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Progress in Nuclear Energy 51 (2009) 649–657

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Progress in Nuclear Energy

journal homepage: www.elsevier .com/locate/pnucene

Availability of a probabilistic cost estimation for the price effect of Cu powderand bentonite on an HLW disposal cost in Korea

S.K. Kim a,*, M.S. Lee a, H.J. Choi a, J.W. Choi a, Shripad T. Revankar b

a Korea Atomic Energy Research Institute, 1045 Daedeokdaero, Yuseung-gu, Daejon 305-353, Republic of Koreab School of Nuclear Engineering, Purdue University, 400 Central Drive West Lafayette, IN 47907, USA

Keywords:Probabilistic estimationSpent fuelRepositoryCost driverCu powderBentonite

* Corresponding author. Tel.: þ82 42 868 8892; faxE-mail address: sgkim1@kaeri.re.kr (S.K. Kim).

0149-1970/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.pnucene.2009.01.005

a b s t r a c t

This study aims to demonstrate the availability of a probabilistic cost estimation related to the priceeffects of Cu powder and bentonite. From a sensitivity analysis of those materials’ prices on the overalldisposal costs, it was found that Cu powder was a more dominant cost driver than that of bentoniteamong the material costs to dispose of 52,000 tU of spent fuels by the deterministic cost estimationmethod even though the used volume of Cu powder will be smaller than that of bentonite, whereasthose conclusions can be changed by a probabilistic cost estimation method. Namely, its conclusiondepends on a decision maker’s personal opinion because of the resultant uncertainties. The disposal costincludes too many uncertainties due to the long construction and operational durations of a repository.Therefore a probabilistic cost estimation can be useful to provide the information related to anuncertainty.

� 2009 Elsevier Ltd. All rights reserved.

1. Background

Korea launched a long-term R&D program for high level waste(HLW) disposal technology development in 1997. In 2005, a pre-conceptual design of a Korean reference HLW disposal system(KRS-1) was established. But no site for the underground repositoryhas been specified in Korea, thus a generic site with granitic rock isconsidered as a reference HLW repository development. The spentfuel generated from a nuclear power plant will be disposed of indeep granite rock. According to a conceptual design of the KRS-1repository, the construction duration of the repository will be over80 years to dispose of 36,000 tU of spent fuels (Kukkola and TimoSaanio, 2003). In the present study the KRS-1 repository isconsidered for disposal of spent fuel for durations longer than80 years because of the life-time extension of nuclear powerplants. An increase in disposal volume from 36,000 to 52,000 tU isconsidered in the present analysis.

From the KRS-1 conceptual design for a repository, it was foundthat the dominant demands for materials are for Cu powder andbentonite. The price of Cu powder, in particular, which is used tocoat the surface of canisters based on the Korean reference disposalsystem, will increase in the future. Also, the price of bentonite willbe greatly increased due to the modernization of developing

: þ82 42 868 8198.

All rights reserved.

countries. We wanted to establish which material will be a signifi-cant driver for disposal costs in Korea. A bentonite block will beused to buffer the surrounding of the canister in the disposal holes.Thus the price of bentonite can potentially be one of the mostuncertain cost drivers. Also the price of Cu power which is used tocoat the surface of canisters as a corrosion-resistance material isvery uncertain due to an exhaustion of natural resources.

To the estimator, contingency is an amount used in the estimateto deal with the uncertainties inherent in the estimating process(AACE, 2004). In order to assess these uncertainties, a probabilisticcost estimation does not use a deterministic input value, so we haveto obtain information related to an uncertainty represented bya probability distribution. To establish a probability distribution ofthe used input variables, the Monte Carlo or Latin Hyper Cubemethod can be used (Kindinger, 2000).

By using the input value of a probabilistic distribution, theresults of a cost estimation can also be represented by a probabi-listic distribution, so we can elicit the cost estimation results undera certain confidence level. This information can provide a betterunderstanding and insights for an uncertainty. However, whenexpert judgement is applied in deciding the type of distribution,we have to be cautious in our interpretation of the cost estimationresults because of an uncertainty.

Under an uncertainty, a decision-making method should bebased on a probability theory of statistics, but a disposal cost hasso far been calculated with a cost estimation by a deterministicestimation method not by a probabilistic estimation method.

Table 1Total amount of spent fuel in Korea.

Spent fuels Amount (MtU) Assemblies Bundles Canisters

PWR 29500 68500 17125CANDU 22500 1185000 3990Total 52000 21115

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657650

Therefore, in this study, a probabilistic cost estimation method wasused to provide more correct and reliable cost estimation results.Generally a probabilistic cost estimation method is more suitablethan a deterministic estimation method as a technique to estimatethe costs for an HLW repository because of uncertainties in theestimation process. Making good use of this probabilistic methodfor a dominant cost driver provides an efficient cost estimation thatis based on accuracy and authoritativeness.

2. Cost estimation terms

The disposal costs are largely divided into investment costs,operational costs and closure costs. Different costs are calculatedwith different methods by taking into account that the items aredesigned at different levels (Horngren et al., 1994). For example,backfilling technique and materials are not yet defined at theoutset, and so their costs can not be calculated in detail. But theuncertainties and contingencies for unspecified costs should becalculated for the disposal costs because the accuracy of an esti-mation depends on these uncertainties.

We considered a representative cost driver related to anuncertainty such as the price of materials, an owner’s costs anda rock uncertainty. Owner’s costs are included in the constructioncosts. These costs contain developing costs, design costs, projectcosts and license costs. These costs are assumed to be 15% of theconstruction costs. It is assumed that about 5.5% more disposaltunnels are needed. This is because not all the disposal holes can be

Fig. 1. The disposal tunnels for the CANDU an

bored at the assumed locations because of unsuitable geologicalconditions. In addition, the real volume of the disposal tunnels andpanel tunnels is estimated to be 8% larger because of an overexcavation.

Each disposal hole has 21.65 m3 bentonite blocks with a densityof 2 ton/m3 that creates 43.29 ton per disposal hole. The price ofbentonite is 150 EUR/ton and the bentonite block compaction costsare estimated to be 200 EUR/ton, totalling 350 EUR/ton (Saanioet al., 2004).

2.1. Amount of waste

As shown in Table 1, the total amount of spent fuel is52,000 MtU resulting from both CANDU and PWR reactors. Thiscorresponds to a total of 21,115 canisters containing spent fuel.

2.2. The conceptual design of a repository

Fig. 1 shows details of the repository disposal tunnels andcanister placement locations for both PWR and CANDU spent fuels.The distance between the PWR canisters is 6 m and for the CANDUcanisters the distance between canister is 4 m. A total of 390disposal tunnels were constructed for the PWR canisters and 60for the CANDU canisters . Table 2 shows the number of tunnels anddisposal holes and canisters for PWR and CANDU spent fuel.

We assumed that the final disposal will start with CANDU fuelcanisters in 2040 and continue with PWR fuel canisters in 2070until 2110. The annual disposal rate of the CANDU spent fuel will be133 canisters per year. The annual disposal rate for the PWR fuelwill be 428 canisters per year for the last 40-year period. In addi-tion, the construction of the repository will begin in the 2020swhen the underground research laboratory (URL) is constructed.Construction includes the excavation, construction works andinstallation of the systems.

d PWR canisters in the KRS-1 repository.

Table 2Number of disposal tunnels.

Canisters þExtra length(5%)

Disposal holesper disposaltunnel

Total number ofdisposal tunnels

PWR 17125 17981 46 390CANDU 3990 4189 69 60Total 21115 22170 450

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657 651

The next step of the construction is to be taken in the 2030swhen the first part of the repository will be constructed. After thisphase in 2040 all the disposal tunnels for the CANDU canisters willbe excavated. After starting the operation, the rest of the disposaltunnels will be excavated in seven phases. Such excavation phasesare presented in Fig. 2. All the tunnels will be excavated witha traditional drill and blast method. First the holes will be drilled,charged and then blasted. After the loading of the muck, the dril-ling of the next drilling pattern can start.

3. Cost estimation method

3.1. A deterministic cost estimation

Generally the disposal cost (DC) can be presented by anexpression given by Eq. (1) (OECD/NEA, 1994). Here, the overnightcosting method using a unique value for an input value was used:

DC ¼ AuUcð1þ iÞt�tb (1)

where Au is disposal volume, Uc is disposal unit cost, i is the esca-lation rate, t is time, and tb is the base date of the monetary unit.

The annual depreciation cost of the equipment can be describedas shown in Eq. (2) based on a straight-line method:

Ec ¼P � R

n(2)

where Ec is the annual depreciation cost, P is the expenditure forthe procurement of a machine, R is the scrap value after n yearsfrom the procurement of a machine, and n is durable years.

Fig. 2. Excavation phase

The annual construction costs (Cc) can be presented as shown inEq. (3) when interest is not considered:

Cc ¼ Ci þkþ 2kþ/þ ðn� 1Þk

n

¼ Ci þknð1þ 2þ/þ ðn� 1ÞÞ ¼ Ci þ

kn

�nðn� 1Þ

2

�

¼ Ci þk2ðn� 1Þ (3)

where Ci is the annual construction costs in the URL phase, k is theincreasing amount of the annual construction costs, and n is years.

Thus, the annual investment costs (IC) for the construction canbe presented as Eq. (4), where we divided the investment costs intoconstruction costs and equipment costs (Yu, 2006):

IC ¼ Cc þ Ec ¼ Ci þk2ðn� 1Þ þ P � R

n(4)

Also the annual operational costs (OC) and annual closure costs (CL)can be presented respectively as Eqs. (5) and (6) by the same elic-itation method as Eq. (3):

OC ¼ Oi þj2ðn� 1Þ (5)

CL ¼ uþ 2uþ/þ ðn� 1Þun

¼ u

2ðn� 1Þ (6)

where Oi is the operating cost in the URL phase, j is the increasingamount of the annual operational costs, and u is the increasingamount of the annual closure costs.

Therefore the total cost (TC) is summation of the annualconstruction costs, the annual operational costs and the annualclosure costs can be written as Eq. (7).

TC ¼ ICþ OCþ CL

¼ Ci þk2ðn� 1Þ þ P � R

nþ Oi þ

j2ðn� 1Þ þ u

2ðn� 1Þ (7)

In order to estimate the economical equipment’s life-time, totalcost is minimized with respect to time as given by Eq. (8):

s of the repository.

Closure costs ofthe undergroundfacilities, 190 ,

2%

Investmentcosts of the

surface facilities,1496 , 17%

Operating costsof the

undergroundfacilities, 2049 ,

23%

Operating costsof the surface

facilities, 3788 ,41%

Investmentcosts of the

undergroundfacilities, 1493 ,

17%

Fig. 3. Overview of the disposal costs.

0 1,000 2,000 3,000 4,000 5,000

110

120

130

140

150

160

170

180

190

200

Ben

toni

te P

rice

[E

UR

/ to

n]

Costs [MEUR]

UndergroundFacilities Costs

Closure Costs

Operating Costs

Bentonite BlockCosts

Tunnel BackfillingCosts

Fig. 5. Cost effects of the bentonite.

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657652

dTCdn¼ �P � R

n2 þ kþ jþ u

2¼ 0 (8)

Thus the economical equipment’s life-time, n* for minimum totalcost is obtained as

n* ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðP � RÞkþ jþ u

s(9)

Disposal costs largely relate to surface facilities and the under-ground facilities of a repository. The costs of those facilities can bedivided into three categories, namely the investment costs, theoperational costs and the closure costs. The cost estimation resultsbased on the conceptual design for the KRS-1 disposal facility todispose of 52,000 tU of spent fuels are provided in Fig. 3. As shownin Fig. 3, the investment costs, operational costs and closures costsof the underground facilities are 1493 , 2049 and 190 MEUR,respectively.

It was found that the most significant item of the disposal costswas the operational costs of the surface facilities because of thehighly expensive Cu powder, which is used as a raw material fora canister’s shell.

To calculate the investment costs and operational costs todispose of 52,000 tU of spent fuels, the overnight cost methodbased on the developed conceptual design was used. This methodhas a linearity for a marginal disposal cost of spent fuels. The costestimation of the surface facilities is an Association for the

0 2,000 4,000 6,000 8,000

10

20

30

40

50

60

70

80

90

100

Cu

Pow

der

Pri

ce [

EU

R /

kg]

Costs [MEUR]

SurfaceFacilities Costs

OperatingCosts

Canister Costs

Fig. 4. Cost effects of the Cu powder.

Advancement of Cost Engineering (AACE) class 5 estimate with anaccuracy range of �20 to �50% on the low side and þ30 to þ100%on the high side, depending on the technological complexity of theproject (AECL, 2006).

Figs. 4 and 5 show the sensitivity of the price effects for the Cupowder and bentonite on the overall disposal costs, which is esti-mated by the deterministic estimation method with a linear costfunction. From the comparison of the sensitivity between Figs. 4and 5, the cost effect of Cu power was more significant than that ofbentonite. Because the marginal cost of a canister was more thanthat of the bentonite block per disposal hole. These two marginalcosts were 126 and 15 kEUR, respectively. Such a marginal cost(MC) can be presented by Eq. (10) (Pindyck and Rubinfeld, 2003) as

MC ¼ DVcDq¼ DODc

Dqh

dCðw; yÞdy

(10)

where Vc is variable costs; ODc is overall disposal costs; w is inputprice; y is unit of disposal; and q is quantity of material.

Fig. 4 shows that the operational costs including the canistercosts were the dominant cost items for the surface facilities costsbecause of the price of the Cu powder. So we can conclude that thedominant cost driver among the material costs is the price of Cupowder by the deterministic cost estimation method. Thepersonnel costs for the full time employees were included in theoperational costs, whereas the costs for other personnel wereincluded in the investment costs because the other personnel areworking on the excavation, construction works, disposal holes,systems and investigations. In addition, social costs are not takeninto account because of uncertainty.

3.2. Probabilistic cost estimation

In this estimation, a probability means an event which willoccur in the future. To estimate a probabilistic cost including anuncertainty of a disposal cost, the expected value method or thethree point estimation method can be used. In addition, the MonteCarlo and Latin Hypercube simulations can be used to elucidatea probabilistic distribution of the input values. In this study, all thecalculations were performed by using the Crystalball Windowsversion 7.2.2 which was developed by the Decisioneering companyin the US (Mun, 2004). In this software, we used the probabilitydistribution as an input value for the probabilistic cost estimation,

Monte Carlo or Latin Hypercube

simulation

50%

total

object

4 6

21

5

3

cost spread(variance)

Object &Variation

ranking of largeuncertainties

Costs for the chosen Degree ofconfidence

stochasticvariableswith selecteddistribution function

Cost Object

Reference cost

Object & Variation

Stochastic variable

total

total

Fig. 6. Process for the probabilistic cost estimation.

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657 653

and an output was also calculated by the probability distribution ofcost estimation results.

To calculate the effect of an uncertainty, a sensitivity analysiscan be performed with certain types of assumed probabilitydistributions (Kim and Kim 2007). The input value of a material’scost has to be defined by a probability distribution which reflectsthe trend of its price as much as possible. Generally an input valueuses a mean value and a deviation of the observations by theexpected value method. So if we consider this input value asa probability distribution, an uncertainty of the disposal costs canbe estimated. But we have to define the input values witha certain reliability. For example, the price of Cu powder andbentonite should be greater than zero, so we assumed these inputvalues as a lognormal distribution. Also, the cost estimationresults were represented by a normal distribution. Fig. 6 showsthe basic process of the probabilistic cost estimation method (SKB,2003).

To understand the trend of a material’s price, we used the pricedata of Cu powder and bentonite from the C&I firm’s database forthe years 1997–2008 and 1999–2008, respectively (Korea PriceInformation Corp., 1997–2008). These annual mean prices for Cupowder and bentonite are presented in Figs. 7 and 8, respectively.

0

10

20

30

40

50

60

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

[Years]

Cu

Pow

der

Pri

ce [

EU

R /

kg]

Fig. 7. Trend of the Cu powder’s price.

3.2.1. Expected value methodThe probability of an input value is a quantitative result for

a future cost. The steps for establishing a probability distributionare as follows:

1. Elicitation of a frequency using an analysis of the past data.2. Approximation under a normal situation.3. Formation of a probabilistic distribution by a subjective point of

view.

We prefer a reliable probability distribution when we estimatean overall disposal cost. But unfortunately such data rarely exists,because it is not an actual value but an estimated future cost.Therefore, an uncertainty must exist in an estimated cost based ona conceptual design of a repository (Lee et al., 2003).

The expected value can be calculated by using a potential riskwith a weighted value, and the estimated value can be calculated bya multiplication of the probability of an occurrence for the esti-mated cost such as Eq. (11):

Ci ¼Xn

j

PjEij (11)

125

130

135

140

145

150

155

160

165

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

[Years]

Ben

toni

te P

rice

[E

UR

/ to

n]

Fig. 8. Trend of the bentonite’s price.

Cu PowderPrice

BentonitePrice

Canisternumber Borehole

number

Boreholevolume

Rockproperties

Buffer/Backfillcost

Constructioncost

Canistercost

Boreholespacing Deposition tunnel

number Deposition tunnelvolume

Backfillcost Tunnel

spacing

Panel tunnelnumber

Panel tunnelvolume

Access length&

cross section

Access tunnelvolume

Panel tunnellength

Repositorydepth

Shaftlength &

crosssection

Shaftvolume

Closurecost

Diameter &depth

Length & crosssection

Operational cost

Overall disposalcost

BentonitePrice

Fig. 9. Variable influence diagram for the disposal costs.

100,000 Trials 146 Outliers

883

1681

2803

Freq

uen

cy

.028

.017

.009

Mean: 64Std.Dev.: 16

Lognormal Distribution

Pro

bab

ility

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657654

where Ci is the estimated value of the alternative i for a conceptualdesign, Eij is the event in the conceptual design for i. Here, Pj meansan independent probability related to Eij, and

Pnj¼1 Pj ¼ 1.

Therefore, the method of cost estimation using an expectedvalue can reveal the level of an uncertainty for the uncertain costdrivers.

3.2.2. The three point estimation methodThe triangular distributions can be assumed as three input

values such as the maximum value, median value, and minimumvalue to use the three point estimation method. This distributionsatisfies the condition of a beta-distribution. Such an expected costand variance can be presented by Eqs. (12) and (13), respectively:

EðCiÞ ¼Lc þ 4Mc þ Hc

6(12)

Table 3Demand of Cu powder and bentonite.

Per disposal hole Total

Cu powder (kg) 1414 29865985Bentonite (tons) 43.29 2797136

VarðCiÞ ¼Hc � Lc

6

2

(13)

� �

where EðCiÞ: the expected cost for an element i, Lc: the minimumcost at the level of 5% from the bottom, Mc: the most likely

40 60 80 100 1200.000196520.005

.002

[EUR/Kg]

Fig. 10. Cu powder’s price.

170 180 190 200 210 220 230 240 250 260 270 280 2900.000

100,000 Trials 138 Outliers

119

325

961

214022522607

Freq

uen

cy

.023

.021

.010

.003

.026

.001

Mean: 211Std. Dev.: 16

[EUR/Ton]

Pro

bab

ility

Lognormal Distribution

Fig. 11. Bentonite’s price. 0 10 20 30 400.000

209 Outliers100,000 Trials

51

1072

2413

F

req

uen

cy

.024

.011

.001

Mean: 20Std. Dev.: 10

Normal Distribution

Pro

bab

ility

[%]

Fig. 13. Owner’s costs.

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657 655

frequency, Hc: the maximum cost at the level of 5% from the top,and VarðCiÞ: variance for an element i.

If we increase the number of simulations with several types ofprobabilistic distributions, the results of a cost estimation are ableto have a normal distribution due to the central limit theorem (Hoelet al., 2000). Namely, if the number of simulations is enough, thedistribution of the cost estimation results will approach a normaldistribution even though the input values have several differenttypes of probabilistic distributions. So P(Cost > Uc) can be calcu-lated by Eq. (14):

Z ¼ Uc � EðCTÞðVarðCTÞÞ1=2

(14)

where Z is the value of a normal distribution, Uc is the subjectiveupper bound cost, EðCTÞ is an expected total cost, and VarðCTÞ is thevariance of the total cost.

A cost estimation method using an expected value needs anobjective probability, whereas the three point estimation methodonly needs three values as an input distribution. But if there isreasonable data for a probability in an expert’s judgment, theexpected value method is worthwhile to estimate the overalldisposal cost. Therefore, we use the expected value method toestimate the price effects of materials for a repository. Fig. 9 showsthe relation of a variable to estimate an overall disposal cost in thisstudy.

3.2.3. Input value for a probabilistic cost estimationTo elicit the mean of the probability distributions related to the

price of Cu powder and bentonite, we assumed an escalation in

80 90 100 110 120 130 1400.000

206 Outliers100,000 Trials

60

602

1749

2504

Freq

uen

cy

.025

.017

.006

.001

Normal Distribution

Mean: 110Std. Dev.: 10

Pro

bab

ility

[%]

Fig. 12. Rock uncertainty.

their price of 2.3%. This measure equals the mean of the pastescalation for a duration of 44 years, which is provided by theelectric business law in Korea. This is because the period for anescalation of a nuclear power plant, except for Gori 1 unit andWolsung 1, 2, 3, 4 units, is 45 years by law.

Table 3 shows the demand for bentonite is more than that for Cupowder based on the KRS-1 conceptual design for an HLW repos-itory in Korea. The elicited input values for probabilities of Cupowder’s price, bentonites’s price, rock uncertainty and owner’scosts based on 2020 are presented in Figs. 10, 11, 12, and 13,respectively.

4. Results of the probabilistic cost estimation

Table 4 shows the summary of cost estimation results fora material’s price, rock uncertainty and owners costs. According tothe results of the deterministic cost estimation, the effect of the Cupowder price is more than that of bentonite. However, from theprobabilistic cost estimation results as shown in Table 4, it wasfound that the effect of Cu powder is not significant because of theintersection of a probability distribution related to the uncer-tainties. But when we consider the demand of a material, the priceof Cu powder can potentially affect the overall disposal costs morethan that of bentonite.

In other words, even though the demand for Cu powder issmaller than that for bentonite, the effect of a material’s price issimilar. Thus, if the demand for Cu powder is increased due toa change in the conceptual design for a canister, the effect of Cupowder may be greater than that of bentonite.

In addition, from a comparison of the cost estimation resultsbetween the probabilistic cost estimation and the deterministiccost estimation related to Cu powder and bentonite, we can see thatthe deterministic cost estimation method has some difficulty inelucidating the effects of an uncertainty for its cost estimationresults, so a decision maker can not establish the level of risk fora specific cost driver.

However the results of the probabilistic cost estimation canprovide useful information about an uncertainty. Namely, theresults of a probabilistic cost estimation method can provide moreavailable information about an uncertainty compared to those ofa deterministic cost estimation method. Finally, the Cu powder’seffect on a disposal cost is more than that of bentonite by a deter-ministic cost estimation, whereas its effect is not significant bya probabilistic cost estimation, as shown in Table 4. According to theprobabilistic estimation as shown in Fig. 14, the difference in priceeffect between Cu powder and bentonite was not significant at a 5%level due to the intersection of an overall disposal cost. Therefore,

Table 4Cost estimation results for a material’s price, rock uncertainty and owner’s costs (unit: MEUR).

Classification Costs for surface’sfacilities

Costs for underground’s facilities Overall disposalcostsa

Operational costs Investment costs Operational costs Closure costs

L U L U L U L U L U

Base 3883 5732 1307 1819 2176 2918 205 349 9588 11680Cu powder 5% [ 3973 5839 1309 1819 2176 2918 205 349 9682 11779

10% [ 4057 5923 1308 1819 2177 2916 206 349 9771 1187115% [ 4148 6017 1306 1820 2176 2916 205 348 9856 11960

Bentonite 5% [ 3884 5749 1308 1817 2238 2999 215 364 9668 1178610% [ 3886 5741 1306 1819 2294 3086 225 379 9742 1186115% [ 3881 5753 1307 1817 2356 3170 234 392 9822 11951

Rock uncertainty 5% [ 3883 5733 1308 1819 2184 2925 206 350 9594 1167910% [ 3880 5747 1307 1822 2186 2930 207 351 9602 1170415% [ 3884 5747 1309 1822 2190 2937 208 352 9609 11713

Owner cost 5% [ 3887 5748 1321 1831 2187 2931 207 351 9622 1171710% [ 3886 5747 1334 1845 2194 2943 209 354 9641 1174415% [ 3888 5736 1347 1858 2207 2955 211 356 9664 11756

L, lower limit of value; U, upper limit of value.a Cost estimation results were calculated at the 5% level.

[MEUR]9609 9664 117561171310661 10710

Rock UncertaintyOwner's Cost

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657656

we can not conclude that the effect of the Cu powder’s price isalways greater than that of bentonite by the probabilistic estima-tion method.

The deterministic cost estimation method can not give all theinformation about an uncertainty, so a decision maker has somedifficulty in understanding its uncertainty, whereas the probabi-listic cost estimation method provides useful information aboutsuch an uncertainty.

Thus, the probabilistic cost estimation method is more appro-priate than the deterministic cost estimation method in the case ofcalculating an overall disposal cost related to an uncertainty.

As shown in Figs. 14 and 15, if we only consider the mean valueof the cost estimation results, the effect of Cu powder and anowner’s cost is greater than that of bentonite and a rock uncer-tainty, respectively. However when we consider the risk of anuncertainty, this conclusion can be reversed due to a decisionmaker’s personal opinion.

For example, if a decision maker has a risk taking character type,he/she may conclude that the effect of bentonite is smaller thanthat of Cu powder, whereas a decision maker with a risk averse

[MEUR]9822 9856 119601195110887 10908

Bentonite

Cu powder

Fig. 14. Variability of a material’s price(15% [).

Fig. 15. Variability of an uncertainty(15% [).

character type may decide that the effect of Cu powder can besmaller than that of bentonite because of the lower deviation of theprobability distribution. Therefore, a probabilistic cost estimationcan provide useful information related to the uncertainty ofa certain cost driver.

5. Conclusions

Traditionally deterministic cost estimation methods have beenused to calculate waste disposal costs. This is because the deter-ministic cost estimation method based on the conceptual design ofan HLW repository offers much more convenience for calculatingthe overall disposal costs than the other cost estimation methods.However, from now on one has to consider the probabilistic costestimation method for calculating a disposal cost which canprovide more available information for an uncertainty becausea disposal cost actually has some uncertainty due to an estimatedfuture cost.

The present study established which material will be thedominant cost driver among a direct material’s costs such as Cu

S.K. Kim et al. / Progress in Nuclear Energy 51 (2009) 649–657 657

powder and bentonite. A comparison was made of the effects ofthese two cost drivers by the deterministic cost estimation methodand the probabilistic cost estimation method.

Using the deterministic cost estimation method, it was foundthat the Cu powder was the dominant cost driver among the directmaterials from the above facilities of an HLW repository, because theouter canister will be made of Cu powder by a cold spray coatingmethod. The canister cost was categorized as an operational cost forthe surface facilities, so this cost became a major charge for theoverall disposal costs. At the same time, bentonite was consideredto be the dominant cost driver for the underground facilities.

The bentonite block surrounding the canister in the disposalhole was one of the important artificial barriers. An approximately43.29 ton bentonite block per disposal hole will be needed todispose of a canister. In addition, the supply chain is not enough todispose of 52,000 tU of spent fuels by using domestic calciumbentonite only. Therefore we have to consider the importing ofbentonite from China due to a transport cost which can potentiallybecome significant . Also the price of bentonite will be increased inthe international raw materials’ market due to the demand ofdeveloping countries. Thus a dominant cost driver with an uncer-tainty can greatly affect an overall disposal cost.

However, from a comparison of the uncertainties between Cupowder and bentonite by the probabilistic cost estimation method,it was found that the effect of these materials’ prices was similar.But when we consider a change in the conceptual design ofa canister, the Cu powder always has the potential to greatly affectthe overall disposal costs.

We believe that this study provides a better understanding andinsight into an uncertainty which exists in an overall disposal cost.The study of disposal costs using a probabilistic cost estimationmethod will be continued to understand the effects of theiruncertainties.

Acknowledgement

This work was supported financially by the Ministry of Educa-tion, Science and Technology under the Mid- and Long-TermNuclear R & D Project. Authors would like to express their gratitudefor its support.

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