David Santillán

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

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.

Dam seepage analysis based on artificial neural networks: The hysteresis phenomenon

Seepage flow measurement is an important behavior indicator when providing information about dam performance. The main objective of this study is to analyze seepage by means of an artificial neural network model. The model is trained and validated with data measured at a case study. The dam behavior towards different water level changes is reproduced by the model and a hysteresis phenomenon detected and studied. Artificial neural network models are shown to be a powerful tool for predicting and understanding seepage phenomenon.

Phase Field Model of Hydraulic Fracturing in Poroelastic Media: Fracture Propagation, Arrest, and Branching Under Fluid Injection and Extraction

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.

Fluid-driven fracture propagation in heterogeneous media: Probability distributions of fracture trajectories

Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model. We model the mechanical response of the material as that of an elastic isotropic material with heterogeneous Young modulus and Griffith energy release rate, assuming that fractures propagate in the toughness-dominated regime. Our study shows that the variance and the spatial covariance of the mechanical properties are controlling factors in the tortuousness of the fracture paths. We characterize the deviation of fracture paths from the homogenous case statistically, and conclude that the maximum deviation grows linearly with the distance from the injection point. Additionally, fracture path deviations seem to be normally distributed, suggesting that fracture propagation in the toughness-dominated regime may be described as a random walk.

Stick‐slip dynamics of flow‐induced seismicity on rate and state faults

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.

On the Barriers to Adaption to Less Water under Climate Change: Policy Choices in Mediterranean Countries

Barriers and constraints to adapting water resources management to climate change in the Mediterranean region are analysed in this paper. First, we analysed the risks to the water resources sector derived from climate change. We then identified the main objective of water adaptation measures: ensuring there is enough water for food, for people, and for ecosystems. This implies visions about availability - being sufficient water -, accessibility - both physical and economic access -, and adequacy - being safe for ecosystems and human consumption. A portfolio of local and collective actions to adapt water management for agriculture to climate change in Mediterranean countries is presented. Adaptation strategies included improved efficiency, optimisation of governance, enhancement of participation, development of risk-based choices, and economic instruments. Finally, the paper categorised the constraints to implement the measures, give specific examples about these issues and also quantify their impact. When considering constraints and opportunities to implement these water management practices, any environmental policy regulating their adoption should be based on recommending the use of extension and training to local actors on the application of the practices.