Nuclear Data Uncertainties Research Articles

Analysis for the ARIANE GU1 sample: Nuclide inventory and decay heat

The present study provides a detailed analysis of the calculations of 50 isotopic compositions for the Post Irradiation Examination sample GU1 from the ARIANE program. Two types of approach are performed: a lattice (2 dimensional) and a full core (3 dimensional) calculations. In the case of lattice calculations, the effect oflocation is also studied. Different code versions (for CASMO5 and SNF) are used in order to contribute to the validation work for specific calculation schemes and to assess the impact of nuclear data libraries as well. The effects of nuclear data are also quantified for cross sections, spectra and fission yields, together with their partial contributions. It is concluded that the consideration of the effect of the mass balance, nuclear data uncertainties, as well as uncertainties from operational conditions and manufacturing tolerances help in obtaining consistency between calculated and measured isotopic concentrations.This study is then complemented with decay heat calculations for the assembly of interest, consistent with the PIE study. It indicates that, without considering geometrical deformation due to the long storage time, nuclear data are still the main source of uncertainties. Expanded uncertainties (including biases, experimental and calculation uncertainties) are finally proposed for both isotopic compositions and decay heat.

Uncertainty assessment for the displacement damage of a pressurized water reactor vessel

The neutron irradiation-induced mechanical property change is a major challenge for nuclear materials. For a Pressurized Water Reactor (PWR), neutron irradiation embrittlement of the reactor pressure vessel is one of the most important issues that determine the whole nuclear power plant lifetime. The present work focuses thus on the uncertainty assessment for the neutron irradiation displacement damage of a PWR vessel. The uncertainties of neutron flux, nuclear data, and atomic displacement models are propagated to Displacement per Atom (DPA) rates with a special emphasis on the importance of correlation matrices. In addition to the uncertainty propagated from the threshold displacement energy, the total uncertainty of damage energy rate is about 10% (at 1 σ ), whereas the uncertainty is largely underestimated if the correlations of damage cross section and neutron flux are not considered. Apart from the complete uncertainty propagation shown in this paper, combining the damage energy rate uncertainty and the displacement threshold energy uncertainty is recommended for estimating the calculated DPA rate uncertainty. Besides the uncertainty, the biases induced by the model defects are preliminarily estimated.

Research Progresses of Uncertainty Quantification Methods for High Fidelity Numerical Nuclear Reactor

Numerical reactor based on high fidelity model and method is with the characteristics of high precision and high resolution, but the inherent uncertainty of nuclear data and other parameters will seriously affect the uncertainty of numerical reactor analysis results. Based on the review of the research progresses of numerical reactors and its uncertainty quantification in the world, this paper focuses on the research progresses in NECP Laboratory of Xi’an Jiaotong University in recent years, including the development of one-step high fidelity numerical reactor program NECP-X, the generation of nuclear data covariance database, the uncertainty propagation method based on deterministic method and sampling method, and the uncertainty quantification in transient calculation. An advanced sampling method COST is proposed. Based on the high fidelity numerical reactor program, the uncertainty propagation of covariance of various nuclear parameters in the steady-state and transient analysis of the reactor core is quantified for the first time, which is of great significance for engineering application of numerical reactors.

Uranium integral fission product yields for a spectrally-shaped 14.1 MeV neutron source at the National Ignition Facility

This paper describes the experimental results for an energy tuning assembly created to modify the National Ignition Facility deuterium–tritium fusion neutron source into a notional thermonuclear and prompt fission neutron spectrum, which has applications in integral measurements, nuclear data benchmarks, and radiation effects on microelectronics. The Monte Carlo neutron transport utilized MCNP5 to estimate the ETA-modified fluence using the ENDF-B/VIII.0 and IRDFF-II continuous energy nuclear data libraries, and SCALE Sampler was used to estimate the systematic nuclear data covariance using ENDF-B/VII.1 and IRDFF-II in a 252-group structure. The experiment fielded eight activation foils and a highly enriched uranium sample. This provided fifteen reaction channels that were used in a forward-fit comparison to the modeled results and to unfold the neutron spectrum using STAYSL. Gamma-ray spectrometry was performed on the activation and highly enriched uranium foils, and the reduced χ2 between the modeled and experimental values was 1.21. The results from the STAYSL unfold, reduced χ2=1.62, indicated that the modeled neutron spectrum was achieved and the systematic nuclear data uncertainty associated with the neutron transport and activation product cross sections was representative of the experiment. Integral cumulative fission product yield data were collected for 37 mass chains with a combination of gamma-ray spectrometry and radiochemical analysis. Fission product analysis was generally in agreement with two models using a semi-empirical fit and the General Observables of Fission code, with the exception of mass chains 88, 109, 111, 112, 113, 129, 139, 142, 144, 151, and 156.

Simulation of low-enriched uranium burnup in Russian VVER-1000 reactors with the Serpent Monte-Carlo code

This work deals with the assessment of the burnup capabilities of the Serpent Monte Carlo code to predict spent nuclear fuel (SNF) isotopic concentrations for low-enriched uranium (LEU) fuel at different burnup levels up to 47 MWd/kgU. The irradiation of six UO2 experimental samples in three different VVER-1000 reactor units has been simulated and the predicted concentrations of actinides up to 244Cm have been compared with the corresponding measured values. The results show a global good agreement between calculated and experimental concentrations, in several cases within the margins of the nuclear data uncertainties and in a few cases even within the reported experimental uncertainties. The differences in the performances of the JEFF3.1.1, ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries (NDLs) have also been assessed and the use of the newly released ENDF/B-VIII.0 library has shown an increased accuracy in the prediction of the C/E's for some of the actinides considered, particularly for the plutonium isotopes. This work represents a step forward towards the validation of advanced simulation tools against post irradiation experimental data and the obtained results provide an evidence of the capabilities of the Serpent Monte-Carlo code with the associated modern NDLs to accurately compute SNF nuclide inventory concentrations for VVER-1000 type reactors.

Uncertainty analyses of spent nuclear fuel decay heat calculations using SCALE modules

Decay heat residuals of spent nuclear fuel (SNF), i.e., the differences between calculations and measurements, were obtained previously for various spent fuel assemblies (SFA) using the Polaris module of the SCALE code system. In this paper, we compare decay heat residuals to their uncertainties, focusing on four PWRs and four BWRs. Uncertainties in nuclear data and model inputs are propagated stochastically through calculations using the SCALE/Sampler super-sequence. Total uncertainties could not explain the residuals of two SFAs measured at GE-Morris. The combined z-scores for all SFAs measured at the Clab facility could explain the resulting deviations. Nuclear-data-related uncertainties contribute more in the high burnup SFAs. Design and operational uncertainties tend to contribute more to the total uncertainties. Assembly burnup is a relevant variable as it correlates significantly with the SNF decay heat. Additionally, burnup uncertainty is a major contributor to decay heat uncertainty, and assumptions relating to these uncertainties are crucial. Propagation of nuclear data and design and operational uncertainties shows that the analyzed assemblies respond similarly with high correlation. The calculated decay heats are highly correlated in the PWRs and BWRs, whereas lower correlations were observed between decay heats of SFAs that differ in their burnups.

Nuclear-data uncertainty analysis for the start-up physics test of CPR1000 reactor

In this paper, the uncertainty propagation has been performed from the nuclear data to the key parameters of start-up physics test for the first cycle of CPR1000 reactor. The start-up physics test is very important for the safety of PWRs, during which the key parameters including the critical boron concentration, temperature coefficient, integral worth of RCCA (Rod Cluster Control Assembly) and power distributions should be measured and used to validate the nuclear-designed ones. In order to guarantee the reactor safety, the errors between the simulation values and measurement values are required to satisfy corresponding engineering limits. However, for the conventional validation method, the uncertainties of the simulation values were ignored. Therefore, the uncertainty analysis has been performed to propagate the nuclear-data uncertainties to these key parameters of the start-up physics test for the CPR1000 reactor. Through the analysis, the absolute and relative uncertainties of these key parameters have been quantified, with the nuclear-data covariance data from ENDF/B-VII.1, ENDF/B-VIII.0 and TENDL-2017.

Propagating neutronic uncertainties for FFTF LOFWOS Test #13

The safety evaluation conducted for licensing a Sodium-cooled Fast Reactor (SFR) may require modeling transients with best-estimate calculation tools that must first be validated against real-world measurements. To provide the community with a valuable benchmarking opportunity for validating SFR analysis tools and methods, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13. The impact of nuclear data uncertainties on neutronics parameters was previously investigated based on the COMMARA-2.0 covariance matrix. Since the transient simulation results are very sensitive to certain reactivity coefficients, it was decided to employ rigorous uncertainty propagation methods to quantify the impact of nuclear data uncertainties on the best-estimate predication of FFTF LOFWOS Test #13. The DAKOTA code is used to propagate neutronic uncertainties through SAS4A/SASSYS-1 transient simulations, while taking into account spatial and reaction-wise correlations within these uncertainties. This study shows that the remaining discrepancies observed between the Argonne National Laboratory (ANL) best-estimate results and the experimental measurements can be partly explained by the uncertainty associated with Gas Expansion Module (GEM) worth, which contributes the majority of the overall nuclear data uncertainty on the output from the FFTF LOFWOS Test #13 transient simulation. This study also confirmed the importance of including spatial and reaction-wise correlations of nuclear data uncertainties on feedback coefficients in the uncertainty propagation to avoid under-estimating their impact during the transient simulations.

ASUSD nuclear data sensitivity and uncertainty program package: Validation on fusion and fission benchmark experiments

Nuclear data (ND) sensitivity and uncertainty (S/U) quantification in shielding applications is performed using deterministic and probabilistic approaches. In this paper the validation of the newly developed deterministic program package ASUSD (ADVANTG + SUSD3D) is presented. ASUSD was developed with the aim of automating the process of ND S/U while retaining the computational efficiency of the deterministic approach to ND S/U analysis. The paper includes a detailed description of each of the programs contained within ASUSD, the computational workflow and validation results.ASUSD was validated on two shielding benchmark experiments from the Shielding Integral Benchmark Archive and Database (SINBAD) - the fission relevant ASPIS Iron 88 experiment and the fusion relevant Frascati Neutron Generator (FNG) Helium Cooled Pebble Bed (HCPB) Test Blanket Module (TBM) mock-up experiment. The validation process was performed in two stages. Firstly, the Denovo discrete ordinates transport solver was validated as a standalone solver. Secondly, the ASUSD program package as a whole was validated as a ND S/U analysis tool. Both stages of the validation process yielded excellent results, with a maximum difference of 17% in final uncertainties due to ND between ASUSD and the stochastic ND S/U approach. Based on these results, ASUSD has proven to be a user friendly and computationally efficient tool for deterministic ND S/U analysis of shielding geometries.

Improvement of sensitivity and uncertainty analysis capabilities of generalized response in Monte Carlo code RMC

The capability of performing nuclear data sensitivity and uncertainty analysis of reaction rates has been developed in continuous-energy Reactor Monte Carlo (RMC) code. The sensitivity coefficients of reaction rates are calculated by using new generalized perturbation theory (GPT) formulation which is also implemented in McCARD. The superhistory based generalized perturbation theory (SH-GPT) formulation is developed in this paper to overcome the huge memory consumption problem encountered by the new GPT formulation. This newly developed capability is tested on several benchmark problems. The sensitivity coefficients are shown to agree within 5% of reference results for most cases. Moreover, the region-specified sensitivity analysis capability enables RMC to be the first continuous-energy Monte Carlo code that can use the first-order uncertainty quantification method to perform uncertainty analysis of the power distribution. The uncertainty results calculated by first-order uncertainty quantification method also agree well with those obtained by using stochastic sampling method.

ANSWERS® TOOLS FOR UNCERTAINTY QUANTIFICATION AND VALIDATION

ANSWERS® is developing a set of uncertainty quantification (UQ) tools for use with its major physics codes: WIMS/PANTHER (reactor physics), MONK (criticality and reactor physics) and MCBEND (shielding and dosimetry). The Visual Workshop integrated development environment allows the user to construct and edit code inputs, launch calculations, post-process results and produce graphs, and recently uncertainty quantification and optimisation tools have been added. Prior uncertainties due to uncertainties in nuclear data or manufacturing tolerances can be estimated using the sampling method or using the sensitivity options in the physics codes combined with appropriate covariance matrices. To aid the user in the choice of appropriate validation experiments, the MONK categorisation scheme and/or a similarity index can be used. An interactive viewer has been developed which allows the user to search through, and browse details of, over 2,000 MONK validation experiments that have been analysed from the ICSBEP and IRPhE validation sets. A Bayesian updating approach is used to assimilate the measured data with the calculated results. It is shown how this process can be used to reduce bias in calculated results and reduce the calculated uncertainty on those results. This process is illustrated by application to a PWR fuel assembly.

NUCLEAR DATA SENSITIVITY/UNCERTAINTY PRE-ANALYSIS OF FNG WCLL FUSION BENCHMARK

To assure tritium self-sufficiency in future fusion reactors such as DEMO the accuracy of TRP calculations has to be demonstrated within the design uncertainties. A new neutronics experiment representing a mock-up of the Water Cooled Lithium Lead (WCLL) Test Blanket Module (TBM) is under preparation at the Frascati neutron generator (FNG) with the objective to provide an experimental validation of accuracy of nuclear data and neutron transport codes for the tritium production rate (TPR) calculations. The mock-up will consist of LiPb bricks, EUROFER plates and Perspex substituting water. The mock-up will be irradiated by 14 MeV neutrons at the FNG facility, and the TPR and detector reaction rates will be measured using Li2CO3 pellets and activation foils placed at different positions up to about 55 cm inside the mock-up. Computational pre-analyses for the design of the WCLL neutronics experiment using the SUSD3D sensitivity/uncertainty (S/U) code system is described and compared with the results of some similar FNG experiments performed in the past, in particular the FNG HCPB Tritium Breeder Module Mock-up (2005) and FNG-HCLL Tritium Breeder Module Mock-up (2009). The objective of the pre-analysis is to provide the calculated nuclear responses including the uncertainties due to the uncertainties in nuclear data and thus contributes to the optimisation of the design of the experimental set-up.

DOSIMETRY MODELING AND EXPERIMENTAL VALIDATION FOR THE PETALE PROGRAM IN THE CROCUS REACTOR

The PETALE experimental program in the CROCUS reactor intends to provide integral measurements on reactivity worth and dosimetry measurement to constrain nuclear data relative to stainless steel heavy reflectors. The experimental setup consists in eight successive plates of pure iron, pure nickel, pure chromium, or nuclear-grade stainless steel set at the close periphery of the core. The plates are interleaved with up to nine dosimeters that consist of thin activation foils with different possible materials to be sensitive to different ranges of the neutron spectrum. A precise measurement with a good estimation of the uncertainties and correlations is required, especially when comparing reaction rates, e.g. transmission measurement and/or spectral indices. The present work focuses on the validation of the dosimetry technics developed in preparation of this experimental program. Different aspects are discussed: monitors, efficiency calibration, self-absorption correction, self-shielding and nuclear data uncertainties. The different sources of uncertainties for the experiment-calculation comparisons are characterized, taking into account all the correlation between the different dosimeters. These correlations are a mandatory element for the aimed Bayesian assimilation in order to avoir overfitting when considering dosimeter providing a similar information.

AN IRSN CONTRIBUTION TO THE UAM PROJECT: THERMAL-HYDRAULIC AND NEUTRONIC UNCERTAINTIES PROPAGATION IN A ROD EJECTION, FIRST RESULTS

The paper presents our first results of the exercise III-I-2c from the OECD-NEA UAM-LWR benchmark intended to an elaboration of the methodology of uncertainty propagation. The considered case studied a full PWR core behavior in fast (~0.1 sec) rod ejection transient. According to the benchmark, the core represented a Hot Zero Power state. Authors used brute-force sampling propagating nuclear data and thermo-fluid uncertainties using 3D computational IRSN chain HEMERA. It couples the reactor physics code CRONOS and thermal-hydraulic core code FLICA4. The nuclear data uncertainties were represented in a form of cross sections standard deviations (in percentage of the mean cross sections values) supplied by the UAM team. In addition to the original benchmark, the study includes a case with an increased power peak by supplementary rod ejection, i.e. with higher reactivity. Both the results are similar to what we obtained in the mini-core rod ejection: the power standard deviation follows, in percentage of the mean power, the mean power curve. We split the variance with a direct calculation: once the cross sections are modified and the thermal-hydraulics inputs are kept constant, another time the contrary. The results show that uncertainties dues to nuclear data dominate over ones due to the thermal-flow area. Furthermore, the major contributors in peak-of-power variance lie in a fast group of cross sections.

FAST REACTOR MULTIPHYSICS AND UNCERTAINTY PROPAGATION WITHIN WIMS

For liquid metal-cooled fast reactors (LMFRs), improved predictive modelling is desirable to facilitate reactor licensing and operation and move towards a best estimate plus uncertainty (BEPU) approach. A key source of uncertainty in fast reactor calculations arises from the underlying nuclear data. Addressing the propagation of such uncertainties through multiphysics calculations schemes is therefore of importance, and is being addressed through international projects such as the Sodium-cooled Fast Reactor Uncertainty Analysis in Modelling (SFR-UAM) benchmark. In this paper, a methodology for propagation of nuclear data uncertainties within WIMS is presented. Uncertainties on key reactor physics parameters are calculated for selected SFR-UAM benchmark exercises, with good agreement with previous results. A methodology for coupled neutronic-thermal-hydraulic calculations within WIMS is developed, where thermal feedback is introduced to the neutronic solution through coupling with the ARTHUR subchannel code within WIMS and applied to steady-state analysis of the Horizon 2020 ESFR-SMART project reference core. Finally, integration of reactor physics and fuel performance calculations is demonstrated through linking of the WIMS reactor physics code to the TRAFIC fast reactor fuel performance code, through a Fortran-C-Python (FCP) interface. Given the 3D multiphysics calculation methodology, thermal-hydraulic and fuel performance uncertainties can ultimately be sampled alongside the nuclear data uncertainties. Together, these developments are therefore an important step towards enabling propagation of uncertainties through high fidelity, multiphysics SFR calculations and hence facilitate BEPU methodologies.

NUCLEAR DATA UNCERTAINTY QUANTIFICATION FOR THE DECAY HEAT OF PWR MOX FUELS USING DATA ASSIMILATION OF ELEMENTARY FISSION BURSTS

Currently there is no integral experimental data for code validation regarding the decay heat of MOX fuels, excepted fission burst experiments (for fission products contributions at short cooling times) or post-irradiated experiments on nuclide inventories (restricted number of nuclide of interest for decay heat). The uncertainty quantification mainly relies on uncertainty propagation of nuclear data covariances. In the recent years, the transposition method, based on the data assimilation theory, was used in order to transpose the experiment-to-calculation discrepancies at a given set of parameters (cooling time, fuel burnup) to another set of parameters. As an example, this method was used on the CLAB experiments and the experiment-to-calculation discrepancies at 13 years were transposed to an UOX fuel between 5 and 27 years and for burnups from 10 to 50 GWd/t. The purpose of this paper is to study to what extent the transposition method could be used for MOX fuels. In particular, the Dickens fission burst experiment of 239Pu was considered for MOX fuels at short cooling times (< 1h30) and low burnup (< 10 GWd/t). The impact of fission yields (FY) correlations was also discussed. As a conclusion, the efficiency of the transposition process is limited by the experimental uncertainties larger than nuclear data uncertainties, and by the fact that fission burst experiments would only be representative to the FY contribution of the decay heat uncertainty of an irradiated reactor fuel. Nevertheless, this method strengthens the decay heat uncertainties at very short cooling times, previously based only on nuclear data covariance propagation through computation.

QUANTIFICATION OF NUCLEAR DATA AND MANUFACTURING UNCERTAINTIES IN VERA

Uncertainty quantification (UQ) was performed using the Consortium for the Advanced Simulation of Light Water Reactors (CASL) multiphysics core simulator VERA. Typically, only nuclear data cross sections are considered when trying to obtain uncertainty information in reactor simulation applications. In this paper, uncertainty in both nuclear cross section data and fuel manufacturing processes is analyzed using VERA. Uncertainties due to cross sections was determined by generating one thousand perturbed cross section libraries using the cross section covariance data provided in the evaluated nuclear data library. Uncertainty due to manufacturing was also determined using stochastic sampling and VERA. The use of similar stochastic sampling techniques for the same problems allows for the direct comparison of uncertainty stemming from the two sources of uncertainty. Sample size is considered due to the potentially large computational cost of stochastic sampling techniques, as is demonstrated in a full core depletion. It was found that for the Pressurized Water Reactor (PWR) pincell case at Hot Zero Power (HZP), the standard deviation in the neutron multiplication factor produced by material uncertainty was 101 pcm, while the standard deviation in the neutron multiplication factor produced by cross section uncertainty was 730 pcm. While the uncertainty in neutron multiplication factor due to cross section uncertainty is larger than uncertainty due to manufacturing uncertainties, neglecting manufacturing uncertainties may be an unacceptable oversight in certain high-precision simulation applications.

MODELING NUCLEAR DATA UNCERTAINTIES USING DEEP NEURAL NETWORKS

A new concept using deep learning in neural networks is investigated to characterize the underlying uncertainty of nuclear data. Analysis is performed on multi-group neutron cross-sections (56 energy groups) for the GODIVA U-235 sphere. A deep model is trained with cross-validation using 1000 nuclear data random samples to fit 336 nuclear data parameters. Although of the very limited sample size (1000 samples) available in this study, the trained models demonstrate promising performance, where a prediction error of about 166 pcm is found for keff in the test set. In addition, the deep model’s sensitivity and uncertainty are validated. The comparison of importance ranking of the principal fast fission energy groups with adjoint methods shows fair agreement, while a very good agreement is observed when comparing the global keff uncertainty with sampling methods. The findings of this work shall motivate additional efforts on using machine learning to unravel complexities in nuclear data research.

UNCERTAINTY ANALYSIS OF SUB-EXERCISES IN UAM-SFR BENCHMARK WITH THE MCS CODE

Uncertainty analysis in Modelling (UAM) for Design, Operation and Safety Analysis of Sodium-cooled Fast Reactors (SFRs) has been formed by OECD/NEA to assess the effect of nuclear data uncertainties on parameters of interest in SFR analysis. In this paper, sub-exercises of a medium 1000 MWth metallic core (MET-1000) and a large 3600 MWth oxide core (MOX-3600) are tested by a Monte Carlo code MCS to perform uncertainty analysis. Classical perturbation theory and generalized perturbation theory are used to calculate sensitivity coefficients. Uncertainty is calculated by multiplying the sensitivity coefficients and relative covariance matrix from ENDF/B-VII.1 library.

SENSITIVITY ANALYSIS OF PWR SPENT FUEL DUE TO MODELLING PARAMETER UNCERTAINTIES USING SURROGATE MODELS

In the BEPU (Best Estimate Plus Uncertainty) framework, uncertainty quantification (UQ) is a requirement to improve confidence and reliability of code predictions. Over the years, a lot of works have been done to quantify uncertainties in code predictions of spent nuclear fuel (SNF) characteristics due to nuclear data uncertainties. The purpose of this study is to quantify the uncertainty in pressurized water reactor (PWR) fuel assembly radiation source terms (isotopic inventory, activity, decay heat, neutron and gamma source) due to uncertainties in modeling parameters. The deterministic code STREAM is used to predict the source terms of a typical PWR fuel assembly following realistic and detailed irradiation history. For the sensitivity analysis (SA) and UQ, surrogate models are developed based on polynomial chaos expansion (PCE) and variance-based global sensitivity indices (i.e., Sobol’ indices) are employed. The global SA identifies the less important uncertain parameters, showing that the number of uncertain input parameters can be reduced. The surrogate model offers a significantly reduced computational burden even with large number of samples required for the SA/UQ of the model response.