Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor

In this paper we present the behavior of the variation of neutron density when the nuclear reactor power is increased using the fractional neutron point kinetic (FNPK) equation with a single-group of delayed neutron precursor. It is considered that there is a relaxation time associated with a rapid variation in the neutron flux and its physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. We analyzed the case of increase the nuclear reactor power when reactor is cold start-up which is a process of inserting reactivity by lifting control rods discontinuously. The results show that for short time scales of the start-up the neutronic density behavior with FNPK shows sub-diffusive effects whose absorption are government by control rods velocity. For large times scale, the results shows that the classical equation of the neutron point kinetics over predicted the neutron density regarding to FNPK.

► Neutron density behavior at reactor start up with fractional neutron point kinetics.
► There is a relaxation time associated with a rapid variation in the neutron flux.
► Physical interpretation of the fractional order is related with non-Fickian effects.
► Effect of the anomalous diffusion coefficient and the relaxation time is analyzed.
► Neutron density is related with speed and duration of the control rods lifting.