Effect of the time variation of the neutron current density in the calculation of the reactivity

• Published in: Annals of nuclear energy Vol. 96; pp. 204 - 211
• Main Authors: Palma, Daniel A.P., Nunes, Anderson Lupo, Martinez, Aquilino Senra
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2016
• Subjects: Approximation; Density; Derivation; Inverse point kinetics equation; Kinetic equations; Mathematical analysis; Nuclear engineering; Nuclear reactor components; Nuclear reactors; P1 approximation; Reactivity; Inverse point kinetics equation; Reactivity; P1 approximation
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2016.05.022

•A modified expression for the reactivity ρmod(t) is proposed.•The conventional expression ρcon(t) overestimates ρmod(t) by Δρ(t).•This result can be used to upgrade the reactimeters that are used nowadays. In the derivation of the conventional set of point kinetics equations from the neutron transport equation, one of the approximations used is to disregard the time variation of the neutron density current in comparison with the other terms resulting from the P1 approximation. When not considering this approximation it is obtained a modified set of point kinetics equations where new terms appear naturally during the derivation. In this paper, the effect from considering the time variation of a neutron density current in the calculation of reactivity is evaluated. The new expression obtained can be written as a correction function Δρ(t) to the reactivity conventionally calculated. For the different types of transients simulated with the use of typical kinetic parameters in PWR reactors it was seen that, for those that have an exponential behaviour, the correction Δρ(t) quickly reaches values that cannot be neglected. Additionally, for this type of transient, it is possible to conclude that the reactivity calculated by the conventional expression overestimates that which is obtained by the new formulation by a value proportional to the argument of the exponential function.