Dual poroelastic response of a coal seam to CO₂ injection

Although the influence of gas sorption-induced coal deformation on porosity and permeability has been widely recognized, prior studies are all under conditions of no change in overburden stress and effective stress-absent where effective stresses scale inversely with applied pore pressures. Here we extend formalism to couple the transport and sorption of a compressible fluid within a dual-porosity medium where the effects of deformation are rigorously accommodated. This relaxes the prior assumption that total stresses remain constant and allows exploration of the full range of mechanical boundary conditions from invariant stress to restrained displacement. Evolution laws for permeability and related porosity are defined at the micro-scale and applied to both matrix and an assumed orthogonal, regular and continuous fracture system. Permeability and porosity respond to changes in effective stress where sorption-induced strains may build total stresses and elevate effective stresses. Gas accumulation occurs in both free- and adsorbed-phases and due to effective grain and skeletal compressibilities. A finite element model is applied to quantify the net change in permeability, the gas flow, and the resultant deformation in a prototypical coal seam under in situ stresses. Results illustrate how the CO₂ injectivity is controlled both by the competition between the effective stress and the gas transport induced volume change within the matrix system and by the dynamic interaction between the matrix system and the fracture system. For typical parameters, initial injection-related increases in permeability due to reduced effective stresses may endure for days to years but are ultimately countered by long-term reductions in permeability which may decline by an order of magnitude. Models suggest the crucial role of stresses and the dynamic interaction between matrix and fractures in correctly conditioning the observed response.