• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.715-731
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• 2021

Uncertainties are calculated for pressurized water reactor (PWR) spent nuclear fuel (SNF) characteristics. The deterministic code STREAM is currently being used as an SNF analysis tool to obtain isotopic inventory, radioactivity, decay heat, neutron and gamma source strengths. The SNF analysis capability of STREAM was recently validated. However, the uncertainty analysis is yet to be conducted. To estimate the uncertainty due to nuclear data, STREAM is used to perturb nuclear cross section (XS) and resonance integral (RI) libraries produced by NJOY99. The perturbation of XS and RI involves the stochastic sampling of ENDF/B-VII.1 covariance data. To estimate the uncertainty due to modeling parameters (fuel design and irradiation history), surrogate models are built based on polynomial chaos expansion (PCE) and variance-based sensitivity indices (i.e., Sobol' indices) are employed to perform global sensitivity analysis (GSA). The calculation results indicate that uncertainty of SNF due to modeling parameters are also very important and as a result can contribute significantly to the difference of uncertainties due to nuclear data and modeling parameters. In addition, the surrogate model offers a computationally efficient approach with significantly reduced computation time, to accurately evaluate uncertainties of SNF integral characteristics.

• Nuclear Engineering and Technology
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• v.54 no.2
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• pp.523-531
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• 2022

In order to study the sensitivity and the uncertainty of the Moroccan research reactor TRIGA Mark II, a model of this reactor has been developed in our ERSN laboratory for use with the N-Particle MCNP Monte Carlo transport codes (version 6). In this article, the sensitivities of the effective multiplication factor of this reactor are evaluated using the ENDF/B-VII.0, ENDF/B-VII.1 and JENDL-4.0 libraries and in 44 energy groups, for the cross sections of the fuel (U-235 and U-238) and the moderator (H-1 and O-16). However, the quantification of the uncertainty of the nuclear data is performed using the nuclear code NJOY99 for the generation and processing of covariance matrices. On the one hand, the highest uncertainty deviations, calculated using the ENDFB-VII.1 and JENDL4.0 evaluations, are 2275, 386 and 330 pcm respectively for the reactions U₂₃₅(n, f), $ U_{235}(n\bar{\nu})$ and H₁(n, γ). On the other hand, these differences are very small for the neutron reactions of O-16 and U-238. Regarding the neutron spectra, in CT-mid plane, they are very close for the three evaluations (ENDF/B-VII.0, ENDF/B-VII.1 and JENDL-4.0). These spectra present two peaks (thermal and fission) around the energies 0.05 eV and 1 MeV.

• Nuclear Engineering and Technology
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• v.53 no.7
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• pp.2151-2161
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• 2021

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.

• Nuclear Engineering and Technology
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• v.46 no.3
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• pp.313-342
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• 2014

A Nuclear Energy Agency (NEA), Organization for Economic Co-operation and Development (OECD) benchmark for Uncertainty Analysis in Modeling (UAM) is defined in order to facilitate the development and validation of available uncertainty analysis and sensitivity analysis methods for best-estimate Light water Reactor (LWR) design and safety calculations. The benchmark has been named the OECD/NEA UAM-LWR benchmark, and has been divided into three phases each of which focuses on a different portion of the uncertainty propagation in LWR multi-physics and multi-scale analysis. Several different reactor cases are modeled at various phases of a reactor calculation. This paper discusses Phase I, known as the "Neutronics Phase", which is devoted mostly to the propagation of nuclear data (cross-section) uncertainty throughout steady-state stand-alone neutronics core calculations. Three reactor systems (for which design, operation and measured data are available) are rigorously studied in this benchmark: Peach Bottom Unit 2 BWR, Three Mile Island Unit 1 PWR, and VVER-1000 Kozloduy-6/Kalinin-3. Additional measured data is analyzed such as the KRITZ LEU criticality experiments and the SNEAK-7A and 7B experiments of the Karlsruhe Fast Critical Facility. Analyzed results include the top five neutron-nuclide reactions, which contribute the most to the prediction uncertainty in keff, as well as the uncertainty in key parameters of neutronics analysis such as microscopic and macroscopic cross-sections, six-group decay constants, assembly discontinuity factors, and axial and radial core power distributions. Conclusions are drawn regarding where further studies should be done to reduce uncertainties in key nuclide reaction uncertainties (i.e.: $^{238}U$ radiative capture and inelastic scattering (n, n') as well as the average number of neutrons released per fission event of $^{239}Pu$).

• Nuclear Engineering and Technology
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• v.55 no.1
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• pp.131-143
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• 2023

Constitutive equations in a nuclear reactor safety analysis code are mostly empirical correlations developed from experiments, which always accompany uncertainties. The accuracy of the code can be improved by modifying the constitutive equations fitting wider range of data with less uncertainty. Thus, the sensitivity of the code with respect to the constitutive equations is evaluated quantitatively in the paper to understand the room for improvement of the code. A new methodology is proposed which first starts by dividing the thermal hydraulic conditions into multiple sub-regimes using self-organizing map (SOM) clustering method. The sensitivity analysis is then conducted by multiplying an arbitrary set of coefficients to the constitutive equations for each sub-divided thermal-hydraulic regime with SOM to observe how the code accuracy varies. The randomly chosen multiplier coefficient represents the uncertainty of the constitutive equations. Furthermore, the set with the smallest error with the selected experimental data can be obtained and can provide insight which direction should the constitutive equations be modified to improve the code accuracy. The newly proposed method is applied to a steady-state experiment and a transient experiment to illustrate how the method can provide insight to the code developer.

• Nuclear Engineering and Technology
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• v.54 no.11
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• pp.4272-4279
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• 2022

In this study, a cross section stochastic sampling (S.S.) capability is implemented into both the McCARD continuous energy Monte Carlo code and MIG multiple-correlated data sampling code. The ENDF/B-VII.1 covariance data based 30 group cross section sets and the SCALE6 covariance data based 44 group cross section sets are sampled by the MIG code. Through various uncertainty quantification (UQ) benchmark calculations, the McCARD/MIG results are verified to be consistent with the McCARD stand-alone sensitivity/uncertainty (S/U) results and the XSUSA S.S. results. UQ analyses for Three Mile Island Unit 1, Peach Bottom Unit 2, and Kozloduy-6 fuel pin problems are conducted to provide the uncertainties of k_eff and microscopic and macroscopic cross sections by the McCARD/MIG code system. Moreover, the SNU S/U formulations for uncertainty propagation in a MC depletion analysis are validated through a comparison with the McCARD/MIG S.S. results for the UAM Exercise I-1b burnup benchmark. It is therefore concluded that the SNU formulation based on the S/U method has the capability to accurately estimate the uncertainty propagation in a MC depletion analysis.

• Nuclear Engineering and Technology
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• v.53 no.9
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• pp.2803-2815
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• 2021

This paper addresses the uncertainty quantification and sensitivity analysis of a depleted light-water fuel assembly of the Turkey Point-3 benchmark. The uncertainty of the fuel assembly decay heat and isotopic densities is quantified with respect to three different groups of diverse parameters: nuclear data, assembly design, and reactor core operation. The uncertainty propagation is conducted using a two-step analysis code system comprising the lattice code STREAM, nodal code RAST-K, and spent nuclear fuel module SNF through the random sampling of microscopic cross-sections, fuel rod sizes, number densities, reactor core total power, and temperature distributions. Overall, the statistical analysis of the calculated samples demonstrates that the decay heat uncertainty decreases with the cooling time. The nuclear data and assembly design parameters are proven to be the largest contributors to the decay heat uncertainty, whereas the reactor core power and inlet coolant temperature have a minor effect. The majority of the decay heat uncertainties are delivered by a small number of isotopes such as ²⁴¹Am, ¹³⁷Ba, ²⁴⁴Cm, ²³⁸Pu, and ⁹⁰Y.

• Nuclear Engineering and Technology
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• v.39 no.2
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• pp.133-142
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• 2007

The Electric Power Research Institute (EPRI) demonstrated a method for monitoring the performance of instrument channels in Topical Report (TR) 104965, 'On-Line Monitoring of Instrument Channel Performance.' This paper presents the results of several models originally developed by EPRI to monitor three nuclear plant sensor sets: Pressurizer Level, Reactor Protection System (RPS) Loop A, and Reactor Coolant System (RCS) Loop A Steam Generator (SG) Level. The sensor sets investigated include one redundant sensor model and two non-redundant sensor models. Each model employs an Auto-Associative Kernel Regression (AAKR) model architecture to predict correct sensor behavior. Performance of each of the developed models is evaluated using four metrics: accuracy, auto-sensitivity, cross-sensitivity, and newly developed Error Uncertainty Limit Monitoring (EULM) detectability. The uncertainty estimate for each model is also calculated through two methods: analytic formulas and Monte Carlo estimation. The uncertainty estimates are verified by calculating confidence interval coverages to assure that 95% of the measured data fall within the confidence intervals. The model performance evaluation identified the Pressurizer Level model as acceptable for on-line monitoring (OLM) implementation. The other two models, RPS Loop A and RCS Loop A SG Level, highlight two common problems that occur in model development and evaluation, namely faulty data and poor signal selection

• Nuclear Engineering and Technology
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• v.46 no.3
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• pp.343-352
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• 2014

Uncertainty and sensitivity analyses with respect to nuclear data are performed with depletion calculations for BWR and PWR fuel assemblies specified in the framework of the UAM-LWR Benchmark Phase II. For this, the GRS sampling based tool XSUSA is employed together with the TRITON depletion sequences from the SCALE 6.1 code system. Uncertainties for multiplication factors and nuclide inventories are determined, as well as the main contributors to these result uncertainties by calculating importance indicators. The corresponding neutron transport calculations are performed with the deterministic discrete-ordinates code NEWT. In addition, the Monte Carlo code KENO in multi-group mode is used to demonstrate a method with which the number of neutron histories per calculation run can be substantially reduced as compared to that in a calculation for the nominal case without uncertainties, while uncertainties and sensitivities are obtained with almost the same accuracy.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1226-1233
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• 2017

Measurements of the isotopic contents of spent nuclear fuel provide experimental data that are a prerequisite for validating computer codes and nuclear data for many spent fuel applications. Under the auspices of the Organisation for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) and guidance of the Expert Group on Assay Data of Spent Nuclear Fuel of the NEA Working Party on Nuclear Criticality Safety, a new database of expanded spent fuel isotopic compositions has been compiled. The database, Spent Fuel Compositions (SFCOMPO) 2.0, includes measured data for more than 750 fuel samples acquired from 44 different reactors and representing eight different reactor technologies. Measurements for more than 90 isotopes are included. This new database provides data essential for establishing the reliability of code systems for inventory predictions, but it also has broader potential application to nuclear data evaluation. The database, together with adjoint based sensitivity and uncertainty tools for transmutation systems developed to quantify the importance of nuclear data on nuclide concentrations, are described.