Influence of Increasing Mean Stress on Fatigue Properties of Shale during Pulsating Hydraulic Fracturing

Abstract

During pulsating hydraulic fracturing (PHF), reservoir rock can be subjected to constant amplitude, constant mean stress (CACMS) cyclic loading or constant amplitude, increasing mean stress (CAIMS) cyclic loading. The influence of increasing mean stress on rock fatigue strength, fatigue lifetime, fatigue damage, and energy evolution of shale is rarely investigated, and which type of cyclic loading is more efficient for PHF has not been determined and demonstrated. In this Article, a series of uniaxial compression tests under these two types of cyclic loading are first conducted. A fatigue lifetime model for CAIMS is established. The shale strength and fatigue lifetime for CACMS and CAIMS are then compared. Their differences are explained by their dissipated energy density evolution and damage evolution. Finally, a nonlinear damage accumulation model to predict damage evolution for CAIMS cyclic loading is proposed. It is suggested that CAIMS is a better cyclic loading type when its amplitude is higher than 30% UCS (uniaxial compressive strength) of rock. This provides a meaningful amplitude threshold for CAIMS parameter optimization in the PHF construction. In this case, compared with CACMS cyclic loading, CAIMS cyclic loading significantly decreases the shale strength by up to 20% UCS and the fatigue lifetime from over 500 to 9. Different from an inverted-S-shaped damage evolution for CACMS cyclic loading, damage evolution for CAIMS cyclic loading exhibits a monotonic increasing trend. The damage variable growth rates of CACMS and CAIMS both show a three-stage trend: (1) their growth rates both decrease; (2) the growth rate for CACMS remains stable, while for CAIMS its growth rate slowly increases; and (3) their growth rates both increase sharply. Correspondingly, the dissipated energy density evolutions for CACMS and CAIMS show a similar three-stage trend. It can be concluded that during the second stage, for CAIMS microfractures and plastic deformation inside specimens are developed and accumulated more and faster than those for CACMS cyclic loading. This explains the phenomenon that the fatigue lifetime and strength of CAIMS cyclic loading are less than those of CACMS. The nonlinear damage accumulation model proposed in this Article can well fit experimental results. This model can be used for accurately describing reservoir rock mechanical property degradation during hydraulic fracture simulation induced by PHF.