  The non-equilibrium transport of inhomogeneous and dense gases highly
confined by surface is encountered in many engineering applications. For
example, in the shale gas production process, methane is extracted from
ultra-tight pores under high pressure so the gas is inhomogeneous and dense.
Currently, the complex non-equilibrium transport of inhomogeneous and dense
gases where gas surface interactions play a key role is commonly investigated
by molecular dynamics or on a continuum-assumption basis. Here, a tractable
kinetic model based on the generalized Enskog equation and the mean-field
theory is employed to couple the effects of the volume exclusion and the
long-range intermolecular attraction forces. The interactions between gas
molecules and confined surface are modelled by a 10-4-3 Lennard-Jones
potential, which can capture gas surface adsorption. The cross-sectional
density profiles of methane under different confinements are in good agreement
with the molecular dynamics results reported in the literature, and the
transport behaviors are validated by the non-equilibrium molecular dynamics.
The velocity of methane flow in shale matrix is plug-like due to its dense
characteristics in nanopores. The influence of pressure, temperature, pore size
and shale composition on density and velocity profiles is analyzed
quantitatively. Our results show that the Klinkenberg correction is not
applicable to model shale gas flow in the production process; the Navier-Stokes
model using the second-order slip boundary condition cannot produce the proper
velocity profiles, and consequently fails to predict the accurate flow rate in
nanopores. This study sheds new light on understanding the physics of
non-equilibrium dense gas flows in shale strata.
