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.

Peridynamics is a non-local mesh-free numerical method which has great advantages in simulating dynamic damage and fracture. This work proposes to use the peridynamics to simulate rock fragmentation by TBM disc cutters and seven tests are simulated to verify this idea. The feasibility of peridynamics in simulating rock fragmentation by TBM disc cutters is demonstrated by comparisons with the punch indentation tests. A nonlinear short-range force contact model is proposed to better reflect the variation of the disc cutter normal force with respect to indentation depth, and can also calculate the changing contact area between the disc cutter and the rock during the indentation. In addition, the proposed non-linear short-range force contact model is used to simulate five 3D TBM disc cutter indentation tests with different bi-directional confining stress conditions, and the numerical results are compared with the experimental results. The simulation results show that the proposed contact model is able to calculate the variation of the cutter peak force with different confining stress and to obtain a reasonable form of rock surface damage. Peridynamics approach is easy to operate and requires only two calibration parameters to simulate the 3D rock fragmentation by disc cutters, which is promising for practical engineering applications.