A method for on-line reactivity monitoring in nuclear reactors

• The problem of the on-line monitoring of reactivity in a source-free nuclear reactor is considered.
• A relationship between the system stable period and the power, its derivative and its integral is derived.
• The reactivity can be reconstructed at each time instant from the measured power-related quantities.
• A study on the sensitivity of the reactivity to the uncertainty on the values of the integral parameters is performed.
• The spatial effects are investigated by applying the method to the interpretation of flux signals.

In the present work the problem of the on-line monitoring of the reactivity in a source-free nuclear reactor is considered. The method is based on the classic point kinetic model of reactor physics. A relationship between the instantaneous value of the system stable period and the values of the neutron flux amplitude (or the power), of its derivative and of the integral convolution term determining the instantaneous value of the effective delayed neutron concentration is derived. The reactivity can then be evaluated through the application of the inhour equation, assuming the effective delayed neutron fraction and prompt generation time are known from independent measurements. Since the power related quantities can be assumed to be experimental observables at each instant, the reactivity can be easily reconstructed. The method is tested at first through the interpretation of power histories simulated by the solution of the point kinetic equations; the effect of the time interval between power detections on the accuracy is studied, proving the excellent performance of the procedure. The work includes also a study on the sensitivity of the reactivity forecast to the uncertainty on the values of the effective delayed neutron fraction and prompt generation time. The spatial effects are investigated by applying the method to the interpretation of flux evolution histories generated by a numerical code solving the space–time dependent neutron kinetic equations in the diffusion model. Also in this case the method proves to be quite effective in providing good estimates of the system reactivity, except at very short times after the introduction of a perturbation inducing a spatial transient. At last, the effect of the experimental noise is investigated, proving that the consequences in the accuracy of the reactivity prediction can be mitigated by using an adequate differentiation algorithm.