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Progress in Nuclear Energy 52 (2010) 813e821

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Progress in Nuclear Energy

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Costebenefit analysis of BeOeUO2 nuclear fuel

S.K. Kim a,*, W.I. Ko a, H.D. Kim a, Shripad T. Revankar b, W. Zhou b, Daeseong Jo b

aKorea 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

a r t i c l e i n f o

Article history:Received 11 February 2010Received in revised form9 July 2010Accepted 9 July 2010

Keywords:Costebenefit analysisBerylliumNuclear fuel cycleBurn-upThermal conductivity

* Corresponding author.E-mail address: sgkim1@kaeri.re.kr (S.K. Kim).

0149-1970/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.pnucene.2010.07.008

a b s t r a c t

This paper provides the results of a costebenefit analysis for BeOeUO2 nuclear fuel, material thatcontains a small volume fraction of Be in uranium oxide matrix. According to the costebenefit analysisresults, the optimized BeO content was about 4.8 wt% when the BeO and uranium oxide prices wereassumed to be $317/kg and $64/kg, respectively. The benefit of increasing the thermal conductivity ofBeOeUO2 fuel was greater than the burden of the expensive BeO material price if the BeO content was4.8 wt%. In addition, the break-even point of the nuclear fuel cycle cost as a function of the burn-up was4.4 mills/kWh when compared economically between BeOeUO2 fuel and UO2 fuel. Therefore, BeOeUO2

fuel seems economically efficient when the burn-up is more than 60 MWD/kg because the nuclear fuelcycle cost of BeOeUO2 fuel was lower than that of UO2 fuel.

� 2010 Elsevier Ltd. All rights reserved.

1. Background

Economicbenefit and technical safetymust be examined inorderto commercialize any new fuel. An enhanced thermal conductivityfuel with BeO impregnated in UO2 fuel has been successfullydeveloped by Solomon et al. (2009), which has potential to enhancethe amount of power generation in a light water reactor (LWR). Therawmaterial of BeOeUO2 fuel was created from the mixture of BeOinto UO2 using twomanufacturing processes slug-bisque and greengranule methods (Sarma et al., 2006; Solomon et al., 2009). It wasfound that an increase of thermal conductivity of the BeOeUO2 fuelby over 40% for 10% volume of BeO in UO2 (Latta et al., 2008).According to the thermal and core analysis, BeOeUO2 fuel had highmerits in terms of thermal conductivity and technical safety(Revankar and Zhou, 2009). A costebenefit analysis explored thepotential economicbenefit of BeOeUO2 fuel, and a close relationshipbetween the BeO content and burn-up was expected. Generally, theincrease of burn-up contributes to the decrease of the nuclear fuelcycle cost (Edsinger and Ozer, 2001).

While the burn-up is increased by the mixture of Be material,the optimal BeO content that might minimize the nuclear fuel cyclecost should be calculated based on the regulatory limitation onincreasing burn-up. In this paper, BeOeUO2 fuel is set up as the costobject, and its economic value is estimated through the comparison

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of cost and benefit in terms of the dominant cost drivers. First of all,the burden of direct material cost must be considered because Be ismore expensive than uranium. The profits of increased fuelperformance through the increase of burn-up can be attributed toan increase of thermal conductivity with appropriate BeO content.

The costebenefit analysis was performed in regard to dominantcost drivers such as disposal cost, Be credit, and the direct materialcost. However, such costebenefit drivers have a trade-off rela-tionship. For example, if the raw material cost of Be increases, thenuclear fuel cycle cost would decrease because of high burn-up(Meyer, 2007).

The economic value of BeOeUO2 fuel lies in decreasing disposalcosts, especially considering the difficulty of securing a high-levelwaste repository site. Consequently, the development of BeOeUO2fuel with technical safety will grow in importance as technologyadvances to sustain the prosperity of nuclear energy. If the profitincrease is more than the increase of Be cost, nuclear utilities willuse BeOeUO2 fuel. Therefore, a costebenefit analysis of BeOeUO2fuel with scientific exactitude is needed.

The manufacturing cost is an important part of front-end fuelcosts, especially since BeO- UO2 fuel has additionally beneficial andreusable Be material (Sarma et al., 2006). In this paper, three mainbenefit drivers are considered: high burn-up, decreased radioactivewaste, and Be credit from reused Be material. BeOeUO2 fuel, whichis being developed at Purdue University, has been found to havea high performance level. The periodical research related to thedirect material cost should be performed because the Be material

Fig. 1. Manufacturing process of BeOeUO2 fuel using SB granules.

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821814

price is comparatively higher than the price of uranium (U.S.Geological Survey, 2008). The Be price is unstable due to the fluc-tuation of demand in the telecommunication industry.

The cost comparison between BeOeUO2 fuel and UO2 fuel withthe current economical condition can give clues into the potentialbenefits of BeOeUO2 fuel (McCoy and Mays, 2008). Therefore, it isworthwhile to decide the optimal content of BeO in an economiccontext.

The objectives of this study are as follows. Firstly, to estimate thecost effects of the price of Be in the fuel cycle cost under currenteconomic terms and technical safety. Secondly, to elicit the break-even point between BeOeUO2 fuel and UO2 fuel in the nuclear fuelcycle cost. Finally, to provide the optimal BeO content to maximizethe economic benefit of BeOeUO2 fuel.

2. BeOeUO2 fuel

2.1. Characteristics of BeO

To improve the performance of nuclear fuel, it was essential todevelop a technology that would use material such as Be asa component of UO2 fuel in order to increase burn-up. BeO fuel withhigh performance provides motivation for the development of suchfuel that can increase the generation revenue of nuclear utilitiesand contribute to the national economy. Be material is found inrock, but the BeO content is less than 5%t. In addition, BeO materialis useful in ceramics and has a melting point of 2570 �C as well asgreat resistance to thermal shock.

The atmospheric corrosion resistance of Be under high temper-ature is greater than that of titanium or zirconium. The ultimatestrength of the sintered powder (at 1000 �C, 3.5 MPa) is 310 MPa(45,000 psi). Its light characteristics make Be material ideal for useby the telecommunication industry. However, inhalation of Be isdangerous to the lung health of a technician. To prevent this, theenvironmental protection agency (EPA) established environmentalstandards of an upper limit value of 0.01 mg/m3.

The current price of Be is very expensive. Its price variation isgreater than that of othermaterials because of its high demand in thematerial industry. For example, the price of Bepowderwas $317/kg atthe end of last year, meaning that the burdens of direct material costwill increase if Be is used as a fuel component. It might give theindustry an incentive to limit the use of them. However, generationrevenuecanstill beexpected.This isbecause theburn-upofBeOeUO2fuel greatly increases with the increase of thermal conductivity.

To elicit the optimal content of BeO, the analysis of thermalconductivity was performed within a certain range. This is becauseof the economic benefit due from increasing the BeO content andbecause technical safety is necessary. The increase of material costdecreases the advantage of BeO fuel because of the higher front-end fuel cost. In addition, when the burn-up is increased due to theBe material, howmuch the BeO content affects the corrosion of thefuel tube and the pressure between the pellet and the tube ofnuclear fuel must be identified. In other words, the optimal contentof BeO must satisfy the safety requirements.

2.2. Manufacturing process of BeOeUO2 fuels

In this paper, the cost object is defined as the BeOeUO2 fuelwhich can be used in a pressurized water reactor (PWR). Similarmanufacturing processes exist when compared with those ofuranium fuel. Those processes should be added in the BeOeUO2manufacturing process in terms of granulation, Be mixture, and thecold pressing of pellets (Solomon et al., 2005).

Cold pressing in the prior sintering process is needed for thehomogeneous mixture of Be and uranium, which is vital to increase

the burn-up of BeOeUO2 fuel. Cold pressing is also necessary forincreasing the integrity of BeO fuel before the sintering process. Inthis way, the complexity of the BeOeUO2 manufacturing processmight be increased.

It is essential, however, that a skilled technicianmust investigatethe homogeneous mixture status regarding Be and uraniumcomponents. Such a process will increase the quality cost which canbe estimated more accurately by the ABC (Activity Based Costing)method (Ben-Arieh and Qian, 2003). Generally, the accuracy of themanufacturing cost depends on the detailed level of activitiesrelated to the manufacturing process (Jerzy Wrobel and MarcinLauda�nski, 2008). For example, the personnel cost due to theincreasing process complexity might affect the manufacturing cost.The additional equipment costs due to the new process can also beone of the dominant cost drivers of the manufacturing cost. Figs. 1and 2 show the manufacturing process of BeOeUO2 fuel using theSB (Slug Bisque) and GG (Green Granule) methods which is basedon the original processes developed by Solomon et al. (2005).

2.3. Thermal analysis results of BeOeUO2 fuel

According to the thermal analysis of BeO fuel, the BeO fuelsatisfied the technical safety requirement, as shown in Fig. 3.Therefore, it can be insisted that the costebenefit analysis ofBeOeUO2 fuel is worthwhile to elicit the optimal BeO content froman economic viewpoint.

As shown in Fig. 3, the temperature difference profile acrossa nuclear fuel pellet was calculated for the enhanced thermalconductivity of oxide nuclear fuels. The results of these calculationsare shown in the Fig. 3, where the centerline temperature of the SB(Slug-Bisque)-BeOeUO2 nuclear fuel was predicted to decrease by217 K from that of 95% dense UO2. The centerline temperature ofthe GG (Green Granule)-BeOeUO2 nuclear fuel was predicted todecrease by 333 K from that of 95% dense UO2.

Fig. 2. Manufacturing process for BeOeUO2 fuel using Green granules.

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821 815

The SB-BeOeUO2 fuel had the least decrease in the centerlinetemperature, followed by the green granule BeOeUO2 fuel. Thegreen granule BeOeUO2 fuel had the larger decrease in centerlinetemperatures.

3. Terms for costebenefit analysis

3.1. Costebenefit drivers

Generally, the coste-benefit analysis method could be recog-nizedas aneconomic estimationmethod toknowwhether theprofitwill be within terms of the new investments. In the costebenefitanalysis, it was expected that the most dominant cost driver wouldbe the Be price, whereas the dominant benefit driver would be thehigh burn-up. Estimating these two dominant costebenefit drivers

Fuel temperature profiles for UO2, SB-UO2/BeO, GG-

UO2/BeO nuclear fuels

800

1000

1200

1400

1600

1800

0 0.2 0.4 0.6 0.8 1

Radial location (r/r(fo))

)K

( e

ru

ta

re

pm

eT

UO2 95%TDSB-UO2/BeO 10vol%GG-UO2/BeO 10vol%

Fig. 3. Results of the thermal analysis for BeOeUO2 nuclear fuel.

made it possible to know whether BeOeUO2 fuel has economicmerit. To know the dominant costebenefit driver’s effects, it shouldbe identified first. If the cost is more than the benefit, the newinvestment or new product cannot be commercialized because ofthe lack of economic sense.

Though the cost is more than the benefit in a certain period, theresearch and development of a new product can be continued forthe acquisition of advanced technology, the improvement ofmarket share, and the cost cut-off.

It is still reasonable that the current expense of dominant costdrivers in a costebenefit analysis must be first estimated in order todecide the economic value. Unfortunately, potential costs in thefuture are difficult to measure, such as the social cost of disposal toa high-level waste repository. Table 1 shows the dominant cost-ebenefit drivers, which can affect the nuclear fuel cycle cost. Asshown Table 1, the dominant benefit driver of BeOeUO2 fuel is thehigh burn-up due to increased thermal conductivity. Thus, theeconomical effects of high burn-up must be estimated withina certain range while maintaining technical safety.

When BeOeUO2 nuclear fuels is developed, both technicalsafety and economic sense must be considered. Especially, in aneconomic analysis, the trade-off relationship between the benefitand the cost has to be estimated. For example, if the expensive Bematerial is used as raw material of nuclear fuel, the burn-up canincrease, meaning the direct material cost will also increase.Therefore the elicitation of the optimized BeO content of BeOeUO2fuel is needed.

The effects of the Be price must be estimated first with thecondition that the conceptual design of BeOeUO2 fuel satisfies thedesign requirements because safety in a nuclear power plant mustbe a first priority. It is reasonable that technical safety should beestimated first through the thermal analysis of BeO fuel before theeconomic analysis of BeO fuel. Finally, the economic effect of theincreased burn-up on the fuel cycle cost is estimated. Fig. 4 showsthe BeOeUO2 fuel cycle.

There is a monotonic increasing relationship between the burn-up and BeO content within a certain range of the BeO content. Thegeneration of homogeneous BeOeUO2 fuel can increase if the BeOcontent increases (Handwerk et al., 2007).

The optimized BeO content can maximize the benefit of BeOfuel. In other words, the optimized BeO content is a significantdeterminant for decreasing the nuclear fuel cycle cost. However,there is a limit for increasing the burn-up because that increaseelevates the possibility of corrosion. It is essential to include theresistance material for corrosion for the cladding of nuclear fuel toimprove its performance.

3.2. Be price

The dominant cost driver is the Be price because this price iscurrently more expensive than that of uranium. It also affects thedirect material cost which is a major part of the front-end nuclearfuel cycle cost (OECD/NEA, 2006).

Table 1Dominant costebenefit drivers of BeOeUO2 fuel.

Benefit drivers Cost drivers

- The high burn-up due to theincrease of thermal conductivity

- The decrease of disposal costs dueto the decrease of radioactivewaste and extending the lifetimeof nuclear fuel.

- The cost reduction of directmaterials by reusing Be, which isthe so-called Be credit.

- The increase of direct materialcost because the Be price ismuch more expensive thanuranium (Wright, 1964a,b).

- The increase of manufacturingcost due to the increase of thecomplexity of the BeOeUO2

manufacturing process such asthe mixture of Be.

Figure 4. Nuclear fuel life cycle of BeOeUO2 fuel.

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821816

The cost effects of the Be price should be estimated as significantfactors in order to analyze the costebenefit of BeO fuel, firstbecause the gap between the Be and uranium prices is currentlywide. When the expensive Be material is mixed with uranium toincrease the fuel performance, the directmaterial cost aswell as thefront-end fuel cycle cost increases. The direct material cost ofBeOeUO2 fuel was charged at about 38% among the nuclear fuelcycle cost. If the generation cost is increased due to the increase ofthe direct material cost, the economic merit of BeOeUO2 fuel candecrease. As shown in Eq. (1), the generation cost can be dividedinto a fixed cost and a variable cost. In this equation, the variablecost indicates a nuclear fuel cycle cost. Therefore, the increase of thedirect material cost can increase the variable cost, and then thegeneration cost will increase due to the increase of the nuclear fuelcycle cost.

C ¼ Fc þ Vc ¼ Cuc$RT$Ur$ð1� IcÞ þNFCC (1)

where, Fc¼ Fixed unit cost, Vc¼ variable unit cost,Cuc¼ construction unit cost($/kW), R¼ fixed charge rate, T¼ 8760(¼365 day� 24 h), Ur¼ load factor, Ic¼ consume rate in powerplant, and NFCC¼Nuclear Fuel Cycle Cost.

However, it is not easy to calculate the nuclear fuel cycle costincluding the disposal cost because this cost has an uncertainty. For

example, the disposal cost has a social cost due to the difficulty ofsecuring the repository site. There is also the disposal method suchas the vertical emplacement and horizontal emplacement ofcanisters. The intermediate storage cost also includes the uncer-tainty of the storage period regarding the disposing time of radio-active waste (IAEA, 2007).

Even though the disposal cost has much uncertainty, this hugecost must be estimated as a part of the annual cost. In manycountries, projects regarding the disposal cost estimation arecurrently being performed to increase the accuracy of the costestimation. By this effort, an appropriate annual disposal fund canbe levied to nuclear utilities without any complaints regardingpayments.

If the disposal cost is underestimated, the disposal project willnot be performed on time, whereas if the cost is overestimated, theproject will bring about a loss of opportunity cost. Especially, theincrease of investment cost due to securing the repository site willbring obstacles in terms of the prosperity of nuclear energy.Another uncertainty in the nuclear fuel cost is the price change ofdirect material such as Be and uranium in the future.

If the Be and uranium prices rise, the necessity of the costestimation of direct material on the nuclear fuel cycle cost willgrow. The fluctuation of the direct material cost due to the imbal-ance between the demand and supply of its material can decrease

Elicitation of cost-benefit drivers

Design requirement

Step 1

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821 817

the accuracy of cost estimation results that identity the nuclear fuelcycle cost in terms of the BeO fuel.

The burdens of the Be material cost will be comparativelyincreased when the increasing slope of the Be price is more thanthat of uranium. In this paper, for the costebenefit analysis of BeOfuel, the nuclear fuel cycle cost was calculated to identify the costeffects of the Be material. If the Be price is greater when comparedto that of uranium, the BeOeUO2 fuel will decrease the economicprofit, whereas if the uranium price is more than that of Be, theburdens of the Be material cost will decrease comparatively.Obviously, the expensive price of Be material creates negativeeffects for the higher content of BeO on BeOeUO2 fuel. Fig. 5 showsthe trend of the Be and uranium price (Energy InformationAdministration, 2008).

It can be assumed that the cost effects of Be rawmaterial will besignificant because the current Be price is about five times moreexpensive than that of uranium so far. Therefore, the Be materialcost could be one of the significant determinants for estimatingwhether or not BeO fuel has economic merit.

As shown in Fig. 5, Be material maintained a higher price untilthe 1990s, and then its price approximately decreased from$800/kg to $200/kg because of the sudden increase of Be supply.

Such a big price gap between the 1990s and 2000s created anuncertainty in the Be price, and its price could be unstable in thefuture. Recently, the demand of Be may rise continuously, so itsprice could remain high. Finally, the Be price will increase due to itscontinuous demand in the communication industry. Therefore, ifthe Be price increases over time, the direct material cost ofBeOeUO2 fuel must be increased. This could be an obstacle tocommercializing BeOeUO2 fuel because of the reduction of profit.Therefore, it is important to know the credit cost effects of Bematerial in order to understand the benefit of Be reuse.

In the last twenty years, the variance of the Be price is muchmore than that of uranium. Thus, a periodic cost effect estimationfor the Be material in the fuel cycle cost will be needed because theBe price might be a significant cost driver of BeOeUO2 fuel.

4. Costebenefit analysis method

It is reasonable that the increased burn-up as well as the longlife of BeOeUO2 fuel could be one of the cost reduction methods ina nuclear fuel cycle. This is because increasing burn-up of BeOeUO2fuel affects the reloading interval time and then changes therecharging date of it. In addition, the long operational period ofBeOeUO2 fuel also decreases its fuel cycle cost.

For the benefit estimation of BeOeUO2 fuel, the Be credit costdue to reusing Be material should be calculated because the Beprice is more expensive than uranium. The equations related to thecostebenefit analysis are shown from Eqs. (2)e(5).

As shown in Eq. (2), the dominant benefit drivers of BeOeUO2fuel on the fuel cycle cost can be divided into the increased

0

200

400600

800

1000

49916991

89910020 002

2 40026002

8002Years

]g

k/$

[s

eci

rp

tn

er

ru

C

BerylliumUranium

Fig. 5. The trend of beryllium and uranium prices.

generation due to the increasing burn-up, the decrease of thedisposal cost, and the Be credit.

Economical benefit ¼ DGeneration� DDisposal cost

� DBe Credit (2)

CdðtÞ ¼Xt

QsfðtÞ$UCd$ð1þ ERdÞDIDðtÞþLAGd�YRc

ð1þ DRÞDIDðtÞþLAGd�YRp(3)

CbcðtÞ ¼Xt

QsfðtÞ$Ber$CDbeð1þ DRÞDIDðtÞþLAGr�YRp (4)

where, Cd(t)¼ disposal cost, Qsf(t)¼ quantity of spent fuel at t year,UCd¼ unit cost of disposal, ERd¼ escalation, DID(t)¼ dischargedate at t year, LAGd¼ lag time of disposal, YRc¼ basic year,DR¼ discount rate, YRp¼ beginning year of NPP (nuclear powerplant) operation, Cbc(t)¼ Be credit, Ber¼ the BeO content inBeOeUO2 spent fuel, and CDbe¼ (cost of uranium, conversion,enrichment and fabrication for manufacturing of natural uraniumfuel 1 kg)� (cost of conversion and fabrication formanufacturing ofrecovered BeO fuel 1 kg).

As shown in Eq. (5), the dominant cost drivers of BeOeUO2 fuelcan be divided into the increase in the material cost and theincrease in the manufacturing cost. This is because the Be price iscurrently expensive and the manufacturing process of BeOeUO2

fuel is more complex than that of UO2 fuels.

Economic costðlossÞ ¼ Dmaterial costþ DManufacturing cost(5)

The cost effect for the dominant costebenefit drivers wascalculated in the nuclear fuel cycle cost.

4.1. Research step

The costebenefit analysis of BeOeUO2 fuel was carried outthrough four steps, as shown in Fig. 6. In the first step, the dominantcostebenefit drivers were elicited to analyze the costebenefit ofBeOeUO2 fuel. The increase in the material cost due to theexpensive Be price and the increasing burn-up were assumed to bepart of the dominant cost and benefit drivers, respectively. In thesecond step, the manufacturing unit cost of BeO fuel was calculatedbased on the conceptual design while satisfying the safetyrequirements of nuclear fuel. In this paper, only the actual

Be price

Manufacturing cost estimation

Nuclear fuel cycle cost estimation

Cost ≤ Benefit

Elicitation of Break-even point

Step 2

Step 3

Step 4

No

Fig. 6. Research steps for a costebenefit analysis.

Table 2Equations for the nuclear fuel cycle cost.

Category Equations

Recharge interval

Ri ¼ CsNb

� BUdMWt� Lf � 365

ðUnit : yearÞ (8)

Quantity of fabrication

QfðtÞ ¼ CsNb

; t ¼ batch (9)

Quantity of enrichment

QeðtÞ ¼�VðELÞ þ

�EL � TaNAT� Ta

� 1�$VðTaÞ � EL � Ta

NAT� TaVðNATÞ

�QfðtÞð1þ LFfÞ (10)

Quantity of conversion

QcðtÞ ¼ EL � TaNAT� Ta

QfðtÞð1þ LFfÞ (11)

Quantity of uraniumQuðtÞ ¼ QcðtÞð1þ LFcÞ (12)

Spent fuel generationQsfðtÞ ¼ QfðtÞ$0:97 (13)

Cost of uranium

Cu ¼Xt

QuðtÞ$UCu$ð1þ EuÞLðtÞ�LEDu�YRc

ð1þ DÞLðtÞ�LEDu�YRp (14)

Cost of conversion

Cc ¼Xt

QcðtÞ$UCc$ð1þ EcÞLðtÞ�LEDc�YRc

ð1þ DÞLðtÞ�LEDc�YRp (15)

Cost of enrichment

Ce ¼Xt

QeðtÞ$UCe$ð1þ EeÞLðtÞ�LEDe�YRc

ð1þ DÞLðtÞ�LEDe�YRp (16)

Cost of fabrication

Cf ¼Xt

QfðtÞ$UCf$�1þ Ef

�LðtÞ�LEDf�YRc

ð1þ DÞLðtÞ�LEDf�YRp(17)

Cost of transportation; applied LAG time

Ct ¼Xt

QsfðtÞ$UCt$ð1þ EtÞDðtÞþLAGt�YRc

ð1þ DÞDðtÞþLAGt�YRp (18)

Cost of storage

Cs ¼Xt

QsfðtÞ$UCs$ð1þ EsÞDðtÞþLAGs�YRc

ð1þ DÞDðtÞþLAGs�YRp (19)

Cost of disposal

Cd ¼Xt

QsfðtÞ$UCd$ð1þ EdÞDðtÞþLAGd�YRc

ð1þ DÞDðtÞþLAGd�YRp(20)

Cost of reprocessing

Cr ¼Xt

QsfðtÞ$UCr$ð1þ ErÞDðtÞþLAGr�YRc

ð1þ DÞDðtÞþLAGr�YRp (21)

Cost of Be-credit

Cbc ¼Xt

QsfðtÞ$Sbe$CDbeð1þ DÞDðtÞþLAGr�YRp (22)

Cost of uranium-credit

Cuc ¼Xt

QsfðtÞ$Ue$Cuð1þ DÞDðtÞþLAGr�YRp (23)

Total cost of direct disposal alternativesCTdðtÞ ¼ CuðtÞ þ CcðtÞ þ CeðtÞ þ CfðtÞ þ CtðtÞ þ CsðtÞ þ CdðtÞ (24)

Total cost of reprocessing alternativesCTrðtÞ ¼ CuðtÞ þ CcðtÞ þ CeðtÞ þ CfðtÞ þ CrðtÞ � CbcðtÞ � CucðtÞ (25)

where, Cs¼ core size, Nb¼ number of batch, BUd¼ Burnup, MWt¼Generation, Lf¼ load factor, L(t)¼ loading time, D(t)¼ discharging time, LED¼ lead times,LAG¼ lag times, Sbe¼ Be ratio in spent fuel, V(x)¼ (2x� 1) ln (x/1� x), CDbe¼ (cost of uranium, conversion, enrichment and fabrication for manufacturingof natural uranium Fuel 1 kg)� (cost of conversion and fabrication for manufacturing of BeOeUO2 fuel 1 kg), and Cu¼ (cost of uranium, conversion,enrichment and fabrication for manufacturing of natural uranium fuel 1 kg)� (cost of conversion and fabrication for manufacturing of recovered uraniumfuel 1 kg).

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821818

dominant costebenefit drivers were considered in order to knowthe economic sense of BeOeUO2 fuel. The manufacturing unit costcan be composed of the direct material cost, the direct labor cost,and the indirect cost. These three categorized costs were addedtogether. In the third step, the nuclear fuel cycle cost was calcu-lated. Then, in the fourth step, the break-even point as a function ofthe BeO content was calculated to know the optimized BeO contentfor BeOeUO2 fuel. The final purpose of this studywas to provide theoptimal BeO content having economic sense.

4.2. Nuclear fuel cycle cost of BeOeUO2 fuel

4.2.1. Calculation methodThe nuclear fuel cycle cost as the variable cost of the genera-

tion cost can be divided into the front-end fuel cycle cost and the

back-end fuel cycle cost (OECD/NEA, 2001). Such costs can becalculated by accounting methods as well as engineeringmethods. Using the engineering method, the current cost such asthe direct material cost can be calculated as the multiplication ofquantity and their unit cost, as shown in Eq. (6), based on theassumption that there is an increasing monotonic relationshipfunction between the quantity and cost.

Ca ¼Xni¼1

Q iUi (6)

where, Qi¼ quantity of i-process, Ui¼ unit cost of i-process.The estimated unit cost, such as the disposal cost, can be

a significant factor in determining the accuracy of the cost esti-mation because this unit cost has some uncertainty. The disposal

Table 3Technical and economic data.

Economicdata

Discount rate 5.0 [%/year]Escalation rate 1.2 [%/year]Base year of cost data 2001Unit cost Direct material cost of

BeO and uraniumBeO: $317/kg,U3O8: $64/kg

Conversion $8.0/kgUEnrichment $100/kgSWUFabrication $250/kgUTransportation $50/kgHMInterim storage $200/kgHMReprocessing $700/kgHMFinal Disposal $500/kgU

Technicaldata

Reactor Life time 40 yearsThermal power 4020 MWtElectrical power 1390 MWeLoad factor 75%Core size 107.91 tU

Enrichmentdata

U-235 content innatural uranium

0.7%

Enrichment of feed 0.71 w/oEnrichment of product 4.6 w/oEnrichment of tails 0.3 w/o

Loss factors Conversion 0.5%Fabrication 1.0%Reprocessing 2.0%

Lead time[unit: months]

Purchase 24Conversion 18Enrichment 12Fabrication 6

Lag time[unit: months]

Transportation 60Reprocessing 72Final disposal 480

Table 4Effect of BeO content on the direct material cost.

Mixed BeO(wt%)

Material unitcost ($/kg)

Effects on directmaterial cost (%)

5 116 7.7 [

10 149 15.4 [

15 183 23.1 [

20 216 30.7 [

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821 819

cost is not an actual cost but an estimated cost, which will occur inthe future. The front-end fuel cycle cost includes the uraniumpurchasing cost, conversion cost, enrichment cost, and fabricationcost (Wright, 1964a,b). The back-end fuel cycle cost can be calcu-lated with two options such as a reprocessing option and a directdisposal option. In the reprocessing option, the back-end fuel cyclecost includes a transportation cost of spent fuel, a storage cost,a reprocessing cost, and a disposal cost of radioactive wastegenerated from reprocessing (Schneider et al., 2009). In the directdisposal option, the back-end fuel cycle cost includes a trans-portation cost, a storage cost, and a disposal cost. For example, thecurrent cost should be calculated first, and then the future costshould be estimated by using a reasonable escalation rate (Caputoand Pelagagge, 2008). The construction of a repository in thefuture and the disposal cost in future rates must be converted intothe present cost using appropriate discount rates (U.S. Departmentof Energy, Office of Civilian Radioactive Waste Management, 2001).Finally, the nuclear fuel cycle unit cost can be calculated by usingthe levelized unit cost method, which is one of the average costs, asshown in Eq. (7) (OECD/NEA, 1994).

Uc ¼

Pstages

Pt

Ct

ð1þrÞt�t0

Pt

Etð1þrÞt�t0

(7)

where, t0¼ base year, r¼ discount rate, Et¼ generation, andCt¼ total cost.

In Eq. (7), Ct indicate Ca in Eq. (6). To calculate the nuclear fuelcycle cost, the economic data must be assumed, including thediscount rate and currency rate. In addition, technical data such asthe burn-up data, the loss factor, and the lead and lag time of eachprocess in terms of the nuclear fuel cycle should be identified. Thelead time means the required period of the process includingconversion, enrichment, and fabrication before the loading time ofnuclear fuel. Lag time indicates the necessary period in the trans-portation for spent fuel, the storage of spent fuel, reprocessing afterdischarging spent fuel, and finally, the disposal of spent fuel.

The characteristics of spent fuel should also be assumed. PWRcore data can be divided into the initial core data, equilibrium coredata, and final core data, and this categorization is based on thedifference of the burn-up and enrichments. In addition, theimportant variables of equilibrium core data are the number ofbatches and the discharging burn-up of spent fuel. Table 2 showsthe needed equations in terms of the nuclear fuel cycle cost. Thiscalculation method was described in the OECD/NEA reports in 1993with the title “The Economics of the Nuclear Fuel Cycle”. Since thepublication of this report, many cost estimators have used thismethod because of the convenience of calculation.

The reloading interval could be determined by the dischargingburn-up and the number of batches. Thus, this interval can becalculated by Eq. (8).

To calculate the fuel cycle cost of BeOeUO2 fuel, the quantity ofuranium, conversion, enrichment, and fabrication was calculatedfrom Eqs. (9)e(17), and the quantity of spent fuel was estimated, asshown in Eq. (13). For the cost estimation of each process, theannual cost should be calculated first, and then their costs shouldbe summated from Eqs. (18)e(23). In this calculation, the annualcash flow can be calculated by the multiplication of the quantityand their unit cost. Such cash flow can be discounted by generationvolume which should be discounted using the lead and lag time forthe nuclear fuel cycle.

The cash flow of the back-end fuel cycle cost can be calculatedusing different options such as a reprocessing option or a directdisposal option. When using the direct disposal option, the cash

flow in the back-end fuel cycle cost can be categorized as thetransportation cost of spent fuel, storage cost, and disposal cost(IAEA, 2009). In the case of the reprocessing option, the cost can becategorized as the reprocessing cost, Be credit, and uranium credit.

The nuclear fuel cycle cost for two such options can be calcu-lated by Eqs. (24) and (25). Especially in the case of the reprocessingoption, the Be credit benefit must be considered as the intrinsicvalue for reusing Be material. However, plutonium credit was notconsidered in this paper because its reuse was not considered.Finally, the nuclear fuel cycle unit cost in terms of the reprocessingand direct disposal options can be calculated as the division of thediscounted total cost by the discounted generation volume. In thiscalculation, the generation volume was discounted from theintermediate loading time of fuel to the beginning of an operationaltime.

4.2.2. Technical and economic data for cost estimationThe nuclear fuel cycle cost can be calculated by using both actual

data and estimated data such as a disposal unit cost. To estimatethe necessary cost, the economic and technical data, as shown inTable 3, was used.

5. Cost estimation results

In this paper, all costs in terms of the nuclear fuel cycle cost werecalculated by using code BNFCC (Beryllium Nuclear Fuel Cycle Cost)

4.0

4.5

5.0

5.5

6.0

45 55 65 75Burnup[MWD/kg]

hWk/slli

M[C

CFN

]PWR

BeO-UO2

Fig. 7. Break-even point between BeOeUO2 fuel and UO2 fuel.

-5 5 15 25 35

DM C

Conversion

Enrichment

Fabrication

Reprocessing

Be Credit

Uranium Credit

[%]

Fig. 9. Component ratio of the NFCC.

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821820

ver. 1.0, which was developed by KAERI (Korea Atomic EnergyResearch Institute) and Purdue University. In addition, the levelizedcost estimation method was used.

5.1. Cost effects of the Be price

The cost effect of the Be price was calculated as a function of theBe content in the front-end nuclear fuel cycle cost. Table 3 showsthe results. The main objective of this calculationwas to discern theeffect of the Be price on the nuclear fuel cycle cost of BeO fuel. Forthe cost estimation, the uranium unit cost was assumed to be $64/kgU, whereas the unit cost of Be material was assumed to be $317/kgBe. Under such a material price, the direct material cost can beapproximately 38% of the fuel cycle cost. In addition, themanufacturing unit cost was assumed to be $250/kgBeU.

Using the assumed variables, the cost effects of the Be pricewere calculated under the condition that the cost function hada linear relationship between the quantity of Be and the directmaterial cost. Table 3 shows the Be price’s effect.

From Table 4, it was found that the cost effect of the BeO contentwas significant on the front-end fuel cycle cost. This was becausethe Be price was about five times more when compared to that ofuranium. However, the increase of BeO content can result in anincrease of burn-up due to the increasing thermal conductivity.Therefore, the increase of burn-up should be taken into account forthe costebenefit analysis of BeOeUO2 fuel.

To know whether BeOeUO2 fuel has economic sense, thedominant benefit driver’s effects must be known. The effectsinclude the increase of burn-up and the decrease in the disposalcost due to the reduction of radioactive waste.

For more information about the dominant cost driver’s effect,the increase of the material cost should also be evaluated becauseof the higher Be price. Finally, the economic sense of BeOeUO2 fuelcan be determined with comprehensive costebenefit driver’s costeffects.

5.2. Analysis of the break-even point

The previous core analysis results were used. From this result, itwas assumed that there is an increasing monotonic relationship

0

2

4

6

8

10

2.5 3.5 4.5 5.5 6.5BeO wt%

]hWk/slli

M[tsoC

Nuclear Fuel Cycle CostDirect Material Cost

Fig. 8. Optimized BeO content of BeOeUO2 fuel.

between the BeO content and burn-up within a certain burn-uprange. A linearity from 45 MWD/kg to 85 MWD/kg was calculatedbased on the assumption of homogeneous BeO content in fuelassemblies (Handwerk et al., 2007).

According to cost estimation results between BeOeUO2 fuel andUO2 fuel, it was found that the break-even point was about4.4 mills/kWh when the burn-up was about 60 MWD/kg. As shownin Fig. 7, BeOeUO2 fuel had a comparative economic advantagefrom 60 MWD/kg. This was because the high burn-up BeOeUO2fuel increases the electricity generation and then covers thedisadvantage of the expensive Be material cost.

5.3. Optimal content of Be material

Actually, if the burn-up increases, the generation volume ofnuclear fuel will increase within a certain burn-up range. To elicitthe optimized BeO content, the NFCC as well as the DMC (DirectMaterial Cost) as a function of BeO content was calculated, asshown in Fig. 8. From this figure, it was found that the optimizedBeO content in view of economic sense was approximately 4.8 wt%.In this calculation, the burn-up limit of 60 MWD/kgwas assumed asper South Korean regulations (Kim et al., 2002).

As shown in Fig. 9, the rawmaterial cost was the most dominantcost driver among the nuclear fuel cycle cost when the BeO contentwas optimal. This was because the Be price was expensive.However, if Be credit is considered, the direct material cost wasapproximately 33% of the nuclear fuel cycle cost. This DMC’sportion might be equivalent to about 5% more than that of theenrichment cost.

6. Conclusions

According to the thermal analysis of BeOeUO2 fuel, Be materialcan increase the burn-up as well as the operational life time ofnuclear fuel due to increased thermal conductivity. Therefore, eventhough the current Be material cost was five times more expensivethan that of uranium, it was found that BeOeUO2 fuel might haveeconomic sense if the burn-up is more than 60 MWD/kg. Conse-quently, BeOeUO2 fuel can improve the fuel performance anddecrease the nuclear fuel cycle cost. It was also found that theoptimized BeO content of BeOeUO2 fuel to minimize the nuclearfuel cycle cost was 4.8 wt%, based on the limited burn-up of60 MWD/kg according to South Korean regulation. In addition, thebreak-even point between BeOeUO2 fuel and UO2 fuel as a functionof the burn-up was 4.4 mills/kWh when the burn-up was about60 MWD/kg. Therefore, BeOeUO2 fuel with BeO content of 4.8 wt%might have economic merit when the burn-up is more than 60MWD/kg. However, if the price gap between the Be material anduranium increases, the economic benefit of BeOeUO2 fuel will

S.K. Kim et al. / Progress in Nuclear Energy 52 (2010) 813e821 821

decrease. Thus, the fuel cycle cost of BeOeUO2 fuel needs to beestimated periodically because the current price of Be material isunstable, and its cost will increase in the future because of therising demand from the communication industry. In addition,periodic research related to the unit cost in terms of the nuclear fuelcycle cost is needed.

The confidence level of cost estimation results for the nuclearfuel cycle cost depends heavily on the accuracy of the unit cost ofthe nuclear fuel cycle. It is necessary for better understanding of thenuclear fuel cycle cost.

Acknowledgement

This work was supported financially by Ministry of Education,Science and Technology under theMid-and Long TermNuclear R&DProject. Authors would like to express their gratitude for itssupport.

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