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
dqqR
dqqR
q
qR
qR
dqqR
dqqR
dRdR
q j
) DIM(
DIM
or
H1
H2
ji qq =
==j
j
i
i
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.