During the normal operation of a pebble bed gas-cooled reactor (PBR), the fuel pebbles undergo a multi-circulation on the basis of online burnup assay. In our last ICONE paper, we proposed a model to describe the relationship between online burnup assay and economy and safety of PBR. It was concluded that improvements on burnup assay accuracy could reduce fuel cost as well as the possibility that excessive burnup of fuel pebble results in unexpected radioactive discharge. However further work was expected on the burnup distribution of pebbles in and out of the core to precisely quantify the relationship. In this paper, the methodology to construct the burnup distribution of fuel pebbles in and out of the core is proposed. Firstly a model for pebble flow circulation is developed to provide a basic simulation framework. Then the irradiation history of fuel pebble could be tracked by combining pebble flow model and burn up calculation. The representative kinematic model and discrete element method (DEM) are introduced to numerically simulate the profiles of pebble flow. The classical batch-tracking methods as well as our newly-introduced DEM-tracking method are presented to perform the time-dependent analysis of pebble burnup. Overall with the burnup data obtained after going through multiple cycles, the burnup distribution of fuel pebbles in and out of the core could be reconstructed through the statistics result according to the pebble circulation model. Finally the quantification of the relationship between the pebble burnup assay and the economy and safety of the PBR would be more precise, thus providing implications on proposing reasonable requirements for accuracy of online burnup assay.

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