Neutron cross section sensitivity analysis of UO2 and MOX core physics experiments on light water reactors

The perturbation theory based on the transport calculation has been applied to study sensitivity of neutron multiplication factors (k_eff's) to neutron cross sections used for the reactivity analysis of UO₂ and MOX core physics experiments on light water reactors. The studied cross sections were neutron capture, fission and elastic scattering cross sections, and a number of fission neutrons, ν. The obtained sensitivities were multiplied to relative differences in the cross sections between JENDL-4.0 and JENDL-3.3 in order to estimate the reactivity effects. The results show that the increase in k_eff, 0.3%Δk/kk′, from JENDL-3.3 to JENDL-4.0 for the UO₂ core is mainly attributed to the decreases in the capture cross sections of ²³⁸U. On the other hand, there are various contributions from the differences in the cross sections of U, Pu, and Am isotopes for the MOX cores. The major contributions to increase in k_eff are decreases in the capture cross sections of ²³⁸U,²³⁸Pu, ²³⁹Pu, and those to decrease in k_eff are decreases in ν of ²³⁹Pu and increases in the capture cross sections of²⁴¹Am. They compensate each other, and the difference in k_eff between JENDL-3.3 and JENDL-4.0 is less than 0.1%Δk/kk′ and relatively small.     

Determination of Multiplication Factors Using Experimental Lattice Parameters of Cluster-Type Fuel Lattices

A new four-factor formula is proposed for deriving a “finite multiplication factor” k*—the ratio between neutron production and absorption rates in a finite medium—from experimentally determined lattice parameters in a slightly-enriched Pu-U lattice.

The “two-group multiplication factor” k* _∞2—related to τ+ L² and equal to (1 τ B² _C). (1 +L²B² _G at criticality—is derived from k*.

The experimental lattice parameters are corrected to account for neutron leakage, from which the “infinite multiplication factor” K∞ is derived.

There are found differences between k*, k*_∞2 and k _∞ amounting to about 1–2% in the Advanced Thermal Reactor (ATR)-type heavy-water lattice, despite the fact that all these three quantities are often indiscriminately called “infinite multiplication factor.”

The proposed four-factor formula for deriving k* was applied to the Deuterium Critical Assembly (DCA) of 1.2%-enriched UO₂ lattices of 28-pin clusters in square arrays spaced at 22.5 cm. The values of k* calculated with a lattice design code METHUSELAHH II were in fairly good agreement wTith those determined by experiment. The calculation tended to somewhat overestimate k*, particularly in lattices of highly voided coolant. A similar tendency was observed in the case of 1.5%-enriched UO₂ lattices of 22.5 cm pitch in the ATR Sumitomo-Two-Region Critical Facility.     

Uncertainty quantification of neutron multiplication factors of light water reactor fuels during depletion

Nuclear data-induced uncertainties of infinite neutron multiplication factors (k_∞) during fuel depletion are quantified in a single cell and a 3×3 multi-cell including burnable absorbers. Uncertainties of reaction cross sections, fission yields, decay half-lives and decay branching ratios provided in the JENDL libraries are taken into account. Hundred percent uncertainties are assumed to nuclear data to which uncertainty information are not provided in JENDL. Uncertainties propagation calculations are carried out with the adjoint-based procedure, and required sensitivity profiles of k_∞ with respect to these nuclear data are efficiently calculated by the depletion perturbation theory. Covariance matrices for fission yields and decay data in a simplified burnup chain are successfully generated by the stochastic-based procedure. k_∞ uncertainties of about 0.6% during fuel depletion are obtained, and it is shown that actinoids reaction cross sections are dominant contributors. Nuclide-wise decomposition of the uncertainties and observation of component-wise sensitivity profiles provide physical interpretations. By virtue of the adjoint-based procedure, several parametric surveys are also conducted. Contributions of uncertainties in fission products (FPs) nuclides are quantified, and important nuclides and energy ranges are identified for further evaluation of nuclear data of FP nuclides. Effect of cooling period on k_∞ uncertainties is also discussed.     

Assessment of the Effect of Microconstants Uncertainties on the Computational Error in the Neutron-Properties of a Brest Reactor Cell

A methodology for assessing the errors arising in calculations of k _eff and the ²³⁹Pu breeding ratio of a BREST cell as a result of microconstants uncertainties and the results of such an assessment are presented. The analysis is performed for the uncertainties in the ²³⁹Pu and ²³⁸U constants, taken from the BNAB-MIKRO library and most important for BREST characteristics, and the incertainties in ENDF/B-VI.2 library values of _in for lead. The correlations of the group uncertainties for individual constants and between constants are taken into account. A specially developed mathematical model of a BREST cell is used to determine the coefficients of sensitivity with respect to a perturbation of the microconstants for the neutron-physical properties. The model is based on computational results obtained using the WIMS-D4 code. The constants component of the computational error determined for a 1 confidence interval is 0.018 for k _eff and 0.051 for the ²³⁹Pu breeding ratio.     

Prediction Uncertainty Analysis of Neutronic Properties of Fast Breeder Reactor by Use of Sensitivity-Based Methodology

The prediction accuracies of key neutronic characteristics including burnup properties evaluated with use of the sensitivity-based methodology have been reviewed for a fast breeder reactor. The bias factor method, the cross section adjustment method and the combined method are used to evaluate the prediction accuracies. The calculation method of sensitivity coefficients used in the uncertainty analysis is discussed. The three methods are compared from the theoretical and numerical points. For the numerical comparison, they are applied to a 1,000 MWe fast breeder reactor. The prediction uncertainties are within the range of 0.7~1.0% for k_eff , 3~5% for control rod worth, 1~2% for ²³⁹Pu fission rate distribution, 12% for burnup reactivity loss and 1.5% for breeding ratio. These values are much smaller than those predicted without any integral data.     

Lattice Parameter Measurements on Cluster-Type Fuel for Advanced Thermal Reactor

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.     

Approximate Calculation Method for Second Order Sensitivity Coefficient

A simple method has been developed for calculating the second order sensitivity coefficient of static and burnup-dependent core performance parameters. The method is applied to a small and a large fast breeder reactors. Changes in core performance parameters due to 10% cross section changes are compared with that predicted by the first and the second order sensitivity analyses. Numerical results reveal that the changes in breeding ratio, reaction rate ratio of the ²³⁸U capture to the ²³⁹Pu fission rate and burnup reactivity loss due to the 10% change in the ²³⁹Pu fission cross section and/or the ²³⁹Pu v-value show nonlinear behavior, and the second order sensitivity can predict the changes accurately.     

Analyses of used BWR fuel assay data with the integrated burnup code system SWAT4.0

Criticality safety of the fuel debris from the Fukushima Daiichi Nuclear Power Plant is one of the most important issues, and the adoption of burnup credit is desired for criticality safety evaluation. To adopt the burnup credit, validation of the burnup calculation codes is required. Assay data of the used nuclear fuel irradiated by the Fukushima Daini Nuclear Power Plant Unit 2 are evaluated to validate the SWAT4.0 code for solving the BWR fuel burnup problem. The calculation results revealed that the number densities of many heavy nuclides and fission products show good agreement with the experimental data, except for those of ²³⁷Np, ²³⁸Pu, and samarium isotopes. These differences were considered to originate from inappropriate assumption of void fraction. Our results implied overestimation of the (n, γ) cross-section of ²³⁷Np in JENDL-4.0. The Calculation/Experiment – 1 (C/E–1) value did not depend on the type of fuel rod (UO₂ or UO₂–Gd₂O₃), which was similar to the case of PWR fuel. The differences in the number densities of ²³⁵U, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu, ¹⁴⁹Sm, and ¹⁵¹Sm have a large impact on k_eff. However, the reactivity uncertainty related to the burnup analysis was less than 3%. These results indicate that SWAT4.0 appropriately analyzes the isotopic composition of BWR fuel, and it has sufficient accuracy to be adopted in the burnup credit evaluation of fuel debris.     

On using alternative perturbation theory methodologies in the evaluation of reactivity effects in ADS cores

Core-average Doppler and coolant void reactivity coefficients, as well as the kinetic parameters (β_eff and Λ), have been determined for sub-critical accelerator-driven systems employing lead–bismuth eutectic (LBE) and helium gas coolants. To determine these parameters use is made of the standard procedure for analyzing critical reactors, which is based on “perturbation-theory” (PT), while in addition two dedicated methodologies for sub-critical systems, i.e. “inhomogeneous perturbation-theory” (IPT) and “heuristically based generalized perturbation-theory” (HGPT), have been employed to compute these parameters in a more rigorous manner.The two methods (PT and IPT/HGPT) are found to give similar results for each application and despite a smaller target k_eff-value, the sensitivity of the method is small in the case of the gas-cooled system, thus confirming the adequacy of the standard procedure. As regards the coolant void reactivity coefficient in the gas-cooled ADS, this finding can mostly be attributed to the fact that the core is always transparent with respect to the source neutrons, irrespective of the specific helium content.The sensitivity of the Doppler coefficient is also rather low in the case of the LBE cooled system. However, the dedicated methods are needed for the correct prediction of the coolant void reactivity coefficient, especially if minor actinides are introduced into the core. More important, in this case, is the fact that the PT-approach does not produce conservative results. Finally the sensitivity of the reactivity and kinetic parameters to the different methods is of the same order as that due to uncertainties in nuclear data and therefore these will need to be included in any overall evaluation of the impact of uncertainties on steady-state and transient ADS performance.     

Effects of Fission Products on Physical Quantities Accompanying Burn-Up of Large Pu-U Fast Reactors

The effects brought by the presence of fission products (F.P.) on the effective multiplication factor k _eff, the Na-void reactivity, the breeding ratio, the fuel composition and kinetics parameters have been calculated as functions of burn-up for Pu-U fast reactor with 3,000l core volume.

The F.P. sharply reduce k _eff and increase the positive values of the Na-void reactivity. Moreover, at a given burn-up, this effect of F.P. on k _eff and Na-void reactivity is governed largely by the total amount of the F.P. found accumulated at the time of observation, and is independent of the history of the material.

The F.P. hardly influence the transformation accompanying burn-up undergone by the ratio of Pu to ²³⁸U atoms and by the isotopic composition of Pu. Similarly, the effect on the internal breeding ratio also is very small. The total breeding ratio increases gradually with accumulation of the F.P. The effect on the effective delayed neutron fraction β_eff is only slight, while that on the prompt-neutron lifetime l _p is appreciably larger.     

Effect of a Boron Screen on the Sensitivity of Neutron Fission Chambers

It is suggested that absorbing screens with ¹⁰B be used to maintain constant sensitivity under prolonged irradiation of fission chambers with natural uranium. The transmission factor T (E) of boron screens with various thicknesses ( = 0.1–2 ge/cm²) for a wide neutron energy range and attenuation of a spectrum of the type _e/E are estimated. The group and average group constants of the transmission factor of boron are calculated for neutron fluxes in 25 energy groups of the neutron cross sections library.The contribution of ²³⁸U and ²³⁵U to the signal of a fission chamber with natural uranium is analyzed as a function of the boron screen thickness. ²³⁹Pu accumulation and ²³⁸U burnup are estimated using ²³⁸U group capture cross sections, ²³⁸U and ²³⁹Pu fission cross sections, and the group values T (E)E/E obtained by the authors. It is shown that in the absence of a boron screen for thermal-neutron fluence 10¹⁷ cm^–2 the sensitivity of a fission chamber with natural uranium increases as a result of the formation of ²³⁹Pu. A boron screen with = 1 g/cm² makes it possible to maintain the sensitivity of the fission chamber constant up to thermal-neutron fluence 5·10²² cm^–2.     

Uncertainty analyses of decay heat summation calculations using JENDL,JEFF, and ENDF files

The uncertainty analyses of decay heat calculation were carried out using major evaluated nuclear data files, JENDL, JEFF, and ENDF. The uncertainties were obtained from the sensitivity of individual fission product nuclide to the decay heat summation calculation. The summation calculation was performed for a burst fission. The sensitivities derived from the analyses were for decay energy, fission yield, and decay constant among the nuclear data included in the summation calculation. The uncertainties of the calculations at 0.1 s after a fission burst are ～10% for JENDL and ～8% for JEFF and ENDF and those at 10⁴ s are less than 2% for all cases. The main differences came from the different adoption of the energy uncertainty. The sensitivity analysis can be used to improve the decay data for decay heat calculation.     

Neutronic analysis of PROMETHEUS reactor fueled with various compounds of thorium and uranium

In this study, neutronic performance of the DT driven blanket in the PROMETHEUS-H (heavy ion) fueled with different fuels, namely, ThO₂, ThC, UO₂, UC, U₃Si₂ and UN is investigated. Helium is used as coolant, and SiC is used as cladding material to prevent fission products from contaminating coolant and direct contact fuel with coolant in the blanket. Calculations of neutronic data per DT fusion neutron are performed by using SCALE 4.3 Code. M (energy multiplication factor) changes from 1.480 to 2.097 depending on the fuel types in the blanket under resonance-effect. M reaches the highest value in the blanket fueled with UN. Therefore, the investigated reactor can produce substantial electricity in situ. UN has the highest value of ²³⁹Pu breeding capability among the uranium fuels whereas UO₂ has the lowest one. ²³⁹Pu production ratio changes from 0.119 to 0.169 according to the uranium fuel types, and ²³³U production values are 0.125 and 0.140 in the blanket fueled with ThO₂ and ThC under resonance-effect, respectively. Heat production per MW (D,T) fusion neutron load varies from 1.30 to 7.89 W/cm³ in the first row of fissile fuel breeding zone depending on the fuel types. Heat production attains the maximum value in the blanket fueled with UN. Values of TBR (tritium breeding ratio) being one of the most important parameters in a fusion reactor are greater than 1.05 for all type of fuels so that tritium self-sufficiency is maintained for DT fusion driver. Values of peak-to-average fission power density ratio, Γ, are in the range of 1.390 and ∼1.476 depending on the fuel types in the blanket. Values of neutron leakage out of the blanket for all fuels are quite low due to SiC reflector. The maximum neutron leakage is only ∼0.025. Consequently, for all cases, the investigated reactor has high neutronic performance and can produce substantial electricity in situ, fissile fuel and tritium required for (D,T) fusion reaction.     

Effect of coolant channel width on group constants and multiplication factor of research reactors using MTR type low enriched uranium fuel

One dimensional transport theory lattice code wims-d/4 and three dimensional diffusion theory code citation have been used to study the effect of fuel loading on critical cores of low enriched uranium (LEU) fuelled material testing reactors (MTRs). The fuel loading in a fuel element was varied by changing the fuel density in the fuel meat. In order to keep the reactor critically moderated, the optimal coolant channel width for a given fuel loading was calculated. For the purpose of optimization, the group constants D, Σ_a and νΣ_f, and infinite multiplication factor (k_∞) were calculated as a function of coolant channel width using wims-d/4. An increase in ²³⁵U loading per fuel plate results in an increase in the optimal coolant channel width and k_∞. The calculated values were found to be in good agreement with the typical design of MTR. citation was then used to determine the critical cores for different fuel loading with optimized fuel dimensions. Both critical mass and volume were found to decrease with an increase in the fuel loading. The criticality studies of Pakistan research reactor-1 (PARR-1) are in good agreement with the predictions.     

Fast Reactor Operating on Uranium–Plutonium Oxide Fuel in a Self-Regulatable Regime

Mathematical simulation is used to show that it is possible to develop a fast reactor operating on uranium–plutonium oxide fuel (UO₂)_1–x (PuO₂) _x , the same for all fuel elements in the core, and with uranium carbide in breeding elements with heavy coolant (PbBi eutectic). A self-regulatable regime is obtained in the reactor. This enhances safety while minimizing control. Tailings uranium with 0.1% ²³⁵U and a mixture of plutonium isotopes, which is obtained from spent fuel, making it possible to conduct operation in an actinide-closed fuel cycle, is used in the fuel and uranium carbide. ²³⁸U is actually consumed in the reactor, but most fission products are produced from ²³⁹Pu.     

Numerical studies of nuclear traveling waves in a supercritical water cooled fast reactor

An axial fuel shuffling strategy is proposed based on the mechanism of the nuclear fission traveling wave and implemented numerically in the calculation for a supercritical water cooled fast reactor (SCWFR). The ERANOS code is adopted to perform the neutronics and burn-up calculations, and the calculation scheme for axial fuel shuffling and coolant density coupling are set up. The parametric studies of a typical PWR with Th-U and U-Pu (²³⁵U instead of ²³⁹Pu) conversions by burn-up and k_eff calculations indicate that the breeding effects only exist in configurations with very low water content and the conversion or breeding becomes worse as the initial enrichment is increasing. The shuffling calculations for the 1-D SCWFR model described in this paper brought about some interesting results for a certain range of water content. The results indicate that the non-enriched fresh fuel is not possible for both Th-U and U-Pu conversions. As could be expected due to the η-values of the main fissile isotopes ²³³U and (²³⁵U, ²³⁹Pu), respectively, the Th-U conversion needs a lower enrichment, and results in a slightly higher burn-up than the U-Pu conversion. The asymptotic power density distribution of the Th-U conversion is broader and lower than that of the U-Pu conversion. By reducing the water volume fraction, an increased burn-up can be achieved with correspondingly reduced fuel shuffling speed and reduced initial enrichment. Furthermore, the steady state calculations for the asymptotic state show that the Th-U conversion is superior to the U-Pu one concerning SCWFR safety aspects, where the absolute value of the Doppler constant is larger and the coolant feedback is negative for the Th-U conversion, while the coolant feedback is positive for the U-Pu one.     

Lattice physics analysis of measured isotopic compositions of irradiated BWR 9 × 9 UO2 fuel

As part of a validation study of burnup calculations of BWR cores, lattice physics analyses were performed on burnups and isotopic compositions of U, Pu and fission product nuclides measured on five samples taken from 9 × 9 BWR fuel assemblies. Burnup calculations in infinite assembly geometry were carried out using MVP-BURN and SRAC codes coupled with major nuclear data libraries. The burnups determined based on the Nd-148 method were from 27.9 to 64.2 GWd/t. The typical relative differences in isotopic compositions (atom/Total-U) between the burnup calculations and measurements were ?2 ～ 19% for ²³⁴U, ?20 ～ 3% for ²³⁵U, ?1.5 ～ 0.1% for ²³⁶U, ?0.04 ～ 0.02% for ²³⁸U, ?4 ～ 11% for ²³⁸Pu, ?11 ～ ?2% for ²³⁹Pu, ?3 ～ 0% for ²⁴⁰Pu, ?12 ～ ?2% for ²⁴¹Pu and ?2 ～ 3% for ²⁴²Pu. They were ?2 ～ 2% for Nd isotopes, ?15 ～ 7% for Eu isotopes, ?13 ～ 1% for Cs isotopes, ?13 ～ 8% for Sm isotopes, 0 ～ 7% for ¹⁴⁷Pm, ?7 ～ ?2% for ⁹⁵Mo, ?2 ～ ?1% for¹⁰¹Ru and 0 ～ 4% for ¹⁰³Rh.     

Investigation on Criticality and Infinite Multiplication Factor of High Conversion Light Water Reactor Using Zone-Type FCA-HCLWR Core Fueled with Enriched Uranium

—A series of reactor physics experiments have been carried out at the FCA to examine the availability of the nuclear data and computational method currently employed to evaluate the nuclear characteristics of the High Conversion Light Water Reactor. Experimental results of the effective and infinite multiplication factors k_eff and k_∞ are compared with the calculated ones for three zone-type FCA-HCLWR cores fueled with enriched uranium. The calculated k_eff and k_∞ values with use of the SRAC system and the cross section set based on the JENDL-2 data file show a good agreement with the measured ones. The calculated-to-experimental (C/E) values for k_eff and k_∞ do not depend on the cell parameters such as the fuel enrichment, the moderator voidage state and the moderator-to-fuel volume ratio, and these values are similar with each other There is also no inconsistency between the C/E values for k_eff and k_∞ : The average C/E values are 989 and 0 988 for k_eff and k_∞ respectively     

Comparison of Cell Models for Analysis of Heterogeneous Fast Critical Assembly

We have investigated cell calculation models to be used in the analysis of neutronic characteristics of a heterogeneous fast critical assembly. As cell models we have considered a single drawer model with a critical buckling, a single drawer model with group dependent bucklings and a multidrawer model which consists of some fuel and blanket drawers. We have compared the cell averaged cross sections obtained from these cell models with the results of a reference transport calculation and estimated the effects of the cell models on k _eff, reaction rate ratios, reaction rate distributions and sodium void worths in the heterogeneous fast critical assembly ZPPR-13A. The multidrawer model and the single drawer model with group dependent buckling give reasonable cell averaged cross sections and have large effects on k _eff and ²³⁸U fission rate distribution.