Fission Product Model for BWR Lattice Calculation Code

A benchmark calculation of full fission product was performed for thermal reactor application using an isotope transmutation code DCHAIN based on 185 nuclides with revised nuclear data library. The fission product model for BWR lattice calculation was studied and tested with the benchmark results, and a model containing 45 explicit nuclides and one pseudo nuclide was selected as a reasonably best model to predict the burn up reactivity with high precision for practically all types of fuel and reactor operating conditions. The evaluated thermal cross section and resonance integral for the pseudo nuclide are σ_2,200 = 2.6b and.RI = 10.6b, combined with the pseudo fission yield values of 1.3898, 1.3233, 1.3675 and 1.2773 for fissions from ²³⁵U, ²³⁸U, ²³⁹Pu and ²⁴¹Pu, respectively. The present results are believed as equally applicable to PWR lattice calculation.     

Expression of Few-Group Effective Microscopic Cross Sections in BWR Burnup Calculations

A practical method is proposed to express few-group effective microscopic cross sections for BWR burnup analysis. A set of few-group cross sections is prepared for an infinite square lattice of fuel rods as a function of the ratios of number density of nuclides such as ²³⁵ U, ²³⁸U and ²³⁹Pu, and the water quantity around a fuel rod. Spatial variation of few-group cross sections in the fuel assembly is taken into account by adjusting the water quantity around a fuel rod.

Numerical studies show that the present method can evaluate effective few-group cross sections within the accuracy of 3% in comparison with a two-dimensional integral transport calculation.     

Estimation of Spent Fuel Compositions from Light Water Reactors

The compositions and quantities of minor actinide (MA) and fission product (FP) in spent fuels will be diversified with the use of high discharged burnup fuels and MOX fuels in LWRs which will be a main part of power reactors in future.

In order to investigate above diversities, we have studied on the calculation method to be used in the estimation of spent fuel compositions and adopted the real irradiation calculation in which axial burnup and moderator distribution are considered in the burnup calculation.

On the basis of the calculations, compositions and burnup quantities of various LWR spent fuels (reactor type: PWR and BWR, discharged burnup: 33, 45 and 60 GWd/tHM, fuel type: U0₂ and MOX) are apparently estimated among various forms of fuels. As an example, it is shown that there are considerable discrepancy in MA burnup between PWR and BWR spent fuels.     

Influence of void fraction change on plutonium and minor actinides recycling in BWR with equilibrium burnup

A study on the influence of void fraction change on plutonium and minor actinides recycling in standard boiling water reactor (BWR) with equilibrium burnup model has been conducted. We considered the equilibrium burnup model since it is a simple time independent burnup method that can handle all possible produced nuclides in any nuclear system.

The uranium enrichment for the criticality of the reactor diminishes significantly for the plutonium and minor actinides recycling case compared to that of the once-through cycle of BWR case. This parameter decreases much lower with the increasing of the void fraction. A similar propensity was also shown in the required natural uranium per annum. The annual required natural uranium was calculated by assuming that the uranium concentration in the tail of the enrichment plant is 0.25 w%. The amount of loaded fuel reduces slightly with the increment of the void fraction for plutonium and minor recycling in BWR.     

Comparison of thorium-based fuels with different fissile components in existing boiling water reactors

With the aim of investigating the technical feasibility of fuelling a conventional BWR (Boiling Water Reactor) with thorium-based fuel, computer simulations were carried out in a 2D infinite lattice model using CASMO-5. Four different fissile components were each homogenously combined with thorium to form mixed oxide pellets: Uranium enriched to 20% U-235 (LEU), plutonium recovered from spent LWR fuel (RGPu), pure U-233 and a mixture of RGPu and uranium recovered from spent thorium-based fuel. Based on these fuel types, four BWR nuclear fuel assembly designs were formed, using a conventional assembly geometry (GE14-N). The fissile content was chosen to give a total energy release equivalent to that of a UOX fuel bundle reaching a discharge burnup of about 55 MWd/kgHM. The radial distribution of fissile material was optimized to achieve low bundle internal radial power peaking. Reactor physical parameters were computed, and the results were compared to those of reference LEU and MOX bundle designs. It was concluded that a viable thorium-based BWR nuclear fuel assembly design, based on any of the fissile components, can be achieved. Neutronic parameters that are essential for reactor safety, like reactivity coefficients and control rod worths, are in most cases similar to those of LEU and MOX fuel. This is also true for the decay heat produced in irradiated fuel. However when Th is mixed with U-233, the void coefficient (calculated in 2D) can be positive under some conditions. It was concluded that it is very difficult to make savings of natural uranium by mixing LEU (20% U-235) homogenously with thorium and that mixing RGPu with thorium leads to more efficient consumption of Pu compared to MOX fuel.     

Nuclear Analysis of PIE Data of Irradiated BWR 8×8-2 and 8×8-4 UO2 Fuel Assemblies

The measured pellet average inventories of actinides and fission product nuclides on the fifteen samples taken from a three-cycle irradiation BWR 8×8-2 UO₂ assembly were compared with those of assembly burnup calculations using a collision probability method (SRAC) with the JENDL-3.2 nuclear data library. The present calculations overestimate the inventories of ²³⁵U, well reproduce those of ²³⁹Pu and ²⁴⁰Pu, yet underestimate those of ²³⁶U, ²³⁷Nd, ²³⁸Pu, ²⁴¹Pu, and ²⁴²Pu. The inventories of minor actinides are underestimated by the present analysis except for ²⁴¹Am. The major FP nuclides contributing to neutron absorption such as Nd, Cs, Eu, and Sm are almost well reproduced by the present calculations. The measured pellet average burnups and major actinide inventories on the twenty samples taken from four BWR 8×8-4 UO₂ assemblies were also compared with those of the burnup calculations using SRAC and a continuous energy Monte Carlo burnup analysis code (MVP-BURN). Most of the calculated pellet average burnups of both codes agree with the measurements within the range of ±10%. The general trends of the measured pellet radial distributions of actinide and FP nuclides on six samples of the 8×8-4 UO₂ assemblies were well reproduced by the burnup calculations of MVP-BURN.     

A fast and reliable calculation model for BWR fuel assembly burnup analyses

A code called superb has been developed for the BWR fuel assembly burnup analyses using a supercell model. Each of the characteristic heterogeneities of a BWR fuel assembly like water gap, poisoned pins, control blade etc. is treated by invoking the appropriate supercell concept. The burnup model of superb is so devised as to strike a balance between accuracy and speed. This is achieved by building isotopic densities in each fuel pin separately while the depletion equations are solved only in a few group of pins or burnup zones and the multigroup neutron spectra are differentiated in fewer group of pincell types. Multiple fuel ring burnup is considered only for Gd isotopes. A special empirical formula allows the microscopic cross section of Gd isotopes to be varied even during burnup integration.The supercell model has been tested against Monte-Carlo results for the fresh cold clean Tarapur fuel assembly with two Gd fuel pins. The burnup model of superb has been validated against one of the most sophisticated codes lwr-wims for a benchmark problem involving all the complexities of a BWR fuel assembly.The agreement of superb results with both Monte-Carlo and lwr-wims results is found to be excellent.     

Benchmark Problem Suite for Reactor Physics Study of LWR Next Generation Fuels

This paper proposes a benchmark problem suite for studying the physics of next-generation fuels of light water reactors. The target discharge burnup of the next-generation fuel was set to 70GWd/t considering the increasing trend in discharge burnup of light water reactor fuels. The UO₂ and MOX fuels are included in the benchmark specifications. The benchmark problem consists of three different geometries: fuel pin cell, PWR fuel assembly and BWR fuel assembly. In the pin cell problem, detailed nuclear characteristics such as burnup dependence of nuclide-wise reactivity were included in the required calculation results to facilitate the study of reactor physics. In the assembly benchmark problems, important parameters for in-core fuel management such as local peaking factors and reactivity coefficients were included in the required results. The benchmark problems provide comprehensive test problems for next-generation light water reactor fuels with extended high burnup. Furthermore, since the pin cell, the PWR assembly and the BWR assembly problems are independent, analyses of the entire benchmark suite is not necessary: e.g., the set of pin cell and PWR fuel assembly problems will be suitable for those in charge of PWR in-core fuel management, and the set of pin cell and BWR fuel assembly problems for those in charge of BWR in-core fuel management.     

PWR核电厂乏燃料贮存临界计算重要核素的选取

信用核素选取是基于燃耗信用制乏燃料贮存临界安全分析的关键一步。通过对不同富集度、燃耗深度及停堆冷却时间下典型PWR燃料组件分析,以核素中子吸收份额大小排序为依据,筛选出对总的中子吸收起主要贡献的核素。结果显示,47个核素即可包络停堆后0~20a内影响乏燃料贮存系统反应性的所有核素中的99%。通过核素敏感性因子分析证明依据中子吸收份额排序选取重要核素的方法是合理的,与基准算例的结果对比证明所筛选出的核素能足够代表影响系统反应性的所有重要核素。     

Reactivity Control Method for Extended Burnup of Boiling Water Reactor Fuel Bundles

Abstract

A reactivity control method was proposed for a boiling water reactor (BWR) fuel bundle, which has a potential for higher burnup with an increase in fuel enrichment. The new method optimized the distribution and amount of nonboiling water area in a fuel bundle in order to enhance the reactivity control capacity.

Using the method, a 9×9 lattice fuel bundle with a small-sized channel box, large-sized water rods and a reduced fuel rod diameter was proposed for the discharged burnup of 70 GWd/t and the operational cycle length of 18 months. The core, which consists of the proposed fuel bundles with the bundle-averaged enrichment of 5.8% and includes other modifications concerning a neutron low leakage loading pattern, natural uranium axial blankets, and spectral shift with recirculation flow control, has a cold shutdown margin greater than the design limit (1%Δk) with minimum fuel bundle shuffling. Further, it has potentials for natural uranium savings of about 20% per unit power and reduction in the amount of reprocessing of about 60% per unit power, compared with current BWR designs.     

Two practical methods for unionized energy grid construction in continuous-energy Monte Carlo neutron transport calculation

A considerable speed-up in continuous-energy Monte Carlo neutron transport calculation can be achieved by using the same unionized energy grid for all point-wise reaction cross sections. This speed-up results from the fact that time-consuming grid iteration is reduced to minimum, and if the unionized grid is constructed by combining the grids of all nuclides, there is no loss of data or accuracy in the calculation. The drawback of this approach is that computer memory is wasted for storing a large number of redundant data points. Memory usage may become a problem, especially in burnup calculation, in which the irradiated materials consist of several hundred actinide and fission product nuclides. The grid size easily increases to over 1 million points, requiring tens of gigabytes of memory for storing the cross section data. This paper presents two practical methods for reducing the memory demand, while trying preserve the accuracy of the original data. The calculation routines are included in the PSG2/Serpent Monte Carlo reactor physics burnup calculation code and the methods are tested in a BWR assembly burnup calculation.     

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.     

Effect of Pu-Rich Agglomerate in MOX Fuel on a Lattice Calculation

The effect of Pu-rich agglomerates in U-Pu mixed oxide (MOX) fuel on a lattice calculation has been demonstrated. The Pu-rich agglomerate parameters are defined based on the measurement data of MIMAS-MOX and the focus is on the highly enriched MOX fuel in accordance with increased burnup resulting in a higher volume fraction of the Pu-rich agglomerates. The lattice calculations with a heterogeneous fuel model and a homogeneous fuel model are performed simulating the PWR 17 × 17 fuel assembly. The heterogeneous model individually treats the Pu-rich agglomerate and U-Pu matrix, whereas the homogeneous model homogenizes the compositions within the fuel pellet. A continuous-energy Monte Carlo burnup code, MVP-BURN, is used for burnup calculations up to 70 GWd/t. A statistical geometry model is applied in modeling a large number of Pu-rich agglomerates assuming that they are distributed randomly within the MOX fuel pellet. The calculated nuclear characteristics include k-inf, Pu isotopic compositions, power density and burnup of the Pu-rich agglomerates, as well as the pellet-averaged Pu compositions as a function of burnup. It is shown that the effect of Pu-rich agglomerates on the lattice calculation is negligibly small.     

燃耗信任制下燃耗计算对临界计算的偏差及不确定度的研究

为量化燃耗信任制中燃耗计算传递给临界计算的不确定度,本文基于参数统计法对燃耗计算的核素偏差及偏差不确定度展开分析,并以蒙特卡罗（MC）抽样方法计算的kinf不确定度为基准,比较不同抽样方法对临界计算不确定度的影响。结果表明,核素偏差与偏差不确定度是随样品燃耗变化的分段函数。对于临界计算,拉丁超立方抽样（LHS）方法与MC抽样方法的kinf不确定度计算结果吻合较好,且LHS方法可考虑参数间的相关性,计算结果更真实,可进一步提升电厂的经济性。     

Validation of decay heat calculation results of ORIGEN2.2 and CASMO5 for light water reactor fuel

Comparing with the fission product nuclide (FP) decay heat summation calculation result in MeV/sec/fission based on the JENDL FP decay and yield data files 2011 for the burst fission, FP decay heat calculated by ORIGEN2.2 coupled with JENDL-4.0 base library ORLIBJ40 was verified at the cooling time from 1 sec to 10⁸ sec for ²³⁵U (thermal), ²³⁸U (fast), ²³⁹Pu (thermal) and ²⁴¹Pu (thermal). For these fission nuclides, FP decay heat calculated by CASMO5 at the same cooling time after a short irradiation (10⁴ sec) was also compared with that of ORIGEN2.2. In the analysis of decay heat measurements at the cooling time from 2.3 years to 27 years consisting of four data sets on the fuel assemblies discharged from the US PWRs and BWRs, and the Swedish PWRs and BWRs, the average values of the ratios of the calculated to measured results (C/E's) were from 0.972 to 1.031 for ORIGEN2.2, and from 0.977 to 1.016 for CASMO5. The standard deviations of C/E's for the four data sets were from 0.02 to 0.03 for the both codes except for those of the US BWR fuel assemblies which were from 0.11 to 0.12. The obtained C/E's were similar to those in the precedent study.     

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

The pin-by-pin fine-mesh core calculation method is considered as a candidate next-generation core calculation method for BWR. In this study, the diffusion and simplified P3 (SP3) theories are applied to the BWR pin-by-pin fine-mesh calculation. The performances of the diffusion and SP3 theories for cell-homogeneous pin-by-pin fine-mesh calculation for BWR are evaluated through comparison with a cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and SP3 theories. The 2 × 2 multi-assemblies geometry consists of 9 × 9 UO₂ fuel assemblies that have two different enrichment splittings. To minimize the cell-homogenization error, the SPH method is applied for the pin-by-pin fine-mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation using that of homogeneous calculation. The calculation results indicated that the diffusion theory shows a discrepancy larger than that of the SP3 theory on the pin-wise fission rate distribution. In contrast to the diffusion theory, the SP3 theory shows a much better accuracy on the pin-wise fission rate distribution. The computation time using the SP3 theory is about 1.5 times longer than that using the diffusion theory. The BWR core analysis consists of various calculations, e.g., the cross section interpolation, neutron flux calculation, thermal hydraulic calculation, and burn-up calculation. The function of the calculation time for the neutron flux calculation is usually less than half in the typical BWR core analysis. Therefore, the difference in the calculation time between the diffusion and SP3 theories would have no significant impact on the calculation time of the BWR core analysis. For these reasons, the SP3 theory is more suitable than the diffusion theory and is expected to have sufficient accuracy for the 2 × 2 multi-assemblies geometry used in this study, which simulates a typical situation of the actual BWR core.     

Comparative Studies of ENDF/B-6.8, JEF-2.2 and JENDL-3.2 Data Libraries by Monte Carlo Modeling of High Temperature Reactors on Plutonium Based Fuel Cycles

We performed a numerical comparative analysis of the burnup capability of the Gas Turbine-Modular Helium Reactor (GT-MHR) by the Monte Carlo Continuous Energy Burnup Code (MCB). The MCB code is an extension of MCNP that includes the burnup implementation; it adopts continuous energy cross sections and it evaluates the transmutation trajectories for over 2,400 decaying nuclides. We equipped the MCB code with three different nuclear data libraries: JENDL-3.2, JEF-2.2 and ENDF/B-6.8 processed for temperatures from 300 to 1,800K.

The GT-MHR model studied in this paper is fueled by actinides coming from the Light Water Reactors waste, converted into two different types of fuel: Driver Fuel and Transmutation Fuel. The Driver Fuel supplies the fissile nuclides needed to maintain the criticality of the reactor, whereas the Transmutation Fuel depletes non-fissile isotopes and controls reactivity excess. We set the refueling and shuffling period to one year and the in-core fuel residency time to three years.

The comparative analysis of the MCB code consists of accuracy and precision studies. In the accuracy studies, we performed the burnup calculation with different nuclear data libraries during the year at which the refueling and shuffling schedule set the equilibrium of the fuel composition. In the precision studies, we repeated the same simulations 20 times with a different pseudorandom number stride and the same nuclear data library.     

Analysis of Measured Isotopic Compositions of High-Burnup BWR MOX Fuel

Analysis of measured isotopic compositions of four high-burnup BWR MOX fuel samples was performed by using a general-purpose neutronic calculation code SRAC and a continuous-energy Monte Carlo burnup code MVP-BURN. The initial Pu fissile content of the samples was 5.52 wt%, and the burnups ranged from 50 to 80 GWd/t. It is confirmed that a geometrical model including the effect of UO₂ assemblies adjacent to the MOX assembly is necessary in the burnup calculations to obtain accurate calculated isotopic compositions. The calculated results of MVP-BURN with JENDL-3.3 taking such effect into account show more accurate results for major actinides (U, Pu, and Am isotopes) and most fission products than those of infinite assembly calculations. The paper also shows the results calculated using SRAC with JENDL-3.3, ENDF/B-VII, and JEFF-3.1.     

Application of Quick Subchannel Analysis Method for Three-Dimensional Pin-by-Pin BWR Core Calculations

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.     

高阶预估-校正燃耗方法在压水堆组件计算中的应用

压水堆燃料组件输运燃耗耦合计算通常采用的是传统的预估-校正(PC)燃耗方法。然而,该方法本身的假设导致其存在一定的计算误差。为进一步提高燃耗计算的精度,本文针对传统的预估-校正燃耗方法的缺陷研究了改进的预估-校正燃耗方法,改进了对核反应率进行修正的高阶预估-校正燃耗方法,并在Bamboo-Lattice程序中进行了程序实现,对该方法进行了验证分析。结果表明:改进的预估-校正燃耗方法和高阶预估-校正燃耗方法在保证计算效率的前提下提高了燃耗计算的精度。