Three-dimensional Poroelastic Simulation of Hydraulic and Natural Fractures Using the Displacement Discontinuity Method

A three-dimensional fully-coupled poroelastic displacement discontinuity method is developed and used to analyze the temporal variation of opening and slip of a natural fracture in a reservoir in response to the sudden application of fluid pressure in the fracture surfaces. Numerical results show that a hydraulic fracture opens in an increasing manner with time as the rock moves towards a drained state under the applied stress. The applied pore pressure induces a time-dependent closure caused by the rock dilation. On the other hand, poroelastic analysis of a natural fracture subjected to shear shows that the fracture slip decreases with the time in response to a pore pressure-induced increase in the normal stresses on the joint. THEORY OF POROELASTICITY One of the main features of the deformation of fluidsaturated porous rock is its transient nature which is related to the presence of a fluid diffusion process, and is described by the linear theory of poroelasticity (Biot, 1941). Since the pioneering work of Biot, the theory of poroelasticity has been reformulated by a number of investigators, such as Rice and Cleary (1976), and Carroll (1980). The coupled constitutive equations of poroelastic material under isothermal conditions are (e.g., Rice & Cleary, 1976):