Transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks under stress boundaries: A 3D phase field modeling

Abstract

The ground (tectonic) stress and layered structures of rocks are the among the main factors that influences the hydraulic fracturing behavior. The purpose of this study is to examine the suitability of the phase field model (PFM) in simulating transverse penny-shaped hydraulic fracture propagation and to investigate the phase field feature for the transverse penny-shaped hydraulic fracture in layered rocks under stress boundaries. A phase field model for 3D transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks considering the effect of initial stress field is established. The mathematical model is based on Biot poroelasticity theory and the phase field fracture theory, while the governing equations are solved by using the finite element method in a staggered manner. The established PFM is validated experimentally and analytically by 2D and 3D examples. At last, the influences of the initial stress field, stiffness contrast and inclination angle of the layer interface on the penny-shaped fracture evolution in naturally-layered rocks are investigated by using the PFM. The study indicates that the phase field model has excellent feasibility and practicability in predicting penny-shaped hydraulic fractures. The layer inclination has nearly no effect on the penny-shaped fracture evolution in naturally-layered rocks. The stress ratio Sv/Sh on the boundaries has a significant effect on propagation of the penny-shaped hydraulic fracture. With the increase in Sv/Sh, the hydraulic fracture deflects and propagates along the direction of the maximum in-situ stress. For a high Sv/Sh, branching scenarios can be observed. The stiffness contrast of the rock layers determines whether the penny-shaped hydraulic fracture can penetrate into the adjacent layer. The predictions on the effects of the initial stress field, stiffness contrast and inclination angle of the layer interface provide new understanding of penny-shaped hydraulic fracture propagation in underground geological environment.