A model for shale gas flow and permeability leveraging coupled transport mechanisms

The extraction of shale gas is challenged by complex flow mechanisms and significant microscale effects within nanoscale pores. Existing models often overlook key flow mechanisms such as end effects, leading to limited predictive accuracy. To address this, we develop a novel capillary-based apparent permeability model that innovatively weights continuum flow and Knudsen diffusion according to the proportion of molecule counts in each flow region. Surface diffusion is further linearly superposed to establish a comprehensive permeability model. Most importantly, this model integrates, for the first time, the effects of effective pressure, adsorption, end effects, real gas effects, and confinement effects. The proposed model is validated against published experimental data under both constant effective pressure and constant confining pressure, showing superior agreement compared to existing theoretical models. Sensitivity analysis reveals that neglecting end effects and surface diffusion leads to underestimation of permeability, while overlooking effective pressure results in overestimation. The influence of each mechanism varies distinctly with pore radius: surface diffusion and real gas effects dominate in smaller pores (≤10 nm), whereas end effects become predominant in larger pores (≥25 nm). This work provides a more reliable theoretical foundation for predicting shale gas permeability and optimizing extraction strategies.