The primary objective
of this study is to investigate the adsorption
and surface diffusion of supercritical methane in shale. An adaptive
Dubinin–Astakhov (ADA) model, with a term taking the adsorbed
phase density, was introduced to interpret measured excess adsorption
isotherms and obtain temperature-independent characteristic curves.
The ADA model can also predict adsorption isotherms at different temperatures.
Combining with the ADA model and the Maxwell–Stefan equation,
a new model was developed to describe the surface diffusion of supercritical
methane in shale. The model was successfully validated against experimental
data. We also studied the effect of fugacity and temperature on the
surface diffusion. With increasing temperature, the surface diffusion
flux reaches a maximum and then decreases, which is the result of
a trade off between the amount adsorbed and the effective Maxwell–Stefan
surface diffusivity. The driving force for surface diffusion is the
chemical potential gradient, which can be related to the gradient
of fractional occupancy by a thermodynamic factor. The absolute adsorption
isotherms of supercritical methane in shale are of Type I in the IUPAC
classification scheme. At high feed fugacity, the adsorbed concentration
at feed side approaches saturation. Further increasing the feed fugacity
can hardly increase the driving force for the surface diffusion. But
increasing temperature can increase the effective Maxwell–Stefan
surface diffusivity, which leads to the increase of the surface diffusion
flux.