Multigroup Cross Sections Research Articles

Improved multi-group cross sections with resonance treatment for future applications involving minor actinides

In the future study for thorium reactors and minor actinide transmutation reactors, resonance self-shielding treatment for them becomes remarkable issue for criticality and isotope depletion. Resonance treatment for important minor actinides and other resonant absorbers has been carried out with subgroup method. The updated multi-group cross sections and subgroup data is replaced with existing multi-group library. The results from neutron transport code nTRACER with updated multi-group cross section library were compared with existing library and solutions from MCNP. The resonance interaction of uranium with important minor actinides has been accommodated through modified interference treatment by interference correction in subgroup method. The results for cross sections and multiplication factor for pin and assembly problems showed improvement from systematic resonance treatment for resonant absorber nuclides including 237Np and 243Am.

Application of an iterative methodology for cross-section and variance/covariance data adjustment to the analysis of fast spectrum systems accounting for non-linearity

The data assimilation benchmark launched by the “Subgroup 33” on “Methods and issues for the combined use of integral experiments and covariance data” of the Working Party on Evaluation Cooperation (WPEC) of the OECD Nuclear Energy Agency Nuclear Science Committee is recalculated by means of a multistep adjustment procedure using the deterministic code system ERANOS in conjunction with a dedicated Generalized Linear Least-Squares approach based on the Bayesian parameter estimation method. Nuclear data in terms of multi-group cross-sections as well as their variances and covariances, are adjusted for 11 nuclides, namely 10B, 16O, 23Na, 56Fe, 52Cr, 58Ni, 235U, 238U, 239Pu, 240Pu and 241Pu and 6 nuclear reactions which are elastic and inelastic scattering, lumped (n,2n) and (n,3n), capture, fission and ν¯. The adjustment is carried out by making use of experimental data for 19 integral parameters obtained in 7 different fast spectrum systems. In the determination of a posteriori values for these integral parameters including effective multiplication factors, spectral indices and void effects, along with their nuclear data uncertainty, the required adjusted data for these nuclides and reactions are generated in conjunction with pre-computed sensitivity coefficients of the analytical integral parameters to the nuclear data to adjust. The suggested multistep scheme aims at accounting for non-linear effects. Correspondingly, the sensitivity coefficients are recalculated within an iterative procedure on the basis of the a posteriori analytical values and adjusted cross-sections. The adjustment is thus repeated several times until convergence is reached for the analytical values and their uncertainties.An important result of the study is that the asymptotic analytical values of the integral parameters are closer to the experimental values as compared to the standard first adjustment results. Moreover, the asymptotic analytical values seem rather independent of the specific a priori variance/covariance data used in the analysis, namely COMMARA-2.0 or BOLNA, despite different a priori analytical values respectively obtained with JEFF-3.1 or ENDF/B-VI.8 data. The asymptotic uncertainties obtained on the basis of the two libraries are also similar.

Calculation of the Neutron Noise Induced by Periodic Deformations of a Large Sodium-Cooled Fast Reactor Core

The subject of this paper is the calculation of the neutron noise induced by small-amplitude stationary radial variations of the core size (core expansion/compaction, also called core flowering) of a large sodium-cooled fast reactor. The calculations were performed on a realistic model of the European Sodium Fast Reactor (ESFR) core with a thermal output of 3600 MW(thermal), using a multigroup neutron noise simulator. The multigroup cross sections and their fluctuations that represent the core geometry changes for the neutron noise calculations were generated by the code ERANOS. The space and energy dependences of the noise source represented by the core expansion/compaction and the induced neutron noise are calculated and discussed.

CONRAD Evaluation Code: Development Status and Perspectives

CONRAD is an object-oriented code developed at CEA Cadarache since 2005 to treat issues occurring during the data assimilation process. The last new features of the code in terms of experimental, theoretical and interface aspects are presented in this paper. The experimental descriptions capabilities have been enhanced thanks to the implementation of both analytical (Chi-Square, Gaussian) and Monte-Carlo resolution functions which are required for neutron resonance shape analysis. On the theoretical aspects, efforts have been focused on the fast energy region with the wrapping of the ECIS and TALYS codes and the management of optical model and statistical parameters. These new features make it possible for CONRAD to currently perform evaluations from 0 to 20 MeV. Concerning the interfacing developments, a multigroup cross-sections generating tool and an ENDF parser have been recently improved to produce multigroup cross-section covariance matrices in the frame of the JEFF project. Several examples and comparisons with other codes (SAMMY, REFIT) are provided to validate each development.

Combined Use of Integral Experiments and Covariance Data

In the frame of a US-DOE sponsored project, ANL, BNL, INL and LANL have performed a joint multidisciplinary research activity in order to explore the combined use of integral experiments and covariance data with the objective to both give quantitative indications on possible improvements of the ENDF evaluated data files and to reduce at the same time crucial reactor design parameter uncertainties. Methods that have been developed in the last four decades for the purposes indicated above have been improved by some new developments that benefited also by continuous exchanges with international groups working in similar areas. The major new developments that allowed significant progress are to be found in several specific domains: a) new science-based covariance data; b) integral experiment covariance data assessment and improved experiment analysis, e.g., of sample irradiation experiments; c) sensitivity analysis, where several improvements were necessary despite the generally good understanding of these techniques, e.g., to account for fission spectrum sensitivity; d) a critical approach to the analysis of statistical adjustments performance, both a priori and a posteriori; e) generalization of the assimilation method, now applied for the first time not only to multigroup cross sections data but also to nuclear model parameters (the “consistent” method).This article describes the major results obtained in each of these areas; a large scale nuclear data adjustment, based on the use of approximately one hundred high-accuracy integral experiments, will be reported along with a significant example of the application of the new “consistent” method of data assimilation.

Evaluation of the HTTR criticality and burnup calculations with continuous-energy and multigroup cross sections

The High Temperature Engineering Test Reactor (HTTR) in Japan is a helium-cooled graphite-moderated reactor designed and operated for the future development of high-temperature gas-cooled reactors. Two detailed full-core models of HTTR have been established by using SCALE6 and MCNP5/X, respectively, to study its neutronic properties. Several benchmark problems were repeated first to validate the calculation models. Careful code-to-code comparisons were made to ensure that two calculation models are both correct and equivalent. Compared with experimental data, the two models show a consistent bias of approximately 20–30mk overestimation in effective multiplication factor for a wide range of core states. Most of the bias could be related to the ENDF/B-VII.0 cross-section library or incomplete modeling of impurities in graphite. After that, a series of systematic analyses was performed to investigate the effects of cross sections on the HTTR criticality and burnup calculations, with special interest in the comparison between continuous-energy and multigroup results. Multigroup calculations in this study were carried out in 238-group structure and adopted the SCALE double-heterogeneity treatment for resonance self-shielding. The results show that multigroup calculations tend to underestimate the system eigenvalue by a constant amount of ∼5mk compared to their continuous-energy counterparts. Further sensitivity studies suggest the differences between multigroup and continuous-energy results appear to be temperature independent and also insensitive to burnup effects.

Homogenized cross section generation considering axial heterogeneity for VHTR fuel block

The HELIOS/CAPP and McCARD/CAPP code system has been developed for analysis of a very high temperature gas cooled reactor. However, the fuel block of a PMR200 has an axial heterogeneity and few group homogenized cross sections generated from a 2D model provide significantly large errors in the case of using HELIOS, a 2D lattice code. Thus, the modified 2D model and three zone 2D model are presented for more accurate homogenized cross sections. First model is designed to conserve the total fuel and graphite number density and second model has three axial homogenized zones, one fuel zone in center and two axial graphite zones in both end sides. The accuracy of two models are evaluated by Monte Carlo simulation. As a result, the modified 2D model and three zone 2D model can similarly provide more accurate cross section which reduces the error from 2000 to 300pcm. Additionally, the homogenized cross sections of a real 3D model are directly generated using McCARD which has the capability of generating multi-group cross sections. Therefore, it is confirmed that the two results show the difference under 150pcm including the stochastic error, when the depletion calculation was carried out using CAPP with the cross sections.

Criticality calculations of the HTR-10 pebble-bed reactor with SCALE6/CSAS6 and MCNP5

HTR-10 is a 10MWt prototype pebble-bed reactor (PBR) that presents a doubly heterogeneous geometry for neutronics calculations. An appropriate unit-cell treatment for the associated fuel elements is vital for creating problem-dependent multigroup cross sections. Considering four unit-cell options for resonance self-shielding correction in SCALE6, a series of HTR-10 core models were established using the CSAS6 sequence to systematically investigate how they affected the computational accuracy and efficiency of PBR criticality calculations. Three core configurations, which ranged from simplified infinite lattices to a detailed geometry, were examined. Based on the same ENDF/B-VII.0 cross-section library, multigroup results were evaluated by comparing with continuous-energy SCALE6/CSAS6 and MCNP5 calculations. The comparison indicated that the INFHOMMEDIUM results overestimated the effective multiplication factor (keff) by about 2800pcm, whereas the LATTICECELL and MULTIREGION treatments overestimated keff values with similar biases at approximately 470–680pcm. The DOUBLEHET results attained further improvement, reducing the keff overestimation to approximately 280pcm. The comparison yielded two unexpected problems from using SCALE6/CSAS6 in HTR-10 criticality calculations. In particular, the continuous-energy CSAS6 calculations in this study present a non-negligible discrepancy with MCNP5, potentially causing a keff value overestimate of approximately 680pcm. Notably, using a cell-weighted mixture instead of an explicit model of individual TRISO particles in the pebble fuel zone does not shorten the CSAS6 computation time in the high-fidelity HTR-10 model because of the presence of graphite balls and the complex modeling of peripheral reflectors.

SCALE Code Validation for Prismatic High-Temperature Gas-Cooled Reactors

Using experimental data published in the International Handbook of Evaluated Reactor Physics Benchmark Experiments for the fresh cold core of the High Temperature Engineering Test Reactor, a comprehensive validation study has been carried out to assess the performance of the SCALE code system for analysis of high-temperature gas-cooled reactor configurations. This paper describes part of the results of that effort. The studies performed included criticality evaluations for the full core and for the annular cores realized during the fuel loading, as well as calculations and comparisons for excess reactivity, shutdown margin, control rod worths, temperature coefficient of reactivity, and reaction rate distributions. Comparisons of the SCALE results with both experimental values and MCNP-calculated values are presented. The comparisons show that the SCALE calculated results, obtained with both multigroup and continuous energy cross sections, are in reasonable agreement with the experimental data and the MCNP predictions.

A Statistical Sampling Method for Uncertainty Analysis with SCALE and XSUSA

A new statistical sampling sequence called Sampler has been developed for the SCALE code system. Random values for the input multigroup cross sections are determined by using the XSUSA program to sample uncertainty data provided in the SCALE covariance library. Using these samples, Sampler computes perturbed self-shielded cross sections and propagates the perturbed nuclear data through any specified SCALE analysis sequence, including those for criticality safety, lattice physics with depletion, and shielding calculations. Statistical analysis of the output distributions provides uncertainties and correlations in the desired responses, due to nuclear data uncertainties. The Sampler/XSUSA methodology is described, and example applications are shown for criticality safety and spent-fuel analysis.

Analysis of implicit and explicit lattice sensitivities using DRAGON

Deterministic lattice physics transport calculations are used extensively within the context of operational and safety analysis of nuclear power plants. As such the sensitivity and uncertainty in the evaluated nuclear data used to predict neutronic interactions and other key transport phenomena are critical topics for research. Sensitivity analysis of nuclear systems with respect to fundamental nuclear data using multi-energy-group discretization is complicated by the dilution dependency of multi-group macroscopic cross-sections as a result of resonance self-shielding. It has become common to group sensitivities into implicit and explicit effects to aid in the understanding of the nature of the sensitivities involved in the calculations, however the overall sensitivity is an integral of these effects. Explicit effects stem from perturbations performed for a specific nuclear data for a given isotope and at a specific energy, and their direct impact on the end figure of merit. Implicit effects stem from resonance self-shielding effects and can change the nature of their own sensitivities at other energies, or that for other reactions or even other isotopes. Quantification of the implicit sensitivity component involves some manner of treatment of resonance parameters in a way that is self-consistent with perturbations occurring in associated multi-group cross-sections. A procedure for assessing these implicit effects is described in the context of the Bondarenko method of self-shielding and implemented using a WIMS-D4 multi-group nuclear library and the lattice solver DRAGON. The resulting sensitivity results were compared to those calculated by TSUNAMI-1D, which computes implicit sensitivities using a different methodology consisting of a combination of linear perturbation theory and automatic differentiation. Energy-dependent sensitivity profiles and integrated sensitivity coefficients are presented, as well as a comparison of calculated sensitivities for different energy group structures and geometry dimensionalities.

Bondarenko method for obtaining group cross sections in a multi-region collision probability model

Correct multigroup cross sections are essential to modeling the physics of nuclear reactors. In particular, the presence of resonances leads to the well-known self-shielding effect that complicates any procedure for obtaining group cross sections. The Bondarenko method for producing self-shielded group cross sections is widely used. For heterogeneous systems, the approach requires the use of an escape cross section that captures the probability that a neutron will leave a cell without interaction, and simple approximations are typically used for this purpose. Here we provide a concise derivation for how to determine group cross sections using the Bondarenko method with an extension to multi-region collision probability models. The accuracy of the method is demonstrated by comparing group cross sections derived this way with those produced by Monte Carlo simulations of thermal and fast spectrum reactors.

Fission Neutron Spectrum Sensitivity Study for the Case of Advanced Heavy Water Reactor

In the WIMSD-IAEA multigroup nuclear data library, the isotopes and weights adopted for WLUP libraries to calculate the average fission spectra for 235U, 238U, and 239Pu are in the ratio of 54%, 8%, and 38%, respectively. The average fission neutron spectrum in the existing multigroup WIMSD-IAEA library applicable for the U-Pu cycle is not rigorously applicable for systems that are based on the thorium fuel cycle because of two aspects. First, the weightage of the fission neutron spectrum of 232Th and 233U nuclides, which are important isotopes in the thorium fuel cycle, are not considered in obtaining the average multigroup fission spectrum in the conventional WIMSD-IAEA library. Second, the 232Th/233U system spectrum is required for condensation of the fission spectrum as done in generating other multigroup cross sections and parameters for the thorium fuel cycle. In this work, we have processed the fission neutron spectrum data from the basic evaluated nuclear data file (ENDF/B-VI.8) for each important isotope in the thorium fuel cycle using the Th/233U spectrum and using a FORTRAN program developed and validated by us for this purpose. The final average fission spectrum to be fed into the WIMSD-IAEA library is prepared by mixing the isotopic multigroup fission spectrum of individual isotopes 233U, 239Pu, and 241Pu with appropriate weights corresponding to their respective power fractions in the advanced heavy water reactor (AHWR) lattice. Using the WIMSD library with modified effective fission spectra, the lattice k-infinity calculations of AHWR are performed as a function of burnup. The difference in the infinite multiplication factor, which is expressed in terms of reactivity in mk, ranges from 0.48 to 0.94 mk as burnup in the AHWR proceeds from 0 to 55 GWd/tonne.

Deep-penetration calculations in concrete and iron for shielding of proton therapy accelerators

Proton accelerators in the energy range of approximately 200MeV have become increasingly popular for cancer treatment in recent years. These proton therapy facilities usually involve bulky concrete or iron in their shielding design or accelerator structure. Simple shielding data, such as source terms or attenuation lengths for various proton energies and materials are useful in designing accelerator shielding. Understanding the appropriateness or uncertainties associated with these data, which are largely generated from Monte Carlo simulations, is critical to the quality of a shielding design. This study demonstrated and investigated the problems of deep-penetration calculations on the estimation of shielding parameters through an extensive comparison between the FLUKA and MCNPX calculations for shielding against a 200-MeV proton beam hitting an iron target. Simulations of double-differential neutron production from proton bombardment were validated by comparison with experimental data. For the concrete shielding, the FLUKA calculated depth–dose distributions were consistent with the MCNPX results, except for some discrepancies in backward directions. However, for the iron shielding, if FLUKA is used inappropriately then overestimation of neutron attenuation can be expected as shown by this work because of the multigroup treatment for low-energy neutrons in FLUKA. Two neutron energy group structures, three degrees of self-shielding correction, and two iron compositions were considered in this study. Significant variation of the resulting attenuation lengths indicated the importance of problem-dependent multigroup cross sections and proper modeling of iron composition in deep-penetration calculations.

A Technique for Accounting for Multigroup Cross-Section Interdependence in Sensitivity Calculations

In this paper a new technique for accounting for multigroup cross section interdependence in sensitivity calculations is proposed and numerically investigated. In this technique the so-called implicit sensitivities representing multigroup cross-section interdependence are calculated through subgroup parameters. The technique turns out to be easy to implement in existing multigroup cross-section preparation codes and can cover both the homogeneous media and the heterogeneous media conventionally considered in such codes. This technique allows further extensions to cover arbitrary heterogeneous structures. The Monte Carlo technique of computing conventional sensitivities of keff to multigroup cross sections used in this paper is also described.

Many-Group Cross-Section Adjustment Techniques for Boiling Water Reactor Adaptive Simulation

Computational capability has been developed to adjust multigroup neutron cross sections, including self-shielding correction factors, to improve the fidelity of boiling water reactor (BWR) core modeling and simulation. The method involves propagating multigroup neutron cross-section uncertainties through various BWR computational models to evaluate uncertainties in key core attributes such as core keff, nodal power distributions, thermal margins, and in-core detector readings. Uncertainty-based inverse theory methods are then employed to adjust multigroup cross sections to minimize the disagreement between BWR core modeling predictions and observed (i.e., measured) plant data. For this paper, observed plant data are virtually simulated in the form of perturbed three-dimensional nodal power distributions with the perturbations sized to represent actual discrepancies between predictions and real plant data. The major focus of this work is to efficiently propagate multigroup neutron cross-section uncertainty through BWR lattice physics and core simulator calculations. The data adjustment equations are developed using a subspace approach that exploits the ill-conditioning of the multigroup cross-section covariance matrix to minimize computation and storage burden. Tikhonov regularization is also employed to improve the conditioning of the data adjustment equations. Expressions are also provided for posterior covariance matrices of both the multigroup cross-section and core attributes uncertainties.

Adjoint-Based Uncertainty Analysis for Essential Reactions in a Laser Inertial Fusion Engine

This study establishes a procedure for constructing explicit and adjoint-based implicit sensitivities with MCNP5. Using these methods, an instantaneous sensitivity-based uncertainty analysis is performed on the depleted uranium hybrid LIFE (Laser Inertial Fusion Energy) blanket. Explicit sensitivities and uncertainties are calculated for (n, 2n), tritium production, fission, and radiative capture reaction rates during the fuel lifecycle. Nuclear data uncertainties and Monte Carlo counting precision are compared in a convergence study and the compounding of the two is quantified to gauge the validity of the analysis. A multi-group cross-section library is generated for adjoint calculations and selected adjoint distributions are shown and discussed.

Application of Time-Dependent Neutron Transport Theory to High-Temperature Reactors of Pebble Bed Type

We introduce a new coupled neutronics/thermal-hydraulics code system for analyzing transients of high-temperature gas-cooled reactors (HTGRs), based on a neutron transport theory approach. At the heart of the coupled code system resides the DORT-TD code, a time-dependent extension of the well-known DORT discrete ordinates code. DORT-TD uses a fully implicit time integration scheme and is coupled via its generalized thermal-hydraulics interface to the THERMIX-DIREKT code, an HTGR-specific heat conduction/convection code for pebble bed-type reactor cores. Feedback is accounted for by interpolating multigroup cross sections from libraries pregenerated with appropriate spectral codes. These libraries are structured for user-specified discrete sets of thermal-hydraulic parameters, e.g., fuel and moderator temperatures. The coupled code system is applied to a pebble bed HTGR model case, i.e., the PBMR 268 MW design. Steady-state studies are performed, and several design-basis and beyond-design-basis transients are simulated in an effort to assess the adequacy of using neutron diffusion theory against the more accurate but yet computationally more expensive neutron transport approach. Relatively small but significant differences arise from using either theoretical approach, from which it is concluded that transport theory as the more versatile tool should be used as reference to quantify the effects of the approximations inherent in diffusion and to gain confidence in its predictive power, especially in safety analyses. In an effort to validate the DORT-TD/THERMIX code system, the neutronics stand-alone solver is benchmarked against available transient benchmark exercises, and the coupled code system is applied to the Organisation for Economic Co-operation and Development/Nuclear Energy Agency/Nuclear Science Committee PBMR 400 MW Coupled Neutronics Thermal Hydraulics Transient Benchmark, demonstrating its remarkable viability for a wide range of safety cases. The final product is a high-fidelity, highly flexible, and well-validated state-of-the-art computer code system, with multiple capabilities to analyze HTGR safety-related transients in an accurate and efficient manner.

SCALE 6: Comprehensive Nuclear Safety Analysis Code System

Version 6 of the Standardized Computer Analyses for Licensing Evaluation (SCALE) computer software system developed at Oak Ridge National Laboratory, released in February 2009, contains significant new capabilities and data for nuclear safety analysis and marks an important update for this software package, which is used worldwide. This paper highlights the capabilities of the SCALE system, including continuous-energy flux calculations for processing multigroup problem-dependent cross sections, ENDF/B-VII continuous-energy and multigroup nuclear cross-section data, continuous-energy Monte Carlo criticality safety calculations, Monte Carlo radiation shielding analyses with automated three-dimensional variance reduction techniques, one- and three-dimensional sensitivity and uncertainty analyses for criticality safety evaluations, two- and three-dimensional lattice physics depletion analyses, fast and accurate source terms and decay heat calculations, automated burnup credit analyses with loading curve search, and integrated three-dimensional criticality accident alarm system analyses using coupled Monte Carlo criticality and shielding calculations.

Monte Carlo Criticality Methods and Analysis Capabilities in SCALE

This paper describes the Monte Carlo codes KENO V.a and KENO-VI in SCALE that are primarily used to calculate multiplication factors and flux distributions of fissile systems. Both codes allow explicit geometric representation of the target systems and are used internationally for safety analyses involving fissile materials. KENO V.a has limiting geometric rules such as no intersections and no rotations. These limitations make KENO V.a execute very efficiently and run very fast. On the other hand, KENO-VI allows very complex geometric modeling. Both KENO codes can utilize either continuous-energy or multigroup cross-section data and have been thoroughly verified and validated with ENDF libraries through ENDF/B-VII.0, which has been first distributed with SCALE 6. Development of the Monte Carlo solution technique and solution methodology as applied in both KENO codes is explained in this paper. Available options and proper application of the options and techniques are also discussed. Finally, performance of the codes is demonstrated using published benchmark problems.