Evolution mechanism of shale microfracture apparent permeability considering dynamic slippage

In order to study the evolution mechanism of microfracture apparent permeability under the effect of effective stress, gas adsorption and slip effect during shale-gas extraction, the fractal theory was used to characterize the total gas flow in microfracture, and an apparent permeability model of the combined effects of microfracture deformation and slip effect based on the Hagen-Poiseuille second-order slip equation was established. Meanwhile, the influence of effective stress and gas adsorption on the slip coefficient was quantified by combining with the functional relationship between the slip coefficient and intrinsic permeability,  the dynamic evolution of the slip coefficient during shale-gas seepage was explored, and the reliability of the model was verified. In addition, the effects of microfracture compressibility coefficient, fractal dimension and internal expansion coefficient on slip coefficient were explored in conjunction with sensitivity analysis. The results shown that: ① Under the conditions of constant external and effective stress, the apparent permeability tended to decrease with the gradual increase of pore pressure, which was influenced by the coupling of gas adsorption and slip effect; ② When the external stress was constant, the average free range of gas molecules decreased with increasing pore pressure, the slip effect was weakened, the first-order and second-order slip coefficientsC₁ andC₂ decreased, and the overall slip coefficient B increased. When the effective stress was constant, the shale-gas seepage channel was subject to gas adsorption and gradually reduced, andC₁,C₂ andBgradually increased; ③ Based on the model sensitivity analysis, the reciprocal feedback mechanism between microfracture compressibility coefficient, fractal dimension, internal expansion coefficient and slip coefficient was explored, in which the microfracture compressibility coefficient and fractal dimension led to an increase in intrinsic permeability, and a decrease inC₁,C₂ andBdecrease. The increase of internal expansion coefficient led to an decrease in the intrinsic permeability, and an increase inC₁,C₂ andB. The findings of this study will provide some theoretical support for shale-gas extraction.