In this work, the fracture propagation in a homogeneous poroelastic rock is considered. A two-dimensional poroelastic displacement discontinuity method is developed and used to model the fracture propagation and to calculate stress and pore pressure distributions around the crack. The model can accurately calculate very short time (undrained) and long time (drained) solutions. A poroelastic crack tip element is also developed and implemented to accurately compute the stress intensity factors at the crack tips. The maximum principal stress criterion is used to predict the crack propagation path. Numerical experiments are carried out to study fracture propagation trajectories compared with elasticity solutions. The numerical results indicate that the fracture growth under undrained condition does not show distinctive differences because the crack growth is so fast that the pore pressure diffusion effect is negligible. However, the fracture grows to the different direction under drained condition due to the impact of pore pressure loading.

Hydraulic fracturing has become one of the major technologies in oil industry for the stimulation of the petroleum reservoirs. Numerous numerical models have been developed to simulate this process for the last decades, but they typically assume that the rock is just an elastic medium. However, in many situations, the rock can be regarded as a poroelastic medium consisting of a fluid saturated matrix. Therefore, the coupling between fluid flow and rock deformation should be considered. In this paper, 2D time-dependent poroelastic displacement discontinuity method is developed to simulate the fracture propagation for both undrained and drained conditions. A special crack tip displacement discontinuity element is used to accurately compute the stress intensity factors. The maximum principal stress criterion to predict the direction of crack growth states that it will occur in a direction perpendicular to the maximum principal stress.

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