advanced modeling and response surface method ology for physical models of level 2 psa event tree

1CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004

ADVANCED MODELING AND RESPONSE SURFACE METHODOLOGY FOR PHYSICAL MODELS OF LEVEL 2

PSA EVENT TREE

CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004

2

Plan

•The physical models of the APET– Principle of the method– Construction of a “physical model”– Comments

•Example of Direct Containment Heating Model

•Example of Ex-vessel steam explosion Model

•Example of Containment thermo-mechanical Model


3

Introduction

For level 2 PSA and the construction of the APET, the IRSN has opted to use, as far as possible, results obtained directly from validated physical codes

One aim is to take benefit of R&D investments in the development and validation of severe accident codes

Three examples from the 900 MW level 2 PSA are provided


4

The physical models of the Accident Progression

Event Tree

Level 1 PSAPlant Damage State

Before Core degradation

During Core degradation

Vessel Rupture

Corium-Concrete Interaction

Before core degradation

I- SGTR

During Core Degradationn

Advanced core

degradatio

CombustionH2

In-vessel steam

explosion

Direct ContaintHeating

Containment mechanical behavior

Corium concrete

interaction

Combustion

Ex-vessels.e.


5

Principles for construction of physical models

Physical models of APET must :

1- give a “best-estimate” evaluation of a physical phenomenon and of its consequences

2- take into account uncertainties

3- be very fast

4- replace sophisticated codes used for severe accident with relative accuracy


6

Schema of a physical model

Upstream uncertain variables

Upstreamstatevariables

Physical model

RVk = F (SVi , UVj) DownstreamResultsVariables


7

Definitions

UPSTREAM “STATE” VARIABLES– They provide relevant information on the plant state for the

evaluated physical phenomena : physical conditions (RCS pressure e.g.) or systems information (pressurizer valve aperture e.g.)

– Generally, they come from previous APET model or PDS variables

UPSTREAM “UNCERTAIN” VARIABLES– They are defined by probabilities distribution ; a value is assigned

by sampling via a Monte-Carlo method– They can have different origins :

•Parameter of sophisticated code not well known but with strong impact on results ;•Expert’s judgment on the accuracy of code result •Statistical uncertainties due to the construction of the APET physical model

DOWNSTREAM “RESULTS” VARIABLES


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Upstreamuncertainvariables


Physical model




Physical model


« SOPHISTICATED SEVERE ACCIDENT

CODE » CALCULATIONS

APET Requirements

Construction of a « physical model »

3 STEPS

• Choice and hierarchy of upstream variables

• Elaboration of a response surface for each downstream variables

• Validation of the response surface accuracyExperimental design


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Construction of a “physical model”

STEP 1 : CHOICE AND HIERARCHY OF UPSTREAM VARIABLES

– Experts provide a first list of upstream (state or uncertain) variables ; for each variable a possible interval of variation is defined

– A first experimental design is defined : each variable can take the extreme values of its variation interval

– For each variables combination of the experimental design, a calculation of downstream variables is led with the sophisticated code

– A statistical analysis is achieved for each downstream variable

– A hierarchy between upstream variables is established ; some of them may be eliminated


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STEP 2 : ELABORATION OF A RESPONSE SURFACE FOR EACH DOWNSTREAM VARIABLE

– A second experimental design plan is defined with more possible values of each upstream variable

– For each combination of variables values obtained in the experimental design plan, a calculation of downstream variables is realized with the sophisticated code

– For each downstream variable, the best response surface of upstream variables is constructed with a statistical analysis (minimal regression)

– The statistical uncertainties of the response surface are estimated


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STEP 3 : VALIDATION OF THE RESPONSE SURFACE ACCURACY

– Other calculations with the sophisticated code are made with new combinations of upstream variables values,

– Results are compared to the response surface

– The first and second steps are completed if the accuracy of the response surfaces is not sufficient


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Comment

This methodology has to be adapted to each case :

•the number of runs with a sophisticated code depends on its execution speed

•a physical and a statistical approach must be associated for the construction of the response surface


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Example 1Direct Containment Heating

CompartimentIntermédiaire

Puits de cuve

Espace Annulaire

Enceinte

Corium + Vapeur

d’eau + H2

« sophisticated code »

RUPUICUV

CPA

(ASTEC system)


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Example 1Direct Containment Heating –

STEP 1 Upstream uncertain variables


DCH model

RVk = F (SVi , UVj)

•Corium particles diameter•Heat exchange coefficient between corium particles and containment atmosphere

•Average flying delay of the corium particles in containment•Vessel heat insulator state•Duration of hydrogen combustion

•Vessel pressure•Mass of melt-corium

DownstreamResultsVariables

•Mass of dispersed corium•Pressure peak in containment


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STEP 2Dispersed corium mass in function of upstream variables :

Correlation derived from experiments (KAERI)

Uncertainties are issued from the analysis of results on the KAERI tests

Statistical distribution of the residues (KAERI Experimental value - Correlation value) for the fraction ofdispersed corium mass - Total number of observations : 49

-20 -15 -10 -5 0 5 10 15 20

Diff

0

2

4

6

8

10

12

14

16

Nu

mb

er

of

Ob

se

rva

tio

ns

Mean value= -1,4 (%), Standard-Deviation= 6,4 (%), Max.=+15,2 (%), Min.=-13,1(%)


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STEP 2Pressure peak : 144 CPA-RUPUICUV runs defined by 2 experimental designs (9 lines for upstream variables that impact dispersed corium mass, 16 lines for other variables)

After statistical correction all over the pressure variation dom ain

Mean = 0 ; Standard-deviation = 0,144 bar

-0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5

Statistical Residue for high Pressure Peaks (>5 bars)

0

5

10

15

20

25

30

35

40

Nu

mb

er of O

bservatio

ns

2 3 4 5 6 7 8 9 10

Fitted Pressure Peak (bar)

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

Re

sid

ue

(b

ar)

= F

itte

d P

res

su

re P

ea

k -

Pre

ss

ure

Pe

ak

es

tim

ate

dw

ith

RU

PU

ICU

V/C

PA


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STEP 3Final validation has shown that the pressure peak is underestimated around 8 bar.This has been checked on sensitivity analyses. 0.3 bar is added to the analytical calculation of pressure peak to guarantee conservatism.

-0,300

-0,250

-0,200

-0,150

-0,100

-0,050

-

0,050

0,100

0,150

0,200

0,250

0 10 20 30 40 50 60 70 80 90

Vessel Pressure (bar)

Eca

rt i

n c

alcu

late

d c

on

tain

men

t p

ress

ure

(b

ar)


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Example 2Ex-vessel steam explosion model

Water can be present in the vessel pit after use of spraying system (CHRS)Consequences of Corium-Water Interaction ?

Vessel Pit

1st Floor

2d Floor

Containment wall

Wall

Vessel


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MC3D code : pre-mixing of corium and waterexplosion

EUROPLEXUS : damage on the structures


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– STEP 1

Vessel Pressure

Corium overheat

Vessel breach diameter

Pre-mixing

N Steam Explosion Runs

Best-estimated Parameters

Results if no steam explosion

N calculations of structure displacement

Water height

Water temperature



Containment failure probability


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– STEP 2The probability of steam explosion is not evaluated

For each pre-mixing conditions, up to 50 steam explosions are achieved

In function of structure displacement calculated for each explosion, pre-mixing conditions are associated to one category that corresponds to a probability of containment failure

After a statistical analysis, a mathematical expression estimates the containment failure probability as a function of upstream variables


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Example 3Containment thermo-mechanical

modelThe APET model has to predict a containment leak size according to pressure and thermal loading

PWR 900 MW containment building :

– Structure : basemat, cylinder and dome– Prestressed reinforced concrete– 6 mm thick steel liner covers the inner surface of the

containment– Design pressure limit 0.5 Mpa

Three steps of modeling with CAST3M code have been performed


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modelA 3D 360 ° for initial containment building state (30 year aged), effect of structure weight, prestressing system with relaxation in tendon and concrete creep and shrinkage

Concrete Passive steel Prestressed tendons


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modelA 3D 90° model calculates the non linear behavior of the containment in function of thermal and pressure loading ;initial conditions come from the 3D 360° model


25


modelA 3D local model for equipment hatch ; boundary conditions of this local model come from the 3D 90°model


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modelOne reference severe accident loading is used (with sensitivity

case)

H2 burning

Melt-corium interaction (MCCI)

Safety injection failure

SCRAM


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modelAnalysis of results shows that :

– the containment leak resistance depends on steel liner integrity because cracks appear quite early in the concrete

– experts have used NUPEC-NRC-SANDAI PCCV tests to define local criteria for liner rupture

– The conclusion is that the liner rupture may occur at around 1 MPa

– local calculation of equipment hatch have confirmed that it is a critical part of the structure :•mechanical contact between the flanges of the equipment hatch closing system may be lost at a pressure not far above the containment design pressure with current screws•containment tightness depends then only on the seal efficiency which could be damaged by radiation


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modelThe APET model only takes into account the leakage through the equipment hatch :

Containment modelPressure Peak in containment Containment leakage size

A parameter to take into account uncertainties on leakage size calculation

Uncertainties are discussed in the frame work of an expert’s group


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Conclusion

•A GENERAL METHODOLOGY FOR PHYSICAL MODEL OF APET

– ONE MODEL FOR ONE PHENOMENA– USE OF VALIDATED CODE AS FAR AS POSSIBLE– GRID METHOD WHEN HIGH DISCONTINUITIES EXIST (CORE DEGRADATION)– RESPONSE SURFACES METHODOLOGY WITH « STATE » AND « UNCERTAIN »

UPSTREAM VARIABLES

•AN ADAPTED APPROACH TO EACH CASE

•EXPERT’S JUDGMENT USED FOR RESULTS INTERPRETATION AND FINAL APET MODEL CONSTRUCTION

•THE METHODOLOGY REQUIRES LARGE SENSITIVITIES STUDIES USEFUL FOR UNCERTAINTIES ANALYSIS

advanced modeling and response surface method ology for physical models of level 2 psa event tree

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physical phenomenon

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