1. Introduction
With the development of society and economy, the shortage of energy is becoming more and more serious. Therefore, the sustainable development of energy has become the focus of much of the world. An efficient, clean, and economic energy, nuclear energy plays an important role in the field of sustainable energy [
1], and the high-temperature gas-cooled reactor (HTGR) is one of the preferred reactors for the fourth generation nuclear power systems in the current international nuclear energy field [
2]. China has been working on HTGRs since the 1970s [
3]. The Institute of Nuclear and New Energy Technology of Tsinghua University built a 10 MW pebble-bed high-temperature gas-cooled experimental reactor (HTR-10). This study is mainly based on the HTR-10, which is still operated by this university.
The HTGR has the characteristics of non-stop refueling and fuel element recycling [
4,
5]. The burn-up measurement system of the reactor uses a high-purity germanium (HPGe) detector for nondestructive on-line measurement of fuel element burnup. The result of the measurement determines the disposition of the fuel element, that is, to unload it as spent fuel or return it to the core [
6]. If the measured burnup is incorrect, and spent fuel is recycled back into the core, the fuel cladding material can be damaged and increase the risk of radioactive material leakage [
7,
8,
9,
10]. In contrast, if the fuel has not yet reached the discharge burnup value, and it is discharged as spent fuel, this leads to increased cost and nuclear fuel waste [
11]. Thus, the accuracy of burnup measurement is very important for the safety and economy of an HTGR.
To improve the accuracy and precision of the HTGR burnup measurement system, scholars all over the world have been carried out a large amount of researches. These researches are mainly on the geometric structure of the collimator, the deviation from the center of the fuel element, the attenuation factor of the measurement system, the detection limit of the detector and the shielding efficiency, and the effect of fuel element cooling time on the burnup [
12,
13]. However, there is currently no research on the application of anticoincidence technology to burnup measurement.
The HTR-10 in China uses a burnup measurement system based on an HPGe detector to measure γ-ray activity from Cs-137 [
14]. However, the HTR-10 has intermittent operation, short operation times, and long shutdown periods; the burnup of two fuel elements with the same activity may be different. This leads to difficulties in calculating the burnup of the fuel elements by measuring only the activity of Cs-137. It is necessary to measure additional radionuclides to improve the burnup measurement results. To solve this problem, this study proposes to add anti-coincidence measurement technology to the original burnup measurement system. The technology uses a common bismuth germanium oxide (BGO) crystal and plastic scintillator as an anticoincidence detector to reduce the Compton plateau of the γ-ray spectrum [
15,
16,
17]. This can make the measurement of some low-activity nuclides possible and at the same time improve the accuracy of Cs-137 detection. The design was developed through Monte Carlo simulation [
18,
19], which provided an important theoretical reference for the construction of the new burnup measurement system.
2. Materials and Methods
The burnup measurement system has five main parts: elevator, collimator, sealing flange, lead chamber, and HPGe detector (
Figure 1) [
20]. Measurement begins after the fuel element is raised to the elevator. After being attenuated by the elevator pipe and sealing flange, the γ-rays pass through the collimator to the HPGe probe. The counts captured by the probe are analyzed for the gamma spectrum using GammaVision and Genie-2000 spectroscopy software to obtain the required nuclide information, which determines the burnup online. Fuel element with burnup greater than the burnup limit is discharged as spent fuel, and fuel with burnup less than the burnup limit is recycled back into the core.
The original burnup measurement method was to calculate the burnup by measuring the activity of Cs-137 in the fuel element, because there is a one-to-one correspondence between the activity of Cs-137 and the fuel element burnup, as shown in Equation (1) [
21].
where
is the activity of Cs-137,
and
are decay constant of Cs-137 and fission yield,
is the mass of heavy metal (unit: g), and
is U-235 in one fission to release the energy of 197 MeV.
is measuring time, and
is a media time.
As discussed in the previous section, intermittent operation of HTR-10 means that the radioactive nuclides (including Cs-137) in some fuel spheres decay during long shutdown periods. This reduces the activity of the nuclide but does not change the burnup of the fuel. (These problems will also exist for the larger HTR-PM modules currently under construction.) This leads to a situation where two elements can show the same activity at the time of burnup measurement but have an actual burnup that is different, causing inaccurate results for judging burnup. To solve this problem, we need to understand the history of fuel element burnup, which tells us how many cycles the fuel elements have experienced and the specific burnup process during operation. To understand the burnup history of fuel elements, it is necessary to measure other nuclides, such as Co-60, in the fuel for supplementary analysis.
The anticoincidence measurement system developed in this study consists of a main detector and an annular detector. During measurement, the γ-rays emitted by radionuclides hit the HPGe detector to generate pulse signals, and the scattered photons escaping from the main detector will enter the peripheral anticoincidence detector and generate anticoincidence pulses. If both the primary detector and the anticoincidence detector output a signal at the same time, the signal pulse is not recorded. The signal pulse is recorded only when the main detector has outputs. In this way, because the signals generated by escaping photons, such as Compton photons, are not recorded, the Compton plateau is greatly reduced by anticoincidence, which improves the nuclide measurement accuracy. The working principle of the system’s anticoincidence measurement process is shown in
Figure 2.
4. Discussion
The results in
Section 3 determined the wall and top thickness parameters that optimized the P/C effects of the two annular detectors, with a diameter of 260 mm and a length of 260 mm for the scintillator and a diameter of 210 mm a length of 140 mm for the BGO detector. The P/C of the burnup measurement system was simulated without an anticoincidence detector. It was found that the P/C was around 69, as shown in
Table 5. According to the data in
Table 4 and
Table 5, after adding the BGO detector, the P/C of the system increased by 685.
Figure 7 shows the anticoincidence effect diagram of the same spectrum with and without the annular BGO detector. As can be seen from the
Figure 7, when the BGO detector was present, the Compton plateau for γ-rays was greatly reduced, and the peaks of the γ-ray spectrum were much more obvious, which shows that, after adding anticoincidence technology, detection performance of the burnup measurement system improved significantly.
4.1. Comparative Analysis of Experimental Results and Simulation Results
To verify the reliability of the simulation, the simulated data and the data measured by the HTR-10 burnup measurement system were compared, as shown in
Figure 8. As can be seen in the figure, the Compton plateau for counts of the two spectra is slightly different because the actual measurement is far more complex than the simulation. The actual measurement environment contains natural radionuclides and other radioactive materials, and the effects of these conditions cannot be accurately simulated by the Geant4 software. Additionally, the peaks in the simulated spectrum are in good agreement with the actual measured peaks of the energy spectrum, which also proves that all simulations performed in this study are accurate and reliable.
4.2. Statistical Error Analysis of Simulated Data
The number of output pulses obtained from radiation measurement is a random variable that follows the Poisson distribution. Therefore, data measured under the same conditions may be completely different. As the simulation run-time approaches infinity, the arithmetic mean value of the experimental value will tend to the mathematical expectation, which is not possible in practice. In fact, we generally regard the arithmetic mean of finite time (usually once) as a real “mathematical expectation,” which leads to error. This error is called statistical error, and it is a special error in the measurement of radiation because of the statistical nature of radiation measurement. In this study, the peak area errors and the background count errors of Co-60 γ-rays were calculated using different shape parameters, and the results are shown in
Table 6. From the data in
Table 6, we can see that the statistical error range of γ-rays for different geometries was between 0.53 and 1.40%. These errors are small, indicating again that the simulated data in this paper are accurate and reliable.