The Development of the Combined Fission Matrix Theory in Burnup Calculation

Abstract

High accuracy and efficiency of nuclear reactor core burnup calculation are both necessary. The Monte Carlo method has been shown to have high fidelity applied to burnup calculations. However, a traditional Monte Carlo criticality-burnup calculation usually requires a lot of computational resources. This study will suggest a new way of burnup calculation to tackle this problem and boost the computing efficiency. Through the fission matrix combination method, the system fission matrix can be estimated with a pre-calculated database. The fission matrix coefficients in the database are obtained by multiple fixed source calculations instead of criticalilty calculations and the process of combination is straightforward so that no additional Monte Carlo simulations are needed. The proposed approach is validated based on the effective multiplication factor and source distribution in a simple two-assembly model with different enrichments. Fixed source calculations under various nuclide information and energy spectrum conditions are performed to obtain the fission matrix database, and the system fission matrix for each depletion step is estimated by combining interpolated database fission matrices. Pins at the boundary between two different assemblies are obviously influenced by the nuclear properties of other materials nearby, which leads to errors. The corrective procedure can minimize the border perturbations to an acceptable range. In the present work, compared to the reference criticalility calculation also by Serpent, the error of k-eigenvalue is within 70 pcm and the RMS error of the source distribution is roughly 0.5% before 100 days. The effective multiplication factor error will gradually increase to 250 pcm as the burnup continues to 800 days, and the RMS error of the source distribution will eventually rises to 2%. Part of planned future work would be to implement correction factors for burnup progress. In conclusion, the fission matrix combination approach can perform burnup calculations with a similar accuracy to the Monte Carlo method but with much less computational cost.