The seepage model for CO₂ in Shale considering dynamic slippage, effective stress and gas adsorption

This paper first conducted a shale injection CO₂ seepage experiment based on an improved single-vessel pressure pulse attenuation method. The experimental results reveal that the evolution pattern of shale permeability with respect to pore pressure can be divided into before and after phase change. The overall trend is that it first decreases and then increases, which is not a simple exponential form. The exponential fit of the permeability before and after the phase change alone is one-sided. A CO₂ adsorption deformation test was subsequently conducted on shale under the same temperature and gas pressure conditions. The results revealed that with increasing CO₂ pressure, the expansion and deformation of shale first increased but then decreased. The entire deformation process involves three deformation stages: a short compression stage, a slow expansion stage, and a stable deformation stage. The slip effect was corrected by combining adsorption expansion, effective stress, the real gas effect and the dynamic slip factor. The modified permeability model is more consistent with the relationship between permeability and pore pressure.