An explicit peridynamics model for hydraulic fracturing in porous media

Purpose The purpose of this paper is to systematically investigate the hydraulic fracture branching phenomena in porous media under different loading conditions and the stepwise phenomenon. The effect of the pore pressure in hydraulic fracturing branching is studied, and more evidence for the stepwise phenomenon with the peridynamics approach is provided. Design/methodology/approach A fully coupled fluid-filled explicit peridynamics model is developed to simulate the complex evolution of crack branching and stepwise phenomena in saturated porous media. Based on the peridynamics theory, an explicit time integration scheme is used to solve the coupled equation system including rock deformation, fluid flow and fracture propagation. Using the proposed model, a series of peridynamic computational tests are performed to examine two common kinds of phenomena observed in hydraulic fracturing: the crack branching phenomenon and the stepwise phenomenon. Findings For crack branching phenomenon, the results obtained indicate that sufficient loading is required in order to initiate the crack branching process. Compared with the stress applied on crack surfaces condition, crack branching is more easily induced with the stress applied on boundaries. In addition, for the fluid-driven crack (stress applied on crack surfaces), the existence of pore pressure will depress the growth and branching of the crack. For stepwise phenomena, the results obtained indicate that the peridynamics is a promising tool to study the stepwise phenomenon. The stepwise phenomenon is more distinct under mechanical loading conditions due to the solid behaviour. A sudden jump or crack extension will happen when enough energy is accumulated in the hydraulic fracturing system. Research limitations/implications In this study, the explicit method is used, which means it is conditionally stable, and the critical time step needs to be decided. The reason to use the explicit method is for the study purpose; the explicit method is faster and has no need for matrix inversions. Originality/value This study helps to understand the effect of the pore pressure in hydraulic fracturing branching and provides more evidence for the stepwise phenomenon with peridynamics.