A Numerical Method for Fracture Crossing Based on Average Stress Levels

Due to the complexity of the interaction between hydraulic fractures (HFs) and natural fractures (NFs), several different interaction behaviours (arrest/cross/offset) may occur, according to hydraulic fracturing experiments. The existing analytical criteria cannot accurately describe this interaction process and predict the interaction behaviours by adopting several simple assumptions. An innovative numerical method combining strength and energy is proposed to determine the critical average stress at the most likely re-initiation position along the NF. The critical average stress for the HF crossing can be calculated by averaging the stresses around the fracture re-initiation point when the NF does not open and slip and simultaneously satisfying the energy criterion. Then, the proposed numerical method is incorporated in an extended finite element method (XFEM) scheme, in which the friction and contact of the NF are solved by a penalty function method. The numerical results suggest that the average stress can be numerically calculated and used to predict the HF crossing behaviour. The varying trends of the required maximum confining stress with respect to the coefficient of friction obtained by the proposed numerical method agree well with those predicted by the R-P and ER-P criteria. In addition, the proposed average stress method can quantitatively predict the crossing behaviour in the presence of slippage and opening after the HF terminates at the NF.