Peridynamic simulation on hydraulic fracture propagation in shale formation

• A modified BB-PD theory is proposed and fluid–solid coupling model is established. • A new fracture criterion is developed for the modified BB-PD theory. • The crack propagation of hydraulic fracturing in bedding shale is numerically simulated. • Horizontal stress and approach angle heavily affect the generation of fracture network. The inhomogeneity of shale reservoirs, bedding properties and in-situ stress make crack propagation paths complex and diverse in hydraulic fracturing. However, the simulations on hydraulic fracture propagation in shale gas reservoirs still require an effective alternative numerical method. In this paper, a peridynamic (PD) fluid–solid coupling model was developed for the numerical simulation on the hydraulic fracturing process in bedding shale formation. Firstly, a modified bond-based peridynamic (BB-PD) theory was formulated by introducing normal bond, tangential bond and pressure bond. This removes the limitation of classical BB-PD theory on Poisson's ratio. Secondly, a fluid–solid coupling model was established by combining the modified BB-PD theory with pressure driven fluid transport in porous medium. Thirdly, a fracturing criterion for the modified BB-PD theory was derived from energy conservation. Fourthly, the PD fluid–solid coupling model was numerically discretized and verified by three-point bending tests on shale beam. Their accuracy was further checked through the Terzaghi's consolidation problem. Finally, numerical simulations were conducted to explore the generation of hydraulic fracturing induced fracture network in bedding shale formation under different dip angles and horizontal stress ratios. The simulation results showed that the horizontal stress ratio has a greater effect on fracturing pressure, and the dip angle plays a crucial role in the shape of fracture network. The increase of horizontal stress ratio leads to the increase of fracturing pressure.