New Depletion Capability for Pebble Bed Reactors in SCALE

Under the sponsorship of the U.S. Nuclear Regulatory Commission (NRC), the SCALE team recently implemented an enhancement to SCALE’s fast depletion modeling sequence, ORIGAMI, that enables users to rapidly simulate the nuclide inventory of pebble bed reactors (PBRs). 

Unlike commercial light-water reactors (LWRs) in the United States, PBRs use an on-line refueling scheme with cores of several thousand spherical fuel pebbles. Fresh pebbles are delivered to the core inlet and flow slowly through the core (e.g., for weeks/months) until they reach the core outlet, where they are nondestructively evaluated for burnup levels. If a pebble’s burnup level is estimated below a threshold value, it is considered to contain sufficient reactivity to be recirculated for another pass through the core. Otherwise, it’s retired and safely stored as spent fuel.

In typical U.S. commercial LWRs, a fuel assembly stays in one core position for an entire cycle, is shuffled at each reload, and can remain in the core for up to two additional cycles. This design results in a simple representation of the assembly operating history. In PBRs, pebbles mix stochastically, and no instrumentation for per-pebble tracking is planned in any known design, so each pebble’s exact path — and its power-flux history — is unknowable. 

A second difference between depletion modeling for LWRs and PBRs is perhaps best explained using the migration length: a metric for the distance from neutron birth to fission. In LWRs, the migration length is ~6 cm and much smaller than the ~20 cm lattice size. This means the LWR assembly inventory depends mainly on the assembly itself and that neighbor effects are negligible. In a graphite-moderated PBR, the migration length is ~50 cm, roughly ten times the ~6 cm pebble diameter, making environment effects much more relevant. As shown in a 2021 report, reflector proximity and local temperature are the most significant environment conditions that depend on the pebble transit path. Spectral sensitivity differs too: LWR assembly burnup hardens the spectrum, but in PBRs individual pebble burnup negligibly shifts the spectrum within the pebble because most fission neutrons come from the surrounding pebbles, which span a wide burnup range.

ORIGAMI’s new capability allows users to define various power histories, residence times, and location-dependent characteristics, such as temperature or reflector proximity, that a pebble experiences in each of its passes. It supports various applications involving irradiated nuclear fuel pebbles, such as the following:

• full-core nuclide inventory generation, in which batches of pebbles are used to characterize aggregate nuclide inventory behavior across the entire core for severe accident applications
• individual pebble inventory generation, which enables detailed modeling of a single pebble’s depletion as it traverses the core, its path determining neutron spectra and irradiation times 

Results from the latter application are particularly valuable in supporting nuclear material control and accounting efforts under the Advanced Reactor Safeguards and Security program (DOE-NE). In support of that work, the team modeled 20,000 individual pebbles in a PBMR-400 reactor model using a random radial channel per pass with 5 radial channels and 22 axial zones with varying power/flux levels. One of the key inputs to ORIGAMI is the reactor library for the PBMR-400, which was generated by SCALE’s reactor physics sequence, TRITON, according to the SLICE method. This library accounts for the spectral effect of burnup levels as well as fuel and reflector temperatures at various radial and axial zones in the reactor core. This modeling effort also supported a nuclear safeguards project sponsored by the US Department of Energy’s Office of Defense Nuclear Nonproliferation Research and Development within the National Nuclear Security Administration. The ORIGAMI results generated for the 20,000 pebbles were used to develop a database that was then applied to train and test machine learning algorithms to predict a pebble’s attributes (e.g., burnup) based on its gamma spectrum.   

Assuming that pebbles are discharged when they reach a target burnup — rather than after a certain number of passes — leads to burnup and nuclide distributions like those shown in Figure 1.