Solution of the isotopic depletion equations using decomposition method and analytical solutions

In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes founding a typical PWR reactor. Part of this chain allows feedback reactions of (n, 2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time.