CH4 diffusion in intra-pore of montmorillonite: From self-diffusion to fick-diffusion

Abstract

Given the low permeability of clay (the main component of shale), diffusion is the main method for transport of methane in shale. Diffusion is a slower process than flow and permeation. Therefore, diffusion is a rate-controlling step during shale gas extraction. Diffusion of CH4 in clay mineral with water is investigated in detail. Dependences of self-diffusivity, Maxwell–Stefan (M–S) diffusivity and Fick diffusivity on various geological conditions are discussed. The practically important Fick diffusivity of methane in montmorillonite is calculated through molecular dynamics for the first time. Results show that self-diffusivity conventionally increases with temperature and its dependence on methane concentration follows the similar behavior of dependence on temperature. However, self-diffusivity displays a maximum at the water concentration of 2.5 molecules/unit-cell. The displacement distribution of CH4 calculated from molecule trajectory follows a logarithmic normal distribution, whose mean reaches the maximum at the same water concentration, resulting in the above-mentioned unusual behavior of self-diffusivity. M–S and Fick diffusivities go up with CH4 concentration and temperature while peak at the water content of 3.125 molecules/unit-cell. On the basis of self-diffusivity and M–S diffusivity, diffusion correlation parameter, Dii, among methane molecules is computed. The diffusion correlation increases with methane concentration, water content, and temperature. Consequently, high methane concentration, temperature and moderately increasing water content result in fast methane diffusion, whereas excessively high water concentration hinders methane diffusion.