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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.
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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
Cloud 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 Scheme 1000 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.
Uncertainty distributions of 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.
A 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.
5% 50% 95% 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 Coefficients Uncertainty 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
Accident 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
M weather sequences K parameters N runs Uncertainty Analysis Procedure Subjective 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)
Total : 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:
Sobol’ Sensitivity Indicesfor a Specific Weather Sequence Dry weather sequence Wet weather sequence
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.