Quantification of uncertainties and correlations in criticality experiments with scale

Uncertainties in benchmark k_eff due to uncertainties in individual components, such as geometry and material compositions, are rigorously quantified and documented in evaluations provided in the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE). Correlations between the uncertainties may affect not only the overall uncertainty for a series of benchmarks but also the magnitude of computational biases and bias uncertainties quantified by validation methods. The impact of the correlations in experimental uncertainties is especially important in the use of advanced validation methods such as Generalized Linear Least Squares (GLLS), as implemented in the SCALE TSURFER code. In a recent study, it was demonstrated that biases computed with GLLS procedures vary by as much as 75%, depending on the selection of the experimental uncertainty correlation value. Of the >4000 benchmarks documented in the IHECSBE, experimental correlation data are only available in the DICE database tool for ∼60 benchmarks. Additional data are available in DICE to identify the potential for correlations between evaluations, but the values of correlations are not quantified. The new Sampler module of SCALE provides stochastic capabilities to quantify uncertainties and correlations in k_eff or any other measured value for one or more benchmark experiments due to uncertainties in individual sources of uncertainty, such as geometry and material composition. The values for individual parameters in the input model are randomly modified within the reported uncertainty, and a distribution function and a series of perturbed k_eff values are obtained. Where sufficient samples are made, the distribution of the perturbed k_eff values is used to determine the uncertainty in the k_eff due to uncertainties in the input parameters. In cases where the same uncertainty parameters influence multiple experiments, such as where the same fissile solution or fuel rods are used for many critical measurements, the simultaneous perturbation of an uncertain parameter for multiple cases provides the correlation in k_eff uncertainties between the different configurations. The parametric uncertainty capabilities of Sampler for a single system are demonstrated for a benchmark exercise from the Organization for Economic Cooperation and Development (OECD) Nuclear Energy Agency (NEA) Working Party on Nuclear Criticality Safety (WPNCS) Expert Group on Uncertainty Analysis for Criticality Safety Assessment (UACSA) Phase II benchmark. Sampler is further applied to quantify correlations among benchmarks from a series of highly enriched uranium (HEU) solution (SOL) thermal spectrum (THERM) systems, through the analysis of the 10 cases from HEU-SOL-THERM-001 from the IHECSBE.