Most of these inversioin methods only work for unipore diffusion system. For diffusion occurring in multi-scale porous coal, bidisperse diffusion models can be used. Correspondingly the gas diffusivities can be determined by two methods described as follows.
By which the apparent macropore and micropore diffusivities are usually retrieved as two fitting parameters by minimizing a least-square function.
Which is proposed by Do and Rice under a given assumption, the contribution of pore diffusion and surface diffusion on overall sorption rate can be determined from a simple linear plot of the inverse of half time of adsorption verse a concentration factor. However, the analytical solution derived from Langmuir isotherm may be not accurat for any cases, especially for the cases of the poor fit of Langmuir isotherm to pure gas adsorption isotherms. Using this method, Karacan and Mitchell studied the surface and pore diffusivity of CO2 sequestration in coal seams, and reported that both of pore diffusion and surface diffusion are important for total sorption rate