Criticality Safety Overview

Introduction by B. T. Rearden

SCALE provides a suite of computational tools for criticality safety analysis that is primarily based on the KENO Monte Carlo code for eigenvalue neutronics calculations [GPJD+11]. Two variants of KENO provide identical solution capabilities with different geometry packages. KENO V.a uses a simple and efficient geometry package sufficient for modeling many systems of interest to criticality safety and reactor physics analysts. KENO-VI uses the SCALE Generalized Geometry Package, which provides a quadratic-based geometry system with much greater flexibility in problem modeling but with slower runtimes. Both versions of KENO perform eigenvalue calculations for neutron transport primarily to calculate multiplication factors (keff) and flux distributions of fissile systems in both continuous energy and multigroup modes. They are typically accessed through the integrated SCALE sequences described below. KENO’s grid geometry capability extends region-based features for accumulating data for source or biasing parameter specifications, as well as for tallying results from a calculation for visualization or communication of data into or out of a calculation. Criticality safety analysts may also be interested in the sensitivity and uncertainty analysis techniques that can be applied for code and data validation as described elsewhere in this document.

Criticality Safety Analysis Sequences

The Criticality Safety Analysis Sequences (CSAS) with KENO V.a (CSAS5) and KENO-VI (CSAS6**)** provide a reliable, efficient means of performing keff calculations for systems routinely encountered in engineering practice. The CSAS sequences implement XSProc to process material input and provide a temperature and resonance-corrected cross section library based on the physical characteristics of the problem being analyzed. If a continuous energy cross section library is specified, no resonance processing is needed, and the continuous energy cross sections are used directly in KENO, with temperature corrections provided as the cross sections are loaded.

A search capability is available with CSAS5 to find desired values of keff as a function of dimensions or densities. The two basic search options offered are (1) an optimum search seeking a maximum or minimum value of keff and (2) a critical search seeking a fixed value of keff.

For continuous energy calculations, reaction rate tallies can be requested within the CSAS input, and for multigroup calculations, reaction rate calculations are performed using the KENO Module for Activity-Reaction Rate Tabulation (KMART) post-processing tools. A conversion tool is provided to up-convert KENO V.a input to KENO-VI either as a direct KENO input (K5toK6) or, more commonly, as a CSAS sequence (C5toC6).

STARBUCS: Burnup-Credit Analysis Sequence

The Standardized Analysis of Reactivity for Burnup Credit using SCALE (STARBUCS) [GB01][RG09] is a control module to perform criticality calculations for spent fuel systems employing burnup credit. STARBUCS automates the criticality safety analysis of spent fuel configurations by coupling the depletion and criticality aspects of the analysis, thereby eliminating the need to manually process the spent fuel nuclide compositions into a format compatible with criticality safety codes.

STARBUCS performs a depletion analysis calculation for each spatially varying burnup region (if an axial or horizontal burnup profile is specified) of a spent fuel assembly using the ORIGEN-ARP methodology of SCALE. If a multigroup calculation is to be performed in KENO, the spent fuel compositions are then used to generate resonance self-shielded cross sections for each burnup-dependent fuel region. Finally, a KENO criticality calculation is performed to determine the neutron multiplication factor for the system.

The STARBUCS input format has been designed around the existing depletion analysis and criticality safety sequences of SCALE. Only a minimal amount of input beyond that typically required for a fresh-fuel calculation is needed to perform a burnup-credit calculation.

STARBUCS was developed to facilitate studies of major burnup-credit phenomena, such as those identified in the US Nuclear Regulatory Commission’s Interim Staff Guidance 8, [Com12] but it is restricted to modeling one assembly type with the same starting enrichment loaded throughout the transportation or storage model. Greater flexibility is available by computing individual assembly burnup compositions with the ORIGAMI code and then creating a KENO model to implement these compositions.

For burnup loading curve iterative calculations, STARBUCS employs the search algorithm from CSAS5 to determine initial fuel enrichments that satisfy a convergence criterion for the calculated keff value of the spent fuel configuration.

Sourcerer: Hybrid Method for Starting Source Distribution

As the fidelity of criticality models continues to increase, especially for storage and transportation systems, the ability of the Monte Carlo codes to consistently provide a converged fission source can be challenging. Studies have shown that using a starting fission distribution similar to the true fission distribution can reduce the number of skipped generations required for fission source convergence, and it can significantly improve the reliability of the final keff result [IPW+11]. The Sourcerer sequence applies the Denovo [ESSC10] discrete ordinates code to generate a starting fission source distribution in a KENO Monte Carlo calculation. The discrete ordinates calculation is performed on a user-defined Cartesian grid geometry where macroscopic material definitions are automatically created from the Monte Carlo model and multigroup group cross sections are appropriately generated.

For many criticality safety applications, the additional step of performing a deterministic calculation to initialize the starting fission source distribution is not necessary. However, for challenging criticality safety analyses such as as-loaded spent nuclear fuel transportation packages with a mixed loading of low- and high-burnup fuel, even a low-fidelity deterministic solution for the fission source produces more reliable results than the typical starting distributions of uniform or cosine functions over the fissionable regions, as demonstrated in a recent study [Ibr13].

Criticality Accident Alarm System Analysis with KENO and MAVRIC

Criticality accident alarm systems (CAAS) safety analyses modeling presents challenges because the analysis consists of a criticality problem and a deep-penetration shielding problem [PPJ09]. Modern codes are typically optimized to handle one of these types of problems, but not both. The two problems also differ in size—the criticality problem depends on materials relatively close to the fissionable materials, whereas the shielding problem can cover a much larger range.

CAAS analysis can be performed using the CSAS6 criticality sequence and the MAVRIC shielding sequence. First, the fission distribution (in space and energy) is determined via CSAS6. This information is collected on a grid geometry that overlies the physical geometry model and is saved as a Monaco mesh source file. The mesh source is then used as the source term in MAVRIC. The absolute source strength is set by the user to the total number of fissions (based on the total power released) during the criticality excursion. MAVRIC can be optimized to calculate a specific detector response at one location or to calculate multiple responses/locations with roughly the same relative uncertainty.


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