Estimation of the equivalent elastic modulus in shale formation: Theoretical model and experiment

Anisotropy is prevalent in sedimentary rock masses, such as shale formations that contain numerous inherent bedding planes (BPs) and natural fractures (NFs). This study proposes a new methodology to determine the equivalent elastic properties of shale formations that uses the weak patches stiffness model and fracture mechanics theory to theoretically consider both BP- and NF-induced anisotropy. First, a series of uniaxial compression tests for Longmaxi shale demonstrates that its apparent elastic modulus ranges from 14.9 to 18.8 GPa. Then, by collecting experimental data and performing a Monte–Carlo simulation method, the NF network is built within the target 3D shale formation, and the equivalent elastic modulus values along a given wellbore wall are estimated. The results reveal that the elastic parameters of shale formations exhibit high directional dependency associated with the presence of BPs and NFs; a higher NF density is also found to lower the BP-induced anisotropy. Wider application of Monte–Carlo simulations in future studies is recommended to calculate the deformation issues of large-scale numerical petroleum engineering modeling when considering the influence of NFs.