Optimization of Fuel Assembly Allocation for Boiling Water Reactors

Abstract

A direct search algorithm is applied to the optimization of fuel assembly allocation of BWR with particular consideration given to the nuclear model and the treatment of operating constraints. A simple expression is derived for evaluating the stuck rod margin, based on regression analysis of data obtained by three-dimensional full core analysis, and the expression is applied to optimization procedure.

The practical applicability of the method is confirmed through trial computations for the second and equilibrium cycles of a medium-sized commercial BWR, with an examination based on various initial guesses and objective functions for radial power peaking.     

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.     

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.     

Analysis of Critical Experiments Using Medium-Enriched-Uranium Fuel in Kyoto University Critical Assembly (KUCA)

The critical experiments using medium-enriched-uranium (MEU) fuel in the Kyoto University Critical Assembly (KUCA), a light-water-moderated and heavy-water-reflected cylindrical core, were started in May 1981, as a part of the international Reduced Enrichment for Research and Test Reactors (RERTR) program.

The following KUCA critical experiments were analyzed: (1) the criticality measurements for high-enriched-uranium (HEU) and MEU cores and (2) the reactivity effect measurements of boron burnable-poison (BP) for MEU cores. Five-group constants were generated using the EPRI-CELL code, and two-dimensional diffusion calculations were performed using a conventional finite-difference code DIF3D(2D), and a finite-element code 2D-FEM-KUR. Some of the results from the two diffusion codes were compared with each other. Advantage was taken of the finite-element method for the application of the 2D-FEM-KUR code to a detailed analysis of the BP effect measurements.

Differences between the results of calculations and experiments were less than 1.8% in C/E ratios for eigenvalues. The agreement between the results obtained using the DIF3D(2D) code and the 2D-FEM-KUR code was excellent. The calculated results of the BP effects with use of the 2D-FEM-KUR code approximately agreed with the experiments.     

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method

Abstract

Whole core calculations have been performed for a commercial size PWR and a prototype LMFBR by using vectorized Monte Carlo codes. Geometries of cores were precisely represented in a pin by pin model. The calculated parameters were k _eff, control rod worth, power distribution and so on. Both multigroup and continuous energy models were used and the accuracy of multigroup approximation was evaluated through the comparison of both results. One million neutron histories were tracked to considerably reduce variances. It was demonstrated that the high speed vectorized codes could calculate k _eff, assembly power and some reactivity worths within practical computation time. For pin power and small reactivity worth calculations, the order of 10 million histories would be necessary. It would be difficult for the conventional scalar code to solve such large scale problems while the present codes consumed computation time less than 30 min for a PWR and 1 hour for an LMFBR. Required number of histories to achieve target design accuracy were estimated for those neutronic parameters.     

Effect of Moderator Density Distribution of Annular Flow on Fuel Assembly Neutronic Characteristics in Boiling Water Reactor Cores

The effect of the moderator density distribution of annular flow on the fuel assembly neutronic characteristics in a boiling water nuclear reactor was investigated using the SRAC95 code system. For the investigation, a model of annular flow for fuel assembly calculation was utilized. The results of the assembly calculation with the model (Method 1) and those of the fuel assembly calculation with the uniform void fraction distribution (Method 2) were compared. It was found that Method 2 underestimates the infinite multiplication factor in the fuel assembly including the gadolinia rod (type 1 assembly). This phenomenon is explained by the fact that the capture rate in the thermal energy region in gadolinia fuel is estimated to be smaller when the liquid film of annular flow at the fuel rod surface is considered. A burnup calculation was performed under the condition of a void fraction of 65% and a volumetric fraction of the liquid film in liquid phase of 1. It is found that Method 2 underestimates the infinite multiplication factor in comparison to Method 1 in the early stage of burnup, and that Method 2 becomes to overestimate the factor after a certain degree of burnup. This is because Method 2 overestimates the depletion rate of the gadolinia.     

Parallel Processing of Boiling Water Reactor Core Analysis

A parallel processing method for the analysis of a Boiling Water Reactor (BWR) core has been developed to drastically reduce the computation time. In the proposed method, a BWR core is divided into smaller segments, each of which is assigned to one of the processing elements (PE) working in parallel. The whole computing task is divided into smaller tasks that are distributed to the PEs as equally as possible.

To solve the neutron diffusion equations in BWR neutronics calculations, the three-dimensional checker-board block iterative method was adopted. In the thermal-hydraulic calculation, the whole task can be divided into parallel tasks except for the coolant enthalpy distribution calculation along a flow channel.

Parallelization efficiency of the proposed method was examined by measuring computing time on a hypercube type parallel processor with 64PEs. The computation speed gradually degrades with the number of segmentation, because of delay due to communications between PEs and to waiting time caused by unequal amount of tasks among PEs.

A 64 PE calculation was found to be from 30 to 50 times faster than the 1PE calculation. Both the axial and the radial segmentations were found to be effective in reducing computing time. If the BWR core analysis is made with a massively parallel processor consisting of more than 4,500 PEs, computing time will be reduced nearly by an order of three.     

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.     

Analysis of SHE Critical Experiments by Neutronic Design Codes for Experimental Very High Temperature Reactor

Analyses have been performed on various experiments conducted using the Semi-Homogeneous Experimental Assembly (SHE) to examine the accuracy of computer codes employed in the neutronic design of experimental Very High Temperature Reactor (VHTR). The neutronic design codes are DELIGHT-6 to obtain the neutron spectrum of a fuel cell and to produce group constants with burnup utilizing the nuclear data from ENDF-B/IV, CITDEGA to calculate the three-dimensional core performance considering the coupling effect between neutronic and thermohydraulic characteristics, and ANISN-JR and TWOTRAN-II for transport calculation. These codes are examined by the analysis on the integral quantities of effective multiplication factor, neutron flux distribution, burnable poison rod worth and control rod worth. The maximum degrees of disagreement with the relevant experiments are 0.57, 5, 7 and 5%, respectively.     

Application of Coarse Mesh Method to Neutron Diffusion Calculation for Fast Breeder Reactors

The improved coarse mesh method, which was originally derived by Askew and extended by Takeda, has been modified and applied to a 1,000-MWe and a 300-MWe homogeneous FBR core. In the present method, mesh average neutron flux and mesh center neutron flux are distinguished, and transverse neutron bucklings are taken into account. The results of numerical calculations showed that, with the present method, the power distribution and CR worths are appreciably improved for the 1,000-MWe FBR core with large-pitch fuel assemblies. When CRs are withdrawn, the use of the present method reduces the error of power distribution by half for both cores. However, it yields less satisfactory results, particularly with repect to CR worths, for the 300-MWe FBR core with small-pitch fuel assemblies.     

New Sampling Method in Continuous Energy Monte Carlo Calculation for Pebble Bed Reactors

A pebble bed reactor generally has double heterogeneity consisting of two kinds of spherical fuel element. In the core, there exist many fuel balls piled up randomly in a high packing fraction. And each fuel ball contains a lot of small fuel particles which are also distributed randomly. In this study, to realize precise neutron transport calculation of such reactors with the continuous energy Monte Carlo method, a new sampling method has been developed. The new method has been implemented in the general purpose Monte Carlo code MCNP to develop a modified version MCNP-BALL. This method was validated by calculating inventory of spherical fuel elements arranged successively by sampling during transport calculation and also by performing criticality calculations in ordered packing models. From the results, it was confirmed that the inventory of spherical fuel elements could be reproduced using MCNP-BALL within a sufficient accuracy of 0.2%. And the comparison of criticality calculations in ordered packing models between MCNP-BALL and the reference method shows excellent agreement in neutron spectrum as well as multiplication factor.

MCNP-BALL enables us to analyze pebble bed type cores such as PROTEUS precisely with the continuous energy Monte Carlo method.     

Comparisons of HELIOS,ORIGEN2, and Monteburns Calculated 241 Am and 243 Am Concentrations to Measured Values for PWR,BWR, and VVER Spent Fuel

A study was performed at Los Alamos National Laboratory to explore the accuracy of several reactor analysis codes in calculating ²⁴¹ Am and ²⁴³Am concentrations in light water reactor spent fuel. Calculated higher-actinide concentrations were compared to measured values from the literature for three reactor fuels. The fuel samples were taken from the Mihama Unit 3 pressurized water reactor, the Garigliano boiling water reactor, and a VVER-440. The ²⁴¹Am and ²⁴³Am concentrations were calculated using the HELIOS-1.4 lattice-physics code, the ORIGEN2 burnup code, and a linked MCNP/ORIGEN2 code named Monteburns 3.01. Comparisons were made between the calculated and measured values. It was determined that all codes performed consistently well for the Mihama Unit 3 measurements (within ±5% for ²⁴¹Am and ±20% for ²⁴³Am) and the Garigliano measurements (within ±12% for ²⁴¹ Am and ±20% for ²⁴³Am). It was determined that the ORIGEN2 pressurized water reactor libraries are insufficient for the VVER-440 measurements. The HELIOS and MONTEBURNS codes both demonstrated good ability to calculate these isotopes for VVER-440 fuel (±10% for ²⁴¹Am and ±12% for ²⁴³Am). The accuracies of these codes and the associated radiochemical measurements of these higher-actinide isotopes may be insufficient for safeguards and fuel management purposes; thus, development of new methods and modification to existing data libraries may be necessary in order to enable cost-effective safeguarding of these higher-actinide materials.     

Estimation of Most Probable Power Distribution in BWRs by Least Squares Method Using In-Core Measurements

Effective combination of measured data with theoretical analysis has permitted deriving a method for more accurately estimating the power distribution in BWRs. Use is made of least squares method for the combination between relationship of the power distribution with measured values and the model used in FLARE or in the three-dimensional two-group diffusion code. Trial application of the new method to estimating the power distribution in JPDR-1 has proved the method to provide reliable results.     

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.     

Accuracy of Cell Calculation Methods Used for Analysis of High Conversion Light Water Reactor Lattice

Validation tests were made for the accuracy of cell calculation methods used in analyses of tight lattices of a mixed-oxide (MOX) fuel core in a high conversion light water reactor (HCLWR). A series of cell calculations was carried out for the lattices referred from an international HCLWR benchmark comparison, with emphasis placed on the resonance calculation methods; the NR, IR approximations, the collision probability method with ultra-fine energy group. Verification was also performed for the geometrical modelling; a hexagonal/cylindrical cell, and the boundary condition; mirror/white reflection. In the calculations, important reactor physics parameters, such as the neutron multiplication factor, the conversion ratio and the void coefficient, were evaluated using the above methods for various HCLWR lattices with different moderator to fuel volume ratios, fuel materials and fissile plutonium enrichments.

The calculated results were compared with each other, and the accuracy and applicability of each method were clarified by comparison with continuous energy Monte Carlo calculations. It was verified that the accuracy of the IR approximation became worse when the neutron spectrum became harder. It was also concluded that the cylindrical cell model with the white boundary condition was not so suitable for MOX fuelled lattices, as for UO₂ fuelled lattices.