Mark L Williams

Development of Depletion Perturbation Theory for Coupled Neutron/Nuclide Fields

A perturbation formulation is developed for the space-energy dependent burnup equations describing depletion and transmutation of nuclide densities in a coupled neutron-nuclide field, such as a reactor core. The formulation is developed in a form consistent with the computational methods used for depletion analysis. The analysis technique currently employed in most burnup calculations is first reviewed as a method for describing the nonlinear coupling between the flux and nuclide fields. It is shown that based on the present formulation three adjoint equations (for flux shape, flux normalization, and nuclide density) are required to account for the coupled variations arising from variations in initial conditions and nuclear data. The adjoint equations are derived in detail using a variational principle, and an algorithm is suggested for solving the coupled equations backward through time. Perturbation expressions are used to define sensitivity coefficients for responses that depend on the coupled interaction between the neutron and nuclide fields. The relation between coupled and noncoupled sensitivity theory is illustrated. Finally, two analytic example problems are solved that determine the sensitivity of some final nuclide concentration to changes in initial conditions. Results obtained from direct calculation and from the coupled perturbation theory are compared.

Isotopic Depletion and Decay Methods and Analysis Capabilities in SCALE

Abstract The calculation of fuel isotopic compositions is essential to support design, safety analysis, and licensing of many components of the nuclear fuel cycle—from reactor physics and severe accident analysis to back-end fuel cycle issues, including spent-fuel storage and transportation, reprocessing, and radioactive waste management. Versions of the ORIGEN code, developed by Oak Ridge National Laboratory, have been used worldwide for isotopic depletion and decay analysis for more than three decades. The supported version of ORIGEN, maintained as the depletion analysis module for SCALE 6, performs detailed time-dependent isotopic generation and depletion for 1946 nuclides for reactor fuel and activation analysis. Stand-alone ORIGEN calculations can be performed using cross-section libraries developed for a wide range of reactor types and fuel designs used worldwide, including light water reactors UO2 and MOX, CANDU, VVER 440 and 1000, RBMK, and graphite reactors. Alternatively, within SCALE 6, ORIGEN can be automatically coupled to two-dimensional discrete ordinates or three-dimensional Monte Carlo transport solvers that provide problem-dependent cross sections for use in the ORIGEN depletion calculation. The hybrid ability to function as either a stand-alone or coupled depletion code provides ORIGEN advanced capabilities to simulate a broad range of applications for various reactor systems. The nuclear data libraries in ORIGEN have been significantly improved recently, using modern ENDF/B nuclear data evaluations. The most recent developments in SCALE 6.1 include the addition of ENDF/B-VII decay data, energy-dependent fission yields, and fine-group ORIGEN neutron cross sections based on the JEFF-3.0/A special purpose activation files. Advanced methods and data for neutron and gamma source energy spectral analysis are also available in the current version of the code. The ORIGEN code and associated nuclear data libraries have been extensively validated against experimental data that include spent nuclear fuel isotopic assay data for actinides and fission products, radiation source spectra, and decay heat measurements.

Sensitivity and Uncertainty Analysis Capabilities and Data in SCALE

Abstract In SCALE 6, the Tools for Sensitivity and UNcertainty Analysis Methodology Implementation (TSUNAMI) modules calculate the sensitivity of keff or reactivity differences to the neutron cross-section data on an energy-dependent, nuclide-reaction-specific basis. These sensitivity data are useful for uncertainty quantification, using the comprehensive neutron cross-section-covariance data in SCALE 6. Additional modules in SCALE 6 use the sensitivity and uncertainty data to produce correlation coefficients and other relational parameters that quantify the similarity of benchmark experiments to application systems for code validation purposes. Bias and bias uncertainties are quantified using parametric trending analysis or data adjustment techniques, providing detailed assessments of sources of biases and their uncertainties and quantifying gaps in experimental data available for validation. An example application of these methods is presented for a generic burnup credit cask model.

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.

Sensitivity and uncertainty analysis for eigenvalue-difference responses

Abstract Equations for sensitivity coefficients of eigenvalue-difference responses such as reactivity are derived from a unified approach based on both eigenvalue and generalized perturbation theory. The sensitivity coefficients are utilized for uncertainty analysis of reactivity responses, and it is shown that these types of responses have inherently larger relative uncertainties than eigenvalue responses. Monte Carlo calculations are used to apply the methodology to the analysis of the coolant void reactivity in a three-dimensional model of a fuel bundle in an advanced CANDU reactor system. The important data sensitivities are identified, and it is shown that the coolant void reactivity has a large uncertainty due to nuclear data uncertainties.

Resonance Self-Shielding Methodologies in SCALE 6

Abstract SCALE 6 includes several problem-independent multigroup (MG) libraries that were processed from the evaluated nuclear data file ENDF/B using a generic flux spectrum. The library data must be self-shielded and corrected for problem-specific spectral effects for use in MG neutron transport calculations. SCALE 6 computes problem-dependent MG cross sections through a combination of the conventional Bondarenko shielding-factor method and a deterministic continuous-energy (CE) calculation of the fine-structure spectra in the resolved resonance and thermal energy ranges. The CE calculation can be performed using an infinite medium approximation, a simplified two-region method for lattices, or a one-dimensional discrete ordinates transport calculation with pointwise (PW) cross-section data. This paper describes the SCALE-resonance self-shielding methodologies, including the deterministic calculation of the CE flux spectra using PW nuclear data and the method for using CE spectra to produce problem-specific MG cross sections for various configurations (including doubly heterogeneous lattices). It also presents results of verification and validation studies.

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.

A Full-Core Resonance Self-Shielding Method Using a Continuous-Energy Quasi–One-Dimensional Slowing-Down Solution that Accounts for Temperature-Dependent Fuel Subregions and Resonance Interference

Abstract A correction-based resonance self-shielding method is developed that allows annular subdivision of the fuel rod. The method performs the conventional iteration of the embedded self-shielding method (ESSM) without subdivision of the fuel to capture the interpin shielding effect. The resultant self-shielded cross sections are modified by correction factors incorporating the intrapin effects of radial variation of the shielded cross section, radial temperature distribution, and resonance interference. A quasi–one-dimensional slowing-down equation is developed to calculate such correction factors. The method is implemented in the DeCART code and compared with the conventional ESSM and subgroup method with benchmark MCNP results. The new method yields substantially improved results for both spatially dependent reaction rates and eigenvalues for typical pressurized water reactor pin cell cases with uniform and nonuniform fuel temperature profiles. The new method is also proved effective in treating assembly heterogeneity and complex material composition such as mixed oxide fuel, where resonance interference is much more intense.

Continuous-energy multidimensional SN transport for problem-dependent resonance self-shielding calculations

Abstract A method is presented to obtain a continuous-energy representation of the neutron spectrum using two-dimensional discrete ordinates calculations with a combination of multigroup (MG) and pointwise (PW) nuclear data. This provides the capability of determining the fine-structure energy distribution of the angular flux and flux moments within the resonance range as well as the smoother spectrum in the high- and thermal-energy ranges. The continuous-energy flux spectra can be utilized as problem-dependent weighting functions within the whole two-dimensional domain to process self-shielded MG cross sections for reactor physics and/or criticality safety analysis so that the two-dimensional heterogeneous effect in the resonance calculation can be fully considered. This calculational method has been implemented in a new PW transport code called GEMINEWTRN that may be executed as a module in the SCALE computer code system. Example applications using ENDF/B cross-section data are presented to study the two-dimensional heterogeneous effect in the resonance calculations.

Submoment Expansion of Neutron-Scattering Sources

Abstract The submoment method was originally introduced to compute spherical harmonic moments of the neutron elastic-scattering source for discrete ordinates calculations with pointwise nuclear data. This work extends the submoment method to include discrete-level inelastic, as well as elastic, S-wave reactions. New applications of the submoment expansion to compute spherical harmonic moments of the slowing-down density and the elastic removal rate are also presented. Numerical stability and computational considerations are discussed.