Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569 

224 RESD © 2015 
http://apc.aast.edu 

 

 
 

 

Economical Feedback of Increasing Fuel Enrichment on 

Electricity Cost for VVER-1000 
Dwiddar,M. S1., Badawi, A1. A., Abou-Gabal, H. H1. El-Osery, I. A.2, Badawy, M. R2, 

1 Faculty of Engineering, Alexandria University 

Alexandria, Egypt.,
 

2Nuclear Power Plants Authority, Nasr City, Cairo, Egypt. 
 

Abstract - A methodology of evaluating the 

economics of the front-end nuclear fuel cycle with a 

price change sensitivity analysis for a VVER-1000 

reactor core as a case study is presented. The effect 

of increasing the fuel enrichment and its 

corresponding reactor cycle length on the energy cost 

is investigated. The enrichment component was found 

to represent the highly expenses dynamic component 

affecting the economics of the front-end fuel cycle. 

Nevertheless, the increase of the fuel enrichment will 

increase the reactor cycle length, which will have a 

positive feedback on the electricity generation cost 

(cent/KWh). A long reactor operation time with a 

cheaper energy cost set the nuclear energy as a 

competitive alternative when compared with other 

energy sources. 

 

Keywords - Front end fuel cycle economics; 

electricity cost; VVER-1000. 

 

NOMENCLATURE – 

 
a: Conversion factor for uranium yellow cake (U3O8) 

AF: Availability Factor 

CL: Cycle length (days) 

Cfab: Cost of fabrication (M$) 

Cen: Cost of enrichment (M$) 

Cconv: Cost of conversion (M$) 

CYC: Cost of yellow cake (M$) 

CTotal: Front-end fuel cycle total cost(M$) 

Celec: Direct electricity generated cost (cent/kWh) 

ef: Fraction of U-235 in the uranium feed 

ep: Fraction of U-235 charged in the reactor 

et: Fraction of U-235 in the tails 

lC: Material losses of uranium conversion process 

lF: Material Losses in fabrication process 

Mcycle: Mass of uranium charged in the reactor  

Mf: Mass of uranium feed to the enrichment process 

Mp: Mass of uranium in the enriched stream 

Mt: Mass of uranium in the tails  

Mconv: Mass of uranium for conversion process 

MYC: Mass of yellow cake 

M$: Million Dollar 

P1: Monetary units per lb U3O8 for uranium purchase 

($/lbU3O8) 

P2: Monetary units per Kg U for fuel conversion ($/kgU) 

P3: Monetary units per SWU for fuel enrichment ($/SWU) 

P4: Monetary units per Kg U for fuel fabrication ($/kgU) 

Qe: Electrical Power (MW) 

Qth: Thermal Power (MW) 

R: average rate of nuclear fuel burn-up (MWd/MTU) 

S: Separative work unit requirements (SWU) 

Vx: Value function - x subscript for f, p or t 
 

I. INTRODUCTION 

 

The economics of nuclear fuel cycle for nuclear 

power plants depends generally on two main issues, 

the nuclear fuel cycle components and the reactor 

core cycle length. The nuclear fuel cycle can be 

divided into three stages: front-end, at-reactor and 

back-end. These, in turn, can be sub-divided into 

more specific components [1].To identify the 

generating electricity costs from a typical nuclear 

power plant, the economics of fuel cycle must be 

clear. Actually, most countries study the economics 

and properties for the first two stages of nuclear fuel 

cycle; front-end and reactor operation time as there is 

no clear long term strategy made for the back-end 

part till now. Moreover the large dependency on 

storage of spent fuels in reactor site increases this 

foggy vision of the nuclear fuel cycle back-end 

strategy. 

 

Over the past decade the discharge irradiation level 

(burn-up) of both Pressurized Water Reactor (PWR) 

and Boiling Water Reactor (BWR) fuels has 

increased steadily. This development is mainly 

attributable to the increased economic benefit that is 

associated with higher fuel burn-up.  

 

This benefit comes from the reduced throughput of 

fuel that results from higher burn-up [2]. In this paper, 

we calculate the generating electricity costs for PWR 

being the most prevalent reactor type in the world as 

it represents 274 of the world’s 436 reactors now 

operating [3]. The calculations are performed 

considering a typical VVER-1000 reactor [4] as a 

case study. 

 

 

 

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II. VVER-1000 GENERATING ELECTRICITY 

COST 

 
A. Front-end Fuel Cycle Cost 

The front-end component is composed of uranium 

purchase, conversion of yellow cake into uranium 

hexafluoride (UF6), enrichment (isotope separation 

process to rise the content of fissile materials, U235, 

in the fuel) and uranium oxide fuel fabrication into 

assemblies. Based on a direct cost analysis for the 

front-end fuel cycle components, the amount and 

price of each component can be defined [1]. Table 1 

gives the magnitude of each front-end component unit 

price [5]. Most fuel contracts are made based on long 

term contracts not on spot prices so the front-end 

components unit prices are taken as average values 

for the past three years. 
 

Table 1. FRONT-END COMPONENTS UNIT PRICES (5) 

 

Component Price* 

Uranium purchase (P1) $45/lbU3O8 

Conversion (P2) $8/KgU 

Enrichment (P3) $120/SWU** 

Fabrication (P4) $260/KgU 

 

* average prices over the past 3 years. 

** SWU: Separative Work Unit 

 

Based on the VVER-1000 reactor core configuration 

and the plant design parameters [4], the amount of 

required fuel charged to the reactor each cycle can 

be calculated using (1) [6]. 

 

Mcycle =
Qth∙ CL

R
         (1) 

Within the context of Dwiddar, M.S., et al.’s previous 

work on the VVER-1000 reactor core and its 

improvements to achieve the new design of VVER-

1200reactor core, MCNP-X code was used to 

calculate the core cycle length and the burn up 

[7].The VVER-1000 validated model showed that for 

a 3000 MWth, the average value of fuel burn-up is 

11800MWd/MTU and the core cycle length is 300 

days [7]. 

 

Using (1) the amount of required fuel is 76.2 tons of 

uranium. The value of burn-up is assumed to be an 

average value for the whole core for one cycle length 

time. The reactor core consists of three batches and 

only one batch will be replaced each cycle. 

Therefore, the output of (1) will be divided by 3 as it 

will be 76.2/3 = 25.4 tons of uranium, which 

represents the amount of required fuel for each cycle 

length. Going backwards through the front-end 

components, this amount of uranium represents the 

output of fabrication stage. 

 

The mass of uranium, Mp, required for the fabrication 

is slightly more than the mass of UO2in the core, 

Mcycle, due to fabrication losses. To calculate the 

amount needed for the fabrication stage, the 

occurring losses must be considered. The loss factor 

of fabrication stage is 1.0% [1]. Thus applying (2) [1], 

a value of 25.65 tons is obtained for Mp. 

 

Mp = Mcycle ∙ (1 + lF)          (2) 

Using (3) [1] the cost of this amount is calculated 

based on the price value in table 1, and is found to be 

equal to 6.669 M$. 

 

CFab = Mp ∙ P4          (3) 

 

Moving to the enrichment stage, to calculate the 

amount of uranium required for the enrichment 

process, both the enriched and depleted assays (ep 

& et) must be well known. The fuel enrichment batch 

charged for the VVER-1000 case study is 3.3% – 

which will be refueled to the reactor core each cycle – 

so the enriched assay output for the enrichment 

process is 3.3%. The depleted assay is assumed to 

be 0.25% which is the prevalent value for the 

enrichment process in Russia. According to (4) [1] the 

feed material for the enrichment process is calculated 

and a value of 169701.73 Kg U is obtained. Equation 

(5) [1] gives the amount of depleted uranium from this 

specific enrichment process and it is equal to 

144051.73 Kg U. 

 

Mf = [
ep−et

ef−et
] ∙ Mp          (4) 

 

 

Mt = Mf − Mp         (5) 

 

Since the price of enrichment services is expressed 

per separative work unit (SWU), the quantity of 

SWUs necessary to obtain the enriched uranium 

quantity (Mp) at the required enrichment level (3.3%) 

must be calculated. This quantity can be estimated 

depending on the 'value' of a mixture (V) which is 

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Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569 

226 RESD © 2015 
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estimated on equation (6) as a function of the U235 

content. Equation (7) [1] gives the SWU required for 

this specific enrichment process. According to (7), the 

separative work need for this process is equal to 

113289 SWU. 

 

Vx = (2 ∙ ex − 1) ∙ ln [
ex

1−ex
]         (6) 

 

S = Mp ∙ Vp + Mt ∙ Vt − Mf ∙ Vf        (7) 

 

Thus, the cost of enrichment is calculated using (8) 

[1] and is found to be equal to 13.7M$. 

 

Cen = S ∙ P3 ∙  (1 +  lF)         (8) 
 

Moving to the conversion stage, the amount of 

uranium required is calculated using (9) [1]. This 

amount is equal to 170550.24Kg U considering the 

loss factor of conversion stage to be 0.5% [1]. 

According to the calculated uranium amount and 

using (10) [1] the cost of conversion process is 

calculated to be 1.364 M$. 

 

Mconv = Mf ∙ (1 + lC)          (9) 

 

Cconv = Mconv ∙ P2        (10) 
 

Finally, the amount and cost of yellow cake to be 

purchased for starting the nuclear fuel cycle 

processes have to be calculated. Equations (11) and 

(12) [1] give the amount and the cost respectively. 

The amount of yellow cake is equal to 443430.63 lb 

and the cost is 19.95 M$. 

 

MYC  = Mconv ∙ a        (11) 

 

CYC = MYC ∙ P1         (12) 
 

Fig. 1 summarizes the actual annual front-end fuel 

cycle requirements for the VVER-1000 case study. 

The total front-end fuel cost is the sum of all its 

components cost. Equation (13) [1] gives the total 

cost which is equal to 41.69 M$. 

 

CTotal = CYC + Cconv +  Cen + CFab     (13)

 
Fig .1. Annual VVER-1000 front-end fuel cycle requirements 

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Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569 

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From the calculated front-end fuel cycle total cost and 

considering a plant’s availability factor of 82%, (14) 

estimates the direct fuel cost for the unit electricity 

generation to be 0.7047 cent/kWh. This value 

represents the direct electricity generation cost 

according to the front-end fuel cycle economics. 

 

Celec =  
CTotal

Qe ∙ CL ∙ AF ∙ 24
 ×

100 (Cent/$)

1000 (kWh/MWh)
              (14) 

 

B. Price Sensitivity Analysis 

A sensitivity analysis has been carried out with 

respect to the unit prices for the front-end fuel cycle 

components. The sensitivity range for front-end 

service prices generally reflects the upper and lower 

bound values seen from the extrapolation of 

component spot prices in international market [1]. 

The values used for the sensitivity analysis are 

shown in table 2. 
 

Table 2. SENSITIVITY RANGE FOR THE FRONT-END COMPONENT UNIT 

PRICES 

Component Price sensitivity range* 

Uranium purchase 22.5-90 $/lb U 

Conversion 3.75-15 $/Kg U 

Enrichment $60-240 $/SWU 

Fabrication 130-520 $/Kg U 

 

Fig. 2 gives the results of the front end fuel cycle 

components prices sensitivity analysis applied on the 

direct electricity cost. It is clear that although the 

uranium purchase is the highly significant component, 

enrichment cost is the most effective because it is the 

dynamic process that affects all other components. 

So it may be deduced that the enrichment cost forms 

a significant component of the front-end fuel cycle 

costs. 
 

 
 

Fig .2. Effect of front end fuel cycle components price 

change on electricity direct costs 
 

C. Effects of Increasing Enrichment and Core Cycle 

Length 
 

For increasing the reactor core cycle length, it is 

required to increase the fissile material content in the 

reactor core. This will affect the economics of fuel 

cycle components. From international practice, the 

maximum allowable enrichment for PWRs is 5%. For 

saving the design basis parameters for the VVER-

1000 case study, the minimum enrichment batch of 

VVER-1000 model is increased by a step of 0.1. The 

enrichments of the other batches are also increased 

keeping the same ratio of enrichment between the 

three batches as in the reference case. According to 

this assumption, the maximum enrichment calculated 

is 4.95 %. [7] Table 3 gives all probable 

improvements of fuel batches enrichment within the 

maximum allowable value with the corresponding 

reactor cycle length and core average burn up. The 

reactor cycle length and the core average burn up are 

out data from the MCNP-X code [7]. 

 
Table 3. CHANGES CONSIDERED IN THE ENRICHMENT OF THE FUEL BATCHES [7] 

 

Cases 
Enrichment of Fuel Batches 

Cycle length (days) 
Average burnup (MWd/ 

MTU) 
Batch 1 Batch 2 Batch3 

A (Ref. Case) 2 3 3.3 300 11800 

B 2.1 3.15 3.465 336 13213 

C 2.2 3.3 3.63 372 14626 

D 2.3 3.45 3.795 408 16039 

E 2.4 3.6 3.96 444 17452 

F 2.5 3.75 4.125 480 18865 

G 2.6 3.9 4.29 516 20278 

H 2.7 4.05 4.455 552 21691 

I 2.8 4.2 4.62 588 23104 

J 2.9 4.35 4.785 624 24517 

K (Max. Enrich.) 3.0 4.5 4.95 660 25930 

 

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110
0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

variation from reference % 

C
o

s
ts

 (
$

/k
W

h
)

Uranium purchaseUranium purchase

EnrichmentEnrichment

FabricationFabrication

ConversionConversion

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Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569 

228 RESD © 2015 
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According to the output data given in table 3, Fig. 3 

shows that the fuel burn-up is directly proportional to 

the core cycle length. 

 

 
 

Fig .3. Relation between core cycle length and fuel burn-up 

 

Similarly to case A already considered in section A, 

(1) to (14) were used to calculate the front end fuel 

cycle economics and its effect on the electricity 

generation cost for the other cases. 

 

Calculating the fuel mass required each cycle for the 

different cases results in a constant value as shown 

in Fig. 4. This can be explained by the proportionality 

relation obtained between the core cycle length and 

the fuel burn-up. As (2) and (3) do not depend on the 

enrichment percentage, this constant value of fuel 

mass required each cycle will be reflected in a 

constant value for both the required mass for the 

fabrication stage and its cost, namely 25.65 tons and 

6.669 M$ respectively. 

 

 
 

Fig .4 Fuel mass required each cycle for the different 
cases in table 3 

 

However as fuel enrichment increases, the feed 

material will increase. Consequently the enrichment 

cost will increase due to the need for more separative 

work units as seen in Fig. 5. Fig. 6 shows that the 

cost of enrichment process is directly proportional to 

the mass of uranium feed. 

 

 
 

Fig .5 Amount of required SWU for different fuel 
enrichments 

 

 
 

Fig .6 Enrichment process cost versus the mass of 
uranium feed 

 

The increase in the uranium feed to the enrichment 

process leads to the need for more uranium for both 

the conversion and the uranium purchase 

components resulting in an increase in their costs as 

illustrated in Figs. 7 and 8. 

 

 
 

Fig .7 Conversion costs versus the mass of uranium 

250 300 350 400 450 500 550 600 650 700
10000

12000

14000

16000

18000

20000

22000

24000

26000

28000

Reactor core cycle length (days)

A
v
e
ra

g
e
 c

o
re

 b
u

rn
-u

p
 (

M
W

d
/M

T
U

) 

300 330 360 390 420 450 480 510 540 570 600 630 660
20

21

22

23

24

25

26

27

28

29

30

Cycle Length (Days)  

F
u

e
l 

M
a
s
s
 (

T
o

n
e
s
)

3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5

120000

135000

150000

165000

180000

195000

210000

Enrichment  

S
W

U

160000 182000 204000 226000 248000 270000
1.200x10

7

1.400x10
7

1.600x10
7

1.800x10
7

2.000x10
7

2.200x10
7

2.400x10
7

2.600x10
7

Mass of uranium feed (Kg)

E
n

ri
c
h

m
e
n

t 
C

o
s
ts

 (
$
/k

W
h

)

170000 190000 210000 230000 250000 270000
1.300x10

6

1.400x10
6

1.500x10
6

1.600x10
6

1.700x10
6

1.800x10
6

1.900x10
6

2.000x10
6

2.100x10
6

2.200x10
6

Uranium mass (Kg)  

C
o

n
v
e
rs

io
n

 C
o

s
ts

 (
$
)

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Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569 

229 RESD © 2015 
http://apc.aast.edu 

 

 
 

 
 

Fig .8 Uranium purchase costs versus the mass of 
uranium 

 

As a consequence of the increase in the costs of the 

uranium enrichment, the conversion and the uranium 

purchase components, the total cost of the front end 

fuel cycle will increase. But since the increase in the 

uranium enrichment will lead to longer reactor core 

cycle length due to the higher fuel burn-up, the 

resulting electricity cost decreases as shown in Fig. 

9. 

 

 
 

Fig .9 Direct electricity cost versus total front-end cost 
 

III.   CONCLUSION 

 

The effect of increasing the nuclear fuel enrichment 

on the electricity cost has been considered. A typical 

VVER-1000 reactor has been selected as the case 

study. The fuel enrichment has been increased up to 

5% which is the maximum allowable value for PWRs. 

Excluding the fabrication component, increasing fuel 

enrichment was found to increase the uranium 

masses needed for all the front-end components and 

consequently their costs. 

 

A sensitivity analysis was performed with respect to 

the unit prices for the front-end fuel cycle components 

and their effects on the electricity direct cost. It was 

noticed that although the uranium purchase is the 

most effective component, the uranium enrichment 

still has the highly priority effect due to its dynamic 

properties and its consequences on the other front-

end fuel cycle components. Although increasing the 

fuel enrichment resulted in a higher total cost of the 

front end fuel cycle, it was found to extend the reactor 

core cycle allowing the reactor to operate for more 

than 12 months. This fact results in a decrease in the 

electricity generation cost.  

Therefore, increasing the nuclear fuel enrichment 

within the limit allowable internationally for the PWRs 

will have a positive economic feedback leading to a 

cheaper electricity cost. This makes the nuclear 

energy a strong competitor to the other energy 

sources 
 

REFERENCES 

 
[1] Nuclear Energy Agency, The economical on 

nuclear fuel cycle (1994) , Organization for 

economic co-operation and development, Paris, 

France. 

 

[2] Christopher S. (June 1998)  Economic and Fuel 

Performance Analysis of Extended Operating 

Cycles in Existing Light Water Reactors (LWRs), 

Handwork, Massachusetts Institute of 

Technology, 

 

[3] PRIS, IAEA,( August 2014) Power Reactor 

Information System.  

www.iaea.org/PRIS/WorldStatistics/Operational 

ReactorByTupe.aspx 

 

[4] IAEA, (November 1995) In-core fuel 

management code package validation for 

WWERs. IAEA-TECDOC-847. 

 

[5] The Ux Consulting Company (August 2014). 

www.uxc.com/review/UxCProces.aspx 

 

[6] Cacuci, D. G. (2010) Handbook of Nuclear 

Engineering, Institute for Nuclear Technology 

and Reactor Safety. KarlsruherInstitut fur 

Technologie, Germany. 

 

[7] Dwiddar, M. S. (May 2014) From VVER-1000 to 

VVER-1200: investigation of the effect of the 

changes in core. The third international 

conference on physics and technology of 

reactors and applications, Tetuan, Morocco. 

400000 450000 500000 550000 600000 650000 700000

1.800x10
7

2.000x10
7

2.200x10
7

2.400x10
7

2.600x10
7

2.800x10
7

3.000x10
7

3.200x10
7

Yellow cake mass (Ib)

U
ra

n
iu

m
 p

u
rc

h
a
s
e
 C

o
s
ts

4.100x107 4.600x107 5.100x107 5.600x107 6.100x107 6.600x107
0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

Front-end fuel cycle total costs ($)

E
le

c
tr

ic
it

y
 p

ri
c
e
 (

c
e

n
t/

k
W

h
)

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http://www.iaea.org/PRIS/WorldStatistics/Operational%20ReactorByTupe.aspx
http://www.iaea.org/PRIS/WorldStatistics/Operational%20ReactorByTupe.aspx
http://www.uxc.com/review/UxCProces.aspx