Accurate Holdup Calculations with Predictive Modeling & Data Integration
In facilities that process special nuclear material (SNM) it is important to account accurately for the fissile material that enters and leaves the plant. Although there are many stages and processes through which materials must be traced and measured, the focus of this project is material that is “held-up” in equipment, pipes, and ducts during normal operation and that can accumulate over time into significant quantities. Accurately estimating the holdup is essential for proper SNM accounting (vis-à-vis nuclear non-proliferation), criticality and radiation safety, waste management, and efficient plant operation. Usually it is not possible to directly measure the holdup quantity and location, so these must be inferred from measured radiation fields, primarily gamma and less frequently neutrons. Current methods to quantify holdup, i.e. Generalized Geometry Holdup (GGH), primarily rely on simple source configurations and crude radiation transport models aided by ad hoc correction factors. This project seeks an alternate method of performing measurement-based holdup calculations using a predictive model that employs state-of-the-art radiation transport codes capable of accurately simulating such situations. Inverse and data assimilation methods use the forward transport model to search for a source configuration that best matches the measured data and simultaneously provide an estimate of the level of confidence in the correctness of such configuration. In this work the holdup problem is re-interpreted as an inverse problem that is under-determined, hence may permit multiple solutions. A probabilistic approach is applied to solving the resulting inverse problem. This approach rates possible solutions according to their plausibility given the measurements and initial information. This is accomplished through the use of Bayes’ Theorem that resolves the issue of multiple solutions by giving an estimate of the probability of observing each possible solution. To use Bayes’ Theorem, one must have a model y(x) that maps the state variables x (the solution in this case) to the measurements y. In this case, the unknown state variables are the configuration and composition of the heldup SNM. The measurements are the detector readings. Thus, the natural model is neutral-particle radiation transport where a wealth of computational tools exists for performing these simulations accurately and efficiently. The combination of predictive model and Bayesian inference forms the Data Integration with Modeled Predictions (DIMP) method that serves as foundation for this project. The cost functional describing the model-to-data misfit is computed via a norm created by the inverse of the covariance matrix of the model parameters and responses. Since the model y(x) for the holdup problem is nonlinear, a nonlinear optimization on Q is conducted via Newton-type iterative methods to find the optimal values of the model parameters x. This project comprised a collaboration between NC State University (NCSU), the University of South Carolina (USC), and Oak Ridge National Laboratory (ORNL). The project was originally proposed in seven main tasks with an eighth contingency task to be performed if time and funding permitted; in fact time did not permit commencement of the contingency task and it was not performed. The remaining tasks involved holdup analysis with gamma detection strategies and separately with neutrons based on coincidence counting. Early in the project, and upon consultation with experts in coincidence counting it became evident that this approach is not viable for holdup applications and this task was replaced with an alternative, but valuable investigation that was carried out by the USC partner. Nevertheless, the experimental 4 measurements at ORNL of both gamma and neutron sources for the purpose of constructing Detector Response Functions (DRFs) with the associated uncertainties were indeed completed.