Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fracture analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Numerical study of the effect of propped surface area and fracture conductivity on shale gas production: Application for multi-size proppant pumping schedule design

Hydraulic fracturing is a technique extensively used in the oil and gas industry, where water, proppant (sand) and additives are injected into unconventional reservoirs to enhance the recovery of shale hydrocarbon. Although some previous studies have developed pumping schedules that maximize gas production for a single-size proppant, there are very few studies that consider the effect of varying proppant diameters across pumping stages on shale gas production. Motivated by this, we carried out an extensive sensitivity analysis to determine the effect of different proppant diameters on the average fracture conductivity (FC), average propped surface area (PSA) and cumulative shale gas production volume. We found out that the cumulative shale gas production volume depends on both the average PSA and average FC. We also found out that small-diameter proppant resulted in higher average PSA and lower average FC, whereas large-diameter proppant resulted in lower average PSA and higher average FC. Hence, we designed a multi-size proppant pumping schedule considering both of these parameters into account for simultaneously propagating multiple fractures to maximize shale gas production from unconventional reservoirs. Since the size of injected proppant particles determines the average PSA and average FC for the propped hydraulic fractures, we developed a novel framework called Sequentially Interlinked Modeling Structure (SIMS) to predict the average PSA, average FC and cumulative shale gas production volume at the end of 10 years for a given pumping schedule. Then, we used this SIMS framework to obtain a multi-size proppant pumping schedule that maximizes shale gas production. In closing, we demonstrated that the obtained pumping schedule gives a cumulative shale gas production volume greater than the values obtained from the existing pumping schedules.

03 NATURAL GAS↗

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

Here, a sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Experimental Evaluation of Deformation and Fracture Mechanisms in Highly Irradiated Austenitic Steels

The present report documents recent experimental results of analysis using scanning electron microscopy/electron backscatter diffraction (SEM-EBSD) of plastic deformation mechanisms and strain localization phenomena in austenitic steels irradiated by neutrons. Experiments were performed with specimens irradiated to 125 dpa and, additionally, with specimens that experienced radiation-induced swelling up to 3%. Section 1 briefly analyzes the deformation localization in irradiated steels and its consequences on the material performance. The section describes the advantages and importance of the SEM-EBSD approach combined with in situ mechanical testing capability. Section 2 briefly introduces the experimental tools and methods (i.e., SEM/EBSD in situ tensile frame, electric discharge machine to manufacture irradiated specimens) and describes the investigated materials (i.e., element composition, irradiation conditions, and general microstructure). Section 3 describes the key experimental results and provides a brief analysis and comparison with the datasets obtained earlier within the same task (i.e., low-dose specimens). The discussion focuses on EBSD microstructure maps with strain localization features, misorientation evolution as a function of strain, and observed deformation mechanisms. Section 4 evaluates data collected in recent years on highly irradiated steel and estimates the possible misorientation evolution under irradiation. The section introduces and discusses the concept of in-service-induced damage as an irradiation-assisted stress-corrosion cracking precursor. Section 5 summarizes the work performed. As expected, the present work results are beneficial for exploring and understanding degradation mechanisms in highly irradiated in-core materials found in light water reactors after long-term in-service life.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Comparison of Geochemical Reactivity of Marcellus and Caney Shale Based on Effluent Analysis

ABSTRACT: In this comparative study, we analyzed the changes in elemental concentrations of hydraulic fracturing fluids after interaction with the Marcellus and Caney Shale formations. The focus was on assessing the inherent risks and environmental implications associated with flowback waters, including their impact on soil, ground, and drinking water quality, and human health safety. The chemical compositions of effluents were determined through Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) and Mass spectrometry (ICP-MS). The Marcellus Shale, showed concentrations of Cd, averaging 0.380 ppm far exceeding safe water thresholds. Significant levels of As, Se, B, and Pb were detected in both shales, raising concerns about soil and water contamination. Analyzing the effluents from representative samples of sections of the Marcellus (S2 and S7) and Caney (R1 and R2) indicates different geochemical responses over 4 weeks of experiments. This comparison underscores the chemical changes and environmental considerations linked to hydraulic fracturing across shale formations, suggesting the value of tailored monitoring and regulatory measures for each type. 1. INTRODUCTION The Caney and Marcellus shales, differing in geology and geochemistry, represent distinct unconventional reservoirs. The Caney shale, is more ductile, with higher produced water volumes, (Smith et al., 2022) contrasts with the brittle Marcellus shale known for lower brine production but significant data availability. This study aims to elucidate the possible environmental health and safety issues that may arise from the hydraulic fracturing processes. The interaction between fracturing fluids and clays presents a significant challenge. The primary base of these fluids is water, which, when introduced to clay, can induce swelling and constrict flow pathways. This phenomenon is attributed to water molecules infiltrating the layers of clay, particularly in 2:1-type clays, leading to an increased distance between layers. To counteract this, clay stabilizers are employed (Awejori et al., 2021). Despite their effectiveness, these stabilizers are considered temporary solutions. Upon completion of the fracturing process, a concomitant amount of contaminated waters (flow back), with varied content is collected at the surface. From these, we can infer the geochemical reactions and the environmental challenges associated with these waters. Flowback waters can be reinjected or used for other purposes such as irrigation. This requires adequate screening and treatment for safe use.

Dje, L. B.↗

Loss circulation prevention in geothermal drilling by shape memory polymer

Geothermal formations are naturally fractured with large fracture openings and networks. This can often lead to frequent drilling fluid loss events which is a major contributor to the cost and non-productive time in geothermal drilling. Development of smarter technologies and methods to tackle problem lost circulation is vital for geothermal drilling cost reduction required for geothermal energy to be recognized as a competitive alternative energy source. Mitigation of this problem and other drilling problems such as stuck pipe can minimize overall project cost. In this report, a thermoset shape memory polymer that can be activated by formation natural heat was assessed to seal near wellbore fractures in geothermal wells. The performance of the shape memory polymer (SMP) was evaluated using artificial fractures created in aluminum discs and cylindrical granite cores. Rheology and particle size distribution were considered. A novel testing setup was built for this work, which allows testing of sealing efficiency under dynamic conditions at high temperature. Analysis showed that the SMP has efficiently succeeded in forming a strong plug inside the fractures and stopped fluid loss at high sealing pressure. This smart loss circulation material can expand within the fractures to reduces non-drilling time and strengthen the wellbore in high-temperature drilling operations.

58 GEOSCIENCES↗

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

Fracture of PC and PMMA cylinders in the Taylor tests

The present paper analyzes failure observed in polymer rods collided with a steel anvil under the Taylor cylinder impact experiments. The experimental and numerical analysis demonstrates that association of the failure patterns with the loading mode depends on the rod material. Two materials are considered in the paper, specifically, polymethylmethacrylate (PMMA) and polycarbonate (PC). Damage in PMMA rods at the Taylor tests is shown to be dominated by the shear load resulting in plastic deformation. In contrast, the major mechanism of damage in PC rods is governed by omni-directional (pressure) mode of load. Analysis of the damage in sections of the rods associated with the glass transition is also addressed in the present theoretical study. Failure in these polymers follows the traditional fracture wave mechanism for brittle glass-type materials due to load in the corresponding mode. Numerical analysis employs a two-phase model with improved inter-phase thermal balance accounting for the inter-phase mass, momentum, and heat exchanges during the glass phase transition, while damage being accumulated in time. In conclusion, the simulation results demonstrate a good correlation with the experimental results.

36 MATERIALS SCIENCE↗

Stress Relaxation Cracking in 347H Stainless Steel Arc Welds: Susceptibility Evaluation of Heat-Affected Zone

Stress relaxation cracking (SRC) is considered one of the major failure mechanisms for 347H stainless steel welds at elevated service temperatures or during post weld heat treatment (PWHT), especially within the heat-affected zone (HAZ). This work focuses on the characterization of SRC susceptibility within 347H physically simulated arc welded HAZ at elevated temperatures. A four-step SRC thermomechanical test in combination with finite element modeling (FEM) of the welding and testing processes is developed to establish a susceptibility map for HAZ. The test first runs a thermal cycle with three different peak temperatures (1335, 1275, and 1150 °C) to duplicate representative HAZ subzone microstructures, followed by time-to-failure examination under a variety of pre-stress (260–600 MPa) and pre-strain conditions (0.03–0.19) as a function of reheat temperatures between 750 and 1050 °C. With the aid of FEM, SRC susceptibility maps are generated to identify the threshold stress, plastic strain, and creep strain as a function of test temperature. It was found out that HAZ subzone with a lower peak temperature (1150 °C) appears to be slightly less susceptible to SRC than the other two subzones that experienced higher peak temperatures. Generally, time-to-fracture reduces with increasing initially applied stress and strain for all test temperatures. The pre-stress thresholds decrease from about 500 to 330 MPa as the testing temperature increases from 800 to 1050 °C, while the corresponding initial plastic strain thresholds reduces from 0.15 to 0.06. The SRC susceptibility was also evaluated through the Larson–Miller Parameter (LMP) analysis as a function of plastic strain, initial stress and starting stress upon reaching the testing temperature, respectively. The 1050 °C test with a high pre-applied strain (0.1) exhibits an extremely short time to failure (t = 3 s) that lies outside the general trend in LMP analysis. Additionally, it was identified that a plastic strain above 0.07 is identified to significantly reduce the bulk creep strain tolerance to fracture and therefore increases SRC susceptibility. Hardness measurement and fractography analysis indicated that the strain aging of niobium carbonitrides and other potential phases in conjunction with intergranular precipitates contributes to an increase in microhardness and increased intergranular cracking susceptibility.

14 SOLAR ENERGY↗

Mechanical behavior of carbonated MgO-based Engineered Cementitious Composite (ECC) after high temperatures exposure

Carbonated MgO-based Engineered Cementitious Composite (ECC) has ultrahigh tensile ductility and tight crack width control behavior. However, the expectation of improved fire-resistant has not been confirmed. This study explored the alterations to mechanical and microstructure characteristics of this material after exposure to temperatures up to 500 °C. Material mass loss, compressive strength, tensile strength, strain capacity, and matrix fracture toughness were measured. Scanning electron microscopy, mercury intrusion porosimetry, thermogravimetric analysis, and X-ray diffraction were used to probe the degradation of the cement matrix and fibers. The effect of elevated temperature on carbonated MgO-based ECC was further assessed via examination of the micromechanical behavior of the fiber-matrix. The objective of this research was to assess the performance of carbonated MgO-based ECC exposed to fire hazards. The tensile ductility of carbonated MgO-based ECC was found to be enhanced when exposed to ~100 °C as compared with those at room temperature ~20 °C. Further increase in exposure temperature, however, posed a negative impact on the composite compressive strength, ultimate tensile strength, and ability to control crack width. Here the results provide a useful database for further investigations into carbonated MgO-based ECC for fire safety enhancement.

36 MATERIALS SCIENCE↗

Stress-controlled fatigue of HfNbTaTiZr high-entropy alloy and associated deformation and fracture mechanisms

The stress-controlled fatigue tests are carried out at a stress ratio of 0.1 and a frequency of 10 Hz, and span both low-cycle and high-cycle regimes by varying the applied stress amplitudes. The high-cycle fatigue regime gives a fatigue strength of 497 MPa and a fatigue ratio of 0.44. At equivalent conditions, the alloy's fatigue strength is greater than all other high-entropy alloys (HEAs) with reported high-cycle fatigue data, dilute body-centered cubic alloys, and many structural alloys such as steels, titanium alloys, and aluminum alloys. Through in-depth analyses of crack-propagation trajectories, fracture-surface morphologies and deformation plasticity by means of various microstructural analysis techniques and theoretical frameworks, the alloy's remarkable fatigue resistance is attributed to delayed crack initiation in the high-cycle regime, which is achieved by retarding the formation of localized persistent slip bands, and its good resistance to crack propagation in the low-cycle regime, which is accomplished by intrinsic toughening backed up by extrinsic toughening. Additionally, the stochastic nature of the fatigue data is neatly captured with a 2-parameter Weibull model.

36 MATERIALS SCIENCE↗

Utilizing machine learning to predict tensile ductility and yield strength of CoNiV-based multi-principal elements alloys

This study explores the use of machine learning (ML) as a computational tool to accelerate the design of multi-principal element alloys (MPEAs) with improved tensile elongation. An ML model was trained using available experimental data from the literature along with theoretically derived features to predict yield strength (YS) and ductility. A subset of ML-predicted compositions—CoNiVFe, CoNiVTi, CoNiVTiFe, and CoCrNiVTi—was synthesized and evaluated through tensile testing. The ML model underpredicted YS by approximately 20–30 % and overpredicted ductility by 60–70 % for Ti-containing alloys. Microstructural analysis revealed that Ti segregation at interdendritic regions contributed to early fracture, leading to discrepancies in ductility predictions. Ti segregation at these regions likely drives the increased YS due to segregation strengthening. In contrast, the CoNiVFe alloy showed good agreement with both experimental YS and elongation, with prediction errors of ∼10.2 % and ∼20.7 %, respectively. Microstructural characterization revealed minimal segregation in this alloy, suggesting that the ML model can reliably predict the properties of alloys with little to no segregation. These findings highlight the capability of ML in predicting YS with good accuracy but underscore its limitations in capturing defect-driven failure mechanisms such as segregation-induced embrittlement.

36 MATERIALS SCIENCE↗

Divergent effects of sex and calcium/vitamin D supplementation on serum magnesium and markers of bone structure and function during initial military training

Maintaining Mg status may be important for military recruits, a population that experiences high rates of stress fracture during initial military training (IMT). The objectives of this secondary analysis were to (1) compare dietary Mg intake and serum Mg in female and male recruits pre- and post-IMT, (2) determine whether serum Mg was related to parameters of bone health pre-IMT, and (3) whether Ca and vitamin D supplementation (Ca/vitamin D) during IMT modified serum Mg. Females (n 62) and males (n 51) consumed 2000 mg of Ca and 25 μg of vitamin D/d or placebo during IMT (12 weeks). Dietary Mg intakes were estimated using FFQ, serum Mg was assessed and peripheral quantitative computed tomography was performed on the tibia. Dietary Mg intakes for females and males pre-IMT were below the estimated average requirement and did not change with training. Serum Mg increased during IMT in females (0·06 ± 0·08 mmol/l) compared with males (–0·02 ± 0·10 mmol/l; P < 0·001) and in those consuming Ca/vitamin D (0·05 ± 0·09 mmol/l) compared with placebo (0·001 ± 0·11 mmol/l; P = 0·015). In females, serum Mg was associated with total bone mineral content (BMC, β = 0·367, P = 0·004) and robustness (β = 0·393, P = 0·006) at the distal 4 % site, stress–strain index of the polaris axis (β = 0·334, P = 0·009) and robustness (β = 0·420, P = 0·004) at the 14 % diaphyseal site, and BMC (β = 0·309, P = 0·009) and stress–strain index of the polaris axis (β = 0·314, P = 0·006) at the 66 % diaphyseal site pre-IMT. No significant relationships between serum Mg and bone measures were observed in males. Findings suggest that serum Mg may be modulated by Ca/vitamin D intake and may impact tibial bone health during training in female military recruits.

59 BASIC BIOLOGICAL SCIENCES↗

Autonomous Fracture Conductivity Using Expandable Proppants in Enhanced Geothermal Systems

Summary Early thermal breakthrough in enhanced geothermal systems (EGS) due to the presence of preferential flow channels is a major challenge that endangers efficient and economic heat extraction in such systems. Previous studies mainly focused on adjusting circulation rates of the working fluid, which still leaves significant amounts of untapped heat behind. Currently, there is a lack of technologies for altering flow distribution within the fracture network to achieve uniform heat sweeping in the reservoir. This work presents a novel concept for making proppants to autonomously control fracture conductivity based on the surrounding temperature. Here, proppants with negative thermal expansion coefficients have demonstrated the capability for appropriate fracture conductivity adjustment as a function of temperature to achieve uniform flow across the fracture network. Particle-particle interactions governing such functions are explicitly modeled, and then the Lattice Boltzmann methods (LBM) is used to determine the potential impact of closure stress and temperature changes on the permeability of the proposed proppant packs. Microscale analyses are further used to determine the required material properties to achieve a certain improvement in the permeability of the proppant pack. Our analyses show an enhancement in permeability and the associated fracture conductivity by half of their initial values. Field-scale analysis further confirms the effectiveness of the proposed concept as 31.4% more heat can be extracted from EGS over 50 years of production when the proposed proppants are used. Such novel proppants may effectively delay thermal breakthrough, sweep heat from larger rock volumes, and elongate the life span of the EGS project.

Engineering↗

DECOVALEX-2023: Task G, SAFENET Final Report

DECOVALEX Task G deals with fracture mechanics at several scales using a combined approach of experimental work, related model development, benchmarking and experimental analysis. Fig. 0.1 provides a graphical abstract for Task G. The experimental basis for the related mechanical (M), hydro-mechanical (HM), and thermo-mechanical (TM) processes comes from the rock mechanics laboratories of Universities of Freiberg (TUBAF) and Edinburgh, as well as the Korea Institute of Civil Engineering and Building Technology (KICT). The experimental work in the rock laboratories is closely linked to the underground research laboratories (URLs) Reiche Zeche (Germany), KURT (Korea), and Mont Terri (Switzerland). The scientific key questions are related to fracture permeability evolution under THM conditions, anisotropy effects on fracturing processes, and thermal fracture slip, which are being addressed in specific steps of the task. A large variety of numerical methods have been developed and applied for experimental analysis, ranging from continuum to discontinuum approaches. A detailed comparison of mechanical and hydro-mechanical processes is given in the section 3 via the benchmarking exercises. As a result of DECOVALEX-2023 Task G we further improved our understanding and predictability of fracturing processes under THM conditions. This was based on robust numerical simulation methods and in-depth experimental analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Detecting and Characterizing Fracture Zones Using a Convolutional Neural Network

This project directly supports the Geothermal Technologies Office (GTO) objectives outlined in the Multi-Year Program Plan (MYPP) by advancing two key research areas: “Exploration and Characterization” and “Data, Modeling, and Analysis.” This project has successfully demonstrated a pre-drilling ability to image and characterize the distribution and connectivity of subsurface faults and fractures, key parameters for identifying permeable pathways that enable geothermal fluids to circulate and produce energy. Specifically, we developed and implemented innovative machine learning methodologies to enhance geothermal exploration. Large-scale faults were detected using a Convolutional Neural Network (CNN), while small-scale fractures were characterized using a novel Double-Beam Neural Network (DBNN). These tools have proven both technically effective and cost-efficient by reducing reliance on expensive exploratory drilling. Through collaboration with our geothermal industry partner, this research has significantly advanced techniques for identifying hidden geothermal systems and extending the productive lifespan of existing geothermal fields. We applied our methods to two geothermal fields—Soda Lake (Nevada) and Lightning Dock (New Mexico)—to identify shallow steam-charged fracture zones and characterize deep faults at depths of 1.5-2 km. The steam zone identified at the Soda Lake geothermal field showed excellent agreement with prior drilling data, validating the effectiveness of our approaches. In addition, the analysis revealed three new prospective drilling targets for further development and verification. The outcomes of this project improve our scientific understanding of geothermal reservoir behavior, enhance exploration efficiency, extend the economic life of existing geothermal plants. Ultimately, these advancements contribute to GTO’s goal of achieving more sustainable, affordable, and data-driven geothermal energy development across the United States.

15 GEOTHERMAL ENERGY↗

Development of Ionic Based Fluid to Improve Fluid Hydraulics in Enhanced Geothermal Systems

This research advances the field of geothermal energy by developing and evaluating novel fluid systems designed explicitly for high-temperature subsurface environments to enhance fracture flow distribution. The project integrates chemical synthesis, environmental assessment, rheological testing, microfluidic analysis, and reservoir-scale laboratory testing and analysis to identify optimal ionic and nonionic fluids for Enhanced Geothermal Systems (EGS).

15 GEOTHERMAL ENERGY↗

Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules

Weibull analysis and weakest link theory are employed to resolve the probability of crystalline silicon PV cell fracture when measured as bare cells and when stressed in reduced- and full-sized modules. Experimental results indicated that the characteristic cell strength is reduced by ~20% once packaged into the laminate of a one-cell module and loaded in four-point flexure (4PF). This experimental observation was shown consistent with a weakest link theory prediction that the strength limiting flaws reside on the surface of the cell's edge. Here, the analysis is ultimately extended to present the equivalent loading of four-cell modules by uniform pressure and 4PF and a uniformly loaded full-sized module and demonstrates that smaller, representative, modules must be loaded to a much higher level than their parent full-sized modules to achieve an equivalent probability for cell fracture.

14 SOLAR ENERGY↗

Wide-blocky veins explained by dependency of crystal growth rate on fracture surface type: Insights from phase-field modeling

Vein microstructures contain a wealth of information on coupled chemical and mechanical processes of fracturing, fluid transport, and crystal growth. Numerical simulations have been used for exploring the factors controlling the development of vein microstructures; however, they have not been quantitatively validated against natural veins. Here we combined phase-field modeling with microtextural analysis of previously unexplained wide-blocky calcite veins in natural limestone and of the fresh fracture surface in this limestone. Results show that the wide-blocky vein textures can only be reproduced if ~10%–20% of crystals grow faster than the rest. This fraction corresponds to the amount of transgranularly broken grains that were observed on the experimental fracture surfaces, which are dominantly intergranular. We hypothesize that transgranular fractures allow faster growth of vein minerals due to the lack of clay coatings and other nucleation discontinuities that are common along intergranular cracks. Our simulation results show remarkable similarity to the natural veins and reproduce the nonlinear relationship between vein crystal width and vein aperture. This allows accurate simulations of crystal growth processes and related permeability evolution in fractured rocks.

Geology↗