A differential equation for inverse point kinetics

Abstract

The reactivity that represents the percentage departure of a nuclear reactor from its criticality condition is perhaps the most important individual property since it is directly related to the nuclear reactor’s safe operation. Control systems are used to limit the rate of increase in reactivity. The development of systems for monitoring the reactivity, from the nuclear power data acquired from the plant's onboard electronics, requires a constant improvement of the nuclear kinetic models.The transient situations that emerge in nuclear reactors can be predicted from the changes in the neutron flux and, therefore, it is possible to make a sufficiently accurate prediction about the consequences of the disturbances relating to the magnitude of the neutron flux, which varies over time, by using the integral parameters that represent the nuclear reactor core. The point kinetic equations relate these parameters and, in this way, allow the transient situations that can occur in a nuclear reactor to be studied.The reactivity is usually determined by solving the inverse point kinetic equation, which is an integral equation that depends on the nuclear power variation history. In this paper, we present a method to calculate the reactivity through the solution of an ordinary differential equation that does not depend on the nuclear power variation history, then allows the prompt recovery of the reactimeter in case of loss of the nuclear power data acquisition or malfunction of such equipment (Zarei, 2022; Ansari, 1991).The presented paper is organized as follows: Section 1 contains the basic concepts of point kinetics equations and the integral formalism for the reactivity calculation. The mathematical formalism that leads to the differential equation for the reactivity is presented in Section 2. The prompt recovery of the reactivity using the proposed method is discussed in Section 3. The results are shown in Section 4 and the conclusion is presented in Section 5.