Advanced modeling and response surface method ology for physical models of level 2 psa event tree
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ADVANCED MODELING AND RESPONSE SURFACE METHOD OLOGY FOR PHYSICAL MODELS OF LEVEL 2 PSA EVENT TREE. Plan. The physical models of the APET Principle of the method Construction of a “physical model” Comments Example of Direct Containment Heating Model

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Advanced modeling and response surface method ology for physical models of level 2 psa event tree
ADVANCED MODELING AND RESPONSE SURFACE METHODOLOGY FOR PHYSICAL MODELS OF LEVEL 2 PSA EVENT TREE


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


Introduction
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


The physical models of the accident progression event tree

Before Core degradation

Vessel Rupture

During Core degradation

Corium-Concrete Interaction

I- SGTR

In-vessel steam explosion

Combustion

Before core degradation

Advanced core degradatio

Level 1 PSA

Plant Damage State

During Core Degradationn

Ex-vessel

s.e.

Corium concrete interaction

Combustion

H2

Direct Containt

Heating

Containment mechanical behavior

The physical models of the Accident Progression Event Tree


Principles for construction of physical models
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


Schema of a physical model

Physical model

RVk = F (SVi , UVj)

Upstream

state

variables

Downstream

Results

Variables

Schema of a physical model


Definitions
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


Construction of a « physical model »

« SOPHISTICATED SEVERE ACCIDENT CODE » CALCULATIONS

APET Requirements

  • 3 STEPS

    • Choice and hierarchy of upstream variables

    • Elaboration of a response surface for each downstream variables

    • Validation of the response surface accuracy

Experimental design


Construction of a physical model
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


Construction of a physical model1
Construction of a “physical model”

  • 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


Construction of a physical model2
Construction of a “physical model”

  • 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


Comment
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


Example 1 direct containment heating

Enceinte

Corium + Vapeur d’eau + H2

Espace Annulaire

Puits de cuve

Compartiment

Intermédiaire

Example 1Direct Containment Heating

« sophisticated code »

RUPUICUV

CPA

(ASTEC system)


Example 1 direct containment heating step 1
Example 1Direct Containment Heating – STEP 1

  • Upstream

  • uncertain

  • variables

  • 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

Upstream

state

variables

DCH model

RVk = F (SVi , UVj)

  • Mass of dispersed corium

  • Pressure peak in containment

  • Vessel pressure

  • Mass of melt-corium

Downstream

Results

Variables


Example 1 direct containment heating step 2
Example 1Direct Containment Heating – STEP 2

  • Dispersed corium mass in function of upstream variables :

    • Correlation derived from experiments (KAERI)

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


Example 1 direct containment heating step 21
Example 1Direct Containment Heating – STEP 2

  • Pressure 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)


Example 1 direct containment heating step 3
Example 1Direct Containment Heating – STEP 3

  • Final 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.


Example 2 ex vessel steam explosion model

Vessel

Containment wall

2d Floor

1st Floor

Wall

Vessel Pit

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 ?


Example 2 ex vessel steam explosion model1
Example 2Ex-vessel steam explosion model

  • MC3D code : pre-mixing of corium and water

  • explosion

  • EUROPLEXUS : damage on the structures


Example 2 ex vessel steam explosion model step 1
Example 2Ex-vessel steam explosion model – STEP 1

Upstream

uncertain

variables

Water height

Water temperature

Best-estimated Parameters

Vessel Pressure

Corium overheat

Vessel breach diameter

Containment failure probability

N calculations of structure displacement

Pre-mixing

N Steam Explosion Runs

Results if no steam explosion

Upstream

state

variables


Example 2 ex vessel steam explosion model step 2
Example 2Ex-vessel steam explosion model – STEP 2

  • The 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


Example 3 containment thermo mechanical model
Example 3Containment thermo-mechanical model

  • The 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


Example 3 containment thermo mechanical model1
Example 3Containment thermo-mechanical model

  • A 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

Prestressed tendons

Passive steel

Concrete


Example 3 containment thermo mechanical model2
Example 3Containment thermo-mechanical model

  • A 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


Example 3 containment thermo mechanical model3
Example 3Containment thermo-mechanical model

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


Example 3 containment thermo mechanical model4
Example 3Containment thermo-mechanical model

  • One reference severe accident loading is used (with sensitivity case)

H2 burning

Safety injection failure

Melt-corium interaction (MCCI)

SCRAM


Example 3 containment thermo mechanical model5
Example 3Containment thermo-mechanical model

  • Analysis 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


Example 3 containment thermo mechanical model6
Example 3Containment thermo-mechanical model

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

A parameter to take into account uncertainties on leakage size calculation

Containment model

Pressure Peak in containment

Containment leakage size

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


Conclusion
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 METHODOLOGYWITH « 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 STUDIESUSEFUL FOR UNCERTAINTIES ANALYSIS


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