Discrete modeling of the fracture-permeability behavior of shale

A three-dimensional discrete dual lattice model is formulated to investigate the permeability and mechanical behavior of fracture-damaged shale. The mechanical lattice model simulates the granular internal structure of material at the grain level, and describes the heterogeneous deformation by means of discrete compatibility and equilibrium equations. A network of fluid transport elements built upon the mechanical lattice is used to simulate fluid flow along intergranular pores and cracks. The variation of permeability for cracked material is captured by coupling mechanical and transport lattice models. A numerical example of direct shear triaxial test on Utica shale is simulated by the formulated framework. Variation of shale shear strength with the angle between the vertical bedding plane and the shear plane is captured. The permeability of the fractured specimens was obtained by simulating water flowing along the specimens. The numerical results show that the simulated effect of cracking on the overall permeability is in general qualitative agreement with available experimental data.