Krylov based burnup model for studying core characteristics of thermal reactors with burnup

Abstract The design calculation of a nuclear reactor is not only limited to the initial core loaded with fresh fuel, but also extended to its subsequent states during the course of fuel burning. Formation of actinides and fission products, with fuel burning, affects the reactor core physics parameters to a significant extent. That is why it is a key step in design calculation to follow up the reactor core characteristic with time. For this, we need to solve the Bateman equation and obtain the core composition in regular interval of time. However, the equation is a time-dependent coupled differential one involving thousands of radioisotopes with a wide spectrum of half-lives starting from seconds to years. Due to the stiffness associated with it, solving the equation with acceptable accuracy is not so trivial. In the current paper, a burnup model is presented to demonstrate the study of core parameters with fuel burning. The actinides and fission products, listed in WIMS cross section library, are only considered in the model. A matrix equation is constructed based on the production and loss of each nuclide listed in the library, discretized by implicit method and finally solved by Krylov subspace iteration. The model is coupled with a 2D, Method of Characteristics based neutron transport code MANTRA to solve benchmark problems related to burning of pin type fuel in power reactors like PHWR, BWR and plate type fuel in research reactor like MTR (Material Test Reactor) and the results show good agreement with well-known international codes like DRAGON, WIMSD, MCNP etc. For MTR, conventional calculation underestimates the worth of absorbing blades. Hence, a supercell approach, for both fresh and burnt core, is attempted to rectify the modeling error and the estimated worth is found to be close to that of Monte Carlo code.