Modeling Nonlinear Diffusion in Fractured Rock With Deformable Fractures and Applications To Injection Induced Seismicity

In fractured rock, the hydraulic and mechanical properties of the fractures are extremely sensitive to fluid pressure and other perturbations. Although the general problem of hydromechanical coupling in fractured rock requires a simultaneously coupled solution of the pressure and stress fields, a partially coupled solution employing pressure-dependent fracture properties (with a time-invariant stress field) is still insightful. Here we present a model for hydromechanical coupling in fractured rock, implemented within the general-purpose finite element solver FEniCS. The model allows representation of a discrete fracture network (DFN) within a rock mass. Fracture aperture and permeability are allowed to vary with fluid pressure, according to the Bandis constitutive model. Pressure diffusion is permitted in the fractures and rock matrix, including hydraulic interactions between them. We present applications of the model to injection-induced seismicity (IIS) where we attempt to replicate a general seismic cloud dataset – providing insights into how the DFN structure and rock type lead to certain spatial-temporal patterns in induced seismic events. Using a frozen background stress field, seismic events are identified with the Mohr-Coulomb failure criteria. This approach to modeling pressure diffusion in the context of IIS improves over uncoupled approaches that typically only model diffusion (most commonly linear diffusion, with some previous works allowing for nonlinear diffusion) in an equivalent porous medium.