Three-dimensional phase field feature of longitudinal hydraulic fracture propagation in naturally layered rocks under stress boundaries

Hydraulic fracturing (HF) has been widely used in the exploitation of oil, shale gas and other resources in recent years, while phase field model (PFM) has immense potential for predicting fracture and has been increasingly applied to HF. However, current studies on combination of PFM and HF seldom consider the influence of initial stress field on hydraulic fracture prediction in naturally layered rocks, which is still a challenging topic for researchers. Therefore, a 3D phase field model for simulating quasi-static longitudinal hydraulic fracture propagation in naturally layered porous rocks subjected to stress boundary conditions is proposed. We involve the effect of initial stress field in a new energy functional and couple it to variational approach for achieving governing equations for the displacement and phase fields. The coupling of fluid pressure field and displacement field is under the framework of Biot poroelasticity and the fluid properties are validly approximately via the phase field. The phase field framework proposed is verified through two examples: 2D domain subjected to an increasing internal pressure and 3D longitudinal fracture in a homogeneous domain. Finally, PFM shows the hydraulic fracture propagation in layered rocks and explores the effects of the initial stress field, stiffness contrast, and inclination angle of the interface on fracture patterns. The proposed PFM can predict penetration, singly deflected, and doubly deflected fracture scenarios and can help guide and optimize the design of HF in naturally layered unconventional reservoirs in an elegant way.