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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)

Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differential equations (PDEs) models fail to capture effects due to long-range forces at the microscale and mesoscale. However, utilization of this capability is seriously compromised by the lack of a rigorous nonlocal interface theory, required for both application and efficient solution of nonlocal models. To unlock the full potential of nonlocal modeling we developed a mathematically rigorous and physically consistent interface theory and demonstrate its scope in mission-relevant exemplar problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress

Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.

58 GEOSCIENCES↗
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 OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
DOE OSTI2021

Heterogeneous multiphase flow properties of volcanic rocks and implications for noble gas transport from underground nuclear explosions

Of interest to the Underground Nuclear Explosion Signatures Experiment are patterns and timing of explosion-generated noble gases that reach the land surface. The impact of potentially simultaneous flow of water and gas on noble gas transport in heterogeneous fractured rock is a current scientific knowledge gap. This article presents field and laboratory data to constrain and justify a triple continua conceptual model with multimodal multiphase fluid flow constitutive equations that represents host rock matrix, natural fractures, and induced fractures from past underground nuclear explosions (UNEs) at Aqueduct and Pahute Mesas, Nevada National Security Site, Nevada, USA. Capillary pressure from mercury intrusion and direct air–water measurements on volcanic tuff core samples exhibit extreme spatial heterogeneity (i.e., variation over multiple orders of magnitude). Petrographic observations indicate that heterogeneity derives from multimodal pore structures in ash-flow tuff components and post-depositional alteration processes. Comparisons of pre- and post-UNE samples reveal different pore size distributions that are due in part to microfractures. Capillary pressure relationships require a multimodal van Genuchten (VG) constitutive model to best fit the data. Relative permeability estimations based on unimodal VG fits to capillary pressure can be different from those based on bimodal VG fits, implying the choice of unimodal vs. bimodal fits may greatly affect flow and transport predictions of noble gas signatures. The range in measured capillary pressure and predicted relative permeability curves for a given lithology and between lithologies highlights the need for future modeling to consider spatially distributed properties.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗
DOE OSTI2026

In situ quantification of fracture slip induced by hydraulic injections in a deep borehole: A comparison of two different borehole techniques

In situ measurements of fracture deformation during fluid injection are rare, yet essential for understanding the mechanical response of fractured rock. In this study, we evaluate the reliability of two methods by comparing their slip vector estimates: high-resolution borehole acoustic televiewer images captured before and after injection tests, and displacement data from a three-component borehole deformation probe recorded during the injections. Acoustic televiewer images capture only final in-plane displacement, whereas three-component borehole deformation measurements provide full 3D, transient fracture movement. Four injection tests in a fractured granitic rock mass along an inclined borehole at the Bedretto Underground Laboratory (Switzerland), beneath more than 1100 m of overburden, were analyzed. The two methods yielded consistent kinematics and comparable slip magnitudes, typically in the range of 0.2 – 0.6 mm. Angular differences between estimated slip directions ranged from 0.2° to 28°. For two test intervals with pre-existing fractures optimally oriented for slip, the measured slip vectors agreed with forward-modeled slip vectors based on the regional in situ stress field, supporting the Wallace–Bott hypothesis. Measurable shear displacement was identified in two test intervals containing fractures oriented nearly perpendicular to the least principal stress, including a newly formed hydraulic fracture. This demonstrates that even fractures unfavorably oriented for slip can undergo shear due to local stress perturbations around an inclined borehole.

Acoustic televiewer↗
DOE OSTI2024

Significance of Low‐Velocity Zones on Solute Retention in Rough Fractures

Natural fractures are characterized by high internal heterogeneity. This internal variability is the cause of flow channeling, which in turn leads to contaminant transport taking place primarily along the high-velocity channels. Mass exchange between the high-velocity channels and the low-velocity zones has the potential to enhance contaminant retention, due to solute diffusion into the low-velocity zones and subsequent exposure to additional surface area for diffusion into the bordering rock matrix. Here, we derive a random walk particle tracking method for heterogeneous fractures, which includes an additional term to account for the aperture gradient. The method takes into account advection, diffusion in the fracture and matrix diffusion. The developed numerical framework is applied to assess the effect of low-velocity zones in rough self-affine fractures. The results show that diffusion into low-velocity zones has a visible but modest impact on contaminant retention. The magnitude of this impact does not change considerably, regardless of whether diffusion into the rock matrix is considered in the model, and increases for a decreasing average Péclet number of the fracture.

58 GEOSCIENCES↗
DOE OSTI2021

Numerical Simulations of Geologic Storage Reservoir Management to Support Risk Mitigation Evaluation

This report provides a detailed description of a set of numerical simulations that represent reservoir behavior over time in response to different operational decision scenarios for detection of potential leakage and reduction or avoidance of leakage impact at a hypothetical geological carbon storage (GCS) site. These simulations serve as the basis for a series of GCS leakage risk forecasts that are to be developed using the National Risk Assessment Partnership’s Open-Source Integrated Assessment Model (NRAP-Open-IAM), and a demonstration of a simple decision support workflow for evaluation of mitigation strategies based on results of those system model forecasts. This risk assessment and decision support study is forthcoming. Four injection scenarios were considered: a constant rate carbon dioxide (CO 2 ) injection case (base case), a case with CO 2 injection rate adjustment, a case with early termination of injection operations, and a case with brine extraction. CO 2 injection operations were controlled to ensure that the pressure transient remains below the defined manageable reservoir fracture pressure, with consideration shown to hypothetical locations within the modeled spatial domain where the overburden was weaker and lower transient pressure increases were allowable. Additionally, a brine extraction alternative was considered as a reservoir management and risk mitigation option to reduce reservoir pressure, steer the plume away from any hypothetical geohazard such as fault as needed, and enhance storage capacity. Such operational actions contribute to risk management overtime. This study explores the potential utility of reservoir management for risk reduction at GCS sites. This study shows that the injection design may modify the time to CO 2 breakthrough at a legacy well; in particular, these results show that brine extraction can add value for mitigating risk both by delaying leakage and reducing pressure build-up. For the scenario considered, both pressure plots and pressure distributions demonstrate that pressure build-up was decreased by 3% with brine extraction. Additionally, extraction of brine afforded enhancement of CO 2 storage capacity by 5% compared to the base case. These findings suggest that brine extraction has substantial potential to steer the risk-related reservoir effects away from known geohazards (e.g., faults and legacy wells) by conducting pressure transient effects and CO 2 plume movement toward the production well. Injection rate adjustment scenarios considered in this study show potential value for managing both reservoir pressure transients and CO 2 plume behavior. Operational actions for reducing injection and/or early termination of injection (as compared to the base case), however, require careful design; tailoring both the extent and timing of injection rate adjustment over the injection and post-injection operational period must be thoroughly planned to balance maximizing storage and minimizing subsurface environmental risk. The study also gives preliminary consideration to the effectiveness that monitoring strategy may play in providing useful information to inform reservoir management decisions for risk reduction. Two types of monitoring were considered: 1) pressure build-up or pressure transient; and 2) potential leakage detection from a CO 2 mass or plume. Four hypothetical legacy wells, two plugged and two abandoned, were placed in the model domain. Monitoring along these wells was measured over time in individual stacked reservoir formations and shale formations to support risk mitigation decisions, especially operational decisions that assisted in risk reduction. These simulations will serve as the basis for a series of GCS leakage risk forecasts that are to be developed using NRAP’s Open-IAM, and demonstration of a simple decision support workflow for comparative assessment of mitigation alternatives based on results of those system model forecasts. This risk assessment and decision support study is forthcoming.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

From Well Log to Formation Model: A Novel Laboratory Calibrated Methodology with Demonstration

This work demonstrates how the characterization and modeling of both elastic and creep properties are essential to describe zones in layered rock formations as either low-stress targets for stimulation or high-stress barriers to fracture growth. Prediction of fracture height is critical for designing stimulation operations in oil and gas wells. Ideally, fractures are placed in target zones which will produce hydrocarbons and should not propagate into zones expected to be unproductive or to produce unwanted fluids such as water which in turn must be treated and/or disposed. The essential task in designing stimulation plans is predicting which zones have low horizontal stresses and which will be high-stress barriers to fracture growth. Despite this importance, there are gaps in current knowledge and a complete workflow from laboratory characterization to a finite element model which includes time dependent rock deformation is required. While the research and methodology presented here also have application to CO 2or hydrogen storage, wastewater injection, and geothermal applications, the focus will be on hydrocarbon extraction. This thesis presents the results of a characterization-to-prediction workflow for the Caney shale, which is an emerging hydrocarbon resource in Oklahoma, USA. It begins with an investigation to enable critical evaluation of the Caney zonation into nominally “brittle” and “ductile” zones based on properties observed from well logs. It shows none of the zones are consistently “brittle” or “ductile” mechanical behavior based on the variety of definitions of these terms. However, the nominally ductile zones are weaker and more prone to creep. A laboratory investigation of samples including strength, elastic, and creep properties, is then used in a finite element model of stress evolution. The model includes both elastic deformation and viscoplastic creep. Results predict the least creep-prone layers to have the lowest horizontal stresses, therefore comprising hydraulic fracturing targets. The most creep-prone layers attain a horizontal stress similar to the vertical stress and therefore are predicted to be high stress barriers to hydraulic fracture stimulation. In addition to defining stimulation target intervals, the model shows how as tectonic strain rate increases, there is a transition from creep-dominated stresses to stresses dominated by elasticity.

Benge, Margaret↗
DOE OSTI2020

Damage and Failure in a Statistical Crack Model

In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes incorporated into an SCM. More specifically, I will assess the importance of including local interactions between cracks into the growth laws of an SCM. My strategy will be to construct a numerical laboratory that represents a single computational cell containing a realization of a statistical distribution of cracks. The cracks will evolve by the microphysical models of the SCM, leading to quantifiable damage and failure of the computational cell. I will use the numerical data generated by randomly generated ensembles of the fracture process to establish scaling laws that will modify and simplify the implementation of the SCM into large scale engineering codes.

42 ENGINEERING↗
DOE OSTI2023

The hidden structure of hydrodynamic transport in random fracture networks

We study the large-scale dynamics and prediction of hydrodynamic transport in random fracture networks. The flow and transport behaviour is characterized by first passage times and displacement statistics, which show heavy tails and anomalous dispersion with a strong dependence on the injection condition. The origin of these behaviours is investigated in terms of Lagrangian velocities sampled equidistantly along particle trajectories, unlike classical sampling strategies at a constant rate. The velocity series are analysed by their copula density, the joint distribution of the velocity unit scores, which reveals a simple, albeit hidden, correlation structure that can be described by a Gaussian copula. Based on this insight, we derive a Langevin equation for the evolution of equidistant particle speeds. In this framework, particle motion is quantified by a stochastic time-domain random walk, the joint density of particle position, and speed satisfies a Klein–Kramers equation. The upscaled theory quantifies particle motion in terms of the characteristic fracture length scale and the distribution of Eulerian flow velocities. That is, it is predictive in the sense that it does not require the a priori knowledge of transport attributes. The upscaled model captures non-Fickian transport features, and their dependence on the injection conditions in terms of the velocity point statistics and average fracture length. It shows that the first passage times and displacement moments are dominated by extremes occurring at the first step. The presented approach integrates the interaction of flow and structure into a predictive model for large-scale transport in random fracture networks.

42 ENGINEERING↗
DOE OSTI2020

Slip Tendency Analysis of Fracture Networks to Determine Suitability of Candidate Testbeds for the EGS Collab Hydroshear Experiment

Experiment 2 of the EGS Collab project is aimed at testing stimulation by hydro-shearing of existing natural fractures, versus Experiment 1, which is focused on hydraulic fracturing a rock mass to enhance permeability. The main criterion for the testbed selection in Experiment 2 is the presence of an interconnected network of fractures, at least 10 meters in extent, and with orientations such that shear slip can be induced at injection pressures less than the minimum horizontal stress (Shmin). The feasibility analysis for this experiment requires a well-constrained stress state along with well-characterized fracture networks. The fracture systems at two candidate locations in the Sanford Underground Research Facility (SURF), the 4850 Level (number refers to depth below ground surface in feet) and the 4100 Level, have been characterized to different extents. The 4850 Level has a well-characterized Discrete Fracture Network (DFN) from borehole (drilled for an experimental test bed) and drift observations. In contrast, the 4100 level has a fracture network characterized only by observations from the drift wall, which provides little constraint on fracture extents. This paper will present assessments for the interpreted slip potential for the natural fractures at the two locations. Data uncertainties are addressed by performing a probabilistic analysis that takes into account the uncertainty in the stress state, uncertainty in the fracture properties, and preliminary borehole locations. There is strong evidence of shear stimulation of some natural fractures in Experiment 1 on the 4850 level. We use examples of natural fractures strongly linked to shear stimulation in Experiment 1 from multiple monitoring indicators to test the consistency of the stress model and guide the uncertainty interpretation. This analysis is intended to guide the site selection process for Experiment 2 by highlighting the fracture orientations that are likely to be shear-stimulated in a majority of modeled realizations.

40 EE - Geothermal Technologies Office (EE-4G)↗
DOE OSTI2020

Hawaii Play Fairway Analysis: Lanai Resistivity and Density 3D Inversion Models

To prepare for its third phase, the Hawaii Play Fairway project conducted groundwater sampling and analyses in ten locations in the Hawaiian islands, magnetotelluric (MT) and gravity surveys, as well as calculations of 3D subsurface stress due to the weight of the rock underlying the topography of the volcano. The subsurface stresses were used to evaluate the potential for fracture-induced permeability. Inversions of the MT and gravity data produce 3D models of resistivity and density, respectively, on Lanai, across Haleakala's SW rift (Maui), and surrounding Mauna Kea (Hawaii Island). The project developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The project then incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. These results were used to identify target sites for exploratory drilling. Spreadsheet information: Each sheet contains data for a particular depth in kilometers. Positive depths are above sea level, and negative below. For more information, go to the Hawaii Groundwater and Geothermal Resources Center website linked in the resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Unlocking multiphysics design guidelines on Si/C composite nanostructures for high-energy-density and robust lithium-ion battery anode

In general, current material fabrication guidance for novel designs of Si/C composite particle materials focuses on electrochemical behavior and redox reactions at the nano/micro level. However, such guidance cannot provide detailed information for predicting mechanical deformations of the composite particles, especially when the mechanical field coupled with electrochemical and thermal fields. Here, we establish an electro-chemo-mechanical model and implement it to quantitatively analyze the multiphysics behavior of five representative Si/C composite nanostructures. Modeling and computation discover that yolk-shell and dual-shell structures are more robust in terms of particle fractures. When considering electrochemical performance, the yolk-shell structure is the best among the compared five Si/C composites. Finally, we map design guidance to further illustrate quantitative structure-property relationships. This study provides novel insights on Si/C composite nanostructure anode material design and additional powerful design tools for next-generation high-energy-density lithium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2024

Accelerating Multiphase Simulations With Denoising Diffusion Model Driven Initializations

This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics‐based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical properties of interest. Pore‐scale simulations enhance our understanding of applications such as assessing hydrogen and storage efficiency in underground reservoirs. Nevertheless, they are computationally expensive and the presence of non‐unique solutions can require multiple simulations within a single geometry. To overcome the computational cost hurdle, we propose a method that couples generative diffusion models and physics‐based simulations. While training the data‐driven model, we simultaneously generate initial conditions and perform physics‐based simulations using these. This integrated approach enables us to receive real‐time feedback on a single compute node equipped with both CPUs and GPUs. By efficiently managing these processes within a single compute node, we can continuously monitor performance and halt training once the model meets the specified criteria. To test our model, we generate realizations in a real Berea sandstone fracture which shows that our technique is up to 4.4 times faster than commonly used flow simulation initializations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Density functional theory calculation of helium segregation and decohesion effect in W110/Ni111 interphase boundary

Density functional theory (DFT) is employed to study the preferential distribution and decohesion effect of He in a W-NiFe composite consisting of W particles embedded in an Ni-based solid solution matrix. A slab containing {110}<100>W//{111}<110>Ni interface is employed as a surrogate model for the W-NiFe system. Firstly, the fracture energy of the W/Ni interphase boundary (IB) (4.37 J/m 2 ) is higher than the cleavage energy of Ni{111} (3.82 J/m^2) and lower than the cleavage energy of W{110} (6.60 J/m 2 ). The comparison shows that the cohesion of the IB is stronger than the Ni{111} planes that are away from the IB. However, the cohesion between the Ni{111} planes adjacent to the IB is found to be the weakest in this system, with a cleavage energy of 3.11 J/m 2 . Subsequently, formation energy of He is calculated in the Ni slab, W slab, and various interstitial sites in the IB. The DFT calculations show that He is significantly more stable in Ni than in W, by about 1.75 eV. Interestingly, He does not prefer to segregate at the IB as compared to bulk Ni. Nevertheless, it prefers to segregate to the region between the Ni{111} planes adjacent to the IB, and decreases the cohesion of the already weakest region. Based on an estimated amount of He gas production in 5 years under first wall neutron irradiation (neutron flux of 1.04x10 15 n/cm 2 /s), the He will decrease the cleavage energy of the weakest region by 21.2%, 15.4%, and 12.2% at 800, 1000, and 1200 C, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗