Criticality aspects of nuclear power reactor cores in the case of emerging nuclear fuels

Reactor cores of PWR and LMFBR, loaded with different commercial and emerging nuclear fuels, have been simulated and compared at BOI with respect to criticality with and without chemical shim, control rods and sodium. The different cases considered, within each of the reactor types, are grouped together according to their fissile content, when compared on the basis of the neutron multiplication factor (k_eff). For both PWR and LMFBR reactor types, the reactivity worths of the control rods do not change significantly when replacing commercial fuels by emerging ones. In the case of the LMFBR, the Na void reactivity effects are small and comparable using either emerging or commercial fuels. Hence, operation and control of the core at beginning of irradiation are similar for emerging or commercial fuels.     

3-D Neutron Transport Benchmarks

Three-dimensional (3-D) neutron transport benchmark problems proposed from Osaka University to NEACRP in 1988 have been calculated by many participants and the results have been summarized. The results of k _eff, control rod worth, and region-averaged group fluxes for proposed four core models calculated by various 3-D transport codes have been compared. There was consistency among the results, when necessary corrections were made. The solutions of the four core models are quite useful as benchmarks for checking the validity of 3-D neutron transport codes.     

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.     

Neutronics Calculations of HTTR with Several Nuclear Data Libraries

Benchmark calculations for several HTTR core states were performed with four cross-section sets which were generated from JENDL-3.3, JENDL-3.2, ENDF/B-VI.8 and JEFF-3.0 using a continuous energy Monte Carlo code MVP. The core states were a critical approach in which an annular core was formed at room temperature and solid cores at room temperature and at full power operation. Study of k_eff discrepancies caused by difference of the nuclear data libraries and identification of nuclides which have large effects on the k_eff discrepancies were carried out. Comparison of the respective k_eff from calculations and experiments was also carried out. As the results, for each of the HTTR core states, JENDL-3.3 yields a k_eff agreeing with the experiments within 1.5%Δk, JENDL-3.2 yields k_eff agreement within 1.7%Δk, and ENDF/B-VI.8 and JEFF-3.0 yield k_eff agreement within 1.8%Δk. There is little k_eff discrepancy between ENDF/B-VI.8 and JEFF-3.0. The k_eff between JENDL-3.3 and JENDL-3.2 is caused by difference of ²³⁵U data and has temperature dependency. The k_eff discrepancy between JENDL-3.3 and ENDF/B-VI.8 or JEFF-3.0 is mainly caused by difference in graphite data.     

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.     

Diffusion Calculation Model for Streaming Effects in Low Density Channels in LMFBRs

A study is made of the use of modified diffusion theory to calculate the negative reactivity worth of recently proposed flow activated reactor shutdown devices, in which sodium is voided from purely sodium filled channels located at the boundary between the core and the radial blanket in a Liquid Metal cooled Fast Breeder Reactor (LMFBR). Three-dimensional diffusion theory calculations using various definitions of modified diffusion coefficients in the channels are compared with each other and with three-dimensional transport theory computations. While normal diffusion coefficient is found to be inadequate for these reactivity worth calculations, the various modified diffusion coefficients appear adequate for the considered case. Modelling method of the small thickness of steel wall and interstitial sodium layer of the modules are also studied.     

Technetium transmutation in thin layer coating on PWR fuel rods

Based on the EFTTRA-T2 experiment results, we study the transmutation characteristics of pressurized water reactors (PWR) after coating a thin layer of Tc-99 on the fuel rods. Our calculation shows that for the same Tc-99 loading amount, the effect on the PWR k_eff after coating Tc-99 on the PWR fuel rods is much less than that of the homogeneous addition of Tc-99 to uranium dioxide nuclear fuel. If we just coat 0.2λ_c (0.0065 mm) thickness Tc-99 on PWR fuel rods, the total Tc-99 coating amount is about 291.37 kg, this is approximately equivalent to the 4 PWR Tc-99 annual outputs, and the system k_eff merely decreases to 0.98530.Loading Tc-99 to the PWR is equivalent to introducing extra poisons to PWR system to control excess reactivity, some control poisons like boric acid concentration in primary coolant or burnable poison rods in fuel assemblies are needed to be removed to keep the reactor in criticality. As Tc-99 coating thickness increases from 0.05λ_c to 0.2λ_c, no matter which substitution pattern is used, B16→12 or C16→12, the system k_eff variations are almost the same and can return to criticality again after removing corresponding burnable poison rods from fuel assemblies. For coating 0.15λ_c or 0.2λ_c thickness on the fuel rods of PWR, the system k_eff is slightly below the criticality either in B16→12 or C16→12 substitution pattern, we may reduce the concentration of the boric acid slightly to let the system in criticality again.Our calculation results indicate that the optimal coating thickness of Tc-99 on PWR fuel rods is probably between 0.15λ_c to 0.2λ_c, i.e. 0.00488–0.0065 mm.     

Treatment of Radioactive Waste Regenerant of Ion Exchange Resin by Preferential Flotation Method

To answer the increasing demand for electric power in Japan, Very Large Fast Reactors of 10,000 MWe unit capacity are expected to make their appearance in due course. The paper describes the method and results of a design study on a 10,000 MWe Liquid Metal Fast Breeder Reactor. First, a reference design was obtained for this unit of unprecedented capacity by extrapolating the various characteristics of a 1,000 MWe LMFBR and the nuclear characteristics thereof were studied. It was found that reactivity increase could be reduced to about 6 ¢ when seven subassemblies were voided in the central part of the core, and that the increase of reactivity and the decrease of breeding ratio with time were rather large for the initial loading core.

Secondly, a design optimization procedure was developed based on complex method of nonlinear programming, and the method was applied to the Very Large Fast Reactor. The process resulted in a relatively large core height and fuel pin diameter, while the power cost was improved due to enhanced breeding gain. The fuel center temperature and the coolant velocity were found close to the upper boundaries of their prescribed ranges. These results concurred qualitatively with calculations using more straightforward optimization techniques.     

Development of a control rod depletion methodology for the Westinghouse NEXUS system

The NEXUS project is an effort to merge and modernize the methods employed in Westinghouse PWR and BWR steady-state reactor physics codes. The NEXUS system relies on a once-through nodal cross-section generation methodology with an innovative and efficient technique for pin power recovery. The pin power methodology overcomes a well-known limitation of existing methodologies, namely the incapacity to properly account for heterogeneity changes due to the depletion environment. The so-called control rod history problem where control rods are repeatedly inserted and withdrawn during core depletion is a good example of such a case. In addition to the control rod history impact on pin power distributions, the insertion of control rods during extended periods leads to significant control rod depletion that affects the reactivity worth of the control rods which in turn can have a significant impact on pin powers. The importance of accurately predicting pin powers, combined with the need to adequately estimate the reactivity worth and nuclear end of life of control rods in BWRs and in generation III+ PWRs, has motivated the development of a novel control rod depletion model. This methodology and its numerical qualification, initially for PWR application only, is the topic of this paper. The focus is on describing the salient features of the model and on illustrating its performance by means of numerical experiments. It is shown that together with the NEXUS pin power recovery model, the control rod depletion methodology accurately predicts the reactivity feedback from repeated control rod insertions in a PWR core.     

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.     

International Symposium on Isotope Separation and Chemical Exchange Uranium Enrichment

From the viewpoint of nuclear criticality safety, it is important to comprehend the reactivity of fuel solutions induced by oscillatory movements such as earthquakes. This paper intends to figure out the reactivity of a fuel solution system with a free surface formed by oscillation by evaluating the fluctuation of the neutron multiplication factor (k _eff ) obtained from a static calculation. To fulfill this intension, criticality calculations with reflecting fluid calculation results have been carried out. In the fluid calculations, the finite volume method and the volume of fluid (VOF) method have been applied in tracking the free surface formed by oscillation. The continuous energy Monte Carlo calculation method has been applied in the criticality calculations. As a result, it has been found that the variation patterns of the k _eff and those of the shape of fuel solutions are classified according to oscillation frequency and the ratio of solution height to the width of the tank (H/L). If a sloshing motion is generated, the k _eff fluctuates widely and has a threshold, with which we can classify the fluctuation type of the k _eff , despite the kind of reflector. If H/L is above the threshold, i.e., H/L =0.4, the k _eff fluctuates to a value below that obtained in the resting state. On the contrary, if H/L is below the threshold, the k _eff fluctuates to a value above that obtained in the resting state. This result implies the criticality calculation for a fuel solution with a free surface using the Monte Carlo method may give a slightly smaller threshold than using other approaches.     

High Efficiency,Prototype Annular Electromagnetic Flow Coupler with Ceramic Insulator

Neutronic modeling for the modular high temperature pebble bed reactor during reactivity accident was investigated for safety analysis purposes. Three existing dynamic models, i.e. the point reactor, adiabatic and improved quasistatic models were compared with each other, and their accuracy was discussed, A one-dimensional numerical experiment was performed for simulating the severest reactivity accident involving withdrawal of all absorber rods in the reflector region. The results showed that the adiabatic model gave the highest estimation of the power excursion since it over-estimated the input reactivity worth. Although the point reactor model required the minimum computation time, it under-estimated the input reactivity worth and gave less accuracy in predicting the power excursion. The improved quasistatic model gave the highest accuracy and its computation time was comparable to the adiabatic model.     

A Proposal of Benchmark Calculation on Reactor Physics for Metallic Fueled and MOX Fueled LMFBR Based upon Mock-up Experiment at FCA

In order to assess the validity of the cross section library for fast reactor physics, a set of benchmark calculation is proposed. The benchmark calculation is based upon mock-up experiments at three FCA cores with various compositions of central test regions, two of which were mock-ups of metallic fueled LMFBR's, and the other was a mock-up of a mixed oxide fueled LMFBR. One of the metallic cores included enriched uranium in the test region, while the others did not.

Physics parameters to be calculated are criticality, reaction rate ratios, plutonium and B₄C sample worth, sodium void reactivity worth, and Doppler reactivity worth of ²³⁸U. Homogenized atomic number densities and various correction factors are given so that anyone can easily perform diffusion calculation in two-dimensional RZ-model and compare the results with the experiments. The validity of the correction factors are proved by changing the calculation method and used nuclear data file.     

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k_eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k_eff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of −2 mk and k_eff-EOC of 0.900 for the first two cases, and a CBCVR-BOC of −2 mk and k_eff-EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study.     

Benchmark Analysis of Criticality Experiments in the TRIGA Mark II Using a Continuous Energy Monte Carlo Code MCNP

The criticality analysis of the TRIGA-II benchmark experiment at the Musashi Institute of Technology Research Reactor (MuITR, 100kW) was performed by the three-dimensional continuous-energy Monte Carlo code (MCNP4A). To minimize errors due to an inexact geometry model, all fresh fuels and control rods as well as vicinity of the core were precisely modeled. Effective multiplication factors (k_eff) in the initial core critical experiment and in the excess reactivity adjustment for the several fuel-loading patterns as well as the fuel element reactivity worth distributions were used in the validation process of the physical model and neutron cross section data from the ENDF/B-V evaluation. The calculated k_eff overestimated the experimental data by about 1.0Δk/k for both the initial core and the several fuel-loading arrangements (fuels or graphite elements were added only to the outer-ring), but the discrepancy increased to 1.8Δk/k for the some fuel-loading patterns (graphite elements were inserted into the inner-ring). The comparison result of the fuel element worth distribution showed above tendency. All in all, the agreement between the MCNP predictions and the experimentally determined values is good, which indicates that the Monte Carlo model is enough to simulate criticality of the TRIGA-II reactor.     

Pin Power Reconstruction Methods of the Few-Group BWR Core Simulator NEREUS

An improved pin power reconstruction method has been incorporated in the few-group nodal BWR core simulator NEREUS, which is based on the analytic polynomial nodal method. With the analytic polynomial nodal method, accurate node surface fluxes are available, which are used later to reconstruct pin powers. The intranodal homogeneous thermal flux is corrected using a semi-empirical proportional relation between surface transition components of the homogeneous and heterogeneous fluxes. This correction method is effective for BWR calculations, especially for controlled assemblies or mixed loading of off-set assemblies. A unified model accounting for effects of spectral histories, caused by spectral interactions between fuel assemblies and the control blade insertion, was also developed for intranodal burnup correction. The change in pin powers due to the control blade history can be predicted well, without laborious assembly depletion calculations with control blade insertion. R-factors used in critical power ratio calculations are also reconstructed from the pin powers. The NEREUS pin power reconstruction method was verified against heterogeneous multi-assembly depletion calculations.     

Effect of Geometrical Approximation on Multiplication Factor in Small Fast Reactor Core

In most of the calculations using analytical methods a reactor core is approximated as cylinder and the reactor parameters are calculated using two-dimensional computer codes. While such calculations are useful in scoping studies in view of azimuthal asymmetry in the actual reactor core these calculations could entail errors of unknown magnitude. The present study reports our estimate of such errors in K _eff with the instance of fast reactor having 22 and 23 fuel subassemblies. The K _eff are calculated using Monte Carlo code KENO and Hansen-Roach cross section set, modelling the core in two different ways, (1) by approximating the core to a cylinder (2-D calculation), (2) by near exact representation of the core (3-D calculation). The difference in K _eff is appreciable between 2-D and 3-D calculations.

Experimental values are adduced in support of these calculations.     

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.