Quantification of Back-End Nuclear Fuel Cycle Metrics Uncertainties Due to Cross Sections

Abstract

This work examines uncertainties in the back end fuel cycle metrics of isotopic composition, decay heat, radioactivity, and radiotoxicity. Most advanced fuel cycle scenarios, including the ones represented in this work, are limited by one or more of these metrics, so that quantification of them becomes of great importance in order to optimize or select one of these scenarios. Uncertainty quantification, in this work, is performed by propagating cross-section covariance data, and later number density covariance data, through a reactor physics and depletion code sequence. Propagation of uncertainty is performed primarily via the Efficient Subspace Method (ESM). ESM decomposes the covariance data into singular pairs and perturbs input data along independent directions of the uncertainty and only for the most significant values of that uncertainty. Results of these perturbations being collected, ESM directly calculates the covariance of the observed output posteriori. By exploiting the rank deficient nature of the uncertainty data, ESM works more efficiently than traditional stochastic sampling, but is shown to produce equivalent results. ESM is beneficial for very detailed models with large amounts of input data that make stochastic sampling impractical. In this study various fuel cycle scenarios are examined. Simplified, representative models of pressurized water reactor (PWR) and boiling water reactor (BWR) fuels composed of both uranium oxide and mixed oxides are examined. These simple models are intended to give a representation of the uncertainty that can be associated with open uranium oxide fuel cycles and closed mixed oxide fuel cycles. The simplified models also serve as a demonstration to show that ESM and stochastic sampling produce equivalent results, because these models require minimum computer resources and have amounts of input data small enough such that either method can be quickly implemented and a numerical experiment performed. The simplified models are followed by more rigorous reactor physics and depletion models showing a PWR uranium oxide fuel and various metal fast reactor fuels composed of transuranics. The more rigorous models include multi-group cross sections, multiple burnup steps, neutron transport calculations to update cross sections, and multi-scale multi-physics code sequences to simulate a complete fuel lifetime. Finally, the fast reactor and PWR fuels are combined in a closed fast reactor recycle fuel cycle, and uncertainties on the resulting equilibrium cycle examined.