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The simulation of fluid‐driven fracture propagation in a porous medium is a major computational challenge, with applications in geosciences and engineering. The two main families of modeling approaches are those models that represent fractures as explicit discontinuities and solve the moving boundary problem and those that represent fractures as thin damaged zones, solving a continuum problem throughout. The latter family includes the so‐called phase field models. Continuum approaches to fracture face validation and verification challenges, in particular grid convergence, well posedness, and physical relevance in practical scenarios. Here we propose a new quasi‐static phase field formulation. The approach fully couples fluid flow in the fracture with deformation and flow in the porous medium, discretizes flow in the fracture on a lower‐dimension manifold, and employs the fluid flux between the fracture and the porous solid as coupling variable. We present a numerical assessment of the model by studying the propagation of a fracture in the quarter five‐spot configuration. We study the interplay between injection flow rate and rock properties and elucidate fracture propagation patterns under the leak‐off toughness dominated regime as a function of injection rate, initial fracture length, and poromechanical properties. For the considered injection scenario, we show that the final fracture length depends on the injection rate, and three distinct patterns are observed. We also rationalize the system response using dimensional analysis to collapse the model results. Finally, we propose some simplifications that alleviate the computational cost of the simulations without significant loss of accuracy.

Earthquake ruptures in poroelastic media involve a suite of complex phenomena arising from stick‐slip frictional instabilities and thermo‐hydromechanical couplings. In this study we propose a fully implicit, time‐adaptive, and monolithically coupled finite element model to simulate dynamic earthquake sequences in poroviscoelastic media. We consider a Kelvin‐Voigt viscoelastic material and characterize the impact of inertial effects on injection‐induced earthquakes. We present, for the first time, dynamic simulations of ruptures in rate‐and‐state faults in poroelastic media. Our simulations resolve the full earthquake cycle, including the interseismic, spontaneous earthquake nucleation, and dynamic rupture phases. We compare dynamic simulations with quasi‐dynamic ones, in which inertial effects are neglected and the slip singularity is resolved through a radiation damping approximation. Viscous dissipation models the physical process of seismic wave attenuation: As viscous damping increases, the patch size and the maximum fault slip become smaller, hence decreasing the expected earthquake magnitude. From a computational perspective, viscoelasticity helps avoid spurious high‐frequency oscillations during wave propagation. By including inertial effects, the dynamic model accounts for transient fluctuations of pressures and solid stresses during rupture, which are neglected in the quasi‐dynamic approach. Understanding these transient perturbations may shed light on the role of pore pressure in the mechanism of dynamic earthquake triggering. The poroviscoelastic dynamic approach is a good compromise between the inviscid, fully dynamic model, and the quasi‐dynamic one. A small amount of viscous damping allows us more efficient calculations, while preserving the most relevant features of dynamic ruptures, in particular slip velocities, accumulated slip, and seismic moment released.

Propagation of fluid‐driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low‐permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi‐static phase field formulation for modeling fluid‐driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. The excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid‐driven fracture.

Changes in pore pressure due to the injection or extraction of fluids from underground formations may induce potentially damaging earthquakes and/or increase the sensitivity of injection sites to remote triggering. The basic mechanism behind injection‐induced seismicity is a change in effective stress that weakens a preexisting fault. The seismic potential of a given fault is controlled by the partitioning between seismic and aseismic slip events, which emerge as a manifestation of stick‐slip instabilities. Through fully coupled hydromechanical simulations, with fault frictional contact described by the Dieterich‐Ruina “aging” law, we investigate the evolution of slip due to pore pressure increase in an underground injection model. For the same flow conditions and rock mechanical properties, different constitutive parameters lead to a variety of stick‐slip patterns, ranging from stable sliding or a sequence of many small slip events, to a single, larger coseismic event after significant aseismic slip has occurred. Our results suggest that good characterization of fault frictional properties and coupled geomechanical simulations are essential to assess the seismic hazard associated with underground flow processes.