A comparative study has been conducted to find out how design approximations and simulation methods of a prismatic-type fuel block of a high-temperature gas-cooled reactor (HTGR) may affect the calculation accuracy of neutronic characteristics of fuel assemblies.

To study the impact, a detailed three-dimensional computational model of a typical fuel block including fuel compacts, burnable absorber compacts, and coolant passages was developed. Changes in neutronic characteristics in the process of fuel assembly irradiation were calculated. The burnup was analyzed based on the SCALE 6.2.4 software package using a calculation module implementing the Monte Carlo method with a multigroup library of cross-sections on the basis of ENDF/B-VII.1 files of assessed nuclear data and the ORIGEN burnup analysis module included in this package.

Different ways of modeling fuel compacts and burnable absorber compacts have been considered: using a built-in tool (DOUBLEHET cell type), by specifying fuel particles in the graphite matrix, and their combination. The calculations were made using the 252-group library of constants except for the option in which fuel compacts and burnable absorber compacts were simulated explicitly by particles in the graphite matrix. In the latter case, a library with a pointwise (CE) representation of cross-sections was used. A series of calculations were also made to assess the way computational statistic parameters affect the results.

The results confirm correct operation of the SCALE complex built-in tool, i.e. cells with the DOUBLEHET-type double heterogeneity, and its prospective use to calculate neutronic characteristics of HTGR fuel. The calculations have also shown that it is acceptable to model burnable absorber compacts both by setting a DOUBLEHET-type cell and explicitly by particles in the graphite matrix. In general, the calculation results for these options agree quite well, within 1-2%, with the direct calculation using the pointwise library of cross-sections.

Based on the computational statistic parameters, it may be recommended to set at least 200,000 histories and the number of particles in a generation or the number of generations should be at least 250.

high-temperature gas-cooled reactor, double heterogeneity, burnup, standard deviation, Monte Carlo, fuel particle, SCALE 6.2.4

Due to their intrinsic safety features and the capability to produce high-grade heat and/or generate high-efficiency electric energy, high-temperature gas-cooled reactors represent a promising trend in nuclear power evolution. A key feature of current HTGRs, as compared with other reactors, is the use of fuel based on particles with a multilayer heat-resistant ceramic coating contained in spherical fuel elements or in fuel compacts and graphite blocks. Resonance self-shielding of microscopic cross-sections manifests itself both on fuel particles and on fuel elements. This requires dedicated calculation procedures and codes that take into account the double heterogeneity effects of the HTGR fuel.

The most precise codes for simulation and calculation of radiation transport in complex geometries are codes based on Monte Carlo methods. These allow reducing the number of approximations with respect to the geometry described and the models of neutron interactions with fuel and moderating compositions. A single FA model is used in this study to investigate the capabilities of the SCALE 6.2.4 package (Wieselquist et al. 2020b) as regards the influence of computational statistics parameters and the method for describing the heterogeneous structure of fuel compacts (FC) and burnable absorber compacts on the FA neutronic performance in the process of burnup.

As shown by the data in Table 1, a detailed 3D calculation model of an FA was developed using the SCALE geometry construction tools. The FA cross-section is presented in Fig. 1.

Figure 1. 

FA model.

The following options have been considered for defining fuel and burnable absorber particles in compacts:

• Fuel and burnable absorber compacts were simulated using tools for defining a double-heterogeneity cell (DOUBLEHET cell type);
• Fuel compacts were simulated using the DOUBLEHET cell, and burnable absorber compacts were simulated explicitly by boron carbide particles in a graphite matrix.
• Fuel and burnable absorber compacts were simulated explicitly by particles.

A fictitious concentration of the fissionable material needs to be defined for the code operation in option 1. For simulation in explicit form, the particles inside the graphite matrix were arranged in a regular square lattice (see Fig. 1). Studies into the random (non-uniform) distribution of particles inside the graphite matrix are presented, e.g., in She et al. 2015.

It was required further to select control sequences and computational models of the SCALE 6.2.4 code. An infinite FA lattice with a mirror boundary condition was calculated. In a general form, the calculation methodology was as follows:

1. A library of constants, including single-group microscopic cross-sections for the burnup calculation, was prepared using the TRITON control module (Jessee et al. 2020) in the T‑DEPL‑1D sequence (a simple multi-region cell in the form of a fuel particle) and in the T6-DEPL sequence (a prismatic fuel block). The T6-DEPL sequence is based on the KENO-VI calculation module used to solve the Monte Carlo transport problem. The sequences make it possible to obtain a library of constants for each material in each burnup step;
2. A neutron spectrum in the process of burnup was calculated using a 252‑group library, including neutron data based on the ENDF/B-VII.1 evaluated nuclear data files (Chadwick et al. 2011). We shall note that no library with a pointwise (CE) representation of cross-sections can be defined for the DOUBLEHET-type double-heterogeneity cells;
3. The resonance self-shielding of microscopic cross-sections was calculated using the CENTRM transport module that calculates the energy-continuous (CE) neutron spectrum used as a weight function (DOUBLEHET cell type). And a white boundary condition was used on the right-hand fuel particle and fuel element cell boundary;
4. Burnup was calculated using the ORIGEN isotope kinetics module (Wieselquist et al. 2020a). The TRITON calls the ORIGEN for defining the changes in the nuclide inventory of the composition‘s materials in each time step based on the obtained space and energy distribution of neutron flux, multi-group microscopic cross-sections, and concentrations and volumes of materials. The ORIGEN is responsible for normalization and preparing of single-group microscopic cross-sections, calculates the burnup, as well as the cooling mode for determining new concentrations of nuclides used at the next calculation stage.

A library with a pointwise (CE) representation of the SCALE 6.2.4 ce_v7.1 cross-sections was used in option 3 in which fuel and burnable absorber compacts were simulated explicitly by particles in the graphite matrix.

Specific to calculations based on the Monte Carlo statistical method is that the accuracy of calculated characteristics depends on the number of the neutron histories played. A series of calculations was undertaken by varying the number of neutrons per generation (npg) and the number of generations (gen) to estimate the influence of statistics parameters on the calculation accuracy. Definition option 1 (DOUBLEHET cell type) was used to estimate the influence of the computational statistics parameters on neutronic performance. The obtained results are presented in Table 2 and in Figs 2–4.

Figure 2. 

Multiplication factor SD value as a function of irradiation time for different computational statistics parameters.

Figure 3. 

SD value for the number of fissions as a function of irradiation time for different computational statistics parameters.

Figure 4. 

SD value for the number of absorptions as a function of irradiation time for different omputational statistics parameters.

It may be noted from the presented information that the number of neutrons per generation (npg) and the number of generations (gen) affect directly the calculation accuracy, and the total number of the neutron histories played has direct effect on the stability of statistics. On the whole, it can be recommended that not less than 200 000 histories should be played to culcalate a similar composition using the SCALE code, the number of particles in the generation or the number of generations to be not less than 250. Parameters of 1000 particles per generation and 1000 generations were used for further calculations.

The calculation results for the fuel and burnable absorber particle definition options are presented in Table 3 and in Figs 5–8. The counting time was determined with equal conditions: one and the same computational server and one and the same number of computational nodes for all problems. Paralleling based on the MPI technology was used for this.

Figure 5. 

Multiplication factor as a function of irradiation time.

Figure 6. 

Multiplication factor SD value as a function of irradiation time.

Figure 7. 

SD value for the number of fissions as a function of irradiation time.

Figure 8. 

SD value for the number of absorptions as a function of irradiation time.

The results obtained confirm that the SCALE code’s built-in tool (DOUBLEHET-type double-heterogeneity cells) operates correctly and can be used to calculate the HTGR fuel neutronics. The calculations have also shown that BA compacts can be reasonably simulated both using DOUBLEHET-type cells and by particles (in explicit form). On the whole, the calculation results for the two first options agree well enough (in the limits of 1 to 2%) with the direct calculation using a pointwise library of cross-sections.

A methodology was developed and computational studies were undertaken to investigate the influence of the methods used to simulate the HTGR fuel block in the SCALE 6.2.4 code on its neutronic performance in the process of burnup. With DOUBLEHET cells used for fuel compacts, the values obtained agree with the results of the HTGR fuel block direct simulation using a pointwise library of cross-sections in the limits of 1 to 2 %. A series of calculations was also undertaken to estimate the influence of the computational statistics parameters on the results. It can be recommended that not less than 200 00 histories should be defined for calculating a similar composition using the SCALE code, the number of particles in the generation or the number of generations to be not less than 250.

The presented results can be helpful to users of the SCALE 6.2.4 and other Monte Carlo codes.