HLW. Vol.9 No.2 [2,3] aleatory uncertainty 10. ignorance epistemic uncertainty. variability. variability ignorance. Keywords:

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1 Vol.9 No.2 HLW 1 varablty2 gnorance varablty gnorance Keywords: Safety assessment for geologcal dsposal of hgh level radoactve waste nevtably nvolves factors that cannot be specfed n a determnstc manner. These are namely: () varablty that arses from stochastc nature of the processes and features consdered, e.g., dstrbuton of canster corroson tmes and spatal heterogenety of a host geologcal formaton; () gnorance due to ncomplete or mprecse knowledge of the processes and condtons expected n the future, e.g., uncertanty n the estmaton of solubltes and sorpton coeffcents for mportant nucldes. In many cases, a decson n assessment, e.g., selecton among model optons or determnaton of a parameter value, s subjected to both varablty and gnorance n a combned form. It s clearly mportant to evaluate both nfluences of varablty and gnorance on the result of a safety assessment n a consstent manner. We developed a unfed methodology to handle varablty and gnorance by usng probablstc and possblstc technques respectvely. The methodology has been appled to safety assessment of geologcal dsposal of hgh level radoactve waste. Uncertantes assocated wth scenaros, models and parameters were defned n terms of fuzzy membershp functons derved through a seres of ntervews to the experts whle varablty was formulated by means of probablty densty functons (pdfs) based on avalable data set. The exercse demonstrated applcablty of the new methodology and, n partcular, ts advantage n quantfyng uncertantes based on expert s opnon and n provdng nformaton on dependence of assessment result on the level of conservatsm. In addton, t was also shown that senstvty analyss could dentfy key parameters n reducng uncertantes assocated wth the overall assessment. The above nformaton can be used to support the judgment process and gude the process of dsposal system development n optmzaton of protecton aganst potental exposure. Keywords: [1] [2,3] 12 6 () 1 varablty aleatory uncertanty 10 () 2 2 gnorance epstemc uncertanty Applcaton of Intellgence Based Uncertanty Analyss for HLW Dsposal, by: Kazuyuk Kato (Kato.Kazuyuk@tepco.co.jp) R&D Center, Tokyo Electrc Power Company

2 March 2003 () 2 PSA 2 [3] [4] 1 [5] 2 [3] 1 2 Boundng Analyss 2 / FANTASY Fuzzy ANd probablstc Transport Analyss SYstem FANTASY What f FANTASY PSA MENTOR[6] MENTOR PSA 1 Laplace PSA 2 () MENTOR 2 [1] () EC MUNVAR [3] BIOMASS AMBER MENTOR 158

3 Vol.9 No.2 HLW 500m 100m 1000m ph TBM 0.1m 0.19m V1 80% 20% 0.4m 0.05m Fg.1 Se-79 Cs-135 Cs-137 Np-237 U Th-229 HAZOP(Hazard & Operablty Study) Na K 2 Table Unfed functon Expert A Expert B Table 1 Defnton of fuzzy membershp Plausblty 1.0 Must be consdered 0.5 Should be consdered 0.1 Could be consdered 0 Need not be consdered 0 1.E E E E E+0.4 Kd for a certan Nuclde Fg.1 Example of fuzzy membershp functon 159

4 March 2003 Input Parameter 1 Input Parameter 2 Output Input Parameter 3 Input Parameter 4 Np,U,Th,Se Np,U,Th 5 2 Mn-Max Sample n values for Type 1 uncertan parameters from pdf s defned by fuzzy mean and varance already sampled FANTASY y y ( y y + ) µ δ x = { [ ( )]} n δ 2 ; 2 = Max Mn µ x j, j = 1,2,..., { x }, (1) j y δy ( x, x x ) y 2 f ( x ) δ y ,..., n x ( ) y = f x x x Fg.2 Nested Fg.2 Nested ntervals n fuzzy arthmetc set Nested nterval Np,U,Th,Se,Cs Np,U,Th Se,Cs [7] 1 2 Np,U,Th,Se Fg.3 Cs Np,U,Th,Se,Cs MENTOR Sample N values from fuzzy membershp ntervals for Type 2 uncertan parameters Nuclde Transport Calculaton Evaluate expectaton value of the annual dose rate for Type 1 uncertan parameters Estmate fuzzy membershp of the expected value of the annual dose rate by applyng Mn-Max rule Fg.3 Dual samplng scheme of hybrd probablstc and possblstc safety assessment 160

5 Vol.9 No.2 HLW Determnstc Method Conservatve Determnstc Method Realstc FAR- RDOSE - TIME- TOTAL Dose Rate Log Sv/y DOSE - Rver HSv yl Tme Log TmeHyL Log Years Rver Water, Travelng length 100m Fg.4 Example of safety assessment consderng the degree of belef Fg Fg.4 Fg.4 Boundng (1) K k k<<k (2) K/k (3) j j s j 161

6 March 2003 Research of Alternatve methodologes Classfcaton of uncertantes Approprate Methodology (Unfy Fuzzy and Probablstc Approach) Quanttatve evaluaton of uncertantes n outputs Senstvty analyss to dentfy key parameters Develop FANTSY code Defne membershp functons and pdf s for uncertan parameters through ntervews wth the experts Samplng and Calculaton Results and Dscusson Evaluate applcablty of methodology to safety assessment Identfy ssues to be resolved n subsequent phase of development Fg.5 Flow chart of study j s j µ µ = σ 1 1 σ k = σ k K k (2) (3) s j Fg.6 90 k Table 2 Se LOG Np Solublty at =0.1 B_SOL_Np MemberShp 0.1 LOG Overpack contanment tme at =0.1 OP_CONT_TIME MemberShp LOG Dose Np237 (a) Senstve LOG Dose Np237 (b) Not senstve Fg.6 Example of senstvty nformaton derved usng Movng Band technque; (a) Senstvty of Np solublty n buffer pore water on the dose rate of Np, (b) Senstvty of canster corroson tme on the dose rate of Np 162

7 Vol.9 No.2 HLW Table 2 Summary of senstvty analyses FP M S µ M S = (4) σ S n-1 t Table 2 n n Γ 2 ξ 2 P ( S ) 2 = d ξ n 1 + n S 1 π n 1 ( 1) Γ 2 S P(S) P(S) S 1 P(S) Fg.7 1 P(S) Fg (5)

8 March 2003 Glass dssoluton tme Hydraulc conductvty of buffer Hydraulc conductvty Log-mean n rock Log-standard devaton Porosty of rock Hydraulc gradent Np Kd n rock U Kd n rock Th Kd n rock Se Kd n rock Flow rate n EDZ Dsperson length Relable perod of dose converson factor Dose converson factor of Se (Present) Dose converson factor of Se (Future) Dose converson factor of Cs (Present) Dose converson factor of Th (Present) Dose converson factor of U (Present) Dose converson factor of Np (Present) Dose converson factor of I (Future) Dose converson factor of Cs (Future) Dose converson factor of Th (Future) Dose converson factor of U (Future) Dose converson factor of Np (Future) Ion concentraton of Na and Ca Equlbrum constant of on exchange 1 / P(S) Fg.7 Evaluaton example of combned effect of parameters ( 0.1, part of results s extracted) 1 2 ICRP Pub.81[8] Potental exposure Constraned optmzaton 164

9 Vol.9 No.2 HLW ICRP abstracton [1] JNC TN , (1999) Bound [2] OECD/NEA: Uncertanty Analyss for Performance Assessments of Radoactve Waste Dsposal Systems, Proceedngs of an NEA Workshop (1987) [8] [3] European Commsson: Robnson, P.C. and N.S.ed Revew Dsaggregated approach PSA on development of methodologes for modellng wth uncertanty and varablty: Munvar project, EUR16174EN (1995) [4] Bardossy, A., Bogard, I., and Kelly, W.E.: Imprecse (Fuzzy) Informaton n Geostatstcs, Mathematcal Geology, 20, (1988) [5] Chles J-P., and Delfner, P.: Geostatstcs; Modelng Spatal Uncertanty, John Wley and Sons, New York (1999) [6] Maul, P.R., Cooper, N.S., and Robnson, P.C.: MENTOR Verson 2.1: A Computer Code for Assessng Dsposal Optons for TRU Wastes, Intera Informaton Technologes Techncal Note IS Verson 2 (1994) [7] Kato, K., et al.: Hybrd Probablstc and Possblstc Safety Assessment: Methodology and Applcaton, The 8th Internatonal Conference on Radoactve Waste Management and Envronmental Remedaton (ICEM 01), September 30 October 4, Sesson 47-3, Bruges, Belgum (2001) [8] ICRP: Radaton Protecton Recommendatons as Appled to the Dsposal of Long-lved Sold Radoactve Waste, ICRP Publcaton 81, Pergamon Press, Oxford, UK (2000) 165

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