Modeling of coal matrix apparent strains for sorbing gases using a transversely isotropic approach

Gas sorption-induced coal deformation is one of the primary geomechanics effect in coalbed methane (CBM) engineering. Coal is known to have transversely isotropic properties because of its cleat structure. We propose a new theoretical approach to modeling the strain behavior of bulk coal by including sorption-induced matrix shrinkage/swelling strain, cleat volume strain and matrix mechanical strain resulting from changes in pore pressure, and external stresses. The new model framework can define the apparent bulk coal volume with respect to the variation in gas pressure. To validate the model, unconstrained gas flooding experiments were conducted with helium, methane and carbon dioxide injections. The experimental data agreed well with the modeled strain evolution results under hydrostatic conditions and at the injection pressure conditions. The results show that the degree of anisotropy is ~ 1.6 for helium injection, comparing the strains perpendicular to and parallel to the bedding plane. The results demonstrate that the volumetric strains closely correlate to the sorption capability of coal. The maximum volumetric strain induced by carbon dioxide injection can reach ~ 2.05% as gas pressure increases up to ~ 5.43 MPa, which is ~ 2.77 times that of the methane-induced volumetric strain of ~ 0.74% at a gas pressure of ~ 5.45 MPa. The proposed model can be simplified to be equivalent to the commonly extended Langmuir-type strain model at relatively low gas pressure for bulk coal with low cleat porosity. The proposed model can also successfully cover the volumetric response of bulk coal for high pressures that range beyond 13 MPa. A sensitivity study shows that Young’s modulus, Poisson’s ratio, and the degree of anisotropy affect the volumetric responses differently at various pressure stages, but the effects are always distinct for high-pressure injections. The proposed model framework can be coupled into a coal dynamic permeability model for defining the permeability evolution—which is important for gas production predictions for CBM wells.