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 lead-cooled reactor models and sodium-cooled reactor models. For the models of advanced BN and BR fast reactors with three fuel types (UO₂, MOX, MNUP), the multiplication factor uncertainty calculations are performed using 252-group covariance matrices based on ENDF/B-VII.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. Lead-cooled reactors have no operational history compared to light-water and sodium-cooled 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 sodium-cooled 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 sodium-cooled reactors in the safety determination of lead-cooled 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. Sodium-cooled fast reactors are one of the most extensively studied and advanced considered commercial-size reactor concepts, greatly supported by industries and research institutions. For large-scale two-component 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 high-density mixed nitride uranium-plutonium (MNUP) fuel allow improving the safety of nuclear reactors notably (Adamov et al. 2022). Increased safety properties of lead (lead-bismuth), including relative chemical inertness, capability to retaining hazardous radionuclides, such as iodine and cesium, and high boiling temperature, contributes to the selection of lead-cooled reactor as an economically competitive Generation IV reactor. However, lead-cooled reactors do not have a comparably considerable operation experience as light water and sodium-cooled reactors do. It is stated in Trottier et al. 2018; Trivedi et al. 2020; Castelluccio et al. 2021; Romojaro et al. 2021, that insufficient experimental data calls in the question about reliability of computational simulation results and requires a comprehensive initial data uncertainty analysis for the neutron transport simulation. Propagating these uncertainties gives a better notion of their influence on the reactor core performance and makes it possible to estimate the design safety limits. Based on the results obtained, the paper supports the statement that the nuclear data sensitivity is close to both lead- and sodium-cooled 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 sodium-cooled reactors to prove the lead-cooled reactor safety.

Russia has the world’s most highest level experience in developing and operating sodium-cooled 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, high-density fuel types on the account of their physical properties have obvious advantages in fast reactors. This is the reason why all countries, developing innovative fast-neutron reactors, are considering transition from oxide to high-density 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 uranium-plutonium 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 Manturov et al. 2022 paper that the uncertainty may be decreased to ± 0.4–0.6% as a result of the compensative effect of the uncertainty correlations of evaluated quantities at different neutron energies and reaction channels.

This paper analyzes the influence of nuclear data uncertainties in lead-cooled (Table 1) and sodium-cooled (Table 2) reactor models. The listed data have been supplemented with own calculations of BR-1200 and BN-1200 reactor models with three fuel types (UO2, MOX and MNUP). In the BR and BN calculations, the sensitivity analysis was provided using the TSUNAMI sequence of the SCALE 6.2.4 code (Bostelmann et al. 2022). The k_eff uncertainty was estimated and quantitatively investigated using the SAMS module applied in the TSUNAMI sequence. The results were compared to identify the potential needs for updating the nuclear data. Own calculations were undertaken to identify the nuclides and reactions that have the greatest effect on the BR and BN neutronic performance.

The following four models of lead-cooled reactors have been selected for the comparative analysis.

SEALER (Trottier et al. 2018) is a modular reactor with 19.9% enriched UO₂ fuel. The electric power is 3 to 10 MW. The reactor core life is 10 to 30 years (full power operation without refuelling).

ALFRED (Romojaro et al. 2017a; Romojaro and Alvarez-Velarde 2020; Castelluccio et al. 2021) is a small-size reactor, its core is divided in two zones (internal and external) with different plutonium contents (20.5% in the external zone) for power field flattening. The electric power is 125 MW and the maximum fuel burnup is 100 MW∙day/kg. Each year, 1/5 of the core is unloaded and replaced with fresh fuel.

DLFR (Trivedi et al. 2020) is a medium-size reactor, its core includes two uranium enrichment zones (17.5% in the external zone). The electric power is 450 MW. The refuelling scenarios are at the development stage.

MYRRHA (Romojaro et al. 2017b; Romojaro et al. 2021) is a small-size reactor capable to operate both in a subcritical state when using a linear 600 MeV proton accelerator and in a critical mode (as a lead-bismuth-cooled fast-neutron reactor). The electric power is 57 MW. Different fuel compositions are considered.

Seven sodium-cooled reactor models have been taken for the comparative analysis.

EBR-II (Bostelmann et al. 2021) is a 20 MW(e) demonstration reactor, consisting of three regions (core, inner and outer shield). Fuel elements are fuelled with enriched uranium metal (67%) and it is chosen stainless-steel cladding.

BN-600 (Ma et al. 2021) is a 600 MW(e) commercial reactor using enriched UO₂ fuel since the start of the operation. The paper considers the results of a benchmark calculation with MOX fuel with a 20% plutonium content.

JOYO (Wan et al. 2020) is an experimental reactor using MOX fuel which comprises 23% enriched uranium and 17.7% plutonium. The fissionable plutonium isotopes content is 80.4%. The thermal power is 140 MW.

ASTRID (Griseri et al. 2017) is a commercial reactor with core comprising two fuel subzones. It is considered as an MA burner. The fuel consists of about 70% depleted uranium, 20% to 22% plutonium, and about 10% MAs. The electric power is 500 MW.

B & BR (Vu and Hartanto 2021) is a modular reactor with UO₂ fuel, enriched to 12.32%. The electric power is 400 MW. The reactor core life is up to 50 years (full power operation without refuelling).

ZPPR-9 (Zheng et al. 2018) is a zero-power reactor using MOX fuel with a 17.7% plutonium content.

ESFR (Romojaro et al. 2021) is a commercial-size reactor with two subzones core with different fuel section heights in the fuel rods. There is a MOX fuel used with a 14.6% and 17% plutonium content in the subzones. The electric power is 1500 MW.

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 new-generation codes for fast reactor neutronic calculations (Ternovykh et al. 2017; Ternovykh and Bogdanova 2020; Tikhomirov et al. 2021). System code SCALE involves several control sequences for neutronic calculations and nuclear safety analysis, it has been developed and evolved by Oak Ridge National Laboratory. It combines modules for criticality calculation, radiation shielding and nuclide kinetics, sensitivity and uncertainty analysis and other problems. A Monte Carlo transport code, KENO-VI, is used to support calculations in a 3D geometry. The neutron transport simulation can be performed both in a multi-group approximation and with continuous representation of cross-sections by energy. TSUNAMI is a sensitivity and uncertainty analysis module. The TSUNAMI module uses the forward and adjoint neutron transport solutions, obtained by a KENO-VI calculation, using SAMS to compute sensitivities via first order perturbation theory. Sensitivity calculations together with the ENDF/B-VII.1 covariance data can be used to estimate the uncertainty of k_eff or other functionals.

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 (Manturov et al. 2022).

Sensitivity analysis of observed fast reactors

There is a comparative analysis of the k_eff sensitivity coefficients using different nuclear data libraries in the observed fast reactors presented.

Fig. 1 presents the k_eff sensitivity coefficients to the seven most important nuclides and reactions for the investigated reactor models with MOX fuel. The k_eff sensitivity coefficients for MYRRHA, using two different libraries (JEFF-3.3 and ENDF/B-VII.0), are close to the k_eff sensitivity coefficients for ALFRED. When comparing ZPPR-9 and ESFR sodium-cooled reactors with MYRRHA lead-cooled reactor, with similar libraries used (ENDF/B-VII.0 and JEFF-3.3), it is noted that the sensitivity coefficients have close values. The sensitivity coefficient differences are explained mainly by the ESFR design features (fertile blankets) and a smaller plutonium content rather than by different coolants used in the reactors.

Figure 1. 

Top 7 integrated k_eff sensitivity coefficients for reactors with MOX fuel.

A common conclusion for lead- and sodium-cooled reactors with MOX fuel is that greater k_eff sensitivity is shown to ν_f and ²³⁹Pu 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.

Analysis of the SCALE calculated reactor results

The BR-1200 and BN-1200 reactor models were calculated with three fuel types: uranium dioxide, MOX and MNUP fuel. The reactor calculations were performed using the TSUNAMI-3D module, the 252-group ENDF/B-VII.1 nuclear data library and 252-group covariance matrices were used. The k_eff calculation statistical error did not exceed 0.0001.

Fig. 2 presents the most important k_eff sensitivity coefficients for reactors with MOX and MNUP fuels. Coolant or fuel type difference does not lead to a great effect on the k_eff sensitivity coefficients. The sensitivity coefficients to ²³⁹Pu reactions are a little smaller for BN compared to BR. We should note that the sensitivity coefficients to ²³⁸U are smaller than to ²³⁹Pu, but the uncertainties for ²³⁸U are larger than for ²³⁹Pu.

Figure 2. 

Top 5 integrated k_eff sensitivity coefficients for BR and BN reactors with MNUP and MOX fuel.

Tables 6 and 7 present the k_eff uncertainties introduced by their major contributors in BR-1200 and BN-1200 reactors. The calculated uncertainties mainly agree with the Andrianova et al. 2014 results.

Table 6.

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k_eff nuclear data uncertainties in reactors with MNUP fuel, %

Covariance	BR-1200	BN-1200
238U (n,n‘) - 238U (n,n‘)	1.28	1.03
238U (n,γ) - 238U (n,γ)	0.32	0.31
239Pu (n, γ) - 239Pu (n, γ)	0.23	0.2
239Pu (n,f) - 239Pu (n,f)	0.22	0.2
239Pu χ - 239Pu χ	0.22	0.18
238U χ - 238U χ	0.17	0.18
238U νf - 238U νf	0.17	0.18
239Pu (n,n‘) - 239Pu (n,n‘)	0.13	0.09
56Fe (n,n‘) - 56Fe (n,n‘)	0.12	0.12
207Pb (n,n‘) - 207Pb (n,n‘)	0.11	-
23Na (n,n) - 23Na (n,n)	-	0.1
Total uncertainty	1.45	1.21

Table 7.

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k_eff nuclear data uncertainties in reactors with MOX fuel, %

Covariance	BR-1200	BN-1200
238U (n,n‘) - 238U (n,n‘)	0.53	0.61
239Pu (n, γ) - 239Pu (n, γ)	0.31	0.25
238U (n,γ) - 238U (n,γ)	0.28	0.27
56Fe (n,n) - 56Fe (n,n)	0.23	0.08
239Pu (n,f) - 239Pu (n,f)	0.23	0.2
56Fe (n, γ) - 56Fe (n, γ)	0.17	0.2
239Pu χ - 239Pu χ	0.15	0.15
207Pb (n,n‘) - 207Pb (n,n‘)	0.13	-
56Fe (n,n‘) - 56Fe (n,n‘)	0.12	0.17
238U νf - 238U νf	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 ²³⁸U (n,n′) and its value is about 0.6%. The major contributor for reactors with uranium fuel is ²³⁵U (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 ²³⁸U (n,n′), which requires an additional analysis. In general, the comparison of the uncertainties shows that the lead- and sodium-cooled 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 lead-cooled fast reactors have been analyzed. The SCALE code was used for BR-1200 and BN-1200 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 cross-sections for ²³⁸U, and, to a smaller extent, uncertainties of the capture and fission cross-sections and the fission neutron spectrum uncertainty for ²³⁹Pu; for reactors with uranium fuel, these are the capture and fission cross-sections and the fission neutron spectrum uncertainty for ²³⁵U.

The operation experience of lead-cooled reactors is not as comparably considerable as light water and sodium-cooled reactors one has to be. The experimental data insufficiency requires an in-depth analysis of the initial data uncertainty during modeling.

The obtained results confirm the statement that nuclear data sensitivity is close to both lead- and sodium-cooled 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 sodium-cooled reactors to prove the lead-cooled reactor safety.