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An Application to Nuclear Safety- UA/SA Using An Accident Consequence Assessment Code -

- T. Homma
- Japan Atomic Energy Research Institute
- SAMO2004 Venice, Sept 12 - 17, 2004

Safety Goal for Nuclear Installations

Level 3 PSA for a reference plant due to internal accidents

- The NSC of Japan issues the interim report on safety goal (2004)
- Individual early fatality risk: the expected (average) value for average individual early fatality risk near the site boundary due to nuclear accidents will be less than about 1×10-6 year-1
- Individual latent cancer fatality risk: the expected (average) value for average individual latent cancer fatality risk in the some region from site boundary due to nuclear accidents will be less than about 1×10-6 year-1

Average individual risk (reactor year -1)

Distance from the release point (km)

Two Types of Uncertainty

- Stochastic (aleatory) Uncertainty
- known as randomness or variability of the system under study
- variability in environmental conditions (e.g. weather condition)
- physical variability will not decrease
- Subjective (epistemic) Uncertainty
- results from the existing state of knowledge
- modeling uncertainty and input parameter value uncertainty
- as we gain more knowledge, uncertainty will decrease

Stochastic Uncertainty

Subjective uncertainty

The Problem Settings

- How do we deal with the stochastic uncertainty (weather conditions) in accident consequence assessments and how much is the statistical variability?
- How much of the overall uncertainty about individual risk is attributable to stochastic uncertainty and how much to parameter uncertainty?
- What are the main contributors to uncertainty in individual risk of early and latent cancer fatality?

OSCAAR Code System

CURRENT

- Off-Site Consequence Analysis of Atmospheric Releases of radionuclides

Meteoro-logicaldata

HEINPUT

PopulationAgriculturaldata

DOSDAC

Meteorologicalsampling

Healtheffect

MS

HE

Protectivemeasure

Earlyexposure

Sourceterm

Atmosphericdispersion

EARLY

PM

Deposition

Economicloss

ADD

Chronicexposure

ECONO

HINAN

CHRONIC

Atmospheric Dispersion and Deposition

- Multi-puff Trajectory Model
- Dry and wet deposition

Atmospheric release

Atmospheric dispersion

Inhalation

Dose to man

Contamination

Ground

Deposition

Resuspension

Foodstuff contamination

Ingestion

Dose Calculation Models- Total dose for a specific organ from different exposure pathways

Reduction factors (shielding and filtering factors)

Dose coefficients

Time-integrated concentration, contamination, intake

i: organ

j: pathway

Health (deterministic) Effects Model

Early and Continuing effects(Early mortality and morbidity)

- Hazard function (two-parameter Weibull function) approach
- Early fatal effects comprise haematopoietic, pulmonary, and gastrointestinal syndrome. Those depend on the level of medical treatment received
- Effectiveness of a specified dose for induction of early effects depends on dose rates.

Health (stochastic) Effects Model

Late Somatic Effects (Cancer mortality and morbidity)

- Linear or linear-quadratic dose-response model and DDREF
- For estimating the life-time risk in the population, the absolute or relative risk projection models are available
- Data of Hiroshima and Nagasaki
- Reassessment of the radiation dosimetry
- Life span study on atomic bomb survivors

Meteorological Sampling

- Aims of Meteorological Sampling
- Strong dependence of the magnitude of the consequences on the weather after an accident
- Huge computer resources using a full year of hourly data
- Select a representative sample of weather sequences which adequately produce the range of consequences
- Sampling Techniques
- Random sampling of the specified number of sequences
- Cyclic sampling (sequences are selected with a set time interval between them)
- but, these tend to sample the commonly occurring groups frequently, while overlooking more unusual sequences
- Stratified or bin sampling (sequences are grouped into a number of categories, which give rise to the similar consequences)

General Consideration for Met. Sampling

- Completeness
- The consequences calculated would reflect the full spectrum of the consequences related to the postulated accident under investigation.
- Consistency
- The parameters selected for classification of weather sequences and the sampling scheme itself should be seamlessly associated with the models, parameters and methods used in the code system.
- Stratification
- The sampling scheme could divide the entire set of meteorological sequences in such a way that the members in each single stratum or group would be very similar.
- Practicability
- A practicable number of samples should be predetermined according the models used in the consequence assessment code.
- Optical Allocation
- A fixed number of samples need to be optically allocated among the groups in order to “maximize” the precision of consequence assessment.

Sensitivities of Early Fatality to Meteorological Parameters

SPD0 : initial wind speed

STPi : travel time to i km

I.SPDi : Inverse of wind speed to i km

STABi:mean stability to i km

DURi : period of rain to i km

RAINi : total rainfall to i km

Classification of New Sampling Scheme

11 Groups x 9 (wind directions) = 99 Groups

144 Weather sequences

New stratified sampling scheme

Cyclic sampling scheme

Conditional Probability, ≧C

Conditional Probability, ≧C

Early Fatalities (normalized), C

Early Fatalities (normalized), C

Performance of New Sampling Scheme1000 sets of 144 sequences

8760 sequences

- The statistical variability of the probability distribution of the early health effect is not large and the performance of this scheme is better than other conventional schemes.
- The advantage of the stratified sampling scheme is to give the rare cases of catastrophic health effects when we use the same number of sequences.

Steps in UA/SA on Input Parameters

- Identify uncertain model parameters
- Assign upper and lower bounds, distribution, and correlation
- 1. PREP
- Perform parameter value sampling
- Simple random sampling
- Latin hypercube sampling
- Sobo\'l quasi-random sampling
- 2. Run OSCAAR with the Sampled Input Values
- 3. SPOP
- Estimate output distribution functions (UA)
- Examine relationships between input and output variables (SA)

Parameter Xk

Parameter X1

Parameter X2

Prediction Y

Expert Judgement Elicitation

Joint EC/USNRC project 「Uncertainty Analysis of Accident Consequence Models for Nuclear Power Plants 」(1993-1996).

- Objectives : to develop credible and traceable uncertainty distributions for the respective ACA code input parameters.
- Two important principles for the application of formal expert judgement elicitations:
- The elicitation questions would be based on the existing models used in their codes such as COSYMA and MACCS.(A library of information can be of use to other models and codes.)
- The experts would only be asked to assess physical quantities which could be hypothetically measured in experiments.

the code input parameter values

Information about 5%、50% and 95% quantiles on the uncertainty distribution from expert judgement

Parameter A

Expert A

Single joint distribution

Obtain

distributions on

code input

parameters

Combine

the uncertainty

distributions

Expert B

Parameter B

Parameter C

Expert C

Expert Judgement Elicitation (Cont.)- Uncertainty distributions for physically observable quantities were provided by experts at each expert panel formed for the following areas of codes: atmospheric dispersion, deposition, external doses, internal dosimetry, food-chains,early health effects and late health effects.
- Combine these uncertainty distributions into a single joint distribution and translate distributions over physically observable quantities into distributions on code input parameters.

kAB

kAC

B

C

Target Variables and Elicitation Variables- Case 1: code input parameters correspond to measurable quantities (e.g. deposition velocity)
- Case 2: some analytical functional dependence (e.g. dispersion parameter )
- Case 3: some numerical relationship(e.g. retention of material is modelled using a set of first-order differential equations with code input parameters)

kAB 、kAC ：transfer coefficient（target variable）

Yi、Zi ：retention of material in compartments, B and C（elicitation variable）

Case 2 and 3 need probabilistic inversion

Example for Dose Coefficient

- Metabolic model of Caesium

ST

- Quantile information from experts

Blood

SI

TBlood

0.1

0.9

ULI

Body

tissue A

Body

tissue B

TBodyA

TBodyB

LLI

Bladder

- In internal dosimetry panel, 8 experts were asked about the retention of

materials in the human body.

- Estimate the distributions of the biological half life TBlood，TBodyA and TBodyB

from the distributions of the retention of Cs-137 in Body tissue from a unit

intake by using probabilistic inversion technique.

ICRP

CDF

Biological half life TBlood (d)

5% 50% 95%

5% 50% 95%

ICRP

CDF

CDF

ICRP

Biological half life TBodyA (d)

Biological half life TBodyB (d)

Result of Probabilistic Inversion- Distributions of the target variables obtained from probabilistic inversion

- Comparison of distributions of elicitation variables

Rank correlation coefficients extracted from the distribution among target variables

+

CDF

1.0E-09

1.0E-07

5% 50% 95%

Effective dose coefficient (Sv/Bq)

Uncertainty Distribution of Dose CoefficientsUncertainty distributions of the biological half lives

DSYS

Calculate inhalation and ingestion

dose coefficients.

ICRP metabolic models

+

Dosimetry data

- Uncertainty on effective dose coefficient for Cs-137 from ingestion

OSCAAR Calculations

- Site Data
- A model plant is assumed to be located at a coastal site facing the Pacific Ocean.
- Population and agricultural production data from the 1990 census
- Source Term

Release start

Duration

Time before release

Sheltering zone (>10 mSv/w)

of release

3 h

Warning time

2 h

30 km

Sheltering

Time for

Duration

direction

24 h

1 h

10 km

Sheltering in concrete building

Evacuation

Time for

completion

Duration

Time for

Time for

Duration

direction

completion

Evacuation zone (>50 mSv/w)

2 h

2 h

1 h

1 h

168

h = 7 d

Relocation zone (>140 mSv/y)

OSCAAR Calculations (cont.)Countermeasures Strategy

Countermeasures Timing

K parameters

N runs

Uncertainty Analysis ProcedureSubjective Uncertainty

Stochastic Uncertainty

Average Individual Risk

- Individual risk as a function of distance : risk at x km, j th sector : population at x km, j th sector : probability of i th weather sequence

Example of CCDFs for Individual Risk

Cumulative distribution

Probability of exceeding X

99th percentile

Average individual risk of early fatality at 1 km, X

Average individual risk of early fatality at 1 km

Uncertainty of Average Individual Risk

(Expected Values due to weather variability)

Conditional probability of cancer fatality

Conditional probability of early fatality

Distance from the site (km)

Distance from the site (km)

Ratio of 95% to mean value

Contribution of Stochastic Uncertainty(weather scenario variance)

- Overall variance

beween-scenario

variance

within-scenario

variance

- Early fatality

- Latent cancer fatality

Sensitivity of Early Fatality

Number of early fatality

Average individual risk of early fatality

R2=0.81

PRCC

SRRC

Distance from the site (km)

Sensitivity of Latent Cancer Fatality

Number of cancer fatality

Average individual risk of cancer fatality

R2=0.73

SRRC

PRCC

Distance from the site (km)

First-order :

Sobol’ Sensitivity Indices- A model output can be decomposed into summands of different dimensions:
- the variance of can be decomposed as:
- Sensitivity measures can be introduced:

Summary

- The uncertainty factors (a ratio of 95% to mean )for the expected values is less than about four for both average individual risks of early and latent cancer fatality near the site boundary.
- The contribution of stochastic uncertainty to the overall uncertainty for average individual risk of fatality is only dominant close to the site boundary at about 20%, and that for average individual risk of cancer fatality is quite stable about less than 6% at all distances.
- When considering the computational costs, the correlation/regression measures are useful for understanding the sensitivity of the expectation value and some percentile of the CCDFs to the input parameters.
- For specific weather conditions, the Sobol’ method with total effect indices is effective in identifying the important input parameters.

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