Transitions From Stochastic to Point Kinetics Models In Fissile Solutions
Fissile solutions form an integral part of the fuel cycle, being used to store and process both fresh fuel and waste. Fissile solutions are also found within Aqueous Homogeneous Reactors (AHRs) including research reactors such as CRAC and SILENE and also potential future systems which could be used for the production of medical isotopes. In the case of fissile solutions in the fuel cycle, avoiding criticality is a priority but accidents have occurred in which a significant number of fissions occurred. In the case of AHRs, a sustained neutron population and fission rate is desired. In both cases the ability to simulate transients where changes in reactivity cause the neutron population to increase are important. A popular method for the simulation of such transients is the point kinetic method which allows the capture of the major features of a transient at a fraction of the computational runtime and code complexity of more comprehensive modelling technologies. A limitation of the point kinetics method and other mainstream methods of predicting neutron behaviour is that they assume the neutron population is large enough that the mean behaviour will be observed. When the neutron population is low, however, the deviation around the mean behaviour is expected to be relatively large as there is an aleatoric uncertainty arising from the uncertain fate of individual neutrons. Such limitations are of particular importance when the reactivity of a system is rapidly increasing while the neutron population is low, which is often true in accident scenarios involving fissile solutions. This provides the motivation for the coupling of point kinetics and a probabilistic models of fissile solutions. This summary aims to explore some of the behaviours resulting from a low neutron population and rising reactivity using a coupled probabilistic and point kinetics model of a fissile solution. As the effects of a low neutron population are the primary concern of this summary, the point kinetics and thermal hydraulic models used will be relatively simple but these models should be sufficient to capture the most important behaviours of the system in the first minute or so of a transient. This work is an extension of the work found in [1]. In that work the methodology was applied to fast pulses produced by systems such as Godiva and its results were found to compare favourably to experimental and analytical results, such as the burst wait time, in [2]. This work focuses on the application of this methodology to a fissile solution but the method could be applied to a number of criticality safety or reactor operation scenarios through suitable modification of the point kinetics model and would produce a more accurate prediction of the peak power obtained when a system first becomes critical compared to the use of a standard point kinetics model. (authors)