Model for Surface Diffusion of Adsorbed Gas in Nanopores of Shale Gas Reservoirs

Surface diffusion plays a key role in gas mass transfer due to the majority of adsorbed gas within abundant nanopores of organic matter in shale gas reservoirs. Surface diffusion simulation is very complex as a result of high reservoir pressure, surface heterogeneity, and nonisothermal desorption in shale gas reservoirs. In this paper, a new model of surface diffusion for adsorbed gas in shale gas reservoirs is established, which is based on a Hwang model derived under a low pressure condition and considers the effect of adsorbed gas coverage under high pressure. Additionally, this new model considers the effects of surface heterogeneity, isosteric sorption heat, and nonisothermal gas desorption. Results show that (1) the surface diffusion coefficient increases with pressure and temperature, while it decreases with activation energy and gas molecular weight; (2) contributions of viscous flow, Knudsen diffusion, and surface diffusion to the total gas mass transfer are varying during the development of shale gas reservoirs, which are mainly controlled by nanopore-scale and pressure; (3) in micropores (pore radius of <2 nm), the contribution of surface diffusion to the gas mass transfer is dominant, up to 92.95%; in macropores (pore radius of >50 nm), the contribution is less than 4.39%, which is negligible; in mesopores (2 nm < pore radius < 50 nm), the contribution is between micropores and macropores.