Criticality Safety Benchmark Evaluation Project Research Articles

Experimental Covariance Determination for Critical Integral Experiments

Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. In general, uncertainty quantification techniques ignore correlations between experiments and shared components. Experiments, such as the Thermal/Epithermal eXperiments (TEX) campaigns, consist of many shared components, such as the Jemima highly enriched uranium (HEU) fuel plates, which create a strong correlation in their uncertainties. While these correlations are known to exist, they are often not estimated because of the complexity of such calculations. This paper describes an intuitive method of determining the covariance for each of the experimental components, providing a correlation for each family of components across the multiple cases examined within a benchmark. A proof-of-principle study using the TEX-HEU experimental campaign was performed and verified that the covariance and correlation matrices can be calculated with information commonly found in the International Criticality Safety Benchmark Evaluation Project benchmarks. This study showed that the introduction of model and experimental covariances reduces the χ2 per degree of freedom from 2.203 to 1.179, indicating that the omission causes overly pessimistic bias quantifications. This technique can be seamlessly integrated to current benchmark evaluations as well as reevaluations of legacy benchmarks.

Validation of MCkeff code using ICSBEP results

Validation of the indigenously developed Monte Carlo program, MCkeff, is carried out by comparing the results of International Criticality Safety Benchmark Evaluation Project (ICSBEP) problems with that of standard legacy code MCNP (general-purpose Monte-Carlo N-particle transport code). Code-to-code criticality validation is essential before the usage of MCkeff to model various kinds of fissile systems. The Evaluated Nuclear Data Files (ENDF/B VII.I in ACE Format) used in MCNP is expended in the present study, thereby avoiding the differences in the results due to cross-section data. Thus, the deviations in the computed results will reflect only the differences arising out of differences in algorithms employed in these codes. Plutonium metal benchmark problems of different geometrical configurations were selected for validation purposes. All problems were simulated using MCkeff with the same inputs as in MCNP validation, and the computed results of keff (neutron multiplication factor) of various systems were compared. The results from MCkeff agree with that of MCNP, and the maximum deviation between them is less than 0.1%. Hence, the code MCkeff can be used to analyze other metal systems problems. Further validation work on the different fissile systems with other physical forms is in progress.

OpenMC interpretation and analysis of two series highly-enriched-uranium thermal-spectrum benchmarks for nuclear data validation

This study aims to provide additional validation of nuclear data performance through a comparative analysis of the evaluated nuclear libraries ENDF/B-VII.1, ENDF/B-VIII.0, JEFF-3.3, and JEFF-4 T1. The study utilizes the OpenMC Monte Carlo neutron transport code and integral benchmarks provided by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) which have not been interpreted since their first modeling. The criticality benchmarks assemblies used in this study cover 2 series which are fueled with Highly Enriched Uranium (HEU) in Metal form (MET) and have Thermal neutron spectra (THERM), referred to as HMT-026 and HMT-027, respectively. The results show that for the HMT-026 benchmarks, ENDF/B-VII.1 and ENDF/B-VIII.0 have results close to experiments. The best global agreement with the HMT-027 experiments was found to be ENDF/B-VII.1. Through relevant critical and nuclear data sensitivity analysis, it is found that Be and BeO are respectively of crucial importance for HMT-026 and HMT-027 and the nuclear data of 9Be (especially for ENDF/B-VIII.0) should be reviewed. Additionally, it is worth noting that the Thermal Scattering Law (TSL) of BeO has a great influence on the keff calculation for the HMT-027 benchmarks, while the influence of TSL of metal Be is negligible for the HMT-026 experimental benchmarks.

A Novel Hybrid Deterministic and Monte Carlo Neutron Transport Formulation and Algorithm (tRAPID) for Accurate and Fast 3-D Reactor Kinetics

The available three-dimensional (3-D), time-dependent neutron transport algorithms and codes (deterministic or Monte Carlo) are very computationally intensive and are impractical for the simulation of real-world reactors. Henceforth, commonly approximate forms of the transport equation (e.g., diffusion or SPn) are used with expected loss of accuracy. We have developed a hybrid deterministic and Monte Carlo algorithm that not only preserve a Monte Carlo–level accuracy but can achieve a solution in seconds or minutes. This algorithm has been incorporated into the RAPID code system and tested for a number of benchmark problems. This novel time-dependent algorithm, referred to as tRAPID, utilizes a transient fission matrix methodology and allows for fast and accurate simulation of 3-D time-dependent neutron transport problems. The tRAPID algorithm is used to calculate neutron kinetics parameters (such as l eff and Rossi- α ) and 3-D time-dependent prompt and delayed fission source distributions for two reference models: the Flattop-Pu critical assembly and the Jožef Stefan Institute TRIGA Mark-II benchmark core. Results are compared to experiments reported in the International Criticality Safety Benchmark Evaluation Project Handbook as well as to a reference Serpent Monte Carlo calculation. The tRAPID results are in excellent agreement with both the experimental data and Serpent predictions, while requiring minimal computing resources.

Engagement opportunities in OECD NEA benchmark development

A myriad of opportunities is available to collaborate via international benchmark exercises and experimental data preservation activities. Many such opportunities abound under the auspices of the Nuclear Science Committee of the Organisation for Economic Co-operation and Development Nuclear Energy Agency (NEA). Key projects and activities of relevance to the development of advanced reactors design include the International Criticality Safety Benchmark Evaluation Project (ICSBEP), the International Reactor Physics Experiment Evaluation Project (IRPhEP), the International Assay Data of Spent Nuclear Fuel Database (SFCOMPO), the Shielding Integral Benchmark and Archive Database (SINBAD), and The International Experimental Thermal HYdraulicS Database (TIETHYS), and various cooperative benchmark exercises. Interested participants are encouraged to contact the leadership and secretariat of the various Technical Working Groups and Working Parties to become more engaged. This paper provides a summary of the current benchmark exercises and experimental databases available for international participation.

Intrinsic value of the international benchmark projects, ICSBEP and IRPhEP, for advanced reactor development

The International Criticality Safety Benchmark Evaluation Project, a sanctioned program under the auspices of the Nuclear Energy Agency of the Organisation for Economic Co-operation and Development, has been a highly successful and productive collaboration, now encompassing over 5,000 evaluated experimental benchmarks trusted and relied upon throughout the international nuclear communities. The success of this project led to the development of the International Reactor Physics Experiment Evaluation Project, which is dedicated to the evaluation of benchmark experiment data to sustain current and future reactor physics validation needs. These exemplary programs, and their widely utilized handbooks, serve as gold standards to which other databases strive to emulate. The purpose of the two projects is to preserve modern and legacy experimental data and evaluate it in a standardized handbook format to provide quality benchmarks to support modern and future criticality safety and reactor physics validation. These two projects have often served as the mechanism through which historic and modern neutronics experiments are evaluated and shared across international borders, to best provide unique, high-quality peer-reviewed, and often otherwise unavailable, benchmark data. The contents of these handbooks are utilized not only in validating criticality safety, reactor physics, and advanced reactor calculations, but are used to validate neutronics calculations and nuclear data for most other nuclear applications. This manuscript discusses both international programs and available content to enable advanced reactor design validation.

Expanded COG criticality validation suite for inter-laboratory benchmark data comparison

The COG suite of criticality benchmarks has been formally expanded from 591 to 3,395 to coverthe entire energy range from thermal to fast neutron spectra under a variety of reflector and moderator conditions and fissile materials. COG results have been compared with benchmark values from the International Criticality Safety Benchmark Evaluation Project Handbook for ENDF/B-VII.1, ENDF/BVIII.0 and JEFF-3.3. COG results have been also compared with a MERCURY validation suite. Most of the results agreed with the benchmark values within ±3σ. Among the three cross section data, cases with ENDF/B-VIII.0 performed best with about 85% of the total cases within ±3σ range. A major intercomparison project between COG, MCNP, MORET, and SCALE for ENDF/B-VIII.0 and JEFF-3.3 is in progress.

Contributions to Integral Nuclear Data in ICSBEP and IRPhEP since ND 2019

The status of the two neutronics international benchmark projects sanctioned by the Organisation for Economic Co-operation and Development Nuclear Energy Agency (OECD NEA), the International Criticality Safety Benchmark Evaluation Project (ICSBEP) and the International Reactor Physics Experiment Evaluation Project (IRPhEP), was last directly discussed with the international nuclear data community at the 14th International Conference on Nuclear Data for Science and Technology (ND2019) in Beijing, China. Since ND2019, the quantity of available integral benchmark experiment data has increased. The primary purpose of the ICSBEP and IRPhEP is to provide extensively peer-reviewed benchmark data to the international nuclear community in support of validation and testing of nuclear data and models. A total of 28 countries have contributed to the past and continued success of these projects as benchmark evaluations, technical reviews, and experimental data using their own time and resources: 26 to the ICSBEP and 25 to the IRPhEP. Key contributions to the handbooks over the past three years can only be highlighted within this paper. Full technical details and benchmark experiment descriptions can be located within the benchmark reports distributed within recent editions of the handbooks.

Using a Random Forest Model to Choose Optimized Group Structures

It is challenging to select an appropriate group structure for any given multigroup neutron transport problem. Many group structures were designed long ago, and the reasoning behind the creator’s choices may be unknown. In this work, we apply the simulated annealing optimization method to develop improved group structures for a set of test problems. We then use a random forest (a machine learning method) to identify which group structure will be the best for any new problem based on input characteristics, such as geometry and isotopics. Simulated annealing spans a large solution space before narrowing in on an optimal solution, avoiding local minima by jumping around. Our solution space, however, is large and inconsistent, making finding the optimal group structure infeasible. Instead, we find potentially optimal group structures, ones that yield more accurate solutions than our standard group structures, but are probably not the “best” possible. Group structures are obtained for six classes of problems, ranging from a fast 233U system to a thermal 239Pu system. These were chosen to encompass a series of critical assemblies from the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook. These optimized group structures were used in PARTISN for a large range of ICSBEP critical assemblies and compared to the traditional Los Alamos National Laboratory group structures. Our reference solution was from 618-group PARTISN runs. The results were used to train a random forest regressor model with bagging, which was then tested on similar benchmarks. The bagging regressor model chose the best group structure from 52% to 65% of the time, and a subjectively “good” group structure up to 91% of the time.

McCARD Criticality Benchmark Analyses with Various Evaluated Nuclear Data Libraries

International Criticality Safety Benchmark Evaluation Project (ICSBEP) criticality analyses were conducted using the McCARD Monte Carlo code for 85 selected benchmark problems with 7 evaluated nuclear data libraries (ENDLs): ENDF/B-VII.1, ENDF/B-VIII.0, JENDL-4.0, JENDL-5.0, JEFF-3.3, TENDL-2021, and CENDL-3.2. Regarding the analyses, it was confirmed that the keff results are sensitive to the ENDL. It is noted that the new-version ENDLs show better performance in the fast benchmark cases, while on the other hand, there are no significant differences in keff among the different ENDLs in the thermal benchmark cases. The sensitivity of the keff results depending on the ENDL may impact nuclear core design parameters such as the shutdown margin, critical boron concentration, and power defects. This study and keff results will be a good reference in the development of new types of nuclear cores or new design codes.

Continuous-Energy ENDF/B-VIII.0 Cross Section and SCALE 6.2.4 Performance for Nuclear Criticality Safety Applications: 1H, C, 58,60Ni, 182,183,184,186W, 235,238U, 239Pu

As part of the nuclear data evaluation and validation cycle, the ENDF/B-VIII.0 cross-section library released in 2018 requires testing to determine areas of improvement and deterioration. Previous work by the authors investigated the performance of 16O, 56Fe, and 63,65Cu cross sections, with this study acting as an extension of the prior work. In addition to the isotopes and nuclear criticality safety benchmarks of interest to the prior work, benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook were selected for their keff sensitivity to 1H, C, 58,60Ni, 182,183,184,186W, 235,238U, or 239Pu cross sections and were modeled in the SCALE code system maintained by Oak Ridge National Laboratory. In total, 253 benchmark configurations were selected for their sensitivities and modeled using SCALE 6.2.4 Criticality Safety Analysis Sequences (CSAS) continuous-energy Monte Carlo keff calculations. This collection includes and expands upon the 99 benchmarks in the prior work. The AMPX-processed ENDF/B-VIII.0 library was decomposed into individual ENDF/B-VIII.0 datum libraries for each isotope of interest. Doing so allowed for the individual substitution of an ENDF/B-VIII.0 cross section in the place of ENDF/B-VII.1, determining isotope-specific effects of ENDF/B-VIII.0 relative to ENDF/B-VII.1. Full library calculations with entirely ENDF/B-VII.1 data or entirely ENDF/B-VIII.0 data were also executed. As a measure of performance, the average relative deviation was determined as the ratio of the deviation between calculated and experimental keff to the propagated calculational and experimental uncertainty. With calculated full library and isotope-specific ENDF/B-VIII.0 keff’s, an optimized combination of data libraries was estimated and confirmed with SCALE calculations. This showed that reverting 239Pu, 58Ni, 16O, and 65Cu cross sections to ENDF/B-VII.1 resulted in improved performance relative to the full ENDF/B-VIII.0 library. Across all 253 benchmarks, the average relative deviation was 1.29σ for the full ENDF/B-VII.1 library, 1.17σ for the full ENDF/B-VIII.0 library, and 0.97σ for the optimized combination. The reversion of 239Pu, 58Ni, 16O, and 65Cu cross sections to ENDF/B-VII.1 in the 99 benchmarks of the prior work resulted in further improved experimental agreement compared to the previously reported improvement from 16O and 65Cu alone. Therefore, it is suggested that applications with significant sensitivities to 239Pu, 58Ni, 16O, and 65Cu consider their choice of nuclear data library.

Nuclear criticality calculations using Geant4

A method for determining the parameters of importance to nuclear reactor kinetics and nuclear criticality analysis using the general-purpose Monte Carlo simulation toolkit Geant4 has been developed. The demonstration of the proposed method is first illustrated by a set of six Godiva-like criticality problems consisting of hypothetical spherical subcritical and supercritical configurations of highly enriched uranium. Next, the performance of the application of Geant4 for criticality evaluations is shown using selected experimental benchmarks from the International Criticality Safety Benchmark Evaluation Project ICSBEP. Results were compared with those obtained by a set of the most used neutron transport codes such as MCNP, TRIPOLI-4®, KENO, APOLLO and SERPENT.

Validation of Continuous-Energy ENDF/B-VIII.0 16O, 56Fe, and 63,65Cu Cross Sections for Nuclear Criticality Safety Applications

Recently completed cross-section evaluations sponsored in part by the Nuclear Criticality Safety Program were incorporated into the 2018 release of the ENDF/B-VIII.0 cross-section library. Evaluated isotopes of interest to the nuclear data and criticality safety community include 16O, 56Fe, and 63,65Cu. For performance validation, benchmark models defined in the International Criticality Safety Benchmark Evaluation Project Handbook were selected based on energy-integrated keff sensitivities to total cross sections of interest and compared with experimental values. Of the 102 benchmark configurations that were utilized, 63 are sensitive to 16O, 32 sensitive to 63,65Cu, and 25 sensitive to 56Fe. Selected benchmarks were modeled in SCALE 6.2.3 Criticality Safety Analysis Sequence (CSAS) continuous-energy Monte Carlo keff calculations with ENDF/B-VII.1, with a hybrid ENDF/B-VII.1 with ENDF/B-VIII.0 data substituted for individual isotopes of interest, and with ENDF/B-VIII.0. ENDF/B-VIII.0 showed improved agreement with experimental keff for 56Fe, 63Cu, elemental copper, and full library substitution while producing lessened agreement for 16O and 65Cu. With full library and isotope-specific ENDF/B-VIII.0 performance, a best-case ENDF library was formed by excluding underperforming isotopes’ ENDF/B-VIII.0 data, reverting 16O and 65Cu cross sections to ENDF/B-VII.1. This resulted in the average relative deviation between calculated and experimental data improving from 1.45σ for the ENDF/B-VIII.0 library to 1.32σ for the best-case library, relative to benchmark uncertainty.

Validation of the Monte Carlo code MONK for thermal 232Th/233U systems using the JEF-2.2 and JEFF-3.1 libraries

There is limited validation of MONK using 232Th/233U benchmarks, and existing validation of Monte Carlo codes has generally used older nuclear data libraries. Here we use MONK-9A to systematically study a series of thermal 232Th/233U-based benchmark experiments, taken from the International Criticality Safety Benchmark Evaluation Project handbook and using JEF-2.2 and JEFF-3.1 libraries. We find that 232Th-dominated thermal systems (those moderated with graphite or light water) with limited 233U content show little difference when modelled with JEF-2.2 or JEFF-3.1. However, when there is significant 233U then JEFF-3.1 is found to give considerably better agreement with experiment. There is likely to be little benefit in utilising JEFF-3.1 instead of JEF-2.2 when modelling systems for which the predominant nuclides are 232Th, 235U and 238U. However, for systems containing large fractions of 233U – such as light water breeder reactors operating on a 232Th-233U cycle – it is recommended that JEFF-3.1 is utilised.

Monte Carlo Criticality Calculation of Random Media Formed by Multimaterials Mixture Under Extreme Disorder

A dynamical system under extreme physical disorder has the tendency to evolve toward the equilibrium state characterized by an inverse power law power spectrum. In this paper, a practical, implementable, three-dimensional model is proposed for the random media formed by a multimaterials mixture under such a power spectrum using a randomized form of the Weierstrass function, its extension covering the white noise, and partial volume pairings of constituent materials. The proposed model is implemented in the SOLOMON Monte Carlo solver with delta tracking. Two sets of numerical results are shown using the JENDL-4 nuclear data libraries. First, the uncertainty of the neutron effective multiplication factor (keff) due to the inherent uncertainty in the formation of random media is shown for a randomized version of the Bigten core in the International Criticality Safety Benchmark Evaluation Project (ICSBEP). Second, the influence of the exponent of the power spectrum on the uncertainty of keff is evaluated for a randomized version of the Topsy core in the ICSBEP.

Assessment of Critical Experiment Benchmark Applicability to a Large-Capacity HALEU Transportation Package Concept

This work presents an assessment of the applicability of existing benchmark critical experiments to the criticality safety code validation for a large-capacity high-assay low-enriched uranium (HALEU) transportation package concept. Numerous next-generation nuclear reactor designs require HALEU fuel, which is characterized by an enrichment between 5 and 20 wt% 235U. The U.S. Department of Energy (DOE) has proposed to recover and downblend highly enriched uranium from DOE-owned used nuclear fuel to accelerate the demonstration of commercially viable microreactor technologies. One element of the infrastructure needed to demonstrate HALEU-fueled reactors is the ability to safely transport enriched product to be used for fuel fabrication. There is uncertainty as to whether existing critical benchmark experiment data are sufficient to support criticality safety code validation for HALEU transportation applications. The anticipated chemical form of the HALEU in the proposed transportation concept is UO2 with 20 wt% 235U/U. The concept uses a combination of an existing transportation packaging design and a novel basket design, including borated aluminum flux traps. The basket provides space for 18 reusable, stainless steel canisters that contain the HALEU. In 10 CFR 71, normal conditions of transport (NCTs) and hypothetical accident conditions (HACs) are defined for fissile material transportation packages. NCT and HAC KENO-VI models of the transportation package were developed using the Standardized Computer Analyses for Licensing Evaluation (SCALE) 6.2.3 computer code package, and optimum moderation conditions were determined using the SCALE SAMPLER sequence. The SCALE Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) sequences were then used to compare the neutronic characteristics of 1584 International Criticality Safety Benchmark Evaluation Project benchmark critical experiments with the NCT and HAC HALEU transportation models. The TSUNAMI integral correlation coefficient ck was the criterion used to rank neutronic similarity. Thirty-four experiments were identified as similar (ck ≥ 0.9) to the NCT model, and 55 experiments were identified as similar to the HAC model. Hundreds of experiments were also identified as at least marginally similar (ck ≥ 0.8) to both models. The results indicate that additional critical experiments are unlikely to be needed to support HALEU transportation criticality safety analyses for package concepts similar to the concept package analyzed.

Methodology for Generating Covariance Data of Thermal Neutron Scattering Cross Sections

This paper details and implements a framework for evaluating thermal neutron scattering cross sections that provide data and covariance data for hydrogen in light water. This methodology involves perturbing model parameters of molecular dynamics potentials and fitting the simulation results to experimental data. The framework is general and can be applied to any material or simulation method. The fit is made using the Unified Monte Carlo method to experimentally measure double-differential scattering cross sections of light water at the Spallation Neutron Source at Oak Ridge National Laboratory. Mean values and covariance data were generated for model parameters, phonon density of states, double-differential cross sections, and total scattering cross sections. These posterior parameter values were very similar to their prior values with a maximum relative error of 0.54%. This falls within in the Unified Monte Carlo–calculated uncertainties on the order of 2.7%. Additionally, posterior double-differential cross sections agree favorably with ENDF/B-VIII.0 cross sections. The new thermal scattering law was tested by comparing it against benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook, which showed a slight improvement over the ENDF/B-VIII.0 library. Additionally, the covariance matrix of the phonon density of states was validated to confirm that the spread of keff from the density of states used to generate the covariance matrix was similar to the spread of keff from the density of states of the sampled covariance matrix.

Validation of UNIST Monte Carlo code MCS for criticality safety calculations with burnup credit through MOX criticality benchmark problems

This paper presents the validation of the MCS code for critical safety analysis with burnup credit for the spent fuel casks. The validation process in this work considers five critical benchmark problem sets, which consist of total 80 critical experiments having MOX fuels from the International Criticality Safety Benchmark Evaluation Project (ICSBEP). The similarity analysis with the use of sensitivity and uncertainty tool TSUNAMI in SCALE was used to determine the applicable benchmark experiments corresponding to each spent fuel cask model and then the Upper Safety Limits (USLs) except for the isotopic validation were evaluated following the guidance from NUREG/CR-6698. The validation process in this work was also performed with the MCNP6 for comparison with the results using MCS calculations. The results of this work showed the consistence between MCS and MCNP6 for the MOX fueled criticality benchmarks, thus proving the reliability of the MCS calculations.

Contributions to integral nuclear data in ICSBEP and IRPhEP since ND2016

The contributions to the International Criticality Safety Benchmark Evaluation Project (ICSBEP) and the International Reactor Physics Experiment Evaluation Project (IRPhEP) was last presented to the international nuclear data community at ND2016. Since ND2016, integral benchmark data that are available for nuclear data testing has continued to increase. The 2018 edition of the International Handbook of Evaluated Criti-cality Safety Benchmark Experiments (ICSBEP Handbook) now contains 574 evaluations with benchmark specifications for 4,916 critical, near-critical, or subcritical configurations, 45 criticality alarm placement/shielding configuration with multiple dose points apiece, and 215 configurations that have been categorized as fundamental physics measurements that are relevant to criticality safety applications. The 2018 edition of the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook) contains data from 159 different experimental series that were performed at 54 different nuclear facilities. Currently 156 of the 159 evaluations are published as approved benchmarks with the remaining three evaluations published as drafts. Measurements found in the IRPhEP Handbook include criticality, buckling and extrapolation length, spectral characteristics, reactivity effects, reactivity coefficients, kinetics, reaction-rate distributions, power distributions, isotopic compositions, and/or other miscellaneous types of measurements for various types of reactor systems. Additional benchmark evaluations will be included in the 2019 editions of these handbooks. These handbooks continue to represent the standard for neutronics benchmark experiment evaluation.

Current overview of ICSBEP and IRPhEP benchmark evaluation practices

Two projects sanctioned by the Organisation for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) have over two decades of experience developing established and comprehensive data sets in handbooks supporting criticality safety and reactor physics. The International Criticality Safety Benchmark Evaluation Project (ICSBEP) and the International Reactor Physics Experiment Evaluation Project (IRPhEP) serve as examples of quality and excellence in preserving our experimental data heritage and establishing integral benchmark standards upon which current and future modeling, validation, and safety efforts can be supported. Evaluation practices have evolved with each year of these projects to include additional benchmark experiment data, establish more comprehensive techniques for evaluation of uncertainties and biases, and encourage established high-quality peer-review efforts. This paper will summarize the current format of the handbooks, best-practices for a comprehensive benchmark evaluation, recent activities and protocol within these projects, and a look into future identified needs and activities.