• Energy Research

Abstract The concept of material or configurational forces, albeit not new, is one of those innovations in theoretical mechanics that has struggled to reach the success of wide-spread acceptance, or even familiarity. Perhaps, one reason for this is to be found in the few available introductory examples or in the non-trivial physical-mathematical approach often taken to establish this concept, although by no means more complex than other treatments in non-linear continuum mechanics. With this work we aim at contributing to the dissemination of configurational mechanics concepts by guiding the reader through an introductory analytical example step by step and comparing it to numerically obtained results. The numerical model is solved with OpenGeoSys (OGS-6), an open-source, C++-based, object-oriented finite element platform for the thermo-hydro-mechanical analysis of coupled processes in fractured porous media. In the spirit of the open-source philosophy, and to enable the readers to reproduce the example themselves, both the source code and the input files are available online. The example highlights—in a simple and intuitive manner—several insightful aspects related to configurational mechanics.

AbstractContrasting deformation mechanisms precede volcanic eruptions and control precursory signals. Density increase and high uplifts consistent with magma intrusion and pressurization are in contrast with dilatant responses and reduced surface uplifts observed before eruptions. We investigate the impact that the rheology of rocks constituting the volcanic edifice has on the deformation mechanisms preceding eruptions. We propose a model for the pressure and temperature dependent brittle-ductile transition through which we build a strength profile of the shallow crust in two idealized volcanic settings (igneous and sedimentary basement). We have performed finite element analyses in coupled thermo-hydro-mechanical conditions to investigate the influence of static diking on the local brittle-ductile transition. Our results show that in active volcanoes: (i) dilatancy is an appropriate indicator for the brittle-ductile transition; (ii) the predicted depth of the brittle-ductile transition agrees with the observed attenuated seismicity; (iii) seismicity associated with diking is likely to be affected by ductile deformation mode caused by the local temperature increase; (iv) if failure occurs within the edifice, it is likely to be brittle-dilatant with strength and stiffness reduction that blocks stress transfers within the volcanic edifice, ultimately damping surface uplifts.

Abstract Failure in brittle rock happens because micro-cracks in the crystal structure coalesce and form a localized fracture. The propagation of the fracture is in turn strongly influenced by dissipation in the fracture process zone. The classical theory of linear elastic fracture mechanics falls short in describing failure when the dissipation in the fracture process zone is non-negligible; thus, a non-linear theory should be employed instead. Here we present a study in which we explore the characteristics of the fracture process zone in granite. We have combined fracture tests on Adelaide black granite with acoustic emission detection and finite element analyses by using a non-local integral plastic-damage constitutive theory. We have further employed the theory of configurational mechanics to support our interpretation of the evolution of the fracture process zone with strong energy-based arguments. We demonstrate that the size of the fracture process zone is non-negligible and dissipative phenomena related to micro-cracking play an important role. Our results indicate this role should be assessed case by case, especially in laboratory-sized analyses, which mostly deflect from theories of both size-independent plasticity and linear elastic fracture mechanics. When strong non-linearities occur, we show that fracture energy can be correctly computed with the help of configurational mechanics and that complex numerical simulation techniques can substantially facilitate the interpretation of experiments designed to highlight the dominant physical mechanisms driving fracture.

AbstractIn every tight formation reservoir, natural fractures play an important role for mass and energy transport and stress distribution. Enhanced Geothermal Systems (EGS) make no exception, and stimulation aims at increasing the reservoir permeability to enhance fluid circulation and heat transport. EGS development relies upon the complex task of predicting accurate hydraulic fracture propagation pathway by taking into account reservoir heterogeneities and natural or preexisting fractures. In this contribution, we employ the variational phase‐field method, which handles hydraulic fracture initiation, propagation, and interaction with natural fractures and is tested under varying conditions of rock mechanical properties and natural fractures distributions. We run bidimensional finite element simulations employing the open‐source software OpenGeoSys and apply the model to simulate realistic stimulation scenarios, each one built from field data and considering complex natural fracture geometries in the order of a thousand of fractures. Key mechanical properties are derived from laboratory measurements on samples obtained in the field. Simulations results confirm the fundamental role played by natural fractures in stimulation's predictions, which is essential for developing successful EGS projects.

AbstractDisplaced faults crossing the reservoir could significantly increase the induced earthquake frequency in geo‐energy projects. Understanding and predicting the stress variation in such cases is essential to minimize the risk of induced seismicity. Here, we adopt the inclusion theory to develop an analytical solution for the stress response to pore pressure variations within the reservoir for both permeable and impermeable faults with offset ranging from zero to the reservoir thickness. By analyzing fault stability changes due to reservoir pressurization/depletion under different scenarios, we find that (1) the induced seismicity potential of impermeable faults is always larger than that of permeable faults under any initial and injection conditions—the maximum size of the fault undergoing failure is 3–5 times larger for impermeable than for permeable faults; (2) stress concentration at the corners results in the occurrence of reversed slip in normal faults with a normal faulting stress regime; (3) while fault offset has no impact on the slip potential for impermeable faults, the slip potential increases with the offset for permeable faults, which indicates that non‐displaced permeable faults constitute a safer choice for site selection; (4) an impermeable fault would rupture at a lower deviatoric stress, and at a smaller pressure buildup than a permeable one; and (5) the induced seismicity potential is overestimated and the injectivity underestimated if the stress arching (i.e., the poromechanical coupling) is neglected. This analytical solution is a useful tool for site selection and for supporting decision making during the lifetime of geo‐energy projects.

The numerical treatment of propagating fractures as embedded discontinuities is a challenging task for which an analyst has to select a suitable numerical method from a range of options. Since their inception in the mid-80s, smeared approaches for fracture simulation such as non-local damage, gradient damage or more lately phase-field modelling have steadily gained popularity. One of the appeals of a smeared implicit fracture representation, the ability to handle complex topologies with unknown crack paths in relatively coarse meshes as well as multiple-crack interaction and multiphysics, is a fundamental requirement for the numerical simulation of hydraulic fracturing in complex situations which is technically more difficult to achieve with many other methods. However, in hydraulic fracturing simulations, not only the prediction of the fracture path but also the computation of fracture width and propagation pressure (frac pressure) is crucial for reliable and meaningful applications of the simulation tool; how to determine some of these quantities in smeared representations is not immediately obvious. In this study, two of the most popular smeared approaches of recent, namely non-local damage and phase-field models, and an approach in which the solution space is locally enriched to capture a strong discontinuity combined with a cohesive-zone model are verified against fundamental hydraulic fracture propagation problems in the toughness-dominated regime. The individual theoretical foundations of each approach are discussed and differences in the treatment of physical and numerical properties of the methods when applied to the same physical problems are highlighted through examples.