Impact of CO₂ injection and differential deformation on CO₂ injectivity under in-situ stress conditions

A fully coupled finite element (FE) model of coal deformation, gas flow and diffusion and competitive adsorption was developed to investigate the net effect on the evolution of CO₂ injectivity. Here we developed new cross coupling relations between coal porosity and mechanical, hydrological, binary gas diffusion and competitive adsorption-induced volumetric strains under variable stress conditions. The cubic relation between porosity and permeability is then applied to relate coal storage capability (changing porosity) to coal transport characteristics (changing permeability) also under variable stress conditions. These two relations coupled the multiphysics of coal-gas interactions. We implemented these two relations into a finite element model to represent the complex interactions of stress and gas composition under in-situ stress conditions. This relaxes the common assumption of prior studies that vertical stress remains constant and allows exploration of the full range of mechanical boundary conditions from invariant stress to restrained displacement. The FE model was verified against experimental data, and then extended to field scale to explore the sensitivity of CO₂ injection rate and ECBM production to in-situ stress conditions. Model results indicated that the net change in coal permeability accompanying binary gas diffusion is controlled competitively by the influence of effective stresses and differential matrix swelling. The balance between these two influences can be altered either by changing mechanical parameters (Young's modulus and Poisson's ratio) or by changing the coal sorption properties such as the swelling strain. The impact of gas sorption-induced deformation on coal permeability increases with the magnitudes of coal modulus or Poisson's ratio, and with the magnitudes of the gas swelling strain constant.