Numerical simulation of fracture height growth with interference of bedding plane and stiffness contrast in shale reservoirs

Shale formations typically exhibit heterogeneous structures, including bedding planes and interlayers. The mechanical differences between layers, together with bedding planes, significantly affect the vertical propagation of hydraulic fractures. In this study, a finite element model incorporating bedding planes was developed to simulate hydraulic fracture height growth. The model employs global cohesive elements based on a traction-separation law to capture multidirectional fracture propagation. Using the presented model, parametric analyses were conducted to investigate the combined effects of key parameters on fracture growth (either traversing or diversion), including the dip angle, bedding strengths, stress conditions and Young's modulus contrast between the reservoir with barrier layers. The research reveals how the failure modes of bedding planes and stiffness contrast can affect the vertical fracture extension. The results indicate that varying stress states resulting from changing dip angles can give rise to two distinct failure modes of bedding planes, namely shear-dominated failure and tensile-dominated failure, thus leading to different fracture propagation behaviors. In each regime, only the corresponding strength parameter (shear or tensile strength) influences the fracture height growth. Higher corresponding strength (R-s > 0.30 or R-t > 0.4) increases the tendency of fractures to traverse bedding planes. Furthermore, it was found that the behavior of fracture propagation under stiffness contrast is influenced by the failure mode. When fractures propagate from a hard layer into a soft layer (Y-c > 1) under tensile- or shear-dominated conditions, a softer barrier layer requires a higher corresponding strength to prevent fracture diversion. Conversely, when fractures propagate from a softer layer into a harder layer (Y-c < 1), the stiffness contrast has little impact on fracture behavior under shear-dominated failure of bedding planes; however, under tensile-dominated failure, the stiffness contrast is almost linearly correlated with the tensile strength required for the bedding planes to resist fracture diversion. The study results provide insights that are expected to improve our understanding of fracture height growth mechanisms and contribute to engineering optimization.