Nuclear Science and Engineering / Volume 183 / Number 3 / July 2016 / Pages 332-346
Technical Paper / dx.doi.org/10.13182/NSE15-99
This work presents the application of the comprehensive predictive modeling methodology for single multiphysics time-dependent systems, developed by Cacuci and Ionescu-Bujor (2010), to a paradigm spent fuel dissolver model of interest to nonproliferation objectives, in order to quantify uncertainties due to dissolver model parameters and subsequently to combine all of the available experimental and computational information to obtain best-estimate values for model responses and parameters, along with reduced predicted uncertainties. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayesâ€™ theorem with the likelihood provided by the multiphysics computational models. Finally, the posterior distribution is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multiphysics models, along with corresponding reduced uncertainties.
The weighting functions used within this predictive modeling methodology are provided by the first-order sensitivities (i.e., functional derivatives) of the modelâ€™s response with respect to the modelâ€™s parameters. The dissolver model comprises 619 model parameters related to the modelâ€™s equation of state and inflow conditions. The sensitivities to all model parameters of the acid concentrations at each of these instances in time were computed exactly and efficiently in an accompanying work by Peltz and Cacuci (2015), using the adjoint sensitivity analysis method. These sensitivities are used in this work to quantify the uncertainties in the acid concentration (system responses) in various dissolver compartments, arising from uncertainties in the model parameters. Subsequently, the sensitivities are used within the predictive modeling methodology to combine the computational results with the available experiments, which were performed solely in the compartment farthest from the inlet. The results of applying the predictive modeling methodology yield optimally calibrated values for all 619 model parameters, with reduced predicted uncertainties, as well as optimal (best-estimate) predicted values for the acid concentrations, also with reduced predicted uncertainties. Notably, even though the experimental data pertain solely to the compartment farthest from the inlet (where the data were measured), the predictive modeling methodology actually improves the predictions and reduces the predicted uncertainties not only in the compartment in which the data were actually measured but also throughout the entire dissolver, including the compartment farthest from the measurements (i.e., at the inlet). This is because the predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations.
The results obtained in this work establish confidence in the dissolver modelâ€™s accuracy for simulating the acid concentrations required to dissolve used nuclear fuel. In turn, these results will be used to generate source terms for key reprocessing facility components downstream and to support material accountability for nuclear safeguards.