Burnup Distribution Research Articles

Optimization layer by layer networks for in-core fuel management optimization computations in PWRs

The optimization layer by layer (OLL) learning algorithm is applied to prediction of assembly-wise power and burnup distribution, the critical soluble boron concentration, and the pin power peaking factor (PPPF) with core burnup in the pressurized water reactor (PWR) of the Korean Nuclear Unit (KNU) 11. It is shown that the OLL trained neural networks can predict core depletion characteristics as accurately as the high-precision modern nodal method codes and that the OLL trained neural networks can compute core depletion characteristics about 40 times faster than the modern nodal method code. The OLL networks are then utilized for determining the optimum fuel assembly (FA) loading pattern (LP) of the equilibrium cycle KNU 11 PWR core by a simulated annealing (SA) scheme. By demonstrating that the FA LP optimization by the SA scheme can be carried out within 10 to 15 min thanks to the speedy neutronics evaluation of the OLL networks, it is proposed that the OLL networks can make a satisfactory substitute for core evaluation codes based on modern nodal methods in in-core fuel management optimization computations where neutronics analysis for a large number of trial loading patterns has to be carried out.

PLUTON: A Three-Group Model for the Radial Distribution of Plutonium, Burnup, and Power Profiles in Highly Irradiated LWR Fuel Rods

A three-group model (PLUTON) is described, which predicts the power density distribution, plutonium buildup, and burnup profiles across the fuel pellet radius as a function of in-pile time and parameters characterizing the type of reactor system with respect to fuel temperature and changes of density during the irradiation period. The PLUTON model is a part of two fuel performance codes (ASFAD and FEMAXI-V), which provide all necessary input for this model, mainly local temperatures and fuel matrix density across the radius. Comparisons between measurements and predictions of the PLUTON model are made on fuels with enrichments in the range 2.9 to 8.25% and with burnup between 21 000 and 64 000 MWd/t. It is shown that the PLUTON predictions are in good agreement with measurements as well as with predictions of the well-known TUBRNP model. The proposed model is flexibly applicable for all types of light water reactor (LWR) fuels, including mixed oxide, and for fuel tested in the Organization for Economic Corporation and Development’s Halden heavy water reactor. The PLUTON three-group model is based on analytical (theoretical) consideration of neutron absorption in a resonant region of the fuel in its apparent form. It makes the model more flexible in comparison with the semi-empirical TUBRNP one-group model and allows the physically based model analysis of commercial LWR-type fuels at high burnup as well as analysis of experimental fuel rods tested in the Halden heavy water reactor, which is one of the main test reactors in the world. The differences in fuel behavior in the Halden reactor in terms of burnup distribution and plutonium buildup can be more clearly understood with the PLUTON model.

The irradiation test of inert-matrix fuel in comparison to uranium plutonium mixed oxide fuel at the halden reactor

Conservative modelling for pin layout shows that the relatively low thermal conductivity of Inert-Matrix Fuel (IMF) causes higher temperatures and therefore higher fission gas release than in uranium plutonium mixed oxide (MOX). According to neutronic calculations, performance differences will also arise from different evolutions of the respective radial power and burnup distributions. Modelling of these effects as well as a ∼10% greater production of Xe in the thermal spectrum of the Halden reactor is well within the capabilities of appropriate codes. Some of the data and models used for the pre-calculations are preliminary and will be revised after the first experimental data have become available.

RAPID model to predict radial burnup distribution in LWR UO 2 fuel

The RAPID ( RA dial power and burnup P rediction by following fissile I sotope D istribution in the pellet) model was developed to predict the radial distribution of power, burnup and fissionable nuclide densities in the LWR UO 2 fuel pellets to be used in the fuel performance analysis code. It considers the specific radial variations of the neutron reactions of all the fissionable nuclides as functions of burnup and 235 U enrichment in the pellet. Comparison of the RAPID prediction with the measured data of the irradiated fuels and the predicted results by other codes showed good agreement, and therefore, the RAPID model can be used for UO 2 fuel of up to 10 w/o 235 U enrichment and 150 MWD/(kg U) pellet average burnup under the LWR environment.

Use of Axially Graded Burnable Boron for Hot-Spot Temperature Reduction in a Pressurized Water Reactor Core

Shortly after the loading of a pressurized water reactor (PWR) core, the axial power distribution in fresh fuel has already attained the characteristic, almost flat shape, typical of burned fuel. At beginning of cycle (BOC), however, the axial distribution is centrally peaked. In assemblies hosting uniform burnable boron rods, this BOC peaking is even more pronounced. A reduction in the axial peaking is today often achieved by shortening the burnable boron rods by some 30 cm at each edge.It is shown that a two-zone grading of the boron rod leads, in a representative PWR cycle, to a reduction of the hot-spot temperature of ~70°C, compared with the nongraded case. However, with a proper three-zone grading of the boron rod, an additional 20°C may be cut off the hot-spot temperature. Further, with a slightly skewed application of this three-zone grading, an additional 50°C may be cut off.The representative PWR cycle studied was cycle 11 of the Indian Point 2 station, with a simplification in the number of fuel types and in the burnup distribution. The analysis was based on a complete three-dimensional burnup calculation. The code system was ELCOS, with BOXER as an assembly code for the generation of burnup-dependent cross sections and SILWER as a three-dimensional core code with thermal-hydraulic feedback.

Measurement of Dose-Equivalent Rates around a Cask and Monte Carlo Analysis with Actual Configuration of Fuel Basket

Gamma ray and neutron dose-equivalent rate distributions are measured with an ionization-type gamma-ray survey meter and a moderator-type neutron survey meter respectively around a TN-12A spent fuel transport cask, and the measured dose-equivalent rate distributions are analyzed by the Monte Carlo method. Two models for the aluminum-alloy fuel basket are considered in the Monte Carlo code MCNP 4B. In one case the configuration of the basket with 12 spent fuel assemblies is modeled in detail and the other is the homogenized basket as employed in the Sn code DOT 3.5. In addition, the burn-up distribution is taken into account to generate source neutrons and gamma rays in the z-axis of the spent fuel assemblies in both cases. The essential difference in the dose-equivalent rates is obtained from the Monte Carlo calculations employing the homogenized model and the actual configuration of the basket. Due to employing the actual configuration, the gamma ray and neutron dose-equivalent rates reduce to 67% and 80%, respectively as compared with the homogenized model on the surface of the TN-12A cask. As the results, the good C/Es are obtained: for the neutron it is approximately 1.0 and 1.25 for the gamma ray it is at the center of the cask surface, respectively The effect of the burn-up distribution appears clearly at the off-center cask surface, and in particular, the neutron dose-equivalent rates come close to the measured ones.

Advanced Nodal Methods of the Few-Group BWR Core Simulator NEREUS

A few-group nodal BWR core simulator NEREUS, which is based on the analytic polynomial nodal method, has been developed. The analytic polynomial nodal method is applicable to multigroups and has good accuracy for analysis of cores having large spectral mismatch between fuel assemblies, since the intranodal thermal flux can be correctly represented. In NEREUS, the following advanced methods are adopted to overcome the shortcomings of the conventional analytic polynomial nodal method. The flux solution iteration matrix is cast into the form of finite difference, by using the flux discontinuity factors which correct the finite difference error as well as the homogenization error. The intranodal burnup and spectral history distributions are considered in the method, and source moments are obtained by orthogonal expansions. Burnup calculations are made by looking-up exposure dependent tables for macroscopic cross sections, which are prepared by single assembly spectrum and depletion calculations. A unified model accounting for effects of spectral histories, caused by the spectral interaction between fuel assemblies and the control blade insertion, was incorporated. The NEREUS code was verified against benchmark problems and core tracking calculations.

Actinide-Only Burnup Credit for Pressurized Water Reactor Spent Nuclear Fuel–III: Bounding Treatment of Spatial Burnup Distributions

A flat, uniform axial burnup assumption, preferred for its computational simplicity, does not always conservatively estimate the pressurized water reactor spent-fuel-cask multiplication factors. Rather, the reactivity effect of the significantly underburned fuel ends, usually referred to as the “end effect,” can be properly treated by explicit modeling of the axial burnup distribution based on limiting axial burnup profiles. An alternative approach to this laborious explicit modeling is to augment the multiplication factor determined from an axially uniform calculation by an appropriate keff bias. Based on the observation that the end effect increases with a decrease in the cask size, conservative keff bias curves are determined by applying the limiting axial burnup profiles and assuming a single-assembly cask configuration. However, because of their conservative nature, the keff bias curves are not recommended unless there is a large reactivity margin in the particular cask of interest.The horizontal burnup distribution poses less reactivity concern simply because the limiting arrangement in a cask is an unlikely event. The possibility of two or more assemblies with low burnup zones placed inward and next to each other is small, while the underburned fuel ends will surely be next to each other. Regardless, the reactivity effect of the horizontal burnup distribution is bounded by assuming a conservative horizontal burnup gradient within individual assemblies and the most reactive arrangement of multiple assemblies in spent nuclear fuel casks. This approach can have a significant effect on small cask designs where the orientation of fuel assemblies has a substantial influence on the calculated multiplication factor because of the large radial neutron leakage.

97/04689 A method for determining the fuel burn-up distribution of nuclear research reactors by measurements at subcritical states: Binh, D. Q. et al. Ann. Nucl. Energy, 1997, 24, (15), 1233–1240

97/04689 A method for determining the fuel burn-up distribution of nuclear research reactors by measurements at subcritical states: Binh, D. Q. et al. Ann. Nucl. Energy, 1997, 24, (15), 1233–1240

A method for determining the fuel burn-up distribution of nuclear research reactors by measurements at subcritical states

This article presents a new method for determining the radial distribution of fuel burn-up by measuring neutron counts from the reactor core at subcritical states by detectors of the reactor control system. Initial results of an experiment carried out for some fuel elements of the Dalat reactor are also introduced.

Interpretation of positive scram reactivity in the RBMK-1000 reactor

The positive scram reactivity in the Chernobyl-4 reactor is interpreted by breaking it up into three components by the use of the exact perturbation method. The three components are absorption, diffusion and slowing down. The negative reactivity contribution of the absorber elements inserted is significantly reduced by the distortion of the axial flux shape and the removal of water from the bottom of the core by the graphite follower contributes to the positive reactivity predominantly through absorption and diffusion effects. The total scram reactivity thus becomes positive. Further, theoretical expression of the higher-order reactivity component induced by the flux distortion is developed on the basis of explicit higher-order perturbation formulation. The expression shows that the positive magnitude of the higher-order term is inversely proportional to the λ-mode eigenvalue separation. The significantly small separation between the fundamental and the first axial-harmonic eigenvalue, which indicates spatial decoupling of the core is confirmed in the λ-mode eigenvalue calculation. It is suggested that to ensure total scram reactivity is negative, the axial burnup distribution should be flattened and the follower dimensions should be modified.

The Influence of Burnup-Dependent Fission Spectra on Reactor Pressure Vessel Irradiation

The neutron source to be used in calculations of the irradiation of nuclear reactor pressure vessels depends not only on the power distribution in the core but also on the burnup distribution. The burnup affects both the strength and the spectrum of the source, with each effect increasing the displacement rate in the pressure vessel as the burnup in the outer parts of the core increases. For a VVER-440 reactor, each effect causes an [approximately]8% increase going from fresh fuel to a burnup representative of a low-leakage loading scheme. For Western light water reactors, the increase due to the spectral effect may be somewhat larger. This work investigates the spectral effect and discusses practical ways of taking it into account in calculations.

Time-Independent Neutronic Analysis of the Chernobyl Accident

Estimates are made of the positive reactivity introduced through the growth of the coolant void fraction in the Chernobyl reactor at both the average burnup value given by the Soviets and the maximum value. Using Monte Carlo models, various possible axial burnup distributions, displacer models, conditions in the control channels, and control rod positions are considered in calculating the insertion of positive reactivity by the manual and emergency control rods, that is, the positive scram. Two possible scenarios are examined for a second reactivity peak: (a) creation of a mixture of fuel, water, and cladding in a number of central fuel channels, resulting in the explosion of these channels, and (b) uniform vaporization throughout the entire reactor, resulting in reactor depressurization. From the data presented in this paper, it can be concluded that vaporization of the cooling water in the fuel channel gave the highest reactivity contribution to the Chernobyl accident. The positive reactivity due to insertion of the manual and emergency control rods played only a minor role in the reactivity balance of the accident.

Solutions of the neutronic design problems of small heating reactor cores based on the BWR principle

Small size, low power density and fuel temperature as well as the tendency to simplicity lead at first to a uniform design and a very simple fuel management strategy for the core of a small heating reactor following boiling water technology. Problems encountered in such a concept include high power and burnup peaking, resulting in poor fuel utilization, a strongly negative void reactivity coefficient, and high control rod reactivity worths exceeding the limit imposed by safety considerations. In order to solve them the following modifications of an original core based on standard BWR designs are investigated: poison zoning, separation of the moderating from the cooling functions of the water, different designs of the control rods according to their radial positions and application of a multiple batch loading scheme. The application of these measures leads to modified core designs which show a significant improvement of core performance as compared to the original uniform core, in particular flatter power and burnup distributions as well as reduced control rod worths and void reactivity coefficient.

しゃへい型イオンマイクロアナライザ（ＳＩＭＡ）による燃焼度測定技術の開発

A new method of the fuel burnup measurement using a shielded ion microprobe analyzer (SIMA) has been developed. This method is based on the direct isotope analysis of U, Pu and Nd in an irradiated fuel by means of the secondary ion mass spectrometry. The sample tests on the irradiated fuels up to 13a/0 burnup have shown an accuracy within 6%.While the conventional isotope dilution method requires the acid-dissolution and the chemical separation of the irradiated fuel by handling samples in a glovebox, the new method can measure the burnup on a fuel in shielded apparatus remotely and directly. Consequently, the time for measurement was reduced to about one tenth of that of the conventional method, and a human radiation exposure became negligible.A microarea surface analysis by the SIMA provides the local burnup distribution in small area. Using this technique, the radial profile of the burnup distribution due to a thermal neutron depression was obtained in the fuel pellet irradiated in JRR-2 reactor. The radial burnup distribution was also measured in the mixed-oxide fuel pellet of the experimental fast reactor JOYO MK-II, which revealed some effects of Pu redistribution on the radial burnup profile.

Development of a New Measurement Method for Fast Breeder Reactor Fuel Burnup Using a Shielded lon Microprobe Analyzer

A new method of burnup measurement using a shielded ion microprobe analyzer (SIMA) has been developed. The method is based on the isotope analysis of uranium, plutonium, and fission products in irradiated mixed oxide fuel by means of secondary ion mass spectrometry (SIMS). Fourteen samples irradiated in the Japanese experimental fast reactor JOYO were examined. The maximum local burnup of JOYO MK-I core fuels was about5.1 at. %. The axial burnup distribution of the fuel pin was in good agreement with that of the sibling pin in the same subassembly, measured by surface ionization mass spectrometry, which requires the chemical separation of fission products and heavy metals. The new method facilitates the rapid and accurate measurement of fast breeder reactor fuel burnup without human radiation exposure during sample preparation and analysis.

Modeling Fragmentation and Spallation of Oxide Reactor Fuel During Transient Heating Including the Effects of Burnup and Fission Product Distribution

Characteristics of solid fuel fragmentation and energetic spallation during hypothetical accident transients are calculated. Fission gas, having migrated to the grain boundaries as intergranular bu...

Optimum Burnup Distribution in a Continuously Fueled Reactor

The Canadian Deuterium-Uranium (CANDU) pressurized heavy water reactor is fueled continuously at power, with alternate channels being fueled in opposite directions (continuous bidirectional fueling...

Reactivity Worths of Plutonium-Uranium Clusters in a Heavy-Water-Moderated Assembly by the Reactor Oscillation Method

The reactivity worths of synthetic plutonium-uranium clustered fuel elements in a heavy-water-moderated assembly have been experimentally determined using the reactor oscillation method.Several test-fuel compositions have been investigated, representing varying degrees of fucl burnup and burnup distributions; two uranium samples with different U enrichment have been used as standard.The technique selected was aimed to establish “clean” experimental conditions, in order to effectively simplify the analysis of the results. Basically, the technique involved oscillating, according to a square-wave pattern, a 6-m-long fuel element containing a 50-cm-high test section with the fuel composition to be investigated the corresponding neutron density modulation was interpreted in terms of a Fourier analysis.The results of the experiment form a consistent set of data that can be used as test values for refined reactor burnup calculation codes. The overall experimental error, typically ±0.015 pcm (1 pcm = 10-5 Δkeff/keff). is considered remarkably low in view of the massive experimental setup required.A method for the theoretical analysis of the measured reactivity worths is presented. A multigroup perturbation transport calculation in one dimension (S4 approximation) has been developed to account for the radial environmental conditions. The axial effects have been evaluated with a two-dimensional transport calculation. The group cross-section data used in the analysis were basically taken from the GAM-II and GATHER-II libraries.Using the same basic one-dimensional code with an appropriately adjusted input parameter, infinite lattice multiplication factors have also been calculated from he experimental reactivity results. These results are compared to the values of k∞ obtained from null-reactivity measurements of identical clusters which were performed in association with the Comitato Nazionale Energia Nucleare, Italy, in RB-1 Reactor in Bologna. The agreement between the two sets of results is satisfactory.

"A Versatile Gamma Scanning System"

A versatile gamma scanning system has been designed and installed for the scanning of irradiated fuels. The system traverses a fuel pin past an area-defining slit in a reproducible and accurate manner. Activity from the examined area is detected by a high resolution solid-state detector. Signals from the detector are amplified and routed to single channel analyzers or to a multichannel analyzer. The use of a four-input multichannel scalar permits storage of four specific energy groups versus position. A scan control module controls the operation of a stepping motor which moves the fuel pin axially past the collimator. Limit switches are used to define the scanned area. The control module also advances the multichannel scalar at selected intervals and determines the rate and direction of scanning. The use of a four-input multichannel scalar allows storage of data in four energy intervals from 512 consecutive points on the scanned element. For a typical pin this means that information is stored from 500 consecutive 27.5-mil increments. The unit is designed to scan fuel lengths of up to 50.2 in. in rods up to 84 in. long and from 0.2 to 1.125 in. in diameter. The collected information can be used to determine the distribution of activity in the fuel rod and to infer the relative distribution of specific isotopes. This information can be used to measure fuel burnup, fuel dimensions and power distribution. Other quantities of interest may be inferred from the obtained information.