Estimation procedures and error analysis for inferring the total plutonium (Pu) produced by a graphite-moderated reactor

Graphite isotope ratio method (GIRM) is a technique that uses measurements and computer models to estimate total plutonium (Pu) production in a graphite-moderated reactor. First, isotopic ratios of trace elements in extracted graphite samples from the target reactor are measured. Then, computer models of the reactor relate those ratios to Pu production. Because Pu is controlled under non-proliferation agreements, an estimate of total Pu production is often required, and a declaration of total Pu might need to be verified through GIRM. In some cases, reactor information (such as core dimensions, coolant details, and operating history) are so well documented that computer models can predict total Pu production without the need for measurements. However, in most cases, reactor information is imperfectly known, so a measurement and model-based method such as GIRM is essential. Here, we focus on GIRM's estimation procedure and its associated uncertainty. We illustrate a simulation strategy for a specific reactor that estimates GIRM's uncertainty and determines which inputs contribute most to GIRM's uncertainty, including inputs to the computer models. These models include a “local” code that relates isotopic ratios to the local Pu production, and a “global” code that predicts the Pu production shape over the entire reactor. This predicted shape is included with other 3D basis functions to provide a “hybrid basis set” that is used to fit the local Pu production estimates. The fitted shape can then be integrated over the entire reactor to estimate total Pu production. This GIRM evaluation provides a good example of several techniques of uncertainty analysis and introduces new reasons to fit a function using basis functions in the evaluation of the impact of uncertainty in the true 3D shape.