On a point kinetic with explicit presence of neutron poisons: reactivity decomposition according to long time scales

Abstract

The present work consists of deducing the point kinetics model considering neutron absorber poisons from the neutron diffusion equation. When considering poisons products, the non-linear system has different orders of magnitude in short and long time scales. The first one represents operational reactor control, whereas the second is due to the change of the chemical composition of the nuclear fuel as a result of burn-up. This represents a first step in a new direction, as it shows how we arrived at the extension of the point kinetics model considering Xenon-135 and Samarium-149 poisons. The non-linear system is solved using the Adomian decomposition method that expands the non-linear terms into an infinite series, obtaining a recursive system, where the recursion initialization is a homogeneous linear equation and the subsequent recursion steps consider the non-linear contributions as source terms constructed from previous recursion steps. The formulation of the source terms of the decomposition method is shown. In order to demonstrate the robustness of the current approach to this type of problem, case studies are presented where nuclear fuel uses reused elements up to third generation, taking a step in a new direction where poisons are already present in the reactor initially.