1.3-Fast Reactor Physics

Fast Reactor Physics – 1 Spectrum and Cross Sections

Robert N. Hill Program Leader – Advanced Nuclear Energy R&D Nuclear Engineering Division Argonne National Laboratory

NRC Fast Reactor Technology Training Curriculum White Flint, MD March 26, 2019

Work sponsored by U.S. Department of Energy Office of Nuclear Energy, Science & Technology Outline

. Introduction to Fast Reactor Physics – Fast energy spectrum • Neutron moderation – Impacts of fast energy spectrum • Fission-to-capture, enrichment, etc. – Comparison to LWR neutron physics

. Nuclear Data and Validation – Typical Power Distributions – Anticipated uncertainties – Modern covariance and data adjustment

2 Comparison of LWR and SFR Spectra

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0.45 LWR (EPRI NP-3787) 0.40 SFR (ufg MC2 -2 metal) 0.35

0.30

0.25

0.20

0.15 Normalized Flux/Lethargy Normalized

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0.05

0.00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Energy (eV) . In LWR, most fissions occur in the 0.1 eV thermal “peak” . In SFR, moderation is avoided – no thermal neutrons; most fissions occur at higher energies (>10 keV) 3 Neutron Moderation Comparison

. Significant elastic scattering of the -1 σs (barn) N (#/barn⋅cm) ξΣs (cm ) neutrons after fission TRU 4.0 3.2E-03 1.1E-04 . In FRs, neutron moderation is avoided by using high A materials U 5.6 5.6E-03 2.7E-04 – Sodium is most moderating Zr 8.1 2.6E-03 4.6E-04 Fe 3.4 1.9E-02 2.3E-03

. In LWRs, neutrons are moderated Na 3.8 8.2E-03 2.7E-03 primarily by hydrogen H 11.9 2.9E-02 3.5E-01 . Oxygen in water and fuel also slows down the neutrons

. Slowing-down power in FR is ~1% that observed for typical LWR . Thus, neutrons are either absorbed or leak from the reactor before they can reach thermal energies

4 Fast Reactor Moderating Materials . Lead has highest scattering of the σ (barn) N (#/barn⋅cm) ξΣ (cm-1) neutrons, but little moderation s s TRU 4.0 3.2E-03 1.1E-04

. Oxide fuel in SFR leads to a significant U 5.6 5.6E-03 2.7E-04 moderation effect – resonances also Zr 8.1 2.6E-03 4.6E-04 observed Fe 3.4 1.9E-02 2.3E-03 . LFR designs also utilize nitride or oxide Na 3.8 8.2E-03 2.7E-03 fuel forms O 3.6 1.4E-02 5.8E-03 . In modern GFR designs, SiC matrix for Pb 8.6 1.6E-03 1.3E-04 fuel is utilized, with most moderation C 3.9 1.6E-02 1.0E-02 of the FR cases He 1.7 3.1E-04 2.3E-04

. Net result is that the SFR-metal has the hardest neutron spectrum – SFR-oxide and LFR similar with slightly more moderation . GFR (with silicon-carbide matrix) has significant low energy tail 5 Comparison of Fast Reactor Spectra

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0.45 SFR - Metal Fuel 0.40 SFR - Oxide Fuel

0.35 Gas cooled FR (GFR)

0.30 Lead cooled FR (LFR)

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Norm. Flux/Lethargy Norm. 0.15

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0.00 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Energy (eV) . Predictable spectral differences between fast reactor concepts . Low energy tail caused by moderating materials (carbon in GFR) . At high energy (>1 MeV) lead is effective inelastic scattering material . Characteristic resonances from oxygen, iron are evident 6 Spectral Variation of Neutron Cross Sections: Pu-239

. Fission and capture cross section >100X higher in thermal range . Sharp decrease in capture cross section at high energy

7 Spectral Variation of Neutron Cross Sections: U-238

. Much smaller thermal increase in capture (~10X) . Unresolved resonance range begins at ~10 keV . Threshold fission at ~1 MeV (~10% of total fission rate in a fast reactor)

8 Spectral Variation of Neutron Cross Sections: Fe and Na

. Capture cross sections much higher in thermal range . Significant scattering resonance structure throughout fast range

9 Fission Probabilities (Fission/Absorption)

Fast Reactor Thermal Isotope (Metal fuel) Reactor U235 0.80 0.81 U238 0.17 0.10 Np237 0.27 0.02 Pu238 0.70 0.08 Pu239 0.86 0.64 Pu240 0.55 0.01 Pu241 0.87 0.75 Pu242 0.52 0.02 Am241 0.21 0.01 Am243 0.23 0.01 Cm244 0.45 0.06

. Fast fission fraction is a bit higher for Pu-239/241, similar for U-235 . However, for non-fissile isotopes in thermal reactor, almost always (>90%) neutron capture, with possible later fission as a higher A fissile isotope

10 Equilibrium Composition in Fast and Thermal Spectra

Fast Thermal Thermal Isotope Reactor Equil. Once-thru Np237 0.008 0.002 0.048 Pu238 0.014 0.046 0.024 Pu239 0.666 0.388 0.476 Pu240 0.243 0.197 0.225 Pu241 0.021 0.111 0.106 Pu242 0.018 0.085 0.066 Am241 0.021 0.019 0.034 Am242m 0.001 0.001 0.000 Am243 0.005 0.033 0.015 Cm242 0.000 0.002 0.000 Cm244 0.002 0.055 0.005 Cm245 0.000 0.018 0.000 Cm246 0.000 0.031 0 Cm247 0.000 0.004 0 Cm248 0.000 0.006 0

. Equilibrium higher actinide content much lower in fast spectrum system . Generation of Pu-241 (key waste decay chain) is suppressed . Once-through LWR composition has not reached thermal higher actinide (Am/Cm) equilibrium, but higher than fast reactor (U-238) equilibrium Salvatores et al, “Fuel Cycle Analysis of TRU or MA Burner Fast Reactors with Variable Conversion Ratio, Nuclear Engineering and Design, 219, 2160 (2009) 11 Impact of Energy Spectrum on Enrichment and Parasitic Absorption

Thermal Concepts (barns) Fast Concepts (barns) Reaction PWR VHTR SCWR SFR LFR GFR U238c 0.91 4.80 0.95 0.20 0.26 0.32 Pu239f 89.2 164.5 138.8 1.65 1.69 1.90 P239f/U238c 97.7 34.3 146.6 8.14 6.59 6.00 Fec 0.4 0.007 Fission Prod.c 90 0.2

. One-group cross sections are significantly reduced in fast system . Generation-IV fast systems have similar characteristics . U-238 capture is much more prominent (low P239f/U238c) in fast reactors – Therefore, a higher enrichment is required to achieve criticality . The parasitic capture cross section of fission products and conventional structural materials is much higher in a thermal spectrum

12 Neutron Balance

SFR PWR CR=1.0 CR=0.5 U-235 or TRU enrichment, % 4.2 13.9 33.3 fission 100.0% 99.8% 99.9% Source (n,2n) 0.2% 0.1% leakage 3.5% 22.9% 28.7% radial 3.0% 12.3% 16.6% axial 0.4% 10.6% 12.1% absorption 96.5% 77.1% 71.3% fuel 76.7% 71.8% 62.2% Loss (U-238 capture) (27.2%) (31.6%) (17.1%)

coolant 3.4% 0.1% 0.1% structure 0.6% 3.7% 3.7% fission product 6.8% 1.5% 2.4% control 9.0% 0.0% 2.9% . Conversion ratio defined as ratio of TRU production/TRU destruction – Slightly different than traditional breeding ratio with fissile focus

13 Summary of Fast Spectrum Physics Distinctions

. Combination of increased fission/absorption and increased number of neutrons/fission yields more excess neutrons from Pu-239 – Enables “breeding” of fissile material . In a fast spectrum, U-238 capture is more prominent – Higher enrichment (TRU/HM) is required (neutron balance) – Enhances internal conversion . Reduced parasitic capture and improved neutron balance – Allows the use of conventional stainless steel structures – Slow loss of reactivity with burnup • Less fission product capture and more internal conversion . The lower absorption cross section of all materials leads to a much longer neutron diffusion length (10-20 cm, as compared to 2 cm in LWR) – Neutron leakage is increased (>20% in typical designs, reactivity coefficients) – Reflector effects are more important – Heterogeneity effects are relatively unimportant

14 Outline

. Nuclear Data and Validation – Typical Power Distributions – Anticipated uncertainties – Modern covariance and data adjustment

15 Typical Design Specifications of LWR and SFR

PWR SFR Specific power (kWt/kgHM) 786 (U-235) 556 (Pu fissile) General Power density (MWt/m3) 102 300 Rod outer diameter (mm) 9.5 7.9 Clad thickness (mm) 0.57 0.36 Fuel Rod pitch-to-diameter ratio 1.33 1.15 Enrichment (%) ~4.0 ~20 Pu/(Pu+U) Average burnup (MWd/kg) 40 100 pressure (MPa) 15.5 0.1 inlet temp. ( ) 293 332 Coolant outlet temp.℃( ) 329 499 reactor Δp (MPa)℃ 0.345 0.827 Thermal average (MW/m2) 0.584 1.1 Hydraulic Rod surface heat flux maximum MW/m2) 1.46 1.8 Average linear heat rate (kW/m) 17.5 27.1 pressure (MPa) 7.58 15.2 Steam temperature ( ) 296 455

℃ 16 Conventional Approximations . Detailed space-energy-direction analysis performed for a repeated portion of the geometric domain (lattice physics) – Lower order approximation of Boltzmann equation for whole-core analysis – Assumed/approximate boundary conditions – Condensed space/energy cross sections – Detailed information recovered by de-homogenization methods . Nuclide depletion and buildup using quasi-steady model – Depletion steps are ~ hours – days . Faster transients modeled with condensed (often single point) model for time-dependent amplitude – Accuracy depends on frequency of kinetic-parameter and space-energy-direction flux shape recalculation

17 Assembly Power (MW) of 1000 MWt ABR – Startup Core

0.07 0.06 0.05 0.02 0.07 0.06 0.05 0.02 A BOC A BOC 0.05 0.05 0.04 0.03 0.08 0.02 B EOC B EOC 0.05 0.05 0.04 0.03 0.08 0.02 0.11 0.11 0.08 0.05 0.03 0.08 0.02 0.12 0.11 0.09 0.06 0.03 0.08 0.02 4.35 4.24 3.80 0.13 0.09 0.05 0.02 0.05 4.68 4.55 4.05 4.35 4.24 3.86 0.14 0.10 0.06 0.02 0.05 4.65 4.53 4.10 5.32 5.24 4.53 3.77 0.13 0.08 0.08 0.06 5.83 5.72 4.90 4.03 5.47 5.27 4.77 4.10 0.14 0.09 0.08 0.06 5.94 5.71 5.13 4.36 0.44 6.02 5.74 0.37 4.53 3.80 0.11 0.03 0.07 6.67 6.33 4.90 4.05 0.30 6.14 5.86 0.26 4.77 3.86 0.11 0.03 0.07 6.73 6.41 5.13 4.10 5.42 5.44 6.20 5.74 5.24 4.24 0.11 0.04 0.07 5.69 5.73 6.88 6.33 5.72 4.55 5.62 5.58 6.26 5.86 5.27 4.24 0.12 0.04 0.07 5.88 5.85 6.87 6.41 5.71 4.53 6.06 5.83 5.65 5.44 6.02 5.32 4.35 0.12 0.05 0.06 6.38 6.13 5.94 5.73 6.33 5.83 4.68 5.99 5.95 5.83 5.58 6.14 5.47 4.35 0.12 0.05 0.06 6.28 6.23 6.10 5.85 6.41 5.94 4.65 6.28 0.42 5.83 5.42 0.44 5.35 4.27 0.11 0.05 0.05 6.61 6.13 5.69 5.86 4.58 6.21 0.30 5.95 5.62 0.30 5.47 4.24 0.11 0.05 0.05 6.50 6.23 5.88 5.94 4.53 6.76 6.51 6.28 6.06 5.49 6.11 5.31 3.85 0.08 0.05 0.02 7.13 6.85 6.81 6.38 5.77 6.77 5.80 4.10 6.40 6.33 6.21 5.99 5.62 6.14 5.27 3.86 0.09 0.05 0.02 6.72 6.64 6.50 6.28 5.88 6.73 5.71 4.10 6.92 6.76 6.47 6.11 5.61 5.86 4.60 0.13 0.05 0.04 7.28 7.13 6.81 6.42 5.91 6.46 4.98 6.48 6.40 6.21 5.95 5.58 5.86 4.77 0.14 0.06 0.04 6.79 6.72 6.50 6.23 5.85 6.41 5.13 0.33 6.94 6.71 0.29 5.98 6.39 0.38 3.83 0.09 0.03 0.03 7.31 7.06 6.28 7.08 4.10 0.33 6.48 6.33 0.30 5.83 6.26 0.26 4.10 0.10 0.03 0.03 6.79 6.64 6.10 6.87 4.36 6.46 6.47 6.11 5.61 5.86 4.60 0.13 0.05 0.08 7.13 6.81 6.42 5.91 6.46 4.98 6.40 6.21 5.95 5.58 5.86 4.77 0.14 0.06 0.08 6.72 6.50 6.23 5.85 6.40 5.13 6.06 5.49 6.11 5.31 3.85 0.08 0.03 0.02 6.38 5.77 6.77 5.80 4.10 5.99 5.62 6.14 5.27 3.86 0.09 0.03 0.02 6.28 5.88 6.73 5.71 4.10 0.44 5.35 4.27 0.11 0.04 0.05 5.86 4.58 0.30 5.47 4.24 0.11 0.04 0.05 5.94 4.53 4.35 0.12 0.05 0.06 4.68 4.35 0.12 0.05 0.06 4.65 0.05 0.07 Fresh Assembly Batch-averaged 0.05 0.07 Power Assembly Power

 Power peaking factor (BOC/EOC) = 1.43 /1.39 18 Power Profiles of 1000 MWt ABR – Startup Core 450 450 Core midplane - BOC Core midplane - EOC 400 Core top - BOC 400 Core top - EOC

350 350

300 300

250 250

200 200 Power density (kW/l) Power Density (kW/l) 150 150 IC - BOC IC - EOC 100 100 OC - BOC OC - EOC

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0 0 0 20 40 60 80 100 120 140 0 10 20 30 40 50 60 70 80 90 Distance from core center (cm) Height from core bottom (cm) . Bottom skewed axial distribution (control assembly tip position at BOC = 57 cm) . Axial power peaking factor at BOC/EOC = 1.20/1.16

19 Estimated Target Accuracies for Fast Reactors  Two main sources of Parameter Current Desired uncertainties Multiplication factor, keff ~1% <0.2-0.3% – Physical data: Relative Power density Cross sections, Peak ~2% ~1% fabrication data, etc. Distribution 5-7% 2% – Modeling: Approximations in Control rod worth computational Element 10% 5% methodology of Total 5% 1-2% design process Burnup reactivity swing 3% <1%  High-fidelity simulation can (of reactivity value) ∆ ∆ or 0.5% k or 0.3% k reduce modeling Breeding gain 0.05-0.06 0.02-0.04 uncertainties Reactivity coefficients  Modern data and analysis Large effects 10% 5% techniques will allow: Small effects 20% 10% – Reliable propagation Kinetics parameters 5-10% 2-5% of uncertainties Local nuclide densities – Correct evaluation of Major constituents 5% 2% impacts of uncertainty from input data Minor constituents 10-20% 10%

20 Covariance Data Status

• Despite significant efforts in generating new high quality neutron cross section data and in producing associated covariance matrices, the state of affairs is not yet fully satisfactory. The user is puzzled by many inconsistencies among evaluated cross sections and corresponding covariance data that in many cases fail to explain discrepancies between measurements and calculations for integral experiments.

• As an example, the Keff of the well known and simple system JEZEBEL, calculated by the three major libraries (ENDF/B, JEFF, and JENDL) is equal to 1 within experimental uncertainties. However, an analysis by component finds that there are huge (thousands of pcm) compensations among reactions (inelastic, fission, χ) and energy range. These differences are not covered, at the one sigma level, by the uncertainty analysis using the associated covariance data. • Noticeable differences have been observed among the covariance matrices in use not only on individual cross section uncertainties, but also on correlation among data. • Some covariance data are still missing and in particular: secondary energy distribution for inelastic cross sections (multigroup transfer matrix), cross correlations (reactions and isotopes), delayed data (nubar and fission spectra). • However, serious and reliable efforts are still going on for improving covaraiance data and a lot of progress has been made in the last 15 years by the nuclear data community. ZPPRs C/E: ENDF/B-VIII vs. JEFF-3.3

ENDF/B- ENDF/B- JEFF-3.3 JEFF-3.3 VIII EXPERIMENT VIII Uncert. (C-E)/E Uncert. (C-E)/E % %

ZPPR-9 Keff 0.717 -0.178 1.220 1.183 ZPPR-9 F28/F25 -5.443 -0.266 8.017 3.285

ZPPR-9 C28/F25 -2.757 -0.322 1.546 1.399

ZPPR-9 VOID STEP 3 8.347 4.325 7.638 6.065

ZPPR-9 VOID STEP 5 4.646 0.802 9.881 8.053

ZPPR-10 Keff 0.781 -0.105 1.135 1.171 ZPPR-10 VOID STEP 2 24.222 19.221 7.006 6.189

ZPPR-10 VOID STEP 3 13.359 8.798 7.070 6.324

ZPPR-10 VOID STEP 6 11.881 7.358 7.952 7.146

ZPPR-10 VOID STEP 9 9.551 5.087 9.058 8.218

ZPPR-10 Central Control Rod reactivity 6.085 6.166 1.611 1.948

ZPPR-15 Keff 1.221 -0.004 0.985 1.242 Questions?