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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 10 -5 (2004) Average individual risk (reactor year -1) 10 -6 Individual early fatality risk: the 10 -7 Safety Goal (draft)： -6 10 expected (average) value for average individual early fatality 10 -8 risk near the site boundary due 10 -9 to nuclear accidents will be less 10 -10 Cancer Fatality than about 1×10-6 year-1 10 -11 Early Fatality Individual latent cancer fatality 10 -12 risk: the expected (average) 10 -13 value for average individual 10 -14 latent cancer fatality risk in the 10 -15 some region from site boundary 0.1 1 10 100 due to nuclear accidents will be Distance from the release point (km) less than about 1×10-6 year-1 2 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 1.0E+00 1.0E+00 Conditional Probability >= X Conditional Probability >= X 1.0E-01 1.0E-01 1.0E-02 1.0E-02 mean 1.0E-03 1.0E-03 95% 5% 1.0E-04 1.0E-04 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 Number of Consequences, X Number of Consequences, X 3 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? 4 OSCAAR Code System Off-Site Consequence Analysis of Atmospheric Releases of radionuclides CURRENT Meteoro- logical HEINPUT data Population Meteorological DOSDAC Agricultural data Health sampling effect MS HE Early Protective Source Atmospheric exposure measure term dispersion EARLY PM Deposition Economic loss ADD Chronic ECONO exposure HINAN CHRONIC 5 Atmospheric Dispersion and Deposition Multi-puff Trajectory Model N N ri2 ( zi z 0 ) 2 (r, z, t ) (2 ) Qi (t ) ( x, y, z, t ) exp exp r2,i z ,i 2 r2,i 2 z ,i i 2/3 2 i 1 i 1 Dry and wet deposition Z d ( x, y ) vd X ( x, y ) X ( x, y, z )dz 0 6 Dose Calculation Models Total dose for a specific organ from different exposure pathways RF j : Reduction factors (shielding and filtering factors) Dtot ,i RFj DCi , j j DCi, j : Dose coefficients j j : Time-integrated concentration, contamination, i: organ intake j: pathway Cloud Atmospheri Atmospheric Inhalation Dose to man c release dispersion Contamination Deposition Ground Resuspension Foodstuff contamination Ingestion 7 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. r f m r m f s r s fi r i 1 Risk of Early Fatality 0.8 r 1 exp ( H H H ) m 1 m m 2 m 3 0.6 d minimal H ln 2 ) dt 0.4 supportive D50 (d 0.2 intensive D50 (d ) 1 / d 0 0 2 4 6 8 10 Dose（Gy） 8 Health (stochastic) Effects Model Late Somatic Effects (Cancer mortality and morbidity) Linear or linear-quadratic dose-response model and DDREF 1 R bD cD 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 Life time risk(/104 person-Gy) Effect Projection Latency Plateau OSCAAR NUREG ICRP60 Leukemia Absolute 2 39 59 49 50 Bone cancer Absolute 2 25 1.1 4.5 5 Breast cancer Relative 10 Life-time 31 54 20 Lung cancer Relative 10 Life-time 110 78 85 G.I. cancer Relative 10 Life-time 230 168 240 Thyroid cancer Absolute 5 Life-time 4.6 7.2 8 Skin cancer Absolute 10 Life-time 0.4 - 2 Other cancers Relative 10 Life-time 56 138 90 Total 490 499 500 9 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) 10 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. 11 Sensitivities of Early Fatality to Meteorological Parameters SPD0 : initial wind speed STABi:mean stability to i km STPi : travel time to i km DURi : period of rain to i km I.SPDi : Inverse of wind speed to i km RAINi : total rainfall to i km 12 Classification of New Sampling Scheme Wind direction 9 groups Wet Rain ＜ 5mm G1 (to 10km) Rain ≧ 5mm G2 Travel time (to 20km) Unstable Neutral Stable Dry (to 10km) ＜ 2.5 hr G3 G6 G9 2.5 - 5 hr G4 G7 G10 5 hr ≦ G5 G8 G11 11 Groups x 9 (wind directions) = 99 Groups 144 Weather sequences 13 Performance of New Sampling Scheme New stratified sampling scheme Cyclic sampling scheme 100 100 Conditional Probability, ≧C Conditional Probability, ≧C 10-1 10-1 1000 sets of 144 sequences -2 10 10-2 10-3 10-3 8760 sequences 10-4 10-4 10-3 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 102 Early Fatalities (normalized), C Early Fatalities (normalized), C 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. 14 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 パラメータ X ParameterX1 1 パラメータ X ParameterX2 2 パラメータ X ParameterXKk – Simple random sampling – Latin hypercube sampling – Sobo'l quasi-random sampling 2. Run OSCAAR with the Sampled Input Y f ( X 1 , X 2 , , X K ) Values 3. SPOP Estimate output distribution functions (UA) Examine relationships between input and output variables (SA) Prediction Y 予測値Y 15 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. 16 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. Information about 5%、50% and Uncertainty distributions of 95% quantiles on the uncertainty the code input parameter values distribution from expert judgement Parameter A Expert A Single joint distribution Obtain Combine distributions on Expert B the uncertainty Parameter B code input distributions parameters Expert C Parameter C 17 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 x yP )x ( y parameter ) yQ Case 3: some numerical relationship (e.g. retention of material is modelled using a set of first-order differential equations with code input parameters) A kAB 、kAC ：transfer coefficient（target variable） kAB kAC Yi、Zi ：retention of material in compartments, B and C （elicitation variable） B C Case 2 and 3 need probabilistic inversion 18 Example for Dose Coefficient Metabolic model of Caesium ST Quantile information from experts Blood Retention of Cs-137 in Body tissue from a SI unit intake 0.1 TBlood 0.9 5% 50% 95% 1 day 8.70E-01 9.62E-01 9.92E-01 ULI Body Body 1 week 7.45E-01 8.59E-01 9.43E-01 tissue A tissue B TBodyA TBodyB 1 month 5.45E-01 7.24E-01 8.93E-01 1 year 2.38E-03 6.48E-02 2.64E-01 LLI 5 years 1.21E-10 1.08E-05 6.30E-03 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. 19 Result of Probabilistic Inversion Distributions of the target variables obtained from probabilistic inversion 5% 5%値 50% 95%値 50%値 95% 1.0 累積確率 0.8 ● ICRP値：0.25 ICRP CDF 0.6 394 0.4 0.2 0.0 1.0E-05 1.0E-02 1.0E+01 1.0E+04 Biological half life TBlood (d) 5% 50% 95%値 5%値 50%値 95% 5% 50% 95%値 5%値 50%値 95% 1.0 Bloodの生物的半減期(d) 1.0 0.8 0.8 累積確率 累積確率 0.6 0.6 ICRP値：110 CDF ● CDF ICRP 0.4 1 8 .5 0.4 0.2 ICRP値：2.0 ICRP 0.2 6 .3 0.0 ● 0.0 1.0E-04 1.0E-01 1.0E+02 1.0E-01 1.0E+01 1.0E+03 1.0E+05 Body tissue Aの生物的半減期(d) Biological half life TBodyA (d) Biological half life TBodyB (d) Body tissue Bの生物的半減期(d) Comparison of distributions of elicitation variables Fraction of amount reaching blood retained in whole body 1 day 1 week 1 month 1 year 5 years DM Pred. DM Pred. DM Pred. DM Pred. DM Pred. 5% 8.70E-01 2.86E-01 7.45E-01 7.45E-01 5.45E-01 5.45E-01 2.38E-03 2.38E-03 1.21E-10 1.20E-10 50% 9.62E-01 9.62E-01 8.59E-01 9.26E-01 7.24E-01 7.24E-01 6.48E-02 2.56E-02 1.08E-05 3.18E-07 95% 9.92E-01 9.92E-01 9.43E-01 9.69E-01 8.93E-01 8.93E-01 2.64E-01 4.71E-01 6.30E-03 3.33E-02 20 Uncertainty Distribution of Dose Coefficients Uncertainty distributions of the biological half lives 1 1 1 Rank correlation coefficients 0.5 0.5 0.5 + extracted from the distribution 0 0 0 among target variables 1.0E-01 1.0E+02 1.0E+05 1.0E-05 1.0E-01 1.0E+03 1.0E-04 1.0E-01 1.0E+02 Calculate inhalation and ingestion ICRP metabolic models dose coefficients. DSYS + Dosimetry data Uncertainty on effective dose coefficient for Cs-137 from ingestion 1.0 0.8 ICRP ：1.3E-8 累積確率 0.6 ● CDF 0.4 7.3 0.2 0.0 4 .0 E- 0 9 1 .2 E- 0 8 2 .9 E- 0 8 1.0E-09 1.0E-09 1.0E-07 1.0E-07 5%値 50%値 95%値 5% 50% Cs-137の経口摂取による一般公衆成人の 95% 実効線量係数(Sv/Bq) Effective dose coefficient (Sv/Bq) 21 Input Parameters Variable Meaning 5% 95% 95%/5% Atmospheric dispersion and deposition: 19 parameters VG Deposition velocity for particulates (m/s) 2.2×10-5 1.3×10-2 570 RA Washout coefficients (hr/mm/s) 5.1×10-3 4.8 941 PY_D Horizontal dispersion coefficient Py for stability D 0.17 0.36 2.2 QY_D Horizontal dispersion coefficient Qy for stability D 0.77 1.03 1.3 PZ_D Vertical dispersion coefficient Pz for stability D 0.23 3.06 13 QZ_D Vertical dispersion coefficient Qz for stability D 0.31 0.87 2.8 Dose model: 33 parameters BRATES Breathing rate (m3/s) 1.5×10-3 3.2×10-3 2.3 FFI1 Filtering factor for wood building (-) 0.037 0.96 26 FFI2 Filtering factor for concrete building (-) 0.015 0.39 26 INH_CS Inhalation effective dose coefficient (Sv/Bq) 4.0×10-9 2.7×10-8 6.8 Health effects model: 13 parameters LD50_PULM LD50 for pulmonary syndrome (Gy) 7.68 156 20 BETA_PULM Shape factor for pulmonary syndrome (-) 5.44 10.1 1.9 L_LUNG Life-time risk for lung cancer (104 person-Gy) 0.00020 453 2.3×106 L_OTHERS Life-time risk for other cancer (104 person-Gy) 0.0011 947 8.6×105 22 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 Item Value Time before release 3.0 h Duration of release 1.0 h Warning time 2.0 h Release height 40 m Energy content of release 0 MW Reference inventory 1100 MW(e) Chemical Xe-Kr Organic-I I Cs-Rb Te-Sb Ba-Sr, Ru La Group Release 0.56 0.004 0.07 0.01 0.03 0.01 0.01 Fraction 23 OSCAAR Calculations (cont.) Countermeasures Strategy Countermeasures Timing Accident Release start Sheltering zone (>10 mSv/w) Duration Time before release 3h of release Warning time 30 km 2h Sheltering 10 km Time for Duration direction 24 h 1h Evacuation zone (>50 mSv/w) Sheltering in concrete building Evacuation Time for Time for Duration Time for Duration direction completion completion 1h 1h 2h 2h 168 h = 7 d Relocation zone (>140 mSv/y) 24 Uncertainty Analysis Procedure Subjective Uncertainty Stochastic Uncertainty M weather sequences K parameters p1 p2 pM pi Y1i X 11 X 12 X 1K Y11 Y12 Y1M i X 21 X 22 X 2K Y21 Y22 Y2 M pi Y2i i N runs X Y X X NK Y YNM N1 X N2 N 1 YN 2 pi YNi i Average Individual Risk Individual risk as a function of distance ri , j ( x ) : risk at x km, j th sector P ( x) r ( x) j i, j R( x) p ( j ) P ( x) i Pj (x ) : population at x km, j th sector i j pi : probability of i th weather sequence j 25 Example of CCDFs for Individual Risk 100 1 0.9 M EA N 0.8 Conditionalof exceeding >=X 99% 10-1 Probability probability, X Cumulative distribution 0.7 0.6 10-2 0.5 99th percentile 0.4 0.3 -3 10 0.2 0.1 0 10-4 10-5 10-4 10-3 10-2 10-1 100 10-4 10-3 10-2 10-1 100 Individual risk of early fatality, X Average individual risk of early fatality at 1 km, X Average individual risk of early fatality at 1 km 26 Uncertainty of Average Individual Risk (Expected Values due to weather variability) Conditional probability of early fatality Conditional probability of cancer fatality 1E 0 1E 0 95% 5% 1E-1 75% 25% 1E-2 Central Es tim ates 1E-1 1E-3 1E-2 1E-4 1E-5 95% 1E-3 5% 1E-6 75% 25% Central Estimates 1E-7 0 5 10 1E-4 0 5 10 15 20 25 30 Distance from the site (km) Distance from the site (km) Ratio of 95% to mean value x (km) 0.5 1.5 2.5 3.5 4.5 5.5 7 9 12.5 17.5 22.5 Early Fatality 2.3 3.1 4.0 5.5 8.6 5.7 12.2 10.5 - - - Cancer Fatality 4.0 3.2 3.3 3.2 2.9 2.6 3.0 3.3 3.1 3.6 3.1 27 Contribution of Stochastic Uncertainty (weather scenario variance) Overall variance M M V ( y ) VS [ E ( y | S )] ES [V ( y | S )] pi ( i ) pi i2 ˆ ˆ ˆ ˆ ˆ 2 ˆ i 1 i 1 M beween-scenario variance within-scenario variance E ( y ) ES [ E ( y | S )] pi i ˆ ˆ ˆ ˆ i 1 Early fatality 0.5km 1.5km 2.5km 3.5km 4.5km 5.5km overall mean individual risk 1.02E-02 5.90E-03 1.68E-03 6.09E-04 3.12E-04 2.77E-04 overall variance V(y) 1.06E-03 7.16E-04 1.91E-04 6.52E-05 4.01E-05 2.90E-05 Vs[E(y|S)] 2.56E-04 1.46E-04 2.26E-05 5.18E-06 2.26E-06 2.02E-06 Es[V(y|S)] 8.09E-04 5.70E-04 1.68E-04 6.00E-05 3.79E-05 2.70E-05 % of variance between scenarios 24.0 20.4 11.8 8.0 5.6 6.9 Latent cancer fatality 0.5km 1.5km 2.5km 3.5km 4.5km 5.5km overall mean individual risk 7.92E-02 1.12E-01 8.99E-02 6.84E-02 5.05E-02 4.99E-02 overall variance V(y) 2.65E-01 3.98E-01 5.83E-01 4.00E-01 1.12E-01 1.06E-01 Vs[E(y|S)] 1.30E-02 2.31E-02 2.50E-02 1.47E-02 6.25E-03 5.12E-03 Es[V(y|S)] 2.52E-01 3.75E-01 5.58E-01 3.86E-01 1.06E-01 1.01E-01 % of variance between scenarios 4.9 5.8 4.3 3.7 5.6 4.8 28 Sensitivity of Early Fatality Number of early fatality Average individual risk of early fatality 1 1 R2=0.81 5 0. R -square 5 0. VG PRCC Q Y_D SRRC 0 B R A TES 0 FFI 2 LD 50_P U L B ETA _P U L 5 -0. 5 -0. -1 -1 0 5 10 Distance from the site (km) 29 Sensitivity of Latent Cancer Fatality Number of cancer fatality Average individual risk of cancer fatality 1 1 R2=0.73 0. 5 R -square 5 0. VG Q Z_D FFI 1 SRRC PRCC 0 FFI 2 0 L_LU N G N I H _C S 5 -0. 5 -0. -1 -1 0 5 10 15 20 25 Distance from the site (km) 30 Sobol’ Sensitivity Indices – A model output f ( x) f ( x1 ,, xn ) can be decomposed into summands of different dimensions: n f ( x1 , , xn ) f 0 f i ( xi ) f ij ( xi , x j ) f12n ( x1 , , xi , x j , , xn ) i 1 1i j n – the variance D of f (x) can be decomposed as: n D Di D ij D12n s i 1 1 i j n – Sensitivity measures S i1 ,,is can be introduced: Di1 ,,is S i1 ,,is D Dj Di Di ,ci D Dci D First-order : S j Total : ST 1 ci D i D D D 31 Sobol’ Sensitivity Indices for a Specific Weather Sequence Dry weather sequence Wet weather sequence S1 FSIGY FFI2 BR S1 FSIGY WCA SFG2 ST FSIGY FFI2 BR ST FSIGY WCA SFG2 1 1 0.8 8 0. Sensi vi i ces Sensitivity indices ti ty ndi 0.6 6 0. 0.4 4 0. 0.2 2 0. 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Distance from the site (km) stance f Di te km rom the si ( ) 32 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. 33