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 (k_eff), 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 the 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. 1Full-screen View

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

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. 2Full-screen View

(Color online) Geometric structure of a fuel pebble

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.

In addition, microscopic pores in the 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

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 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 k_eff 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.