comparative study on neutronics characteristics ... - j-stage

J-STAGE Advance Publication date: 28 February, 2017Paper No.16-00592

© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/mej.16-00592]

Vol.4, No.3, 2017Bulletin of the JSME

Mechanical Engineering Journal

Comparative study on neutronics characteristics of a 1500 MWe metal fuel sodium-cooled fast reactor

Kazuya OHGAMA*, Gerardo ALIBERTI**, Nicolas E. STAUFF**, Shigeo OHKI* and Taek K. KIM ** * Advanced Fast Reactor Cycle System Research and Development Center, Japan Atomic Energy Agency

4002, Narita, O-arai-machi, Higashi-Ibaraki-gun, Ibaraki, 311-1393, Japan

E-mail: [email protected]

**Nuclear Engineering Division, Argonne National Laboratory

9700 S. Cass Avenue, Argonne, IL 60439, USA

Abstract Under the cooperative effort of the Civil Nuclear Energy R&D Working Group within the framework of the U.S.-Japan bilateral, Argonne National Laboratory (ANL) and Japan Atomic Energy Agency (JAEA) have been performing benchmark study using the Japan Sodium-cooled Fast Reactor (JSFR) design with metal fuel. In this benchmark study, core characteristic parameters at the beginning of cycle were evaluated by the best estimate deterministic and stochastic methodologies of ANL and JAEA. The results obtained by both institutions show a good agreement with less than 200 pcm of discrepancy in the neutron multiplication factor, and less than 3% of discrepancy in the sodium void reactivity, Doppler reactivity, and control rod worth. The results by the stochastic and deterministic approaches were compared in each party to investigate impacts of the deterministic approximation and to understand potential variations in the results due to different calculation methodologies employed. From the detailed analysis of methodologies, it was found that the good agreement in the multiplication factor from the deterministic calculations comes from the cancellation of the differences in the methodology (0.4%) and nuclear data (0.6%). The different treatment in reflector cross section generation was estimated as the major cause of the discrepancy between the multiplication factors by the JAEA and ANL deterministic methodologies. Impacts of the nuclear data libraries were also investigated using a sensitivity analysis methodology. The differences in the inelastic scattering cross sections of U-238, ν values and fission cross sections of Pu-239 and μ-average of Na-23 are the major contributors to the difference in the multiplication factors. Key words: Sodium-cooled fast reactor, Metal fuel, Benchmark, Verification, Monte Carlo, JSFR

1. Introduction

The sodium-cooled fast reactor (SFR) with metal fuel has higher heavy metal density compared to the SFR with

MOX fuel. These advantages enable us to design a superior core with high breeding ratio and low fuel inventory features. Furthermore, some favorable safety features such as negative feedback caused by extrusion and dispersion of fuel in postulated severe accident scenarios can be expected.

For these reasons, the metal fuel core concept has been studied and U.S. has a lot of experience in the development of the metal fuel core such as operational experience of EBR-II. Recently, under the Global Nuclear Energy Partnership (GNEP) project, ANL has developed 1000 MWt Advanced Burner Reactor (ABR-1000) with U-TRU-Zr ternary metal alloy fuel (Kim et al., 2009). Japan also has been studying the metal fuel core concept (Uematsu et al., 2012). In the development of the Japan Sodium-cooled Fast Reactor (JSFR), the metal fuel core concept was chosen as a possible alternative to the MOX fuel core concept.

Recently, within the framework of the U.S.-Japan bilateral, the Civil Nuclear Energy R&D Working Group (CNWG) was formed to coordinate nuclear energy R&Ds in advanced reactor and fuel cycle technologies, and the existing reactor fleet sustainability. In this cooperative framework, a core conceptual design study and a numerical

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Received: 31 October 2016; Accepted: 20 February 2017

2© 2017 The Japan Society of Mechanical Engineers

Ohgama, Aliberti, Stauff, Ohki and Kim, Mechanical Engineering Journal, Vol.4, No.3 (2017)

[DOI: 10.1299/mej.16-00592]

benchmark study on nuclear characteristics of a SFR with metal fuel was proposed as one of the projects in the CNWG, and conducted by ANL and JAEA.

For the core conceptual design study, it is essential to ensure the credibility of its modeling methodology. For this purpose, numerical benchmark studies of ANL and JAEA in different core designs were planned. In the previous study, ANL and JAEA have carried out a benchmark study using the ABR-1000 (Stauff et al., 2015), as the extended study to the previous study, an additional benchmark study using the 3530 MWth JSFR design with metal fuel was conducted and the results are summarized in this paper.

2. Benchmark Condition 2.1 Reference core specifications

The core specifications of JSFR are summarized in Table 1 and the fuel compositions are provided in Refs. (Ohki et al., 2006, Ogawa et al., 2007). Thermal and electric power outputs are 3530 and 1500 MW, respectively. The core outlet and inlet temperatures are 550 and 395 °C, respectively. The active core height is about 0.8 m, and the equivalent core diameter is 5.2 m. The core contains 645 inner and outer core fuel subassemblies and 28 control rods (CRs), and it is surrounded by one layer of radial stainless steel reflector and two layers of Zr-H shielding as shown in Fig. 1.

Table 1 Specifications of JSFR metallic-fuel core

Item (Unit) Specification

Thermal power output (MWt) Electric power output (MWe) Outlet/inlet temperature (°C) Operational cycle length (Month) Refueling batch Core height / Active core height (m)

Core equivalent diameter (m) Circumscribed circle diameter of shielding (m) Subassembly pitch (m) Number of fuel subassemblies Number of fuel pins per subassembly Fuel pin diameter (mm)

Pu enrichment (wt%) Zr content rate (wt%) Fuel slug smear density (%TD)

3530 1500 550/395 24.5 3 0.75/0.81*1 5.2 6.5 0.192 150/495*2 331/331*2 8.5/8.5*2

12.2/12.2*2 10.0/6.0*2

75/75*2 *1 8% axial fuel slug elongation is considered.

*2 Inner core/outer core.

Fig. 1 Configuration of JSFR metallic-fuel core

Radial direction 1

Radial direction 2Inner core fuel

Outer core fuel

Primary control rod

Secondary control rodRadial shielding(Zr-H)

Radial reflector(Stainless steel)

S

S

S

S

SS

S

P

P

P

PP

P

P

P P

P

P

PP

P P

P

P

P

P

P

P

2



[DOI: 10.1299/mej.16-00592]

The composition of the U-TRU-Zr ternary fuel was obtained through multi-recycling of metallic fuel discharged

from the JSFR. In order to achieve flat radial power distribution during power operation, Zr-concentrations of inner core and outer core fuels were set to be 10 and 6 wt%, respectively. 2.2 Methodologies

The JAEA and ANL neutronic calculation methodologies are summarized in Table 2. JAEA utilized its suite of deterministic codes such as the lattice code SLAROM-UF (Hazama et al., 2006), the diffusion calculation code CITATION (Fowler and Vondy, 1971) for this evaluation with the JENDL-4.0 nuclear data library (Shibata et al., 2011). The results obtained by the diffusion calculations were corrected with transport correction factors evaluated by the transport code TRITAC (Yamamoto, 1995). ANL used its suite of fast reactor neutronics tools, which includes the MC2-3 code system (Lee and Yang, 2012) for generating multi-group cross-sections using the ENDF/B-VII.0 nuclear data file (Chadwick et al., 2006) and the VARIANT solver option (Palmiotti et al., 1993) of the DIF3D/REBUS-3 code system (Toppel, 1983) for performing flux and burnup calculations.

Both institutions used a 1D-heterogeneous ring model shown in Fig. 2 for lattice calculation and solve the transport equation for flux calculation. As for control rod 1D-heterogeneous model, JAEA used the reaction rate ratio preservation (RRRP) method (Kitada et al., 1994). In addition, high-fidelity stochastic calculations were performed by JAEA and ANL using the MVP (Nagaya et al., 2005, Okumura and Nagaya, 2011) and MCNP5 codes (X-5 Monte Carlo Team, 2008), respectively.

Table 2 Comparison of methodologies

JAEA ANL

Nuclear Data JENDL-4.0 ENDF/B-VII.0

Lattice code Energy groups Heterogeneous

treatments

SLAROM-UF175 *1

Yes (1D) *3

MC2-3 2082 *2

Yes (1D)

Core code Calculation

Energy groups Geometry

CITATION Diffusion *4

175 3D

DIF3D/REBUS-3 Transport

33 3D

*1 175 group above 50keV and 100,000 group below 50keV.

*2 2082 group from 20MeV to 0.4 eV.

*3 Reaction Rate Ratio Preservation (RRRP) method for control rods. *4 Transport correction by the TRITAC code.

Fig. 2 Lattice calculation model

Fuel subassembly

4.270

Gap sodiumWrapper tube

FuelCladding

Coolant1D-heterogeneous ring model

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[DOI: 10.1299/mej.16-00592]

3. Results In this benchmark study, core characteristic parameters at the beginning of cycle were evaluated by the best

estimate deterministic and stochastic methodologies of JAEA and ANL. The results by deterministic methodologies are shown in Table 3. The JAEA results were corrected by transport correction factors in Table 4.

The sodium void reactivity is defined by Eq.(1) as the reactivity change by voiding the sodium in the active core region. ∆ρactive core = ρvoid (active core) - ρnominal (1) Where the subscripts “void” and “nominal” indicate the sodium voided state (sodium coolant and inter-assembly sodium gap are 100% voided) and nominal state, respectively. The Doppler constant is defined by Eq.(2). KD = (ρhigh - ρnominal )/ln2 (2) Where the subscript “high” indicates the core temperature state when the fuel temperature in Kelvin is a factor of two of that of the nominal average (903.15 K) fuel temperature. Finally, the control rod worth is determined by the reactivity change due to full insertion (i.e., up to the bottom of the active core) of all primary and secondary control rods.

The results obtained by both institutions show a good agreement with less than 200 pcm of discrepancy in the neutron multiplication factor, and less than 3% of discrepancy in the sodium void reactivity, Doppler reactivity, and control rod worth. Radial power distributions evaluated by JAEA and ANL at the beginning of cycle along the radial directions 1 and 2 indicated in Fig. 1 are shown in Fig. 3. Both results show a good agreement with less than 3% discrepancy.

Table 3 Results of JAEA and ANL calculations

JAEA ANL Difference*3

keff 1.03997 1.03823 0.2% ΔρNa (pcm) *1 2632 2628 0.2% ΔρDoppler (pcm) -419 -408 2.7% ΔρCR (pcm) *2 -6121 -6290 -2.7% βeff (pcm) 366 359 1.9% *1 Core void. *2 All control rods.

*3 JAEA - ANL.

Fig. 3 Radial power distribution

0 5 10 150

5

10

0 5 10 15

Control rod channelControl rod channel

Radial direction 1

Core radial position (Row)

JAEA ANLRadial direction 2

Core radial position (Row)

Pow

er (

MW

/Sub

asse

mbl

y)

015

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[DOI: 10.1299/mej.16-00592]

Table 4 Transport correction for JSFR large metallic-fuel core

Transport correction *1

keff 0.5% ΔρNa 3.0% ΔρDoppler -0.2% ΔρCR -3.5% *1 Evaluated by the transport code TRITAC with 18 energy group using heterogeneous lattice model.

4. Discussion 4.1 Verification of methodologies

To verify the calculation results by deterministic methodologies, comparison between deterministic and stochastic

calculations was essential. Since a stochastic calculation with continuous-energy and heterogeneous precise geometry model is a less approximated method, it can provide a reference solution to verify a calculation by the deterministic methodology. The results of stochastic calculations using the MVP with the JENDL-4.0 and the MCNP with the ENDF/B-VII.0 are provided in Table 5.

The differences between JAEA and ANL stochastic calculations are about 0.6% in the core multiplication factor, and 1.5 – 4.8% in sodium worth, Doppler constant, and CR worth. The differences in the stochastic calculations are mainly due to the used nuclear data files by both participants. The detailed impacts of nuclear data are discussed in section 4.2.

Table 5 Results of JAEA and ANL stochastic calculations

JAEA ANL MVP MCNP Difference*1

JENDL-4.0 ENDF/B-VII.0

keff 1.04324 1.03719 0.6% ΔρNa (pcm) 2656 2534 4.8% ΔρDoppler(pcm) -404 -421 -4.0% ΔρCR (pcm) -6120 -6031 1.5%

*1 JAEA - ANL.

4.1.1 Deterministic approximation

The differences between calculations by the deterministic and stochastic approaches are shown in Table 6. The difference in multiplication factors between JAEA and ANL deterministic calculations is about 0.2% (~200 pcm) in Table 3, while it was 0.6% in the stochastic calculations. Thus, there are some error cancelations in the differences of deterministic calculations of both institutions. Although the ANL results in the multiplication factor by the deterministic and stochastic methodologies show good agreement, there was 0.3% difference in the multiplication factor in JAEA results. This discrepancy was also observed in the past study (Stauff et al., 2015).

Table 6 Deterministic approximation

JAEA ANL MVP/CITATION*1 MCNP/DIF3D

keff 0.3% -0.1% ΔρNa 0.9% -3.6% ΔρDoppler -3.6% 3.2% ΔρCR 0.0% -4.1%

*1 Including transport correction.

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[DOI: 10.1299/mej.16-00592]

4.1.2 Heterogeneous lattice effect

Heterogeneous effects in lattice calculations were analyzed to investigate the difference shown in Table 6, since

appropriate treatment of heterogeneity of lattice is important to ensure the accuracy of the calculations by the deterministic methodologies. In both deterministic methodologies, the 1D-heterogeneous model is applied to treat heterogeneity of lattice. Comparisons of heterogeneous lattice effects between both deterministic approaches were performed.

JAEA evaluated differences in the core characteristics between calculations with the 1D heterogeneous and homogeneous lattice models. The results are shown in Table 7. JAEA also conducted comparison of calculations using the MVP code with heterogeneous (precise geometry model) and homogeneous models. These results are shown in parentheses in Table 7. The results obtained by the deterministic show a good agreement with those by the stochastics. ANL also evaluated differences between calculations by the deterministic with the 1D heterogeneous and homogeneous lattice models. The results of the heterogeneous effects in the multiplication factor obtained by JAEA and ANL with deterministic and stochastic approaches display a good agreement. The other results by JAEA and ANL were qualitatively consistent.

Table 7 Heterogeneous effects in lattice calculations

JAEA ANL

keff 0.60% (0.60%) *1 0.61% (0.59%) *1 ΔρNa -7.5% (-7.4%) -3.5% ΔρDoppler 8.5 (10.5%) 4.6% ΔρCR -10.3 (-10.1%) -6.6% *1 Values in ( ) show results by the stochastic calculations.

4.1.3 Investigation of the difference on multiplication factor

The analysis of the heterogeneous lattice effect of the multiplication factor indicated that the treatment of

heterogeneity of lattice wasn’t a cause of the difference in the deterministic approximation shown in Table 6 between JAEA and ANL. From the further detailed comparison of both methodologies, the treatment of direct contact of driver fuels to reflectors was expected to be a cause of difference.

The impact of direct contact of driver fuels to radial reflectors in a SFR core has been studied (Lebrat et al., 2002, Aliberti et al., 2004, Chiba, 2005), and the results indicate that appropriate treatment in reflector cross section generation is important to estimate the physics parameters accurately. ANL developed a methodology to generate reflector cross sections of a core that does not have radial blankets and have applied it to their standard analysis methodology.

The JAEA standard analysis methodology didn’t include a methodology for the treatment of direct contact of driver fuels to reflectors. The lack of this treatment was estimated as the major factor of the discrepancy in the multiplication factor by the deterministic and stochastic methodologies in JAEA results. Currently, JAEA is improving their methodology. 4.2 Analysis of nuclear data

Since there were differences in the core characteristics by the stochastic between JAEA and ANL in Table 5, these differences were caused by differences in the nuclear data library employed.

To investigate the differences in the core characteristics such as the multiplication factor and sodium void reactivity, impacts of differences between the JENDL-4.0 and ENDF/B-VII.1 libraries were analyzed using sensitivity coefficients evaluated by the sensitivity analysis code SAGEP (Hara et al., 1984) based on the generalized perturbation theory (Usachev, 1964). Sensitivity coefficients describe changes of the core characteristics per unit change in the nuclear data. Thus, impacts of the core characteristics caused by differences in the nuclear data can be calculated by multiplying the sensitivity coefficients with the cross section variation between the two libraries.

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[DOI: 10.1299/mej.16-00592]

The evaluations of the major actinides in the ENDF/B-VII.1 were not changed from the ENDF/B-VII.0 (Chadwick et al., 2011). Thus, similar results can be observed if the ENDF/B-VII.0 was used in the sensitivity analysis instead of the ENDFB-VII.1.

4.2.1 Multiplication factor

From the results of Table 5, there was about 0.6% difference in the multiplication factor between the results by the

MVP with the JENDL-4.0 and the MCNP with the ENDF-B/VII.0. Figure 4 shows the results of sensitivity analysis of multiplication factor. The differences between the ENDF/B-VII.1 and JENDL-4.0 libraries in the inelastic scattering cross sections of U-238, ν values and fission cross sections of Pu-239, μ-average of Na-23 contributed to increase the multiplication factor. On the other hand, the inelastic cross section of Fe-56, inelastic and elastic scattering cross section of Na-23 worked oppositely.

4.2.2 Sodium void reactivity

The difference in the sodium void reactivity between JAEA and ANL stochastic methodologies was about 5% in

Table 5. To investigate the major factor of the difference in the sodium void reactivity, the sensitivity analysis by the SAGEP code was performed. The result of sensitivity analysis in Fig. 5 indicated that the differences in the inelastic and elastic scattering cross sections of Na-23 were the major factor of difference in the sodium void reactivity.

Fig. 4 Sensitivity analysis of multiplication factor

Fig. 5 Sensitivity analysis of sodium void reactivity

U-2

38 F

issi

onU

-238

Cap

ture

U-2

38 E

last

icU

-238

Ine

last

icPu

-238

Fis

sion

Pu-2

39 F

issi

onPu

-239

nu

Pu-

239

Cap

ture

Pu-

239

Inel

asti

cPu

-240

Fis

sion

Pu-2

40 n

uP

u-24

0 C

aptu

rePu

-241

Fis

sion

Fe-5

6 C

aptu

reFe

-56

Ela

stic

Fe-5

6 In

elas

tic

Fe-5

6 m

uN

a-23

Cap

ture

Na-

23 E

last

icN

a-23

Ine

last

icN

a-23

mu

Cr-

52 E

last

icC

r-52

mu

Tot

al

-0.5

0.0

0.5

Mil

tipl

icat

ion

fact

or(%

) JENDL-4.0 / ENDF/B-VII.1

U-2

38 F

issi

onU

-238

Cap

ture

U-2

38 E

last

icU

-238

Ine

last

icPu

-238

Fis

sion

Pu-2

39 F

issi

onPu

-239

nu

Pu-

239

Cap

ture

Pu-

239

Inel

asti

cPu

-240

Fis

sion

Pu-2

40 n

uP

u-24

0 C

aptu

rePu

-241

Fis

sion

Fe-5

6 C

aptu

reFe

-56

Ela

stic

Fe-5

6 In

elas

tic

Fe-5

6 m

uN

a-23

Cap

ture

Na-

23 E

last

icN

a-23

Ine

last

icN

a-23

mu

Cr-

52 E

last

icC

r-52

mu

Tot

al

-10

-5

0

5

10

Sod

ium

voi

d re

acti

vity

(%

) JENDL-4.0 / ENDF/B-VII.1

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[DOI: 10.1299/mej.16-00592]

5. Conclusions In this benchmark study, the core characteristic parameters at the beginning of cycle were evaluated by the best

estimate deterministic and stochastic methodologies of JAEA and ANL. The best estimate deterministic results obtained by both institutions show a good agreement with less than 200 pcm of discrepancy in the multiplication factor, and less than 3% of discrepancy in the sodium void reactivity, Doppler reactivity, and control rod worth. The radial power distributions evaluated by JAEA and ANL show a good agreement with less than 3% discrepancy.

From the detailed analysis of the methodologies, it was concluded that the good agreement in multiplication factor from the deterministic calculations comes from the cancellation of the differences on the methodology (0.4%) and nuclear data (0.6%). The different treatment in reflector cross section generation was estimated as the major cause of the discrepancy between the multiplication factors by the JAEA and ANL deterministic methodologies. Currently, JAEA is improving its methodology.

The differences in the inelastic scattering cross sections of U-238, ν values and fission cross sections of Pu-239, μ-average of Na-23 are the major contributors to the difference in the multiplication factors. In the case of the sodium void reactivity, the differences in the core characteristics come from the differences in the inelastic and elastic scattering cross sections of Na-23.

Acknowledgements

The authors from JAEA thank Mr A. Soga and Mr H. Komoda from NESI Inc. for their assistance with the preparatory work for calculations. Argonne National Laboratory’s work was supported under U.S. Department of Energy (DOE) contract DE-AC02-06CH11357.

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