Neutron Anisotropic Scattering Effect in Heterogeneous Cell Calculations of Light Water Reactors

A study on the anisotropic scattering effects in heterogeneous square cells of light water reactors has been performed using the characteristics method. It was found that the effects of the anisotropic scattering were relatively large for the MOX fuel cell because of the large neutron current from the moderator to the fuel region and the k _inf value by the P₀ calculation became 0.10–0.16% larger than that by the P₅ calculation. With the transport correction, the k _inf difference from the P₅ calculation became even larger than that from the P₀ calculation and the k _inf value by the transport correction became 0.18–0.25% larger than that by the P₅ calculation for the MOX fuel cell. The transport corrected self-scattering cross sections of the moderator region become smaller than the non-transport corrected ones and the angular flux distribution becomes more anisotropic with the transport correction. Therefore, more neutrons toward the moderator region between the fuel pellets can slow down to the lower energy region with the transport correction. As a result, the k _inf value by the transport correction becomes larger than that by the P₀ calculation, which is opposite effect to that by the P₅ calculation.     

Analysis of measured isotopic compositions by CASMO5 coupled with a JENDL-4.0 base library for irradiated fuel of light water reactors

Measured isotopic compositions of UO₂ and MOX fuel samples taken from irradiated light water reactor fuel assemblies were analyzed by CASMO5 coupled with a JENDL-4.0 base library to assess the uncertainties in the calculated isotopic compositions on heavy and fission product nuclides. The burnup calculations for the analysis were performed based on a single-assembly model taking into account the detail fuel assembly specifications and irradiation histories. For the MOX fuel samples, a multiple-assembly model was also adopted taking into account the effect of the surrounding UO₂ fuel assemblies. The average and standard deviation of the biases (C/E ? 1's (here C and E are calculated and measured results, respectively)) were calculated for each nuclide separately on the PWR and BWR UO₂ fuel samples. The averaged biases for ²³⁵U, ²³⁶U, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu and ²⁴²Pu were 2.7%, ?0.9%, 0.3%, 0.7%, ?2.4% and ?1.7% for PWR UO₂ samples, and 6.7%, ?1.5%, 2.5%, ?0.6%, 0.4% and ?0.1% for BWR UO₂ samples, respectively. The biases with the single-assembly model on the MOX fuel samples showed large positive values of ²³⁹Pu, and application of the multiple-assembly model reduced the biases as reported in our previous studies.     

Application of Multiband Method to Pin Cell Calculations

Abstract

In order to accurately calculate effective neutron cross sections in the resonance energy region, the multiband method has been applied to cell calculations. Cell calculations for UO² and MOX fuels of light water reactors have been performed and the results were compared with those of a continuous energy Monte Carlo code VIM and the conventional self-shielding method using the Dancoff factor.

The k∞values calculated by the multiband method agreed with those of the VIM calculations within 0.20% Δk for the UO² fuel cell and within 0.30% Δk for the MOX fuel cell, respectively, whereas the Dancoff factor method yielded about l.l%Δk errors for the two cells. The element- wise contribution to this error was investigated, and it was found that the effective microscopic cross sections, particularly those for the giant resonances of ²³⁸U, calculated by the multiband method were in good agreement with those of VIM. It was also found that interference effect between ²³⁸U and ²³⁵U resonances in the UO² fuel and that between ²³⁸U and ²³⁹Pu resonances in the MOX fuel made about 0.20%Δk contributions to k∞ in both fuel cells.     

Axial SPN and Radial MOC Coupled Whole Core Transport Calculation

The Simplified P_N (SP_N) method is applied to the axial solution of the two-dimensional (2-D) method of characteristics (MOC) solution based whole core transport calculation. A sub-plane scheme and the nodal expansion method (NEM) are employed for the solution of the one-dimensional (1-D) SP_N equations involving a radial transverse leakage. The SP_N solver replaces the axial diffusion solver of the DeCART direct whole core transport code to provide more accurate, transport theory based axial solutions. In the sub-plane scheme, the radial equivalent homogenization parameters generated by the local MOC for a thick plane are assigned to the multiple finer planes in the subsequent global three-dimensional (3-D) coarse mesh finite difference (CMFD) calculation in which the NEM is employed for the axial solution. The sub-plane scheme induces a much less nodal error while having little impact on the axial leakage representation of the radial MOC calculation. The performance of the sub-plane scheme and SP_N nodal transport solver is examined by solving a set of demonstrative problems and the C5G7MOX 3-D extension benchmark problems. It is shown in the demonstrative problems that the nodal error reaching upto 1,400 pcm in a rodded case is reduced to 10pcm by introducing 10 sub-planes per MOC plane and the transport error is reduced from about 150pcm to 10pcm by using SP₃. Also it is observed, in the C5G7MOX rodded configuration B problem, that the eigenvalues and pin power errors of 180 pcm and 2.2% of the 10 sub-planes diffusion case are reduced to 40 pcm and 1.4%, respectively, for SP₃ with only about a 15% increase in the computing time. It is shown that the SP₅ case gives very similar results to the SP₃ case.     

Applications of the multidimensional equations to complex fuel assembly problems

For the analysis of reactors with complex fuel assemblies or fine mesh applications as pin by pin neutron flux reconstruction, the usual approximation of the neutron transport equation by the multigroup diffusion equation does not provide good results. A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P_L equations. In this line, a nodal collocation method for the discretization of these equations on a rectangular mesh is used in this paper to analyse reactors with MOX fuel assemblies. Although the 3D P_L nodal collocation method becomes feasible due to the improvements in computer hardware, a complete treatment of the detailed structure of the fuel assemblies in actual three-dimensional geometry is still prohibitive, thus, an assembly homogenization method is necessary. A homogenization method compatible with our multidimensional P_L code is proposed and tested performing heterogeneous and homogenized calculations. In this work, we apply the method to 2D complex fuel assembly configurations.     

Wavelet-based angular dependence analysis of the heterogeneous calculation on MOX fuel lattice

A wavelet-based transport method is developed to satisfy the high order angular approximation, which has been proved to be necessary in the heterogeneous calculation of MOX fuel lattice. Based on the new angular discretization scheme, the angular dependence of flux is analysed to find out the origin of complicated angular anisotropy and its effects on the heterogeneous calculation. Both of the geometric and neutronic effects are investigated quantitatively to find out the angular dependence in heterogeneous calculations. Comparisons between the traditional S_N angular discretization scheme and wavelet-based scheme are analysed to indicate the challenges brought from the MOX fuel lattice heterogeneous calculation. An effective solution is given by using wavelets in the angular discretization of neutron transport equation. Improvements of high order angular approximation are suggested.     

Analysis of Core Physics Experiments on Fresh and Irradiated PWR UO2 Fuels in the REBUS Program

Critical experiments of two cores each loaded with fresh 5 × 5 test PWR-type fuel rods of ²³⁵U enrichment of 3.8 wt% or irradiated 5 × 5 test rods of rod average burnup of 55 GWd/t in the REBUS program were analyzed using diffusion, transport, and continuous-energy Monte Carlo calculation codes coupled with nuclear data libraries based on JENDL-3.2 and JENDL-3.3. Biases in effective multiplication factors k _eff's of the critical cores were about ?1:2%Δk for the diffusion calculations (JENDL-3.2), ?0:5%Δk for the transport calculations (JENDL-3.3), and ?0:5 and 0.1%Δk for the Monte Carlo calculations (JENDL-3.3 and JENDL-3.2, respectively). The measured core fission rate and Sc- or Co-activation rate distributions were generally well reproduced using the three types of calculation. The burnup reactivity determined using the measured water level reactivity coefficients was ?2:35 ± 0:07Δk/kk′. The calculated result of the Monte Carlo calculations agreed with it; however, the diffusion and transport calculations overestimated the absolute value by about 7%, which would be mainly attributed to the errors in the calculation of the reactivity caused by changing the fuel compositions from fresh fuel to irradiated fuel.     

Development and verification of a nodal approach for solving the multigroup SP3 equations

The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length, and the consideration of new reactor types are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P₃ (SP₃) approximation of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. The method described in the paper is verified with pinwise calculations of a steady state of the OECD/NEA and US NRC PWR MOX/UO₂ Core Transient Benchmark. The used 16-group cross section library was generated for DORT calculations with homogenized pin cells. Two different approximations of the diffusion coefficient which occurs in the within-group form of the SP₃ equations are investigated. Using the transport cross section for the calculation of the diffusion coefficient gives much better results than those obtained with the removal cross section. The improvement of the results in comparison to a pinwise diffusion calculation is shown. The results are compared with the DORT and the heterogeneous reference solution of the code DeCART. Concerning the SP₃ calculation using the diffusion coefficient based on the transport cross section (DYN3D-SP3-TR) the deviations of the eigenvalue k_eff and the assembly powers from the transport solutions of DORT and DeCART are in the same order as those between the two transport solutions themselves. The improvement of the DYN3D-SP3-TR results in comparison to the diffusion calculation is presented. As the DYN3D-SP3-TR and DORT calculations are performed with homogenized pin cells, the pin powers of the two calculations are closer to each other than to the pin powers of the DeCART solution. To estimate the contribution of higher flux-moments, the ratio of the second flux moment to the zeroth flux moment is investigated along a horizontal row of pins. It is shown that it is low in the fuel assemblies with small peaks at the water channels. Considering the baffle and the water reflector regions higher values are obtained in the fast neutron groups.     

Thermal conductivity degradation analyses of LWR MOX fuel by the quasi-two phase material model

The temperature measurements of mixed oxide (MOX) and UO₂ fuels during irradiation suggested that the thermal conductivity degradation rate of the MOX fuel with burnup should be slower than that of the UO₂ fuel. In order to explain the difference of the degradation rates, the quasi-two phase material model is proposed to assess the thermal conductivity degradation of the MIMAS MOX fuel, which takes into account the Pu agglomerate distributions in the MOX fuel matrix as fabricated. As a result, the quasi-two phase model calculation shows the gradual increase of the difference with burnup and may expect more than 10% higher thermal conductivity values around 75 GWd/t. While these results are not fully suitable for thermal conductivity degradation models implemented by some industrial fuel manufacturers, they are consistent with the results from the irradiation tests and indicate that the inhomogeneity of Pu content in the MOX fuel can be one of the major reasons for the moderation of the thermal conductivity degradation of the MOX fuel.     

Trend in criticality calculation results of borated-water-moderation experimental cores relating to 10B(n, α) cross section

ABSTRACT

In connection with the accuracy of the ¹⁰B(n, α) cross section in the thermal- and epithermal-neutron energy regions, criticality calculation results were examined for six benchmark sets of light-water-moderation critical experiments of UO₂ and MOX fuel lattice cores with un-borated and borated water. Two of the benchmark sets were those implemented in the Tank-Type Critical Assembly (TCA). The others were taken from the International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP), and the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP). The enrichments of the UO₂ fuel range from 1.9 wt% to 2.6 wt%, and the Pu contents of the MOX fuel do from 2.0 to 6.6 wt%. The boron concentrations in water are up to 1511 ppm. The effective neutron multiplication factors (k_eff ) were taken from the published documents. They were calculated with continuous-energy Monte Carlo calculation codes in combination with JENDL-4.0, and other evaluated nuclear data libraries. It was confirmed that the k_eff values of the critical cores increased with the boron concentrations, which indicates that the ¹⁰B(n, α) cross section in the thermal- and epithermal-neutron energy regions should be larger than those in JENDL-4.0 and other libraries.     

ACP1000中MOX燃料组件管理初步研究

使用SCIENCE程序包对MOX燃料组件进行了初步设计和研究。在此基础上,对采用部分MOX燃料组件的ACP1000堆芯开展燃料管理研究,得到由全堆装载UO₂燃料组件向部分MOX燃料组件堆芯过渡的燃料管理方案,并对MOX燃料组件和部分MOX燃料组件堆芯的安全参数及其他重要参数进行分析和比较。分析结果表明,各种安全参数均满足设计要求,证明在ACP1000堆芯应用MOX燃料是可行的,并为进一步研究提供了参考。     

Analysis of VIP-BWR reactor core physics experiments on UO2 and MOX mockup fuel assemblies - part 2: analysis with SIMULATE5

Analysis of the three test cores in the VIP-BWR program was performed in a two-dimensional geometrical model with CASMO5 coupled with the JENDL-4.0-based neutron data library, and reported in the previous paper. Following the study, interpretation of the experiments were carried out in a three-dimensional geometrical model with SIMULATE5 for the code validation study. The nuclear libraries for the SIMULATE5 calculations were generated with CASMO5 with the JENDL-4.0-based neutron data library. The effective multiplication factors of the critical cores ranged from 0.9983 to 1.0023 with measurement uncertainties of 0.0003 to 0.0004 (one σ). The root mean squares of (the calculated/the measured-1) for the fission rates at the core-mid plain of all the measured fuel rods were about 3% for the three cores. It was noticed that the calculations underestimated the fission rates of the UO₂ fuel rods and overestimated those of the MOX fuel rods for the test cores loaded with MOX fuel rods, which was consistent with trends in the preceding analysis studies of the VIP-BWR program and other MOX core experiments, and the biases were confirmed in the calculation results of power distributions in MOX-fueled light water reactor cores.     

On the influence of spatial discretization in LWR-burnup calculations with HELIOS 1.9 – Part II: Mixed oxide (MOX) fuel

Cell and burnup calculations are the basis for all deterministic static and transient 3D full core calculations for different operational states of the reactor. The arising differences in the integral transport solution (neutron flux and k_inf) for different discretization strategies during the burnup of mixed oxide (MOX) fuel due to different spatial discretization are demonstrated. The influence of different discretization strategies on the calculation of homogenized few group cross-sections is investigated. The influence of the discretization strategies on the calculation time is evaluated.     

Non destructive determination of PuO2 content in MOX fuel pins for fast reactors using Passive Gamma Scanning

Use of Passive Gamma Scanning for non destructive evaluation of PuO₂ content in mixed oxide (MOX) fuels for fast reactors is demonstrated. Experiments have been carried out on MOX fuel pins for the hybrid core of Fast Breeder Test Reactor having nominal PuO₂ content of 44% and MOX pins having nominal PuO₂ content of 21% for the Prototype Fast Breeder Reactor. A comparison of results obtained using a conventional NaI(Tl) detector and that using a through well shaped detector is also presented.     

Instructions to authors

Abstract

The sea transport of fresh MOX fuel from Europe to Japan is under consideration. For the structure and equipment of transport ships for fresh MOX fuels, there is a special safety standard called the INF Code of the IMO. For transport of radioactive materials, there is a safety standard stipulated in the Regulations for the Safe Transport of Radioactive Material issued by the IAEA. Under these, code and standard, fresh MOX fuel will be transported safely by sea. However, a dose assessment has been made by assuming that a fresh MOX fuel package might be sunk from some unexpected cause. In both cases, for a package sunk in the coastal region and for one sunk in the open sea, the evaluated results of the dose equivalent by radiation exposure of the public are far below the dose equivalent limit of the ICRP recommendation (1 mSv.y^?1).     

Helios, current coupling collision probability method, applied for solving the NEA C5G7 MOX benchmark

As part of an effort to test the ability of current transport codes to treat reactor core problems without spatial homogenization, the lattice code HELIOS was employed to perform criticality calculations. The test consists in seven-group calculations of the C5 MOX fuel assembly problem specified by Cavarec et. al. [1]. This problem, known as C5G7 MOX Benchmark, is described in the Benchmark Specification [2] and comprises two cases — two and three-dimensional geometry. There are four fuel assemblies — two with MOX fuel, the other two with UO₂ fuel. Each fuel assembly is made up of a 17×17 lattice of square fuel-pin cells. Fuel pin compositions are specified in the Benchmark Specification, which also provides seven-group transport-corrected isotropic scattering cross-sections for U0₂, the three MOX enrichments, the guide tubes, the fission chamber and the moderator. This paper preset is the methodology employed in solving the C5G7 MOX Fuel Assembly Problem using the transport code HELIOS.     

Analysis of fuel pin behavior under slow-ramp type transient overpower condition by using the fuel performance evaluation code ‘FEMAXI-FBR’

FEMAXI-FBR has been developed as the one module of the core disruptive accident analysis code ‘ASTERIA-FBR’ in order to evaluate the mixed oxide (MOX) fuel performance under steady, transient and accident conditions of fast reactors consistently. On the basis of light water reactor (LWR) fuel performance evaluation code ‘FEMAXI-6’, FEMAXI-FBR develops specific models for the fast reactor fuel performance, such as restructuring, material migration during steady state and transient, melting cavity formation and pressure during accident, so that it can evaluate the fuel failure during accident. The analysis of test pin with slow transient over power test of CABRI-2 program was conducted from steady to transient. The test pin was pre-irradiated and tested under transient overpower with several % P ₀/s (P ₀: steady state power) of the power rate. Analysis results of the gas release ratio, pin failure time, and fuel melt radius were compared to measured values. The analysis results of the steady and transient performances were also compared with the measured values. The compared performances are gas release ratio, fuel restructuring for steady state and linear power and melt radius at failure during transient. This analysis result reproduces the measured value. It was concluded that FEMAXI-FBR is effective to evaluate fast reactor fuel performances from steady state to accident conditions.     

Determination of fissile fraction in MOX (mixed U + Pu oxides) fuels for different burnup values

When spent Light Water Reactor fuels are processed by the standard Purex method of reprocessing, plutonium (Pu) and uranium (U) in spent fuel are obtained as pure and separate streams. The recovered Pu has a fissile content (consisting of ²³⁹Pu and ²⁴¹Pu) greater than 60% typically (although it mainly depends on discharge burnup of spent fuel). The recovered Pu can be recycled as mixed-oxide (MOX) fuel after being blended with a fertile U makeup in a MOX fabrication plant. The burnup that can be obtained from MOX fuel depends on: (1) isotopic composition of Pu, which is closely related to the discharge burnup of spent fuel from which Pu is recovered; (2) the type of fertile U makeup material used (depleted U, natural U, or recovered U); and (3) fraction of makeup material in the mix (blending ratio), which in turn determines the total fissile fraction of MOX. Using the Non-linear Reactivity Model and the code MONTEBURNS, a step-by-step procedure for computing the total fissile content of MOX is introduced. As was intended, the resulting expression is simple enough for quick/hand calculations of total fissile content of MOX required to reach a desired burnup for a given discharge burnup of spent fuel and for a specified fertile U makeup. In any case, due to non-fissile (parasitic) content of recovered Pu, a greater fissile fraction in MOX than that in fresh U is required to obtain the same burnup as can be obtained by the fresh U fuel.     

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.     

An Improvement of the Transverse Leakage Treatment for the Nodal SN Transport Calculation Method in Hexagonal-Z Geometry

To overcome the divergent behavior of the NSHEX code, a nodal S_N code for hexagonal geometry, for some transport calculations, an improvement has been made in the calculation of the axial leakage. The axial leakage, previously calculated by using the quadratic transverse leakage approximation (QLA), is calculated by a new method of analytically treating the spatial distribution within a node, based on the axial homogeneity of the ordinary core. The verification tests were performed for the KNK-II model geometry of the NEACRP 3-D Neutron Transport Benchmarks and the large assembly-size KNK-II model. It is found that k_ett values obtained by introducing the new method agree with the reference Monte Carlo calculation results within 0.1% Δk/k for the KNK-II model, although the QLA method did not converge for two cases. Furthemore the new method succeeded in calculations for the large assembly-size model, in which the QLA method failed for all cases. Thus the new method has been found accurate and convergence achieved for the cases in which the QLA method failed.