The fluid velocity is higher in the near wellbore region or in the hydraulic fractured wells, which would lead to non-Darcy flow and significantly decrease the deliverability of the well. In this work, the inertia resistance factor and transition point between Darcy flow and non-Darcy flow are investigated by using lattice Boltzmann method based on stochastically constructed three-dimensional porous media, with porosity ranging from 0.19 to 0.39. The results show that gas flow in porous media shows a transition from Darcy flow to non-Darcy flow with an increase of Reynolds number. The transition occurs when the Reynolds number is between 0.2 and 0.3. Meanwhile, the inertia resistance factor of porous media decreases with increasing porosity and permeability. Compared with the porous media generated by regular grains, the stochastically constructed three-dimensional porous media better represents the reservoir rocks, and the derived inertia resistance factors are closer to rock samples. Finally, a relation of inertial resistance factor with porosity and permeability was established for the porous media with irregular grain sizes and shapes. This work provides a useful method to investigate non-Darcy flows in reservoir rocks.

Marine shale is highly prone to wellbore collapse due to its high pore pressure, propensity for hydration and swelling, distinct bedding planes, and low tensile strength. Horizontal in situ stress serves as a critical parameter for wellbore stability analysis; however, its accurate prediction is extremely challenging in complex geological environments. Conventional studies often simplify the wellbore as a circular shape, neglecting its natural elliptical deformation under non-uniform in situ stress, which leads to reduced predictive accuracy. To address this limitation, this study establishes an elliptical wellbore model that incorporates the strain-softening characteristics of shale. Theoretical models for stress distribution in both elastic and plastic zones were derived. The strain-softening behavior was validated through triaxial compression tests, providing a foundation for analytical solutions of stress distributions around circular and elliptical wellbores. Furthermore, an elliptical wellbore-based model was developed to derive a new prediction equation for horizontal in situ stress. Numerical programming was employed to compute stress distributions, and finite element simulations under various aspect ratios corroborated the theoretical results, showing excellent agreement. Results demonstrate that the elliptical wellbore model captures the near-wellbore stress state more accurately. As the aspect ratio increases, the extreme values of radial and tangential stresses increase significantly, with pronounced stress concentrations observed around the 180° and 360° positions. Predictions of horizontal in situ stress based on the proposed model achieved over 89% accuracy when verified against field data, confirming its reliability. This study overcomes the limitations inherent in the traditional circular wellbore assumption, providing a more precise analytical method for wellbore stability assessment in Marine shale under complex geological conditions. The findings offer a valuable theoretical basis for wellbore stability management and drilling engineering design.