Degradation Analysis and Risk-Informed Management of Feedwater System in Nuclear Power Plants

Wen-Fang Wu, Hung-Ta Kuo, Chih-Hsien WuNational Taiwan University

Jang-Shyong You National Taipei University of Education

This research is supported jointly by the National Science Council and the Atomic Energy Council (through Institute of Nuclear Energy Research) of Taiwan

Degradation or Aging Mechanisms of Feedwater HeatersDegradation or Aging Mechanisms of Feedwater Heaters

Formulas for Prediction Degradation Rate of HeaterFormulas for Prediction Degradation Rate of Heater--WallWall

Probabilistic Analysis of Individual Probabilistic Analysis of Individual FeedwaterFeedwater HeatersHeaters

Risk Ranking of Components of a Feedwater SystemRanking of Components of a Feedwater System

Case StudyCase Study

Contents

Degradation Phenomenon of Feedwater HeatersDegradation Phenomenon of Feedwater Heaters

Steam InletSteam Inlet

Buffering PlateBuffering Plate

Flow Accelerated Corrosion (FAC) at the Steam Inlet of Heater (Reflected Steam Impact from Buffering Plate)

Inlet of Inlet of Condensed WaterCondensed Water

Outlet of Outlet of Condensed WaterCondensed Water

Outlet of Condensed Outlet of Condensed SteamSteam

Forming droplet by shear force

Fe3O4

Water flux

Aging MechanismAging Mechanism

Corroded AreaCorroded Area

TwoTwoPhase FACPhase FAC

Examination Grids:Examination Grids:

Divide the Shell Side of Steam Inlet to L1, L2, R1 and R2 Areas Divide the Shell Side of Steam Inlet to L1, L2, R1 and R2 Areas

33--inchinch--long Grids expanded to twice the diameter of inlet tube at both long Grids expanded to twice the diameter of inlet tube at both sides sides

NDT Examination of HeatersNDT Examination of Heaters:: PointPoint--byby--Point MethodPoint Method

CodeCode--Based Safety AssessmentBased Safety Assessment

Make Required Repair Make Required Repair according to ASME B & PV according to ASME B & PV Sec VIII, Division 1 UGSec VIII, Division 1 UG--27& 27& Suggestions made by EPRISuggestions made by EPRI

(mil/yr)

FW-LP3A-L1SA-515-70630.5420.4920.88

5.8

ASME VIII250 psi405 F

PSEPRt0.6

0.9L =

ttLL: min. wall thickness required (inch): min. wall thickness required (inch)PP: design pressure (: design pressure (psipsi))RR: inner radius (inch): inner radius (inch)SS: max. allowable stress (: max. allowable stress (psipsi))EE: welding efficiency : welding efficiency

HP1A/1B LP3A/3B LP4A/4B LP5A/5B LP6A/6B

(psi) (in) (psi) (in)

40062

175001

0.6466

25062

175001

0.4020

10063

175001

0.1625

5064

175001

0.0824

5068

175001

0.0876

WallWall--Thickness Required by ASME B & PV Sec VIII Thickness Required by ASME B & PV Sec VIII Division 1 UGDivision 1 UG--2727

To Replace the Deterministic Assessment by To Replace the Deterministic Assessment by RiskRisk--Based AssessmentBased Assessment

To Reduce the Maintenance Cost through To Reduce the Maintenance Cost through RiskRisk--Based ManagementBased Management

ReliabilityReliability--Based AssessmentBased Assessment

Safety FactorSafety Factor--Based AssessmentBased Assessment

Present ResearchPresent Research

Incorporating Aging Mechanism into QRAIncorporating Aging Mechanism into QRA

PDF of wall-thickness corrosion

Wall-Thickness Corrosion (inch)

Allowed wall-thickness corrosion

Obs

erve

d P

roba

bilit

y (%

)

=

=

=

k

n

k

ji

m

ij

p

pq

MCS

MCS)(FV

1

1

U

U

++

AgingPhysics

Risk metricFV, RRW, DIM

Importance measure& Risk ranking

Reliability model

( )o

jj R

Rq

+

=RAW

FTA, ETAFTA, ETA

==Risk RankingRisk Ranking

Importance MeasureImportance Measure

( )

=

kk

k

jj

j

dqqR

dqqR

qDIM

FAC Empirical ModelsFAC Empirical Models

1. KWU/KR Model: Siemens Co. & WATHEC Software Package

2. ERPI-CH Model: EPRI & CHECWORKS Software Package (not released to public)

3. BRT-Cicero Model: Electricite de France by Cicero Test Loop (not released to public)

KWU SingleKWU Single--Phase FACPhase FAC Empirical ModelEmpirical Model

( )[ ]( ) )(18.1775.0135.6 118.02 tfepHeBk gWNcR +=

( ) 5.13279.010375.95.10 24 += TThB( ) ( ) 15.210078.110275.10875.0 225 += TThN

( ) 3162117 10849972.310624812.510356901.39999934.0 ttttf +=

= R

=ck=W=pH

=g

=h

=Tfluid velocity (m/s)

oxygen content (g/kg)

pH value

geometric factor (0.8 for T junction) Cr and Mo in steel ( 0% for SA515-70)

temperature (K)

FAC rate (g/cm2h)

t = exposure time (1.5 yr=13140 hrs per EOC)

KWU TwoKWU Two--Phase FAC Empirical ModelPhase FAC Empirical Model

=11 st

w

xmW&

Modified Flow Velocity:Modified Flow Velocity:

m&

w

stx

= steam quality

= void fraction

= mass flux(kg/m s)

= density of compressed liquid (kg/m )3

( )stxWTgpHf ,,,,KWU =Parameter Sensitivity AnalysisParameter Sensitivity Analysis

FAC rateFAC rate--pHpH FAC rateFAC rate--Fluid velocityFluid velocity

FAC rateFAC rate--Oxygen contentOxygen content FAC rateFAC rate--Steam qualitySteam quality

FAC rateFAC rate--TemperatureTemperature

Parameter Symbol Mean valueStandard deviation Distribution

Temperature (F)

Fluid velocity (ft/s)

Oxygen content (ppb)

Water chemistry (pH)

Steam quality

Piping geometry ck

pH

g

W

stx

Cr + Mo in % h

tExposure time (hr)405

13.2

30

0.88

7

0.8

0

13140

40.5

N/A

3

0.7

N/A

N/A

N/A

13.2

Normal

Normal

Normal

Normal

Point estimate

Point estimate

Point estimate

Point estimate

Monte Carlo Simulation of FAC RateMonte Carlo Simulation of FAC Rate

T

Temperature Fluid Velocity g pH FAC Rate (mil/yr)

387 11.6321 31.9058 6.3728 6.0569

337 10.2929 28.1958 7.0946 9.2151

410 14.5020 31.6536 6.9027 6.3281

416 12.5154 26.7005 6.1856 8.2137

358 13.6321 30.2580 7.8286 7.4289

453 13.5090 23.9863 6.9892 9.5993

453 13.2283 28.5207 7.3754 6.4162

FAC Rate (mil/yr)

Obs

erve

d fr

eque

ncy

141210864

25

20

15

10

5

0

Distribution of Thinning RateDistribution of Thinning Rate

Distribution

Normal

Lognormal

Weibull

Test value ( )=

=

11

1

2

i i

ii

EOE

Critical value 8,95.0

Goodness of fit

16.8625

13.7310

6.4282

15.5

Acceptable

Acceptable

Not acceptable

FAC Rate (mil/yr)

Per

cent

(%)

101

99.999

9080706050403020

10

5

32

1

0.1

Weibull

FAC Rate (mil/yr)P

erce

nt (%

)

15109876543

99.9

99

95

90

80706050403020

10

5

1

0.1

Lognormal

FAC Rate (mil/yr)

Perc

ent (

%)

14121086420

99.9

99

95

90

80706050403020

10

5

1

0.1

Normal

GoodnessGoodness--ofof--Fit TestFit Test

PDF of wall-thickness corrosion

Wall-Thickness Corrosion (inch)

Allowed wall-thickness corrosion

Obs

erve

d P

roba

bilit

y (%

)

HP1A/1B LP3A/3B LP4A/4B LP5A/5B LP6A/6B

(psi) (in) (psi) (in)

40062

175001

0.6466

25062

175001

0.4020

10063

175001

0.1625

5064

175001

0.0824

5068

175001

0.0876

RandomRandom--Fixed Reliability ModelFixed Reliability Model

Wall-thickness corrosion (in)

Freq

uenc

y

0.240.200.160.120.080.040.00

300

250

200

150

100

50

0

Loc

-3.561 0.2802 100-3.357 0.3147 100-3.199 0.2827 100-3.008

Scale

0.3186 100-2.847 0.3264 100-2.739 0.3132 100-2.599 0.3078

N

100-2.435 0.2974 100

-4.587 0.2812 100-3.927 0.2994 100

Variable

EO C 22EO C 23EO C 24EO C 25EO C 26EO C 27

EO C 18EO C 19EO C 20EO C 21

Lognormal

Allowed wall-thickness corrosion

ReliabilityReliability--Based Aging AssessmentBased Aging Assessment

?

Risk Metric & Importance MeasuresRisk Metric & Importance Measures

),( IE ji qfhR =

Risk Metric:Risk Metric: A Function of Frequencies of Initiating Events & A Function of Frequencies of Initiating Events & Conditional Probabilities of Failure Modes of Conditional Probabilities of Failure Modes of SSCsSSCs

(i) FV IM: (i) FV IM: Focus onFocus on Weight ofWeight of Failure of Failure of CutsetsCutsets containing containing BEBEjj

=

=

=

k

n

k

ji

m

ij

p

pq

MCS

MCS)(FV

1

1

U

U

Probability of union of all min cutsets (MCS) containing BEj

Nominal risk (probability of all MCSs)

0

0)(FVR

RRq jj

= or

(ii) RAW IM:(ii) RAW IM: Focus on Weight (Increase) of Risk owing to Focus on Weight (Increase) of Risk owing to BEBEjj

( )o

jj R

Rq

+

=RAW

(iii) Differential IM (DIM): (iii) Differential IM (DIM): Focus on Risk Change due to Variation of Focus on Risk Change due to Variation of BEBEjj((BorgonovoBorgonovo & & ApostolakisApostolakis, 2001), 2001)

( )

=

=

=

=

kk

k

jj

kk

k

k

k

jj

j

jj

k k

j

kk

k

jjq

j

qqR

qqR

qq

dqqR

qq

dqqR

q

qR

qR

dqqR

dqqR

dRdR

q j

) DIM(

DIM

or

H1

H2

ji qq =

==j

j

i

i

qq

qq

Case Study: PRA of a BWR Feedwater SystemCase Study: PRA of a BWR Feedwater System

LP6A LP6B

LP5A LP5B

LP4A LP4B

LP3A LP3B

LP2A LP2B

HP1A HP1B

CC

CD

FP

1B

1A

LP6A LP6B

LP5B

LP4B

LP3B

LP2B

LP4A

LP3A

LP2AHP1BHP1A

LP5A

Fault Tree AnalysisFault Tree Analysis

Break down of feedwater system

feedwater pumps fail to start

Cond. & dem. system fail to start

Failure of HP heaters

1A 1B

Main cond. & cond. pumps fail

to start

Failureof LP heaters

CC

Failure of

LPA segmentFailure of

LPB segment

5B 6B4B3B5A 6A4A3A

FP

2A 2B

CD

Operational Conditions (by assumption):Operational Conditions (by assumption):

Numerical AnalysisNumerical Analysis

Failure Probability of Series Systems:

( )( ) ( )nseries qqqF = 1...111 21

Failure Probability of Parallel Systems:nparallel qqqF ...21=

Feedwater Pumps

Condenser & De-Mining Units

High-Pressure FW Heaters

Low-Pressure FW Heaters

Hot Well & Pump of Main Condensers

1qFFP =

2qFCD =

43qqFHP =

( )( )( )( )( )[ ] ( )( )( )( )( )[ ]141210861311975 111111 111111 qqqqqqqqqqFLP =

15qFCC =

Example: LP2A at EOC 26 (assuming no repair)

Risk Metric of Feedwater SystemRisk Metric of Feedwater System( ) ( )( )( )( )( )

CCHPLPCDFPCCHPCDFPCCLPCDFP

CCCDFPCCHPLPCDCCHPCDCCLPCDCCCD

CCHPLPFPCCHPFPCCLPFPCCFPCCHPLP

CCHPCCLPCCHPLPCDFPHPCDFP

LPCDFPCDFPHPLPCDHPCDLPCDCD

HPLPFPHPFPLPFPFPHPLPHPLP

CCHPLPCDFPj

FFFFFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFqR

++++

+++++

++++++=

= 111111

02E64.5)(

)()(

)DIM( :H115

1

55 =

=

=k k

j

j

qqR

qqR

q

( ) 02E59.8)()(

)DIM( :H215

1

55

5 =

=

=k

kk

j

j

qqqR

qqqR

q

In R(qj), delete all terms not related to q5 to obtain MCS containing BE5

3548.1)(

)RAW( 55 ==+

jqRqq

( ) ( )( )( )( )( )

CCHPLPCDFPCCHPCDFPCCLPCDFP

CCCDFPCCHPLPCDCCHPCDCCLPCDCCCD

CCHPLPFPCCHPFPCCLPFPCCFPCCHPLP

CCHPCCLPCCHPLPCDFPHPCDFP

LPCDFPCDFPHPLPCDHPCDLPCDCD

HPLPFPHPFPLPFPFPHPLPHPLP

CCHPLPCDFPj

FFFFFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFFFFFFFFFFFFFFFFFFFFF

FFFFFqR

++++

+++++

++++++=

= 111111

( )( )( )( )( )]111

111)[(

141210

86131197513117513975137513119513115

1395135119751175975751195115955

qqqqqqqqqqqqqqqqqqqqqqqqqqqq

qqqqqqqqqqqqqqqqqqqqqqqqqFLP

+++

++++=

( ) 02-9.84EMCS

)FV(

)(15

15

5

=

==

qR

pq

qi

iU

RAW IM FV IM

DIM H1 DIM H2

FP CD 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B C

C

EOC1820

2224

2628

0

20

40

60

80

100

120

FP CD

1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B CC

EOC1820

2224

2628

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

FP CD

1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B CC

EOC18

21

2427

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

FP CD

1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B CC

EOC1820

2224

2628

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Risk Rank by FV IMRisk Rank by FV IM Risk Rank by RAW IMRisk Rank by RAW IM

Risk Rank by DIM H1 Risk Rank by DIM H1 Risk Rank by DIM H2 Risk Rank by DIM H2

0

2

4

6

8

10

12

18 19 20 21 22 23 24 25 26 27 28

EOC

Ran

king

1A1B2A2B3A3B4A

4B5A5B6A6B

0

2

4

6

8

10

1218 19 20 21 22 23 24 25 26 27 28

EOC

Ran

king

1A1B2A2B

3A3B4A4B5A5B

6A6B

0

2

4

6

8

10

1218 19 20 21 22 23 24 25 26 27 28

EOC

Ran

king

1A1B2A2B3A3B4A4B5A5B6A6B

0

2

4

6

8

10

1218 19 20 21 22 23 24 25 26 27 28

EOC

Ran

king

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

6A

6B

Concluding RemarksConcluding Remarks KWU model predicts FAC of FWH wellKWU model predicts FAC of FWH well

FAC Rate (mil/yr)

Obs

erve

d fr

eque

ncy

141210864

25

20

15

10

5

0

5.8

(mil/yr)

FW-LP3A-L1SA-515-70630.5420.4920.88

5.8

ASME VIII250 psi405 F

In studied case, In studied case, FWHsFWHs atat highhigh--pressure section have pressure section have lower risk rankslower risk ranks, and can be allowed for less intensive , and can be allowed for less intensive examination if so desiredexamination if so desired

Those Those deserve more intensive examinationsdeserve more intensive examinations are are LP6BLP6BLP6ALP6ALP5ALP5ALP5BLP5BLP4BLP4B

As compared to RAW IM, As compared to RAW IM, FV IM & DIM are more FV IM & DIM are more effective to distinguish risk differenceseffective to distinguish risk differences among among componentscomponents

The case study indicates The case study indicates a riska risk--based inspection plainbased inspection plain or or riskrisk--based management program based management program can be employedcan be employed to to replace the current codereplace the current code--based inspection programbased inspection program

Although Although LP2A & LP3ALP2A & LP3A locate close to highlocate close to high--pressure pressure section, their risks are section, their risks are moderately highmoderately high (owing to smaller (owing to smaller allowable thicknesses) and need to be paid attention to allowable thicknesses) and need to be paid attention to

Thank you for your attention.

The above viewpoints do not necessarily reflect those of AEC and NSC of Taiwan.