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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

CIEL ∗ Ch color map for visualization and analysis of sea ice motion

The International Commission on Illumination (CIE) designed its color space to be perceptually uniform so that a given numerical change in the color code corresponds to perceived change in color. This color encoding is demon- strated to be advantageous in scientific visualization and analysis of vector fields. The specific application is analysis of ice motion in the Arctic where patterns in smooth monthly-averaged ice motion are seen. Furthermore, fractures occurring in the ice cover result in discontinuities in the ice motion. This vector jump in displacement can also be visualized. We then analyze modeled and observed fractures through the use of a metric on the color space, and image amplitude and phase metrics. Amplitude and phase met- rics arise from image registration that is accomplished by sampling images using space filling curves, thus reducing the image registration problem to the more reliable functional alignment problem. We demonstrate this through an exploration of the metrics to compare model runs to an observed ice crack.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Surfactants are Ineffective for Reducing Imbibition of Water-Based Fracturing Fluids in Deep Gas Reservoirs

Minimizing loss of injected hydraulic fracturing fluids into shale along fracture-matrix boundaries is desired because imbibed water restricts gas production and wastes valuable water resources. This problem has motivated the addition of surfactants into water-based hydraulic fracturing fluids in order to reduce the capillary driving force for imbibition. Here, we show that reduction in interfacial tension and wettability alteration has negligible ability to reduce imbibition in deep gas reservoirs. The effectiveness of altering capillary forces acting at the wetting front also depends on the injection pressure acting at the fracture-matrix boundary. The pressure at the interface between the fracture and the shale matrix is constrained between the reservoir pore pressure and formation pressure (rock fracture pressure, also known as breakdown pressure of the rock) and increases with depth to magnitudes that greatly exceed that of capillary pressures. Furthermore, the analyses presented here show that even maximum alteration of interfacial properties that result in strongly hydrophobic interactions between the fracturing fluid and reservoir rock is incapable of significantly reducing imbibition in deep reservoirs. Instead of using surfactants, this analysis points to decreases in wellbore shut-in pressures and shut-in times as practical options for reducing imbibition losses of water-based fluids.

03 NATURAL GAS↗
DOE OSTI2026

Evaluation of the interfacial bonding strength between hafnia and silica layers deposited by electron-beam evaporation

Factors contributing to the mechanical strength of multilayer optical coatings involving alternating layers of electron-beam evaporated hafnia and silica is investigated. It is observed that upon rupture resulting from nanosecond laser damage, fragments consisting of layer pairs are produced. These pairs are formed as a result of a strong asymmetry in adhesion strength between interfaces, leading to preferential delamination at interfaces where silica is deposited on hafnia, and not the reverse, despite the fact that both interface types consist of the same pair of materials. The observed disparity in adhesion strength was further studied using nanomechanical scratch tests, revealing loads at which fracture occurs, and fracture morphology, both of which are highly dependent on deposition order. Based on these measurements, along with the morphological analysis of the nanostructure of the coatings, we conclude that the surface microstructure in each coating layer affects its adhesion strength with the succeeding layer. The findings outlined here are particularly relevant to the production of large aperture, high-performance optics designed for use in next-generation lasers.

adhesion strength↗
DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Technical and Economic Evaluation of the First Ever Polymer Flood Field Pilot to Enhance the Recovery of Heavy Oils on Alaska's North Slope via Machine Assisted History Matching

Polymer flooding has become globally established as a potential enhanced oil recovery method for heavy oils. To determine whether this technology may be useful in developing the substantial heavy oil resources on the Alaska North Slope, a polymer flood field pilot commenced at the Milne Point Unit in August 2018. This study seeks to evaluate the results of the field pilot on a technical and economic basis. A reservoir simulation model is constructed and calibrated to predict the oil recovery performance of the pilot through machine-assisted reservoir simulation techniques. To replicate the early water breakthrough observed during waterflooding, transmissibility contrasts are introduced into the simulation model, forcing viscous fingering effects. In the ensuing polymer flood, these transmissibility contrasts are reduced to replicate the restoration of injection conformance during polymer flooding. Transmissibility contrasts are later reinstated to replicate fracture overextension interpreted in one of the producing wells. The calibrated simulation models produced at each stage of the history matching process are used to forecast oil recovery. These forecasts are used as input for economic analysis, incremental to waterflooding expectations. The simulation forecasts indicate that polymer flooding significantly increases the heavy oil production for this field pilot compared to waterflooding alone, yielding attractive project economics. However, meaningful variations between simulation scenarios demonstrate that a simulation model is only valid for prediction if flow behavior in the reservoir remains consistent with that observed during the history matched period. Critically, this means that a simulation model calibrated for waterflooding may not fully capture the technical and economic benefits of an enhanced oil recovery process such as polymer flooding. Subsequently, the simulation model and economic model are used in conjunction to conduct a sensitivity analysis for polymer flood design parameters, from which recommendations are provided for both the continued operation of the current field pilot and future polymer flood designs. The results demonstrate that a higher polymer concentration can be injected due to the development of fractures in the reservoir. The throughput rate should remain high without exceeding operating constraints. A calculated point-forward polymer utilization parameter demonstrates the decreasing efficiency of the polymer flood at later times in the pattern life. Future projects will benefit from starting polymer injection earlier in the pattern life. A pattern with tighter horizontal well spacing will observe a greater incremental benefit from polymer flooding.

Keith, Cody↗
DOE OSTI2024

Sub-Diurnal Methane Variations on Mars Driven by Barometric Pumping and Planetary Boundary Layer Evolution

In recent years, the Tunable Laser Spectrometer within the Sample Analysis at Mars (TLS-SAM) instrument on board the Mars Science Laboratory (MSL) Curiosity rover has detected methane variations in the atmosphere at Gale crater. Methane concentrations appear to fluctuate seasonally as well as sub-diurnally, which is difficult to reconcile with an as-yet-unknown transport mechanism delivering the gas from underground to the atmosphere. To potentially explain the fluctuations, we consider barometrically induced transport of methane from an underground source to the surface, modulated by temperature-dependent adsorption. The subsurface fractured-rock seepage model is coupled to a simplified 1-D atmospheric mixing model to provide insights on the pattern of atmospheric methane concentrations in response to transient surface methane emissions, as well as to predict sub-diurnal variation in methane abundance for the northern summer period, which is a candidate time frame for a MSL Curiosity sampling campaign. Our analysis suggests that there is a lower limit to the subsurface fracture density that can produce the observed methane patterns, below which the atmospheric methane variations would be out of phase with the observations. The best-performing model scenarios indicate a significant, short-lived methane pulse just prior to sunrise, the detection of which by TLS-SAM would be a potential indicator of the contribution of barometric pumping to Mars' atmospheric methane variations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Physically rigorous reduced-order flow models of fractured subsurface environments without explosive computational cost

Fractured media models comprise discontinuities of multiple lengths (e.g. fracture lengths and apertures, wellbore area) that fall into the relatively insignificant length scales spanning millimeter-scale fractures to centimeter-scale wellbores in comparison to the extensions of the field of interest, and challenge the conventional discretization methods imposing highly-fine meshing and formidably large numerical cost. By utilizing the recent developments in the finite element analysis of electromagnetics that allow to represent material properties on a hierarchical geometry, this project develops computational capabilities to model fluid flow, heat conduction, transport and induced polarization in large-scale geologic environments that possess geometrically-complex fractures and man-made infrastructures without explosive computational cost. The computational efficiency and robustness of this multi-physics modeling tool are demonstrated by considering various highly-realistic complex geologic environments that are common in many energy and national security related engineering problems.

42 ENGINEERING↗
DOE OSTI2021

Process-Structure-Property Relations for As-Deposited Solid-State Additively Manufactured High-Strength Aluminum Alloy

Solid-state additive manufacturing methods provide innovative solutions to circumvent problems associated with materials susceptible to hot cracking by avoiding liquid solid phase transformations. In this work, the process parameter influence on microstructural evolution and mechanical response of a fully dense aluminum alloy 7050 (AA7050) component manufactured via a rapid, solid-state additive manufacturing process known as Additive Friction Stir Deposition (AFS-D) was quantified for the first time. Three sections (starting dwell, transient, crossover of roads) of the deposition that exhibit differing thermomechanical processing histories were evaluated for the resulting microstructure and mechanical response. The microstructural characterization was performed on the as-deposited AA7050 via Electron Backscatter Diffraction (EBSD), TEM, optical microscopy, and Scanning Electron Microscopy (SEM). The microstructural characterization revealed refined constituent particles and grains throughout the as-deposited AA7050 microstructure. Furthermore, quasi-static tensile experiments were conducted in both the build and transverse directions, in order to quantify the orientation influence on tensile properties of the as-deposited AA7050 build. Spatially dependent tensile properties were observed in the material due to heat input variation coarsening of secondary phases towards the initial layers of the AFS-D build. Post-mortem analysis revealed that voids nucleated and coalesced from the overgrowth of the strengthening precipitates present in the material, resulting in fracture.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microbial Community Composition in Deep‐Subsurface Reservoir Fluids Reveals Natural Interwell Connectivity

Abstract The identification of natural fractures and the wells they connect is crucial for the development of geological reservoirs because it may have an important impact on reservoir model construction and hydraulic fracture propagation. In this study we investigated the use of a novel data source, the microbial community composition in the reservoir formation fluids, for identification of interwell connectivity caused by natural fractures. We verified this concept at a newly developed mesoscale enhanced geothermal system (EGS) field testbed located 4,850 ft (1,478 m) beneath ground surface at the Sanford Underground Research Facility in Lead, SD. Fluids produced at or near the EGS testbed were sampled and subjected to high‐throughput 16S rRNA gene amplicon sequencing to analyze the microbial community profile therein. Despite the typically substantial heterogeneity across the community profiles of samples spatially distributed (10 m to 1.9 km apart) throughout the site, samples from two wells at the EGS testbed showed highly similar microbial community composition, suggesting the two wells intersected the same natural fracture. This evidence of natural connectivity between the two wells at the EGS testbed was later corroborated by core log analysis and sewer camera surveys into the boreholes. Besides the field case described in this study, microbial community composition as a reservoir diagnostic tool would be applicable in a much broader context such as unconventional hydrocarbon exploitation, groundwater reservoir characterization, and environmental remediation, adding valuable “hard” data capable of pinpointing the origins of fluids unambiguously.

Zhang, Yuran↗
DOE OSTI2024

Updimensioning strategy derived from synthetic equiaxed grain structures for approximating 3D grain size distributions from 2D visualizations with 1D parameters

We generated synthetic equiaxed grain structures using computer graphics software to explore the relationship between various grain size determination methods and true three-dimensional (3D) grain diameters. Mirroring grain measurement techniques, the synthetic 3D grain structures are imaged as 2D micrographs which are measured to yield 1D grain size parameters. Synthetic grain structures provide data at a mass scale and permit exploration of both polished and fractured surface micrographs, revealing one-to-one correspondence between exposed 2D grain cross-sections and individual 3D grains. Analysis of this correspondence yielded a procedure to approximate 3D equiaxed grain size and volume distributions based on the mode of the 2D fractograph grain size distribution. The 3D approximation procedure is shown to be less susceptible to different imaging conditions that affect small, undiscernible grains compared to the standard planimetric and linear intercept methods, which by design also tend to underestimate the 3D grain diameter. The procedure requires larger sample sizes to lower variance and a deeper analysis which could become more practical with machine learning (ML) models for grain boundary segmentation, which synthetic grain structures can help train. This work lays the foundation for analyzing other grain distributions such as columnar and composite grains in similar depth.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Performance Evaluation of a High Salinity Produced Water Treatment Train: Chemical Analysis and Aryl Hydrocarbon Activation

Water scarcity and increased energy demands have put a strong focus on improving industries at the heart of the water–energy nexus. Treatment of oil and gas produced water (PW) can help reduce freshwater consumption during hydraulic fracturing, especially in arid regions, while also removing harmful contaminants from entering the environment. However, it is also difficult to treat because PW contains high concentrations of many environmentally toxic contaminants, which require complex and expensive treatment processes to achieve their removal. To demonstrate the possibility of PW treatment and reuse in the O&G industry, a comprehensive environmental toxicity and water quality analysis throughout a five-process treatment train was performed on high salinity (>120 g/L) Permian basin raw PW. Here, the concentrations of naturally occurring radioactive materials were reduced by over 99%, total organic carbon was reduced by 93%, and inorganic constituents, including total dissolved solids, were reduced by over 99%. Compounds that induced the aryl hydrocarbon receptor and caused cytotoxicity in MCF-7 cells were also removed. Overall, the results of this study show that a short treatment train (five distinct unit processes) can be effective in treating PW to a level suitable for use outside of the oil industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Emergence of Unstable Focused Flow Induced by Variable‐Density Flows in Vertical Fractures

Abstract Fluids with different densities often coexist in subsurface fractures and lead to variable‐density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable‐density fluids in vertical fractures by combining three‐dimensional (3D) pore‐scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce the unstable runlet using 3D numerical simulations and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh‐Taylor instability (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough‐walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications.

Environmental Sciences & Ecology↗
DOE OSTI2022

Sulfur Biogeochemical Cycling and Redox Dynamics in a Shale-Dominated Mountainous Watershed

Sulfur (S) is an essential macronutrient and important component of the earth’s crust, and its cycling has critical impacts on trace metal mobility, water quality, and human health. Pyrite weathering is the primary pathway by which sulfur enters surface waters. However, biogeochemical cycling of sulfur in soils and the river corridor mediates sulfate exports. In this study, we identified the major forms of sulfur across multiple compartments and scales in a pristine mountainous watershed, including shale bedrock weathering profiles, hillslope soils, and alluvial floodplain sediments, in order to provide insight into biogeochemical sulfur cycling in a hydrologically variable alpine system. X-ray absorption near-edge spectroscopy (XANES) analysis of shale weathering profiles showed clear evidence of pyrite oxidation to sulfate, with large accumulations of intermediate S(0) (20%–53%). Micro-scale XANES showed evidence of reprecipitation of pyrite at fracture surfaces within the permanently saturated zone. Organic sulfur dominated S speciation in shallow hillslope soil and floodplain sediment, with little evidence of reduced inorganic S. However, mackinawite formation, representing active sulfate reduction, was observed in saturated oxbow sediments and saturated weathered shale underlying floodplain sediments. Further evidence of sulfate reduction from aqueous sulfur isotopic analysis was observed in shallow groundwater transects across an Fe-reducing meander, whereas increases in pore water sulfate concentrations implied sulfur oxidation at other locations. Furthermore, the data present an integrated picture of sulfur cycling in a shale-dominated watershed, where riverine sulfate exports are mediated by biological cycling, particularly in redox-stratified and temporally dynamic hyporheic zone sediments.

58 GEOSCIENCES↗
DOE OSTI2021

Fracture Network Localization Preceding Catastrophic Failure in Triaxial Compression Experiments on Rocks

We quantify the spatial distribution of fracture networks throughout six in situ X-ray tomography triaxial compression experiments on crystalline rocks at confining stresses of 5–35 MPa in order to quantify how fracture development controls the final macroscopic failure of the rock, a process analogous to those that control geohazards such as earthquakes and landslides. Tracking the proportion of the cumulative volume of fractures with volumes >90th percentile to the total fracture volume, ∑ v 90 / v t o t indicates that the fracture networks tend to increase in localization toward these largest fractures for up to 80% of the applied differential stress. The evolution of this metric also matches the evolution of the Gini coefficient, which measures the deviation of a population from uniformity. These results are consistent with observations of localizing low magnitude seismicity before large earthquakes in southern California. In both this analysis and the present work, phases of delocalization interrupt the general increase in localization preceding catastrophic failure, indicating that delocalization does not necessarily indicate a reduction of seismic hazard. However, the proportion of the maximum fracture volume to the total fracture volume does not increase monotonically. Experiments with higher confining stress tend to experience greater localization. To further quantify localization, we compare the geometry of the largest fractures, with volumes >90th percentile, to the best fit plane through these fractures immediately preceding failure. The r 2 scores and the mean distance of the fractures to the plane indicate greater localization in monzonite than in granite. The smaller mean mineral diameter and lower confining stress in the granite experiments may contribute to this result. Tracking these various metrics of localization reveals a close association between macroscopic yielding and the acceleration of fracture network localization. Near yielding, ∑ v 90 / v t o t and the Gini coefficient increase while the mean distance to the final failure plane decreases. Macroscopic yielding thus occurs when the rate of fracture network localization increases.

58 GEOSCIENCES↗
DOE OSTI2022

Geological activity shapes the microbiome in deep-subsurface aquifers by advection

Subsurface environments host diverse microorganisms in fluid-filled fractures; however, little is known about how geological and hydrological processes shape the subterranean biosphere. Here, we sampled three flowing boreholes weekly for 10 mo in a 1478-m-deep fractured rock aquifer to study the role of fracture activity (defined as seismically or aseismically induced fracture aperture change) and advection on fluid-associated microbial community composition. We found that despite a largely stable deep-subsurface fluid microbiome, drastic community-level shifts occurred after events signifying physical changes in the permeable fracture network. The community-level shifts include the emergence of microbial families from undetected to over 50% relative abundance, as well as the replacement of the community in one borehole by the earlier community from a different borehole. Null-model analysis indicates that the observed spatial and temporal community turnover was primarily driven by stochastic processes (as opposed to deterministic processes). We, therefore, conclude that the observed community-level shifts resulted from the physical transport of distinct microbial communities from other fracture(s) that outpaced environmental selection. Given that geological activity is a major cause of fracture activity and that geological activity is ubiquitous across space and time on Earth, our findings suggest that advection induced by geological activity is a general mechanism shaping the microbial biogeography and diversity in deep-subsurface habitats across the globe.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

HFTS-2 (Final Report)

This report delves into the research program, identified tasks, various studies, observations, results, and conclusions under the Hydraulic Fracturing Test Site (HFTS-2) project. This test site is located in Loving County close to the Texas, New Mexico border. The program targeted the Wolfcamp formation in Delaware Basin. The aim of the project was to improve our understanding of hydraulic fracturing processes to not only optimize unconventional resource development in US Basins but to minimize environmental footprint as well. Various new diagnostic technologies were demonstrated at this site, including distributed acoustic microseismic, high resolution strain using Rayleigh frequency band (DSS-RFS), and in-fill proppant logging tool. Significant conclusions from this study include: 1) lateral and vertical fracture growth mapping as well as proppant transport behavior, 2) Use of DSS-RFS as a diagnostic tool to understand cluster level behavior, 3) Validation of proppant log, both at core scale as well as in-fill well implementation, and 4) New modeling tools to map far-field strain response using distributed strain sensing data. Specifically, far-field fracture distribution is influenced by linear fracture corridors defined by the stress-state as well as clustering behavior influenced by spatio-temporal effects. Depletion impacts on new stimulation was demonstrated and technically quantified. Significant vertical fracture height growth was observed. However, our understanding is limited by available gauge data availability. Numerical strain modeling techniques have been developed and demonstrated to help understand observed strain response behavior. Finally, proppant log has been further validated as a useful tool to map propped zones within the SRV. It has also shown very strong correlation with observed drawdown behavior at this test site. This report will detail many of these studies as well as technical results and conclusions from said studies. These include general subsurface characterization work, completion designs as implemented, studies looking at fracture geometry, high resolution microseismic study including source mechanisms, advanced DSS-RFS studies including drainage characterization, core characterization results, proppant analysis (core and in-fill child well), geochemistry, etc.

02 PETROLEUM↗
DOE OSTI2022

Impact of Polymer Rheology on Gel Treatment Performance of Horizontal Wells with Severe Channeling

Summary Gel treatment has been a cost-effective method to control the conformance of a reservoir with severe heterogeneity problems. The water channels in such reservoirs can be classified as open fractures or high permeability porous media with pore-throat network. Many simulation studies have been conducted to discuss gel treatment performance for conformance control. However, nobody considered the polymer rheology difference in open fractures and porous media in simulation. Previous simulation studies also ignored the residual resistance factor as a function of rock permeability rather than a constant parameter. In this study, a conceptual simulation model was established to simulate the linear flow system for the reservoir with horizontal wells considering the two factors mentioned above. The results demonstrate that the gel treatment always provides the better placement results in the open fracture type channel than pore-throat network type channel. Moreover, it is very necessary to consider residual resistance factor as a function of permeability, which is based on the experimental results and can provide much greater plugging efficiency in the higher permeable channels than constant residual resistance factor. Sensitivity analysis studies and multifactor analysis indicate that increasing oil viscosity and permeability ratio has a strong positive influence on conformance control results, which indicate in-situ gel treatment can be better applied in heavy or viscous oil reservoirs with fracture-like channels. Besides, the results also indicate that in reservoirs with severe channeling problem where channel velocity was high, the differences of gelant placement and profile improvement in models with two different types of channels could be enlarged greatly.

Engineering↗
DOE OSTI2026

DEMO-FTES: Development, Monitoring, and Control of Fracture Thermal Energy Storage in Crystalline Rock Formations (CRADA Final Report)

The DEMO-FTES project investigated the feasibility of Fracture Thermal Energy Storage (FTES) as a seasonal energy storage solution in crystalline rock formations. FTES leverages hydraulically induced fractures to exchange heat between circulating fluids and the surrounding rock mass, enabling long-term thermal energy retention due to the high specific heat and low thermal conductivity of rock. This approach has the potential to reduce heating and cooling energy demands and enhance building energy resilience. The project combined dimensional analysis, numerical modeling, laboratory experiments, and meso-scale field tests to evaluate FTES performance and advance its technology readiness level from 3 to 5. Scaling analysis identified key dimensionless parameters governing heat transfer and fluid flow, ensuring laboratory and field tests were representative of larger-scale systems. Numerical simulations using TOUGH and iTOUGH2 frameworks supported experiment design and interpretation, modeling fracture geometry, thermal-hydraulic behavior, and thermo-mechanical coupling. Laboratory tests at EPFL involved creating single and multiple fractures in 25 cm cubic samples of Gabbro and Granite under true triaxial stress.

25 ENERGY STORAGE↗