Corresponding author: Olga N. Andrianova ( oandrianova@ippe.ru ) Academic editor: Boris Balakin
© 2019 Olga N. Andrianova, Yury Ye. Golovko, Gennady N. Manturov .
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Andrianova ON, Golovko YYe, Manturov GN (2019) Verification of the ROSFOND/ABBN nuclear data based on the OECD/NEA benchmark on criticality safety of moxfueled systems. Nuclear Energy and Technology 5(2): 9196. https://doi.org/10.3897/nucet.5.35577

The paper presents the results of a computational analysis of the OECD/NEA benchmark conducted to estimate the accuracy of the critical safety parameters of multiplying MOXfueled systems. The computational test is a set of 15 spherical multiplying systems that differ in their compositions and geometries. According to the test conditions, the k_{eff} values of the analyzed systems are unknown in advance. As part of the computational analysis of the test involving national codes and nuclear data libraries, along with the k_{eff} calculations, it is also necessary to estimate the a priori (due to the accuracy of the nuclear data used) and a posteriori (based on the accumulated experimental information) errors in the calculated k_{eff} values. Based on the benchmark, an updated version of the ROSFOND/ABBNRF nuclear data was tested. The results of estimating the a priori and a posteriori errors in k_{eff} using the INDECS system for the proposed test models are presented. The analysis of the calculated data shows that (1) the observed spread in the k_{eff} values obtained from the Russian ROSFOND library and foreign evaluated nuclear data libraries (ENDF/BVII.0, JEFF3.2, JENDL4.0) varies from –0.3 up to 0.8%; and (2) the deviation of the calculation results in the k_{eff} values obtained from the ROSFOND library and its group version, ABBNRF, does not exceed 0.1%. The average a priori error in k_{eff} for all the tested options of multiplying systems is about 1% and, taking into account the selected set of experimental criticality data for MOXfueled systems, including experiments at the BFS facilities, the average a posteriori error in k_{eff} can be reduced to 0.3%. The performed estimations confirm the high accuracy of the ROSFOND/ABBNRF nuclear data for calculating the critical safety parameters of multiplying MOXfueled systems.
MOX fuel, integral experiments, BFS critical facility, accuracy estimation, effective multiplication factor, neutron data uncertainty, OECD/NEA benchmark, maximum likelihood method
Following the main objective of the Organization for Economic Cooperation and Development Nuclear Energy Agency (OECD/NEA) to contribute to the safe development of nuclear energy for peaceful purposes in the participating countries through international scientific and technical cooperation, the Agency’s various expert and working groups, along with collecting, analyzing and improving neutron data libraries, computational methods, programs, and experimental databases, pay considerable attention to the development and computational analysis of various benchmark tests (
Under the auspices of the OECD/NEA, nuclear and critical safety issues are addressed by the Working Party on Nuclear Criticality Safety (WPNCS) Expert Group, which includes a separate Working Expert Group on Uncertainty Analysis for Criticality Safety Assessment (EGUACSA) (Webpage of WPNCS 2018).
The EGUACSA experts were offered a “blind” computational benchmark test for estimating errors in calculating the effective neutron multiplication factor, k_{eff}, (the k_{eff} values of the analyzed systems were unknown in advance) for simplified models of external MOX fuel cycle systems, which makes it possible to test national calculation codes and nuclear data used to substantiate the critical safety of projected reactor plants and external fuel cycle systems. As part of the test, tasks were also set to estimate the accuracy of the calculated predictions, reduce the a priori error by involving the results of previously performed integral and reactorphysical experiments, and adjust the neutron crosssections.
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.
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
Test option  M_{H2O} / M_{UO2+PuO2}  Radius, cm  M_{PuO2} /M_{UO2+PuO2}  ^{239}Pu/Pu  ^{240}Pu/Pu  ^{241}Pu/Pu  ^{242}Pu/Pu 
1  2  3  4  5  6  7  8 
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:
This benchmark test is primarily aimed at verifying methods for determining displacements and errors in the k_{eff} values and testing libraries of evaluated nuclear data and crosssections uncertainties. Since the test itself is purely computational (there is no comparison with experimental data), according to the benchmark conditions, the k_{eff} values were assumed to be unknown. This circumstance makes it impossible to focus the calculations on a previously known result; therefore, the emphasis in the analysis shifts from a comparison of the calculated and experimental discrepancies to an analysis of the spread in the calculated data obtained from different libraries (the socalled observed constant error). This task setting allows us to test the computational methods and codes used to improve the accuracy in estimating the a posteriori and a priori constant errors.
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 (
Z ^{2} = S·W^{–1}·S^{T} + (Δk + H^{T}·S)·U^{–1}(Δk + H_{T}·S)^{T}, (1)
where S is the desired vector of corrections to the parameters; H is the matrix of coefficients of k_{eff} sensitivity to the parameters; U and W are the covariance matrices of crosssections uncertainties of the experimental results (the k_{eff} values) and desired parameters (neutron cross sections); Δk is the vector of discrepancies between the calculated and experimental k_{eff} values.
From expression (1), we can obtain the relation for the desired corrections:
S = W·H^{T}·(U + H·W·H^{T})^{–1}Δk, (2)
and also the expression for the covariance matrix of the parameters W¢, which takes into account the corrections found:
W′ = W – W·H·(U + H·W·H^{T})^{–1}Δk. (3)
By means of the matrix (W′), we can estimate the new matrix (V′) of the expected calculated errors using corrected constants, the a posteriori constant calculation error taking into account the data of integral experiments and corrections to the calculated Δk′:
V′ = H·W^{–1}·H^{T}, (4)
Δk′ = Δk + H^{T}·S. (5)
The k_{eff} values for the proposed test options were calculated by the MCNP code (
Comparison of calculation results for different nuclear data systems
Test option  ABBNRF/ ROSFOND  ENDF/BVII/ ROSFOND  JEF3.2/ ROSFOND  JENDL4.0/ ROSFOND 
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 k_{eff} values calculated using various libraries of evaluated nuclear data lies in the range from –0.26 to 0.79%. The maximum discrepancies correspond to Option 7, in which only PuO_{2} is included in the fuel composition, with a maximum content of the ^{239}Pu isotope equal to 96%.
The analysis of the onegroup sensitivity coefficients showed that the options with large values of coefficients of k_{eff} sensitivity to ^{239}Pu neutron cross sections (Fig.
To estimate the a posteriori error of the models under consideration, experiments were selected from the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook (
List of benchmark experiments
No.  Experiment identifier in ICSBEP  Critical configuration identifier  No.  Experiment identifier in ICSBEP  Critical configuration identifier 
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 δk_{eff} calculated for all the 15 benchmark models were obtained (see Table
Benchmark a priori δk_{eff} and a posteriori δ′k_{eff} errors caused by the neutron cross section errors
No.  dk_{eff}, %  δ′k_{eff}, %  No.  dk_{eff}, %  δ′k_{eff}, %  No.  dk_{eff}, %  δ′k_{eff}, % 
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.
In accordance with the calculation program of the OECD/NEA numerical benchmark test to substantiate the critical safety of MOXfueled systems proposed by the Expert Group on Uncertainty Analysis for Criticality Safety Assessment (EGUACSA), a series of calculations were performed aimed at verifying the ROSFOND/ABBNRF nuclear data library. The analysis of the calculated data shows that: