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DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗

DOE OSTI2018

Fracture Toughness of Thick Boride Layers Estimated by the Cross-Sectioned Scratch Test

New results about the fracture toughness (K{sub c}) of thick boride layers estimated by the cross-sectioned scratch test are presented in this study. The FeB-Fe{sub 2}B layers developed at the surface of borided AISI 1018 and AISI 1045 steels and the Fe{sub 2}B layer formed on the borided AISI 1045 steel exposed to a diffusion annealing process (DAP) were used for this purpose. The cross-sectioned scratch tests were performed with a Vickers diamond stylus drawn across the thick boride layer under a constant load to produce a half-cone-shaped fracture near to the top surface of the borided steels. The height of the half-cone-shaped fracture as a function of the cross-sectioned scratch loads was used to determine the fracture toughness of the FeB and Fe{sub 2}B layers. The results showed a fracture resistance of ∼2.8 MPa√m for the FeB layer formed at the surface of borided AISI 1045 steel. Likewise, the effect of the DAP on the surface of the borided AISI 1045 steel promoted the formation of an exclusively Fe{sub 2}B layer, with an increase in the fracture toughness of the whole boride layer around 5 MPa√m. Finally, the principle of the technique can be used to minimize the influence of the anisotropic properties on the fracture toughness along the depth of boride layers.

36 MATERIALS SCIENCE↗

DOE OSTI2024

PYSIMFRAC: A Python library for synthetic fracture generation and analysis

In this paper, we introduce PYSIMFRAC, an open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. PYSIMFRAC allows the user to specify one of three fracture generation techniques (Box, Gaussian, or Spectral) and perform statistical analysis including the autocorrelation, moments, and probability density functions of the fracture surfaces and aperture. This analysis and accessibility of a python library allows the user to create realistic fracture realizations and vary properties of interest. In addition, PYSIMFRAC includes integration examples to two different pore-scale simulators and the discrete fracture network simulator, dfnWorks. The capabilities developed in this work provides opportunity for quick and smooth adoption and implementation by the wider scientific community for accurate characterization of fluid transport in geologic media. We present PYSIMFRAC along with integration examples and discuss the ability to extend PYSIMFRAC from a single complex fracture to complex fracture networks.

58 GEOSCIENCES↗

DOE OSTI2022

Fracture toughness and crack propagation in LX-17 and PBX 9502 insensitive high explosives

High explosive materials, and in particular insensitive high explosive (IHE) materials, are of significant interest. TATB-based LX-17 and PBX 9502 are two IHE’s and mechanical properties are an important metric of performance. In this work we present, for the first time, a study of fracture as a function of temperature and displacement rate and starter crack length on billet pressed IHE materials using a standard three point bend technique. We demonstrated that the technique can yield consistent results over time by measuring samples from the same lots 4 years later and observed that the fracture toughness of LX-17 and PBX 9502 are similar. We also determined the temperature dependence for different starter crack lengths and found that the fracture toughness generally decreases with larger starter crack sizes and temperatures. For the LX-17, where a wide temperature range of -60 C to 50 C was investigated, the impact of temperature on fracture toughness between -20 C and 23 C was less than expected. For the PBX 9502 we observed the difference in fracture toughness values between -20 C and 23 C did depend on the particular lot, and also there was a tendency of the fracture toughness to scale with the tensile strength. We also investigated the effect of a lower displacement rate and observed that while the impact on the fracture toughness was relatively small, the samples surprisingly did not break (fail) after exceeding the peak load. We took advantage of this to perform x-ray computed tomography (CT) of the samples to image crack propagation in the intact samples. We observed that cracks were generally straight and unaffected by the microstructure in the LX-17, in contrast to the PBX 9502 where the direction of the cracks would frequently change and were likely influenced by the underlying microstructure.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Role of water in fracture of modified silicate glasses

Decarbonizing the glass industry requires alternative melting technology, as current industrial melting practices rely heavily on fossil fuels. Hydrogen has been proposed as an alternative to carbon-based fuels, but the ensuing consequences on the mechanical behavior of the glass remain to be clarified. A critical distinction between hydrogen and carbon-based fuels is the increased generation of water during combustion, which raises the equilibrium solubility of water in the melt and alters the behavior of the resulting glass. A series of five silicate glasses with 80% silica and variable [Na 2 O]/([H 2 O] + [Na 2 O]) ratios were simulated using molecular dynamics to elucidate the effects of water on fracture. Several fracture toughness calculation methods were used in combination with atomistic fracture simulations to examine the effects of hydroxyl content on fracture behavior. Here, this study reveals that the crack propagation pathway is a key metric to understanding fracture toughness. Notably, the fracture propagation path favors hydrogen sites over sodium sites, offering a possible explanation of the experimentally observed effects of water on fracture properties.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Effect of water on critical and subcritical fracture properties of Woodford shale

Subcritical fracture behavior of shales under aqueous conditions is poorly characterized despite increased relevance to oil and gas resource development and seal integrity in waste disposal and subsurface carbon sequestration. In this paper, we measured subcritical fracture properties of Woodford shale in ambient air, dry CO 2 gas, and deionized water by using the double-torsion method. Compared to tests in ambient air, the presence of water reduces fracture toughness by 50%, subcritical index by 77%, and shear modulus by 27% and increases inelastic deformation. Comparison between test specimens coated with a hydrophobic agent and uncoated specimens demonstrates that the interaction of water with the bulk rock results in the reduction of fracture toughness and enhanced plastic effects, while water-rock interaction limited to the vicinity of the propagating fracture tip by a hydrophobic specimen coating lowers subcritical index and increases fracture velocity. Finally, the observed deviation of a rate-dependent subcritical index from the power law K-V relations for coated specimens tested in water is attributed to a time-dependent weakening process resulting from the interaction between water and clays in the vicinity of the fracture tip.

58 GEOSCIENCES↗

DOE OSTI2019

Statistical analyses of reservoir and fracturing parameters for a multifractured shale oil reservoir in Mississippi

The use of multifractured horizontal wells has improved the efficiency of hydrocarbon extraction from shale gas and oil plays. It is highly desirable to estimate the characteristics of the reservoir and well fracturing through production data analysis. Production rate transient data from 16 wells in the Mississippi sections were analyzed to estimate local reservoir permeability and hydraulic fracture parameters. Key factors affecting well productivity have been identified for optimizing future well completion. Based on the theory of distance of investigation during transient linear flow, the reservoir matrix permeability of TMS was estimated to be between 53 nd and 210 nd, averaging at 116 nd. The matrix permeability follows the lognormal distribution and is considered homogeneous according to the coefficient of variation. The fracture half-length was estimated using the matrix permeability data from the rate transient analysis. The fracture half-length was found to have a mean value of 234 ft with a standard deviation of 66 ft in a normal distribution. The fracture conductivity was back-calculated by matching pseudosteady production rate data to Guo et al's (SPE Reserve Eval Eng.12, 2009, 879) productivity model for boundary-dominated flow. The fracture conductivity was estimated to range from 0.4 md-ft to 3.2 md-ft, averaging at 1.4 md-ft. Based on Guo et al's (SPE Reserve Eval Eng.12, 2009, 879) well productivity model applied to TMS condition, well productivity can be improved significantly by increasing fracture length and conductivity. Future TMS wells should be completed with conductivity values of greater than 10 md-ft.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

DOE OSTI2019

A Stochastic Study of Flow Anisotropy and Channelling in Open Rough Fractures

The quantification of fluid flow in rough fractures is of high interest for reservoir engineering, especially for deep geothermal applications. Herein, rough self-affine fractures are stochastically generated with incremental shear displacement and geometrically described by two aperture definitions, the vertical aperture a vert and the effective aperture a eff . In order to compare their effect on fracture flow, such as anisotropy and channelling, Local Cubic Law (LCL) model-based 2D fluid flow is simulated. The particularity of this approach is the combination of a stochastic generation of self-affine fractures with a statistical analysis (560 individual realizations) of the impact of the LCL’s aperture constraint on fracture flow. The results show that aperture definition affects the quantitative interpretation of flow anisotropy and channeling as well as the aperture distribution of the fractures with shearing. Higher values of mean aperture for a given fracture are found using a vert , whereas the aperture standard deviation is larger with a eff . In addition, flow anisotropy is significantly sensitive to aperture definition for small shear displacements and shows a relative higher dispersion with a eff . Thus, LCL prediction models based on a vert are expected to lead to higher dispersion of anisotropy results with a higher uncertainty (factor ~ 2). Realizations based on avert lead to an enhanced clustering of high flow rates for higher shearing displacements. This channeling development results in higher total flow rates for these simulations. Finally, these findings support the direct calibration of pre-existing LCL anisotropy simulations based on avert towards more representative results using a eff .

58 GEOSCIENCES↗

DOE OSTI2018

Immobile Pore-Water Storage Enhancement and Retardation of Gas Transport in Fractured Rock

The effect of immobile pore-water on gas transport in fractured rock has implications for numerical modeling of soil vapor extraction, methane leakage, gaseous CO 2 leakage from sequestration operations, radionuclide transport from underground nuclear explosions, and nuclear waste disposal. While the ability for immobile pore-water storage to effect gas transport has been recognized in the past, the details and specific scenarios leading to enhanced, retarded, or unaffected gas transport have not been explored. In this paper, we performed numerical investigations into the enhancement and retardation of gas transport due to immobile pore-water storage in order to identify implications for gas transport applications. To do this, we developed a numerical approach to model gas transport with a single-phase flow solution coupled to the advection–dispersion equation modified to account for immobile pore-water storage. Other than the immobility of pore water, the formulation contains all other physics included in two-phase formulations (advective and diffusive gas transport in fractures and rock matrix and dissolution in immobile pore water). The assumption of immobile pore water is valid here since for many applications involving transport of soluble gases in fractured rock, the rate of aqueous transport is insignificant compared to gas transport. We verify our modeling approach with analytical solutions of: (1) 1D gas diffusion, (2) 1D gas advection, (3) barometric pumping of a fracture, and (4) gas transport with uniform fracture flow and diffusion into the matrix. We account for pore-water storage in our model by implementing a kinetic formulation of gas dissolution wherein the dissolved (aqueous) phase is considered an immobile constituent. Using this formulation, we model the effect of dissolution rate and saturation on the retardation of gas transport during pure diffusion and pure advection. We also demonstrate that although it is commonly believed that pore-water storage will always enhance gas transport in fractures during oscillatory flow (e.g., during reversing pressure gradients such as barometric pumping cycles), our simulations indicate that this may not always be the case. Our numerical investigations indicate that scenarios with lower effective diffusion coefficients ( ⪅ 10 − 5  m 2 / s ) and lower dissolution coefficients (i.e., the dissolution diffusion coefficient) ( ⪅ 10 − 11  m 2 / s ) will result in enhanced gas transport. Other combinations of gaseous diffusion and dissolution coefficients result in delayed gas transport or insignificant effect on gas transport. Based on these results, and given the fact that the free-air diffusion coefficients for many gases are slightly above 10 − 5  m 2 / s (near the boundary of enhanced/non-enhanced gas transport), tortuosity would have to be significant for gas transport enhancement to occur. Similarly, if we consider the free-water diffusion coefficient of gases (around 10 − 9  m 2 / s for many gases of interest) to be a maximum bound for the effective dissolution coefficients (i.e., the rate of diffusion into the water away from the air/water interface will limit the dissolution rate), the effective dissolution coefficient would have to be at least 2 orders of magnitude less for enhanced gas transport to occur. Otherwise, pore-water storage will delay or have negligible effect on the gas transport. The results also indicate that the assumption of instantaneous equilibrium, often invoked in numerical codes for dissolution processes (i.e., dissolution coefficient is effectively infinite), will fail to accurately capture important details of soluble gas transport. Finally, the implication of our results is that gas breakthrough times in fractured rock during oscillatory flow may be highly dependent on the effective gaseous diffusion and dissolution coefficients.

58 GEOSCIENCES↗

DOE OSTI2023

Comparative Analysis of Imaging and Measurements of Micrometer-Scale Fracture Aperture Fields Within a Heterogeneous Rock Using PET and X-ray CT

Knowledge of the spatial distribution of fracture apertures is essential for reliable characterization of flow and transport processes in fractured systems and for better understanding of physicochemical matrix–fracture interactions. Here, we propose and test two image-based methods, thereby extending the current experimental capabilities to characterize aperture size distribution in structurally heterogeneous geologic porous media noninvasively. The first approach utilizes an inversion method based on the dataset acquired from positron emission tomography (PET) and the second approach considers an extension of the classic missing attenuation technique that relies on clinical X-ray computed tomography (X-ray CT). Independent sets of imaging experiments are conducted on a fractured basalt core with heterogeneous matrix properties and aperture distributions to compare the two methodologies. A repeat of each experiment is conducted to verify the proposed workflows. The performance of these two imaging techniques is systematically evaluated through the analysis of signal-to-noise ratio, minimum fracture size detectability, and measurement errors. While both approaches provide a reliable estimation of fracture aperture distributions, PET yields a signal-to-noise ratio that is substantially higher than the corresponding X-ray CT measurements. Furthermore, uncertainties of the aperture values for PET are considerably lower ($\bar {\sigma}_{\text {d}} = 15\%$) compared to those obtained from X-ray CT ($\bar {\sigma}_{\text {d}} = 29\%$), allowing for the detection of minimum aperture sizes of 20 $\mu$m with 70% confidence level. Finally, these approaches provide key experimental tools for better understanding dynamic hydromechanical fracture properties in geologic systems.

58 GEOSCIENCES↗

DOE OSTI2018

Investigation on Cracking Behavior and Development of a Fracture Model of Ti-47Al-2Nb-2Cr Alloy During Hot Deformation

When alloys are strained to a certain limit under the plastic deformation, ductile fracture occurs. Whether the required deformation can be put into effect before fracture appears has become a serious concern. A combination of compression tests, ductile fracture criteria as well as finite element simulation (FEM) were employed in this study to establish the fracture initiation prediction model of Ti-47Al-2Nb-2Cr alloy. To obtain the critical fracture strain, a technique was proposed to calculate the data for deformed cylindrical samples through isothermal compression tests in the temperature range between 1223 and 1423 K with strain rates ranging from 0.001 to 1 s{sup −1}. Five commonly used ductile fracture criteria were compared by FE simulation of compressing tests. It was found that the Brozzo criterion was found to be suitable and accordingly a failure criterion, considering temperature and strain ratio was established. Hot working parameters (critical fracture value and critical strain) in deformation could be obtained through the finite element simulation, revealing that this newly established failure criterion could accurately predict cracking initiation in compressing deformation of Ti-47Al-2Nb-2Cr alloy ingot.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Construction of occipital bone fracture using B-spline curves

Treating trauma to the cranio-maxillofacial region is a great challenge and requires expert clinical skills and sophisticated radiological imaging. The aim of reconstruction of the facial fractures is to rehabilitate the patient both functionally and aesthetically. In this article we employed B-spline curves to construct the occipital bone fracture using Digital Imaging and Communications in Medicine (DICOM) format data. The construction of occipital bone fracture starts with the boundary extraction followed by corner detection, construction of fractured part inner outer curve for each DICOM data using B-spline curves and finally the construction of fractured part in DICOM format. Method used in this article is based on DICOM data only and does not require any technique such as mirror imaging, technical help, reference skull, or to take average thickness of skull bone. Using the proposed method, the constructed fractured implant is custom made for every individual patient. At the end of this article we present a real case, in which we have constructed the occipital bone fracture using B-spline. The proposed method has been validated using post-operation DICOM data. For practical application, Graphical User Interface (GUI) has been developed.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2025

Influence of Initial fabric and water-wetting on particle fracture and force chain evolution in natural silica sand

Particle fracture has a significant influence on the engineering behavior of granular materials. However, the combined influence of the initial fabric and wetting on particle fracture and force chain evolution in granular materials, particularly in sands, remains insufficiently explored in the current literature. Here, in this paper, one-dimensional (1D) confined compression experiments were conducted on dry and wet specimens, and particle-level fracture was captured using three-dimensional (3D) in-situ Synchrotron Micro-Computed Tomography (SMT). A quantitative assessment of particle fracture revealed that wet specimens, which have disturbed fabric, exhibited a higher fracture percentage in comparison to dry specimens. Complementary 3D finite element (FE) simulations were performed using dry and wet (only solid fabric was considered and the influence of pore water is not considered) sand assemblies to assess interparticle contact forces and particle-scale stress distributions within the specimens. Force chain analysis was subsequently conducted, encompassing quantification of interparticle forces, characterization of force network structures, and monitoring the dynamic evolution of force chains under different strain levels. The results show that the specimens with disturbed fabric led to a more dynamic and less persistent force network, more fabric instability, and thus more reorganization of force chain structures. In addition, the frequent rearrangement of the force network in the presence of water (with reduced inter-particle contact friction) likely exacerbates localized stress concentrations, promoting failure in previously unengaged or weakly connected particles. The results reported in this paper offer a new insight into how the initial fabric and wetting cause different fracture behavior. The findings can also pave the way for more in-depth future investigations into the mechanics governing particle fracture in granular assemblies.

Finite element analysis↗

DOE OSTI2019

Effect of alkali-silica reaction on the fracture properties of confined concrete

Alkali-silica reaction (ASR), which was recently discovered in nuclear power plant structures commonly without shear reinforcement, has previously been shown to induce anisotropic expansion in confined concrete. The fracture properties (strength, stiffness, and specific fracture energy) of ASR-induced anisotropically-damaged concrete specimens were quantified by varying both the damage level and relative direction of the ASR-induced cracking orientation against the loading direction corresponding to the fracture propagation. Here, the effect of different orientations (0, 45, and 90° relative to the notch of the specimen) of expected ASR-induced cracks on the fracture properties was investigated using a wedge-splitting test (WST). Specimens without ASR expansion generally showed the highest fracture properties; however, the specific fracture energy was highest for ASR-affected specimens in which the expected orientation of ASR-induced cracks was perpendicular to the WST specimen notch. Specimens in which the ASR-induced cracks were parallel to the notch exhibited the lowest strength and fracture energy.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗

DOE OSTI2017

Lamellae spatial distribution modulates fracture behavior and toughness of african pangolin scales

Pangolin scales form a durable armor whose hierarchical structure offers an avenue towards high performance bio-inspired materials design. In this paper, the fracture resistance of African pangolin scales is examined using single edge crack three-point bend fracture testing in order to understand toughening mechanisms arising from the structures of natural mammalian armors. In these mechanical tests, the influence of material orientation and hydration level are examined. The fracture experiments reveal an exceptional fracture resistance due to crack deflection induced by the internal spatial orientation of lamellae. An order of magnitude increase in the measured fracture resistance due to scale hydration, reaching up to ~ 25 kJ/m 2 was measured. Post-mortem analysis of the fracture samples was performed using a combination of optical and electron microscopy, and X-ray computerized tomography. Interestingly, the crack profile morphologies are observed to follow paths outlined by the keratinous lamellae structure of the pangolin scale. Most notably, the inherent structure of pangolin scales offers a pathway for crack deflection and fracture toughening. Finally, the results of this study are expected to be useful as design principles for high performance biomimetic applications.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Microstructure and fracture toughness characterization of three 9Cr ODS EUROFER steels with different thermo-mechanical treatments

Ferritic martensitic ODS steels are one of the candidate structural materials for future Gen-IV nuclear fission and fusion reactors. Here, the dependence of fracture toughness on microstructure was investigated by comparing three 9Cr ODS EUROFER steels manufactured through different thermo-mechanical processing routes. Quasi-static fracture toughness testing was performed with sub-sized C(T) specimens and microstructural characterization was carried out using scanning electron microscopy, electron backscatter diffraction, and transmission electron microscopy. It was found that at lower test temperatures (-100 – 22 °C), the fracture toughness was primarily controlled by crack initiation at sub-micron particles and by production of secondary cracks during fracture. At higher temperatures (above 100 °C), fracture toughness was predominantly controlled by the matrix ductility and the grain boundary strength with a relatively ductile coarse-grained alloy demonstrating higher fracture toughness compared to high-strength fine-grained alloys. These results and discussion show that variations in thermomechanical treatments can produce significant differences in microstructure and fracture toughness behavior of ferritic martensitic ODS steels.

36 MATERIALS SCIENCE↗