Mathematical Model of the Migration of the CO₂-Multicomponent Gases in the Inorganic Nanopores of Shale

Nanopores in shale reservoirs refer to extremely small pores within the shale rock, categorised into inorganic and organic nanopores. Due to the differences in the hydrophilicity of the pore walls, the gas migration mechanisms vary significantly between inorganic and organic nanopores. By considering the impact of irreducible water and the variations in effective migration pathways caused by pore pressure and by superimposing the weights of different migration mechanisms, a mathematical model for the migration of CO₂-multicomponent gases in inorganic nanopores of shale reservoirs has been established. The aim is to accurately clarify the migration laws of multi-component gases in shale inorganic nanopores. Additionally, this paper analyses the contributions of different migration mechanisms and studies the effects of various factors, such as pore pressure, pore size, component ratios, stress deformation, and water film thickness, on the apparent permeability of the multi-component gases in shale inorganic nanopores. The research results show that at high pressure and large pore size (pore pressure greater than 10 MPa, pore size greater than 4 nm), slippage flow dominates, while at low pressure and small pore size (pore pressure less than 10 MPa, pore size less than 4 nm), Knudsen diffusion dominates. With the increase of the stress deformation coefficient, the apparent permeability of gas gradually decreases. When the stress deformation coefficient is less than 0.05 MPa⁻¹, the component ratio significantly impacts bulk apparent permeability. However, when the coefficient exceeds 0.05 MPa⁻¹, this influence becomes negligible. The research results provide a theoretical basis and technical support for accurately predicting shale gas productivity, enhancing shale gas recovery, and improving CO₂ storage efficiency.