Constitutive equations for coal containing gas considering gas adsorption

Coupled gas flow and solid deformation processes in porous media have received considerable attention because of its importance in CBM exploitation and gas outbursts during coal mining. Coalbed methane is mainly adsorbed on coal. The dependence of gas adsorption on gas pressure has significant effect on the mechanical properties of coal, however, the effect was ignored in most of the previous modeling studies. Based on Truesdell’s postulate of the theory of mixtures, a new set of constitutive equations for the saturated mixtures of gas-filled coal which is composed of coal matrix, adsorbed gas and free gas is developed. Adsorbed gas pressure and the volume fraction of each component of the saturated mixtures are also presented. The proposed constitutive equations show that mechanical response of coal is determined by stress condition, mechanical properties of solid phase, gas pressure, gas adsorption, pore structure and its evolution. Without considering the adsorption effects and pore evolution, the effect of gas pressure in coal seam would be underestimated.