Dynamic stress response in reservoirs stimulated by fluctuating fluid pressure during pulsating hydraulic fracturing

Determining the most effective scheme for fracturing operations depends on accurate calculations of reservoir stress. Traditional fracturing theories usually focus on stable fluid injection modes, which employ static assumptions in modelling and analysis. However, pulsating hydraulic fracturing (PHF) introduces fluctuating fluid pressure to stimulate reservoirs, which requires considering dynamic factors and exploring the dynamic stress response within the reservoir. Furthermore, reservoirs are often classified as homogeneous continuous or porous media materials, but the boundaries between these classifications are sometimes apparent. This paper investigated the development of both an elastodynamics model and a poroelastodynamics model for calculating dynamic stress responses during PHF. The staggered grid finite difference method addressed these models, with the outer boundary employing the perfectly matched layer (PML) method to simulate an infinite reservoir. The numerical simulation results were extensively verified and compared with analytical solutions, and the differences between various models and their relevant conditions were thoroughly analyzed. Analyzing fluid pressure fluctuation parameters revealed noteworthy insights into reservoir stress response characteristics. Results indicate that as the Biot coefficient and permeability increase, the disparities between the elastodynamics and poroelastodynamics models become prominent. In practical terms, high Biot coefficient or high permeability reservoirs necessitate using the poroelastodynamics model for accurate reservoir stress analysis. As the frequency of fluid pressure fluctuation increases, the amplitude of response of reservoir circumferential stress also increases, while the response amplitude of radial stress and fluid pressure decreases. These findings offer valuable theoretical guidance for parameter design in engineering applications during PHF.