Nuclear Data Uncertainties Research Articles

Decay heat uncertainty quantification of MYRRHA

MYRRHA is a lead-bismuth cooled MOX-fueled accelerator driven system (ADS) currently in the design phase at SCK·CEN in Belgium. The correct evaluation of the decay heat and of its uncertainty level is very important for the safety demonstration of the reactor. In the first part of this work we assessed the decay heat released by the MYRRHA core using the ALEPH-2 burnup code. The second part of the study focused on the nuclear data uncertainty and covariance propagation to the MYRRHA decay heat. Radioactive decay data, independent fission yield and cross section uncertainties/covariances were propagated using two nuclear data sampling codes, namely NUDUNA and SANDY. According to the results, 238 U cross sections and fission yield data are the largest contributors to the MYRRHA decay heat uncertainty. The calculated uncertainty values are deemed acceptable from the safety point of view as they are well within the available regulatory limits.

Artificial neural network surrogate development of equivalence models for nuclear data uncertainty propagation in scenario studies

Scenario studies simulate the whole fuel cycle over a period of time, from extraction of natural resources to geological storage. Through the comparison of different reactor fleet evolutions and fuel management options, they constitute a decision-making support. Consequently uncertainty propagation studies, which are necessary to assess the robustness of the studies, are strategic. Among numerous types of physical model in scenario computation that generate uncertainty, the equivalence models, built for calculating fresh fuel enrichment (for instance plutonium content in PWR MOX) so as to be representative of nominal fuel behavior, are very important. The equivalence condition is generally formulated in terms of end-of-cycle mean core reactivity. As this results from a physical computation, it is therefore associated with an uncertainty. A state-of-the-art of equivalence models is exposed and discussed. It is shown that the existing equivalent models implemented in scenario codes, such as COSI6, are not suited to uncertainty propagation computation, for the following reasons: (i) existing analytical models neglect irradiation, which has a strong impact on the result and its uncertainty; (ii) current black-box models are not suited to cross-section perturbations management; and (iii) models based on transport and depletion codes are too time-consuming for stochastic uncertainty propagation. A new type of equivalence model based on Artificial Neural Networks (ANN) has been developed, constructed with data calculated with neutron transport and depletion codes. The model inputs are the fresh fuel isotopy, the irradiation parameters (burnup, core fractionation, etc.), cross-sections perturbations and the equivalence criterion (for instance the core target reactivity in pcm at the end of the irradiation cycle). The model output is the fresh fuel content such that target reactivity is reached at the end of the irradiation cycle. Those models are built and then tested on databases calculated with APOLLO2 (for thermal spectra) and ERANOS (for fast spectra) reference deterministic transport codes. A short preliminary uncertainty propagation and ranking study is then performed for each equivalence models.

Work plan for improving the DARWIN2.3 depleted material balance calculation of nuclides of interest for the fuel cycle

DARWIN2.3 is the reference package used for fuel cycle applications in France. It solves the Boltzmann and Bateman equations in a coupling way, with the European JEFF-3.1.1 nuclear data library, to compute the fuel cycle values of interest. It includes both deterministic transport codes APOLLO2 (for light water reactors) and ERANOS2 (for fast reactors), and the DARWIN/PEPIN2 depletion code, each of them being developed by CEA/DEN with the support of its industrial partners. The DARWIN2.3 package has been experimentally validated for pressurized and boiling water reactors, as well as for sodium fast reactors; this experimental validation relies on the analysis of post-irradiation experiments (PIE). The DARWIN2.3 experimental validation work points out some isotopes for which the depleted concentration calculation can be improved. Some other nuclides have no available experimental validation, and their concentration calculation uncertainty is provided by the propagation of a priori nuclear data uncertainties. This paper describes the work plan of studies initiated this year to improve the accuracy of the DARWIN2.3 depleted material balance calculation concerning some nuclides of interest for the fuel cycle.

Determining the nuclear data uncertainty on MONK10 and WIMS10 criticality calculations

The ANSWERS Software Service is developing a number of techniques to better understand and quantify uncertainty on calculations of the neutron multiplication factor, k-effective, in nuclear fuel and other systems containing fissile material. The uncertainty on the calculated k-effective arises from a number of sources, including nuclear data uncertainties, manufacturing tolerances, modelling approximations and, for Monte Carlo simulation, stochastic uncertainty. For determining the uncertainties due to nuclear data, a set of application libraries have been generated for use with the MONK10 Monte Carlo and the WIMS10 deterministic criticality and reactor physics codes. This paper overviews the generation of these nuclear data libraries by Latin hypercube sampling of JEFF-3.1.2 evaluated data based upon a library of covariance data taken from JEFF, ENDF/B, JENDL and TENDL evaluations. Criticality calculations have been performed with MONK10 and WIMS10 using these sampled libraries for a number of benchmark models of fissile systems. Results are presented which show the uncertainty on k-effective for these systems arising from the uncertainty on the input nuclear data.

Propagation of nuclear data uncertainties for fusion power measurements

Neutron measurements using neutron activation systems are an essential part of the diagnostic system at large fusion machines such as JET and ITER. Nuclear data is used to infer the neutron yield. Consequently, high-quality nuclear data is essential for the proper determination of the neutron yield and fusion power. However, uncertainties due to nuclear data are not fully taken into account in uncertainty analysis for neutron yield calibrations using activation foils. This paper investigates the neutron yield uncertainty due to nuclear data using the so-called Total Monte Carlo Method. The work is performed using a detailed MCNP model of the JET fusion machine; the uncertainties due to the cross-sections and angular distributions in JET structural materials, as well as the activation cross-sections in the activation foils, are analysed. It is found that a significant contribution to the neutron yield uncertainty can come from uncertainties in the nuclear data.

The path for innovative severe accident neutronics studies in ZPRs. part I.2 - Interpretation of SNEAK-12A experiment for core disruption in LMFBRs impact of nuclear data uncertainties on reactivity coefficients

The present work details a further investigation of the SNEAK-12A experimental program, which aimed to study material relocation in Sodium Fast Reactors (SFRs) leading to core degradation. The further investigation include sensitivity and uncertainty propagation analysis. In this paper, a comparison is made using two codes, a Monte Carlo based code Serpent 2 and the deterministic system code ERANOS. A sensitivity analysis was made utilizing the two codes, with comparison of two nuclear data libraries (ENDF/B-VII.1 and JEFF-3.1.1). The code-to-code comparison resulted in a very good agreement, while the comparison of libraries showed large discrepancies, manly due to the differences in the sodium cross-section data. The sensitivity analysis, was followed by a complete propagated uncertainty analysis based on the covariance evaluated data available in the COMAC data evaluation. The results of the uncertainties show that there are still large discrepancies linked to the nuclear data. This work is done within the frame work of new core design capacities and new ways of conducting in Zero Power Reactors, such as the ZEPHYR project led independently by CEA.

Combining Total Monte Carlo and Unified Monte Carlo: Bayesian nuclear data uncertainty quantification from auto-generated experimental covariances

The Total Monte Carlo methodology (TMC) for nuclear data (ND) uncertainty propagation has been subject to some critique because the nuclear reaction parameters are sampled from distributions which have not been rigorously determined from experimental data. In this study, it is thoroughly explained how TMC and Unified Monte Carlo-B (UMC-B) are combined to include experimental data in TMC. Random ND files are weighted with likelihood function values computed by comparing the ND files to experimental data, using experimental covariance matrices generated from information in the experimental database EXFOR and a set of simple rules. A proof that such weights give a consistent implementation of Bayes' theorem is provided. The impact of the weights is mainly studied for a set of integral systems/applications, e.g., a set of shielding fuel assemblies which shall prevent aging of the pressure vessels of the Swedish nuclear reactors Ringhals 3 and 4.In this implementation, the impact from the weighting is small for many of the applications. In some cases, this can be explained by the fact that the distributions used as priors are too narrow to be valid as such. Another possible explanation is that the integral systems are highly sensitive to resonance parameters, which effectively are not treated in this work. In other cases, only a very small number of files get significantly large weights, i.e., the region of interest is poorly resolved. This convergence issue can be due to the parameter distributions used as priors or model defects, for example.Further, some parameters used in the rules for the EXFOR interpretation have been varied. The observed impact from varying one parameter at a time is not very strong. This can partially be due to the general insensitivity to the weights seen for many applications, and there can be strong interaction effects. The automatic treatment of outliers has a quite large impact, however.To approach more justified ND uncertainties, the rules for the EXFOR interpretation shall be further discussed and developed, in particular the rules for rejecting outliers, and random ND files that are intended to describe prior distributions shall be generated. Further, model defects need to be treated.

Nuclear data sensitivity and uncertainty analysis of effective neutron multiplication factor in various MYRRHA core configurations

A sensitivity and uncertainty analysis was carried out to estimate the uncertainty in the neutron multiplication factor keff and to identify the most important nuclear data for neutron induced reactions for criticality calculations of the latest MYRRHA designs. Sensitivity profiles, i.e. sensitivity to the nuclear data as a function of incoming neutron energy, were derived for both a critical and sub-critical core. They were calculated using codes that are based on different methodologies including stochastic and deterministic calculations (i.e. SCALE, MCNP and XSUN). The neutron induced nuclear data sensitivity analysis outlined the following quantities to be of special importance for the MYRRHA reactor concept: 239Pu(n,γ) both in resonance and fast energy region, (n,f) fast, χ and ν fast; 238U(n,n′) fast, (n,γ) resonance and fast, (n,n) resonance and fast; 240Pu ν fast; 238Pu(n,f) both resonance and fast; 56Fe(n,γ) both resonance and fast. Differences of less than 4% between codes were obtained for these quantities, with few exceptions (238Pu(n,f), 238U(n,n) and 56Fe(n,γ) reactions). Nuclear data covariance matrices of different libraries (SCALE-6, COMMARA-2 and JENDL-4.0m) were used to derive the uncertainty in keff based on the calculated sensitivities. This study reveals that the largest contributions to keff uncertainty result from the uncertainty in the average prompt neutron fission multiplicity of 239Pu, in the 238U inelastic scattering cross section and 239Pu fission cross section, using the covariances from SCALE-6, COMMARA-2 and JENDL-4.0m, respectively.

The path for innovative severe accident neutronics studies in ZPRs. Part I.1 - Analysis of SNEAK-12A experiments for core disruption in LMFBRs

The present work details a new benchmark to be produced to the International Community, for dealing with neutronics code validation in the frame of the analysis of severe accidents in Sodium Fast Reactors (SFRs) leading to core degradation and material relocation. The benchmark is based on analysis of selected experiments performed at the Schnelle Null-Energie-Anordnung Karlsruhe (SNEAK). The SNEAK-12A experiments have been considered where core distorted configurations have been simulated. In the paper, the experimental results have been analyzed by using TRIPOLI-4, MCNPX2.7, and Serpent-2 Monte Carlo codes as reference tools, and the ERANOS system of codes for deterministic calculations, all based on JEFF-3.1.1 nuclear data libraries. The complete material balance, and the main degradation sequences are provided within the manuscript. Preliminary results on available experimental results (keff) are given, and additional local quantities are calculated, such as axial flux distributions, as well as detector responses as function of the distance to the degraded part. The benchmark offers an excellent opportunity to validate calculation schemes for strongly heterogeneous interfaces, in particular the preparation of homogenized self-shielded neutron cross-sections for deterministic core calculations, as well as leakage treatment in locally very heterogeneous media. This work is done within the frame of new core design capacities and new ways of conducting experiment in Zero Power Reactors, such as the ZEPHYR project led independently by CEA. The present analysis will be completed by a full nuclear data sensitivity and uncertainty analysis of the reactivity coefficients and keff in a companion paper.

Nuclear-data uncertainty propagations in burnup calculation for the PWR assembly

In this paper, our home-developed lattice code NECP-CACTI has been implemented into our UNICORN code to perform sensitivity and uncertainty analysis for the lattice calculations. The verified multigroup cross-section perturbation model and methods of the sensitivity and uncertainty analysis are established and applied to different lattice codes in UNICORN. As DRAGON5.0 and NECP-CACTI are available for the lattice calculations in UNICORN now, the effects of different neutronics methods (including methods for the neutron-transport and resonance self-shielding calculations) on the results of sensitivity and uncertainty analysis were studied in this paper. Based on NECP-CACTI, uncertainty analysis using the statistical sampling method has been performed to the burnup calculation for the fresh-fueled TMI-1 assembly, propagating the nuclear-data uncertainties to k∞ and two-group constants of the lattice calculation with depletions. As results shown, for different neutronics methods, it can be observed that different methods of the neutron-transport calculation introduce no differences to the results of sensitivity and uncertainty analysis, while different methods of the resonance self-shielding calculation would impact the results. With depletions of the TMI-1 assembly, for k∞, the relative uncertainty varies between 0.45% and 0.60%; for two-group constants, the largest variation is between 0.35% and 2.56% for vΣf,2. Moreover, the most significant contributors to the uncertainty of k∞ and two-group constants varied with depletions are determined.

Feasibility study of decay heat uncertainty reduction using nuclear data adjustment method with experimental data

ABSTRACTThe accurate prediction of the decay heat is essential, especially for nuclear power plant safety purposes. However, it is known that the decay heat predicted by nuclear fuel burn-up calculations is uncertain because of uncertainty of nuclear data employed in the calculations. If the decay heat uncertainty can be reduced, the safety margin of the predicted decay heat can also be reduced, and feasible design ranges of various types of equipments related to the decay heat can be extended. In the present study, we use the nuclear data adjustment method for the decay heat uncertainty reduction with several types of the experimental data. As a result, we clarify that the decay heat uncertainty with short- and long-term cooling periods can be reduced by this method with appropriate experimental data.

Testing the Sampling-Based NUSS-RF Tool for the Nuclear Data—Related Global Sensitivity Analysis with Monte Carlo Neutronics Calculations

NUSS-RF is a tool for nuclear data uncertainty propagation through neutronics calculations with continuous-energy Monte Carlo codes and ACE-formatted nuclear data libraries. Many existing codes, including the original version of NUSS (Nuclear data Uncertainty Stochastic Sampling), are based on simple random sampling algorithms. The NUSS-RF extension now uses a frequency-based sampling algorithm, called the random balance design (RBD), to analyze individual nuclear data uncertainty contributions in regard to the total output (e.g., keff) uncertainty. The implementation of the RBD method into NUSS-RF is initially verified by comparing the computed individual input variance contributions with analytical solutions for two analytical test cases. As well, it is assessed against the alternative approach based on the use of correlation coefficients. NUSS-RF is then used for an analysis of the Jezebel and Godiva fast-spectrum criticality benchmarks: in a first step, the overall effect of the 239Pu(n,f) and 235U(n,f) cross-section uncertainties on keff is evaluated, while in a second step, the contributions from the individual energy groups are quantified. As an additional verification, the NUSS-RF results are assessed against sensitivity and uncertainty analysis based on perturbation theory, showing good agreement between the two solutions. Finally, the capability of NUSS-RF is demonstrated for ranking the input parameters with respect to their influence on the total uncertainty of the output parameters, taking into account possible correlations between input parameters. Possible future improvements for the current computational scheme are discussed in the conclusions.

New strategies for quantifying and propagating nuclear data uncertainty in CUSA

The uncertainties of nuclear cross sections are propagated to the key parameters of nuclear reactor core through transport calculation. The statistical sampling method can be used to quantify and propagate nuclear data uncertainty in nuclear reactor physics calculations. In order to use statistical sampling method two key technical problems, method of generating multi-group covariance matrices and sampling method, should be considered reasonably and efficiently. In this paper, a method of transforming nuclear cross section covariance matrix in multi-group form into users' group structures based on the flat-flux approximation has been studied in depth. And most notably, an efficient sampling method has been proposed, which is based on Latin Hypercube Sampling (LHS) combined with Cholesky decomposition conversion. Based on those method, two modules named T-COCCO and GUIDE have been developed and have been successfully added into the code for uncertainty and sensitivity analysis (CUSA). The new modules have been verified respectively. Numerical results for the TMI-1 pin-cell case are presented and compared to TSUNAMI-1D. The comparison of the results further support that the methods and the computational tool developed in this work can be used to conduct sensitivity and uncertainty analysis for nuclear cross sections.

Development of sensitivity analysis capabilities of generalized responses to nuclear data in Monte Carlo code RMC

Capabilities for nuclear data sensitivity and uncertainty analysis have been recently implemented in numerous continuous-energy Monte Carlo codes, including the Reactor Monte Carlo (RMC) code. Previous work developed the capability for RMC of computing sensitivity coefficients of the effective multiplication factor and related uncertainties, due to nuclear data. In this work, such capability was extended to generalized responses in the form of ratios of linear response functions of the forward flux based on the collision history-based approach as implemented in SERPENT2. The superhistory algorithm was also adopted in RMC to reduce memory consumption for generalized sensitivity calculations. These new capabilities of RMC were verified by comparing results of TSUNAMI-1D in SCALE6.1 code package, and SERPENT2 through Jezebel, Flattop and the UAM TMI PWR pin cell benchmark problems.

Total Uncertainty Analysis for PWR Assembly Based on the Statistical Sampling Method

The nuclear-data uncertainties impact the best-estimate predictions of the nuclear reactor system. In this paper, total uncertainty analyses have been performed for the TMI-1 assembly at both hot zero-power and hot full-power conditions to evaluate the impacts of nuclear-data uncertainties on the predictions of lattice calculations, based on the statistical sampling method. With an improved multigroup cross-section perturbation model, the contributions of various basic cross sections to the uncertainties of k∞ and two-group macroscopic cross sections are obtained. For the total uncertainty analyses, a 172-group cross-section covariance library produced from ENDF/B-VII.1 is used to generate the samples for the multigroup microscopic cross-section library, and DRAGON 5.0 is applied to perform lattice calculations for each sample. The numerical results show that the relative uncertainty of k∞ can reach about 4.7‰ using the vp covariance matrix of 235U-v and 7.1‰ using the vt covariance matrix of 235U-v. The relative uncertainties of two-group macroscopic cross sections vary from about 2.9‰ (for the total cross section of the thermal group) to about 11.9‰ (for the scattering cross section from the fast group to the thermal group). Moreover, through detailed analysis toward uncertainty origins, it has been observed that 235U, 238U, 16O, and 1H are the four most significant contributors, and the uncertainties of 235U-(v, σf, σγ), 238U-(σγ, σ(n,inel), σ(n,elas), v), 16O-(σ(n,elas)), and 1H-(σ(n,elas), σγ) are the most significant cross-section contributors.

Memory-efficient calculations of adjoint-weighted tallies by the Monte Carlo Wielandt method

The current Monte Carlo (MC) adjoint-weighted tally techniques based on the iterated fission probability (IFP) concept require a memory amount which is proportional to the numbers of the adjoint-weighted tallies and histories per cycle to store history-wise tally estimates during the convergence of the adjoint flux. Especially the conventional MC adjoint-weighted perturbation (AWP) calculations for the nuclear data sensitivity and uncertainty (S/U) analysis suffer from the huge memory consumption to realize the IFP concept. In order to reduce the memory requirement drastically, we present a new adjoint estimation method in which the memory usage is irrelevant to the numbers of histories per cycle by applying the IFP concept for the MC Wielandt calculations. The new algorithms for the adjoint-weighted kinetics parameter estimation and the AWP calculations in the MC Wielandt method are implemented in a Seoul National University MC code, McCARD and its validity is demonstrated in critical facility problems. From the comparison of the nuclear data S/U analyses, it is demonstrated that the memory amounts to store the sensitivity estimates in the proposed method become negligibly small.

XGPT: Extending Monte Carlo Generalized Perturbation Theory capabilities to continuous-energy sensitivity functions

The XGPT method extends the Generalized Perturbation Theory capabilities of Monte Carlo codes to continuous-energy sensitivity functions. In this work, this method is proposed as a new approach to nuclear data uncertainty propagation. XGPT overcomes some of the limitations of legacy perturbation-based approaches. In particular, it allows the nuclear data uncertainty propagation to be performed adopting continuous energy covariance matrices, instead of discretized (multi-group) data. The XGPT capabilities are demonstrated in three simple fast criticality benchmarks for 239Pu and 208Pb cross section uncertainties. The new method is also applied in selected cases to estimate higher moments of the keff distribution, starting from TENDL random evaluations. The XGPT estimates, when compared against reference Total Monte Carlo (TMC) results, show a good agreement and a significant reduction in computational requirements with respect to the TMC approach. Finally, the capabilities for uncertainty propagation involving adjoint-weighted response functions are demonstrated.

Improving PWR core simulations by Monte Carlo uncertainty analysis and Bayesian inference

The Monte Carlo-based Bayesian inference model MOCABA is applied to the prediction of reactor operation parameters of a PWR nuclear power plant. In this non-perturbative framework, high-dimensional covariance information describing the uncertainty of microscopic nuclear data is combined with measured reactor operation data in order to provide statistically sound, well founded uncertainty estimates of integral parameters, such as the boron letdown curve and the burnup-dependent reactor power distribution. The performance of this methodology is assessed in a blind test approach, where we use measurements of a given reactor cycle to improve the prediction of the subsequent cycle. As it turns out, the resulting improvement of the prediction quality is impressive. In particular, the prediction uncertainty of the boron letdown curve, which is of utmost importance for the planning of the reactor cycle length, can be reduced by one order of magnitude by including the boron concentration measurement information of the previous cycle in the analysis. Additionally, we present first results of non-perturbative nuclear-data updating and show that predictions obtained with the updated libraries are consistent with those induced by Bayesian inference applied directly to the integral observables.

Uncertainty quantification in (α,n) neutron source calculations for an oxide matrix

We present a methodology to propagate nuclear data covariance information in neutron source calculations from (α,n) reactions. The approach is applied to estimate the uncertainty in the neutron generation rates for uranium oxide fuel types due to uncertainties on 1) 17,18 O(α,n) reaction cross-sections and 2) uranium and oxygen stopping power cross sections.The procedure to generate reaction cross section covariance information is based on the Bayesian fitting method implemented in the R-matrix SAMMY code. The evaluation methodology uses the Reich-Moore approximation to fit the 17,18 O(α,n) reaction cross-sections in order to derive a set of resonance parameters and a related covariance matrix that is then used to calculate the energy-dependent cross section covariance matrix. The stopping power cross sections and related covariance information for uranium and oxygen were obtained by the fit of stopping power data in the α-energy range of 1 keV up to 12 MeV.Cross section perturbation factors based on the covariance information relative to the evaluated 17,18 O(α,n) reaction cross sections, as well as uranium and oxygen stopping power cross sections, were used to generate a varied set of nuclear data libraries used in SOURCES4C and ORIGEN for inventory and source term calculations. The set of randomly perturbed output (α,n) source responses, provide the mean values and standard deviations of the calculated responses reflecting the uncertainties in nuclear data used in the calculations. The results and related uncertainties are compared with experiment thick target (α,n) yields for uranium oxide.

Nuclear data uncertainty propagation analysis for depletion calculation in PWR and FR pin-cells

In order to assess the nuclear data uncertainty propagation in the depletion calculation, a computational code named SUNDEW has been developed based on the home-developed lattice code NECP-CACTI. In the SUNDEW, Generalized Perturbation Theory (GPT) is applied to calculate sensitivity coefficients of response function with respect to the nuclear cross sections. Method of Characteristics (MOC) is employed to solve the transport equation, adjoint and generalized adjoint transport equations. Chebyshev Rational Approximation Method (CRAM) is implemented to solve the depletion equation and adjoint depletion equation. The sensitivity coefficients of Keff and nuclide density with respect to the nuclear cross sections are verified by comparing with the results of direct perturbation calculation. The uncertainties on Keff and the nuclide density at different depletions, which are induced by the nuclear cross sections uncertainties, are analyzed based on ENDF/B-VII.1 covariance data for LWR and fast reactor pin-cells. The numerical results show that there are significant differences between LWR and fast reactor pin-cells. The differences are mainly caused by the differences of the sensitivity coefficients between the LWR and fast reactor pin-cells. In addition, to identify the cross section improvement priority for nuclides, reactions and energy ranges, the dominant contributors to Keff and nuclide density uncertainties are analyzed at different depletions.