1.
Evaluation of HEU-Beryllium
Benchmark Experiments to
Improve Computational
Analysis of Space Reactors
John D. Bess
Idaho National Laboratory
Keith C. Bledsoe
www.inl.gov
Bradley T. Rearden
Oak Ridge National Laboratory
Nuclear and Emerging Technologies for Space (NETS-2011)
February 7-10, 2011, Albuquerque, NM
This paper was prepared at Idaho National Laboratory for the U.S. Department of
Energy under Contract Number (DE-AC07-05ID14517)

2.
Background for Current Work
• Parry, J. R., Bess, J. D., Rearden, B. T., and Harms, G. A.,
“Assessment of Zero Power Critical Experiments and Needs for
a Fission Surface Power System, NETS 2009, Atlanta, GA, June
14-19, 2009.
• Evaluation of current computational modeling capabilities and
biases
• Minimize necessary nuclear experiments and tests for FSP
• Results:
– Computational bias increases with Be reflector worth
– Bias up to +0.5% Δk/k for HEU Metal Fast Spectrum systems
– Largest bias in subcritical experiments (1.3 – 1.7%)
– Need to improve 235U(n,γ) cross section data
• Dominate uncertainty when modeling an individual experiment
– Need to improve Be cross section data, especially Be(n,n)
• Dominate uncertainty in reactor design using benchmark database
– Cold-critical experiment unnecessary but still useful
– Subcritical submersion experiments still necessary
2

3.
Fission Surface Power (FSP) System
• Design concept for this
study
– Lunar outpost power
supply
– 20 – 50 kW
– <8 yr operation
– Ready for launch by
2020
– Provide a power-rich
mission environment
3

4.
Previous Evaluation of Benchmark Data
• International • Ideal benchmark:
Handbooks for of – Fast spectrum
Evaluated Criticality – NaK cooled
Safety and Reactor – Stainless steel cladding
Physics Benchmark – HEU-O2
Experiments – Be reflectors
– ICSBEP and IRPhEP – B4C control drums
Handbooks
• Best available:
– ZPPR-20 mockups of
SP-100 experiments
– Four configurations
4

5.
ZPPR-20 Benchmark Data
• ZPPR-20C(105)
– HEU-MET-FAST-075
– Critical Core
• ZPPR-20D(129)
– HEU-MET-MIXED-012
– Critical Water Immersion
Accident
• ZPPR-20D(136)
– SUB-HEU-MET-MIXED-001
– Subcritical Water Immersion
Accident
• ZPPR-20E(160)
– SUB-HEU-MET_FAST-001
– Subcritical Earth Burial
Accident
5

6.
Objective of Current Study
• Reduce computational uncertainty in the FSP
design using additional benchmark data
– Identify high-quality experiments
• HEU fuel
• Be reflected
• Fast spectrum
– Benchmark these experiments
– Evaluate benchmark experiments using sensitivity and
uncertainty analysis capabilities found in SCALE 6
– Establish a path forward based on evaluated results
6

7.
Oak Ridge Critical Experiments Facility (ORCEF)
• Hundreds of HEU
oralloy experiments
– Bare, graphite-,
polyethylene-, and
beryllium-reflected (3)
• 1960s and 1970s
• Support criticality safety
at Y-12
– Storage, casting, and
handling
– Verification of
calculation methods and
cross section data
7

8.
Vertical Lift Assembly
8

9.
Annular Experiments: 15-inch Annulus
• June 4, 1963 • ~7 in. diameter Be core
• ~15 in. outer diameter • ~4 in. high
9

10.
Annular Experiments: 13-inch Annulus
• July 12, 1963 • ~7 in. diameter Be core
• ~13 in. outer diameter • ~5 in. high
10

11.
Top-Reflected Experiment
• August 20, 1963 • ~4-1/8 in. high HEU
• ~7 in. diameter • ~5-9/16 in. high Be
11

12.
Unique Uncertainty Conditions
• Parts manufactured at • Now uncertainties that
Y-12 to very tight are typically
tolerances insignificant become
– Dimensions: significant
• ±0.0001 in. – Temperature:
– Mass: • ±2 ºF
• ±0.5 g – Reactivity
– Isotopic Composition: measurement:
• ±0.005 wt.% • ±10%
– Part Placement: – Beryllium impurities
• ±0.001 in. • Nominal quantities known
but deviation unknown
12

13.
Evaluated Biases
• Small biases are now • Model Simplifications
significant due to small – Removal of impurities
uncertainties – Homogenization of like
components
• Room return • Removal of gaps
• Removal of support • Uniform material
properties
structure • Nominal experiment
– Measured/evaluated by dimensions
experimenter
• Temperature
– Treated as uncertainty

14.
Summary of Benchmark Eigenvalue Comparison
14

15.
Reflector Effects
• Compared reflected Mass Reflector
experiment to bare Experiment Difference Worth (ρ$)
(kg)
HEU configuration in
previous benchmark Top-Reflected 9.922 10.7 ± 0.5
– Mass difference
– Most reactive
portion of HEU discs 13” Annular -13.497 8.5 ± 0.4
replaced with Be for
annuli
15” Annular -3.258 4.2 ± 0.2
• Calculated reflector
worth using MCNP5
Small reflector worths, indicative
of small modeling bias

16.
TSUNAMI Analysis
• Tools for Sensitivity and Uncertainty Analysis
Methodology Implementation in Three Dimensions
(TSUNAMI-3D)
– Comprehensive analysis of relative deviation of keff due
to cross-section covariance data
• TSUNAMI-IP (Indices and Parameters)
– Comparison of TSUNAMI-3D analyses for multiple
configurations
– Compute relational parameters between two
configurations to assess a degree of similarity
– i.e. proposed designs to existing experimental data
16

17.
TSUNAMI-3D Results
Typical of ZPPR-20 Experiments
Total Uncertainty Component Uncertainty
Model Major Components
(%Δk/k) (%Δk/k)
235
U(n,γ) 1.9171 ± 0.0090
235
U(ν-bar ) 0.5702 ± 0.0000
235
U(n,n) to 235U(n,γ) 0.2460 ± 0.0020
235
U(n,f) 0.2294 ± 0.0007
187
Re(n,γ) 0.1891 ± 0.0008
235
ZPPR-20C (105) 2.0684 U(n,n’) 0.1796 ± 0.0124
93
Nb(n,γ) 0.1618 ± 0.0006
93
Nb(n,n) 0.1557 ± 0.0057
185
Re(n,γ) 0.1461 ± 0.0005
235 235
U(n,n) to U(n,n’) -0.1350 ± 0.0121
16
O(n,n) 0.1072 ± 0.0075
17

18.
Correlation Coefficient, ck
• Rigorous uncertainty analysis
– Propagates tabulated cross-section uncertainty
information to keff
– Energy-dependent sensitivity coefficients
• Represents estimate of the correlated uncertainty
between systems
• Measures degree of similarity of the systems in
terms of relative uncertainty
σ ij
2
ck =
(σ iσ j )
18

19.
TSUNAMI-IP Results
• Good correlation
between individual
experiments and the
FSP model
• Less cross-section
uncertainty in the
ORCEF HEU-Be
experiments
19

20.
Penalty Assessment (TSUNAMI-IP)
• Determine additional margins of uncertainty where
experimental information is unavailable
• Provides added measure of safety where
validation coverage is lacking
• Covariance data uncertainty reduced to 0.29
%∆k/k, which is mostly from the Be(n,n) reaction
uncertainty, in the original ZPPR-only assessment
• Can be used to assess bias and bias uncertainty
for additional margins in subcriticality experiments
to account for lack of experimental coverage for
beryllium
20

21.
Results of the Penalty Assessment
• Addition of three HEU- ZPPR-20 ZPPR-20 &
Be experiments only HEU-Be
FSP cross 2.09 %δk/k 2.02 %δk/k
– Were not sufficient to section
reduce the uncertainty uncertainty
in the Be(n,n) reaction
Penalty 0.29 %δk/k 0.29 %δk/k
– Smaller reflector worth assessment
– Smaller configurations Be(n,n) only 0.28 %δk/k 0.28 %δk/k
– Smaller sensitivities
(see next page)
21

22.
Sensitivity Profiles for the ZPPR-20 Experiments
22

23.
Sensitivity Profiles for the HEU-Be Experiments
23

24.
TSURFER Analysis
• Tool for Sensitivity/Uncertainty analysis of
Response Functionals using Experimental Results
• Alternative method for uncertainty quantification
• Uses sensitivity data (TSUNAMI-3D) and cross-
section covariance data to determine uncertainty
using the measured keff values of the benchmark
experiments
• Generalized linear least squares approach to
adjusting experimental and nuclear data to
calculate keff values close to their experimental
value
24

25.
TSURFER Results
ZPPR-20s & HEU-Be
ZPPR-20s Only
25

26.
TSURFER Results
• Slight reduction in the • TSURFER uncertainties
total uncertainty with typically larger than
the addition of the HEU- TSUNAMI-IP penalty
Be experiments calculations
• Some general benefit – Penalties account for
under-coverage of the
but not for the targeted sensitivity data
uncertainty in Be(n,n) – TSURFER assesses the
lack of or inconsistency
in data from multiple
benchmarks
26

27.
Future Work
• ORCEF (early 1960s)
space reactor mockup
• HEU-O2 pellets
• SS-347 tubes
• Al container
• Be reflector
• Reactivity Effects
– SS-347, W, Cb (now Nb),
CH2, C, B4C, Al, & Cd
– K coolant
• Fission Rate Distributions
& Cd Ratios
27

28.
Fission Rate Distributions – HEU-O2 Experiment
Axial
Radial
28

29.
Conclusions
• Three HEU-Be experiments were evaluated and
compared with the ZPPR-20 benchmarks and FSP
model
– No reduction in Be(n,n) uncertainty
– Sensitivity of experiments to a given cross section is
important when trying to reduce uncertainties
– Overall uncertainty in the FSP system was slightly
reduced
• Evaluation of additional experiments isneeded to
further reduce the uncertainties in the FSP design
– Past experiments (hopefully)
– Future experiments
• Subcriticals, high reflector worth, sensitivity to Be(n,n) reaction
29

30.
Questions?

31.
Additional Slides
31

32.
Simple Benchmark Models
D 38.1 cm (15 in.)
D 17.78 cm (7 in.)
D 17.78 cm (7 in.)
10.16 cm
(4 in.) HEU Be
10-GA50002-54-2 14.12875 cm
Be (5.5625 in.)
D 33.02 cm (13 in.) 24.60625 cm
(9.6875 in.)
D 17.78 cm (7 in.)
10.4775 cm
HEU (4.125 in.)
12.7 cm
(5 in.) HEU Be
09-GA50001-177-2
10-GA50002-54-1

33.
Detailed 17.770920
9/16" Be
1.42875
Benchmark 17.770920
1.27
1.42875
0.004826
1.27
Model: 1/2" Be
0.004826
2.54
Top-Reflected 17.770920
2.54 0.004826
Be parts
1" Be 5.08
17.770920
0.004826
5.08
2" Be 3.81
3.81 0.004826
17.770920 0.3175
0.001778
2.543175
1.5" Be
0.001778
0.3175
17.771110
3.814191
2768 HEU
2.543175 0.003556
17.769840
3.816604
2732 HEU
HEU parts
3.814191
17.770856 Drawing not to scale
Diaphragm
location
2734 HEU
Bottom layer
3.816604
17.772060
Dimensions in cm
2733 HEU 09-GA50001-177-4

34.
Top layer
Detailed 17.7
22.849840
866
04 0.955929
27.931110 22.8
663
50
0.949960
33.009967
27.9
450
80
0.317119
Benchmark
HEU 2736 HEU 2743 HEU 2780
17.770920
1.270000
0.5" Be
Model: 27.932380 22.8 33.006030
6 0.637540 27.9 0.953643
381 438
0 10
17.7 HEU 2779 HEU 2750
13 in. Annulus
83
22.851110 810 1.428750
HEU 2737 27.931110 22.8 33.008570
6 508 0.637540 27.9 0.958596
0 476
20
17.770920
3.810000 HEU 2778 HEU 2749
1.5" Be
17.7 27.931110 22.8 33.009840
895 6 381 27.9
22.850475 25 2.538095 0 2.543810 463 2.543937
50
HEU 2762 HEU 2776 HEU 2757
Bottom layer
17.7 27.931872 22.8 33.008062
880 0.955675 7 651 0.321945 27.9 1.279144
22.850475 01 501
0 60
HEU 2829 HEU 2744
HEU 2754
17.770920 27.931872 22.8 33.011745
6 381 0.952754 27.9 1.273302
1.0" Be 2.540000 0 476
20
17.7
22.850475
863
50 HEU 2742 HEU 2753
3.810000
HEU 2740 33.008570
27.9
463 1.278255
50
27.931872 22.8
6 508 HEU 2752
0 3.809746
17.770920 17.7 33.009332
838 0.317500
22.852380 10 HEU 2747 27.9
438 1.279017
5.080000 10
2.0" Be HEU 2773
HEU 2751
17.7 27.931110 22.8 33.011618
895 625 27.9
22.849205 25 2.543048 40 2.537460 491 2.540508
44
HEU 2738 HEU 2745 HEU 2756
Dimensions in cm

35.
0.5" 1.270000 2736 0.955929
2743 0.949960 2780 0.317119
Detailed
Void 0.003881
2750 0.953643
2779 0.637540
Benchmark 2737 1.428750
2778 0.637540
Void 0.003881
Model: 1.5" 3.810000
2749
Void
0.958596
0.003881
13 in. Annulus 2762 2.538095 2776 2.543810
2757 2.543937
Void 0.026247 Void 0.016087 Void 0.019050
2754 1.279144
2744 0.321945
2829 0.955675 Void 0.008537
Void 0.004085
Void 0.008086 2742 0.952754
1" 2.540000
2753 1.273302
Void 0.008537
Void 0.004085
Void 0.020320
2740 3.810000
2752 1.278255
2747 3.809746
Void 0.004085
2751 1.279017
Void 0.008086
2773 0.317500
2" 5.080000 Void 0.008086 Void 0.008537 Void 0.004085
2738 2.543048 2745 2.537460 2756 2.540508
Drawing not to scale
Dimensions in cm
10-GA50002-53-8

36.
Detailed
Benchmark
Model: Top layer
22.851110
17.7
876
20 0.635000
27.931872 22.8
765
10
0.321945
15 in. Annulus
HEU 2774 HEU 2744 33.008570 38.086030
27.9 0.958596 33.0 0.946150
476 238
20 10
17.770920 17.7 27.931110 22.8
1.270000 901 0.631190 650 0.637540
22.851745 60 80
0.5" Be HEU 2749 HEU 2784
HEU 2775 HEU 2778
17.7 27.932380 22.8
896 638 0.637540
22.849332 52 0.315722 10
HEU 2763 HEU 2779 33.009840 38.091110
27.9 1.431290 33.0 1.430020
476 225
20 40
17.7
866 27.931110 22.8
22.849840 04 0.955929 663 0.949960
50
HEU 2755
17.770920 HEU 2766
3.810000
HEU 2736 HEU 2743
1.5" Be
17.7 27.931110 22.8 33.009840 38.088570
895 638 27.9
22.849205 25 2.543048 10 2.543810 463 2.543937 33.0 2.526030
50 268
58
HEU 2738 HEU 2776 HEU 2757 HEU 2739
Bottom layer
17.7 27.931872 22.8 33.009332 38.086665
838 0.317500 638 0.952754 27.9 1.279017 0.321310
22.852380 10 10 438 33.0
10 225
40
HEU 2773
HEU 2742
HEU 2751 HEU 2761
38.089332
33.0 0.951738
273
66
17.770920 17.7
880
27.931110 22.8 0.326771
33.008062 HEU 2785
22.850475 01 0.955675 644 27.9 1.279144
45 501
5.080000 60
2.0" Be HEU 2829 HEU 2746
38.090856
HEU 2754 33.0 1.274826
278
74
HEU 2848
17.7 27.933650 22.8 33.011618 38.083490
863 663 27.9
22.850475 50 50 491 2.540508 33.0 2.536190
3.810000 3.810000 44 250
80
HEU 2740 HEU 2748 HEU 2756 HEU 2735
Dimensions in cm
10-GA50002-53-3

37.
Detailed
Benchmark
Model:
2744 0.321945
2774 0.635000
Void 0.002762
Void 0.002191
0.5" 1.270000 2778 0.637540
15 in. Annulus Void 0.002540
2775
Void
0.631190
0.002191
Void
2779
0.002762
0.637540
2749
Void
0.958596
0.001969
2784
Void
0.946150
0.012446
2763 0.315722
Void 0.002191 Void 0.002762
2755 1.431290 2766
2736 0.955929 2743 0.949960
1.430020
Void 0.002191 Void 0.002762 Void 0.001969 Void 0.012446
1.5" 3.810000
2738 2.543048 2776 2.543810 2757 2.543937 2739 2.526030
Void 0.018669 Void 0.007662 Void 0.008509 Void 0.001978
2773 0.317500 2761 0.321310
2742 0.952754 2751 1.279017 Void 0.004209
Void 0.003916
Void 0.000317 2785 0.951738
2829 0.955675
2746 0.326771
Void 0.004209
Void 0.003916 Void 0.000317 2754 1.279144
2848 1.274826
2" 5.080000
Void 0.004209
2740 3.810000 2748 3.810000
2756 2.540508
2735 2.536190
Drawing not to scale
Dimensions in cm
10-GA50002-53-4