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DOE OSTI2016

Tensile deformation and fracture properties of a 14YWT nanostructured ferritic alloy

Here, a new larger heat of a 14YWT nanostructured ferritic alloy (NFA), FCRD NFA-1, was synthesized by ball milling FeO and argon atomized Fe-14Cr-3W-0.4Ti-0.2Y (wt%) powders, followed by hot extrusion, annealing and cross rolling to produce an ≈10 mm-thick plate. NFA-1 contains a bimodal size distribution of pancake-shaped, mostly very fine scale, grains. The as-processed plate also contains a large population of microcracks running parallel to its broad surfaces. The small grains and large concentration of Y–Ti–O nano-oxides (NOs) result in high strength up to 800 °C. The uniform and total elongations range from ≈1–8%, and ≈10–24%, respectively. The strength decreases more rapidly above ≈400 °C and deformation transitions to largely viscoplastic creep by ≈600 °C. While the local fracture mechanism is generally ductile-dimple microvoid nucleation, growth and coalescence, perhaps the most notable feature of tensile deformation behavior of NFA-1 is the occurrence of periodic delamination, manifested as fissures on the fracture surfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Towards real-time forecasting of natural gas production by harnessing graph theory for stochastic discrete fracture networks

In this work, we compare hydrocarbon production curves obtained from a graph-based reduced-order model with the high-fidelity Discrete Fracture Network (DFN) predictions for a fracture network created using data from a real shale site. We observe that the bounds for the high fidelity DFN model lie within the bounds for the reduced order model, implying that the reduced-order model provides a conservative estimate. Moreover, we found that except for first-passage times and late arriving mass, the production curves from the reduced-order model predict transport accurately. However, it is to be noted that the results are inspite of trading a three-dimensional geometry for a reduced system in the form of a graph, one that is 500–1000 times faster in terms of computational efficiency (for this particular application). In addition, we also compare the production curves for large drawdown and small drawdown using our graph approach. The reduced-order model is successful in showing that the long term productivity is higher in case of small drawdown although the initial productivity is higher for large drawdown. Thus, this reduced-order model offers great potential in uncertainty quantification for production, as well as in providing operators with information to make real-time decisions for optimal production.

03 NATURAL GAS↗

DOE OSTI2022

Fe Oxidation and Species Distribution at the Rock–Fluid Interface of Marcellus Shale Reacted with Hydraulic Fracturing Fluid

Hydraulic fracturing of shale reservoirs resulted in significant opportunity for increased oil and gas production in the United States. Rock-fluid interactions can cause mineral dissolution and precipitation reactions that lead to permeability changes in the shale matrix, which ultimately may affect transport pathways and hydrocarbon production. Understanding the distribution of secondary precipitates, such as barite and Fe(III) (hydro)oxides, and cation leaching at the rock-fluid interface is an important step to further investigate how these geochemical processes can change permeability and transport pathways. In this study, thin sections of the fracture-matrix interface were made from reacted Marcellus shale cores. The thin sections were characterized using synchrotron X-ray fluorescence imaging and synchrotron X-ray absorption spectroscopy. Fe species with different oxidation states were identified in the maps, together with barite and Ca distribution. The results show that ferrihydrite, as newly formed Fe(III)-bearing precipitates, aligned well with the border of the Ca (e.g., calcite) leaching region in the reaction front. Some Fe-containing clay also dissolved, but the dissolution region for the clay was not as deep as the calcite. Further, the reaction front is about three times deeper in the direction parallel to the shale bedding than that perpendicular to the bedding. The Ca leaching region can be an index for reaction front detection for Marcellus shale. Reactive transport modeling was conducted and the predicted Ca leaching boarder align well with ferrihydrite precipitation, consistent with the experimental observation. The carbonate mineral dissolution can be crucial to promote fluid access into the shale matrix. Together with our previous study on the shale reactive surface, this follow-up study showed similar Ca leaching region and Fe(III) precipitates distribution in the reaction front regardless of barite precipitation on the surface, indicating that the barite coatings on the surface may not pose a significant impact on reactive transport at the shale-fluid interface.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2020

Chemical Speciation and Stability of Uranium in Unconventional Shales: Impact of Hydraulic Fracture Fluid

Uranium and other radionuclides are prominent in many unconventional oil/gas shales and is a potential contaminant in flowback/produced waters due to the large volumes/types of chemicals injected into the subsurface during stimulation. In this work, to understand the stability of U before and after stimulation, a geochemical study of U speciation was carried out on three shales (Marcellus, Green River, and Barnett). To do so, two types of samples for each shale were subjected to sequential chemical extractions: unreacted and shale-reacted with a synthetic hydraulic fracture fluid. Furthermore, a significant proportion of the total U (20–57%) was released from these three shales after reaction with fracture fluid, indicating that U is readily leachable. The total U released exceeds labile water-soluble and exchangeable fractions in unreacted samples, indicating that fluids leach more recalcitrant phases in the shale. Radiographic analysis of unreacted Marcellus shale thin sections shows U associated with detrital quartz and the clay matrix in the shale. Detrital zircon and TiO2 identified by an electron microprobe could account for the hot spots. This study shows that significant proportions of U in three shales are mobile upon stimulation. In addition, the extent of mobilization of U depends on the U species in these rocks.

58 GEOSCIENCES↗

DOE OSTI2019

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Here, we develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ~ time -(1+α) ), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late-time decay rate of the breakthrough curve is -(1+α/2) rather than the classical -3/2. Yet, if α>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

58 GEOSCIENCES↗

DOE OSTI2020

Anomalous Transport in Three-Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

In this work, we study how the interplay between fracture aperture heterogeneity and tracer injection mode controls fluid flow and tracer transport in three-dimensional (3D) discrete fracture networks (DFNs). The direct 3-D DFN simulations show that tracer injection mode has substantial effects on tracer spreading across all levels of aperture heterogeneity. The key controlling factor for effective transport is the initial Lagrangian velocity distribution, which is determined by the interplay between injection mode and aperture heterogeneity. The fundamental difference between initial Lagrangian velocity distribution and domain-scale Eulerian velocity distribution plays a vital role in determining anomalous transport. We effectively capture the observed anomalous transport using an upscaled transport model that incorporates initial velocity distribution, stationary velocity distribution, velocity correlation length, and average advective tortuosity. With the upscaled transport model, we accurately capture the evolution of Lagrangian velocity distribution and predict longitudinal spreading in 3-D DFN.

58 GEOSCIENCES↗

DOE OSTI2015

Kinetics and fracture resistance of lithiated silicon nanostructure pairs controlled by their mechanical interaction

Following an explosion of studies of silicon as a negative electrode for Li-ion batteries, the anomalous volumetric changes and fracture of lithiated single Si particles have attracted significant attention in various fields, including mechanics. However, in real batteries, lithiation occurs simultaneously in clusters of Si in a confined medium. Hence, understanding how the individual Si structures interact during lithiation in a closed space is necessary. Here, we demonstrate physical and mechanical interactions of swelling Si structures during lithiation using well-defined Si nanopillar pairs. Ex situ SEM and in situ TEM studies reveal that compressive stresses change the reaction kinetics so that preferential lithiation occurs at free surfaces when the pillars are mechanically clamped. Such mechanical interactions enhance the fracture resistance of lithiated Si by lessening the tensile stress concentrations in Si structures. Lastly, this study will contribute to improved design of Si structures at the electrode level for high-performance Li-ion batteries.

25 ENERGY STORAGE↗

DOE OSTI2022

Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue

Abstract Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J 2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J 2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J -integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Plastic flow anisotropy drives shear fracture

Abstract Fracture of initially crack-free bodies often occurs due to plastic instabilities known as shear bands. Previous computer simulations advanced a myriad of mechanisms to rationalize shear banding. However, they were restricted to planar geometries. We investigate the relevance of anisotropic plasticity by picking an axisymmetric tensile test rig, in which shear localization is rarely observed. The three-dimensional finite-element simulations of shear banding in this type of specimens are the first of their kind. The micromechanical modeling covers a range of competing mechanisms believed to be responsible for such failure. We show that anisotropic plasticity can effectively trigger shear bands thereby causing failure of ductile solids. Our results enable shear fracture to be rationalized in ductile rocks and mitigated against in designing advanced materials.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

A higher-order finite element reactive transport model for unstructured and fractured grids

Abstract This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

58 GEOSCIENCES↗

DOE OSTI2018

Brittle fracture to recoverable plasticity: polytypism-dependent nanomechanics in todorokite-like nanobelts

Atomic force microscopy (AFM) based nanomechanics experiments involving polytypic todorokite-like manganese dioxide nanobelts reveal varied nanomechanical performance regimes such as brittle fracture, near-brittle fracture, and plastic recovery within the same material system. These nanobelts are synthesized through a layer-to-tunnel material transformation pathway and contain one-dimensional tunnels, which run along their longitudinal axis and are enveloped by m × 3 MnO 6 octahedral units along their walls. Depending on the extent of material transformation towards a tunneled microstructure, the nanobelts exhibit stacking disorders or polytypism where the value for m ranges from 3 to up to ~20 within different cross-sectional regions of the same nanobelt. The observation of multiple nanomechanical performance regimes within a single material system is attributed to a combination of two factors: (a) the extent of stacking disorder or polytypism within the nanobelts, and (b) the loading (or strain) rate of the AFM nanomechanics experiment. Controllable engineering of recoverable plasticity is a particularly beneficial attribute for advancing the mechanical stability of these ceramic materials, which hold promise for insertion in multiple next-generation technological applications that range from electrical energy storage solutions to catalysis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2022

Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental–computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS 2 and MoSe 2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).

Zhang, Xu↗

DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗

DOE OSTI2020

Quantum-well states in fractured crystals of the heavy-fermion material CeCoIn5

Quantum-well states appear in metallic thin films due to the confinement of the wave function by the film interfaces. Using angle-resolved photoemission spectroscopy, we unexpectedly observe quantum-well states in fractured single crystals of CeCoIn5. We confirm that confinement occurs by showing that these states’ binding energies are photon-energy independent and are well described with a phase accumulation model, commonly applied to quantum-well states in thin films. This indicates that atomically flat thin films can be formed by fracturing hard single crystals. For the two samples studied, our observations are explained by free-standing flakes with thicknesses of 206 and 101 Å. We extend our analysis to extract bulk properties of CeCoIn5. Specifically, we obtain the dispersion of a three-dimensional band near the zone center along in-plane and out-of-plane momenta. We establish part of its Fermi surface, which corresponds to a hole pocket centered at G. We also reveal a change of its dispersion with temperature, a signature that may be caused by the Kondo hybridization.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Universality class for loopless invasion percolation models and a percolation avalanche burst model for hydraulic fracturing

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. In this work, we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic b-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing (“fracking”). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths l. But since the networks are characterized by their large-scale behavior, l << L, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

58 GEOSCIENCES↗

DOE OSTI2024

3D modeling of deep borehole electromagnetic measurements with energized casing source for fracture mapping at the Utah Frontier Observatory for Research in Geothermal Energy

Here, we present a 3D numerical modelling analysis evaluating the deployment of a borehole electromagnetic measurement tool to detect and image a stimulated zone at the Utah Frontier Observatory for Research in Geothermal Energy geothermal site. As the depth to the geothermal reservoir is several kilometres and the size of the stimulated zone is limited to several 100 m, surface-based controlled-source electromagnetic measurements lack the sensitivity for detecting changes in electrical resistivity caused by the stimulation. To overcome the limitation, the study evaluates the feasibility of using a three-component borehole magnetic receiver system at the Frontier Observatory for Research in Geothermal Energy site. To provide sufficient currents inside and around the enhanced geothermal reservoir, we use an injection well as an energized casing source. To efficiently simulate energizing the injection well in a realistic 3D resistivity model, we introduce a novel modelling workflow that leverages the strengths of both 3D cylindrical-mesh-based electromagnetic modelling code and 3D tetrahedral-mesh-based electromagnetic modelling code. The former is particularly well-suited for modelling hollow cylindrical objects like casings, whereas the latter excels at representing more complex 3D geological structures. In this workflow, our initial step involves computing current densities along a vertical steel-cased well using a 3D cylindrical electromagnetic modelling code. Subsequently, we distribute a series of equivalent current sources along the well's trajectory within a complex 3D resistivity model. We then discretize this model using a tetrahedral mesh and simulate the borehole electromagnetic responses excited by the casing source using a 3D finite-element electromagnetic code. This multi-step approach enables us to simulate 3D casing source electromagnetic responses within a complex 3D resistivity model, without the need for explicit discretization of the well using an excessive number of fine cells. We discuss the applicability and limitations of this proposed workflow within an electromagnetic modelling scenario where an energized well is deviated, such as at the Frontier Observatory for Research in Geothermal Energy site. Using the workflow, we demonstrate that the combined use of the energized casing source and the borehole electromagnetic receiver system offer measurable magnetic field amplitudes and sensitivity to the deep localized stimulated zone. The measurements can also distinguish between parallel-fracture anisotropic reservoirs and isotropic cases, providing valuable insights into the fracture system of the stimulated zone. Besides the magnetic field measurements, vertical electric field measurements in the open well sections are also highly sensitive to the stimulated zone and can be used as additional data for detecting and imaging the target. We can also acquire additional multiple-source data by grounding the surface electrode at various locations and repeating borehole electromagnetic measurements. This approach can increase the number of monitoring data by several factors, providing a more comprehensive dataset for analysing the deep-localized stimulated zone. The numerical analysis indicates that it is feasible to use the combination of the energized casing and downhole electromagnetic measurements in monitoring localized stimulated zone at large depths.

58 GEOSCIENCES↗

DOE OSTI2018

Threshold angle and valid fracture of the sectored flexural specimen

Here, the sectored flexural specimen was developed over a decade ago to measure the strength of ceramic and glass tubes and cylinders in which flaws on a tube's or cylinder's outer surface are limiters of axial tensile failure stress. Using the specimen's geometry, the associated axial tensile failure stress can be analytically calculated from the failure force measured from simple uniaxial bending, and multiple specimens (and test data) can be harvested from a single tube or cylinder. The sector angles of specimens in previous studies were somewhat arbitrarily chosen and usually produced validly occurring fractures and data; however, if the angle used was too small (relative to the tube's or cylinder's geometry), then undesirable application–irrelevant edge–located failures resulted. To avoid such failures in specimen design, a threshold sector angle was identified to guide the selection of a minimum sector angle (and consequential cross section) for any arbitrary sector flexural specimen harvested from a tube or cylinder. If the sector angle of the specimen is larger than the threshold value, then fracture will not occur at a specimen's edge and the measured axial failure stress will be limited by surface–located flaws on the tube's or cylinder's outer surface.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Fracture Toughness of Advanced Structural Ceramics: Applying ASTM C1421

The three methods of determining the quasi-static Mode I fracture toughness (K Ic ) (surface crack in flexure – SC, single-edge precracked beam – PB, and chevron notched beam – VB) found in ASTM C1421 were applied to a variety of advanced ceramic materials. All three methods produced valid and comparable KIc values for the Al 2 O 3 , SiC, Si 3 N 4 and SiAlON ceramics examined. However, not all methods could successfully be applied to B 4 C, ZrO 2 and WC ceramics due to a variety of material factors. The coarse-grained microstructure of one B 4 C hindered the ability to observe and measure the precracks generated in the SC and PB methods while the transformation toughening in the ZrO 2 prevented the formation of the SC and PB precracks and thus made it impossible to use either method on this ceramic. The high strength and elastic modulus of the WC made it impossible to achieve stable crack growth using the VB method because the specimen stored a tremendous amount of energy prior to fracture. Even though these methods have passed the rigors of the standardization process there are still some issues to be resolved when the methods are applied to certain classes of ceramics. We recommend that at least two of these methods be employed to determine the K Ic , especially when a new or unfamiliar ceramic is being evaluated.

36 MATERIALS SCIENCE↗