A simple permeability model for shale gas and key insights on relative importance of various transport mechanisms

Abstract

Gas transport mechanism in a shale nanopore is investigated by considering convective flow, gas diffusion, and surface diffusion. A common practice in modeling shale gas permeability is to use Knudsen diffusion coefficient when calculating diffusive flux, but the use of Knudsen diffusion coefficient would be incorrect if the shale gas flow regime is lying either in the transition diffusion or Fick’s diffusion, in which case the diffusion coefficient must correspond to that regime. This study proposes an apparent permeability model of shale based on a unified diffusion coefficient that transforms its value per the flow regime, including the effect of molecular diffusion, viscous flow, and surface diffusion of adsorbed gas through linear superposition. The proposed model is verified by comparing against other models for shale gas permeability. Results of sensitivity analysis indicate that permeability of gas due to diffusive transport is independent of pressure and pore size when pressure is larger than 6.895 MPa, but is dominant at lower pressures and increases with pore size. For pore diameters larger than 100 nm, the permeability due to surface diffusion is independent of pressure or pore size, indicating negligible gas transport due to surface diffusion in relatively larger pores (>100 nm) at any pressure, but it is dominant in small pore sizes when pressure is below 10 MPa. Permeability of gas (with or without surface diffusion) increases with the decrease of pressure when the pore diameters are smaller than 100 nm, whereas for pore diameters larger than 300 nm it is not affected by pressure, but increases with the increase of pore size, indicating that Darcy’s law is applicable in pores with the diameters larger than 300 nm.