On a point kinetic model for nuclear reactors considering the variation in fuel composition

Abstract

The present discussion is an extension of a new model recently developed for neutron point kinetics, where the reactivity is decomposed in terms of short and long timescales. The short timescale corresponds to the operational control of the reactor, while the long timescale corresponds to the effects of the chemical composition variation in the nuclear fuel as a consequence of fission and neutron capture processes. This work considers not only the effects of the main neutron poisons but contains also a first analysis of the effects of some transuranium. The proposed model consists of a system of non-linear equations, which is solved by the use of the Adomian decomposition method. This method expands the solution into an infinite series, whose contributions are obtained by the solution of a recursive equation system where the non-linear terms are treated as source terms. These are calculated by so-called Adomian polynomials and are constructed from the solutions obtained in previous recursion steps. An approach is proposed, that diagonalizes the linear matrix in order to circumvent the existing stiffness problem, which is also responsible for instabilities in the computational algorithm. Two case studies are presented, analysing the non-linear behaviour of nuclear reactor kinetics with constant reactivity using input parameters for which the algorithm was stable. Further, a standard point kinetics case with periodic reactivity is performed in order to compare the present model to a standard point kinetics simulation from the literature.