Permeability model for shale and ultra-tight gas formations: Critical insights into the impact of dynamic adsorption

Gas transport in ultra-tight rock is non-Darcian. In addition to continuum flow, there are multiple other flow mechanisms such as slip flow and pore and surface diffusion. Various multi-physics models have been put forth in the literature to forecast the apparent permeability of gas in shales and ultra-tight formations. However, a means of accurately describing the relative contributions of physics in multiscale pore systems remains a challenge. Moreover, it is important to explain pore size, pressure dependency, and the relationships among adsorption, diffusion, and permeability in porous media. For these reasons, a semi-analytical model is proposed to predict gas permeability according to the viscous flux, pore diffusion and surface diffusion and establish control of the adsorbed gas layer. The reliability of the equations developed was checked by validation using experimental and molecular simulation data obtained from macropore- and micropore-sized nanotubes systems respectively. Furthermore, the equations’ performance for micropores was compared to existing theoretical shale permeability models. The subsequent sensitivity analysis showed that permeability is sensitive to the nanoscale geometry factor and adsorption mechanisms. Moreover, the relevance of the surface diffusion was found to increase as the pore size decreased. For instance, surface diffusion constituted over 50% of the apparent permeability below the 10 MPa and 5.0 MPa conditions in micro- and mesopore systems, respectively, while the Darcy scale phenomenon controlled the transport of gas in macropores. Across all diffusion regimes, the microstructure geometry and sorption dynamics significantly influenced the total diffusion of methane, particularly at low pressures and decreased pore sizes. The decline in reservoir pressure during production shifted the relative importance of the adsorption and diffusion mechanisms, consequently altering the apparent gas permeability. Therefore, reservoir management teams should take into account the dynamics of gas permeability at different pressures and representative pore sizes throughout the life cycle of the asset.