Corresponding author: Svetlana G. Usynina (
Academic editor: Georgy Tikhomirov
A comparative study has been conducted to find out how design approximations and simulation methods of a prismatictype fuel block of a hightemperature gascooled reactor (HTGR) may affect the calculation accuracy of neutronic characteristics of fuel assemblies.
To study the impact, a detailed threedimensional 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 crosssections on the basis of ENDF/BVII.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 builtin tool (DOUBLEHET cell type), by specifying fuel particles in the graphite matrix, and their combination. The calculations were made using the 252group 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 crosssections 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 builtin tool, i.e. cells with the DOUBLEHETtype 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 DOUBLEHETtype cell and explicitly by particles in the graphite matrix. In general, the calculation results for these options agree quite well, within 12%, with the direct calculation using the pointwise library of crosssections.
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.
Due to their intrinsic safety features and the capability to produce highgrade heat and/or generate highefficiency electric energy, hightemperature gascooled 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 heatresistant ceramic coating contained in spherical fuel elements or in fuel compacts and graphite blocks. Resonance selfshielding of microscopic crosssections 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 (
As shown by the data in Table
Key characteristics of the computational model (
Characteristic  Value 

Fuel  
– fuel composition material  UO_{2} 
– density, g/cm^{3}  10.4 
– ^{235}U enrichment, wt %  15 
Fuel block  
– width across flats, cm  360 
– height, cm  800 
– triangular pitch, cm  1.9 
– fuel compact hole diameter, cm  1.27 
– coolant hole diameter, см  1.27 
Fuel compacts  
– diameter, cm  1.25 
– height, cm  5 
– number of fuel particles per compact  4884 
Fuel particles  
– kernel radius, cm  0.02 
– PyC buffer layer thickness/density, cm/g/cm^{3}  0.0095/1.0 
– PyC inner layer thickness/density, cm/g/cm^{3}  0.004/1.9 
– SiC layer thickness/density, cm/g/cm^{3}  0.0035/3.2 
– PyC outer layer thickness/density, cm/g/cm^{3}  0.004/1.8 
Burnable absorber compacts  
– diameter, cm  1.25 
– height, cm  5 
– number of B_{4}C particles per compact  15618 
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 doubleheterogeneity 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.
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:
A library of constants, including singlegroup microscopic crosssections for the burnup calculation, was prepared using the TRITON control module (
A neutron spectrum in the process of burnup was calculated using a 252‑group library, including neutron data based on the ENDF/BVII.1 evaluated nuclear data files (
The resonance selfshielding of microscopic crosssections was calculated using the CENTRM transport module that calculates the energycontinuous (CE) neutron spectrum used as a weight function (DOUBLEHET cell type). And a white boundary condition was used on the righthand fuel particle and fuel element cell boundary;
Burnup was calculated using the ORIGEN isotope kinetics module (
A library with a pointwise (CE) representation of the SCALE 6.2.4 ce_v7.1 crosssections 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 (
Influence of computational statistics parameters on the neutronic performance calculation accuracy

gen  Number of histories played  Burnup step average value of standard deviation (SD), %  


Number of fissions  Number of absorptions  
100  100  10000  0.803/1.051  0.586  0.555  0.271 
100  250  25000  0.797/1.054  0.369  0.353  0.170 
250  100  25000  0.794/1.055  0.374  0.358  0.174 
100  500  50000  0.797/1.057  0.248  0.248  0.122 
500  100  50000  0.796/1.061  0.268  0.245  0.123 
250  200  50000  0.796/1.062  0.256  0.251  0.126 
1000  200  200000  0.795/1.055  0.125  0.126  0.062 
500  400  200000  0.796/1.053  0.122  0.125  0.062 
200  1000  200000  0.796/1.053  0.118  0.125  0.061 
1000  400  400000  0.795/1.054  0.088  0.087  0.043 
2000  200  400000  0.794/1.055  0.092  0.090  0.044 
1000  1000  1000000  0.795/1.055  0.055  0.056  0.027 
Multiplication factor SD value as a function of irradiation time for different computational statistics parameters.
SD value for the number of fissions as a function of irradiation time for different computational statistics parameters.
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 (
The calculation results for the fuel and burnable absorber particle definition options are presented in Table
Influence of definition options for fuel and burnable absorber particles on calculation results
Option No.  1  2  3  

doublehet/ doublehet  doublehet/ particles  particles/ particles  
Counting time, h  3.8  3.4  38.5  
Group structure  252  252  CE  
K_{inf} as of radiation start / end time  0.795/1.055  0.797/1.042  0.799/1.041  
Relative deviation of 
Irradiation start  0.4  0.3  – 
Irradiation end  1.3  0.1  –  
Irradiation step average value  1.4  0.1  –  
Relative deviation of actinide and fission product content as of irradiation end from option 3, %  ^{235}U  0.16  0.17  – 
^{239}Pu  2.24  0.21  –  
^{240}Pu  0.49  0.22  –  
^{241}Pu  1.25  0.45  –  
^{241}Am  1.57  0.39  –  
^{244}Cm  1.46  0.81  –  
^{85}Kr  0.12  0.06  –  
^{90}Sr  0.15  0.07  –  
^{137}Cs  0.02  0.00  –  
^{135}Xe  1.07  0.29  – 
Multiplication factor as a function of irradiation time.
Multiplication factor SD value as a function of irradiation time.
SD value for the number of fissions as a function of irradiation time.
SD value for the number of absorptions as a function of irradiation time.
The results obtained confirm that the SCALE code’s builtin tool (DOUBLEHETtype doubleheterogeneity 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 DOUBLEHETtype 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 crosssections.
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 crosssections 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.
Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2024, n. 1, pp. 159–169.