Corresponding author: Olga N. Andrianova (oandrianova@ippe.ru)
Academic editor: Georgy Tikhomirov
The paper presents the results of a computational analysis of the
Following the main objective of the Organization for Economic Cooperation and Development Nuclear Energy Agency (
Under the auspices of the
The
Based on this benchmark test, a cycle of studies was performed at the JSC “SSC RFIPPE n.a. A.I. Leipunsky” on verification of the ROSFOND/ABBNRF nuclear data (
The proposed computational test is a simplified model of an external MOX fuel cycle system with a simple spherical geometry (Fig.
Computational benchmark test geometry
The ratios of evenodd isotopes of plutonium (^{239}Pu, ^{240}Pu, ^{241}Pu, ^{242}Pu) for the proposed fuel compositions (plutonium vector) correspond to the plutonium vector of MOX fuel used in SFR and LWR plants. The task is set in this way because of the interest in studying the influence of plutonium nuclear properties and characteristics due to changes in the plutonium vector in the PuO_{2} fuel compositions as well as water slowing properties on the critical mass. Table
Composition and geometry of the multiplying systems
















1  3%  17.0  100%  71%  17%  11%  1% 
2  3%  22.5  30%  
3  3%  46.0  12.5%  
4  3%  17.7  100%  64%  23%  10%  3% 
5  3%  24.1  30%  
6  3%  52.5  12.5%  
7  3%  15.0  100%  96%  4%  0%  0% 
8  3%  19.0  30%  
9  3%  40.0  12.5%  
10  1%  17.0  100%  71%  17%  11%  1% 
11  1%  22.5  30%  
12  1%  46.0  12.5%  
13  5%  17.0  100%  71%  17%  11%  1% 
14  5%  22.5  30%  
15  5%  46.0  12.5% 
The benchmark test specification defines the following design characteristics calculated using the ROSFOND/ABBNRF nuclear data library:
Effective multiplication factor, keff
Onegroup integral sensitivity coefficients to keff of all isotopes that make up the fuel compositions;
The a priori constant error in keff due to the uncertainties in covariance nuclear data;
A list of integral experiments selected to adjust the calculated keff predictions;
The a posteriori error in keff obtained with account of the selected integral experiments by adjusting the nuclear data on the basis of the approaches, methods and codes implemented in the INDECS system.
This benchmark test is primarily aimed at verifying methods for determining displacements and errors in the
The a posteriori and a priori constant errors were estimated using the INDEX system of codes and data archives. The basis of computational methods implemented in the INDEX system is the maximum likelihood method (
where
From expression (1), we can obtain the relation for the desired corrections:
and also the expression for the covariance matrix of the parameters
By means of the matrix (
The
Comparison of calculation results for different nuclear data systems





1  0.07%  0.21%  –0.25%  0.21% 
2  –0.01%  0.21%  –0.10%  0.04% 
3  –0.09%  0.07%  –0.12%  –0.06% 
4  0.07%  0.28%  –0.16%  0.21% 
5  –0.02%  0.22%  –0.07%  0.04% 
6  –0.07%  0.07%  –0.13%  –0.06% 
7  0.02%  0.71%  0.36%  0.79% 
8  –0.03%  0.48%  0.34%  0.42% 
9  –0.08%  0.28%  0.21%  0.22% 
10  0.07%  0.18%  –0.26%  0.15% 
11  0.05%  0.18%  –0.11%  –0.04% 
12  0.04%  0.19%  –0.23%  –0.05% 
13  0.06%  0.24%  –0.23%  0.22% 
14  –0.07%  0.15%  –0.02%  0.05% 
15  –0.12%  0.00%  –0.03%  –0.05% 
The spread in the
The analysis of the onegroup sensitivity coefficients showed that the options with large values of coefficients of
Coefficients of
To estimate the a posteriori error of the models under consideration, experiments were selected from the International Criticality Safety Benchmark Evaluation Project (
List of benchmark experiments






1  PST001  16  19  PST032  2, 6, 11. 
2  PST002  1, 7  20  PMF001  1 
3  PST003  1, 5  21  PMF002  1 
4  PST004  3, 5, 6, 13  22  PMF011  1 
5  PST005  1, 9  23  PMF022  1 
6  PST006  2  24  PMF024  1 
7  PST009  3  25  PMF027  1 
8  PST010  1–3, 9, 11  26  PMF029  1 
9  PST011  1, 8  27  PMF031  1 
10  PST012  7–13  28  MST002  2, 3 
11  PST018  1, 5, 9.  29  MST003  4, 7, 9, 10 
12  PST020  3, 5, 8, 9  30  MST004  2, 5, 7. 
13  PST021  1, 3, 4.  31  MST005  2, 3, 4, 7 
14  PST022  1, 2, 3, 8  32  MST006  1 
15  PST023  1, 8, 17, 34  33  MST007  1 
16  PST025  3, 10, 17, 22, 31, 36, 42  34  MST010  1 
17  PST026  3, 16  35  BFS  315, 382, 42, 971, 972, 973, 974, 991, 992, 1011, 1012, 1012А, 1013 
18  IMF007  1 
Based on the covariance matrices of neutron cross sections for the ABBN group library, according to formula (4), the values of the relative a priori constant error in δ
Benchmark a priori δ




1  0.95  0.31  6  0.95  0.33  11  0.81  0.29 
2  0.84  0.32  7  1.16  0.22  12  0.81  0.28 
3  0.90  0.32  8  0.95  0.24  13  0.92  0.33 
4  0.93  0.31  9  0.95  0.22  14  0.89  0.35 
5  0.84  0.32  10  1.01  0.29  15  0.96  0.33 
Based on the experimental data (see Tab.
Summary of benchmark test calculation results
In accordance with the calculation program of the
The maximum deviation in the calculated keff values obtained using different libraries of evaluated nuclear data (ENDF/BVII.0, JEFF3.2, JENDL4.0), in comparison with the results obtained from the ROSFOND library, reaches 0.8%. The a priori error in the calculated keff value, caused by the uncertainty in the nuclear data and calculated using the ABBN covariance matrices data, ranges from 0.8 to 1.2%. Thus, the estimated a priori constant error in keff coincides with the observed spread in the calculated keff values, which indicates the reliability of the data on the errors in the ABBN neutron cross sections.
The maximum deviation in the calculated keff values ~ 0.8% and the maximum a priori error value ~ 1.2% correspond to Option 7 (the highest 239Pu content in the fuel) and are caused by the spread in neutron data for this isotope in different libraries of evaluated nuclear data.
The deviation in the calculated keff values obtained from the ROSFOND library and its group version, ABBNRF, does not exceed 0.1%, which demonstrates the high accuracy of the ROSFOND/ABBNRF nuclear data for calculating the critical safety parameters of multiplying MOXfueled systems.
Using the data on previously performed experimental studies of the integral MOX fuel characteristics, it is possible to reduce the constant error in keff by three times (on average, from 1 to 0.3%) for simple systems with an intermediate neutron spectrum.
* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2018, n. 3, pp. 160–170.