Modeling of Change of Coal Permeability Induced by Gas Adsorption

In the present study we focuses on developing the poroelasticity model that deals with adsorptioninduced permeability change mostly occurred in porous media constituted several phases such as coal. The underlying pressure induced by adsorption is obtained by Virial expansion form, which is substantially founded on statistical physics. The corresponding thermodynamic pressure applying on the pore surface is then used to detail the pore pressure and further to evaluate the macroscopic volumetric strain and the porosity. In the process of physical adsorption, the adsorbed phase is in thermodynamic equilibrium with the gas phase regardless of pore size, and the corresponding chemical potentials are all equal. The relationship between surface strain and volumetric strain is derived under infinitesimal deformation conditions to gain an explicit formulation of pore surface area with respect to volumetric strain and porosity. After the formulation of surface stress modified by the Langmuir isothermal adsorption is derived, the differential micromechanical constitutive equations of porous media are obtained. By supposing that the ratio of current permeability to initial is equal to the cubic ratio of current porosity to initial porosity, the differential equations for permeability change is consequently derived. The numerical simulations by the present model for permeability change of coal induced by adsorption of CO2 and CH4, respectively, are presented under confined stress conditions. The predictions from the model are good in agreement with the experimental data of sorption-induced permeability change of coals in the literature.