An analytical model for shale gas transport in kerogen nanopores coupled with real gas effect and surface diffusion

Understanding the behavior of shale gas transport in kerogen is a key issue in predicting gas production. The reservoir structure is characterized by widespread micro/nanoscale pores, various occurrence states, and typical high pressure. An analytical model is proposed to effectively reveal the gas transport behavior in kerogen nanopores. The model can fully consider the real gas effect, gas slippage, and surface diffusion derived from absorbed gas. In particular, a method based on dense gas theory with the Redlich-Kwong equation of state is used to acquire the viscosity of shale gas under high pressure. The second-order slippage boundary condition coupled with surface diffusion is presented to describe the free gas slippage, and Langmuir isotherm theory and Fick's law are adopted to calculate the surface diffusion. The real gas effect has a significant effect on the physical properties of methane, Knudsen number, and the flow behaviors of free gas and adsorbed gas. The surface diffusion velocity can enhance the free gas flow. The mass flow rate of total adsorbed gas increases as pore size increases, and its major influence is obtained from the induced free gas at the increased pore size. The slippage effect is reduced as the pressure increases and the temperature decreases. The absorbed gas comprises a substantial proportion of the total gas produced when the pore size is less than 2 nm. The combined influences of slippage effect and absorbed gas cannot be ignored when the pore size is less than 10 nm. This work provides a comprehensive and theoretical guidance for the effective development of shale gas.