Predictive Modeling of Coupled Systems: Uncertainty Reduction Using Multiple Reactor Physics Benchmarks

This work illustrates reactor physics applications of the predictive modeling of coupled multiphysics systems (PMCMPS), formulated by Cacuci (2014), by means of the benchmarks Godiva (a bare uranium sphere) and Jezebel-239 and Jezebel-240 (bare plutonium spheres). The PMCMPS methodology was ab initio developed in the response space, to reduce as much as possible the computational memory requirements for predictive modeling of very large systems involving not only many model parameters but also many model responses. The model parameters considered in this work include individual cross sections for each material, nuclide, reaction type, and energy group, giving the following totals: 2241 parameters for Jezebel-239, 1458 parameters for Jezebel-240, and 2916 parameters for Godiva. Eight responses were considered for Jezebel-239 (the effective multiplication factor; the center core fission rates for ²³³U, ²³⁸U, ²³⁷Np, and ²³⁹Pu; and the center core radiative capture rates for ⁵⁵Mn, ⁹³Nb, and ⁶³Cu). Three responses (the effective multiplication factor and the center core fission rates for ²³³U and ²³⁷Np) were selected for Jezebel-240, and eleven responses were selected for Godiva (the reaction rate types listed for Jezebel-239, along with the radiative capture rates for ¹⁰⁷Ag, ¹²⁷I, and ⁸¹Br). The PMCMPS methodology ensures that increasing the amount of information yields more accurate predictions, with smaller predicted uncertainties, as long as the considered information is consistent. This fact is amply illustrated in this work, which shows that the interdependence of responses that were measured in more than one benchmark is stronger than for responses that were measured in a single benchmark. More generally, the consideration of the complete information, including couplings, provided jointly by all three benchmarks (as opposed to consideration of the benchmarks as separate systems) leads to more accurate predictions of nominal values for responses and model parameters, yielding larger reductions in the predicted uncertainties that accompany the predicted mean values of responses and model parameters.