uncertainty analyses using the melcor severe accident
TRANSCRIPT
Uncertainty Analyses Using the MELCOR Uncertainty Analyses Using the MELCOR Severe Accident Analysis CodeSevere Accident Analysis Code
Randall O. GaunttAnalysis and Modeling Department, Sandia National
Laboratories, Albuquerque NM, 87112, USA+1 (505) 284 3989 [email protected]
CSNI Workshop on the Evaluation of Uncertainties in
Relation to Severe Accidents and Level 2 Probabilistic Safety Analysis
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration
under contract DE-AC04-94AL85000.
OutlineOutline•Background•Methods and tools for uncertainty analysis•Example 1: Computationally intensive uncertainty analysis using LHS sampling
•Example 2: Simplified fast running analysis using Monte Carlo sampling
•Observations and Conclusions
How Did We Get Here ?How Did We Get Here ?
Where are we going ?Where are we going ?
Deterministic Bounding Analysis
Probabilistic Risk Informed AnalysisRisk Informed Regulation
MOX, High Burnup, Life Exension
9-11-2001
NRC
Chicago Critical Pile
USS NautilusShippingport
Atomic Energy Act of 1954Atomic Energy Act of 1946 (AEC)
WASH 1400
TMI-2 Chernobyl
1940 1950 1960 1970 1980 1990 2000 2010
NUREG-1150AEC
Environmental ConcernsGlobal Warming andVulnerability to Terrorism
Timeline of Nuclear Safety Technology Evolution
Timeline of Nuclear Safety Technology Evolution
Nuclear TechnologyOutlook
Optimistic
Guarded
Pessimistic
Emerging Issues
NP-2010 and Gen-IVNUREG 0772
NUREG 1465alternate source term
Windscale
TID 14844source term
NPP Siting Study
MOX LTArevised 1465
Phebus FP, VERCORSEuropean Codes
Phenomenological Experiments(PBF, ACRR, FLHT, HI/VI, HEVA)
Tier 1: MELCOR Integrated Code
Tier 2: Mechanistic CodesSCDAP, CONTAIN, VICTORIA
Consolidated Codes
MELCOR: Integrated Severe MELCOR: Integrated Severe Accident Analysis CodeAccident Analysis Code
• Integrated multi-physics treatment– RCS thermal hydraulic response to transients and
loca’s– Core uncovering and heatup– Cladding oxidation and H2 generation– Fission product release from fuel– FP transport and deposition in RCS– Core melt progression and vessel failure– Molten core/concrete interaction– Containment thermal hydraulics– Aerosol mechanics, transport deposition– Hydrogen burns
MELCOR Users WorldwideMELCOR Users Worldwide
Canada
USA
Argentina
Russia
Czech Rep
Sweden
S. KoreaJapan
S. Africa
Finland
England
Germany
Slovenia
ItalySpainSwitzerland
France
Taiwan
Hungary
Belgium
PRC
MELCOR Uncertainty MELCOR Uncertainty AnalysisAnalysis
Rich access to internal model parameters combined with flexible sequence control access lends MELCOR well to Monte Carlo Uncertainty
Analysis Methods
randomlysample
uncertainparameters
N-times
establishuncertaintydistributionsfor uncertainparameters
0
1
values0
1
values
Input File 1
Input File 2
Input File 3
Input File N
MELCORInput Files
MELCORUncertainty
Software
MELCORExecutable
Output File 1
Output File 2
Output File 3
Output File N
MELCOROutput Files
MELCORBatch Execution
Software
StatisticalAnalysis
sample of distributionfor figure of merit
confidence intervalsusing non-parametricmethod
correlation analysis
0
1
values
Order Statistics and Order Statistics and Distribution CharacterizationDistribution Characterization
• Monte Carlo sampling produces un-ordered (random) collection of observations taken from the true distribution
• Zk is collection of rank-ordered observations
• Placing “observations” in rank order and calculating the fraction of observations less than or equal to a given observation forms an estimate of the CDF
• Confidence intervals are estimated based on number of samples and non-parametric statistics
)Pr()Pr()Pr(
)1()!(!
!)Pr(
jijpi
inin
kipk
ZZZZ
ppini
nZ
−=<<
−⋅−
=< −
=∑
ξ
ξ
Non-parametric Order StatisticsAnd Confidence Intervals…
Z1 , Z2 , Z3 , Z4 ,…….. Z100
Percent of observationsWith value less than or equal to Zi
1% 2% 3% 4% 100%
Number of Samples NeededNumber of Samples Needed
• More samples enables greater percentage of distribution to be sampled with higher confidence
• To have 95% confidence that you have sampled 99 percent of the distribution requires 473 samples
nn pnpnC ⋅++⋅−= − )1(1 1
Number of samples required for desired confidence…
Confidence Level
Sample Size to span p =
(%) 0.9 0.95 0.99 0.999 90 37 76 388 3888 95 46 93 473 4742 99 64 130 661 6635
99.9 88 180 919 9228
MELCOR Uncertainty MELCOR Uncertainty SoftwareSoftware
• User defined MELCOR input uncertainty– Wide range of available distributions
• Software produces collection of MELCOR decks by sampling distributions• Batch processing software produces distribution of results
Example 1Example 1Computationally Intensive ExampleComputationally Intensive Example
Hydrogen Production Uncertainty in Full System Hydrogen Production Uncertainty in Full System Analysis using LHS SamplingAnalysis using LHS Sampling
Motivation for StudyMotivation for Study
• Hydrogen uncertainty analysis– Motivated by Hydrogen Rulemaking (10CFR50.44)– Provide estimate of range of in-vessel hydrogen
expected in Station Blackout– Specific focus: Should hydrogen igniters have
backup power in Station Blackout– Issue for Ice Condenser and Mark III plants– Resulted in recommendations for backup
• Presentation focus on methodology and recommendations
• Deterministic Probablistic
MELCOR RCS MELCOR RCS NodalizationNodalizationfor Station Blackout Sequencesfor Station Blackout Sequences
• 3 lumped SG loops
• 1 single loop with pressurizer
• Pump seal leakage
• Full loop water circulation
• Counter current natural circulation with steam
• Creep failure modeled in SG, hot leg and lower head
CV399
310
310
ReactorVessel
CV320
CV522
FL521
CV575
CV580
CV
517
CV
515
FL577
CV585
FL596PORV/ADV
FL597
CV590
CV598(Steam line/turbine)
CV599(Environment)
FL579
FL58
5
FL595
CV
511
CV
513
CV518 CV514
CV510
CV
519
FL508
FL509
FL513FL512
FL504FL505
CV512
CV516
FL50
6 FL507
FL510FL511
FL575
Steam LineSRV
MSIV
CV
675
CV680
CV
617
CV
615
FL677
CV685
FL696PORV/ADV
FL697CV690
CV
695
FL679
FL685
FL695
CV
611
CV
613
CV618CV614
CV
610
CV
619
FL608
FL609
FL613FL612
FL604FL605
CV612
CV616
FL606FL60
7
FL610
FL611
FL675
Steam LineSRV
MSIV
FL690
3-LUMPEDLOOPS
CV603
CV600
CV602
CV601
FL616
FL615
FL614
FL601
FL602FL6503
CV623CV622FL623PUMP
FL622
CV503
CV500
CV502
CV501
FL516
FL515
FL514
FL501
FL502FL503
FL523
SINGLELOOP
FL617
FL600
PUMPFL522
CV521
CV
520
CV523FL624 FL524
FL517
FL500
FL621
CV
621
CV
620
CV400
PR
T450
SRV492
PORV491
PressurizerReliefTank
450
FL410
FL406 FL405
CV4
90
FL631
CV632 CV633FL633
CV534 CV532
FL533
PUMPFL532
FL5234
FL531
CV531
CV530
CV630
CV631
PUMPFL632
FL630FL620
FL530FL520
Ice Condenser Containment Ice Condenser Containment ModelModel
• Multi-compartment containment
• Ice beds modeled
• Hydrogen burns suppressed
Primary System Pressure in SBOPrimary System Pressure in SBO
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8
time [hr]
Pres
sure
[MPa
]
CVH-P.390
hot leg nozzle fails by creep rupture
steam generator dryout
pressurizer empty
core material relocation to lower head
accumulator injections
accumulator setpoint
Full loop natural circulation cools RCS
system pressure at relief valve setpoint low water in core
reduces steam production and pressure drops
Vessel Water Level in SBOVessel Water Level in SBO
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8
time (hr)
Wat
er L
evel
[m]
Top of Fuel
Bottom of Fuelaccumulatorsdribble water inat setpoint
Hot leg fails andaccumulators
dump
second boildown
of vessel water
lower headfailure
Uncertain ParametersUncertain Parameters
•Uncertain parameters selected based on experience
•Parameters included:–Oxidation correlations–Cladding melt release parameters–melt progression–Fuel collapse parameters–Debris quenching parameters–Thermal radiation and heat transfer
•LHS sampling of 8 uncertain parameters using 40 samples
Example of Uncertain MELCOR InputExample of Uncertain MELCOR Input
Zr Melt Release Temperature
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2100 2200 2300 2400 2500 2600 2700
Temperature [K]
Cum
ulat
ive
Dis
trib
utio
n
LHS SamplingSpecified Distribution
Uncertainty Analysis for Hydrogen Uncertainty Analysis for Hydrogen Produced in Sequoyah SBOProduced in Sequoyah SBO
• LHS sampling produced distribution of results
• Uncertainty band increases with accident progression
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10 12
Time [hr]
Hyd
roge
n M
ass
[kg]
Hydrogen DistributionsHydrogen Distributions(3 points in time)(3 points in time)
• Observations portrayed in “rank order” forms estimate of cumulative distribution
• Confidence intervals determined from non-parametric statistics (not shown here)
• Distributions broaden in time
Sampled Hydrogen Distribution
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
200 300 400 500 600 700 800hydrogen mass [kg]
cum
ulat
ive
dist
ribut
ion
4 hr
5 hr
8 hr
MELCOR HMELCOR H22 Uncertainty Compared to Uncertainty Compared to NUREGNUREG--1150 Expert Elicitation1150 Expert Elicitation
• Uncertainty increases in time
• MELCOR produces narrower distribution compared to subjective expert elicitation
• Code approach provides objective estimates with greater certainty
• One expects decreased uncertainty attributed to greater knowledge
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5fraction of Zr oxidized
cum
ulat
ive
dist
ribut
ion
MELCOR 4 hrMELCOR 5 hrMELCOR 8 hrexpert Aexpert Bexpert Cexpert Dexpert Eaggregateaverage
Example 2Example 2High Fidelity Plant RCS Analysis Used to Drive High Fidelity Plant RCS Analysis Used to Drive Simplified Fast Running Containment AnalysisSimplified Fast Running Containment Analysis
Containment Boundary Containment Boundary ConditionsConditions
• Full detailed RCS and containment model of AP1000 3BE accident established TH boundary conditions
• Boundary conditions used to drive simple fast running containment analysis of aerosol fallout behavior
Steam Sources to Containment
0
20000
40000
60000
80000
100000
120000
140000
0 2 4 6 8 10
time [hr]
Inte
grat
ed F
low
[kg]
ADS1-3 to IRWSTADS4-1 to SGRM 1ADS4-2 to SGRM 2Acc 1 to CavityIRWST to CavityCMT 1 to CavityDVI brk to PXS
Uncertain Aerosol Physics ParametersUncertain Aerosol Physics Parameters
Parameter Bounds Distribution
Non-radioactive structural aerosol mass 50 – 300 kg uniform Aerosol mass mean diameter 1 – 4 μm uniform Aerosol GSD for log normal distribution 1.2 - 3 uniform Aerosol shape factors for diffusive, thermophoretic and gravitational settling deposition velocities
1 – 5 Beta (p=1,q=3)
Particle slip factor in Cunningham slip correction 1.2 – 1.3 Beta (p=4, q=4) Particle-particle agglomeration sticking probability
0.5 – 1.0 Beta biased to 1 (p=2.5, q=1)
Boundary layer thickness for diffusion deposition 5 - 20 μm uniform Factor in Thermal Accommodation Coeff. 2.2 – 2.5 uniform Gas/particle thermal conductivity ratio in thermophoresis deposition velocity
0.006 – 0.06 log uniform
Turbulent energy dissipation in agglomeration coefficients
0.00075 – 0.00125 uniform
Aerosol particle effective material density 1000 – 5000 kg/m3 Beta biased to 2000 (p=1.5, q=2.5) Heat/Mass Transfer multiplier for steam condensation in containment
0.75 – 1.25 Beta (p=1.5, q=1.5)
Decontamination CoefficientDecontamination Coefficient
⎥⎦⎤
⎢⎣⎡ −⋅=
⋅−=
dtdmtS
tmt
tmttSdtdm
)()(
1)(
)()()(
&
&
λ
λ
Aerosol Airborne MassAerosol Airborne Mass
• Monte Carlo sampling – 150 samples
• Depletion time constant characterizes fallout rate
• Time constant assessed at different points in time
• Compared to industry deterministic point value
Airborne Cs Mass All Cases
0
1
10
100
0 1 2 3 4 5 6 7 8 9 10
time [hr]
mas
s [k
g]
sourceperiod
fallout period
λ = 1.0
λ = 0.7
λ = 0.3
Decontamination Time Constant Decontamination Time Constant at 2.5 hrsat 2.5 hrs
• Sampled values shown in green symbols
• 95% confidence intervals derived from non-parametric order statistics methods
Sampled Distribution with 95% Confidence Intervals at 2.5 Hr
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0decontamination coefficient [1/hr]
cum
ulat
ive
prob
abili
ty
5%95%samples
Analysis of VarianceAnalysis of Variance
• Regression on decontamination coefficient versus uncertain parameters
• R-square measure of parameter importance
• Reveals most important uncertain parameters
• Research prioritization
Parameter Importance - MAAP Thermal Hydraulics
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5 6 7 8 9 10
time [hr]
para
met
er s
igni
fican
ce m
easu
re
AMASS(Uniform) AMEAN(Beta) CHI(Beta) DELDIF(Uniform) F_COND(Beta) FSLIP(Beta) FSTICK(Beta) FTHERM(Uniform) GSTD(Uniform) RHONOM(Beta) TKGOP(Loguniform) TURBDS(Uniform)
Deterministic versus ProbabilisticDeterministic versus Probabilistic
• Traditional bounding safety analyses– Deterministic methods– Conservative input assumptions– Produce defensible bounding analyses– Can be overly conservative
• Excessive regulatory burden• Objective Uncertainty Analyses
– Quantification of uncertainty– Doesn’t combine unrealistically all worst case
parameters– Characterizes safety margins
• What is likely and expected vs. regulatory boundaries
SummarySummary• Uncertainty analysis provides objective view of
variances– Best estimate from mean or median
– Objective assessment of variances
• Alternative to Expert elicitation
• Defense of uncertainty ranges and completeness of coverage are most difficult aspects
• Examples shown illustrate means of handling complexity of models
• Significant tool for risk-informing regulatory decisions