Fluid-induced seismicity is observed in several engineering systems, including civil infrastructure projects, oil and gas recovery, and subsurface storage. There is a rising concern in the energy industry about the geohazard posed by induced and triggered seismicity. Understanding how induced earthquakes begin requires a firm grasp of the nucleation process, which is an important and open question, especially in heterogeneous environments. In this work, we examine the influence of the pressure distribution on the nucleation length by adjusting the injection pressure to establish a heterogeneous stress profile along the fault. A novel time-step controller is implemented to detect the onset of fracture rupture and nucleation, should they occur. Combining discretization error and Coulomb failure considerations, the controller automatically resolves dynamic rupture with allowable precision. The model offers a solution in situations where the theoretical nucleation length estimates cannot accommodate heterogeneity. The controller is implemented in a posteriori form in a mixed discretization scheme. The numerical scheme couples an extended finite element method (XFEM) for poromechanics and the embedded discrete fracture model (EDFM) for multiphase flow. An implicit Newmark time integration is used to approximate inertial mechanics, and the slip-weakening friction model is incorporated to simulate the contact tractions. Our numerical experiments show that the shape of the pore pressure contours running along the fault affects the nucleation length. Specifically, smaller pressure field curvature appears to deteriorate the accuracy of the theoretical estimates.
The nucleation process is strongly influenced by the physical properties of the fault, such as its frictional behavior and the normal stress acting on it (Dieterich, 1978; Okubo and Dieterich, 1984; Ohnaka and Shen, 1999). Reported theoretical and numerical efforts have quantified the aspects of the nucleation process under ideal conditions. A particular focus is the derivation of an instability criterion for slip-weakening or rate-and-state friction models (e.g., Campillo and Ionescu, 1997; Favreau and Ionescu, 1999; Uenishi and Rice, 2003; Rubin and Ampuero, 2005; Ampuero and Rubin, 2008; Kaneko and Ampuero, 2011; Latour et al., 2013; Gvirtzman and Fineberg, 2021). As a critical instability criterion for initiating seismic nucleation, the theoretical nucleation length is derived based on linear stability analysis (LSA) assuming a pre-existing crack. Such analyses consider various factors such as mechanical properties, friction coefficients, and normal stress. After the size of the slipping area reaches the nucleation length, a seismic event occurs, and the dynamic rupture along the fault expands. A commonly used theoretical value for the nucleation length in the slip-weakening friction model from Uenishi and Rice (2003) is calculated in a homogeneous linear-elastic field intersected by a fault. The model assumes a uniform normal stress field along the fracture and a symmetric shape of the shear stress profile along the fault. In practical settings, significant complexity, including spatial and temporal heterogeneity and geological structure, can perturb the pore pressure distribution from ideal symmetry. Despite the importance of this process, there are only a handful of comprehensive experimental observations of the nucleation process dynamics under general conditions, such as with varying injection rates (Ji et al., 2022) or periodically heterogeneous interfaces (Gounon et al., 2022). In light of this, we intend to investigate the effects of pore pressure distribution on the local stress along a fracture and its subsequent influence on nucleation length. This investigation can provide significant insights into earthquake mechanisms.
