Criticality calculations for homogeneous fuel-moderator configurations using the one-group diffusion equation

Abstract

This thesis investigates reactor criticality in homogeneous fuel-moderator configurations using one-group and modified one-group neutron diffusion theory. A Python-based computational model is developed to determine the critical size for a given fuel–moderator composition, and to determine the required fuel atomic fraction for a given critical size. In the forward approach, the critical size is determined for a given fuel-moderator atomic fraction, while in the inverse approach, the required fuel atomic fraction is obtained from a specified critical size. The model is developed for three foundational geometries: sphere, cylinder, and parallelepiped. The modified one-group model introduces neutron age and migration area based on the physical representation of neutron behaviour. The results demonstrate a consistent inverse relationship between fuel atomic fraction and critical size across all geometries. As the fuel fraction increases, the critical size decreases rapidly, particularly in the low-fuel region. The results are validated against benchmark problems. This study confirms that diffusion-based modelling provides a reliable framework for preliminary reactor criticality analysis.