A Comprehensive Model of a Hydraulic Fracture Interacting with a Natural Fracture: Analytical and Numerical Solution

In this paper, a comprehensive model combining analytical and numerical solution has been developed to study the interaction between a hydraulic fracture (HF) and a natural fracture (NF). A new analytical solution is presented to analyze the interaction mechanism with consideration of fluid lag and stress singularities near the HF tip, and to predict whether the HF crosses the NF when the propagating tip reaches the interface and the fluid front remains farther back. A new numerical solution based on the displacement discontinuity method and finite-volume method is derived to solve the problem of coupled rock deformation, fluid transport, stress interference, interface slipping, and opening, and to investigate the interaction between an HF and an NF after the fluid front reaching the interface. Based on the comprehensive model, sensitivity analyses of key influence parameters are implemented. The analyses indicate that the HF tends to cross the NF under conditions of high principal stress difference, high intersection angle, high interfacial friction, high injection rate, high fracturing fluid viscosity, and low initial conductivity of the NF. Moreover, the morphology of HF is significantly affected by two engineering parameters, the injection rate and the fracturing fluid viscosity. The same value of the product of these two parameters results in the same HF morphology at the times of the same injected fluid volumes. The new comprehensive model is validated with published analytical and numerical criterions and laboratory tests.