Sensitivity Analysis of Cell Neutronic Parameters in High-Conversion Light-Water Reactors

To estimate the uncertainty of the neutronic parameters it is required to calculate sensitivity coefficients to cross section changes. The sensitivity coefficients are usually calculated based on the diffusion theory. However, the accuracy of the sensitivity coefficients becomes doubtful because of the use of diffusion theory. The purpose of this paper is to derive the generalized perturbation theory using the transport theory, and to evaluate transport effect on the sensitivity coefficients. Sensitivity calculations were performed in 70 energy groups. The calculated sensitivity coefficients were compared with those obtained from direct transport calculations to check the accuracy of the present method, and those obtained from the generalized perturbation calculation based on the diffusion theory to investigate the transport effect on sensitivity coefficients. From the comparison, the difference was remarkably large for the neutronic parameters such as reaction rate distribution, reaction rate ratio, and reactivity worth. For example, the sensitivity coefficient of the 238U capture to 239Pu fission rate ratio in the lower core region of the under-moderated LWR core was large in the energy range 17.6–22.6 eV, and the sensitivity to 238U capture cross section calculated by the transport theory was 20% larger than that by the diffusion theory.

Using the substitution method combined with the pulsed neutron techniques, coolant void reactivities of PuO/sub 2/-UO/sub 2/ fuel lattices in pressure-tube-type heavy water reactors have been determined as functions of PuO/sub 2/ enrichment in PuO/sub 2/-UO/sub 2/(0.54 and 0.87 wt%), fissile content of plutonium (91 and 75% fissile plutonium), lattice pitch (V/sub m//V/sub f/: 7.4 and 9.9), and coolant void fraction (0, 30, 70, 87 and 100%). The reference loading of 1.2 wt% enriched UO/sub 2/ clusters was progressively replaced by PuO/sub 2/-UO/sub 2/ test clusters. The void reactivities were obtained from Simmons King's formula in which correction was made for a change of the prompt generation time. As decay constants can be maintained invariable due to substitution, buckling differences were analyzed by the first-order perturbation method, on the assumption that lattices are homogeneous and no difference in diffusion coefficients exists between the two lattices. Void reactivities of test lattices were determined with an accuracy of --10% when the minimum number of test fuel clusters was -- 5% of the total. The void reactivity shifted farther to the negative side as the proportion of fissile plutonium was increasingly in the PuO/sub 2/-UO/sub 2/ fuel of the same enrichment of plutonium.

Measurements and analysis for reaction rate ratio of 238U capture to 239Pu fission (C8/F9) and that of 238U capture to 235U fission (C8/F5), which are important as indexes of breeding behavior of a fast breeder reactor, were made at Fast Critical Assembly (FCA) of Japan Atomic Energy Research Institute. The measurements were made by a foil activation technique at two assemblies simulating metallic-fueled liquid metal fast breeder reactor and an assembly simulating a MOX-fueled one. The analysis was made based on JENDL3.2 nuclear data file. Calculation to experiment ratios of C8/F9 and C8/F5 were 0.99–1.02 and 1.0–1.03 respectively. Furthermore, the 238U capture rate and the 235U fission rate were measured in a thermal neutron standard field in Heavy Water Facility of Kyoto University Research Reactor to verify accuracy of the present foil activation technique itself and to confirm these C/E values.

The windowed multipole formalism and applications to uncertainty quantification

Abstract The behavior of neutrons in a highly heterogeneous unit cell consisting of D2O moderator, H2O coolant and a 28-pin fuel cluster contained in a pressure tube has been studied through lattice parameter measurements covering three different 235U enrichments, four coolant void fractions and two lattice pitches. A single-region core configuration was adopted, with which measurements were made to determine—in relation to coolant void fraction—the critical D2O level, as well as various lattice parameters A strong dependence on coolant void was observed for the critical level and the lattice parameters, in the case of the smaller 22.5 cm pitch lattice, due to the positive effect on core reactivity exerted by the slowing-down faculty of H2O in the epithermal energy region. With the larger 25.0 cm pitch, however, no meaningful dependence on void fraction was shown by any of the measured values, and this was ascribed to a compensating negative effect due to enhanced thermal neutron self-shielding in the fuel region produced by the H2O coolant. The results of cell calculations obtained by means of the METHUSELAH-II code showed generally good agreement with experimentally determined data, for both critical D2O levels and lattice parameters, in the case of coolant-filled lattices (0, 30 and 70% void fractions). For lattices devoid of coolant (100% void fraction), however, discrepancies in lattice parameters—particularly in p 28—produced corresponding deviations in core reactivity amounting to 1% in excess of those incurred with other void fractions. KEYWORDS: lattice parametercluster-type fuelATR reactorsneutron behaviorheterogeneitycell design codesingle region corecritical levelvoid reactivityneutron leakageuranium dioxide

Material bucklings have been determined as functions of 235U enrichment in UO2 (0.7, 1.2, and 1.5 wt% 235U), PuO2 enrichment in PuO2-UO2 (0.54 and 0.87 wt% PuO2), fissile content of plutonium (91 and 75% Pu-fissile), lattice pitch (Vmod/Vfuel: 7.4 and 9.9), and coolant void fraction. The reference loading of 1.2 wt% 235U-enriched UO2 clusters was progressively replaced by the test clusters.Buckling differences resulting from the substitutions were analyzed by the new second-order (iterative) perturbation method, on the assumption that neutron diffusion is isotropic and that no difference in diffusion coefficients exists between the two lattices. This analysis takes into account the effect of distortion in radial neutron flux distribution in the substituted core without any iterative correction procedure that is usually adopted in the first-order perturbation method. Also, it is not necessary in the case of the present analysis to introduce any usual intermediate region for taking into account the effect of spectrum mismatch between the two lattices. The material buckling differences between the test and reference lattices, which are in the range of −10.2 to 9.1 m−2, were determined within 3% of uncertainty.

JEFF-3.1.1 is the reference nuclear data library in CEA for the design calculations of the next nuclear power plants. The validation of the new neutronics code systems is based on this library and changes in nuclear data should be looked at closely. Some new actinides evaluation files at high energies have been proposed by CEA/Bruyeres-le-Chatel in 2009 and have been integrated in JEFF3.2T1 test release. For the new release JEFF-3.2, CEA will build new evaluation files for the actinides, which should be a combination of the new evaluated data coming from BRC-2009 in the high energy range and improvements or new evaluations in the resolved and unresolved resonance range from CEA-Cadarache. To prepare the building of these new files, benchmarking the BRC-2009 library in comparison with the JEFF-3.1.1 library was very important. The crucial points to evaluate were the improvements in the continuum range and the discrepancies in the resonance range. The present work presents for a selected set of benchmarks the discrepancies in the effective multiplication factor obtained while using the JEFF-3.1.1 or JEFF-3.2T1 library with the deterministic code package ERANOS/PARIS and the stochastic code TRIPOLI-4. They have both been used to calculate cross section perturbations or other nuclear data perturbations when possible. This has permittted to identify the origin of the discrepancies in reactivity calculations. In addition, this work also shows the importance of cross section processing validation. Actually, some fast neutron spectrum calculations have led to opposite tendancies between the deterministic code package and the stochastic code. Some particular nuclear data (MT=5 in ENDF terminology) seem to be incompatible with the current MERGE or GECCO processing codes.

The physics characteristics of large axially heterogeneous liquid-metal fast breeder reactors (LMFBRs), particularly the parameters for use in design and safety assessment, were examined using the JAERI fast critical assembly facility, arranged in Assembly XH-1, a partial mock-up of axially heterogeneous LMFBR. The properties measured were (1) criticality, (2) reaction rates and reaction rate ratios, (3) material sample worths, (4) sodium-void worths and (5) B4C control rod worths. The results were compared with those of prior experiments with assemblies representing conventional homogeneous core. Confirmation was obtained of the typical nuclear characteristics attributed to axially heterogeneous LMFBRs, including flattening of the axial distribution of power and of the differential worth of control rod, as also lower sodium void worth. Theoretical analyses paralleling the experiments, using JENDL-2 cross section library and JAERI standard calculation code system for fast reactor neutronics, resulted in some discrepancies, particularly for the internal blanket, in respect of plutonium sample worth, fission rate and fission rate ratio.

Critical mass calculations of various HEU-fueled fast reactors result in large discrepancies in C/E values, depending on the nuclear data library used and the configuration modeled. Thus, it seems relevant to use integral experiments to try to reassess cross sections that might be responsible for such a dispersion in critical mass results. This work makes use of the Generalized Least Square method to solve Bayes equation, as implemented in the CONRAD code. Experimental database used includes ICSBEP Uranium based critical experiments and benefits from recent re-analyses of MASURCA and FCA-IX criticality experiments (with Monte-Carlo calculations) and of PROFIL irradiation experiments. These last ones provide very specific information on 235U and 238U capture cross sections. Due to high experimental uncertainties associated to fission spectra, we chose to consider either fitting these data or set them to JEFF-3.1.1 evaluations. The work focused on JEFF-3.1.1 235U and 238U evaluations and results presented in this paper for 235U capture and 238U capture, and inelastic cross sections are compared to recent differential experiment or recent evaluations. Our integral experiment assimilation work notably suggests a 30% decrease for 235U capture around 1–2.25 keV, a 10% increase in the unresolved resonance range when using JEFF-3.1.1 as “a priori” data. These results are in agreement with recent microscopic measurements from Danon et al. [Nucl. Sci. Eng. 187, 291 (2017)] and Jandel et al. [Phys. Rev. Lett. 109, 202506 (2012)]. For 238U cross sections, results are highly dependent on fission spectra.

The effect on reactivity of changes in the coolant levels in the pressure tubes of a pressure-tube heavy water reactor is experimentally studied to clarify the effect of an axial coolant void fraction distribution. The coolant void fraction distribution is simulated by stepwise changes in the coolant levels in the Deuterium Critical Assembly (DCA). The reactivity is measured for a 25.0-cm-pitch square-lattice core with a positive coolant void reactivity. The reactivity changes resulting from changes in the coolant levels are measured as changes in the critical heavy water levels. The axial distribution of the thermal neutron flux is also measured by the copper activation method.In these measurements, the critical heavy water levels show a sinuous curve having a maximum and a minimum, and a positive reactivity larger than those of both the 0% and the 100% void uniform cores is introduced at certain coolant levels by stepwise changes in the coolant levels.An experimental analysis is performed with the coupled WIMS-ATR/CITATION code system, whose analytical method was established through DCA critical experiments. Agreement between experiment and analysis is fairly good. Furthermore, the peculiar reactivity behavior resulting from changes in the coolant levels is analyzed using a simplified model to take note of typical reactor physics parameters. It is clarified that this anomalous phenomenon is caused by the combined effect of the flattened S curve change in the thermal neutron absorption and the even flatter S curve change in the neutron leakage caused by the changes in the coolant levels. Useful information is obtained regarding reactivity behavior with an axial coolant void fraction distribution.

Improved generalized perturbation theory method for sensitivity analysis of generalized response function

The OECD/NEA proposes a new international benchmark based on data collected during an instability transient occurred at the Oskarshamn-2 NPP. This benchmark is aimed at testing the coupled 3D Neutron Kinetic–Thermal Hydraulic (3D NK–TH) codes on challenging situations. The ENEA “Casaccia” Research Center, is participating to this benchmark, developing a computational model using the RELAP5-3D© code. The 3DNK model has been already developed from the cross sections dataset calculated by OKG, the Oskarshamn-2 licensee, through the CASMO lattice code. In order to use this neutron cross sections database in RELAP5-3D© a n-dimensional polynomials data fitting and base cross sections values calculations are required. An ad-hoc tool, named PROMETHEUS, has been developed for automatically generating RELAP5-3D©-compatible cross sections libraries. This tool allows at easily visualizing the complex structure of the neutronic datasets; moreover it is exploited for deriving different cross sections libraries needed to evaluate neutronic parameters effects on the reactor instability prediction. Thus, the effects of the fuel temperature and control rod histories, of the discontinuity factors (averaged/not averaged) and of the neutron poisons has been assessed. A ranking table has been produced, demonstrating the relevance of the not-averaged discontinuity factors and of the on-transient neutron poisons calculations for the correct prediction of the Oskarshamn-2 event.

In 2012 CEA produced a entire new evaluation of sodium nuclear data for the release of the JEFF-3.2 evaluated nuclear data library. During the evaluation process performed with the CONRAD code, several differential measurements (total and discrete inelastic cross-sections) have been used. However double differential data (elastic angular distribution) that were yet available in the EXFOR database were not incorporated in the analysis at that time. The experimental elastic angular distribution were discarded because of it was impossible to obtain a good agreement for both angle-integrated cross-sections and double differential ones. The underlying cause of this disagreement is expected to be due to the attribution of quantum numbers to resonance and related channel amplitudes. Indeed these numbers are imposed during the analysis but impact differently angular distributions and angle-integrated cross-sections. An automated search for an accurate set of quantum numbers has been implemented in order to produce a reliable quantum numbers set. In this paper we present a new evaluation of Na-23 taking into account both differential and double differential measurements. The analysis performed with the CONRAD code reached the level of agreement with experimental data for the total and inelastic cross-sections but this time with a significant improvement for the elastic angular distributions. This new evaluation produced in the ENDF-6 format has then been tested and validated on critical facilities calculation (MASURCA and ZPPR) in different configurations (nominal and voided) in order to assess its performances.

The scattering term within the Boltzmann equation was for decades approximated either through the Legendre polynomial for deterministic solvers or by /free gas model approach for Monte Carlo solvers. This, to some extent, inaccurate approach led to the assumption in several cases that the scattering term can be further “tuned” to simplify complex mathematical solver of the transport equation, mainly by reducing considerably the computation time, assuming no consequences on the physical results. The introduction of the resonant dependent scattering kernel to MONTE CARLO code and in particular the experimental validation within the resolved resonance range for Uranium and Thorium, in RPI (Renselear Polytechnic Institute), pointed out that the scattering term cannot be taken as a second order negligible term, but rather should be accurately regarded for any solution of the transport equation. Corollary to the considerable high impact of that “physical” scattering kernel, this study extends its importance beyond the epithermal resolved resonance range and aims to proof that the scattering kernel can and should be accurately dealt also at higher energies at least up to about several tens of keV. Moreover, in the debate between the purely quantum mechanics treatment known as the Optical Model -OM and the Doppler broadening based classical approach, the latter seems to be correct for this extended energy range. Strictly speaking, Newton’s Laws for the scattering kernel evaluation remain intact, yet in accordance to their quantum mechanics based integrated scattering cross section values as was shown for example by the well-known fundamental Breit Wigner formula.

Sensitivity coefficients describe the fractional change in a response that is due to perturbations or uncertainties in system parameters. Several codes (TSUNAMI, Serpent, MCNP, OpenMC) estimate sensitivity coefficients for critical eigenvalue or reaction rate ratio responses: Several codes (TSUNAMI, Serpent, MCNP, OpenMC) estimate sensitivity coefficients for critical eigenvalue or reaction rate ratio responses: The goal of this work was to explore whether recently developed reaction rate sensitivity methods can be extended to coupled photon-electron Monte Carlo radiation transport simulations. This new sensitivity methodology was implemented into a 1-D Monte Carlo code and Direct Perturbation calculations were used to confirm its accuracy.