A computationally simple model for determining the time dependent spectral neutron flux in a nuclear reactor core

The balance of isotopes in a nuclear reactor core is key to understanding the overall performance of a given fuel cycle. This balance is in turn most strongly affected by the time and energy-dependent neutron flux. While many large and involved computer packages exist for determining this spectrum, a simplified approach amenable to rapid computation is missing from the literature. We present such a model, which accepts as inputs the fuel element/moderator geometry and composition, reactor geometry, fuel residence time and target burnup and we compare it to OECD/NEA benchmarks for homogeneous MOX and UOX LWR cores. Collision probability approximations to the neutron transport equation are used to decouple the spatial and energy variables. The lethargy dependent neutron flux, governed by coupled integral equations for the fuel and moderator/coolant regions is treated by multigroup thermalization methods, and the transport of neutrons through space is modeled by fuel to moderator transport and escape probabilities. Reactivity control is achieved through use of a burnable poison or adjustable control medium. The model calculates the buildup of 24 actinides, as well as fission products, along with the lethargy dependent neutron flux and the results of several simulations are compared with benchmarked standards.