Transcript ADVANCED MODELING AND RESPONSE SURFACE METHODOLOGY FOR PHYSICAL MODELS OF LEVEL 2 PSA EVENT TREE CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT.

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
1
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
2
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
3
The physical models
of the Accident Progression Event Tree
Before Core
degradation
Vessel
Rupture
During Core
degradation
I- SGTR
Level 1 PSA
Plant Damage State
Before core
degradation
During Core
Degradationn
Corium-Concrete
Interaction
In-vessel
steam
explosion
Combustion
Advanced
core
degradatio
Ex-vessel
s.e.
Combustion
H2
Corium
concrete
interaction
Direct
Containt
Heating
Containment mechanical behavior
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
4
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
5
Schema of a physical model
Upstream
uncertain
variables
Physical model
Upstream
state
variables
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
RVk = F (SVi , UVj)
Downstream
Results
Variables
6
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
7
Construction of a « physical model »
« SOPHISTICATED
SEVERE ACCIDENT
CODE »
CALCULATIONS
APET
Requirements
3 STEPS
• Choice and hierarchy of
upstream variables
Upstream
uncertain
variables
Physical model
Upstream
state
variables
RVk = F (SVi , UVj)
Downstream
Results
Variables
Experimental design
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
• Elaboration of a response surface
for each downstream variables
• Validation of the response surface
accuracy
8
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
9
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
10
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
11
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
12
Example 1
Direct Containment Heating
Enceinte
« sophisticated code »
RUPUICUV
CPA
Corium + Vapeur
d’eau +
H2
Espace Annulaire
(ASTEC system)
Puits de cuve
Compartiment
Intermédiaire
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
13
Example 1
Direct Containment Heating – STEP 1
Upstream
uncertain
variables
Upstream
state
variables
•Vessel pressure
•Mass of melt-corium
•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
DCH model
RVk = F (SVi , UVj)
•Mass of dispersed corium
•Pressure peak in
containment
Downstream
Results
Variables
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
14
Example 1
Direct 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
Statistical distribution of the residues (KAERI Experimental value - Correlation value) for the fraction of
dispersed corium mass - Total number of observations : 49
16
14
Number of Observations
12
10
8
6
4
2
0
-20
-15
-10
-5
0
5
10
15
20
Mean value= -1,4 (%), Standard-Deviation=
6,4 (%), Max.=+15,2 (%), Min.=-13,1(%)
Diff
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
15
Example 1
Direct Containment Heating – STEP 2
After statistical correction all over the pressure variation domain
Mean = 0 ; Standard-deviation = 0,144 bar
0,6
40
35
0,4
30
0,2
Number of Observations
Residue (bar) = Fitted Pressure Peak - Pressure Peak estimated
with RUPUICUV/CPA
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)
0,0
-0,2
-0,4
25
20
15
10
-0,6
5
-0,8
2
3
4
5
6
7
8
9
Fitted Pressure Peak (bar)
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
10
0
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
Statistical Residue for high Pressure Peaks (>5 bars)
16
0,4
0,5
Example 1
Direct 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.
Ecart in calculated containment pressure (bar)
0,250
0,200
0,150
0,100
0,050
0
10
20
30
40
50
60
70
80
90
-0,050
-0,100
-0,150
-0,200
-0,250
-0,300
Vessel Pressure (bar)
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
17
Example 2
Ex-vessel steam explosion model
Water can be present in the vessel pit after use of spraying system (CHRS)
Consequences of Corium-Water Interaction ?
Vessel
Containment wall
2d Floor
Wall
1st Floor
Vessel Pit
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
18
Example 2
Ex-vessel steam explosion model
MC3D code :
EUROPLEXUS :
pre-mixing of corium and water
explosion
damage on the structures
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
19
Example 2
Ex-vessel steam explosion model –
STEP 1
Upstream
uncertain
variables
Water height
Water temperature
Best-estimated
Parameters
Vessel
Pressure
Pre-mixing
Corium
overheat
Vessel
breach
diameter
N Steam
Explosion
Runs
Containment
failure
probability
N calculations of
structure
displacement
Results if no
steam explosion
Upstream
state
variables
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
20
Example 2
Ex-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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
21
Example 3
Containment 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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
22
Example 3
Containment 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
Concrete
Passive steel
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
Prestressed tendons
23
Example 3
Containment 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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
24
Example 3
Containment thermo-mechanical model
A 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
25
Example 3
Containment thermo-mechanical model
One reference severe accident loading is used (with sensitivity case)
H2 burning
Safety injection failure
Melt-corium interaction (MCCI)
SCRAM
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
26
Example 3
Containment 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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
27
Example 3
Containment 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
Pressure Peak in
containment
Containment model
Containment leakage size
Uncertainties are discussed in the frame work of an expert’s group
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
28
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
CSNI/WG-RISK – LEVEL 2 PSA AND ACCIDENT MANAGEMENT WORKSHOP – MARCH 2004
29