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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 - PowerPoint PPT Presentation
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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
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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.
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Schema of a physical model
Upstream uncertain variables
Upstreamstatevariables
Physical model
RVk = F (SVi , UVj) DownstreamResultsVariables
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Upstreamuncertainvariables
Upstreamstatevariables
Physical model
RVk = F (SVi , UVj) DownstreamResultsVariables
Upstreamuncertainvariables
Upstreamstatevariables
Physical model
RVk = F (SVi , UVj) DownstreamResultsVariables
« 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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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)
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 1Direct Containment Heating –
STEP 1 Upstream uncertain variables
Upstreamstatevariables
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 1Direct Containment Heating –
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(%)
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 1Direct Containment Heating –
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 1Direct Containment Heating –
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)
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 2Ex-vessel steam explosion model
MC3D code : pre-mixing of corium and waterexplosion
EUROPLEXUS : damage on the structures
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 2Ex-vessel steam explosion model
– 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
Upstreamstatevariables
Upstreamuncertainvariables
Containment failure probability
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 2Ex-vessel steam explosion model
– 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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
modelA 3D local model for equipment hatch ; boundary conditions of this local model come from the 3D 90°model
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
modelOne reference severe accident loading is used (with sensitivity
case)
H2 burning
Melt-corium interaction (MCCI)
Safety injection failure
SCRAM
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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Example 3Containment thermo-mechanical
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
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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