Predicting Surface Diffusivities of Gas Molecules in Shale

Carbon dioxide injection can be utilized as a means of both enhancing gas recovery from shales and sequestering carbon and thereby simultaneously addressing the growing worldwide gas demand, as well as the challenge of greenhouse gas emissions. Greater mobility of CO2 within the shale improves the displacement efficiency of the originally present CH4, as well as increasing the CO2 penetration of the shale formation. Previous investigations have indicated that surface diffusion is much more significant than the bulk gas transport in shale gas reservoirs because of the larger fraction of the adsorbed phase found in the nanopores of shales. The surface diffusivities of CO2 on different shales, at various temperatures, have been measured. A fractal theory for predicting the Arrhenius parameters of the surface diffusivity of molecules on heterogeneous surfaces has been applied to the surface diffusion of CO2 in shales. In line with the theory, it was found that both the pre-exponential factor and the activation energy are functions of the surface fractal dimension. Hence, the surface diffusivity, around a monolayer coverage, on shales could be established from an equilibrium gas adsorption isotherm, once the Arrhenius parameters have been calibrated for the specific chemical species. To the best of our knowledge, this study is the first to apply the fractal theory and effectively predict, a priori, surface diffusivity parameters for such structurally and chemically heterogeneous natural samples as shales. This theory now enables the optimization of the designs of CO2 injection in field applications since surface diffusion is of major importance in the apparent permeability and, thus, in the gas flow mechanisms.