Development of a Burnup Module DECBURN Based on the Krylov Subspace Method

This report is to develop a burnup module DECBURN that is essential for the reactor analysis and the assembly homogenization codes to trace the fuel composition change during the core burnup. The developed burnup module solves the burnup equation by the matrix exponential method based on the Krylov Subspace method. The final solution of the matrix exponential is obtained by the matrix scaling and squaring method. To develop DECBURN module, this report includes the followings as: (1) Krylov Subspace Method for Burnup Equation, (2) Manufacturing of the DECBURN module, (3) Library Structure Setup and Library Manufacturing, (4) Examination of the DECBURN module, (5) Implementation to the DeCART code and Verification. DECBURN library includes the decay constants, one-group cross section and the fission yields. Examination of the DECBURN module is performed by manufacturing a driver program, and the results of the DECBURN module is compared with those of the ORIGEN program. Also, the implemented DECBURN module to the DeCART code is applied to the LWR depletion benchmark and a OPR-1000 pin cell problem, and the solutions are compared with the HELIOS code to verify the computational soundness and accuracy. In this process, the criticality calculation method and the predictor-corrector scheme are introduced to the DeCART code for a function of the homogenization code. The examination by a driver program shows that the DECBURN module produces exactly the same solution with the ORIGEN program. DeCART code that equips the DECBURN module produces a compatible solution to the other codes for the LWR depletion benchmark. Also the multiplication factors of the DeCART code for the OPR-1000 pin cell problem agree to the HELIOS code within 100 pcm over the whole burnup steps. The multiplication factors with the criticality calculation are also compatible with the HELIOS code. These results mean that the developed DECBURN module works soundly and produces an accurate solution. Therefore, it can be concluded that the development of the DECBURN module and the implementation to the DeCART code are well performed