Research Article 
Corresponding author: Dimitar G. Chereshkov ( dgchereshkov@mephi.ru ) Academic editor: Yury Korovin
© 2023 Dimitar G. Chereshkov, Mikhail Yu. Ternovykh, Georgiy V. Tikhomirov, Alexander A. Ryzhkov.
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:
Chereshkov DG, Ternovykh MYu, Tikhomirov GV, Ryzhkov AA (2023) Nuclear data uncertainty on generation IV fast reactors criticality calculations analysis comparison. Nuclear Energy and Technology 9(3): 157162. https://doi.org/10.3897/nucet.9.111919

The new calculation code capabilities are applied in the current work as well as important fast reactor criticality parameters uncertainty assessment articles’ results based on different nuclear data libraries and covariance matrices. A comparative analysis of uncertainty estimations related to neutron reactions is presented for leadcooled reactor models and sodiumcooled reactor models. For the models of advanced BN and BR fast reactors with three fuel types (UO_{2}, MOX, MNUP), the multiplication factor uncertainty calculations are performed using 252group covariance matrices based on ENDF/BVII.1 library via the SCALE 6.2.4 code system. The main nuclear data uncertainty contributors in the multiplication factor are determined. Recommendations are formulated for improving the cross sections accuracy for several nuclides in order to provide more reliable results of fast reactor criticality calculations. Leadcooled reactors have no operational history compared to lightwater and sodiumcooled reactors. The experimental data insufficiency calls in the question about reliability of the simulation results and requires a comprehensive initial data uncertainty analysis for the neutron transport simulation. The obtained results support the idea that lead and sodiumcooled reactors have close nuclear data sensitivity using one and the same computation tools, nuclear data libraries and fuel compositions. This makes it possible to use the accumulated data of benchmarks for sodiumcooled reactors in the safety determination of leadcooled reactors.
Fast reactors, Generation IV, covariance matrices, sensitivity coefficient, nuclear data uncertainty, SCALE, MNUP, MOX
Generation IV International Forum has identified and selected six nuclear power systems for further investigations and development making world’s future energy demand supply possible. Sodiumcooled fast reactors are one of the most extensively studied and advanced considered commercialsize reactor concepts, greatly supported by industries and research institutions. For largescale twocomponent nuclear power system (fast reactors with a closed nuclear fuel cycle), it is so far theoretically proven and computationally and experimentally attested that such three conceptual requirements as core BR close to unity, lead coolant and highdensity mixed nitride uraniumplutonium (MNUP) fuel allow improving the safety of nuclear reactors notably (
Russia has the world’s most highest level experience in developing and operating sodiumcooled fast reactors. During the initial stage of the BN technology development and adoption process, the use of oxide fuel, due to its maturity in terms of application in thermal reactors, was a reasonable decision. However, highdensity fuel types on the account of their physical properties have obvious advantages in fast reactors. This is the reason why all countries, developing innovative fastneutron reactors, are considering transition from oxide to highdensity fuel types, though Russian and the international experience in using nitride fuel is not enough for predicting reliably the represented fuel elements serviceability working at the BN and BR reactor parameters.
The initial data uncertainties together with the obtained results uncertainties are an integral part of the studies aiming to demonstrate the reactor facilities nuclear safety. Analyzing innovative fast reactor models with mixed uraniumplutonium fuel, the cumulative nuclear data uncertainty contribution to the multiplication factor k_{eff} calculation without taking into account integral experiments is ± 1.5–1.9% [6]. Besides, it is noted in the
This paper analyzes the influence of nuclear data uncertainties in leadcooled (Table
Reactor  Nuclear data library  Reference 
SEALER  JEFF3.1, ENDF/BVII.1 

ALFRED  JEFF3.3, ENDF/BVIII.0 

ENDF/BVII.0, ENDF/BVII.1 


ENDF/BVIII.0 


DLFR  ENDF/BVII.0 

MYRRHA  JEFF3.1.2, ENDF/BVII.0, ENDF/BVII.1 

JEFF3.3, ENDF/BVIII.0 

Reactor  Nuclear data library  Reference 

EBRII  ENDF/BVII.1, ENDF/BVIII.0 

BN600  ENDF/BVII.1, ENDF/BVIII.0 

JOYO  ENDF/BVII.1 

ASTRID  ENDF/BVII.1 

B & BR  ENDF/BVII.0, ENDF/BVII.1 

ZPPR9  ENDF/BVII.0 

ESFR  JEFF3.3, ENDF/BVIII.0 

The following four models of leadcooled reactors have been selected for the comparative analysis.
SEALER (
ALFRED (
DLFR (
MYRRHA (
Seven sodiumcooled reactor models have been taken for the comparative analysis.
EBRII (
BN600 (
JOYO (
ASTRID (
B & BR (
ZPPR9 (
ESFR (
The sensitivity and uncertainty calculations were performed in the software suite SCALE 6.2.4. In particular, the package was used to test the developed newgeneration codes for fast reactor neutronic calculations (
Increased reactor safety requirements call for improving the characteristics prediction accuracy of the fast reactors both in operation and under design. One of the key objectives is to refine the available and develop new, more advanced software tools and databases to support neutronic calculations, estimate the existing uncertainties and work out recommendations for reducing them (
There is a comparative analysis of the k_{eff} sensitivity coefficients using different nuclear data libraries in the observed fast reactors presented.
Fig.
A common conclusion for lead and sodiumcooled reactors with MOX fuel is that greater k_{eff} sensitivity is shown to ν_{f} and ^{239}Pu fission. We should note that these reactions with highest sensitivity coefficients usually do lead to the largest uncertainties with different used libraries in the reactor calculations.
The k_{eff} nuclear data uncertainties introduced by their major contributors in the different libraries used in ALFRED reactor calculations are provided in Table
Covariance  JEFF3.3  ENDF/BVIII.0  ENDF/BVII.1  ENDF/BVII.0 

^{240}Pu (n,f)  ^{240}Pu (n,f)  0.52       
^{240}Pu (n,f)  ^{240}Pu (n,γ)  0.42       
^{239}Pu ν_{f}  ^{239}Pu ν_{f}  0.32  0.19  0.06  0.7 
^{239}Pu (n,f)  ^{239}Pu (n,f)  0.3  0.58  0.2  0.2 
^{238}U (n,n‘)  ^{238}U (n,n‘)  0.23  0.13  0.54  0.53 
^{239}Pu (n, γ)  ^{239}Pu (n, γ)  0.14  0.21  0.25  0.27 
Total uncertainty  0.79  0.75     
The k_{eff} nuclear data uncertainties introduced by their major contributors in the different libraries used in the MYRRHA reactor calculations are provided in Table
Covariance  JEFF3.3  ENDF/BVIII.0  JENDL 4.0 m  ENDF/BVII.0 

^{240}Pu (n,f)  ^{240}Pu (n,f)  0.54       
^{240}Pu (n,f)  ^{240}Pu (n,γ)  0.42       
^{239}Pu ν_{f}  ^{239}Pu ν_{f}  0.32  0.19  0.11  0.7 
^{239}Pu (n,f)  ^{239}Pu (n,f)  0.3  0.55  0.27  0.19 
^{238}U (n,n‘)  ^{238}U (n,n‘)      0.15  0.32 
^{239}Pu (n, γ)  ^{239}Pu (n, γ)  0.15  0.23  0.19  0.27 
Total uncertainty  0.77  0.77  0.55  0.96 
The k_{eff} nuclear data uncertainties introduced by their major contributors in the different libraries used in BN600 and ESFR reactors are provided in Table
k_{eff} nuclear data uncertainties in different libraries in ESFR and BN600, %
Reactor  ESFR  BN600  

Covariance  JEFF3.3  ENDF/BVIII.0  ENDF/BVII.1  
^{240}Pu (n,f)  ^{240}Pu (n,f)  0.59    0.01  0.01 
^{238}U (n,γ)  ^{238}U (n,γ)  0.3    0.24  0.27 
^{239}Pu χ  ^{239}Pu χ  0.46  0.22    0.24 
^{239}Pu (n,f)  ^{239}Pu (n,f)  0.31  0.55  0.71  0.25 
^{238}U (n,n‘)  ^{238}U (n,n‘)  0.48  0.24  0.15  0.7 
^{239}Pu (n, γ)  ^{239}Pu (n, γ)    0.25  0.28  0.29 
Total uncertainty  1.05  0.8  0.88  0.9 
The total BN600 and ESFR uncertainties are close to each other. In BN600, the uncertainty of ^{238}U (n,n′) is decreased from 0.7 to 0.15%. The uncertainty of ^{239}Pu (n,f) is increased from 0.25 to 0.7% when changing library from ENDF/BVII.1 to ENDF/BVIII.0. In ESFR, using ENDF/BVIII.0 instead of JEFF3.3, the uncertainty of ^{238}U (n,n′) changed from 0.48 to 0.24%, and the uncertainty of ^{239}Pu (n,f) changed from 0.31 to 0.55%. The total uncertainty, using ENDF/BVIII.0, has the smallest value and the closest one for sodium and leadcooled reactors.
The BR1200 and BN1200 reactor models were calculated with three fuel types: uranium dioxide, MOX and MNUP fuel. The reactor calculations were performed using the TSUNAMI3D module, the 252group ENDF/BVII.1 nuclear data library and 252group covariance matrices were used. The k_{eff} calculation statistical error did not exceed 0.0001.
Fig.
Tables
Covariance  BR1200  BN1200 

^{238}U (n,n‘)  ^{238}U (n,n‘)  1.28  1.03 
^{238}U (n,γ)  ^{238}U (n,γ)  0.32  0.31 
^{239}Pu (n, γ)  ^{239}Pu (n, γ)  0.23  0.2 
^{239}Pu (n,f)  ^{239}Pu (n,f)  0.22  0.2 
^{239}Pu χ  ^{239}Pu χ  0.22  0.18 
^{238}U χ  ^{238}U χ  0.17  0.18 
^{238}U ν_{f}  ^{238}U ν_{f}  0.17  0.18 
^{239}Pu (n,n‘)  ^{239}Pu (n,n‘)  0.13  0.09 
^{56}Fe (n,n‘)  ^{56}Fe (n,n‘)  0.12  0.12 
^{207}Pb (n,n‘)  ^{207}Pb (n,n‘)  0.11   
^{23}Na (n,n)  ^{23}Na (n,n)    0.1 
Total uncertainty  1.45  1.21 
Covariance  BR1200  BN1200 

^{238}U (n,n‘)  ^{238}U (n,n‘)  0.53  0.61 
^{239}Pu (n, γ)  ^{239}Pu (n, γ)  0.31  0.25 
^{238}U (n,γ)  ^{238}U (n,γ)  0.28  0.27 
^{56}Fe (n,n)  ^{56}Fe (n,n)  0.23  0.08 
^{239}Pu (n,f)  ^{239}Pu (n,f)  0.23  0.2 
^{56}Fe (n, γ)  ^{56}Fe (n, γ)  0.17  0.2 
^{239}Pu χ  ^{239}Pu χ  0.15  0.15 
^{207}Pb (n,n‘)  ^{207}Pb (n,n‘)  0.13   
^{56}Fe (n,n‘)  ^{56}Fe (n,n‘)  0.12  0.17 
^{238}U ν_{f}  ^{238}U ν_{f}  0.11  0.12 
Total uncertainty  0.85  0.86 
It is to be noted that the major contributor to the k_{eff} uncertainty in reactors with MOX fuel is ^{238}U (n,n′) and its value is about 0.6%. The major contributor for reactors with uranium fuel is ^{235}U (n,γ) with an uncertainty of 2%. The contribution of the structural material reactions to the k_{eff} uncertainty is about 0.2%, which agrees with the papers analyzed above.
For reactors with MNUP fuel, the BR and BN total uncertainties differ by 20% and are defined, basically, by differences in the uncertainties of ^{238}U (n,n′), which requires an additional analysis. In general, the comparison of the uncertainties shows that the lead and sodiumcooled reactors have close nuclear data sensitivity using one and the same calculation tools, nuclear data libraries and fuel compositions.
The calculated results of the sensitivities and uncertainties for Generation IV sodium and leadcooled fast reactors have been analyzed. The SCALE code was used for BR1200 and BN1200 reactors with three fuel types to calculate the sensitivities and uncertainties for the multiplication factor due to nuclear data.
The major uncertainty contributors for multiplication factor have been identified. For MOX and MNUP fuel, these are uncertainties of inelastic scatter and capture crosssections for ^{238}U, and, to a smaller extent, uncertainties of the capture and fission crosssections and the fission neutron spectrum uncertainty for ^{239}Pu; for reactors with uranium fuel, these are the capture and fission crosssections and the fission neutron spectrum uncertainty for ^{235}U.
The operation experience of leadcooled reactors is not as comparably considerable as light water and sodiumcooled reactors one has to be. The experimental data insufficiency requires an indepth analysis of the initial data uncertainty during modeling.
The obtained results confirm the statement that nuclear data sensitivity is close to both lead and sodiumcooled reactors with analogous fuel compositions using one and the same computational tools and nuclear data libraries. This allows us to use the accumulated benchmarks of sodiumcooled reactors to prove the leadcooled reactor safety.