EFFECTS OF UNCERTAINTIES IN LEAD CROSS SECTION DATA IN MONTE CARLO ANALYSIS OF LEAD COOLED AND REFLECTED REACTORS

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EFFECTS OF UNCERTAINTIES IN LEAD CROSS SECTION DATA IN

MONTE CARLO ANALYSIS OF LEAD COOLED AND REFLECTED

REACTORS

Miodrag Milošević

Centre for Nuclear Technologies and Research

Vinča Institute of Nuclear Sciences, P.O.Box 522, 11001 Belgrade, Serbia [email protected]

Ehud Greenspan and Jasmina Vujić

Department of Nuclear Engineering

University of California, Berkeley, CA 94720-1730, USA [email protected]; [email protected]

ABSTRACT

This paper describes the problems encountered in the analysis of the Encapsulated Nuclear Heat Source (ENHS) core benchmark and the new cross section libraries developed to overcome these problems. The ENHS is a new lead-bismuth or lead cooled novel reactor concept that is fuelled with metallic alloy of Pu, U and Zr, and is designed to operate for 20 effective full power years without re-fuelling and with very small burn-up reactivity swing. There are numerous

uncertainties in the prediction of core parameters of this and other innovative reactor designs, arising from approximations used in the solution of the transport equation, in nuclear data processing and cross section libraries generation. In this paper we analyzed the effects of uncertainties in lead cross sections data from several versions of ENDF, JENDL and JEFF for lead-cooled and reflected computational benchmarks.

Key Words: ENHS fast reactor, lead cross-section data uncertainties 1. INTRODUCTION

The use of lead or lead-alloy cooled fast reactors in the future can increase nuclear power sustainability, proliferation resistance, inherent safety, and improve economics of small reactors. Furthermore, there has been an 80 reactor-year experience with lead/bismuth eutectic cooled reactors in Russia [1], and there are several new conceptual designs of small lead-bismuth or lead cooled reactors one of which is the Encapsulated Nuclear Heat Source (ENHS) that features natural circulation cooling [2]. The ENHS core contains uniform composition fuel rods without blanket elements and is designed to operate for 20 effective full power years without refueling by maintaining the effective multiplication factor k_eff nearly constant during the fuel burn-up. This paper describes the problems encountered in the analysis of the Encapsulated Nuclear Heat Source (ENHS) benchmark core and the new cross section libraries developed to overcome these problems.

The effect of the lead-coolant on the neutron slowing-down source was considered, and

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Joint International Topical Meeting on Mathematics & Computation and

Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, 2007 2/7

using MCNP-4C [3]. Cross section data for all remaining nuclides were from the new VMCCS continuous energy MCNP library based on the ENDF/B-VI.8 evaluation. This library was created with the NJOY-99 (version 112) code for seven temperatures (300, 600, 700, 750, 800, 900 and 1200 K). Unresolved resonance self-shielding effects were included via subgroup parameters prepared on the basis of probability table method. Significant differences in the cross sections data for lead were found in analyzing several lead-cooled and lead-reflected

computational benchmarks, including the ENHS benchmark.

2. COMPUTATIONAL BENCHMARKS

The single zone model of the ENHS core benchmark [2] is shown in Figure 1.

Figure 1. ENHS core benchmark geometry and dimensions (in cm) The reactor thermal power is 250 MW and the average specific power is 14.3 Wper gram of heavy metal (HM) corresponding to an average linear heat rate of 120 W cm-1. The core is assumed to be homogeneous. The fuel is a metallic alloy of 90 weight % HM and 10% Zr. Its density is assumed to be 75% of the nominal density. The HM consists of 9.81% Pu and 80.19% U. The uranium is depleted to 0.2% 235U. The isotopic composition of the loaded plutonium is 67.2% 239Pu, 21.7% 240Pu, 6.4% 241Pu and 4.7% 242Pu. The clad is made of ferritic - martensitic steel having 17% Cr, 14% Ni, 2.8% Mo and 1.5% Mn; the rest is Fe. The coolant is lead.

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In addition, the following benchmarks with lead reflector were analyzed:

• lead (3 cm) reflected 235U(90%) assembly (benchmark HMH027 [4]);

• lead (3 cm) reflected 239Pu(δ,90%) assembly (benchmark PMH035 [5]);

• subcritical experiments of highly enriched uranium (HEU) 235U (93%) spheres (benchmarks HMF057 S1 and S2) and cylinders (benchmarks HMF057 C2 and C4) with lead reflectors [6];

• three cylinders of lead-reflected HEU; [7] and

• water-reflected clusters of aluminium clad U(4.31)O2 fuel rods in a large water-filled

tank with reflecting walls of depleted uranium, lead, and steel on two opposite sides of the cluster array (benchmarks: LCT010 C1, C2, C3, C4, C20, C21, C22 and C23 [8]).

3. RESULTS

In the ENDF/B-VI releases there are two evaluations for lead nuclides: from 1989 (releases 1, -2, -3, an –4), and from 1996 (releases 5, -6, -7 and –8). Because the ENDF/B-VI.8 evaluation lacks cross-sections data for 204Pb, and since the scattering cross section for 207Pb at fission energies most closely resembles that of 204Pb, the content of 207Pb in the ENDF/B-VI.8 based calculations was increased, atom for atom, to account for the missing 204Pb. The MCNPTM libraries were prepared by using the most recent evaluations:

• ENDF/B-VI.8 (1996), JEFF-3.1 and JENDL-3.3 evaluations for 206Pb, 207Pb and 208Pb nuclides, and

• JEFF-3.1 and JENDL-3.3 evaluations for 204Pb.

Also, additional MCNP libraries were prepared on the basis of some older evaluations:

• ENDF/B-VI.2 (1989) evaluation for 206Pb, 207Pb and 208Pb nuclides, and

• ENDF/B-V.2 and JENDL-3.1 evaluations for Pb nuclide.

The older evaluations of lead cross section data were included in this analysis because:

• ENDF/B-V.2 data are used in the general purpose 238-group SCALETM libraries;

• ENDF/B-VI.2 data were applied for the TAMU libraries preparation (widely used at California University at Berkeley); and

• JENDL-3.1 data were provided the best agreement between calculated and measured results obtained at the BFS-61, -64, -77, -85 and -87 critical configurations with lead located in the core and in the reflector [1].

Results of this analysis for the ENHS benchmark, given in Fig. 2, show a good agreement between calculations based on the ENDF/B-VI.8, JEFF-3.1 and the newest ENDF/B-VIIb2 evaluated cross section data for lead; a notable difference (about 600 pcm) between calculations based on the VI.8 and older evaluated cross section data (V.2 and ENDF/B-VI.2) for lead; and a notable difference (about 700 pcm) between calculations based on the ENDF/B-VI.8 and JENDL-3.3 evaluated cross section data for lead.

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0 5 10 15 20 25 30 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 EOC

One fuel zone 2D-rz model, Pb-nat coolant

MOCUP/M4C (Pb/B-VI.2; Rest/B-VI.2, TAMUlibs/noptable)

MOCUP/M4C (Pb/B-VI.8; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/B-VIIb2; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/B-V.2; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/JEFF-3.1; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/JENDL-3.3; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/JENDL-3.1; Rest/B-VI.8, VMCCS/ptable)

MOCUP/M4C (Pb/Present paper; Rest/B-VI.8, VMCCS/ptable)

E ff e c ti v e ne ut ro n m u lt ip li ca ti on f a c tor

Irradiation time (Years)

Figure 2. ENHS benchmark k_eff burnup evolution calculated using different lead cross section data.

We observed some errors (probably typos) in the resonance parameters for 208Pb in all ENDF/B-VI releases and also in the JEFF-3.1 and newest ENDF/B-ENDF/B-VIIb2 evaluations. To avoid the uncertainty due these errors and the Rich-Moor representation of cross section data in the resolved resonance energy range, we prepared our own evaluation of natural lead cross sections by using experimental results given in the EXFOR collection of cross section data. The

experimental results for 208_{Pb cross section data, that we used, are given in Fig. 3, together with}

the JEFF-3.1, a most recent evaluation.

Although, the energy spectra of lead-reflected experimental benchmarks and ENHS core benchmark are different, the influence of lead cross sections on the k_eff (Fig. 4) is very

important. The results for eight thermal neutron critical systems reflected with lead are given in Fig. 5.

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103 104 105 106 100 101 102 Carlton (1991) Harvey (1999) JEFF-3.1 JENDL-3.1 Voss (1999) Wisshak (1997) Farrell (1965) Aleksandrov (1997) 208 Pb to ta l cr os s se ct ion [b ar n] Energy [eV]

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0 1 2 3 4 5 6 7 8 9 10 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 Benchmarks uncertainty HMF27 PMF35 HMF57 HMF57 HMF57 HMF57 HMF64 HMF64 HMF64 S S S1 S2 C2 C4 C1 C2 C3 JEFF-3.1 JEFF-3.1M ENDF/B-VIIb2 ENDF/B-VI.8 ENDF/B-VI.2 ENDF/B-V.2 JENDL-3.3 JENDL-3.1 Present paper React iv it y [ p cm ]

Figure 4. k_eff calculations for fast neutron experimental benchmarks

0 1 2 3 4 5 6 7 8 9 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 Benchmarks uncertainty LCT010 LCT010 LCT010 LCT010 LCT010 LCT010 LCT010 LCT010 C1 C2 C3 C4 C20 C21 C22 C23 JEFF-3.1 JEFF-3.1M ENDF/B-VIIb2 ENDF/B-VI.8 ENDF/B-VI.2 ENDF/B-V.2 JENDL-3.3 JENDL-3.1 Present paper React iv it y [ p c m ]

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4. CONCLUSION

This paper describes the problems encountered in the analysis of the lead-cooled ENHS core with fast spectrum and several lead-reflected benchmarks due to differences in lead cross sections from various cross section libraries. We also prepared our own cross section library for lead isotopes. Based on the presented results, our own cross section librabry and JEFF-3.1 evaluation gave the best results for fast reactors (with very hard energy spectrum) and also for thermal system reflected by lead. This means that we can also expect that our evaluation and JEFF-3.1 evaluation can provide the best results for the intermediate energy spectra system like ENHS cores.

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