1 Introduction

The high-temperature reactor pebble-bed module (HTR-PM) [1] is the world’s first 200 MWe modular pebble-bed high-temperature gas-cooled reactor (HTGR) in a demonstration power plant with the safety features of fourth-generation nuclear energy systems. It was designed by the Institute of Nuclear and New Energy Technology (INET), Tsinghua University, based on technologies and experiences obtained from the 10 MW high-temperature gas-cooled test reactor (HTR-10) [2].

As one milestone of the HTR-PM project, the first criticality experiment is scheduled for the latter half of 2021. According to the design, the first criticality of the HTR-PM will be reached by loading a mixture of fuel pebbles and graphite pebbles into the core in an air atmosphere at ambient pressure. The critical loading height, or the number of mixed pebbles, will be experimentally obtained.

The HTR-PM first criticality experiment provides a good opportunity to validate computer codes for analyzing the physics of HTGR reactors. At the beginning of the 2000s, prior to the HTR-10 first criticality, INET published the HTR-10 first criticality benchmark and invited the international reactor physics community to submit prediction calculations [3]. Although the result predicted by INET was reportedly very close to the experimental result [4], the overall benchmark exercise yielded a deviation of ± 4% in the effective multiplication factor (keff), which indicates that reactor physics analysis in pebble-bed HTGRs is far from a well-established art [5]. Since the HTR-PM is a scaled-up and developed version of the HTR-10, it has particular value for reactor physics analysis in large commercial pebble-bed HTGRs.

The prediction calculation of the HTR-PM first criticality was recently performed using PANGU [6], a state-of-the-art computer code developed at INET for pebble-bed HTGR neutronics analyses and fuel cycle simulations. PANGU implements a unique two-step calculation flow scheme with an in-line leakage feedback iteration. In addition, it employs some advanced methodologies and capabilities, such as treatment of mixed-type particles and mixed-type pebbles, neutron streaming correction, control rod homogenization, micro-burnup calculation, and iterative searching of the equilibrium cycle. Because of these features, PANGU can be used for the physical design of both traditional and new conceptual pebble-bed HTGRs.

This paper presents the calculation details of the HTR-PM first criticality, including the input data, numerical results, and uncertainty analysis. Moreover, the detailed model for the HTR-PM first criticality is provided so that all interested researchers in the community can participate in this prediction exercise as soon as possible.

The remainder of this paper is organized as follows. Section 2 describes the detailed model and parameters for calculating the first criticality of the HTR-PM. Section 3 presents the calculation results and uncertainty analysis obtained using PANGU. The discussion and conclusions are presented in Sect. 4.

2 Detailed model and parameters for HTR-PM first criticality

The HTR-PM full-core layout is illustrated in Fig. 1. The core equivalent diameter is 150.275 cm, and the equivalent height is 1100 cm in the full loading state. The pebble-bed core is surrounded by the top, bottom, and side graphite reflectors, which are in turn surrounded by carbon bricks. The control rod channels, absorber ball channels, and cold helium channels are located in the graphite reflectors. An R-Z axial view with detailed dimensions and materials is shown in Fig. 1(a). It should be noted that materials #19 and #46 are reflectors containing void channels, whose detailed structures are shown in Fig. 1(b). The neutron streaming effect [7] should be considered if these reflectors are treated as a homogeneous medium in deterministic codes. Table 1 provides a detailed description and the composition of the materials illustrated in Fig. 1. The impurities in the materials have been converted to the equivalent boron content (EBC) [8], represented by an equivalent density of natural boron.

Fig. 1
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(Color online) Full core layout of the HTR-PM. a Axial view; b Cross-sectional view

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Table 1 Material description and composition
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For simplicity, the cone shape of the core bottom is converted into a cylindrical shape, while preserving the core volume. Prior to performing the first criticality experiment, the core will be filled with graphite pebbles to a height of 6.05 m. In the first criticality experiment, a mixture of fuel pebbles and graphite pebbles, with a ratio of 7:8, will be continuously loaded into the core until the reactor reaches criticality. The volumetric packing density of the entire pebble bed is 0.61.

As shown in Fig. 2, a fuel pebble consists of an outer graphite shell and an inner fuel region comprising coated fuel particles (CFPs) embedded in a graphite matrix. A CFP consists of a spherical fuel kernel of UO2 with multi-layer coatings, namely a low-density pyrolytic carbon (PyC) buffer layer, an inner high-density PyC layer, a silicon carbide (SiC) layer, and an outer high-density PyC layer. The detailed physical parameters of the pebbles and CFPs are listed in Table 2.

Fig. 2
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(Color online) Geometric structure of a fuel pebble

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Table 2 Physical parameters of the fuel pebble and the coated fuel particle
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Because the first criticality experiment will be performed in an air atmosphere, the upper cavity and pebble bed pores should be filled with saturated moist air in the calculation model. The air composition is temperature dependent, as shown in Table 3.

Table 3 Composition of saturated moist air at different temperatures
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In addition, microscopic pores in graphite can absorb water. Thus, the water content of graphite is usually in the order of several hundreds of ppm. The water content of the graphite in the HTR-PM is estimated to be approximately 600 ppm. However, the reflector and the pre-loaded graphite pebbles have been dehumidified before the first criticality experiment; therefore, it is recommended that only the water content of the mixed pebbles should be considered in the calculation.

The input model and parameters introduced above can be used as preliminary benchmarks for the HTR-PM first criticality. The data provided in this paper will enable readers to perform calculations and conduct comparison studies using their own computer codes. The formal HTR-PM first criticality benchmark will be updated after the experiment and will be published as part of the Computational Methods Validation and Benchmarking (CMVB) project of the Very High-Temperature Reactor (VHTR) system in the Generation-IV International Forum (GIF).

3 Numerical results and uncertainty analysis

3.1 Comparison calculation with base conditions

Before performing the prediction calculation, it is necessary to evaluate the deviation of the PANGU code itself. The “base conditions” of the HTR-PM are assumed to be as follows: the reactor is in an air atmosphere, all components of the reactor are at room temperature (20 °C), and the water content of graphite is neglected. Under these conditions, the PANGU code and the RMC Monte Carlo code [9] were used to calculate the keff at different loading heights of mixed pebbles. PANGU uses a 2D R-Z model based on equivalent homogenization schemes that have been thoroughly validated by our previous studies [10, 11]. RMC uses a high-fidelity 3D model with explicit modeling of the detailed geometric structures of the coated fuel particles, pebble beds, and reflector channels. The most recent ENDF/B-VIII.0 nuclear data library [12] was adopted by both codes.

Table 4 lists the keff results calculated by PANGU and RMC; the latter was used as the reference solution. It was found that the PANGU results agree well with the high-fidelity RMC Monte Carlo solution. The differences in keff are generally below 0.15% over a wide range of loading heights. This demonstrates the accuracy of the PANGU code.

Table 4 Variation of keff with different loading heights under base conditions
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3.2 Uncertainty analysis

The HTR-10 first criticality benchmark [5] revealed that there are many uncertainties when analyzing the reactor physics of a pebble-bed HTGR. Consequently, the uncertainty of the HTR-PM criticality calculation, caused by uncertainties in the input data, was investigated.

Starting from the base condition at a loading height of 275 cm, the variation of keff with the change in a single input variable was calculated using the PANGU code. The sensitivity of keff with regard to particular key input variables is summarized in Table 5.

Table 5 Sensitivity of keff to changes in input data
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Noticeably, ENDF/B-VIII.0 was found to underestimate keff by approximately 1.3% compared with ENDF/B-VII.0. Further analysis suggests that this is mainly due to the update of the graphite thermal scattering cross section and the nuclear data of 235U and 238U in ENDF/B-VIII.0. Nevertheless, nuclear data uncertainty does have a significant influence on the criticality calculation of pebbled-bed HTGRs, which conforms to some previous studies [13, 14].

In addition, keff is sensitive to the water content and EBC of graphite. Because the measurement of water content and EBC tends to involve large degrees of uncertainty, these datasets are expected to cause considerable uncertainty in the criticality calculation. In addition, the degree of graphitization can also influence the keff value, which has been studied in our previous work [15].

X-ray photographs show that the actual fuel-zone radius of the fuel pebble is slightly smaller than the nominal value of 2.5 cm, which can lead to a somewhat higher keff in the HTR-PM criticality calculation.

The influence of the reactor temperature on keff was found to be approximately 25 pcm/°C. There are several detectors in the HTR-PM reflector for measuring the temperatures during the first criticality experiment, so that the prediction results can be corrected according to the actual temperatures.

In summary, keff is largely affected by the uncertainties of the input data. For this reason, it is quite challenging, in practice, to perform an accurate criticality prediction for the HTR-PM.

3.3 Predicted critical loading height under design conditions

In this section, PANGU is used to predict the critical loading height of the HTR-PM first criticality using the following “design conditions”: all components of the reactor temperature are assumed to have a temperature of 30 °C, the water content of the mixed pebbles was assumed to be 600 ppm, and the nominal values were used for all input parameters.

The ENDF/B-VIII.0 nuclear data library was adopted for this prediction calculation, although there is no particular reason for choosing ENDF/B-VIII.0 over ENDF/B-VII.0 or some other nuclear data. According to the authors’ experience, using PANGU with ENDF/B-VIII.0 seems to provide better results in simulating the HTR-10 initial criticality and power operation history [16], but it is not certain whether this will hold true for the HTR-PM case.

Table 6 presents the resulting keff values obtained at different loading heights under the design conditions. By interpolating between the heights of 275 cm and 300 cm, a critical loading height of 276.5 cm, corresponding to 105,821 mixed pebbles, can be obtained. Note that there may be differences between the experimental and design conditions. For example, the actual temperature may deviate from the assumed temperature of 30 °C; In such cases, the prediction results will be corrected according to the experimental conditions.

Table 6 keff at different loading heights under design conditions
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4 Conclusion

This work presents the prediction calculations of the HTR-PM first criticality obtained with the PANGU code and provides a preliminary benchmark model with detailed input parameters for the calculation of the first criticality in the HTR-PM.

By using the same input configurations, PANGU exhibits excellent consistency with the high-fidelity Monte Carlo solution, which demonstrates the accuracy of the PANGU code itself.

However, it is clear that the calculated keff is sensitive to the nuclear data and certain key input parameters, and therefore, it is challenging in practice to obtain an “accurate” prediction result that agrees well with the experimental results. This could explain why there were large deviations among the results of different participants in the benchmark exercise of the HTR-10 first criticality.

Under the design conditions of the HTR-PM first criticality and using the ENDF/B VIII.0 nuclear data library, PANGU predicted a critical loading height of 276.5 cm. Considering the uncertainties resulting from the input data, as well as the variations in the actual experimental conditions, some luck is required to achieve a good consistency between the predicted and experimental results.