Monte-Carlo calculations in reactor design

Monte-Carlo calculations in reactor design

G.B. Bruna

FRAMATOME-ANP

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Monte-Carlo calculations in reactor design

• Samples :– HTR-10 Benchmark analysis,– Rhodium SPND detectors,– Mock-up experiments with void,– Others ....

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• Benchmark problem definition

• Sensitivity studies

• Main Results

HTR-10 Benchmark analysis

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• Benchmark problem definition

• 1) Cold (Temperature 300°K)• 2) U235 enrichment 3.3% à to 9.9%• 3) 31 or 33 element assemblies• 4) Two types of B4C burnable poisons

• 5) 20 different mediums (colors)• 6) He core-cooling channels• 7) 150 fuel elements (30 columns, cylindrical core)• 90 fuel elements (18 columns, annular core)• 8) Four Benchmark configurations :• - 18 columns - 19 columns • - 24columns - 30 columns


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• Heterogeneity levels– Coated micro-balls (first level)

Compact (second level)Fuel assembly : 31 or 33 element compacts (third level)Axial superposition of 5 elements (forth level)

– Radial core loading (fifth level)


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Compact/Element

Burnable Poison

31-Element Assembly

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Hexagonal Compact


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Hexagonal Lattice


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Cubic Lattice


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Radial Heterogeneity inside the Hexagonal Compact


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Unclustered 18-Column Core


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1/4 30-Column Unclustered Core


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Clusters inside 30-Column Core


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Clustered 30-Column Core


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Adjusted Clustered 30-Column Core


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• Sensitivity-studies (1 pcm = 1.E-5)

• Graphite impurities > 5000 pcm (total)• Dummy assemblies ~3000 pcm • Helium channels ~2000 pcm• Bullets lattice arranged vs. random < 200 pcm• Compact heterogeneity < 200 pcm• First-level homogenization < 500 pcm• Second-level homogenization 10000 pcm• Data Libraries JEFF2 vs. ENDF-BVI ~500 pcm


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• Configuration Experiment Calculation

• 18 col. ann. core Sub-critical 0.99700• 19 col. ann. core Over-critical 1.01300

• clustered 24 col. • ann. core 1.0000 1.00110• clustered 30 col.• cylindrical core 1.0000 0.99980


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• Core Average 5 Labs Japan(2), Holland, Russia, USA (ORNL)

• 18 col. ann. core Keff 1.02150

• clustered 24 col. critical rod ins. 82 cm ann. core

• clustered 30 col.• cylindrical core critical rod ins. 123 cm


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• US-3D Device

• Physics of Rhodium SPN Detectors

• Monte-Carlo studies on :– heterogeneity– Rhodium burn-out

Rhodium SPN Detectors

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CORE

MOVABLEFLUX

MAPPINGSYSTEM

US-3DALARMS

OPERATION AID SYSTEM

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Detectors

n

Generic detector (i, j, k)


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Real Geometry (Sec. R-R)

Geometry Representation in APOLLO

MCNP APOLLO

Axial heterogeneity

Radial heterogeneity


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0

0

1

10

100

1000

10000

1112131415161718191

Groupes MAI99

ba

rn

Rh103_DE Rh103_DETGTI

Six Groups Condenseted SectionsGroup E (eV) Without

SelfshieldingWith

SelfshieldingRatio

1 10.E+06 0.0428135 0.0428135 1.0002 9.07E+06 0.460451 0.4583355 0.9953 7.47E+03 3.824724 2.7712796 0.725

4 4.13 117.494919 117.624245 1.0015 0.625 63.2371979 63.316185 1.0016 0.134 82.2589493 82.2589645 1.000

Self-shielding effect


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Rh10345

0.134 ev 0.625 ev 4.129 ev

5000 b

Gr. 6 Gr. 5 Gr. 4 Gr. 3

7.466 Kev

Gr.2

Gr. 1

0.907 Mev

10 Mev

The Rh microscopic absorption cross-section


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88%

90%

92%

94%

96%

98%

100%

102%

0 1 2 3 4

GR.1

GR.2

GR.3

GR.4

GR.5

GR.6

Rh reaction rates


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Relative contribution of groups to RR.

0%5%

10%15%20%25%30%35%40%45%

1 2 3 4 5 6

Rh reaction rates

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50.4%

28.4%

21.3%

RR per annular region

Rh reaction rates

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0,0%

5,0%

10,0%

15,0%

20,0%

25,0%

30,0%

35,0%

40,0%

45,0%

1 2 3

Apollo

MCNP


Rh reaction rates

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• Physical analysis of heterogeneous void

• Monte-Carlo calculations of mock-up experiments:– EPICURE– ERASME– Others

Mock-up experiments with void

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Homogeneous VoidInfinite Medium

Heterogeneous VoidCluster

Void of mock-up experiments

IAEA Benchmark Sample Geometry

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Homogeneous Void Infinite Medium

Heterogeneous Void Cluster


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UO2

MOX


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• Cluster of 9 {10*10 pin} assemblies in Inf. Med. (pitch 1.26 cm), with a central MOX assembly with Pu enrichment:– HMOX 14.40– MMOX 9.70– LMOX 5.40– (UO2 3.35)


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ii

i

ii

i

i

i

i

ii

i

ii

A

PIkk

A

AI

AP

k

*

,

,


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• In the wet MMOX cluster, typical values of Kinf* and Imp* are the following:

• Zone Imp* Kinf*

• UO2 0.88 1.3697• MOX 0.12 1.1447• Whole Cluster 1.3427

– *Rouded off values


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• In the MMOX cluster with central void, typical values of Kinf*and Imp* are the following:

• Zone Imp* Kinf*

• UO2 1.3697 0.96• MOX 0.7738 0.04• Whole Cluster 1.3458

– *Rounded off values


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Wet MOX

XS

Flux

Dry


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Dried zone

3.7% UOX

UOX-UOX EPICURE


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MOX

3.7% UOX

Low and High Enrich. UOX-MOX EPICURE

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KEFF SSI INDEX inthe 7*7 pin

sample

MeasuredVoid Effect

Computed void effect(MCNP4/JEF2.2)

UH1.2 1.0016 7.5 _ _

UH1.2 30%void

1.0004 < 20 -543 50 -660 80

UH1.2 50%void

1.0005 < 20 -1111 50 -1220 80

UH1.2 100%void

1.0000 20 -2165 50 -2330 80

AVERAGE 1.0006 -1273 50 -1403 80

(Low Enrich. UOX-UOX EPICURE)


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CONFIGURATION KEFF SSI INDEX in theVoided Zone

Measured Effect Computed Effect(MCNP4/JEF2.2)

UM 17x17 MOX 7%Reference

0.9986 30 0 0

UM 17x17 MOX 7%Central Bubble

0.9977 (1) < 80 -103 8 -90 40

UM 17x17 MOX 7%Bubble at +30 cm

0.9986 (1) < 80 -40 8 0 40

UM 17x17 MOX 7% 3Piled-up Bubbles

0.9961 (1) < 80 -230 8 -250 40

UM 17x17 MOX 17x17 5Piled-up Bubbles

0.9957 (1) < 80 -282 8 -290 40

UM 17x17 MOX 11%Reference

1.0007 40 0 0

UM 17x17 MOX 11%Central Bubble

0.9991 (1) < 150 -130 16 -160 40

AVERAGE VOIDEFFECT

_ -157 10 -158 40

(UOX-MOX EPICURE)


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1) CONFIGURATION MODERATIONRATIO

SSI INDEX(Fuel)

MCNP4JEF2.2

MCNP4BVI

PU 11% ERASME SHexagonal

0.5 235 1.0042 1.0123

PU 11% ERASME R Hex. 0.9 100 1.0032 1.0065

PU 11% ERASME R Hex.SBC = 1150 ppm

0.9 106 1.0060 _

PU 11% ERASME RHex. SBC = 2490 ppm

0.9 110 1.0030 1.0077

AVERAGE _ _ 1.0041 1.0088

2) CONFIGURATION

PU 11% ERASME LPSqrd

2.1 30 1.0020 0.9994

PU 11% ERASME LGSqrd

2.1 < 40 1.0032 1.0032

PU 11% ERASME LGSqrd Control Rods

2.1 < 40 1.0039 1.0026

AVERAGE _ _ 1.0030 1.0017

(ERASME Series Experiments)


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CONFIGURATION MODERATION

RATIO

SSI INDEX MCNP4JEF2.2

MCNP4BVI

GODIVA (5) 0 > 200 1.0003 0.9993

JEZEBEL (4) 0 > 360 0.9955 0.9968

ERASME (7) 0.5 à 2.1 >30<235

1.0036 1.0053

URANIUM LowCoolant/Fuel Ratio (4)

0.27 à 0.78 >10<80

1.0036 _

EPICURE (15) 1.2 >7<150

0.9993 _

AVERAGE (35) 1.0004

(Synopsis of All Experiments)


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20 21 22 23 24 25 26 27 28

28 -0.2

27 2.9 -0.2

26 -0.6 1.7 2.3

25 -2.9 -0.7 -1.4 -1.6

24 -2.7 -1.7 -2.6 -5.0 -3.1

23 -1.3 -3.1

22 0.0 -3.7

21 -2.5

20 1.4 1.3

20 21 22 23 24 25 26 27 28

28 -3.3

27 --3.0 -5.0

26 -2.5 -1.6 -4.6

25 0.2 -1.6 -0.3 -1.8

24 2.8 -0.7 -1.9 -3.9 -1.9

23 2.1 1.2 2.6 0.1 -1.5 -0.5

22 2.0 5.2 4.2 1.1 1.2 3.1 -1.6

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(Low Enrich. EPICURE with bubble)


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20 21 22 23 24 25 26 27 28

28 2.0

27 -1.0 2.2

26 2.7 0.3 2.3

25 3.2 -1.0 -1.4 1.3

24 4.7 0.7 -2.9 1.7 0.0

23 -1.5 1.6

22 0.7 2.9

21 2.7 -3.7

20 0.0 0.9

20 21 22 23 24 25 26 27 28

28 -7.0

27 --6.0 -6.2

26 -4.8 -6.0 -5.5

25 -2.7 -4.0 -7.0 -4.0

24 -0.8 -0.7 -1.8 -0.3 -1.6

23 -3.0 -2.1 -2.2 -0.7 0.0 -2.0

22 -2.8 -1.4 -2.3 -1.1 0.7 -1.5 -2.3

21 -0.4 -1.4 -4.3

20 0.0 -1.4

(High Enrich. EPICURE with bubble)


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• Discrepancies on reactivity are lower than 100 pcm on the average of 35 experiments, without any significant trend;

• No biases have been observed between JEF-2.2 and ENDFB-VI libraries, except for very hard spectra where ENDFB-VI overestimates reactivity up to 1000 pcm.


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Others ...

• Other Monte-Carlo studies :– Criticality,– Sub-critical approach to divergence, – Fluence and vessel life-time.

Monte-Carlo calculations in reactor design

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