development of integrated analytical tools for level-2 psa ... · 2.2 for the core disruption phase...

1

Japan Nuclear Energy Safety Organization

Development of Integrated Analytical Tools for

Level-2 PSA of LMFBR

FR09, Dec.7-11, 2009, ＫＫＫＫyoto

December 8, 2009

K. Haga, H. Endo, T. Nakajima, T. IshizuNuclear Energy System Safety Division

Japan Nuclear Energy Safety Organization (JNES)

H. IizukaMHI Nuclear Engineering Company

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Contents1. Background and Objectives2. Computer codes2.1 For the plant response phaseNALAP-IIACTOR

2.2 For the core disruptive phaseARCADIAN-FBRAPK

2.2 For the Containment vesselAZORES

3. Phenomenological Relation Diagram : PRD4. Summary

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１１１１．．．．Background and Objectives� JNES is engaged in the technical support for the regulatory activity for Monju, the Nuclear and Industrial Safety Agency (NISA). � The major areas of the supportive work are

Inspection and Safety analysis .� To the safety analysis, JNES has been developing the own tools for several years.� Our reset big activity is the effectiveness evaluation of the proposed accident management (AM) of Monju by using PSA. � The developed tools for the PSA are not only computer codes but also the decision method for the balancing points of event trees.� This presentation presents the outline of each tool.

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�Hydrogen behavior due to Na-concrete and –debris reactions�Hydrogen burning�Aerosol and FP transports

・・・・Coolant temp.*System pressure

・・・・FP evap. from fuel・・・・FP transport in Na, from Na to cover gas, ・・・・ Cover gas heating by FP within cover gas space・・・・FP deposition on piping wall

Plant response phase Core disruption phase

・・・・Large deformation and inelastic deformation analysis

CV response phase

AZORESContainment Vessel responses & FP transport

ACTORFP behavior

in PHTS

Boundary failure

FP release

ABAQUSStructure Analysis

Sodium boiling

Core disruptio

n

Re-criticali

ty

・・・・Keff and reactivity coeffs. of degraded core

Sodium temp. & press. increase APK

Super-prompt criticality

ARCADIAN-FBRNeutronics

・・・・ Na-concrete reaction.debris-conc. reaction・・・・Na spray burning・・・・H2 burning・・・・Aerosol release・・・・FP release

・・・・Power and reactivity transient of Super prompt criticality

EFD*Phenomenological ET expansion

PRDQuantification pf

phenomenological ET

Containment failure FrequencyCFF

NALAP-IIPlant kinetics

�Hydrogen behavior due to Na-concrete and –debris reactions�Hydrogen burning�Aerosol and FP transports

・・・・Coolant temp.*System pressure

・・・・FP evap. from fuel・・・・FP transport in Na, from Na to cover gas, ・・・・ Cover gas heating by FP within cover gas space・・・・FP deposition on piping wall

Plant response phase Core disruption phase

・・・・Large deformation and inelastic deformation analysis

CV response phase

AZORESContainment Vessel responses & FP transport

ACTORFP behavior

in PHTS

Boundary failure

FP release

ABAQUSStructure Analysis

Sodium boiling

Core disruptio

n

Re-criticali

ty

・・・・Keff and reactivity coeffs. of degraded core

Sodium temp. & press. increase APK

Super-prompt criticality

ARCADIAN-FBRNeutronics

・・・・ Na-concrete reaction.debris-conc. reaction・・・・Na spray burning・・・・H2 burning・・・・Aerosol release・・・・FP release

・・・・Power and reactivity transient of Super prompt criticality

EFD*Phenomenological ET expansion

PRDQuantification pf

phenomenological ET

Containment failure FrequencyCFF

NALAP-IIPlant kinetics

Process of severe accidents of LMFBR and JNES’s Analysis tools

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2. Computer codes 2.1 For the plant response phase（（（（１１１１））））NALAP-II code

Functions: Plant kinetics of the primary and secondary loopsSales point: A function to evaluate the degree of high-temperature creep of the location by SCDF (Structural cumulative damage factor, Dc ).

� Dc=Σ（Δti/tr）, (1)where,

Δti: computation time step (s), tr: creep failure time (s).

In eq. (1), tr depend on the material, temperature and pressure. It is calculated by using the Larson-Miller Parameter.It was considered that the location will fail when Dc=0.2～1.0.

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The thermo-hydraulic behavior analyzed by NALAP-II to PLOHS-Reactor inlet and outlet temperatures, cover gas pressures, and SCDF of major locations-

•The RV outlet temperature exceeded 800℃℃℃℃ at 51hr.•PHTS pressure began to increase at 22 hr due to the sodium volume expansion.•The SCDF is evaporator cylindrical wall made of 2.25Cr-1Mo steel firstly exceeded the line of 0.2.•Another locations exceeded the line of SCDF=0.2 after about 10 hr.

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2.1 For the plant response phase（（（（2））））[ACTOR code]Functions: FP behavior from fuel to cover gas or flowing sodium

Cover gas

Fuel BubbleSodium Primary loop

Sales point: Analysis of FP gas bubble behavior with other FP nuclides

Released to inside of reactor containment vessel due to a failure in the deck shield

Deck shield

Adsorption behavior on wall surface Cover gas space

Transferred into cover gas by N percent

Recirculation

Adsorption behavior on wall surface

Air-liquid diffusion process

Breakup into Z bubbles

Primary system piping →→→→

After 50 cm ascension

Gas plenum

Fuel pin

BubbleBubble

Gas plenum

In sodium

In the event of fuel failure In the event of cladding breach

Release behavior from fuel pin

Atomic FP

FP associated with bubble

FP on wall surfaces

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Calculations by ASFOR

0.010.010.010.01

0.100.100.100.10

1.001.001.001.00

10.0010.0010.0010.00

0.00.00.00.0 0.50.50.50.5 1.01.01.01.0 1.51.51.51.5 2.02.02.02.0

距離距離距離距離 [[[[mmmm]]]]

移行

量移

行量

移行

量移

行量

// //初

期体

積

初期

体積

初

期体

積

初期

体積

[[ [[m

ol

mol

mol

mol// //mm mm

33 33]] ]]

試験(1mol%) 試験(4mol%)


試験(40mol%) 浸透モデル(1mol%)

浸透モデル(4mol%) 浸透モデル(8mol%)


バルクモデル(1mol%) バルクモデル(4mol%)


バルクモデル(40mol%)

Amoun

t of iod

ine tra

nsferr

ed/Init

ial vol

ume [m

ol/m3 ]

Distance [m]



試験(40mol%) 浸透モデル(1mol%)





バルクモデル(40mol%)

Test (1mol%) Test (8mol%) Test (40mol%) Permeation model (4mol%) Permeation model (20mol%) Bulk model (1mol%) Bulk model (8mol%) Bulk model (40mol%)

Test (4mol%) Test (20mol%) Permeation model (1mol%) Permeation model (8mol%) Permeation model (40mol%) Bulk model (4mol%) Bulk model (20mol%)

Fu e l p i n sC o o l a n t

W a l l ( C o o l a n t )

C o v e r g a s

W a l l ( C o v e r g a s ) Ni b b l e g a s e s

H a l og e n

Al ka l i n e m e ta l s

Su l f u r g r ou p

Al ka l i n e e a r th

P r e c i ou s m e ta l s

Ce r i u m g r ou p

La n th a n oi d

1.E-03

1.E-02

1.E-01

1.E+00

Z on es

N u c l i d e G r o u p s

Perce

ntag

e of N

uclid

e Gro

ups t

o Init

ial In

vent

ories

[-]

Amount of iodine transferredper bubble volume: Experiment & Calculation

N u c l i d e G rZones i n reactor

Tran

sfer

red

iodi

ne (m

ol/m3 )

Distribution of FP nuclides in reactor 100s after cladding failure in PLOHS

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ARCADIAN-FBR codeFunctions: Neutronics for degraded coreSales point: The combination of (1)a deterministic calculation part to provide the various reactivity coefficients and those spatial distributionsand

(2) a Monte Carlo calculation partto provide reference results against the deterministic calculations and to evaluate approximation effects employed in the deterministic calculations

2.2 For the core disruption phase (1)

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Constitution of ARCADIAN-FBR

70707070----group Effective Cross Sections group Effective Cross Sections group Effective Cross Sections group Effective Cross Sections σσσσeffeffeffeff

JFSJFSJFSJFS----3333----J3.3J3.3J3.3J3.3

Cell Code SLAROMCell Code SLAROMCell Code SLAROMCell Code SLAROM

Kinetics ParameterKinetics ParameterKinetics ParameterKinetics Parameter

Calculation ModuleCalculation ModuleCalculation ModuleCalculation Module

Diffusion CodeDiffusion CodeDiffusion CodeDiffusion Code

DIF3DDIF3DDIF3DDIF3D

Transport CodeTransport CodeTransport CodeTransport Code

VARIANTVARIANTVARIANTVARIANT

kkkkeffeffeffeff

、、、、φφφφ、、、、φφφφ

＊＊＊＊

kkkkeffeffeffeff


＊＊＊＊

JJJJENDLENDLENDLENDL----3.33.33.33.3

Monte Carlo CodeMonte Carlo CodeMonte Carlo CodeMonte Carlo Code

MVPMVPMVPMVP

kkkkeffeffeffeff

、、、、φφφφ

Perturbation Perturbation Perturbation Perturbation CodeCodeCodeCode

PERKY PERKY PERKY PERKY

ρρρρ、、、、、、、、ββββ l

Monte Carlo CodeMonte Carlo CodeMonte Carlo CodeMonte Carlo Code

GMVPGMVPGMVPGMVP

kkkkeffeffeffeff


＊＊＊＊

Deterministic Calculation PartDeterministic Calculation PartDeterministic Calculation PartDeterministic Calculation Part MonteMonteMonteMonte CCCCarloarloarloarlo Calculation Part Calculation Part Calculation Part Calculation Part

、、、、ββββ lNNNN

Burnup CalBurnup CalBurnup CalBurnup Cal....

CodeCodeCodeCode REBUSREBUSREBUSREBUS

NNNN

Burnup CalBurnup CalBurnup CalBurnup Cal....

CodeCodeCodeCode MVPMVPMVPMVP----BURNBURNBURNBURN

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2.2 For the core disruption phase (2)APK codeFunctions: Reactivity evaluation by solving 6-group point reactor kinetics equations to debris beds of some temperature

Sales point: Simple using one point temperature

Validation: Comparison with SAS4A

0

1000

2000

0.000 0.005 0.010 0.015 0.020 0.025 0.030

time(s)

Ｐｏｗ

ｅｒ（P0)

POWER-APK

POWER-sas4a

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.000 0.005 0.010 0.015 0.020 0.025 0.030

time(s)

reactivity($)

NET-APK

NET-sas4a

1000

1500

2000

2500

3000

3500

4000

0.000 0.005 0.010 0.015 0.020 0.025 0.030

time(s)

Tem

perature(K)

TEMP(PK)

TEP-sas4a

0

5

10

0.000 0.005 0.010 0.015 0.020 0.025 0.030

time(s)

energy(FP

S)

FPS-APK

FPS-sas4a

(a) Power history (b) Net reactivity (c) Average fuel temp. (d) Input energy

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2.3 For the CV response phaseAZORES codeFunctions: To analyze various reactions caused by the sodium and core materials leaked through a failed coolant boundary.

Sales point: Radioactive materials behaviours to the environment are also solved with the thermo-chemical reactions.

窒素雰囲気窒素雰囲気窒素雰囲気窒素雰囲気

炉容器炉容器炉容器炉容器

PHT SHTSSHTSSHTSSHTS

冷却系冷却系冷却系冷却系

炉炉炉炉

N

水素燃焼水素燃焼水素燃焼水素燃焼

PHT

HVA

補助建家補助建家補助建家補助建家

空気雰囲空気雰囲空気雰囲空気雰囲

ＦＰＦＰＦＰＦＰ

エアロゾルエアロゾルエアロゾルエアロゾル挙動挙動挙動挙動

格納容格納容格納容格納容

コアｺﾝｸﾘｰﾄコアｺﾝｸﾘｰﾄコアｺﾝｸﾘｰﾄコアｺﾝｸﾘｰﾄ反応反応反応反応 NaNaNaNaｺﾝｸﾘｰﾄｺﾝｸﾘｰﾄｺﾝｸﾘｰﾄｺﾝｸﾘｰﾄ反応反応反応反応

NaNaNaNa燃焼燃焼燃焼燃焼

NaNaNaNa燃焼燃焼燃焼燃焼

ＦＰＦＰＦＰＦＰ

Air atmosphere

炉心

Containment VesselHydrogen burning

Cooling

vessel

system

SodiumburningHVACSodiumburning

Core-concrete reactions reactionsSodium-concrete

Nitrogen atmosphere

FPaerosol

Auxiliary building

SHTSReactor

Core

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0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 5 10 15 20 25 30 35 40

Time (hour)

Core tem

perature (K)

Fig. 7-22(1) Core Temperature (Case 15: PLOHS, Non-CVBP,　PL-NSL-H-γ）

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

8.0E+05

9.0E+05

1.0E+06

0 10 20 30 40

Time (hour)

Pressure (Pa)

Reactor chamber

PHTS chamber: AC Loop

HVAC room: AC Loopﾟ

PHTS chamber: B Loopﾟ

HVAC room: B Loop

On the containment vessel floor

Inside the Reactor vessel/the primary

system pipe

Inside the secondary system pipe

Annulus.

SHTS chamber

Environment

Fig. 7-22(2). Pressure （Case 15:　PLOHS, Non-CVBP　PL-NRL-H-γ）

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 10 20 30 40

Time (hour)

Hydrogen m

ol fraction (-)

Reactor chamber


HVAC room: AC Loop

PHTS chamber: B Loop

HVAC room: B Loop



system pipe


Annulus

SHTS chamber

Environment

Fig. 7-22(3). Hydrogen Mol Fraction (Case 15:　PLOHS, Non-CVBP, PL-NRL-H-γ）

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 10 20 30 40

Time (hour)

Xe (-)

Reactor chamber


HVAC room: AC Loop


HVAC room: B Loop



system pipe


Annulus.

SHTS chamber

Environment

Fig. 7-23(1) Xe Gr Initial Inventory Ratio (Case 15: PLOHS, Non-CVBP　PL-NRL-H-γ）

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 10 20 30 40

Time (hour)

I (-)

Reactor chamber


HVAC room: AC Loop


HVAC room: B Loop



system pipe


Annulus.

SHTS chamber

Environment

Fig. 7-23(2) I Gr Initial Inventory Ratio (Case 15,　PLOHS, Non-CVBP　PL-NRL-H-γ）

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 10 20 30 40

Time (hour)

Ce (-)

Reactor chamber


HVAC room: AC Loop


HVAC room: B Loop



system pipe


Annulus.

SHTS chamber

Environment

Fig. 7-23(3) Ce Gr Initial Inventory Ratio (Case 15:PLOHS, Non-CVBP　PL-NRL-H-γ）

Example of CV response calculated by AZORES

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� Objectives of PRD: To eliminate the subjective decision for the probability of blanching points in ETs.� Procedure: (i) Constructs an event tree from the top event (an event considered at a branching point of an phenomenological event tree) to lower events. (2) Function gate is settled to calculate by a certain function with lower events.(3) To lower events the probabilities are to be give by any method as much as possible. The probability distributions are transferred to the upper events.

3. Phenomenological Relation Diagram : PRDProbability decision method for the blanching

points in event trees (ET)

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-ＰＲＤＰＲＤＰＲＤＰＲＤＡｐｐｏａｃｈＡｐｐｏａｃｈＡｐｐｏａｃｈＡｐｐｏａｃｈ for the top event of acceleration -

Function gate [Motion equation: F=ma]

Events (outputs from the function gate)

Top event[ Acceleration: a]

Top eventConditionalbranch

Yes

No

Events[Force: F]

Sub-PRD [Mass: m]

Probability distribution function

Elementary event ②［F2］

Elementary event ①［F1］

Elementary event ③［F3］

To be expanded in detail in a lower PRD

Bottom event

Probability distributions are given to events that are considered to have a margin of uncertainties. Distributions to be given are defined by “the probability distribution function.”

-Events are composed of several events. This case represents that events are composed of elementary events① to ③

To be calculated by a certain function with lower events as inputs. The details of calculation are indicated in the adjoining blue fames.

-The top event that will be evaluated by the PRD approach. -[Acceleration a incidence probability distribution]

The probability distribution function to be given to a certain variable:Example）U[1,10]： A uniform distribution between 1 and 10N[10,5]： A normal distribution with the average value of 10 and the standard deviation of 5[L,U]=[0,100]： Lower limit – 0; Upper limit - 100 ]

Incidence probability Incidence probability Incidence probability Incidence probability

distributiondistributiondistributiondistribution

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Evaluation procedures of ROAAM used LWR and PRD

図-1 RO AAM とPRD における評価手順

(1)着目現象に対する支配要因の抽出とダイヤグラムの展開

●着目現象の支配要因を抽出して下位事象へと分解し、相互に関連付ける。

●下位事象の相互関係をダイヤグラムに展開

●モンテカルロ法などで関数関係を上位に辿り着目現象の分岐確率を評価

(2) 支配要因のパラメータ設定と確率分布の導入

(3) 決定論的知見の援用

(4) 着目現象に対する分岐確率の評価

●着目現象を記述するパラメータをDeterm inistic(D)、Probabilistic(P)、intangible variables（I）の3 種に分類

●展開した下位事象のP パラメータについて確率分布を設定

●Iパラメータについて工学的判断による値を設定

●下位事象の代表値(D パラメータ)を解析コードによる解析、単純な相関式などを援用して設定

●下位事象の代表値(D パラメータ)を実験的知見を援用して設定

PRD RO AAM

Fig.D1-1 Evaluation Procedures of ROAAM and PRD

(1) Selection of the dominant factors and development of diagram regarding the concerned phenomenon

● Select the dominant factors of the concerned phenomenon, break them down into low-order events, and relate them to each other. ● Develop the reciprocal relations among the lower-order events into a diagram

(2) Establishment of parameters of the dominant factors and introduction of probability distribution

● Parameters, which describe the concerned phenomenon, are classified into three categories including deterministic (D), probabilistic (P) and intangible variables (I).

● Establishment of the probability distribution regarding the P parameter of the developed lower-order events ● Establishment of the value based on engineering judgment regarding the I parameter

(3) Supplementary use of deterministic findings ● Establishment of the representative value of the lower-order events (D parameter) by using analysis based on the analytical

codes, supported by a simple correlation equation ● Establishment of the representative value of the lower-order events (D parameter) supported by the empirical findings

(4) Evaluation of branching probability regarding the concerned phenomenon ● Evaluation of the branching probability of the concerned phenomenon, tracing the functional relation

upwards using the Monte Carlo method and others

ROAAM PRD

Both methods seem basically identical.

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Summary� With the developed integrated analytical tools, one-through evaluation for severe accidents including FP release ratio became possible to LMFBR. The tools were used for the effective evaluation of AM for Monju. � Now, further efforts are being made to make analyses more realistic for the Monju with an advance core and the Japanese demonstration LMFBR. � These improvements are very helpful in constructing data-bases of the Emergency Response Support System (ERSS) for Monju by conducting more reliable analyses to the conceivable scenarios after initiating events.

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� Many thanks for your audience.

19


Characteristics of PLOHS� After the reactor shutdown, the plant temperature increases slowly but monotonously both in the primary cooling system (PHTS) and in the secondary cooling system (SHTS).� Many plant locations will fail due to the high-temperature creep. � Among several conceivable accident scenarios, the containment vessel by-bass (CVBP) would be most important event due to the high probability and the high potential of large scale FP release to the environment.� We evaluated the frequency of PLOHS/CVBP in this study.

20


FP leak passes in PLOHS/CVBP

Ｐ

Annulus ac ＳＧ

Ｎａ burn → aerosol generation pressure increase

ＣＶ

SHTS

ＮａＮａＮａＮａ leakage↓↓↓↓

ＮａＮａＮａＮａ/Concrete reaction↓↓↓↓

Hydrogen generation↓↓↓↓

Pressure increase

CVBP case

Non-ＣＶＢＰＣＶＢＰＣＶＢＰＣＶＢＰ

case

IHX

RVPHTS

In the case of PLOHS/CVBP, some early failure in SHTS is postulated.When some interface between PHTS and SHTS failed, FP from the molten fuel will run through PHTS and SHTS piping.

21


Boundaries of IHX that have a high potential of first failure in PHTS

PHTSPHTSPHTSPHTS

coolant inletcoolant inletcoolant inletcoolant inlet

Bottom headBottom headBottom headBottom head

PHTS coolant outletPHTS coolant outletPHTS coolant outletPHTS coolant outlet

BellowsBellowsBellowsBellows

SHTSSHTSSHTSSHTS

coolant outletcoolant outletcoolant outletcoolant outlet

Heat Heat Heat Heat

transfer tubestransfer tubestransfer tubestransfer tubes

IHX Bottom Head

IHX bellows

Cover gasbellows

Bottom head (interface between

PHTS/SHTS)Diameter: 2190mmThickness：：：：２５２５２５２５ｍｍｍｍｍｍｍｍ

Material: SUS304

Diameter: 700mmThickness：：：： 1.5, 2.0 mmMaterial: SUS3316

Heat transfer tube

22


An vent tree of PLOHS PowerPowerPowerPower

suppliessuppliessuppliessupplies

Leakage from theLeakage from theLeakage from theLeakage from the

shield plug of RVshield plug of RVshield plug of RVshield plug of RV

Eearlier secondaryEearlier secondaryEearlier secondaryEearlier secondary

system failuresystem failuresystem failuresystem failure

Failure in some areasFailure in some areasFailure in some areasFailure in some areas

of promary systemof promary systemof promary systemof promary system

（（（（aaaa））））

yesyesyesyes　　　　↑↑↑↑

nononono　　　　 ↓↓↓↓

0.250.250.250.25

（（（（bbbb))))

(c)(c)(c)(c)

0.960.960.960.96 （（（（aaaa））））

PLOHSPLOHSPLOHSPLOHS

0.750.750.750.75 (d)(d)(d)(d)

（（（（bbbb))))

0.0440.0440.0440.044

CVBPCVBPCVBPCVBP

The probabilities of branching point (a), (b), (c),(d) are obtained through present analyses.

23


2. Analyses to obtain the probability of the branching points

Failure mechanismFailure mechanismFailure mechanismFailure mechanism Objects for analysis Objects for analysis Objects for analysis Objects for analysis Analysis codeAnalysis codeAnalysis codeAnalysis code

High-temperature creepHigh-temperature creepHigh-temperature creepHigh-temperature creep Vessel, PipingVessel, PipingVessel, PipingVessel, Piping NALAP-IINALAP-IINALAP-IINALAP-II

BucklingBucklingBucklingBuckling ABAQUSABAQUSABAQUSABAQUS

Tensile (or breaking) stressTensile (or breaking) stressTensile (or breaking) stressTensile (or breaking) stress FINASFINASFINASFINAS

Bellows and bottomBellows and bottomBellows and bottomBellows and bottom

head of IHXhead of IHXhead of IHXhead of IHX

Ｔｈｅｒｍａｌ－ｈｙｄｒａｕｌｉｃＴｈｅｒｍａｌ－ｈｙｄｒａｕｌｉｃＴｈｅｒｍａｌ－ｈｙｄｒａｕｌｉｃＴｈｅｒｍａｌ－ｈｙｄｒａｕｌｉｃＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓ

ＳｔｒｕｃｔｕａｌＳｔｒｕｃｔｕａｌＳｔｒｕｃｔｕａｌＳｔｒｕｃｔｕａｌＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓＡｎａｌｙｓｉｓ

24


2.1 Thermal-hydraulic AnalysisFBR plant thermal-hydraulic analysis code NALAP-II

� NALAP-II has been developed in JNES.� For the present study a function was added to evaluate the degree of high-temperature creep of the location: SCDF (Structural cumulative damage factor, Dc ).

� Dc=Σ（Δti/tr）, (1)where,

Δti: time step (s), tr: creep failure time (s).

In eq. (1), tr depend on the material and it is calculated by using the Larson-Miller Parameter.It was considered that the location will fail when Dc=0.2～1.0.

25


Specifications of proto-type LMFBR plant and locations where high-temperature creep was evaluated

� The locations with large value of D(diameter)/t(thickness) were chosen for the present calculation of SCDF.

Thermal powerThermal powerThermal powerThermal power 714 MW714 MW714 MW714 MW

Number of loopsNumber of loopsNumber of loopsNumber of loops 3333

Primary heat transferPrimary heat transferPrimary heat transferPrimary heat transfer

system (PHTS)system (PHTS)system (PHTS)system (PHTS)

Temperature at reactor Temperature at reactor Temperature at reactor Temperature at reactor

inlet/outletinlet/outletinlet/outletinlet/outlet

397397397397////529 529 529 529 ℃℃℃℃

Flow rate Flow rate Flow rate Flow rate 5100510051005100　　　　tttt////hhhh

Pressure at reactor Pressure at reactor Pressure at reactor Pressure at reactor


0.8/0.1 MPa0.8/0.1 MPa0.8/0.1 MPa0.8/0.1 MPa

Main circulatiion pump Main circulatiion pump Main circulatiion pump Main circulatiion pump One unit per loopOne unit per loopOne unit per loopOne unit per loop

IHXIHXIHXIHX

Number of unit Number of unit Number of unit Number of unit 3333

Type Type Type Type

Vertical parallel flow withVertical parallel flow withVertical parallel flow withVertical parallel flow with

no sodium surfaceno sodium surfaceno sodium surfaceno sodium surface

Secondary heat transferSecondary heat transferSecondary heat transferSecondary heat transfer

system (SHTS)system (SHTS)system (SHTS)system (SHTS)

325325325325////529 529 529 529 ℃℃℃℃

Temperature at IHX Temperature at IHX Temperature at IHX Temperature at IHX


3700370037003700　　　　tttt////hhhh

Flow rate Flow rate Flow rate Flow rate 0.8/0.1 MPa0.8/0.1 MPa0.8/0.1 MPa0.8/0.1 MPa

Main circulatiion pump Main circulatiion pump Main circulatiion pump Main circulatiion pump One unit per loopOne unit per loopOne unit per loopOne unit per loop

Auxiliary cooling systemAuxiliary cooling systemAuxiliary cooling systemAuxiliary cooling system

By-pass of the secondaryBy-pass of the secondaryBy-pass of the secondaryBy-pass of the secondary

cooling system with onecooling system with onecooling system with onecooling system with one

air cooler per loopair cooler per loopair cooler per loopair cooler per loop

D (inner dia .) D ( inner dia .) D ( inner dia .) D ( inner dia .) t (thickness)t (thickness)t (thickness)t (thickness)

(mm)(mm)(mm)(mm) (mm)(mm)(mm)(mm)

RV cylindrical wallRV cylindrical wallRV cylindrical wallRV cylindrical wall 7100710071007100 50505050 142142142142 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

Reactor outlet pipingReactor outlet pipingReactor outlet pipingReactor outlet piping 788788788788 11111111 72727272 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

Reactor inlet pipingReactor inlet pipingReactor inlet pipingReactor inlet piping 591591591591 9.59.59.59.5 62626262 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

ＩＨＩＨＩＨＩＨX vessel cylindrical wallX vessel cylindrical wallX vessel cylindrical wallX vessel cylindrical wall 2940294029402940 30303030 98989898 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

IHX heat transfer tubeIHX heat transfer tubeIHX heat transfer tubeIHX heat transfer tube 19.319.319.319.3 1.21.21.21.2 16161616 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

IHX SHTS-side outletIHX SHTS-side outletIHX SHTS-side outletIHX SHTS-side outlet

pipingpipingpipingpiping

540540540540 9.59.59.59.5 56565656 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

EV cylindrical wallEV cylindrical wallEV cylindrical wallEV cylindrical wall 2900290029002900 50505050 58585858 2.25Cr-1Mo steel2.25Cr-1Mo steel2.25Cr-1Mo steel2.25Cr-1Mo steel

Air-cooler heat transferAir-cooler heat transferAir-cooler heat transferAir-cooler heat transfer

tubetubetubetube

45454545 2.92.92.92.9 16161616 SUS304 stainless steelSUS304 stainless steelSUS304 stainless steelSUS304 stainless steel

Fuel pin claddingFuel pin claddingFuel pin claddingFuel pin cladding 5.565.565.565.56 0.470.470.470.47 11.811.811.811.8

20% cold-worked modi f ied20% cold-worked modi f ied20% cold-worked modi f ied20% cold-worked modi f ied

316 stainless steel316 stainless steel316 stainless steel316 stainless steel

LocationLocationLocationLocation MaterialMaterialMaterialMaterialD/tD/tD/tD/t

(a) Spec. of LMFBR (b) Locations of plant evaluated high-temperature creep

26


IHXIHXIHXIHX下部鏡下部鏡下部鏡下部鏡((((SUSSUSSUSSUS304304304304))))のののの座屈限界応力座屈限界応力座屈限界応力座屈限界応力とととと破断限界応力破断限界応力破断限界応力破断限界応力

0000

50505050

100100100100

150150150150

200200200200

250250250250

300300300300

800800800800 810810810810 820820820820 830830830830 840840840840 850850850850 860860860860 870870870870 880880880880 890890890890 900900900900

1111次系次系次系次系NaNaNaNaののののIHXIHXIHXIHX出口温度出口温度出口温度出口温度((((℃℃℃℃))))

限界応力

限界応力

限界応力

限界応力(( ((MPa

MPa

MPa

MPa)) ))

破断限界応力破断限界応力破断限界応力破断限界応力((((σσσσFFFF))))

((((200000200000200000200000ssss、、、、846846846846℃℃℃℃、、、、100100100100MPaMPaMPaMPa))))

IHXIHXIHXIHX下部鏡下部鏡下部鏡下部鏡のののの応力応力応力応力とととと圧力圧力圧力圧力のののの関係式関係式関係式関係式

σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)

aaaa====89898989....89898989、、、、

PPPP((((MPaMPaMPaMPa))))：：：：1111次系圧力次系圧力次系圧力次系圧力

θθθθ：：：：近似式近似式近似式近似式のののの不確定幅不確定幅不確定幅不確定幅

　　　　　　　　確率変数確率変数確率変数確率変数((((0000....95959595～～～～1111....05050505))))

座屈限界応力座屈限界応力座屈限界応力座屈限界応力((((σσσσBBBB))))

::::ABAQUSABAQUSABAQUSABAQUSのののの結果結果結果結果（（（（座屈座屈座屈座屈））））


Buckling critical stress and fracture critical stress in IHX bottom head (SUS304)Stress-pressure relationship equation in IHX bottom headσ(MPa)=θ×a×(P-0.1)a=89.89,P(MPa): Primary system pressure θ： A margin of uncertainties in an approximate expression

Probability variable (0.95～1.05)

Fracture critical stress (σF)

Buckling critical stress (σB)Critic

al str

ess (

MPa)

Results of the ABAQUS-based analyses (backling)

IHXIHXIHXIHX下部鏡下部鏡下部鏡下部鏡((((SUSSUSSUSSUS304304304304))))のののの座屈限界応力座屈限界応力座屈限界応力座屈限界応力とととと破断限界応力破断限界応力破断限界応力破断限界応力

0000

50505050

100100100100

150150150150

200200200200

250250250250

300300300300

800800800800 810810810810 820820820820 830830830830 840840840840 850850850850 860860860860 870870870870 880880880880 890890890890 900900900900


限界応力

限界応力

限界応力

限界応力(( ((MPa

MPa

MPa

MPa)) ))

破断限界応力破断限界応力破断限界応力破断限界応力((((σσσσFFFF))))


IHXIHXIHXIHX下部鏡下部鏡下部鏡下部鏡のののの応力応力応力応力とととと圧力圧力圧力圧力のののの関係式関係式関係式関係式

σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)σ(MPa)=θ×a×(P-0.1)

aaaa====89898989....89898989、、、、

PPPP((((MPaMPaMPaMPa))))：：：：1111次系圧力次系圧力次系圧力次系圧力

θθθθ：：：：近似式近似式近似式近似式のののの不確定幅不確定幅不確定幅不確定幅


座屈限界応力座屈限界応力座屈限界応力座屈限界応力((((σσσσBBBB))))

::::ABAQUSABAQUSABAQUSABAQUSのののの結果結果結果結果（（（（座屈座屈座屈座屈））））


Buckling critical stress and fracture critical stress in IHX bottom head (SUS304)Stress-pressure relationship equation in IHX bottom headσ(MPa)=θ×a×(P-0.1)a=89.89,P(MPa): Primary system pressure θ： A margin of uncertainties in an approximate expression

Probability variable (0.95～1.05)

Fracture critical stress (σF)

Buckling critical stress (σB)Critic

al str

ess (

MPa)

Results of the ABAQUS-based analyses (backling)

2.2 Structual analysis ABAQUS 3-d analysis to IHX bottom head - Buckling critical stress and fracture critical stress -

The buckling of IHX bottom head became marked at the end of calculation: Temperature: 838.7℃℃℃℃; Pressure: 0.89MPa)

The obtained stress-pressure relation curve encountered with the buckling critical stress line and the fractional critical stress line at one point, respectively. The IHX bottom head is expected to fail at the condition between the two points.

IHX exit temperature (℃)

Results of ABAQUS-based analyses （buckling）

27


The results of FINAS 2-d analysis to IHX bellows - Yield stress and tensile stress -

IHXIHXIHXIHXベローズベローズベローズベローズ((((SUSSUSSUSSUS316316316316))))のののの座屈座屈座屈座屈・・・・破断限界応力破断限界応力破断限界応力破断限界応力

0000

50505050

100100100100

150150150150

200200200200

250250250250

300300300300

350350350350

400400400400

700700700700 720720720720 740740740740 760760760760 780780780780 800800800800 820820820820 840840840840 860860860860 880880880880 900900900900


限界

応力

限界

応力

限界

応力

限界

応力

(( ((MPa

MPa

MPa

MPa)) ))

降伏応力降伏応力降伏応力降伏応力

引張引張引張引張((((破断破断破断破断))))応力応力応力応力

((((189000189000189000189000ssss、、、、828828828828℃℃℃℃、、、、97979797....4444MPaMPaMPaMPa))))


IHXIHXIHXIHXベローズベローズベローズベローズ応力応力応力応力

σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)

aaaa====136136136136....25252525、、、、

PPPP((((MPaMPaMPaMPa))))：：：：1111次系圧力次系圧力次系圧力次系圧力((((MPaMPaMPaMPa))))

φφφφ：：：：応力近似式応力近似式応力近似式応力近似式のののの不確定幅不確定幅不確定幅不確定幅


Yield stress

Tensile (or breaking) stress (MPa)

Critic

al str

ess (

MPa)

IHX bellows stress-pressure σ(MPa)=φ×a×(P-0.1)a=136.25P(MPa): Primary system Φ:A margin of uncertainties

IHX bellows (SUS316) buckling critical stress and fracture critical stress

relationship equation

pressure in an approximateexpression (0.95～1.05)

(189000s、828℃、97.4MPa)

(198000s、843℃、

139MPa)

IHX outlet temperature of primary-system sodium

IHXIHXIHXIHXベローズベローズベローズベローズ((((SUSSUSSUSSUS316316316316))))のののの座屈座屈座屈座屈・・・・破断限界応力破断限界応力破断限界応力破断限界応力

0000

50505050

100100100100

150150150150

200200200200

250250250250

300300300300

350350350350

400400400400

700700700700 720720720720 740740740740 760760760760 780780780780 800800800800 820820820820 840840840840 860860860860 880880880880 900900900900


限界

応力

限界

応力

限界

応力

限界

応力

(( ((MPa

MPa

MPa

MPa)) ))

降伏応力降伏応力降伏応力降伏応力

引張引張引張引張((((破断破断破断破断))))応力応力応力応力

((((189000189000189000189000ssss、、、、828828828828℃℃℃℃、、、、97979797....4444MPaMPaMPaMPa))))


IHXIHXIHXIHXベローズベローズベローズベローズ応力応力応力応力

σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)σ(MPa)=φ×a×(P-0.1)

aaaa====136136136136....25252525、、、、

PPPP((((MPaMPaMPaMPa))))：：：：1111次系圧力次系圧力次系圧力次系圧力((((MPaMPaMPaMPa))))

φφφφ：：：：応力近似式応力近似式応力近似式応力近似式のののの不確定幅不確定幅不確定幅不確定幅


Yield stress

Tensile (or breaking) stress (MPa)

Critic

al str

ess (

MPa)

IHX bellows stress-pressure σ(MPa)=φ×a×(P-0.1)a=136.25P(MPa): Primary system Φ:A margin of uncertainties

IHX bellows (SUS316) buckling critical stress and fracture critical stress

relationship equation

pressure in an approximateexpression (0.95～1.05)

(189000s、828℃、97.4MPa)

(198000s、843℃、

139MPa)

IHX outlet temperature of primary-system sodium

Deformed IHX bellows (Temperature: 750℃℃℃℃; Pressure: 0.388 MPa) (The results of the FINAS 3-d calculation

The obtained stress-pressure relation curve encountered with the yield stress line and the tensile stress line at one point, respectively. The IHX bellows is expected to fail at the condition between the two points.

28


The Range of Primary System Component Fracture Pressures

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2

Names of components

Pres

sure

(MPa

)

RV cylindricalwall

RV outlet piping IHX cylindricalwall

RV inlet piping IHX bellows IHX bottom head

0.768M

2.316MPa

1.476MPa 1.165MPa

1.928MPa

0.928MPa1.117MPa

0.768

3.8MPa

2.6MPa

0.961MPa1.075MPa

3. DiscussionPressure range for failure of PHTS components

Five locations (RV cylindrical wall, RV outlet piping, IHX cylindrical wall, IHX bellows and IHX bottom head) fail at the pressure between 0.77 to 2.3 MPa) .

29


Time range for failure of PHTS components

The five locations fail at a narrow time period (between 52hr to 59hr) . Thus, it will be hard to say the failure order in these locations. In PSA, it will be reasonable to assign the equal probability of first failure to these locations, that is 0.2.

30


4. Conclusion(i) A model to analyze the high temperature creep progression by introducing the calculation function of SCDF was added to the LMFBR plant thermal-hydraulics code, NALAP-II.

（ii）The model was applied to the PLOHS event of the typical proto-type LMFBR. The results indicated that the evaporator made of 2.1/4Cr-1Mo steel in SHTS firstly failed when the system temperature exceeded 800 ℃. The main plant components and piping made of SUS 304 stainless steel failed when the system temperature exceeded 870 ℃.

(iii) In addition, detailed structural analyses were performed by using ABAQUS and FINAS codes and the temperature and pressure histories to the locations where the buckling and the tensile stresses are the causes of failure.

(iv) Comparing the failure time information of each location, itwas concluded that the probability of CVBP was 0.2 to the plant.

31


Appendix –additional information

Present trial evaluation shows that the frequency of CVBP is one order smaller than that of retained RV integrity scenario. However, the frequency is more than one order larger than that of other scenarios.

PowerPowerPowerPower

suppliessuppliessuppliessupplies

Leakage from theLeakage from theLeakage from theLeakage from the

shield plug of RVshield plug of RVshield plug of RVshield plug of RV

Eearlier secondaryEearlier secondaryEearlier secondaryEearlier secondary

system failuresystem failuresystem failuresystem failure

Failure in some areasFailure in some areasFailure in some areasFailure in some areas

of promary systemof promary systemof promary systemof promary system

（（（（aaaa））））

yesyesyesyes　　　　↑↑↑↑

nononono　　　　 ↓↓↓↓

0.250.250.250.25

（（（（bbbb))))

0.80.80.80.8

0.960.960.960.96 1.01.01.01.0

PLOHSPLOHSPLOHSPLOHS

0.750.750.750.750.20.20.20.2

0.00.00.00.0

0.0440.0440.0440.044

CVBPCVBPCVBPCVBP

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

Loss of

annulus

function

RV isolaiton

failure

RV failure by

hydrogen

burning

RV failure by

sodium

burning

CVBP Retained RV

integrity

CFF F

requ

ency

(1/R

Y)Terminal conditions of containment response process

(a) Evaluated provability of the branching points (b) Results of trial evaluation of CFF to each level-2 scenario

These numbers were assigned from present study

32


33


Flow network of the NALAP-II code for RV and PHTS

RV flow networkRV flow networkRV flow networkRV flow network

PHTS flow networkPHTS flow networkPHTS flow networkPHTS flow network

IHX

PUMP

R/V

R/V

H/L

M/L C/L

Fig.5 Flow network of the NALAP-II code for RV and PHTS

Cold legMiddle legHot leg

Pump

R/V

R/V

IHXCover gas

Inner

vessel

Core channel

　Inner core Ch.

　Outer core Ch,

　Radial blanket Ch,

　Shield Ch,

　Bypass Ch,

Primary loop

Primary

loop

Maintenance cooling

system

Maintenance cooling

system

Lower plenum

UCS

Flow hole

Outlet

plenum

RV flow networkRV flow networkRV flow networkRV flow network


IHX

PUMP

R/V

R/V

H/L

M/L C/L


IHX

PUMP

R/V

R/V

H/L

M/L C/L


IHX

PUMP

R/V

R/V

H/L

M/L C/L

IHX

PUMP

R/V

R/V

H/L

M/L C/L

Fig.5 Flow network of the NALAP-II code for RV and PHTS

Cold legMiddle legHot leg

Pump

R/V

R/V

IHXCover gas

Inner

vessel

Core channel

　Inner core Ch.

　Outer core Ch,

　Radial blanket Ch,

　Shield Ch,

　Bypass Ch,

Primary loop

Primary

loop

Maintenance cooling

system

Maintenance cooling

system

Lower plenum

UCS

Flow hole

Outlet

plenum

34


IHX inlet and outlet temperatures, and PHTS flow rate

300

350

400

450

500

550

600

650

700

750

800

850

900

950

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

時間（×10,000秒）

温度(℃）

0

1

2

3

4

5

6

7

8

9

10

流量比(%)

IHX-1次入口温度

IHX-1次出口温度

IHX-2次入口温度

IHX-2次出口温度

1次流量定格比

35


Temperature and the Mises stress behavior of IHX bellows (Stress with the maximal element of equivalent creep strain: the center

of plate pressure)(The results of the FINAS-based two-dimensional elasto-plastic

large=scale deformation and creep analysis)�

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 10000 20000 30000 40000 50000 60000

時間(秒)

応力

(N/mm

2

)

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

温度

(℃

)

ミーゼス応力

周方向応力

子午線方向応力

温度

Time (s)

Stress (N/㎟)

Temperature (℃)

Mises stressCircumferential stressStress in the meridiandirectionTemperature

36


Temperature and the Mises stress behavior of IHX bellows (Stress with the maximal element of equivalent creep strain:

the center of plate pressure)(The results of the FINAS-based two-dimensional elasto-plastic

large=scale deformation and creep analysis)

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 10000 20000 30000 40000 50000 60000

時間(秒)

応力

(N/mm

2

)

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

温度

(℃

)

ミーゼス応力

周方向応力

子午線方向応力

温度

Time (s)

Stress (N/㎟)

Temperature (℃)

Mises stressCircumferential stressStress in the meridiandirectionTemperature

37


Comparison of initiating events frequency between JAEA and JNES

37

38


4. Results of PSA4.1 Effects of AM measures to keep the RV coolant level

10

-12

10

-11

10

-10

10

-9

10

-8

10

-7

10

-6

炉心

損傷

頻度

（/炉

年）

1次主冷却系

循環ポンプ

トリップ失敗

原子炉

ｶﾊﾞｰｶﾞｽ

供給停止

失敗

1次ﾅﾄﾘｳﾑ

の原子炉

容器への

汲み上げ

失敗

1次ﾒﾝﾃﾅﾝｽ

冷却系漏えい

箇所の隔離

失敗

ｶﾞｰﾄﾞﾍﾞｯｾﾙ

の健全性

喪失

1次主冷却系

漏えい後の

二重漏えい

(SsLより下端）

LORL-全体

■：AM前

■：AM後

Core Damage

Frequencies / Reactor

Year

Before AM MeasuresAfter AM Measures

Primary main coolant system circulation pump trip failureReactor cover-gas feeding cut failure Keeping

sodiumtemperature

high

A failure to isolate the leakage from the primary maintenance cooling system

Loss of guard vessel integrityDouble leak (in an area below SsL) following leakage from the primary main coolant system

All loss of reactor level (LORL) eventIsolation of argon supply line to RV

Siphon break of maintenance cooling system

39


4.2 Effects of initiating events frequency

1.0E-09

1.0E-08

1.0E-07

1.0E-06

Basic Conditions Reference Analysis 5 Basic Conditions Reference Analysis 5

Loss of reactor shutdown functions

Loss of functions to maintain a proper reactor coolant level

Loss of decay heat removal functions

All relevant events

JNES JAEA JNES JAEAbefore AM after AM

Frequency(/ry)

40


1.0E-09

1.0E-08

1.0E-07

1.0E-06

Basic Conditions Reference Analysis 7 Basic Conditions Reference Analysis 7

Loss of reactor shutdown functions

Loss of functions to maintain a proper reactor coolant level

Loss of decay heat removal functions

All relevant event

Before After AM

2.7 times3.8 times

ATWS

LORL

PLOHS

AllAll All

AllATWS

LORL

PLOHSATWSincreases

No AM Measures for ATWS

4.3 Effects of choosing common cause failure

JNES JAEA JNES JAEAbefore AM after AM

Frequency(/ry)

(In the PSA of JAEA, common cause failure is considered between the main reactor shutdown system and the backup reactor shutdown system)

41


4.4 Contribution of initiating events to CDF(b) after AM （ｂｙ（ｂｙ（ｂｙ（ｂｙ JNES））））

1.6E-07

1.0E-13

1.0E-12

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

PLOHS LORL ULOF UTOP ULOHS ULOPI UTOP/ULOF Full core damage

frequencies

Core

Dam

age

Freq

uenc

ies/R

eacto

r Yea

r

PLOHS24%

LORL76%

ULOF0%

UTOP0%

ULOPI0%

ULOHS0%

UTOP/ULOF0%

Full core damage frequency：1.6×10-7/reactor year

ATWS

42


1.0E-09

1.0E-08

1.0E-07

1.0E-06

basal condition

-beforeAM

basal condition

-after AM

JAEA-before-AM JAEA--after AM

原子炉停止機能喪失原子炉液位確保機能喪失崩壊熱除去機能喪失全体

JAEAJNES

0.6倍

0.3倍

ATWS

LORL

PLOHS

全体

全体

全体

全体

ATWS

LORL

PLOHS

4.5 Comparison of estimated CDF between JNES and JAEA

42

Frequency(/ry)

Total Total

Total

Total

0.6 times 0.3 times

development of integrated analytical tools for level-2 psa ... · 2.2 for the core disruption phase...

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