An Analytical Solution to Sensitivity/Uncertainty Equations at Different Enrichments for Criticality Code Validation - 059

This paper reviews current Sensitivity/Uncertainty (S/U) methodology as applied to code validation for criticality safety and shows how the method may be used to analyze the correlation of a single parameter through the application of suitable approximations. S/U methodology based upon perturbation theory has been used to develop special parameters called sensitivity coefficients which may be used to determine the applicability of benchmarks. Uncertainty analysis uses the sensitivity coefficients to determine the propagated error in k_eff due to the experimental uncertainties in the underlying cross sections, which are major contributors to the bias. An overview of S/U methodology is provided to highlight the principle assumptions and components of the method and show drawbacks of the method due to complexity. An analytical approximation is then developed for a single parameter, enrichment, to show how the method may be used to demonstrate correlation when all but one parameter is constant. The correlation parameters determined for this special case are graphically displayed. Enrichment was chosen as the trending parameter because validation of criticality code calculations for enrichments >5 wt% ²³⁵U is currently of interest and because the effect on the combined cross section of changing the enrichment is easily predicted and expressed in equation form. (author)