A multiscale pore network modelling of gas flow in the nano-porous structure of shale

Flow simulation in shale is challenging due to its multiscale porous structure and multi-physics gas flow in these pores. Because network of pores is capable of characterizing the three dimensional (3D) distribution of pores and throats, it is widely used to estimate the apparent gas permeability of porous media, such as shale. Pores residing in shale have a broad spectrum of size ranging from a few nanometers to micrometers, therefore, multiple flow regimes, including the continuum flow, slip flow, transition flow and sometimes Knudsen diffusion are controlling the flow in the porous structure of shale. In addition, surface diffusion occurs on the adsorption layer of organic matters also contributes to the total flow rate. For the network modelling in the literature, the employed equaitons fail to account for these flow mechanisms. In view of this, Beskok and Karniadakis (1999)'s equation and Fick's equation are employed to describe the noncontinuum flow and surface diffusion, respectively, in a reconstructed network of shale. The simulation results provide an improved understanding of gas flow behaviour in shale matrix. It has been observed that the apparent gas permeability increases by a factor of 2.4, with 21% contribution arising from surface diffusion when the downstream pressure depletes from 9 MPa to 2 MPa. Sensitivity analyses imply that the apparent gas permeability is dependent on the size and shape of throats, compressibility factor and type of gas, Langmuir adsorption parameters and reservoir conditions.