B.L. Broadhead

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.

Application of the LEPRICON unfolding procedure to the Arkansas Nuclear One-Unit 1 Reactor

The development and demonstration of a new unfolding procedure involving pressure vessel surveillance dosimetry in pressurized water reactors are described. The complete methodology is contained in the LEPRICON code system, and provides techniques for calculating pressure vessel fluences and then adjusting them, with reduced uncertainties, on the basis of surveillance dosimetry measurements and a benchmark data base. An application of these techniques to an existing on-line commercial reactor is presented. Results indicate that the best estimate of the pressure vessel lifetime based on a limiting fluence above 1 MeV of 2 x 10/sup 19/ n/cm/sup 2/ is approx. =129+.11 effective full-power years, whereas the unadjusted estimate has an uncertainty twice as large.

Theory of a new unfolding procedure in pressurized water reactor pressure vessel dosimetry and development of an associated Benchmark data base

The theory of a new methodology for quantifying and then reducing the uncertainties in the pressure vessel fluences (or fluxes) of a pressurized water reactor (PWR) is described. The theory involves combining the results of calculated and measured dosimetry integral experiments along wit differential data used in the calculations, together with covariances, into a generalized linear leastsquares adjustment code named LEPRICON. The procedure solves the translation problem necessitated by the use of ex situ PWR dosimetry, and its covariance reducing potential is further enhanced by simultaneously combining the PWR data with a data base consisting of the results of analysis of simpler benchmark experiments. Development of this data base and a demonstration of the uncertainty reduction with application to one of the benchmark experiments are also described. For the example chosen, covariances of the calculated fluxes were reduced by factors of between 4 and 8.

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...

Accounting for Changing Source Distributions in Light Water Reactor Surveillance Dosimetry Analysis

AbstractA technique is described to account for effects of space- and time-dependent core source variations on pressure vessel surveillance dosimetry analysis. The procedure first defines an easily implemented geometry for a single adjoint transport calculation. The results from the adjoint calculation can then be combined with those from a single forward calculation, in conjunction with an adjoint scaling technique, to yield activities and pressure vessel fluxes simultaneously for a wide range of source distributions, dosimeter response functions, and detector locations. This method has been implemented in the LEPRICON code system for vessel fluence determination. An application to an R-θ model of an operating power reactor shows that effects of source perturbations resulting in 20% changes in the core leakage can be predicted within ∼3% at both downcomer and cavity dosimeter locations, for six different dosimeters, by choice of a single suitable adjoint response function.

Investigation of nuclide importance to functional requirements related to transport and long-term storage of LWR spent fuel

The radionuclide characteristics of light-water-reactor (LWR) spent fuel play key roles in the design and licensing activities for radioactive waste transportation systems, interim storage facilities, and the final repository site. Several areas of analysis require detailed information concerning the time-dependent behavior of radioactive nuclides including (1) neutron/gamma-ray sources for shielding studies, (2) fissile/absorber concentrations for criticality safety determinations, (3) residual decay heat predictions for thermal considerations, and (4) curie and/or radiological toxicity levels for materials assumed to be released into the ground/environment after long periods of time. The crucial nature of the radionuclide predictions over both short and long periods of time has resulted in an increased emphasis on thorough validation for radionuclide generation/depletion codes. Current radionuclide generation/depletion codes have the capability to follow the evolution of some 1600 isotopes during both irradiation and decay time periods. Of these, typically only 10 to 20 nuclides dominate contributions to each analysis area. Thus a quantitative ranking of nuclides over various time periods is desired for each of the analysis areas of shielding, criticality, heat transfer, and environmental dose (radiological toxicity). These rankings should allow for validation and data improvement efforts to be focused only on the most important nuclides. This study investigates the relative importances of the various actinide, fission-product, and light-element isotopes associated with LWR spent fuel with respect to five analysis areas: criticality safety (absorption fractions), shielding (dose rate fractions), curies (fractional curies levels), decay heat (fraction of total watts), and radiological toxicity (fraction of potential committed effective dose equivalent). These rankings are presented for up to six different burnup/enrichment scenarios and at decay times from 2 to 100,000 years. Ranking plots for each of these analysis areas are given in an Appendix for completeness, as well as summary tables in the main body of the report. Summary rankings are presented in terms of high (greater than 10% contribution to the total), medium (between 1% and 10% contribution), and low (less than 1% contribution) for both short- and long-term cooling. When compared with the expected measurement accuracies, these rankings show that most of the important isotopes can be characterized sufficiently for the purpose of radionuclide generation/depletion code validation in each of the analysis areas. Because the main focus of this work is on the relative importances of isotopes associated with LWR spent fuel, some conclusions may not be applicable to similar areas such as high-level waste (HLW) and nonfuel-bearing components (NFBC).

Generalized Linear Least-Squares Adjustment, Revisited

TSURFER, a generalized linear least-squares (GLLS) code, is a new module of the SCALE system. After a short introduction outlining the history and applications of the GLLS methodology in reactor physics, a new application of the GLLS methodology in criticality safety is discussed. Some characteristic TSURFER input data are discussed in detail.

Criticality Analysis Support for the Three Mile Island Unit 2 Fuel Removal Operations

AbstractBeginning in 1984, the Three Mile Island Unit 2 Defueling Design Team requested Oak Ridge National Laboratory to supply criticality safety analyses in support of the licensing activities for all fuel removal operations. The computational methods and basic analytic models employed in the work are discussed, the areas where computational analyses were requested are reviewed, and the pertinent results are tabulated and discussed.

Combining integral and differential dosimetry data in an unfoluing procedure with application to the arkansas nuclear one-unit 1 reactor

Abstract The LEPRICON adjustment procedure involves combining both differential and integral data, including covariances and sensitivities, in such a way that calculated spectral fluences at important locations within a pressure vessel of an operating PWR can be adjusted with significantly reduced uncertainties. The procedure allows simultaneous combination of integral dosimetry measurements performed at a reactor surveillance location with measurements performed in geometrically simpler benchmark facilities. An application of this technique is given to an existing PWR, and the results consistently indicate a need for significant (∼ 8%) adjustments in the total inelastic cross section of iron in the region between 3 and 8 MeV using cross sections and covariances from ENDF/B-V. Dosimetry cross sections were taken mainly from a revised version of ENDF/B-V and were found to require relatively small adjustments. Covariances of the spectral fluences are reduced by factors lying between two and four.