Uncertainty Analyses Using the MELCOR Uncertainty Analyses Using the - - PowerPoint PPT Presentation

Uncertainty Analyses Using the MELCOR Uncertainty Analyses Using the MELCOR Severe Accident Analysis Code Severe Accident Analysis Code

Randall O. Gauntt Analysis 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.

Outline Outline

• 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 Analysis

Risk Informed Regulation

MOX, High Burnup, Life Exension 9-11-2001 NRC Chicago Critical Pile USS Nautilus Shippingport Atomic Energy Act of 1954 Atomic Energy Act of 1946 (AEC) WASH 1400

TMI-2

Chernobyl 1940 1950 1960 1970 1980 1990 2000 2010 NUREG-1150 AEC Environmental Concerns Global Warming and Vulnerability to Terrorism

Ti Tim eline of ne of Nu Nucl clear Sa Safety Te Tech chno nology Ev Evolut ution Ti Tim eline of ne of Nu Nucl clear Sa Safety Te Tech chno nology Ev Evolut ution

Nuclear Technology Outlook

Optimistic Guarded Pessimistic Emerging Issues NP-2010 and Gen-IV

NUREG 0772 NUREG 1465

alternate source term

Windscale TID 14844

source term

NPP Siting Study MOX LTA

revised 1465

Phebus FP, VERCORS European Codes Phenomenological Experiments (PBF, ACRR, FLHT, HI/VI, HEVA) Tier 1: MELCOR Integrated Code Tier 2: Mechanistic Codes SCDAP, CONTAIN, VICTORIA Consolidated Codes

MELCOR: Integrated Severe MELCOR: Integrated Severe Accident Analysis Code Accident 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 Worldwide MELCOR Users Worldwide

Canada USA Argentina Russia Czech Rep Sweden

• S. Korea

Japan

• S. Africa

Finland England Germany Slovenia Italy Spain Switzerland France Taiwan Hungary Belgium PRC

MELCOR Uncertainty MELCOR Uncertainty Analysis Analysis

Rich access to internal model parameters combined with flexible sequence control access lends MELCOR well to Monte Carlo Uncertainty Analysis Methods

randomly sample uncertain parameters N-times establish uncertainty distributions for uncertain parameters

1 values 1 values Input File 1 Input File 2 Input File 3 Input File N

MELCOR Input Files MELCOR Uncertainty Software MELCOR Executable

Output File 1 Output File 2 Output File 3 Output File N

MELCOR Output Files MELCOR Batch Execution Software Statistical Analysis sample of distribution for figure of merit confidence intervals using non-parametric method correlation analysis

1 values

Order Statistics and Order Statistics and Distribution Characterization Distribution Characterization

• Monte Carlo sampling produces

un-ordered (random) collection

• f observations taken from the

true distribution

• Zk is collection of rank-ordered
• bservations
• Placing “observations” in rank
• rder and calculating the fraction
• f 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(

j i j p i i n i n k i p k

Z Z Z Z p p i n i n Z − = < < − ⋅ − = <

− =

∑

ξ ξ

Non-parametric Order Statistics And Confidence Intervals… Z1 , Z2 , Z3 , Z4 ,…….. Z100 Percent of observations With value less than or equal to Zi

1% 2% 3% 4% 100%

Number of Samples Needed Number 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

n n

p n p n C ⋅ + + ⋅ − =

−

) 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 Software Software

• 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 1 Example 1 Computationally Intensive Example Computationally Intensive Example Hydrogen Production Uncertainty in Full System Hydrogen Production Uncertainty in Full System Analysis using LHS Sampling Analysis using LHS Sampling

Motivation for Study Motivation 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 Nodalization Nodalization for Station Blackout Sequences for 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

Reactor Vessel

CV585

CV598 (Steam line/turbine) CV599 (Environment)

CV685

Ice Condenser Containment Ice Condenser Containment Model Model

• Multi-

compartment containment

• Ice beds

modeled

• Hydrogen

burns suppressed

Primary System Pressure in SBO Primary System Pressure in SBO

2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 7 8

time [hr] Pressure [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 SBO Vessel Water Level in SBO

1 2 3 4 5 6 7 1 2 3 4 5 6 7 8

time (hr) Water Level [m]

Top of Fuel Bottom of Fuel accumulators dribble water in at setpoint Hot leg fails and accumulators dump second boildown

• f vessel water

lower head failure

Uncertain Parameters Uncertain 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 Input Example of Uncertain MELCOR Input

Zr Melt Release Temperature

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] Cumulative Distribution

LHS Sampling Specified Distribution

Uncertainty Analysis for Hydrogen Uncertainty Analysis for Hydrogen Produced in Sequoyah SBO Produced in Sequoyah SBO

• LHS sampling

produced distribution of results

• Uncertainty

band increases with accident progression

100 200 300 400 500 600 700 800 2 4 6 8 10 12

Time [hr] Hydrogen Mass [kg]

Hydrogen Distributions Hydrogen Distributions (3 points in time) (3 points in time)

• Observations

portrayed in “rank

• rder” forms estimate
• f cumulative

distribution

• Confidence intervals

determined from non- parametric statistics (not shown here)

• Distributions broaden

in time

Sampled Hydrogen Distribution 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 300 400 500 600 700 800 hydrogen mass [kg] cumulative distribution

4 hr 5 hr 8 hr

MELCOR H MELCOR H2

2 Uncertainty Compared to

Uncertainty Compared to NUREG NUREG-

• 1150 Expert Elicitation

1150 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

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 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 1.5 fraction of Zr oxidized cumulative distribution

MELCOR 4 hr MELCOR 5 hr MELCOR 8 hr expert A expert B expert C expert D expert E aggregate average

Example 2 Example 2 High Fidelity Plant RCS Analysis Used to Drive High Fidelity Plant RCS Analysis Used to Drive Simplified Fast Running Containment Analysis Simplified Fast Running Containment Analysis

Containment Boundary Containment Boundary Conditions Conditions

• Full detailed RCS and

containment model

• f AP1000 3BE

accident established TH boundary conditions

• Boundary conditions

used to drive simple fast running containment analysis

• f aerosol fallout

behavior

Steam Sources to Containment

20000 40000 60000 80000 100000 120000 140000 2 4 6 8 10

time [hr] Integrated Flow [kg]

ADS1-3 to IRWST ADS4-1 to SGRM 1 ADS4-2 to SGRM 2 Acc 1 to Cavity IRWST to Cavity CMT 1 to Cavity DVI brk to PXS

Uncertain Aerosol Physics Parameters Uncertain 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 Coefficient Decontamination Coefficient

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⋅ = ⋅ − = dt dm t S t m t t m t t S dt dm ) ( ) ( 1 ) ( ) ( ) ( ) ( & & λ λ

Aerosol Airborne Mass Aerosol 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

1 10 100 1 2 3 4 5 6 7 8 9 10

time [hr] mass [kg]

source period fallout period

λ = 1.0 λ = 0.7 λ = 0.3

Decontamination Time Constant Decontamination Time Constant at 2.5 hrs at 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 0.1 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 2.0 decontamination coefficient [1/hr] cumulative probability

5% 95% samples

Analysis of Variance Analysis of Variance

• Regression on

decontamination coefficient versus uncertain parameters

• R-square measure
• f parameter

importance

• Reveals most

important uncertain parameters

• Research

prioritization

Parameter Importance - MAAP Thermal Hydraulics

0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 2 3 4 5 6 7 8 9 10

time [hr] parameter significance measure

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 Probabilistic Deterministic 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

Summary Summary

• 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