Solving Bateman Equation for Xenon Transient Analysis Using Numerical Methods

Abstract

After a nuclear reactor is shutdown, xenon-135, an isotope with a very high thermal neutron absorption cross-section, will build up and reduce the reactivity considerably for a while. This is known as poisoning. However, the concentration xenon-135 would gradually decrease through decaying or absorbing neutron, making it necessary to suppress the reactivity in order to prevent the reactor to go critical or supercritical. Thus, it is important to predict the relationship between xenon poisoning and time after the reactor is shutdown to ensure the safety of the reactor. This paper reports the research on the prediction of xenon poisoning in a hypothetical nuclear reactor after it is shut down. In order to make the prediction, the Bateman equations of xenon (Xe) and iodine (I), which is of the form of an Ordinary Differential Equation (ODE) system, need to be solved. Two different methods, the fourth-order Runge-Kutta method and the matrix exponential method, were applied to solve the ODE system with MATLAB codes. The accuracies and computational efficiencies of the two method is also studied and compared.