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Conference Paper BENCHMARK COMPARISONS OF LATTICE PHYSICS CALCULATIONS FOR THORIUM-BASED FUELS IN COMPANY WIDE CW-123740-CONF-028 Revision 0

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CW-123740-CONF-028 2016 ANS Winter Meeting and Nuclear Technology Expo November 6-10, 2016, Las Vegas, NV, U.S.A. Extended Abstract / Short Paper for ANS Transactions Editing changes made on Aug. 8, 2016 to address comments made by Brock Sanderson

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Benchmark Comparisons of Lattice Physics Calculations for Thorium-Based Fuels in Pressure-Tube Heavy Water Reactors A.V. Colton, Blair P. Bromley*, C. Dugal, H. Yan, and S. Golesorkhi * Canadian Nuclear Laboratories, Chalk River, ON, Canada, K0J 1J0, [email protected]

INTRODUCTION Thorium is a fertile nuclear fuel resource that is nearly three times as abundant as uranium in the earth’s crust [1] and that can be exploited and used to extend uranium resources. The pressure tube heavy water reactor (PTHWR) is an excellent existing technology for utilizing thorium-based fuels [2,3], due to its high neutron economy achieved by using heavy water as a moderator and coolant, the ability to perform online refueling, and its flexibility in fuel management. Reactor physics studies are underway at the Canadian Nuclear Laboratories (CNL) to evaluate several types of thoriumbased fuels that could be implemented in PT-HWRs in the near-term and intermediate future, building upon past experience [3,4]. For preliminary, conceptual studies, deterministic lattice physics and core physics codes such as WIMS-AECL [5] and RFSP [6] are used to provide quick and more approximate estimates of performance and safety characteristics. The objective of this study was to perform 2D lattice physics benchmark comparisons between WIMS-AECL and MCNP5 [7] for several types of thorium-based fuel bundle lattices for potential use in PT-HWRs. Benchmark comparisons will help confirm the validity of deterministic calculation results, and provide estimates of the potential magnitude of calculation errors and uncertainties. Areas for potential improvements in the WIMS-AECL calculations may also be identified. DESCRIPTION OF PROBLEM Two types of PT-HWR fuel bundle lattices were investigated for benchmarking and are illustrated in Fig. 1. The reactor and lattice specifications are also shown in Table I and Table II. Not all lattice concepts (designated by LC-XX) that have been evaluated are shown in this paper. These lattices are intended for potential use in a 700-MWe-class PT-HWR operating on a once-through thorium (OTT) fuel cycle. It is expected that the spent fuel will be put into storage until it is economically attractive to reprocess and recycle. The first lattice type is a 37-element fuel bundle (B37), similar to what is used in current PT-HWRs operating with natural uranium (NU) fuel (such as lattice concept LC-01). The B37 lattices use mainly uraniumbased fuels (such as NU, recovered uranium (RU), or

slightly enriched uranium (SEU). Small amounts of ThO2 are added to improve performance and safety characteristics. In LC-02, the equivalent of 2×0.5-cm of ThO2 is used to downblend the fissile content in the end region to help reduce axial power peaking. Lattice concept LC-03 is a pure ThO2 bundle, which could be used as blanket fuel in a heterogeneous seed/blanket PT-HWR core [8] for breeding a stockpile of 233U. Lattice concepts LC-04 (RU) and LC-05 (SEU) use the equivalent of 2×1.0-cm of ThO2 to downblend the fissile content in the end regions, and also use a central pin of pure ThO2 to help maintain a low coolant void reactivity (CVR) in the lattice. It is expected that the B37 lattices, which involve relatively small changes to existing technology, could be implemented in the very near term.

a) 37-element Bundle b) 35-element Bundle (B37) with Central NUO2 (B35) with Central or ThO2 Rod Graphite Rod Fig. 1. B37 and B35 Lattice / Fuel Bundles The second lattice type is a 35-element fuel bundle (B35), which has slightly smaller fuel pins for improved heat transfer. The B35 lattices, which involve more significant changes relative to B37, and use more thorium, could be implemented at a later date. A central displacer rod of graphite is used to help maintain a low CVR. The fuel is a homogeneous mixture of (Pu,Th)O2, or (LEU,Th)O2, or (233U,Th)O2. Higher-burnup options user higher fractions of Pu, LEU, or 233U. The Pu is assumed to be reactor-grade (~67 wt% Pu-fissile/Pu), obtained from recycled light water reactor fuel [9]. The LEU is 5 wt% 235U/U, readily available from enrichment facilities. The 233U could be obtained from a stockpile of recycled thorium blanket fuel (ThO2), (Pu,Th)O2, or (233U,Th)O2. Similarly, additional amounts of ThO2 (equivalent to 2×1.0-cm) are used to downblend the fissile content in the end regions to reduce axial power peaking. Page 1 of 6

CW-123740-CONF-028 2016 ANS Winter Meeting and Nuclear Technology Expo November 6-10, 2016, Las Vegas, NV, U.S.A. Extended Abstract / Short Paper for ANS Transactions Editing changes made on Aug. 8, 2016 to address comments made by Brock Sanderson TABLE I. PT-HWR Lattice Specifications Quantity Nominal Reactor Power # of fuel channels # bundles per channel Bundle Power Lattice pitch (square) Length of fuel channel Reflector thickness Moderator Pressure Tube (PT) Calandria Tube (CT) Coolant Number of Fuel Pins Fuel Density/Temp. Cladding Material Bundle/Fuel Stack Length Fuel Element Radius Bundle Heavy Element Mass Specific Power

Value, Units 2,061 MWth 380 12 150 kW (ThO2); 600 kW 28.575 cm 594 cm 66 cm 99.8 wt% D2O, ~69C Zircaloy-2.5-Niobium (Zr-2.5Nb) Zircaloy-2 (Zr-2) 99.1 wt% D2O, ~288C B37: 37; B35: 35 9.7 to 10 g/cm3, ~668C Zircaloy-4 (Zr-4) 49.5 cm / 48 cm 0.65 cm (B37); 0.57 cm (B35) ~18.9 kg (B37); ~13.1 kg (B35) 8.5 kW/kg (ThO2), 31.5-46 kW/kg

TABLE II. Lattice Concepts Lattice Concept LC-01 LC-02 LC-03 LC-04b LC-05b LC-06b LC-08b LC-10b LC-12b LC-14b

Bun

Fuel*

Central ThO2 in Rod Ends B37 NU: 0.71 wt% 235U/U NUO2 None B37 NU: 0.71 wt% 235U/U NUO2 0.5-cm B37 ThO2 ThO2 N/A B37 RU: 0.95 wt% 235U/U ThO2 1-cm B37 SEU: 1.2 wt% 235U/U ThO2 1-cm B35 3.5 wt% PuO2 Graphite 1-cm B35 4.5 wt% PuO2 Graphite 1-cm B35 40 wt% LEUO2 Graphite 1-cm B35 50 wt% LEUO2 Graphite 1-cm B35 1.8 wt% 233UO2 Graphite 1-cm * For B35 bundles, the balance of fuel is ThO2.

METHODS AND ANALYSES WIMS-AECL Version 3.1 [5], in combination with an 89-group nuclear data library based on ENDF/B-VII.0 [10] was used for detailed lattice physics modeling. As an approximation for 2D calculations, the higher content of ThO2 in the end regions was homogenized with the oxide fuel in the main fuel stack. The density of fuel was then reduced by a factor of 48/49.53 to smear the fuel over the length of the fuel bundle. The mass of the Zr-4 in the end regions of the bundle (end plugs and end plates, which are not explicitly modeled in 2D lattice calculations) was taken into account by artificially increasing the density of the Zr-4 clad by a factor of 1.13. Burnup (BU) calculations were performed using an assumed bundle power of ~150 kW for lattice concept LC-03, and ~600 kW for all other lattices. An estimate of the exit BU for each lattice was determined by the BU at which the BU-averaged value of kinf equals 1.050, which assumes a 35-mk (1 mk = 100 pcm = 0.001 k/k)


reactivity allowance for neutron leakage in a full reactor core, and a 15-mk allowance for various reactivity devices in a PT-HWR [11]. Fuel compositions at three BU levels (near-zero, mid-BU, and exit BU) were extracted from the WIMS-AECL calculations, and used in subsequent perturbation calculations. To represent the effect of coolant voiding, the coolant density was set to nearly zero (void=0.001 g/cm3). The resulting kinf was then used to evaluate the coolant void reactivity: CVR = (kinf-void-kinf-cool)/(kinf-cool×kinf-void). For benchmark comparisons, MCNP5 Version 1.40 [7] was used in conjunction with a continuous energy nuclear data library based on ENDF/B-VII.0 [10]. The 2D MCNP5 lattice models were identical to the 2D WIMS-AECL lattice models in terms of geometry, material compositions, densities, and temperatures. The fuel compositions at different BU levels in the MCNP5 models were based on those obtained from the WIMS-AECL calculations. A sufficient number of neutron histories were run in the MCNP5 calculations such that the statistical uncertainty in kinf was less than ±0.0002 (±0.2 mk). The key parameters evaluated with both codes at the three BU steps were kinf (cooled), kinf (voided), CVR, and the differences between the codes. RESULTS Results of the lattice physics benchmark comparisons are shown in Table III for the B37 concepts, and in Table IV for the B35 concepts. Associated data plots are shown in Fig. 3 to Fig. 10. According to the calculations with WIMS-AECL, the B37 concepts (see Fig. 3) achieve exit BUs ranging from 4.4 MWd/kg (for LC-02) to 18.4 MWd/kg (for LC-05). By comparison, the conventional, pure NU lattice (LC-01) achieves a BU of 7.3 MWd/kg, which is consistent with previous studies [2]. The exit BU for the LC-03 (ThO2) blanket bundle is arbitrary, given that the lattice is always subcritical, but it is expected that such fuel would be withdrawn from a reactor at a BU of ~5 MWd/kg or less in order to maximize the 233U production rate [12]. The B35 concepts (see Fig. 4) achieve exit BUs ranging from 18.4 MWd/kg (LC-14b) to 40.6 MWd/kg (LC-12b). The CVR for the B37 concepts (see Fig. 5) typically range from +12 mk to +17 mk. Although the CVR drops as the initial uranium enrichment increases, the CVR also increases with BU as the 235U is depleted in the outer pins. The buildup of plutonium isotopes causes the CVR to drop for the LC-01 and LC-02 lattices [13]. The CVR for the B35 lattices (see Fig. 6) typically range from +7 mk to +12 mk, increasing with BU as the fissile fuel in the outer fuel pins is depleted. The fuels with a larger thorium content (such as (Pu,Th)O2 and (233U,Th)O2) clearly have lower values of CVR, than the uranium-based fuels, due

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to the reduced resonance neutron absorption of 232Th relative to 238U. The differences between WIMS-AECL and MCNP5 for kinf (cooled) at different BU levels are shown in Fig. 7 for B37 and Fig. 8 for B35. For the uranium-based fuels in B37 (Fig. 7), the difference at zero BU tends to increase with 235U enrichment, ranging from +0.2 mk to +1.6 mk. As the 235U is depleted, the difference drops, and the bias even goes negative. The small addition of thorium also appears to increase the bias. For the LC-04b and LC-05b lattices, the kinf bias ranges between +1.6 mk and 0.2 mk, potentially suggesting that WIMS-AECL may be giving a slight over prediction of the discharge BU, on the order of 1%. For the thorium-based fuels in B35 (Fig. 8), the kinf bias varies slightly with BU, decreasing by 0.6 mk to 2.3 mk between fresh fuel and exit BU. The bias varies more widely between the different fuel types. For (Pu,Th)O2, the bias ranges from 4.4 mk to -5.9 mk; for (LEU,Th)O2, the bias ranges from +5.2 mk to +2.9 mk, and for (233U,Th)O2, the bias ranges from +1.5 mk to +1.0 mk. The negative biases for the (Pu,Th)O2 may be attributed to differences in the cross section data between the 89-group WIMS-AECL nuclear data library, and the continuous nuclear data library used in MCNP5, particularly for the low-energy resonances in 239 Pu (~0.3 eV), 240Pu (~1 eV) and 241Pu (~0.2 eV). The large positive biases for the (LEU,Th)O2 fuels may also be attributed to differences between libraries for the various neutron resonances in 235U in the range of 1 eV to 1 keV. The kinf bias results suggest that the exit BU could be slightly over-predicted for the (LEU,Th)O2 fuels, perhaps by 1% to 2%, and slightly under-predicted for the (Pu,Th)O2 fuels, by 1% to 2%. The differences in CVR between WIMS-AECL and MCNP5 are shown in Fig. 9 for B37 and Fig. 10 for B35. For the uranium-based fuels, the CVR bias ranges between -0.6 mk and +0.4 mk, which is relatively small. With the exception of LC-05b, the bias goes through an initial increase and then a decrease, which is likely due to the buildup of plutonium. However, considering that the uncertainty in the MCNP5 kinf calculations is ±0.2 mk, there could be no statistically significant bias in CVR, within two standard deviations. For the thorium-based fuels, the CVR bias ranges between -0.5 mk to -1.5 mk, and generally decreases with BU. The CVR biases for the LC-10b and LC-14b lattices, which have lower fissile uranium content, remain relatively constant.

ENDF/B-VII.0. Results demonstrate relatively small biases in kinf for cooled lattices, ranging from -6 mk to +5 mk. Biases in CVR are small as well, ranging between -1.4 mk and +0.4 mk. Discrepancies may be partially attributed to the approximations in the 89-group nuclear data library used with WIMS-AECL, which may not represent the various neutron absorption resonances found in the isotopes of 239Pu, 240Pu, 241Pu, 235U, and others. While there are opportunities for improvements, these preliminary results are encouraging and give confidence that the deterministic calculations are giving good estimates of the performance and safety characteristics of potential thorium-based fuels for use in PT-HWRs. In future work, improvements to the WIMS-AECL library may be implemented, such as using a 172-group, or perhaps a 400-group library. MCNP5 calculations can be improved further through running more neutron histories and reducing the statistical uncertainty to less than ±0.1 mk. Three-dimensional lattice physics models with MCNP5 for benchmark comparisons may also be tested, along with using alternative deterministic and stochastic codes, such as DRAGON [14] and Serpent [15].

CONCLUSIONS AND FUTURE STUDIES

7.

Benchmark lattice physics calculations have been performed for various types of thorium-based fuels that could be implemented in PT-HWRs. Results for kinf and CVR have been determined using WIMS-AECL and MCNP5, both using nuclear data libraries based on

8.

ACKNOWLEDGMENTS The authors thank S. Pfeifer, F. Adams, S. Gimson, D. Radford, and B. Sanderson (CNL), for their assistance. REFERENCES 1.

2.

3. 4.

5.

6.

OECD Nuclear Energy Agency and the International Atomic Energy Agency, “Uranium 2014: Resources, Production and Demand (The Red Book)”, (2014). “Heavy Water Reactors: Status and Projected Development”, IAEA Technical Report Series No. 407, International Atomic Energy Agency (2002). M.S. MILGRAM, “Thorium Fuel Cycles in CANDU Reactors: A Review”, AECL-8326, January (1984). B.P. BROMLEY, “High-Utilization Lattices for Thorium-Based Fuels in Heavy Water Reactors”, Nuclear Technology, Vol. 186, No. 1, pp. 17-32, April, (2014). D.V. ALTIPARMAKOV, “New Capabilities of the Lattice Code WIMS-AECL”, Proc. of PHYSOR 2008, Interlaken, Switzerland, Sept. 14-19, (2008). W. SHEN, et al., “Evolution of Computer Codes for CANDU Analysis”, Proc. of PHYSOR 2010, Pittsburgh, PA, U.S.A., May 9-14, (2010). X-5 MONTE CARLO TEAM, “MCNP - A General Monte Carlo N-Particle Transport Code, Version 5 – Vol. I: Overview and Theory”, LA-UR-03-1987, Los Alamos National Laboratory, October (2005). B.P. BROMLEY and B. HYLAND, “Heterogeneous Cores for Implementation of Thorium-Based Fuels in

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9.

10.

11.

12.

13.

14.

15.


Heavy Water Reactors”, Nuclear Technology, Vol. 186, No. 3, pp. 317-339, June, (2014). Y. NAKAHARA , et al., 2002, “Nuclide Composition Benchmark Data Set for Verifying Burnup Codes on Spent Light Water Reactor Fuels”, Nuclear Technology, Vol. 137, No. 2, pp. 111-126, February, (2002). D.V. ALTIPARMAKOV, “ENDF/B-VII.0 versus ENDF/B-VI.8 in CANDU Calculations”, Proc. of PHYSOR 2010, Pittsburgh, PA, May 9-14, (2010). J. GRIFFITHS, “Reactor Physics and Economic Aspects of the CANDU Reactor System”, AECL7615, Atomic Energy of Canada Limited, (1983). S. GOLESORKHI, B.P. BROMLEY, and M.H. KAYE, “Simulations of a Pressure-Tube Heavy Water Reactor Operating on Near-Breeding Thorium Cycles”, Nuclear Technology, Vol. 194, No. 2, pp. 178-191, May, (2016). J. WHITLOCK, “Effects Contributing To Positive Coolant Void Reactivity in CANDU”, ANS Transactions, Vol. 72, p. 329, (1995). G. MARLEAU, A. HÉBERT and R. ROY, “A User Guide for DRAGON”, Technical Report IGE-174, École Polytechnique de Montréal, (2012). J. LEPPANEN, “PSG2 / Serpent – a Continuousenergy Monte Carlo Reactor Physics Burnup Calculation Code”, VTT Technical Research Centre of Finland, (2009).

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CW-123740-CONF-028 2016 ANS Winter Meeting and Nuclear Technology Expo November 6-10, 2016, Las Vegas, NV, U.S.A. Extended Abstract / Short Paper for ANS Transactions Editing changes made on Aug. 8, 2016 to address comments made by Brock Sanderson 2.0

LC-01 (NU)

1.2 1.1

LC-04b (RU+Th)

LC-03 (ThO2)

0.9 0.8 0.7 5

10 15 Burnup (MWd/kg)

LC-04b (RU+Th) LC-05b (SEU+Th)

0.5 0.0 -0.5 -1.0

20

1.4

0

5

LC-06b (3.5 wt% Pu + Th)

6

1.3

LC-08b (4.5 wt% Pu + Th)

4

1.2

LC-12b (50 wt% LEU + Th)

LC-10b (40 wt% LEU + Th)

20

k-cool (mk)

2

LC-14b (1.8 wt% U-233 + Th)

1.1 1.0 0.9 0.8

LC-06b (3.5 wt% Pu + Th) LC-08b (4.5 wt% Pu + Th) LC-10b (40 wt% LEU + Th) LC-12b (50 wt% LEU + Th) LC-14b (1.8 wt% U-233 + Th)

0 -2 -4 -6 -8

0

5

10

15 20 25 30 Burnup (MWd/kg)

35

40

45

0

5

10


35

40

45

Fig. 8. k (WIMS-AECL - MCNP5) vs. BU for B35

Fig. 4. k-infinity vs. BU for B35 17

0.4

16

0.2

CVR (mk)

15 14 13

LC-01 (NU)

12

LC-03 (ThO2)

11

LC-04b (RU+Th)

LC-02 (NU+Th)

0.0

LC-01 (NU)

-0.2

LC-02 (NU+Th) LC-04b (RU+Th)

-0.4

LC-05b (SEU+Th)

-0.6

LC-05b (SEU+Th)

10

-0.8 0

5


20

0

5

13 12

10 LC-06b (3.5 wt% Pu + Th) LC-08b (4.5 wt% Pu + Th) LC-10b (40 wt% LEU + Th) LC-12b (50 wt% LEU + Th) LC-14b (1.8 wt% U-233 + Th)

7 6 0

5

10


35

40

Fig. 6. CVR vs. BU for B35 Bundles

45

CVR (mk)

11

8

20

LC-06b (3.5 wt% Pu + Th) LC-08b (4.5 wt% Pu + Th) LC-10b (40 wt% LEU + Th) LC-12b (50 wt% LEU + Th) LC-14b (1.8 wt% U-233 + Th)

0.0

9


Fig. 9. CVR (WIMS-AECL - MCNP5) vs. BU for B37

Fig. 5. CVR vs. BU for B37 Bundles

CVR (mk)


Fig. 7. k (WIMS-AECL - MCNP5) vs. BU for B37

Fig. 3. k-infinity vs. BU for B37

k-infinity

LC-03 (ThO2)

-1.5 0

CVR (mk)

LC-02 (NU+Th)

1.0

LC-05b (SEU+Th)

1.0

LC-01 (NU)

1.5

LC-02 (NU+Th)

k-cool (mk)

k-infinity

1.3


-0.5 -1.0 -1.5 -2.0 0

5

10 15 20 25 30 35 40 45 Burnup (MWd/kg)

Fig. 10. CVR (WIMS-AECL - MCNP5) vs. BU for B35

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TABLE III. Benchmark Comparison Results for 37-Element Fuel Bundles Lattice Concept

BU (MWd/t)

∆k_cool (mk)

kinf_cool WIMSAECL 1.1144 1.0538 0.9922

∆k_void (mk)

kinf_void

0.2 -1.0 -1.0

MCNP5 * 1.1353 1.0700 1.0070

WIMSAECL 1.1349 1.0690 1.0057

∆CVR (mk)

CVR (mk)

LC-01 LC-01 LC-01

3.2 3,641.0 7,261.5

MCNP5 * 1.1142 1.0548 0.9931

-0.5 -1.0 -1.3

MCNP5 * 16.7 13.5 13.8

WIMSAECL 16.1 13.5 13.5

-0.6 0.0 -0.3

LC-02 LC-02 LC-02

3.2 2,223.5 4,428.8

1.0875 1.0538 1.0258

1.0886 1.0537 1.0255

1.1 -0.1 -0.2

1.1084 1.0696 1.0404

1.1089 1.0696 1.0403

0.6 0.0 -0.1

17.3 14.0 13.7

16.8 14.1 13.8

-0.5 0.1 0.1

LC-03 LC-03 LC-03

0.4 2,501.4 5,010.6

0.0355 0.7962 0.8696

0.0359 0.7967 0.8703

0.3 0.6 0.6

0.0370 0.8052 0.8793

0.0374 0.8054 0.8782

0.4 0.3 -1.2

N/A 13.9 12.7

N/A 13.6 10.3

N/A -0.4 -2.4

LC-04b LC-04b LC-04b

3.2 5,527.5 11,036.2

1.1643 1.0520 0.9655

1.1656 1.0526 0.9661

1.4 0.6 0.6

1.1835 1.0668 0.9793

1.1846 1.0676 0.9795

1.2 0.8 0.2

13.9 13.2 14.6

13.8 13.3 14.1

-0.2 0.1 -0.5


3.2 9,144.0 18,428.3

1.2563 1.0510 0.9151

1.2579 1.0515 0.9153

1.6 0.6 0.2

1.2761 1.0663 0.9273

1.2774 1.0673 0.9278

1.3 0.9 0.5

12.3 13.7 14.4

12.1 14.0 14.8

-0.2 0.3 0.4

* Uncertainty in MCNP5 kinf calculations is ±0.2 mk, and CVR uncertainty is ±0.3 mk

TABLE IV. Benchmark Comparison Results for 35-Element Fuel Bundles Lattice Concept

BU (MWd/t)

∆k_cool (mk)

kinf_cool WIMSAECL 1.3197 1.0419 0.9089

-4.4 -4.6 -5.0

∆k_void (mk)

kinf_void MCNP5 1.3379 1.0571 0.9233

WIMSAECL 1.3326 1.0510 0.9169

-5.3 -6.1 -6.3

∆CVR (mk)

CVR (mk)


4.6 11,938.3 23,865.1

MCNP5 * 1.3240 1.0465 0.9140

MCNP5 7.8 9.5 11.0

WIMSAECL 7.3 8.3 9.6

-0.5 -1.2 -1.4


4.6 18,591.8 37,395.3

1.3783 1.0458 0.9021

1.3735 1.0402 0.8962

-4.7 -5.6 -5.9

1.3943 1.0573 0.9120

1.3881 1.0506 0.9048

-6.1 -6.6 -7.2

8.3 10.4 12.0

7.7 9.5 10.6

-0.7 -0.8 -1.4


4.6 12,187.2 24,587.4

1.2362 1.0432 0.9475

1.2408 1.0471 0.9510

4.7 3.9 3.5

1.2514 1.0560 0.9587

1.2552 1.0592 0.9617

3.8 3.2 3.0

9.9 11.6 12.4

9.2 10.8 11.7

-0.7 -0.8 -0.6


4.6 20,217.4 40,642.9

1.3481 1.0443 0.8914

1.3532 1.0486 0.8943

5.2 4.3 2.9

1.3643 1.0579 0.9020

1.3684 1.0612 0.9041

4.2 3.3 2.1

8.8 12.4 13.2

8.2 11.3 12.2

-0.6 -1.0 -1.0


4.6 9,204.5 18,394.0

1.2122 1.0378 0.9901

1.2137 1.0389 0.9911

1.5 1.1 1.0

1.2237 1.0481 1.0000

1.2243 1.0484 1.0003

0.6 0.3 0.3

7.7 9.5 10.0

7.1 8.7 9.3

-0.6 -0.8 -0.7

* Uncertainty in MCNP5 kinf calculations is ±0.2 mk, and CVR uncertainty is ±0.3 mk

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