The HTR-10 is a pebble bed High-temperature gas-cooled reactor (HTGR) with a nominal thermal power of 10 MW. The on-line nondestructive burn-up (BU) measurement for the spherical fuel elements with TRISO coated fuel particles is an important issue in the fuel management of the HTR-10. The HTR-10 employs an HPGe gamma spectroscopy system to determine the BU values of the discharged fuel elements, and the accuracy of the BU measurement system is a crucial issue. The calibration requirement and the absolute calibration method are discussed and analyzed in this paper. In this work, the long-lived fission product (137)~Cs is demonstrated as the best BU indicator in the HTR-10, whereas the inner-calibrating source method using the ratio of the amounts of (134)~Cs to (137)~Cs is not suitable. The BU value of a fuel element is proportional to the intensity of (137)~Cs gamma-ray and independent on the irradiation history of the fuel element, except for a small correction term related to the radioactive decay of (137)~Cs. The efficiency of the measurement system is calibrated by using a (137)~Cs standard source embedded into the center of a graphite sphere with the same size and the same graphite material as the fuel element, which was located at the measurement position of the fuel sphere, to eliminate the possible systematic errors from the measurement system. The difference in geometry and self-absorption between the BU measurement and the calibration measurement is corrected by applying the MCNP simulation. The error sources of the calibration results are analyzed, in which the uncertainty of the source activity (~5%) is found to dominate. The other major error sources include the fluctuation of the uranium loading in the fuel elements, the errors of the nuclear data, the counting errors of the detector, and thecorrection procedure for the detection efficiency. More than 1,900 fuel elements discharged from the HTR-10 have been measured by far, and the BU values of these elements spread in the range from 8.4±0.5 GWD/t to 20±1.0 GWD/t, where the relative errors of the burn-ups consist of the calibration errors about 5.2% and the counting errors around the order of 1%. The behavior of the measured burn-ups has been discussed qualitatively.
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