Permeability evolution of gas-infiltrated coal under varied stress paths

We explore the conundrum of how permeability of coal decreases with swelling-induced sorption of a sorbing gas, such as CO₂. We show that for free swelling of an unconstrained homogeneous medium where free swelling scales with gas pressure then porosity must increase as pressure increases. The volume change is in the same sense as volume changes driven by effective stresses and hence permeability must increase with swelling. An alternative model is one where voids within a linear solid are surrounded by a damage zone. In the damage zone the Langmuir swelling coefficient decreases outwards from the wall and the modulus increases outwards from the wall. In each case this is presumed to result from micro-fracturing-induced damage occurring during formation of the cleats. We use this model to explore anticipated changes in porosity and permeability that accompany gas sorption under conditions of constant applied stress and for increments of applied gas pressure. This model replicates all important aspects of the observed evolution of permeability with pressure. As gas pressure is increased, permeability initially reduces as the material in the wall swells and this swelling is constrained by the far-field modulus. As the peak Langmuir strain is approached, the decrease in permeability halts and permeability increases linearly with pressure. The rate of permeability loss is controlled by crack geometry, the Langmuir swelling coefficient and the void "stiffness" and the rate of permeability increase is controlled by crack geometry and void "stiffness" alone. Correspondingly, this represents a mechanistically plausible model for the evolution of permeability in swelling materials.