Title: The Current State of High-Fidelity PBR Neutronics Modelling
Author: Liam Carlson, Texas A&M University
Traditional methods for simulating depletion in Pebble Bed Reactors (PBRs) typically involve treating representative batches of fuel elements. Pebbles that share the same pass number or similar burnup values within a given spectral zone or volume are assumed to have identical characteristics (isotopic concentrations, temperature, cross sections, etc.). This homogenization of material and environmental properties overlooks the unique flux histories of individual pebbles. Additionally, two-dimensional (RZ) representations of PBRs in traditional approaches fail to account for the angular dependence of flux histories. For example, proximity to control rods may uniquely affect a subset of pebbles.
Recent advancements in PBR-specific high-fidelity three-dimensional approaches to solving steady-state eigenvalue problems have opened the door for high-precision depletion modeling. These approaches, which can be categorized into Monte Carlo and deterministic methods, explicitly model pebble distributions, enabling pebble-wise reaction rate distributions to be evaluated efficiently with modern supercomputing resources.
The Monte Carlo approach explicitly models each pebble, including the TRISO distribution within. Full-core eigenvalue simulations are performed without the need for material homogenization. The efficient modeling of a full-scale PBR is achieved using specialized techniques such as Woodcock delta-tracking, collision-based domain decomposition, and lattice tallies. In contrast, the Pebble Tracking Transport (PTT) technique employs the discontinuous finite element method (DFEM) to obtain a piecewise-defined scalar flux solution.
PTT utilizes a unique tetrahedral mesh, where all vertices within the pebble packing region correspond to pebble centroids. This approach enables pebble modeling without explicitly meshing their geometries. Instead, pebble domains are implicitly defined by their centroid locations and radii, with their material characteristics represented by pebble-wise homogenized multi-group cross sections.
The Monte Carlo approach has the advantage of fully modeling pebble geometries while avoiding systematic errors commonly associated with deterministic methods, such as discretization errors. On the other hand, PTT can achieve higher precision reaction rates and offers the added benefit of straightforward coupling with other finite-element-based reactor physics codes. Both approaches have comparable computational requirements in terms of runtime and memory usage.
The high-fidelity modeling techniques presented in this work enable detailed pebble-wise isotopic concentration distributions to be evaluated, offering significant advantages for nonproliferation research. By preserving the unique flux histories of individual pebbles, these methods allow for precise tracking of fissile material production and the isotopic evolution of spent fuel. This level of detail may enhance the accuracy of safeguards assessments, support advanced fuel monitoring techniques, and strengthen nuclear forensic capabilities.