A diffusion–viscous flow model for simulating shale gas transport in nano-pores

A model for gas flow in nano-pores was developed based on the extended Navier–Stokes equations with the assumption of neglecting adsorption and desorption. The model describes multiple flow regimes, including continuum regime, slip flow regime, transition regime, as well as molecular regime. The total mass flux includes a convective motion term and a diffusion mass transport term. The latter was obtained as a weighted superposition of bulk and Knudsen diffusion. The mass flux, contributed by different transport mechanisms, was analyzed by varying the Knudsen number (ratio between mean free path of the molecules and the pore diameter). The effect of the ratio coefficient (the power-law exponent in the relation between bulk and Knudsen diffusion), the pore size and the pressure on the gas transport was investigated using the proposed model. The predictions of the newly developed model are in good agreement with the Direct Simulation Monte Carlo (DSMC) method and with the results of the experiments. Our results show that: (1) As the Knudsen number increases, the contribution of viscous flow to gas transport decreases monotonically, bulk diffusion increases to a peak, and then decreases, whereas the Knudsen diffusion increases monotonically. (2) For a larger ratio coefficient, the bulk diffusion changes more rapidly and the peak is higher. The changing trend of the bulk diffusion is opposite to the Knudsen diffusion. (3) The pressure range in which the viscous flow dominates becomes larger and the peak of bulk diffusion is smaller in larger pores. When the pore pressure is higher, the viscous flow and the bulk diffusion tend to dominate.