IYNC 2008 Interlaken, Switzerland, 20 – 26 September 2008 Paper No. 020
Uncertainty Evaluation of Reactivity Coefficients for a large advanced SFR Core Design Wassim Khamakhem1, Gérald Rimpault1 1 DER/SPRC Cadarache Center, Commissariat à l’énergie atomique (CEA), 13108 Saint Paul lez Durance, France;
[email protected] ABSTRACT Sodium Cooled Fast Reactors are currently being reshaped in order to meet Generation IV goals on economics, safety and reliability, sustainability and proliferation resistance. Recent studies have led to large SFR cores for a 3600 MWth power plants, cores which exhibit interesting features. The designs have had to balance between competing aspects such as sustainability and safety characteristics. Sustainability in neutronic terms is translated into positive breeding gain and safety into rather low Na void reactivity effects. The studies have been done on two SFR concepts using oxide and carbide fuels. The use of the sensitivity theory in the ERANOS determinist code system has been used. Calculations have been performed with different sodium evaluations: JEF2.2, ERALIB-1 and the most recent JEFF3.1 and ENDF/B-VII in order to make a broad comparison. Values for the Na void reactivity effect exhibit differences as large as 14% when using the different sodium libraries. Uncertainties due to nuclear data on the reactivity coefficients were performed with BOLNA variances–covariances data, the Na Void Effect uncertainties are near to 12% at 1 . Since, the uncertainties are far beyond the target accuracy for a design achieving high performance, two directions are envisaged: the first one is to perform new differential measurements or in a second attempt use integral experiments to improve effectively the nuclear data set and its uncertainties such as performed in the past with ERALIB1. 1
INTRODUCTION
Sodium Cooled Fast Reactors (SFR) are currently being reshaped in order to meet Generation IV goals on economics, safety and reliability, sustainability and proliferation resistance. Recent studies have led to large SFR cores for a 3600 MWth power plants, cores which exhibit interesting features. The designs have had to balance between competing aspects such as sustainability and safety characteristics. Sustainability in neutronic terms is translated into positive breeding gain and safety into rather low Na void reactivity effects. Two preliminary basic images have been issued, one using oxide fuel, the other carbide fuel [1]. As a matter of fact, before going any further in the core description, it is paramount to evaluate the integral characteristic uncertainties. The use of the sensitivity theory in the ERANOS determinist code system has hence been used for that purpose [12]. For the study of reactivity coefficients, the sensitivities are based on the equivalent perturbation theory [5,6,17]. The sensitivity and uncertainty studies have been done on two SFR concepts (using oxide and carbide fuels respectively) and results have been compared to the design target accuracies.
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2 2.1
PHYSICS OF THE BASE SFR CORE DESIGNS Core design approach
The GEN-IV criteria, in a first conceptual phase, translate into a search for breakeven cores (i.e., zero net breeding gain) and enhanced safety features. An improved safety for a sodium cooled reactor requires revisiting many aspects of the design and is a rather lengthy process. As a first step, studies have focused on the reduction of the sodium voiding reactivity effect, together with an increase in the Doppler Effect. This is essential to achieve a satisfactory transient behaviour, as well as to reduce the risk of getting into a generalized core fusion. In design studies, it is customary to distinguish two categories of core concepts, depending on the required Research & Development efforts: • Concepts called “innovative”, based on variations around established technologies, such as oxide fuel pins inserted in a hexagonal wrapper. • Concepts called “breakthrough”, based on more radical changes, such as the use of dense carbide fuel, and very innovative fuel forms and sub-assembly geometries. Once defined, the core designs have to be checked for their viability. This typically includes calculating the following neutronic characteristics at Beginning of Life (BOL) and Beginning of Cycle (BOC): sodium void worth, ΔρVoid Na Doppler effect, ΔρDop (T° Nom -> Fusion) and control rod worth for the two rings, Δρ2 CR rings. Two main nuclear data sets are being used to evaluate the different core neutronic characteristics: the JEFF-3.1 library and the ERALIB1 adjusted library [3,4].
2.2
Core neutronic characteristics using JEFF-3.1
Table 1 shows that the both cores exhibit rather excellent neutron characteristics, with, in particular, SFR sodium void worth around 3$, while the Doppler effect is especially large for the Carbide version. There is a large spectrum change occurring in these cores when sodium is removed but the void effect is limited in amplitude primarily from a smaller sodium volume fraction. Table 1 Core Neutronic Characteristics with JEFF3.1
2.3
Integrals Parameters
Carbide SFR
Oxide SFR
Keff (BOC)
0.98249
1.00051
ΔρVoid Na ($) (BOL)
3.3
2.9
ΔρDop (T° Nom -> Fusion) ($) (BOL)
-2.8
-1.9
Δρ2 CR rings ($) (BOL)
-32.7
-17.1
$ (pcm) (BOL)
410
384
Core neutronic characteristics using ERALIB-1
The core neutronic characteristics performed with ERALIB-1 are presented in table 2. By comparing the integrals parameters obtained with ERALIB-1 with these obtained with JEFF-3.1 (see table 1), we note that the use of an adjusted library such as ERALIB-1 allows a significant decrease of the sodium void effect which will be studied further in the following. 020.2
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Table 2 Core Neutronic Characteristics with ERALIB-1
3
Integrals Parameters
Carbide SFR
Oxide SFR
Keff (BOC)
0.97920
0.99775
ΔρVoid Na ($) (BOL)
3.2
2.7
ΔρDop (T° Nom -> Fusion) ($) (BOL)
-2.5
-1.7
Δρ2 CR rings ($) (BOL)
-31.8
-17.1
$ (pcm) (BOL)
410
384
IMPORTANCE OF THE NA23 FOR THE SODIUM VOID EFFECT
In order to put in evidence the importance of the Na23 in the sodium void effect and it uncertainty, we have performed in this section a breakdown of the perturbations and of the uncertainties. The calculations have been performed with JEFF-3.1 evaluation and BOLNA variances-covariances data [14]. The results are given in the following tables 3 and 4, just only significant values are being shown. In the case of the Oxide SFR, we can notice that the sodium void effect is due mainly to inelastic and elastic scattering cross sections, with an increase in reactivity of respectively 524.6 pcm and 90.2 pcm. The sodium void effect is also due to a decrease of the neutronic capture by Na which increases the reactivity by 84.7 pcm. In the case of the Carbide SFR, we can notice that the sodium void effect is still mainly due to inelastic and elastic scattering cross sections, with respectively an increase and a decrease in reactivity by 800.7 pcm and 163.1 pcm. The Na void effect is still also due to a decrease of the neutronic capture by Na which increases the reactivity by 95.3 pcm. The uncertainties associated to the sodium void effect are primarily due to Na23, Pu241 and U238. In the case of Na23, the uncertainties are first due to uncertainties linked to the inelastic Na23 cross section, and then due to uncertainties linked to the elastic and capture Na cross section.
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Table 3 Breakdown of Na void effect per isotope and reaction perturbations & uncertainties for Oxide SFR Cross Section U235 -Capture U235 -Fission U238 -Capture U238 -Fission U238 -Elastic U238 -Inelastic Pu239 -Capture Pu239 -Fission Pu240 -Capture Pu240 -Fission Pu241 -Capture Pu241 -Fission Pu242 -Fission Pu242 -Capture O16 -Capture O16 -Elastic O16| -Inelastic Na23 -Capture Na23 -Elastic Na23 -Inelastic Fe56 -Capture Fe56 -Elastic Fe56 -Inelastic Fe57 -Elastic Cr52 -Capture Cr52 -Elastic Ni58 -Capture Ni58 -Elastic
Perturbations Breakdown (in pcm) -1.0 1.0 230.8 -1.7 -4.4 12.7 41.5 76.8 11.6 27.5 1.8 -10.4 4.6 2.9 45.3 0.4 0.4 84.7 90.2 524.6 1.2 -2.0 5.3 1.1 1.7 0.003 0.7 -7.2
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Uncertainties Breakdown (in % at 1 σ) 0.1 0.1 3.4 0.1 2.1 5.7 1.2 1.8 0.3 0.3 0.4 6.1 0.1 0.8 0.7 1.2 1.2 0.9 1.2 7.2 1.1 0.4 0.6 0.0 0.0 0.2 0.3 0.1
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Table 4 Breakdown of Na void effect per isotope and reaction perturbations & uncertainties for Carbide SFR Cross Section U235 -Capture U235 -Fission U238 -Capture U238 -Fission U238 -Elastic U238 -Inelastic Pu239 -Capture Pu239 -Fission Pu240 -Capture Pu240 -Fission Pu241 -Capture Pu241 -Fission Pu242 -Fission Pu242 -Capture C12 -Capture C12 -Elastic C12| -Inelastic Na23 -Capture Na23 -Elastic Na23 -Inelastic Fe56 -Capture Fe56 -Elastic Fe56 -Inelastic Fe57 -Elastic Cr52 -Capture Cr52 -Elastic Ni58 -Capture Ni58 -Elastic
Perturbations Breakdown (in pcm) 1.5 -1.2 304.6 10.5 -10.1 34.4 32.5 84 8.6 32.0 1.4 -10.4 2.2 6.1 27.4 0.0 0.0 95.3 -163.1 800.7 1.4 5.5 6.1 1.9 1.8 6.7 -10.2 -0.3
Uncertainties Breakdown (in % at 1 σ) 0.1 0.1 3.6 0.1 2.1 6.5 0.6 1.5 0.2 0.9 0.4 4.8 0.1 0.7 0.0 1.0 0.1 0.8 1.4 6.8 0.9 0.3 0.8 0.0 0.0 0.2 0.2 0.1
These results mean that the Na23 plays a major role for the sodium void effect and its associated uncertainty. As a matter of fact, we have chosen in the next sections to illustrate the impact of Na23 evaluations and their uncertainties on the sodium void effect.
4
IMPACT OF DIFFERENT NA 23 EVALUATIONS ON THE NA VOID EFFECT
To quantify the impact of the sodium evaluations on the core characteristics, the sodium void worth was calculated with the latest Na23 evaluations: JEF-2.2, JEFF-3.1 and ENDF/B-7.0 libraries [2, 7, 8, 9, 11, 12, 15, 16]. The complementary use of the ERALIB1 adjusted library illustrates what reduced uncertainty integral experiments could bring to the sodium void worth through the improved importance shape coming from actinides and sodium adjusted cross sections. The results are presented in tables 5 and 6; they give separately the two components of the sodium void worth.
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Table 5: Oxide SFR Na void effect with different data sets (in pcm) Nuclear Data Evaluation JEF-2.2 ERALIB1 JEFF-3.1 ERALIB1 + Na23 JEFF-3.1 ERALIB1 + Na23 ENDF/B-VII.0
ΔρVoid
Leakag e Term
1241 1046 1092
-1335 -1250 -1418
Nonleakage Term 2576 2295 2510
1069
-1381
2450
1194
1309
2502
Table 6: Carbide SFR Na void effect with different data sets (in pcm) Nuclear Data Evaluation JEF-2.2 ERALIB1 JEFF-3.1 ERALIB1 + Na23 JEFF-3.1 ERALIB1 + Na23 ENDF/B-VII.0
ΔρVoid 1565 1296 1365
Leakage Term -1316 -1207 -1378
Non-leakage Term 2881 2504 2743
1463
-1337
2800
1498
-1267
2765
In the case of the Oxide SFR, the use of JEF-2.2 yields the largest sodium void worth, according to table 4. ERALIB1 and JEFF-3.1 give similar results, but for different reasons as they are compensating effects between the leakage and non-leakage terms. In the case of the Carbide SFR, the use of JEF-2.2 still yields the largest sodium void worth, according to table 5. ERALIB1 and JEFF3.1 still lead to similar results because of compensation of the leakage and non-leakage components. We should precise that the compensation of the components of sodium void effect is particular to these cores. Actually, we have done the same king of calculation for others cores not presented here (SFR cores using oxide fuel and characterized by spectrum harder than our cores) and we found that there was no more compensations between the 2 components. Additional calculations were performed, with the JEFF-3.1 and ENDF/B-VII.0 sodium data substituted for the corresponding ERALIB-1 data. When the ENDF/B-VII.0 sodium data are used, the sodium void worth increases significantly, mainly because of the change in the non-leakage term. The differences with the ERALIB1 results are 14.14% for the Oxide SFR and 15.58% for the Carbide SFR, These differences between the results of the sodium void effects using different nuclear data sets are very important, far too important for core design and safety studies. In fact, the sodium void reactivity variations are due to differences existing in evaluated nuclear data files. In the next chapter, the uncertainties on the sodium void reactivity are computed from the BOLNA covariances (see table 7). This will enable a comparison with the different sodium void reactivity values. Since, they do not look consistent, this suggests that Na evaluation has to be improved.
5
UNCERTAINTIES ON REACTOR CORE CHARACTERISTICS
We calculated the uncertainties on the core characteristics due to the nuclear data by using either the BOLNA variance-covariance data which we associate to JEFF-3.1 evaluation or the ERALIB1 adjusted library (both variance-covariance and nuclear data).
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5.1
Uncertainties on the core characteristics due to the nuclear data using the BOLNA variance-covariance data
The uncertainties on the core characteristics due to the nuclear data using the BOLNA variancecovariance data are presented in table 7. The last column in the table shows the target uncertainties for the Gen-IV feasibility phase. Table 7 Uncertainties on the core characteristics (in % at 1 σ) with BOLNA Uncertainties on
Carbide SFR
Oxide SFR
Target Uncertainties
keff
± 2.16
± 1.80
± 0.30
ΔρVoid Na
± 11.8
± 12.4
± 7.0
ΔρDop
± 6.0
± 5.1
± 7.0
± 4.7
± 2.9
± 4.0
(T° Nom -> Fusion)
Δρ2 CR rings
The uncertainty for the keff of the Oxide SFR is 1.80% whereas that of the Carbide SFR is 2.16%, value more important. This difference can be explained by a hardest spectrum (see Figure 1) in the case of the Oxide SFR which decreases the sensitivity coefficients to the keff in the intermediate energy range region and increases them in the fast region, an energy region characterized by lower uncertainties. For the both cores, the uncertainties for the keff are significantly larger than the corresponding target uncertainty. Regarding the Doppler Effect, the uncertainties are quite similar for the both core. The fact that sensitivity calculation in this case does not take into account the resonance uncertainties would not enlarge the values significantly (less than 1%). Regarding the Doppler Effect, uncertainties are within the required bound. For control rod worths, the situation appears to be satisfactory for the Oxide SFR, although this would have to be checked once the exact number and position of the control elements are known. Finally, for the sodium void worth, the values for the SFR cores are of the order of 12% at 1σ, exceeding the target uncertainties. 5.00E+14
CARBIDE SFR 4.00E+14
OXIDE SFR
Flux
3.00E+14
2.00E+14
1.00E+14
0.00E+00 1.00E-07
1.00E-05
1.00E-03
1.00E-01
Energy (MeV)
Fig. 1. Flux Spectrum.
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1.00E+03
Proceedings of the International Youth Nuclear Congress 2008
5.2
Uncertainties on the core characteristics due to the nuclear data using the ERALIB-1 variance-covariance data
The uncertainties on the core characteristics due to the nuclear data using the ERALIB-1 variancecovariance data are presented in table 8. The last column in the table shows the target uncertainties for the Gen-IV feasibility phase. Table 8Uncertainties on the core characteristics (in % at 1 σ) with ERALIB-1 Uncertainties on
Carbide SFR
Oxide SFR
Target Uncertainties
keff
± 0.20
± 0.15
± 0.30
ΔρVoid Na
± 4.7
± 5.3
± 7.0
ΔρDop
± 1.8
± 2.0
± 7.0
± 0.7
± 0.8
± 4.0
(T° Nom -> Fusion)
Δρ2 CR rings
The keff uncertainties are quite similar and are under the corresponding target uncertainty. Then, the Doppler Effect uncertainties are once again quite similar for the two cores and are within the required bound. For control rod worths, the situation is greatly satisfactory for the two cores. Finally, the sodium void worth uncertainties are of the order of 5% at 1σ, lower to the target uncertainties. Using of an adjusted library such as ERALIB-1 allows a significant decrease of the sodium void effect and the associated uncertainties. However, the process of producing an adjusted library such as ERALIB-1 library is a long and huge process which contains many possibility of mistakes and in particular rely as a starting point in well known evaluation produced with a best practice approach and to which nuclear data variance covariance should be associated. In order to illustrate traps which must be overcome, the following chapter evaluates the importance of having appropriate correlations between different reactions of the sodium nuclear data evaluation. 5.3
Importance of correlations between different reactions: Case of correlations between inelastic and elastic Na23 reactions
Since in recent Na evaluations, elastic is deduced from total and inelastic differential measurements, correlations between different reactions should exist. In order to test the importance of these correlations between different reactions, we did calculate uncertainties on sodium void reactivity effect by using: • the BOLNA covariance set which is given without correlation between elastic and inelastic reactions • the BOLNA covariance set with correlation between elastic and inelastic reactions from a previous Na23 evaluation being added. The use of the elastic-inelastic correlations from the old Na23 evaluation associated with BOLNA covariance set decreases the uncertainties on the reactivity effect of the Carbide SFR and Oxide SFR cores by only 0.4% and 0.3%, while the decrease on the sodium void reactivity effect uncertainties is of only 0.2% (see tables 9 & 10). However, the impact of the inelastic-elastic correlations to the uncertainty should lead to more important reduction if variances were larger. Hence, the use of correlations between different cross sections allows a decrease of uncertainties to integrals parameters but this has a major impact when cross section variances are large. It is therefore recommended to start with the most precise possible evaluation and have associated to it the most adequate variance-covariance especially when performing a cross section adjustment. 020.8
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Table 9 Impact of Elastic-Inelastic Correlations for the Oxide SFR uncertainties (in % at 1 σ) Integral Parameters And Na23 contribution Keff
BOLNA 1.8
BOLNA and Elastic-Inelastic Correlations from Old Na Evaluation’s Covariances Data 1.8
Na23 for Keff
0.10
0.12
ΔρNa Void
12.4
12.2
Na23 for ΔρNa Void
7.3
7.0
Table 10 Impact of Elastic-Inelastic Correlations for the Carbide SFR uncertainties (in % at 1 σ) Integral Parameters And Na23 contribution Keff
6
BOLNA 2.16
BOLNA and Elastic-Inelastic Correlations from Old Na Evaluation’s Covariances Data 2.16
Na for Keff
0.12
0.12
ΔρNa Void
11.8
11.6
Na for ΔρNa Void
7.0
6.6
CONCLUSION
Recent studies have led to large SFR cores for a 3600 MWth power plants, cores which exhibit interesting features. As a first step, studies have focused on the reduction of the sodium voiding reactivity effect, together with an increase in the Doppler Effect. This is essential to achieve a satisfactory transient behaviour, as well as to reduce the risk of getting into a generalized core fusion. These criteria drive us to two images of cores: • An “innovative” SFR concepts based on variations around established technologies and using oxide fuel pins inserted in a hexagonal wrapper. • A “breakthrough” concepts based on more radical changes and using dense carbide fuel, and very innovative fuel forms and sub-assembly geometries. The uncertainties on the core characteristics due to the most recent nuclear data sets have been evaluated using the BOLNA variance-covariance data. The target uncertainties for the Gen-IV feasibility phase are not met for reactivity and sodium void reactivity effect. Moreover, since the sodium void reactivity effect is extremely sensitive to the sodium cross section, different Na23 evaluations have been used. The difference on the sodium void reactivity effect can differ by more than 15% which is too important according to the design request. It is hence concluded that a new Na23 evaluation is required with an improved Na23 variance–covariance data. The Keff and the Na void effect uncertainties calculated with BOLNA for the SFR are too big when compared to the GEN-IV target uncertainties. The search for an improvement is very much linked to the possibility of tracking the source of major discrepancies when analyzing integral experiments and for this the most precise variance-covariance data are required. Starting from an improved Na23 nuclear data evaluation in an energy region around the Na23 inelastic threshold and an associated revision of Na23 cross section uncertainties, it could be possible to get closer to the requested GEN-IV target uncertainties. A last step to meet the target once this been done could be to go to cross section adjustments. Illustration of the potential of that method is given by the 020.9
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ERALIB1 adjusted library with which uncertainties on sodium-cooled oxide fast reactor characteristics are very much reduced. ACKNOWLEDGEMENTS The help and support received from our CEA colleagues was greatly appreciated during this study. REFERENCES [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
Buiron et al., 2007. Innovative Core Design For Generation IV Sodium-Cooled Fast Reactors, Proc. ICAPP 2007 Int. Conf., Nice, France May 13-18, 2007. Cierjacks et al., 1969. High Resolution Total Neutron Cross Section for Na, Cl, K, V, Mn and Co between 0.5 and 30 MeV, KFK-1000. Fort et al., 1996. Realisation and Performance of the Adjusted Nuclear Data Library ERALIB1, Proc. of Int. Conf. on the Physics of Reactors (PHYSOR-1996), Session F03, Mito, Japan. Fort et al., 2003. Improved performance of the fast reactor calculational system ERANOSERALIB1 due to improved a priori nuclear data and consideration of additional specific integral dat,., Annals of Nuclear Energy, 30, pp. 1879-1898. Gandini and al., 1985. Equivalent Generalized Perturbation Theory. Gandini et al., 1986. Simplified GPT Calculational Procedure. Kopecky et al., 1997. High Resolution Inelastic Scattering Cross Sections of 23Na and 27Al, Proc. Intern. Conf. on Nuclear Data for Science and Technology, Trieste, Italy, 19-24 May 1997. Larson et al., 1976. Measurement of the Neutron Total Cross Section of Sodium from 32 keV to 37 MeV, ORNL-TM-5614, Oak Ridge National Laboratory. Märten et al., 1994. IRMM Report GE/R/ND/02/94. OECD/NEA, 2000. The JEF-2.2 Nuclear Data Library, JEF Report 17. Rimpault et al., 1996. Assessment of Latest Developments in Sodium Void Reactivity Worth Calculations, Proc. Int. Conf. on the Physics of Reactors, Mito, Japan, Vol. 2, E-11. Rimpault and al, 2002. The ERANOS code and data system for fast reactor neutronic analyses, Proceedings of PHYSOR 2002, Seoul, Korea. Rimpault et al., 2007. Sodium cross sections and covariance data for the assessment of SFR neutronic characteristics, NEMEA-4. Rochman et al., 2007. BNL Report BNL-77407-2007-IR, prepared for OECD/WPEC SG26. Shibata, 2002. Evaluation of Neutron Nuclear Data for Sodium-23, Journal of Nuclear Science and Technology, Vol. 39, N°10, pp. 1065-1071. Trykov and Svinin, 2000. Analysis and Reevaluation of the Neutron Cross Sections for 23Na, INDC(CCP)-425. Williams, 1979. Perturbation and Sensitivity Theory for Burnup Analysis, These, The University of Tennessee, Knoxville.
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