Swelling and embedment induced by sub- and super-critical-CO₂ on the permeability of propped fractures in shale

Swelling and embedment exert significant influence on the evolution of permeability in propped fractures, potentially consuming significant proportions of the original gain in permeability. We measure the evolution of permeability in propped fractures of shale to both adsorbing CO₂ and non-adsorbing He – accommodating the impacts of aperture change due to proppant pack compaction and both reversible and irreversible modes of embedment. A linear relation between pressure and log-permeability is obtained for He, representing the impact of effective stresses in proppant pack compaction, alone. Permeability change with pressure is always concave upwards and U-shaped for gaseous subcritical CO₂ and W-shaped for supercritical CO₂. One exception is for liquid CO₂ at high injection pressure where effective stress effects and swelling contribute equally to the change in permeability and result in a linear curve with the lowest permeability. Approximately ~50–70% of the permeability recovers from the recovery of swelling after the desorption of CO₂. The magnitude of swelling is recovered from measurements of permeability change and ranges from 0.005 to 0.06 mm, which contributes ~9–56% of the total swelling and induced embedment as evaluated from the adsorbed mass. Swelling also increases embedment by a factor of ~1.84–1.93 before and after the injection of CO₂. A new calibration equation representing swelling and induced embedment is generated accommodating Langmuir isothermal sorption and verified against experiments on rocks both admitting and excluding swelling and embedment and for various sorbing and non-sorbing gases. Stability and accuracy of the predictions demonstrate the universality of the approach that may be applied to both enhanced gas recovery and CO₂ sequestration.