrix. In the LBM simulations of CO2 injection into heterogenous CH4-saturated nanoporous media, gas movements are modeled by two separate advection-diffusion lattices driven by the velocity solved from the third Navier-Stokes lattice. Langmuir adsorption kinetics is employed at the fluid-solid interfaces to simulate the mass exchange between the bulk free space and the solid matrix. Mass transfer inside the solid matrix is considered with adsorption and diffusion parameters obtained from molecular dynamics studies. CO2 adsorption and CH4 desorption are simulated simultaneously. The coupling scheme is successfully validated for advection, diffusion, and surface adsorption. Results show that the global mass transfer process is sensitive to intra-matrix diffusion. When the solid diffusion rate is similar to 10-4 of the bulk one, selectivity can significantly impact the outflux con-centration. Changing the CO2 adsorption rate constant 0.1-10 times nearly has no impact on gas adsorption in the solids. In comparison, the CH4 desorption rate constant strongly correlates to the CH4 desorption pathway. Increasing the particle size under a given porosity may benefit advection and lead to fast adsorption/desorption in the solids.