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 rogaunt@sandia.gov

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