C.V. Parks

Sensitivity- and Uncertainty-Based Criticality Safety Validation Techniques

Abstract The theoretical basis for the application of sensitivity and uncertainty (S/U) analysis methods to the validation of benchmark data sets for use in criticality safety applications is developed. Sensitivity analyses produce energy-dependent sensitivity coefficients that give the relative change in the system multiplication factor keff value as a function of relative changes in the cross-section data by isotope, reaction, and energy. Integral indices are then developed that utilize the sensitivity information to quantify similarities between pairs of systems, typically a benchmark experiment and design system. Uncertainty analyses provide an estimate of the uncertainties in the calculated values of the system keff due to cross-section uncertainties, as well as correlation in the keff uncertainties between systems. These uncertainty correlations provide an additional measure of system similarity. The use of the similarity measures from both S/U analyses in the formal determination of areas of applicability for benchmark experiments is developed. Furthermore, the use of these similarity measures as a trending parameter for the estimation of the computational bias and uncertainty is explored. The S/U analysis results, along with the calculated and measured keff values and estimates of uncertainties in the measurements, were used in this work to demonstrate application of the generalized linear-least-squares methodology (GLLSM) to data validation for criticality safety studies. An illustrative example is used to demonstrate the application of these S/U analysis procedures to actual criticality safety problems. Computational biases, uncertainties, and the upper subcritical limit for the example applications are determined with the new methods and compared to those obtained through traditional criticality safety analysis validation techniques. The GLLSM procedure is also applied to determine cutoff values for the similarity indices such that applicability of a benchmark experiment to a criticality safety design system can be assured. Additionally, the GLLSM procedure is used to determine how many applicable benchmark experiments exceeding a certain degree of similarity are necessary for an accurate assessment of the computational bias.

Eigenvalue sensitivity theory for resonance-shielded cross sections

Abstract A method is presented to compute sensitivity coefficients for the eigenvalue of a critical assembly, including implicit effects associated with changes in resonance-shielded multigroup cross sections. Two alternative approaches, based on a forward and an adjoint solution, respectively, are developed to determine the effect of perturbations on the weight function used in group averaging of resonance cross sections. The forward method uses an automated methodology to compute the flux derivative with respect to various cross-section processing parameters. The adjoint method introduces adjoint equations for a multigroup cross-section functional and presents adjoint slowing-down equations for two common methods of resonance self-shielding. Expressions are presented for sensitivity coefficients of self-shielded group cross sections. These sensitivity coefficients are combined with conventional eigenvalue sensitivity coefficients to obtain a general perturbation expression for the multiplication factor. An example application determines the sensitivity of the critical eigenvalue to hydrogen density changes in a homogeneous sphere containing low-enriched uranium. It is shown that changes in 238U-shielded cross sections caused by perturbations in hydrogen concentrations are important components in the overall eigenvalue sensitivity coefficient, which is predicted well by the developed method.

Validation of the scale system for PWR spent fuel isotopic composition analyses

The validity of the computation of pressurized-water-reactor (PWR) spent fuel isotopic composition by the SCALE system depletion analysis was assessed using data presented in the report. Radiochemical measurements and SCALE/SAS2H computations of depleted fuel isotopics were compared with 19 benchmark-problem samples from Calvert Cliffs Unit 1, H. B. Robinson Unit 2, and Obrigheim PWRs. Even though not exhaustive in scope, the validation included comparison of predicted and measured concentrations for 14 actinides and 37 fission and activation products. The basic method by which the SAS2H control module applies the neutron transport treatment and point-depletion methods of SCALE functional modules (XSDRNPM-S, NITAWL-II, BONAMI, and ORIGEN-S) is described in the report. Also, the reactor fuel design data, the operating histories, and the isotopic measurements for all cases are included in detail. The underlying radiochemical assays were conducted by the Materials Characterization. Center at Pacific Northwest Laboratory as part of the Approved Testing Material program and by four different laboratories in Europe on samples processed at the Karlsruhe Reprocessing Plant.

Adjoint Sensitivity Analysis of Extremum-Type Responses in Reactor Safety

A recently developed sensitivity theory for nonlinear systems with responses defined at critical points, e.g., maxima, minima, or saddle points, of a function of the systems state variables and parameters is applied to a protected transient with scram on high-power level in the Fast Flux Test Facility. The single-phase segment of the fast reactor safety code MELT-IIIB is used to model this transient. Two responses of practical importance, namely, the maximum fuel temperature in the hot channel and the maximum normalized reactor power level, are considered. For the purposes of sensitivity analysis, a complete characterization of such responses requires consideration of both the numerical value of the response at the maximum, and the location in phase space where the maximum occurs.

Review and Prioritization of Technical Issues Related to Burnup Credit for LWR Fuel

The present invention relates to a polymer composition, to a layer element, preferably to at least one layer element of a photovoltaic module, comprising the polymer composition and to an article which is preferably said at least one layer of a layer element, preferably of a layer element of a photovoltaic module.

Application of Differential Sensitivity Theory to a Neutronic/Thermal-Hydraulic Reactor Safety Code

A recently proposed sensitivity technique called differential sensitivity theory is applied to the neutronic/thermal-hydraulic fast reactor safety code MELT-IIIB. This application centers on the development and solution of the appropriate adjoint and sensitivity equations, resulting in an adjoint version of the MELT code called MELTADJ. Proper integration of the forward MELT solution with the corresponding adjoint MELTADJ solution formally yields sensitivity information for all input parameters. 16 refs.

Automatic rapid process for the generation of problem-dependent SAS2H/ORIGEN-S cross-section libraries

A methodology is described that serves as an alternative to the SAS2H path of the SCALE system to generate cross sections for point-depletion calculations with the ORIGEN-S code. Automatic Rapid Processing (ARP) is an algorithm that allows the generation of cross-section libraries suitable to the ORIGEN-S code by interpolation over pregenerated SAS2H libraries. The interpolations are carried out on the following variables. burnup, enrichment, and water density. The adequacy of the methodology is evaluated by comparing measured and computed spent-fuel isotopic compositions for pressurized water reactor and boiling water reactor systems.

Evaluation of Shielding Analysis Methods in Spent-Fuel Cask Environments

The three-dimensional Monte Carlo code MORSE-SGC, as implemented in the SCALE system calculational sequence SAS4, is applied to the analysis of a series of simple geometry benchmark experiments and prototypic spent-fuel storage cask measurements. The simple geometry experiments were performed in Japan and at the General Electric-Morris Operation facility; the cask measurements were performed at the Idaho National Engineering Laboratory. The quantification of uncertainties in a typical shielding analysis process for transport/storage casks can be accomplished by comparison of consistent trends between calculated and measured dose rate quantities in both benchmark and prototypic environments. Benchmark results typically measure the validity of cross-section data and computer code adequacy; prototypic environments, however, generally measure the overall validity of the calculational procedure. A total of five storage cask problems and two simple geometry problems were analyzed to determine the expected accur...

Validation of SCALE-4 for Burnup Credit Applications

In the past, criticality analysis of pressurized water reactor (PWR) fuel stored in racks and casks has assumed that the fuel is fresh with the maximum allowable initial enrichment. If credit is allowed for fuel burnup in the design of casks that are used in the transport of spent light water reactor fuel to a repository, the increase in payload can lead to a significant reduction in the cost of transport and a potential reduction in the risk to the public. A portion of the work has been performed at Oak Ridge National Laboratory (ORNL) in support of the U.S. Department of Energy (DOE) efforts to demonstrate a validation approach of criticality safety methods to be used in burnup credit cask design. The date, the SCALE code system developed at ORNL has been the primary computational tool used by DOE to investigate technical issues related to burnup credit. The SCALE code package is a well-established code system that has been widely used in away from reactor applications. Criticality safety analyses are performed via the criticality safety analysis sequences (CSAS) and spent-fuel characterization via the shielding analysis sequence (QSAS) and spent-fuel characterization via the shielding analysis sequence (SAS2H). The SCALE 27-group burnup library containing ENDF/B-IV (actinides) and ENDF/B-V (fission products) data has been used for all calculations. The American National Standards Institute/American Nuclear Society (ANSI/ANS)-8.1 criticality safety standard requires validation and benchmarking of the calculational methods used in evaluating criticality safety limits for applications outside reactors of correlation against critical experiments that are applicable. Numerous critical experiments for fresh PWR-type fuel in storage and transport configurations exist and can be used as part of a validation database. However, there are no critical experiments with burned PWR-type fuel in storage and transport configurations. As an alternative, commercial reactors offer an excellent source of measured critical configurations. Part of the work that has been performed to date to validate the SCALE-4 code system for burnup credit applications using measured critical configurations includes: 1. fresh fuel critical experiments having geometric and nuclear characteristics similar to PWR spent fuel in storage and transport configurations 2. commercial PWR hot-zero-power and hot-full-power reactor critical configurations. The ability to closely predict reactor critical conditions is important in the validation of a methodology for spent-fuel applications because input data are determined based on relatively little detail of reactor core operation. Such limited information is expected to be representative of data available when burnup credit calculations are being performed in the determination of optimum cask loadings. The results reported demonstrate the ability of the ORNL SCALE-4 methodology to predict a value of k eff very close to the known value of 1.0, both for fresh fuel criticals and for the more complex reactor criticals. Beyond these results, additional work in the determination of biases and uncertainties is necessary prior to use in burnup credit applications

OECD/NEA burnup credit calculational criticality benchmark Phase I-B results

In most countries, criticality analysis of LWR fuel stored in racks and casks has assumed that the fuel is fresh with the maximum allowable initial enrichment. This assumption has led to the design of widely spaced and/or highly poisoned storage and transport arrays. If credit is assumed for fuel burnup, initial enrichment limitations can be raised in existing systems, and more compact and economical arrays can be designed. Such reliance on the reduced reactivity of spent fuel for criticality control is referred to as burnup credit. The Burnup Credit Working Group, formed under the auspices of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development, has established a set of well-defined calculational benchmarks designed to study significant aspects of burnup credit computational methods. These benchmarks are intended to provide a means for the intercomparison of computer codes, methods, and data applied in spent fuel analysis. The benchmarks have been divided into multiple phases, each phase focusing on a particular feature of burnup credit analysis. This report summarizes the results and findings of the Phase I-B benchmark, which was proposed to provide a comparison of the ability of different code systems and data libraries to perform depletion analysis for the prediction of spent fuel isotopic concentrations. Results included here represent 21 different sets of calculations submitted by 16 different organizations worldwide and are based on a limited set of nuclides determined to have the most important effect on the neutron multiplication factor of light-water-reactor spent fuel. A comparison of all sets of results demonstrates that most methods agree to within 10% in the ability to estimate the spent fuel concentrations of most actinides. All methods agree within 11% about the average for all fission products studied. Most deviations are less than 10%, and many are less than 5%. The exceptions are Sm 149, Sm 151, and Gd 155.