Corresponding author: Daria V. Panova (
Academic editor: Yury Kazansky
The subject of constant support development is currently becoming increasingly important in connection with the national strategy of transition to a closed nuclear fuel cycle. At the same time, the importance of the tasks of refining calculation models and minimizing methodological, statistical, and constant errors is increasing. In this connection, the idea of creating a universal system of constants describing with equal accuracy both uranium loading and loading with mixed oxide uraniumplutonium fuel and the possibility to perform on its basis both precision Monte Carlo calculations (data format – ACE) and multigroup calculations (formats – ABBN and ANISN) was laid in the basis of this work. In this paper we analyze the freely available libraries of evaluated nuclear data in order to justify the choice of source files for the formation of a new system of group constants for neutronphysical calculations of fast reactor cores, describe the process of formation of a new library of reactor constants, and verify the obtained system on computational test models of BN800 reactor and critical systems. The process of formation of the new system of group constants included selection of initial neutron data files, updating of data tables of basic neutron crosssections, selfshielding factors and Doppler coefficients, as well as data on fission spectra for the main fuel nuclides. The methodological component of the error for test models of the BN800 core was evaluated. Using the ABBNRF22 system of group constants it was possible to estimate the correction in the 299 groups calculation, which amounted to 0.3%. Previously, when using the ABBN93 library, there was no such possibility due to the lack of continuity between the files of evaluated neutron data and the group constants used.
Design of and computational support for nuclear power plants require estimating, mandatorily, the uncertainty of the design parameters. One way to minimize this uncertainty is to use reliable and proven set of constants.
Computational studies into the neutronic performance of fast neutron reactors are based on using threedimensional diffusion codes, such as JARFR (
Increased productivity and reliability of computer equipment over the past decade have made it possible to calculate a reactor using complex detailed models in codes based on the Monte Carlo method. The most common of these are MCNP5 (
Cross verification based on all of the above codes, as well as estimating the methodological component of the calculation error require using a unified set of constants, which is currently provided via the CONSYST constant preparation system (
Currently, the composition of effective fast reactor cores has begun to change. Thus, in the autumn of 2022, the BN800 reactor reached criticality following the tenth refueling with a core, which had a 93% share of fuel assemblies (FA) with uraniumplutonium. The eleventh cycle between refueling is usually looked upon as the initial interval of the BN800 operation fully loaded with mixed oxide uraniumplutonium fuel. It needs to be noted that this is the first experience of commercially operating a reactor core with such type of fuel. It is planned that minor actinides will be added to the fuel composition at the next stage in the framework of the national strategy for closing the nuclear fuel cycle. As a result, the share of plutonium and the mass of minor actinides in the core will increase. This means that the established balance of the constant set will move into the increased uncertainty area. Fig.
Change in
The increase in the share of plutonium in the core has led to the constant error scatter increased to ~ 1% in the
In this connection, it is essential to develop a new version of the group library of constants, capable to describe equally accurately both the uranium and mixed uraniumplutonium fuel loads in reactor cores. It will be reasonable to introduce the new constant library, similarly to the existing ABBN93 library, in codes used by different organizations for the fast reactor calculations.
To form a unified verification, in terms of calculating uranium and plutonium systems, one needs to analyze the currently available libraries of evaluated nuclear data. The following versions of evaluated neutron data libraries were used for verification calculations: ENDF/BVII.1 (
The ROSFOND2010 data library accumulates current estimates of neutron crosssections for more than 680 primary and secondary materials (nuclides). It contains complete sets of neutron data for all stable periodic system elements (for individual isotopes as a rule). A complete set means a set of data sufficient to take into account the interaction of neutrons with nuclei in the process of the neutron propagation in the medium.
The ROSFOND2020.2 estimates for fuel and structural materials were updated and taken from the CIELO (Collaborative International Evaluation Library Organization) project results (
The verification of the above constant libraries was conditionally divided into two stages, including verification based on a set of benchmark models from the ISCBEP Handbook (
The benchmark models were calculated at the initial verification stage. The models were selected based on the extent of consistency with real reactor systems in terms of the composition and characteristics of the energy spectrum. They were conditionally divided into two groups.
Compact metal assemblies (
To verify nuclear data and methods for preparing constants, critical assemblies were used with characteristics more consistent with real fast reactor systems (
Test models of the BN800 critical states were used for the second verification stage. Refueling cycles (8 through 11) were selected for the BN800, which characterized the 100% increase in the share of mixed uraniumplutonium fuel.
All test models were developed in the framework of the BNcode (
To verify the set of constants, a series of calculations was undertaken using benchmark models based on the libraries described above. Figs
Discrepancies in the criticality calculation results for the
Discrepancies in the criticality calculation results for the
The following conclusions can be made from the presented calculated data of the constant set verification for the series of benchmark models:
the deviation of the calculated values from experimental data does not exceed 1% for all libraries of evaluated nuclear data;
the most accurate description of the selected critical systems was provided by the ROSFOND2020.2 library: the average deviation for the CMA systems was –0.06 ± 0.10%, and the average deviation for the RS systems was 0.05 ± 0.14%.
To verify the set of constants using a set of the BN800 test models, a series of calculations was undertaken based on the above libraries.
Fig.
Changes in
The following conclusions can be made based on the reactor neutronic performance calculation results:
the results of the BN800 calculations using the ROSFOND2010 and JENDL4.0 systems of constants have shown a trend towards a decreased/increased criticality value with mixed oxide uraniumplutonium fuel loaded into the core;
the results of the BN800 calculations using the ROSFOND2020.2 library of constants describe the criticality in the event of transition to mixed oxide uraniumplutonium fuel with an accuracy of ~ 0.2%.
Therefore, it has been recommended that the ROSFOND2020.2 files of evaluated neutron data should be used to form a group library of constants and its further implementation in practical computational support for the Beloyarsk NPP units.
The process of forming a new system of group constants consists in establishing a library of 28group and 299group constants of a versatile format based on the ROSFOND2020.2 neutron data.
The data in this constant system should be presented in a format with an increased accuracy, which has the same content as the ABBN93 format.
The process of forming a new group library of neutron data in a format with an increased accuracy was divided into a number of stages:
compiling the list of nuclides from the ROSFOND2020.2 library files required for calculating the neutronic performance of fast neutron reactors and justifying safety;
preparation of the key neutron crosssections for 28 and 299 groups;
preparation of selfshielding factors and Doppler coefficients for the same group breakdown;
formation of a constant system in a format with an increased accuracy;
conversion of the library to a binary form.
At the initial stage, nuclides were selected from the ROSFOND2020.2 library files, the data of which are required in the process of calculating the key neutronic characteristics of operating reactors:
fuel nuclides (^{235}U, ^{238}U, ^{238}Pu, ^{239}Pu, ^{240}Pu, ^{241}Pu);
structural materials (Al, Cr, Fe, Mo, Nb, Ni, Zr);
coolant materials (Nd and Pb).
The next stage used the NJOY program (
Further, after the ROSFOND2020.2 files were processed using the NJOY program, two types of files were formed (for the 28 and 299group breakdowns). This step formed files containing tables of the key neutron crosssections and files containing data on selfshielding factors (MF = 4/304) and Doppler coefficients (MF = 5/305). The files were prepared at temperatures of 300 K, 900 K, and 2100 K in a fast spectrum approximation. The output files were integrated then on a group basis.
Tables MF = 5/305 are presented for the key and reactor nuclides, the contributions of which to the Doppler effect are decisive.
Data for natural mixtures have been obtained for those materials where possible, including Fe, Cr, Ni, Pn, Mo, and Zr. The process of obtaining constants for natural mixtures is based on the calculation of pointwise data for each stable isotope (
The process of convoluting neutron data of stable isotopes into microconstants for a natural mixture has two constituents.
Initially, data with an additive property are convoluted which include interaction crosssections and their energyangular dependencies.
This is followed by convoluting data which do not have an additive property: these include data on the resonant selfshielding of crosssections, the socalled Bondarenko factors, or selfshielding factors.
Based on the list of the nuclides selected from the ROSFOND2020.2 and ROSFOND2010 neutron data libraries, a new system of group constants, called ABBNRF22, was formed and converted to a binary form.
The criticality of the BN800 test model was calculated using the MMKKENO code as of the refueling cycle (RC) start time for the “cold” reactor state between refueling cycles 8 and 11. The statistical error was ± 0.00003.
Fig.
Changes in
The methodological component of the error was estimated for the test model of the BN800 reactor core for the case of its conversion to a mixed oxide uraniumplutonium fuel load (cycles 8 through 11). The calculation was undertaken using the design ABBN93 library of constants and a new system of group constants (ABBNRF22).
The criticality value was calculated in a P_{5} approximation using the MMKKENO code (299 groups) for a homogeneous test model and a heterogeneous test model. The statistical error of the
Table
TRIGEX
RC 8  RC 9  RC 10  RC 11  

ABBN93  ABBNRF22  ABBN93  ABBNRF22  ABBN93  ABBNRF22  ABBN93  ABBNRF22  


TRIGEX_6p  0.9821  0.9844  0.9817  0.9840  0.9802  0.9823  0.9814  0.9834  
Methodological allowance, %  
TRIGEX_1p  1.2  1.2  1.2  1.3  1.3  1.3  1.3  1.3  
MMKК (hom.)  0.7  0.6  0.7  0.7  0.7  0.7  0.6  0.6  
MMКK (het.)  1.4  1.3  1.5  1.5  1.6  1.5  1.5  1.4  
MMКC (het.)  –  1.6  –  1.8  –  1.8  –  1.7 
Based on the results presented in the table, conclusions can be made on the methodological allowances for the diffusion calculation:
the kinetic allowance of the diffusion calculation, along with the allowance for the 299group calculation, was about +0.7%;
the heterogeneous allowance changes as the result of conversion to mixed oxide uraniumplutonium fuel and was +0.7% for the conversion region, and +0.9% for the core with MOX fuel;
the allowance for the 299group calculation does not depend on the type of fuel used and is about +0.3%.
The complete methodological allowance for the diffusion calculation was +1.6% for the conversion region, and 1.7% for the core with mixed oxide uraniumplutonium fuel.
Based on the results of the computational studies, the following should be noted:
the change in the methodological allowance of the diffusion calculation for the case of conversion to mixed oxide uraniumplutonium fuel is not significant;
the allowances introduced to the design ABBN93 library of constants and the new system of group constants (ABBNRF22) are consistent;
using the ABBNRF22 system of group constants made it possible to estimate the allowance associated with the 299group calculation (0.3%); it was not possible to do this when the ABBN93 library was used due to the lack of continuity of the evaluated neutron data files and the group constants used;
using a solution with one point per assembly in the diffusion calculation led to a +0.4% smaller methodological allowance.
In connection with the BN800 conversion to a full load with mixed uraniumplutonium oxide fuel and plans for minor actinides to be involved in the fuel cycle, the resultant balance in the set of constants shifts to the increased uncertainty region, this leading to an increase in the error’s constant component.
To minimize the methodological and constant errors, a unified system of group constants, ROSFOND2020.2, was developed based on the ABBNRF22 evaluated neutron data files, which describes equally accurately both the uranium load and the load with mixed oxide uraniumplutonium fuel. The process of forming a new system of group constants included updating data in the tables of the key neutron crosssections, selfshielding factors and Doppler coefficients, as well as data on the fission spectra for the key fuel nuclides.
The key advantage of the ABBNRF22 constant library, as compared with its earlier counterpart (ABBN93), is as follows:
current estimates of neutron crosssections are used for fuel and structural materials;
299group data on the crosssections are available for all nuclides contained in the library (there are only 16 nuclides presented in the ABBN93 in a 299group breakdown);
there are neutron data for both isotope mixtures and mixtures (the ABBN93 does not include data for individual isotopes of structural materials);
due to the continuity of the evaluated neutron data files and the prepared group constants, it was possible to estimate correctly the methodological component of the error associated with the group representation of neutron crosssections; it was not possible altogether to do this in the ABBN93 constant system;
it is possible to promptly add other neutron data estimates to the ABBNRF22 group library of constants;
there is a matrix fission spectrum for each fuel nuclide.
In the process of the study, the methodological component of the error for the BN800 core test models was estimated as part of the calculation with a new system of group constants, which has shown the following:
the change in the methodological allowance of the diffusion calculation for the case of conversion to mixed oxide uraniumplutonium fuel is not significant;
the allowances introduced to the design ABBN93 library of constants and the new system of group constants (ABBNRF22) are consistent;
using the ABBNRF22 system of group constants made it possible to estimate the allowance associated with the 299group calculation (0.3%); it was not possible to do this when the ABBN93 library was used due to the lack of continuity of the evaluated neutron data files and the group constants used;
using a solution with one point per assembly in the diffusion calculation led to a +0.4% smaller methodological allowance.
It is planned to update further other neutron data estimates for the remaining sections. The obtained version of the ABBNRF22 group constant system is planned to be added to the design codes and to the GEFESTM unified coupled code for the computational support of the BN600 and BN800 reactors at the Beloyarsk NPP.
Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2024, n. 2, pp. 155–169.