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Reliable reservoir characterization of the strata, fractures, and hydraulic properties is needed to determine the energy storage capacity of geothermal systems. We apply the state-of-the-art Physics-Informed Neural Networks (PINN) to model subsurface flow in a geothermal reservoir. A PINN can incorporate any physical laws that can be described by partial differential equations. We obtain a ground truth dataset by running a virtual pumping-well test in the numerical code “Code_Bright”. This model consists of a low-permeability rock matrix, intersected by high-permeability fractures. We approximate the reservoir permeability with an Artificial Neural Network (ANN) denoted by . Secondly, we model the fluid pressure evolution with the PINN by informing it about the experimental well-testing data. Since observation wells are sparse in space (only the injection well in our case), we feed into a hydraulic mass balance equation. The residual of this equation enforces the loss function of for random collocation points inside the domain. Our results indicate that the ANN is able to approximate even for a high permeability contrast. In addition, the successful interpolation of proves the PINN is a promising method for matching field data with physical laws. In contrast to numerical models PINNs shift the computational efforts toward the training, while reducing the resources needed for the forward evaluation. Nevertheless, training a 3D reservoir model can hardly be achieved on an ordinary workstation since the training data may include several millions of entries. In addition, computational costs increase due to the inclusion of multiphysics processes in the PINN. We plan to prepare the PINN model for training using parallelized GPUs to significantly increase the training speed of the ANNs.

Superhot geothermal environments with temperatures of approximately 400–500 °C at depths of approximately 2–4 km are attracting attention as new kind of geothermal resource. In order to effectively exploit the superhot geothermal resource through the creation of enhanced geothermal systems (superhot EGSs), hydraulic fracturing is a promising technique. Laboratory-scale hydraulic fracturing experiments of granite have recently demonstrated the formation of a dense network of permeable fractures throughout the entire rock body, referred to as a cloud-fracture network, at or near the supercritical temperature for water. Although the process has been presumed to involve continuous infiltration of low-viscosity water into preexisting microfractures followed by creation and merger of the subsequent fractures, a plausible criterion for cloud-fracture network formation is yet to be clarified. The applicability of the Griffith failure criterion is supported by hydraulic fracturing experiments with acoustic emission measurements of granite at 400 °C under true triaxial stress and at 450 °C under conventional triaxial stress. The present study provides, for the first time, a theoretical basis required to establish the procedure for hydraulic fracturing in the superhot EGS.

Geoenergies such as underground gas storage and energy storage, geothermal energy and geologic carbon storage are key technologies on the way to the foreseeable energy transition. The reservoir characterization in these projects remains challenging since predictive modeling approaches face limitations in identifying the spatial distribution of distinct lithologies and their hydro-mechanical properties from downwell testing procedures. Pumping tests are usually carried out to infer permeability, but offer only few observation points in space and require large extrapolation through inversion. The application of Physics Informed Neural Networks (PINN) offers a promising solution which can seamlessly incorporate field data, while enforcing the accordance with physical laws in the domain of study. This concept is implemented via two distinct loss terms for both the physical constraints and for the observational data in the loss function of an Artificial Neural Network (ANN). The physics-informed loss term contains a mass balance equation consisting of a storage and a diffusion component. The process is considered to be purely hydraulic and Darcy flow is assumed. The observational loss term compares the output of the ANN to a set of training data. This set consists of the system’s initial fluid pressure, as well as of a fluid pressure time series at the domain boundaries and at the borehole location. Preliminary results suggest that our PINN model is able to forecast the spatiotemporal fluid pressure distribution in a 2D domain for a variety of pumping test schemes. In this way, we give a first impression of the opportunities that PINN applications offer in the field of reservoir modeling.

Enabling a widespread exploitation of Enhanced Geothermal Systems (EGS) around the world by tapping into the heat trapped by the radioactive granites demands a better understanding of the fluid-induced seismicity associated with their stimulation. Induced seismicity occurs not only during hydraulic stimulation, but also after shut-in. The induced earthquakes of Mw > 3 at Basel and Mw = 5.5 at Pohang are two well-known examples that have caused a negative public perception on EGS. Here, we numerically compare the effect of bleed-off on the mitigation of post-injection seismicity for three stimulation schemes: constant rate, step rate and cyclic injection. We find that applying bleed-off in the post-injection phase significantly reduces the post-injection induced seismicity when compared to not applying bleed-off in all the injection schemes.

With the urgent necessity of geo-energy resources to achieve carbon neutrality, fluid injection and production in the fractured media will significantly increase. Applications such as enhanced geothermal systems, geologic carbon storage, and subsurface energy storage involve pressure, temperature, and stress changes that affect fracture stability and may induce microseismicity. To eventually have the ability to control induced seismicity, it is first necessary to understand its triggering mechanisms. To this end, we perform coupled thermo-hydro-mechanical (THM) simulations of cold water injection and production into a rock containing two fracture sets perpendicular between them. The permeability of fractures being four orders of magnitude higher than the one of the rock matrix leads to preferential pressure and cooling advancement, which induce stress changes that affect fracture stability. We find that the fracture set that is oriented favorably to undergo shear slip in the considered stress regime becomes critically stressed, inducing microseismicity. In contrast, the fracture set that is not favorably oriented for shear remains stable. These results contrast with those obtained for an equivalent porous media that does not explicitly include fractures in the model, which fails to reproduce the direction-dependent stability of fractures present in the subsurface. We contend that fractures should be directly embedded in the numerical models when inhomogeneities are of the spatial scale of the reservoir to enable reproducing the THM coupled processes that may lead to induced microseismicity., V.V. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program through the Starting Grant GEoREST (www.georest.eu (http://www.georest.eu)) under Grant agreement No. 801809. IDAEA-CSIC is a Centre of Excellence Severo Ochoa (Spanish Ministry of Science and Innovation, Grant CEX2018-000794-S, funded by MCIN/AEI/ 10.13039/501100011033). R.M. is thankful for the support from US DOE through CarbonSAFE Macon County Project DE-FE0029381. F.P. acknowledges funding from the European Union’s Horizon 2020 Research and Innovation Program through the Marie Skłodowska-Curie Individual Fellowship ARMISTICE under Grant agreement No. 882733.

Developing high-enthalpy geothermal systems requires a sufficiently permeable formation to extract energy through fluid circulation. Injection experiments above water’s critical point have shown that fluid flow can generate a network of highly conductive tensile cracks. However, what remains unclear is the role played by fluid and solid rheology on the formation of a dense crack network. The decrease of fluid viscosity with temperature and the thermally activated visco-plasticity in rock are expected to change the deformation mechanisms and could prevent the formation of fractures. To isolate the solid rheological effects from the fluid ones and the associated poromechanics, we devise a hydro-fracture experimental program in a non-porous material, polymethyl methacrylate (PMMA). In the brittle regime, we observe rotating cracks and complex fracture patterns if a non-uniform stress distribution is introduced in the samples. We observe an increase of ductility with temperature, hampering the propagation of hydraulic fractures close to the glass transition temperature of PMMA, which acts as a limit for brittle fracture propagation. Above the glass transition temperature, acoustic emission energy drops of several orders of magnitude. Our findings provide a helpful guidance for future studies of hydro-fracturing of supercritical geothermal systems.

In this study, we present results of an in situ stress state estimation for the Los Humeros geothermal field (Mexico) located in the eastern section of the Trans-Mexican Volcanic Belt. During more than 40 years of geothermal energy production, issues related to induced seismicity, reservoir depletion, subsidence, and wellbore stability have occurred in Los Humeros. The in situ stress tensor, being one of the major controls on the above-mentioned phenomena, remains highly uncertain. The high temperatures of the geothermal reservoir at Los Humeros, often exceeding the critical point of water, promote difficulties in performing in situ stress measurements. In this study, based on data commonly acquired from drilling operations from eleven high-temperature wells within the Los Humeros caldera, we constrain the in situ stress state of the geothermal field. For this purpose, we employ borehole observations including borehole breakouts, instances of fluid circulation loss, and injection tests. Results from this study indicate predominantly strike-slip regime with a strong reverse component and NE-SW acting maximum horizontal stress. Utilizing slip and dilation tendency analysis, permeability and seismic activity of major fault zones within the geothermal field could be aptly explained by the acting stress regime. The outcome of this study provides valuable insights into the in situ stress state of the Los Humeros caldera and supports the exploration of conventional and unconventional (i.e., supercritical) geothermal resources., This work was carried out within the framework of the GEMex (Cooperation in Geothermal energy research Europe-Mexico for development of Enhanced Geothermal Systems and Superhot Geothermal Systems) project, which received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No 727550. M.K. and E.H.S acknowledge funding from the German Federal Ministry of Education and Research (BMBF) and geomecon GmbHfor the 3DRuhrMarie (“FHprofUnt2016”) project. F.P. acknowledges funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Sklodowska-Curie Action ARMISTICE with grant agreement No. 882733.

Supercritical geothermal systems are appealing sources of sustainable and carbon-free energy located in volcanic areas. Recent successes in drilling and exploration have opened new possibilities and spiked interest in this technology. Experimental and numerical studies have also confirmed the feasibility of creating fluid conducting fractures in sedimentary and crystalline rocks at high temperature, paving the road towards Enhanced Supercritical Geothermal Systems. Despite their attractiveness, several important questions regarding safe exploitation remain open. We dedicate this manuscript to the first thermo-hydro-mechanical numerical study of a doublet geothermal system in supercritical conditions. Here we show that thermally-induced stress and strain effects dominate the geomechanical response of supercritical systems compared to pore pressure-related instabilities, and greatly enhance seismicity during cold water re-injection. This finding has important consequences in the design of Supercritical Geothermal Systems., The contribution of F.P. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number PA 3451/1-1 and by the GEMex project, which is supported by the European Union’s Horizon 2020 programme for Research and Innovation under grant agreement No 727550. V.V. acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme through the Starting Grant GEoREST, grant agreement No. 801809 (http://www.georest.eu). The contribution of W.W. is funded by the Advanced Earth System Modelling Capacity (ESM) project by the Helmholtz Association.

Fractures control fluid flow and the coupled geomechanical response of geological media in many geo-engineering applications. For instance, fractures dominate fluid flow and deformation in enhanced geothermal systems, underground radioactive waste repositories, and CO2 storage. Coupled thermo-hydro-mechanical processes in rock masses are a result of perturbations in the pore pressure, as in fluid injection and/or production, and/or temperature, as in cold fluid injection and disposal of radioactive waste. For example, fractures open as a result of pore pressure increase, which simultaneously increases permeability and reduces overpressure. Geo-engineering and geo-energy applications involve a large portion of rock masses that include several fractures. Numerical computations of coupled processes occurring in rock masses while considering a large number of fractures pose several challenges. In this study, we firstly focus on a simple problem to fully understand the hydro-mechanical behavior of a single fracture subjected to a constant injection flow rate. We use the FEM software CODE_BRIGHT, which solves the thermohydro- mechanical governing equations in a fully coupled way. Since standard FEM can solve equations in continuum media, we investigate the behavior of a single fracture by analyzing the hydro-mechanical parameters that control the fracture response in a continuum fashion. However, simulating fractures with the real aperture is not simply feasible, hence, we search the equivalent properties of thicker fractures that are more feasible to be discretized in large-scale models with several fractures.

Geoenergy and geoengineering applications usually involve fluid injection into and production from fractured media. Accounting for fractures is important because of the strong poromechanical coupling that ties pore pressure changes and deformation. A possible approach to the problem uses equivalent porous media to reduce the computational cost and model complexity instead of explicitly including fractures in the models. We investigate the validity of this simplification by comparing these two approaches. Simulation results show that pore pressure distribution significantly differs between the two approaches even when both are calibrated to predict identical values at the injection and production wells. Additionally, changes in fracture stability are not well captured with the equivalent porous medium. We conclude that explicitly accounting for fractures in numerical models may be necessary under some circumstances to perform reliable coupled thermohydromechanical simulations, which could be used in conjunction with other tools for induced seismicity forecasting., A.Z. acknowledges the financial support received from the “Iran's Ministry of Science, Research and Technology” (PhD students' sabbatical grants) for visiting IDAEA‐CSIC. The contribution of F.P. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number PA 3451/1‐1. R.M. is thankful for the support from US DOE through Carbon SAFE Macon County Project DE‐FE0029381. V.V. acknowledges funding from the Spanish National Research Council (CSIC) through the Intramural project 201730I100 and from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program through the Starting Grant GEoREST (www.georest.eu) (Grant agreement No. 801809). IDAEA‐CSIC is a Center of Excellence Severo Ochoa (Spanish Ministry of Science and Innovation, Project CEX2018‐000794‐S). The authors declare no conflict of interest.

Superhot geothermal environments with temperatures of approximately 400-500︒C at depth of approximately 2-4 km are expected as a new geothermal energy frontier. In order to efficiently exploit the superhot geothermal resources, fracture systems are necessary as flow path of working fluid. Hydraulic fracturing is a promising technique because it is able to create a new fracture system or enhance the permeability of preexisting fracture system. Laboratory-scale hydraulic fracturing experiments of granite have demonstrated the formation of densely distributed network of permeable fractures throughout the entire rock body at or near the supercritical temperature for water. Though the process has been presumed to involve continuous infiltration of low-viscosity water into preexisting microfractures followed by creation and merger of the subsequent fractures, plausible criterion for the fracturing is yet to be clarified. The possibility that the Griffith failure criterion is available to predict the occurrence of fracturing was shown by hydraulic fracturing experiments with acoustic emission measurements of granite at 400︒C under true triaxial stress. The present study provides a theoretical basis required to establish the procedure for hydraulic fracturing in superhot geothermal environment.

Calderas are major volcanic features with large volcanic and seismic hazards. They also host diverse microbiota, provide heat, energy, mineral and economic benefits. Despite their scientific and socio-economic importance, we still do not completely understand calderas and the interactions between volcanism, tectonism, fluid circulation and the deep biosphere because in-situ and subsurface observations are sparse.The Okataina Volcanic Centre (OVC) in Aotearoa New Zealand, is one of two active giant calderas of the Taupō Volcanic Zone within the rapidly extending continental intra-arc Taupō Rift. This superb natural laboratory has: 1) numerous past eruptions of varied size and style, 2) documented co-eruptive earthquakes, 3) vigorous hydrothermal manifestations, 4) diverse microbial communities in hot springs but unknown in the subsurface.We propose to establish a scientific drilling programme at the OVC to address:What are the conditions leading to volcanic eruptions; and volcano-tectonic feedbacks in intra-rift calderas? What controls fluid circulations in active calderas/rift regions? Does subsurface microbial community composition vary with tectonic and/or volcanic activity? High temperatures complicate drillhole design, restrict data collection and prevent exploration of the biosphere. By targeting the cooler parts of the caldera, this project will use conventional engineering to maximise sampling (drill cores and fluids), downhole logging and establish long-term observatories.Two preliminary drill targets are suggested: (1) in the centre of the caldera; (2) through the caldera margin. Drill data will provide a comprehensive record of past activity, establishing eruption frequency-magnitude relationships and precursors. Combined with well-known fault rupture history, the relative timing of tectonic and magmatic activity will be untangled. Drill data will unravel the relationships between the groundwater and hydrothermal systems, magma, faults and stress, informing thermo-hydro-mechanical regional caldera models with findings applicable worldwide. Drill cores and a dedicated fluid sampler triggered by nearby earthquakes will reveal the composition, function and potential change of microbial activity in response to rock and fluid variations.The programme is informed by indigenous Māori, regulatory authorities and emergency managers to ensure scientific, cultural, regulatory and resilience outcomes. The programme will underpin 1) community resilience to volcanic and seismic hazards; 2) sustainable management of groundwater and geothermal resources, and 3) understanding of subsurface microbial diversity, function and geobiological interactions. At these early stages of planning, we invite the scientific community to contribute to the concept of this project in the exceptional OVC settings and strengthen linkages with other ongoing research and scientific drilling programmes.

Geologic carbon storage is needed to reach carbon neutrality and eventually achieve negative emissions. In the classical concept of storing CO2 in deep sedimentary aquifers, supercritical CO2 has a lower density than the resident brine. CO2 is therefore buoyant and the safety and effectiveness of the storage concept rely on the caprock sealing capacity to prevent CO2 leakage. To reduce the risk of CO2 leakage and widen the CO2 storage options, we propose an innovative concept that consists in injecting CO2 in reservoirs where the temperature and pressure of the resident brine are above the critical point ( 373.95 ºC and 22.064 MPa for pure water). At such conditions, which can be found at depths between 3 to 5 km in volcanic areas, CO2 is denser than the resident water and thus, sinks. The sinking tendency reduces the risk of CO2 leakage to the surface even in case of damaged or absent caprock. CO2 storage in supercritical reservoirs can potentially become an additional option to the existing storage concepts aimed at significantly reduce CO2 emissions. We estimate that every 100 wells drilled into supercritical reservoirs could store between 50 to 500 Mt/yr of CO2.

Displaced 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., H. Wu acknowledges the financial support received from the AGAUR (Generalitat de Catalunya) through the ‘‘grant for universities and research centers for the recruitment of new research personnel (FI‐2019)''. V. Vilarrasa acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme through the Starting Grant GEoREST (www.georest.eu), Grant agreement no. 801809. V. Vilarrasa also acknowledges support by the Spanish Ministry of Science and Innovation (Project CEX2018‐000794‐S). S.D. Simone acknowledges financial support from the SAD2018 project funded by the Brittany Region and from ANR LabCom Project eLabo ANR‐17‐LCV2‐0012. M. Saaltink acknowledges financial support from the “HEATSTORE” project (170153–44011), which has been subsidized through the ERANET Cofund GEOTHERMICA (Grant agreement no. 731117), from the European Commission and the Spanish Ministry of Science, Innovation and Universities (PCI2018‐092933). F. Parisio acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number PA 3451/1‐1. The authors thank Tomas Aquino for his advice on the integral solutions.

Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy‐driven leakage risk. Supercritical reservoirs are found at drilling‐reachable depth in volcanic areas, where high pressure (p > 21.8 MPa) and temperature (T > 374°C) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50–500 Mt yr−1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach., Key Points We propose a novel geologic carbon storage concept that reduces the buoyancy‐driven CO2 leakage riskBy injecting CO2 in reservoirs where the resident water stays in supercritical conditions, CO2 sinks because it is denser than pore waterSupercritical reservoirs are found at relatively shallow depths between 3 and 5 km in deep volcanic areas

Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at ...

G eological media is envisioned as a strategic resource to store large volumes of CO2 and mitigate climate change. Geo-energy applications, such as geologic carbon storage, geothermal energy, and subsurface energy storage, involve injection and extraction of fluids that cause pressure diffusion. Pore pressure changes may induce seismicity, especially in faults that intersect the injection formation or are hydraulically connected with it. We numerically study with finite element analysis of coupled hydro-mechanical conditions how fault stability is affected by fluid injection into a porous aquifer that is overlaid and underlain by low permeability clay-rich formations. We model a layered sedimentary basin with alternating soft and low permeability with stiff and high permeability formations and include the crystalline basement at the bottom. Additionally, a low permeability steep fault, whose offset ranges from zero to the reservoir thickness, crosses the system. We consider a normal faulting stress regime typical of extensional environments. Simulation results show that the reservoir pressurization as a result of fluid injection causes significant stress changes around the fault that affect its stability. The stress changes depend on the stiffness of the rock juxtaposed to the pressurized reservoir. If there is no offset, the rock is stiff on both sides of the fault, inducing a homogeneous horizontal total stress increase along the thickness of the reservoir. As a result, the deviatoric stress becomes smaller and the induced seismicity potential is low. As the fault offset increases, some part of the base rock gets juxtaposed to the pressurized reservoir. The soft base rock deforms more than the reservoir rock in response to the reservoir expansion, inducing a lower horizontal total stress. Thus, fault stability reduces when the pressurized reservoir rock is juxtaposed with the softer base rock. This finding shows that the induced seismicity potential may increase with the fault offset.

Material instabilities are critical phenomena which can occur in geomaterials at high stress and temperature conditions. They generally result in the degradation of the microstructure organisation, ultimately leading to material failure. These phenomena are relevant to a large variety of geoscientific and geotechnical applications including earthquake physics, fault mechanics, successful targeting of unconventional georesources and mitigation of induced seismicity. Quantifying and predicting the onset of material degradation upon instability remains a major challenge due to our lack of understanding of the physics controlling the behaviour of porous rocks subject to high temperature and pressure conditions.In the laboratory, rocks gradually transition from a time-independent brittle behaviour to a transient semi-brittle, semi-ductile behaviour upon an increase in pressure and/or temperature. Furthermore, even when subject to constant subcritical stress conditions rocks have been observed to macroscopically fail due to growth of subcritical processes such as stress corrosion. Brittle creep is a phenomenon observed on a variety of rock types (volcanic and sedimentary) and shows a high sensitivity to temperature and stress conditions. In the field, such subcritical transient processes are difficult to detect and can jeopardise the safety of geothermal projects. Transient failure mechanisms in the reservoir have set back geotechnical projects through induced seismicity occurring days or even weeks after stimulation shut in as observed at the Basel geothermal site in Switzerland or at the Pohang geothermal project in South Korea. These observations demonstrate how conventional techniques fail at describing the physics responsible for fault reactivation, which is controlled by dynamic processes resulting from transient multiphysics coupling.In this contribution, we detail the theory and procedure to develop a constitutive model for rate-dependent damage poro-elasto-plastic material behaviour suitable for porous rocks. To allow for a generic framework for assessing geomaterials instabilities, this model incorporates the potential for microstructure degradation and a path- and rate-dependence. To that purpose, we rely on thermodynamic principles to derive in the frame of the hyperplasticity theory a coupled hydro-mechanical rate-dependent plasticity and damage rheology. We present numerical examples of this new constitutive model at the laboratory scale using experimental data on brittle creep in sandstones and discuss the implications upon upscaling at the reservoir and lithosphere scale.

Dike propagation in the earth crust, often a precursor of major volcanic eruptions, usually generates a seismic response by activating small fractures (micro-seismicity) and larger existing faults (greater magnitude events). The conceptual interpretation is essentially viewed as a fluid-driven fracture advancing in the rock mass and altering the existing state of stress in its surroundings. Because dikes are filled with high-temperature magma, which can exceed 1000 °C, it is likely that they will alter the initial temperature while propagating. The temperature increase can generate pore water pressurization as a function of its rate of change. Pore pressure in turns diffuses through the porous and fractured rock, altering the initial effective stress state. Additionally, hot dikes also generate thermally-induced stresses. The stress changes in the rock are therefore affected by temperature and pore pressure as much as they are by mechanically induced fracturing. In this contribution, we have studied the coupled processes of temperature, pore pressure and deformation induced by diking. We have employed finite element analyses to solve the boundary value problem of a progressing dike. The main goal is to highlight the effects generated by temperature increase in the rock surrounding the dike. Thermal pressurization depends on heat loading rate, hence on diking advancement speed, and on surrounding rock permeability. Rock permeability also controls the diffusion of pore pressure, the size of the area affected by pressurization and the magnitude of pressurization. Results from numerical models show that positive Coulomb stress changes (instabilities) can be triggered by thermal effects at several hundred meters away from the dike, implying that even non-advancing dikes could generate a seismic response. We prove the importance of accounting for thermo-poromechanical effects in studying the seismic response during diking, a widely unexplored field which could have major implications for the assessment of volcanic eruptions’ precursory signals.

In 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.

Geothermal systems, including hydrothermal systems [1], enhanced geothermal systems (EGS) [2], and superhot or supercritical systems [3–5], are receiving an increasing interest because they provide carbon-free energy that is necessary to shift the current dependency on fossil fuels and thus significantly reduce CO2 emissions to the atmosphere [6]. Geothermal energy can potentially provide continuous energy output without daily or seasonal fluctuations—a strong advantage when compared to other renewable sources—and negative emissions if CO2 is used as the working fluid [7–9]. However, the deployment of geothermal systems is being hindered by insufficient permeability of the reservoir rock [10], excessive induced seismicity during reservoir stimulation [11], and geochemical reactions accelerated by high temperature that lead to corrosion and scaling [12]. To overcome these challenges, interdisciplinary approaches that investigate relevant processes occurring during geothermal energy exploitation are necessary. The focus of this special issue is on geomechanical aspects of geothermal systems, including coupled processes occurring in multiphase systems, experimental characterization of rock and inelastic deformation that may induce seismicity, and geochemistry of geothermal systems. This special issue compiles the most recent advances in geothermal energy and combines the complex interactions between geomechanics, fluid flow, and geochemical reactions., The guest editors thank all the authors of this special issue and their perseverance during the publication process. We also thank the many anonymous reviewers who helped to evaluate and contributed to these papers. The guest editors would also like to acknowledge their sources of funding. V.V. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme through the Starting Grant GEoREST, grant agreement No. 801809 (http://www.georest.eu). R.M. is thankful for the support provided by the UIUC-ZJU Research Collaboration program (grant # 083650). The contribution of F.P. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number PA 3451/1-1.

Geothermal energy is a fundamental piece of the puzzle in the carbon-free energy transition necessary to mitigate adverse effects of climate change. In this context, so-called supercritical geothermal systems (where resident brine is above its critical point) can reach a power output of up to 50 MW per-well and are becoming a reality thanks to the research effort of the international community. Supercritical systems are inherently complex because of fluid and solid rheology and because of the non-linear couplings involved between pore pressure, temperature and deformation in the porous and fractured rock. In this contribution, we have performed finite element analyses of coupled thermo-hydro-mechanical (THM) conditions in a supercritical geothermal system. The formulation employed includes a porosity-dependent permeability relationship that is derived through mass balance equations of the solid skeleton. The equations of state of water are based on IAPWS standards and span the whole range of temperature and pressure of interest in supercritical geothermal systems. We have analyzed an injectionproduction doublet scenario at 5.5 km depth, where the two wells are spaced 500 m apart and a major fault lies between them. When injecting in isothermal conditions, because of water mobility of the supercritical phase is higher than the liquid phase, minor perturbations are observed in the major fault. Seismicity increases rapidly following a pressure-diffusion response and only microseismicity is expected as the stress in the major fault shows minor changes. On the contrary, cold fluid injection generates large thermal-induced stress changes that diffuse following advective heat transport laws. Micro-seismicity is quickly triggered and, within 10 years in the current setting, the perturbation reaches the 250 m distant fault, where larger magnitude events are possible. Our findings bear important consequences in terms of safety of supercritical geothermal systems and proved that seismic response in amplified by re-injection-induced cooling.

The correct representation of the failure of geomaterials that feature strength anisotropy and polyaxiality is crucial for many applications. In this contribution, we propose and evaluate through a comparative study a generalized framework that covers both features. Polyaxiality of strength is modeled with a modified Van Eekelen approach, while the anisotropy is modeled using a fabric tensor approach of the Pietruszczak and Mroz type. Both approaches share the same philosophy as they can be applied to simpler failure surfaces, allowing great flexibility in model formulation. The new failure surface is tested against experimental data and its performance compared against classical failure criteria commonly used in geomechanics. Our study finds that the global error between predictions and data is generally smaller for the proposed framework compared to other classical approaches.

The constitutive modeling of shales is an important topic in the geomechanics community as it is often encountered in advanced applications such as nuclear waste storage, CO2 sequestration, and unconventional oil and gas exploitation. The goal of this work is to describe, within a unique plastic-damage framework, the full mechanical behavior of shales such as pre-peak hardening plasticity, non-linearity in the onset of inelastic strains, dilatancy, post-peak softening, and degradation of the elastic parameters. The model validation against three sets of triaxial experimental results on shale demonstrates its capability to reproduce the main mechanical characteristics.

Contrasting 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.

Scientific visualization developed successful methods for scalar and vector fields. For tensor fields, however, effective, interactive visualizations are still missing despite progress over the last decades. We present a general approach for the generation of separating surfaces in symmetric, second-order, three-dimensional tensor fields. These surfaces are defined as fiber surfaces of the invariant space, i.e. as pre-images of surfaces in the range of a complete set of invariants. This approach leads to a generalization of the fiber surface algorithm by Klacansky et al. [16] to three dimensions in the range. This is due to the fact that the invariant space is three-dimensional for symmetric second-order tensors over a spatial domain. We present an algorithm for surface construction for simplicial grids in the domain and simplicial surfaces in the invariant space. We demonstrate our approach by applying it to stress fields from component design in mechanical engineering.

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.

The disposal of highly radioactive spent nuclear fuel in deep geological media will require excavating a large number of galleries in low-permeable rocks, altering initial rock integrity at the repository site. The FE-tunnel excavated in Opalinus Clay at the Mont Terri Underground Research Laboratory (Switzerland) is a unique full scale experiment to study this process. We conducted a numerical study of the excavation of the FE-tunnel in a coupled hydro-mechanical Finite Element framework and employing an anisotropic plasticity coupled with damage constitutive model. A second gradient of dilatancy formulation is employed to avoid spurious mesh dependent behavior originating from the softening of the coupled damage-plasticity model. The approach is validated by comparing numerical predictions and in-situ observations during and after tunnel excavation in terms of displacements, pore water pressure evolution and degradation of elasticity. Mechanical parameters are calibrated using laboratory experiments and values available in the literature. The model well reproduces the coupled hydro-mechanical processes induced by excavation, giving a good agreement between numerical predictions and experimental in-situ monitored data. Furthermore, the evolution of the Excavation Damaged Zone is correctly predicted. Thus, this modeling approach is suitable for the purpose of simulating tunnel excavation in low-permeable anisotropic quasi-brittle shales.

Shales have become increasingly important because they play key roles in modern energy and environmental geomechanics applications, such as nuclear waste storage, non-conventional oil and gas operations and CO2 geological storage. Shale behaves in a quasi-brittle manner, often exhibiting linear elasticity before reaching its peak stress. Furthermore, softening of the material leads to a residual state in which pure plastic flow is observed under constant values of deviatoric stress. Degradation of the elastic moduli and the accumulation of irreversible strains are believed to be primarily caused by the debonding and decohesion mechanisms in the structure, as well as the growth of microcracks. To capture these features, a constitutive model that couples elastic, plastic and damage theories is developed. The isotropic damage model is based on the Weibull probabilistic theory and describes the failure of brittle materials. This model is coupled with a modified version of the Lade-Duncan criterion to account for non-linear dependency of shear resistance with a mean stress typical of geomaterials. The two surfaces of damage and plasticity and the rate equations for the internal variables are postulated and thermodynamic consistency is subsequently investigated. The coupled plastic-damage constitutive model is integrated with an implicit stress return algorithm for multi-dissipative materials. Numerical back-calculations of experimental results from two quasi-brittle shales demonstrate the ability of the model to reproduce the primary features of their mechanical behavior.

Current geomechanical applications imply nonisothermal processes of unsaturated geomaterials, in most cases following stress paths different from the classical triaxial compression often used in laboratory testing. Although the effects of temperature, suction, and stress-path direction (Lode's angle) on the strength of geomaterials have been investigated independently, an integrated analysis combining the three effects has not yet been performed. In this paper, a thermoplastic constitutive model for unsaturated conditions that accounts for the effect of Lode's angle on the strength of geomaterials is presented. The yield surface evolves-shrinking for increasing temperature and expanding for increasing suction-and has its maximum strength for triaxial compression and its minimum for triaxial extension. Examples that can be related to geoenergy applications highlight the importance of accounting for the effects of temperature, suction, and Lode's angle on the evolution of the strength of geomaterials. Numerical results show that not considering these effects may give rise to misleading predictions of the strength of geomaterials. © 2017 American Society of Civil Engineers., V.V. acknowledges support from the ‘EPFL Fellows’ fellowship programme co-funded by Marie Curie, FP7 Grant agreement no. 291771. We would also like to acknowledge financial support from NAGRA (Swiss National Cooperative for the Disposal of Radioactive Waste).

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.

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.

A constitutive model that couples elastic-plastic and damage theories is developed to predict the mechanical behavior of a shale from the Mont Terri rock laboratory (Opalinus Clay). The framework of continuum damage mechanics allows to predict the degradation of the elastic parameters with strains, while the coupling with plasticity correctly reproduces the irreversible strains typical of hard clayey materials. The yield surfaces (one for damage and one for plasticity) are postulated and the evolution equations of the internal variables are derived throughout the application of normality rule. Thermodynamic consistency of the model is investigated. The plastic behavior is described with a non-linear strain hardening function and is coupled with an isotropic damage model suitable for brittle and quasi-brittle geomaterials. The model is integrated with an implicit scheme that guarantees convergence and accuracy. Numerical simulations carried out with the proposed model in triaxial conditions well reproduced observed behavior from experiments.

Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy‐driven leakage risk. Supercritical reservoirs are found at drilling‐reachable depth in volcanic areas, where high pressure (p > 21.8 MPa) and temperature (T > 374°C) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50–500 Mt yr−1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach., The authors acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme through the Starting Grant GEoREST (www.georest.eu), grant agreement No. 801809 and the support by the Spanish Ministry of Science and Innovation (Project CEX2018‐000794‐S); F. P. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number PA 3451/1‐1.