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EMH
11,2

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Uncertainty associated with
radioactive waste chacteristics
Branko Kontic and Matjaz Ravnik

118
Submitted 3 April 1999
Accepted 21 June 1999

Jozef Stefan Institute, Slovenia

Peter Stegnar
International Atomic Energy Agency, Austria, and


Burton C. Kross
CIREH-Center for International Rural and Environmental Health,
The University of Iowa, USA
Keywords Policy making, Uncertainty, Environmental management strategy,
Radioactive environment, Waste disposal
Abstract To clarify uncertainty in predictions of the quantity, radionuclide inventory and
activity of waste from the Krsko nuclear power plant, and to illuminate its role in related policymaking, we made a scenario analysis in order to find out the variation in waste characteristics if
the plant operates five years shorter or longer than anticipated, or if it uses fuel of a higher
enrichment (levels between 3 per cent and 5 per cent of U-235). We used ORIGEN2 computer
code for calculations connected to spent fuel, and developed a code for calculating low- and
intermediate-level waste. We present and interpret our results using language which can be
understood by decision makers and the general public. We believe that the clarification of the
issues gained through our analysis will contribute to more informed decision making and be
effective in building confidence among professionals, the public and politicians in the process of
identifying the most appropriate waste management options.

Environmental Management and
Health, Vol. 11 No. 2, 2000,
pp. 118-132. # MCB University

Press, 0956-6163

Introduction
Slovenia has a single nuclear power plant of 632MW electric power at Krsko. It
is a pressurised water reactor using Westinghouse technology. The plant was
built in 1981 and is the main source of radioactive waste in the country. The
other producers are a research reactor at the Jozef Stefan Institute (250kW
TRIGA type), the uranium mine and mill at Zirovski vrh, and various sources
in industry, research and medicine.
At present, there is no disposal facility for radioactive waste in the country.
An attempt to acquire a disposal site in the early 1990s failed in 1993 due to
public opposition. An atmosphere of mistrust appeared afterwards between the
project heads and the public, as well as certain professionals. The site-selection
process, which did not include broader environmental interests and concerns,
and was without active public participation, came under strong criticism.
Information about waste characteristics, especially the quantities and activity
of different categories of waste, was not provided in a consistent manner
during the process. Moreover, the interpretation of uncertainty associated with
the predictions, including dose and risk evaluation for the anticipated
repository, was not clear or was biased.


The Slovene Agency for Radwaste Management (Agency RAO) began
creating a new strategy for radioactive waste management in 1998. The
strategy focuses on low- and intermediate-level waste disposal due to the
urgency of the issue of the low remaining capacities for intermediate storage
for operational waste at the Krsko NPP; however, high-level waste is also given
consideration in this strategic planning. The following two elements of the
strategy are at the forefront: selection of the disposal concept (shallow land
burial or deep geological disposal); and a site-selection process for the
repository, with its overall approval (by the regulators, the public, scientists
and others).
A plan for the replacement of the steam generators at Krsko NPP in 2002
has, again, mobilised the Green movement in Slovenia to launch criticisms of
nuclear energy. The criticism is accompanied by requirements for the
immediate shutdown of the plant. Generally, the critics justify their claims with
the problem of radioactive waste disposal. Specifically, they attack the
uncertainty (inaccuracy) associated with predictions of the waste inventory, the
poor validity of safety evaluations for repositories for the distant future (more
than 102 years), and unresolved ethical issues appearing in regulatory decisionmaking in the presence of uncertainty (IAEA, 1994; 1997).
In this situation, which places the greatest burden on regulators and other

decision makers, it is of the utmost importance that approvals (permits) coming
from the licensing process, and their justification, are understandable and
transparent. Evaluations of the repository's performance, of safety and of the
environmental and health consequences must be explicit, credible and
tractable, i.e. they need to be systematically documented so that they can be
subjected to review and verification. A scientific approach is therefore
inevitable. Our analysis has been done in this particular context.
It is also important to note that the analysis which we performed is part of
broader research work associated with uncertainties in long-term predictions
within the framework of the EIA (Environmental Impact Assessment). In this
research, we investigated different sources of uncertainty in the methodology
of drawing up an EIA, focusing on the uncertainty of expert opinion (Kontic
and Kross, 1999). The case study we used was radioactive waste disposal in
Slovenia. We discovered that dose and risk assessments, as health impact
indicators, may be so uncertain in distant-future evaluations (thousands of
years) that they are not appropriate as numerical indicators/criteria in the
process of siting radioactive waste repositories. Based on this, we suggested a
different approach in identifying and justifying the appropriateness of a site for
the repository. The new approach builds on the identification of potentials in
the environment, interpreting them in the form of multiple land-use indicators.

A paper which describes this approach is under review for publication (Kontic
et al., 1999).

Radioactive
waste
characteristics
119

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120

Approach to the analysis
The main purpose of the analysis, as we have already indicated, was to clarify
the issues raised by the Green movement, particularly the issue of uncertainty
associated with the quantity of radioactive waste produced by Krsko NPP in its
anticipated operational time, the radionuclide inventory of the waste, its
activity, and changes in these waste characteristics due to the increased power
and extended operational period of the plant after the replacement of the steam

generators in 2002. We evaluate the relevance of these changes in terms of their
influence on the waste-disposal strategy, particularly the selection of the
disposal option, i.e. repository type. The dilemma is whether to build a shallow
land repository for the LILW and to treat all high-level and long-lived waste
separately; or to adopt deep geological disposal as an option for all waste types
produced in the country. Tightly connected to these questions is the credibility
of the evaluation of health consequences due to radioactive waste disposal with
indicators such as dose and risk in the presence of uncertainty associated with
the waste characteristics on the one hand, and societal characteristics and
human habits in the distant future on the other.
The approach and methods applied in the analyses were as follows:
.
First, information about the present status of the waste was gathered.
The attention was on the variability and accuracy of data on quantity,
the radionuclide inventory and the activity of different types of waste.
.
Then, based on this information, a best estimate in terms of what we
may expect (with regard with these waste characteristics) by the end of
the anticipated operational period of Krsko NPP, i.e. 2023 was
performed. The ORIGEN2 computer code was used for calculating

isotope generation, activity build-up and depletion, and the decay heat of
spent fuel (Croff, 1983; ORNL, 1987), while a specific code was developed
for calculations associated with LILW. This code calculates the activity
of the optional mixture of 88 radionuclides which are expected in LILW.
Verification of the code was carried out based on the QA/QC procedure
for scientific software qualification at the Jozef Stefan Institute. Using
the results of these estimates as a basis, extended calculations for a
period of one million years was done. The purpose of this calculation
was to identify and clearly present the longevity of certain waste
categories.
.
Given the concerns of decision-makers, as well as the criticisms
expressed by the Green movement, the interpretation of the results of
these predictions in a way which is useful for policy-making gained
importance. In this sense, the specific activity of the LILW (Becqurels
per m3 of waste) and its time changes were identified as the main
parameters and the basis for the selection of the waste disposal option
for this waste category. This was in accordance with the national
regulation (Official Gazette, 1986) on radioactive waste categorisation,
which implicitly and generally predefines the waste-disposal options for


.

a certain category, is based on this parameter. In this way, i.e. by
knowing the time evolution of the specific activity of the LILW, it is
possible to clearly determine the ``lifetime'' of this waste. Based on this
transparent approach, a more reliable process of selection of a disposal
option can be achieved.
With regard to spent fuel, the total activity, its time changes and the
identification of radionuclides, which mainly contribute to the activity in
long timeframes, were used instead of a specific activity as key
information for discussing waste-disposal options for this waste
category. Changes (variations, uncertainty) in these characteristics were
evaluated based on technical specifications which will be in place after
the replacement of steam generators at the plant in the 17th fuel cycle in
2002. The variations considered were 3-5 per cent of U-235 in the fuel,
and an operational period of the plant of five years more or five years
less than that envisaged. The basic estimate was that Krsko NPP uses
fuel with 4 per cent U-235 in all future cycles and that it operates for 35
years.


Results
Sources and quantities of radioactive waste in Slovenia ± the present status
Low- and intermediate-level waste. The main producer of nuclear waste is Krsko
NPP. Approximately 2000m3 of this waste was stored at Krsko NPP at the end
of 1998, mainly in 210-litre standard steel drums with a total activity of around
67TBq (NPP Krsko, 1999; Biurrun et al., 1998). Based on gamma spectrometric
analyses, and the information available in the updated safety analysis report
(USAR, 1996), the following radionuclides are seen to contribute up to 90 per
cent of total beta-gamma activity: Co-58, Co-60, Cs-134 and Cs-137. The total
activity of alpha emitters is about 0.2 per cent of total beta-gamma activity
(NPP Krsko, 1999).
Other users of radioactive materials (medicine, industry and research
institutions) produce minor amounts of LILW. The total amount of this waste is
about 50m3 (SNSA, 1998) with an activity of 5.6TBq. The waste is stored in a
central temporary facility located at the reactor centre of the Jozef Stefan
Institute. No considerable change in the origin and type of these wastes is
expected in the future.
The uranium mine and mill at Zirovski vrh are in the process of being shut
down after less than six years in operation (the reasons for closure are

economic). A total of 670,000 tonnes of ore-processing waste, with a content of
about 5TBq Ra-226, and a certain amount of Th-230, as well as other
radionuclides and chemical pollutants (ammonia, sulphate, amines, etc.), was
produced and disposed of at the site of the mine. This waste will most likely
remain at existing disposal locations.
High-level waste (HLW). HLW is expected from Krsko NPP either in the form
of spent fuel, which will not be reprocessed, or as residues after reprocessing.
Reprocessing is not feasible in Slovenia. However, about 560 tonnes of spent

Radioactive
waste
characteristics
121

EMH
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122

fuel (after 35 operational fuel cycles at Krsko NPP) are expected to be

reprocessed, or will become waste without reprocessing. At the moment, spent
fuel (after 14 fuel cycles) is stored in the spent fuel pit (pool) at the plant.
Predictions
Low- and intermediate-level waste. Predictions are based on data collected since
1981 by Krsko NPP, the Jozef Stefan Institute, the Slovene Nuclear Safety
Administration, and the RAO Agency (USAR, 1996; SNSA, 1995; 1996; 1997;
1998; ARAO, 1998; IBE, 1997; IJS, 1998).
So far, the only prediction of the quantity and activity of LILW at Krsko
NPP was made by Westinghouse (FSAR, 1981). However, these predictions are
rather obsolete. They were a general picture of the total solid waste generated
per year and the maximum expected concentrations of selected radionuclides in
the waste. For comparative purposes, information about total annual solid
radioactive waste processed in four other Westinghouse-designed operating
reactors is also given in the final safety analysis report. The latest revision of
the updated safety analysis report still includes the same information (USAR,
1996).
Recent data show that the quantity of different types of LILW at Krsko NPP
may vary within two orders of magnitude in a single operational year (ARAO,
1998).
Based on the information presented above, the best estimate of the specific
activity (Bq/m3) of selected radionuclides in the annual amount of each type of
waste was made (see Table I). This was the input data for the evaluation of the
quantity and activity of the waste which would be collected by 2023, and for
the calculation of changes in the activity during later periods. Estimates are
based on measurement data (monitoring and control of the packed waste).
Uncertainty in the measured data for LILW was estimated to be up to 12 per
cent (SNSA 1995; NPP Krsko, 1997; IJS, 1996). The specific activity, as already
mentioned, was selected as the calculation parameter because it is used as a
basis for waste categorisation by Slovene regulations (Official Gazette, 1986). In
this way, the calculation of changes in specific activity over time provides a
direct answer to the question as to when activity will drop below the prescribed
Specific activity of selected radionuclides in the waste collected in one year (Bq/m3)
Waste type
Co-58
Co-60
Cs-134
Cs-137

Table I.
Specific activity of
selected radionuclides
in LILW of the NPP
Krsko (best estimate)

SR
CW
EB
F
O

2.3*1011
1.9*108
1.4*109
1.8*1011
3.9*107

2.7*1010
2.3*108
1.7*108
2.1E10
2.5*108

9.5*1010
8.6*106
5.8*108
7.4*1010
6.2*107

1.4*1011
2.3*107
8.5*108
1.1*1011
1.9*108

Notes: SR ± spent resins; CW ± compressible waste; EB ± evaporator bottom; F ± filters;
O ± other waste

level. With conservative estimates, the adopted variability (uncertainty) in the
assessed specific activity of LILW at the end of the operational period of the
plant was within a factor of 10. This estimation was used as an input for
identifying the difference in the time period which is needed for the activity to
drop below the prescribed level (see Figure 1).
According to the model, the total activity of all LILW will drop below the
required level of 1*102 MBq per m3 (Slovene legislation) in 341 years. This time
period is determined primarily by the content of Cs-137 in spent resins (SR);
other radionuclides have shorter half-lives and diminish earlier. In the event
that the initial activity of the SR is ten times higher or lower (variation within a
factor of ten), changes in this period are presented in Figure 1, as stated above.
It is seen that the changes are about a hundred years, i.e. approximately 30 per
cent compared to the basic prediction.
The anticipated decommissioned waste was evaluated separately. Emphasis
in these evaluations was placed upon the content of long-lived radionuclides in
the waste. The reactor vessel and steam generators are of primary importance
in this sense. The evaluated total activity of long-lived radionuclides in 2023 is
summarised in Table II.
Spent fuel. The key input data for calculations associated with spent fuel,
especially burn-up and fuel characteristics in future cycles, are not available at
the moment. Consequently, certain assumptions had to be made. These are
presented in more detail in the Appendix.
The calculated time changes of the activity of activation products (AP),
actinides (ACT), fission products (FP) and total activity per fuel batch are
presented in Figure 2. The illustration is for model Batch 6; however, the

Radioactive
waste
characteristics
123

1.00E+07
Basic Assumptions (BP)

1.00E+06

Specific activity (MBq/m3)

BP/10
BP* 10

1.00E+05

1.00E+04

1.00E+03

1.00E+02

1.00E+01
215years

1.00E+00

0

50

100

150

200

250
300
Time (years)

316years

350

417years

400

450

500

Figure 1.
Change in time period
when the activity drops
below the prescribed
level due to uncertainty
in input data

EMH
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124

figures are similar for other model batches. Batch 6 goes into the reactor in the
fourth cycle (year). At the moment of irradiation, the total activity immediately
increases to about eight orders of magnitude. Before that, the activity is
constant at a level of 1.9*106 MBq (the activity of approximately 16 tonnes of
non-irradiated fuel). During irradiation, this activity rises slightly from 1.23 to
1.28*1014 MBq, while during the cooling period of 45 days it drops to
approximately two orders of magnitude. Each batch stays in the reactor for
three successive cycles (except the first, the second, the penultimate and the last
± see Appendix for details), whereupon the batch goes into the spent fuel pit for
ultimate cooling and decay. This can be seen in Figure 2. It should be noted that
the scale of both axes is logarithmic, which is also the reason that zeroes, i.e. the
origins of axes, are avoided in the illustrations.
Model results for all fuel are presented in Figure 3, which shows time
changes in total activity. With regard to activity during first 34 cycles, an
almost linear increase can be identified due to the collection of spent fuel in the
spent fuel pit ± one batch per cycle/year. After the 35th cycle, i.e. at the end of
the assumed operation of the plant, all three batches from the reactor are placed

Isotope

Half-life (years)

Total activity (Bq)

C-14
Ni-59
Ni-63
Mo-93
Nb-94

5,730
75,000
96
3,500
20,300

8.1*1012
4.4*1013
6.6*1015
2.1*1010
2.6*1011

Table II.
Anticipated total
activity of selected
long-lived radionuclides
Note: anticipated volume of these wastes is 200m3
in LILW (IBE, 1997)

Figure 2.
Activity of model batch
6 over a million years

Radioactive
waste
characteristics
125
Figure 3.
Total activity of all the
spent fuel

into the spent fuel pit at the same time, which is seen as an intermittent increase
in activity. Afterwards, activity decreases depending on the radionuclides
contained in the spent fuel. Note again that the scale of the axes is logarithmic.
The values of total activity and decay heat for all spent fuel at selected timepoints are summarised in Table III.
These results were obtained based on the assumptions presented in the
Appendix. The model adequately represents the overall operation of the plant.
This was proved in the process of calibrating the model, where data for the past
13 cycles were used for comparison. However, fuel enrichment, as well as other
key operational elements in future cycles, may not remain constant, since an
Time (years)

Total activity (MBq)

Decay heat (W)

1
2
3
4
5
10
15
20
25
30
35
75
100
300
1,000
10,000
100,000
300,000
1,000,000

5.30*1012
6.72*1012
7.92*1012
8.70*1012
9.23*1012
1.09*1013
1.21*1013
1.31*1013
1.40*1013
1.48*1013
2.69*1013
2.63*1012
1.46*1012
1.08*1011
4.11*1010
1.04*1010
1.28*109
8.12*108
4.81*108

5.55*105
7.19*105
8.71*105
9.54*105
1.01*106
1.13*106
1.22*106
1.31*106
1.38*106
1.45*106
2.72*106
3.08*105
2.23*105
8.44*104
3.52*104
8.23*103
6.82*102
3.80*102
2.53*102

Table III.
Total activity and
decay heat of all the
fuel from the Krsko
NPP at selected timepoints over a million
years

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126

Figure 4.
Influence of fuel
enrichment on activity
of actinides (it is
assumed that the change
in fuel enrichment starts
with the 17th cycle)

Figure 5.
Influence of extended or
shortened operation of
the Krsko plant on the
activity of actinides in
the complete spent fuel
(basic estimate is that
the plant will operate 35
cycles)

upgrade of the plant's power is anticipated in parallel with the replacement of
the steam generators. Extension of the fuel cycles is also anticipated. This was
the reason for the analysis of the changes in the activity and radionuclide
inventory of spent fuel due to different fuel enrichment and the prolonged
operation of the plant. The adopted variation in fuel enrichment was 1 per cent
above and below the value presently applied, i.e. 4 per cent of U-235. With
regard to the prolonged operation of the plant, a five-year variation was
applied. All the variations were simulated for the period following the
replacement of the steam generators, i.e. after the 17th cycle. The differences
are presented in Figures 4 and 5 respectively. It is clear that the differences are
so small that they can be neglected, since they are of no relevance for the overall
waste management strategy. Moreover, the conclusion which can be drawn
from this result is that no benefit can be expected in terms of improved safety
connected with radioactive waste disposal if Krsko NPP were closed down
immediately or operated for almost a further 25 years.

Summary of results and a discussion of the radioactive waste
management strategy
The results of the modelling show that the main contributors to fuel activity
during the period approximately 200 years after irradiation are the fission
products; after that, actinides will prevail. The total expected activity of the
spent fuel after one million years is 4,8*1014 Bq. The main contributors to this
activity are the radionuclides of U- and Np-chains. Residual thermal power is
about 1.0*105 W approximately 200 years after irradiation, about 1.0*104 W
after 10,000 years, and about 250 W after one million years.
The results of the calculations for LILW show that the most important type
in this waste category at Krsko NPP is spent resins. The critical radionuclide in
this waste is Cs-137 with a half-life of approximately 30 years. According to
calculations, the activity of this waste will drop below the level prescribed by
Slovene regulations after approximately 340 years.
With regard to other LILW in Slovenia (interim storage at the Jozef Stefan
Institute, for radioactive waste from the users other than Krsko NPP) and
decommissioned waste from Krsko NPP (e.g. the reactor vessel), an important
characteristic which should be taken into account when designing radwaste
management is the content of long-lived radionuclides, such as Ra-226 (half-life
of 1,620 years) or Ni-59 (half-life of 75,000 years). According to the modelling
results, one must wait 830,000 years before the specific activity of the reactor
vessel from Krsko NPP drops below the required level, and around 25,000 years
for the radium-contaminated waste stored at the Jozef Stefan Institute. This
would indicate that the longevity of the waste (content of long-lived
radionuclides) is one of the key characteristics in terms of establishing a
strategy for radwaste management.
The strategy being prepared by the RAO Agency focuses on the
determination of the type of the final repository ± shallow land burial or deep
geological disposal ± as well as on the repository site-selection process with its
overall approval (by the regulators, the public, scientists and others).
According to the results of the calculations performed, and the poor possibility
of accurately predicting biosphere states and societal characteristics in the
distant future, which are at the same time inevitable for dose assessments, the
following remains for consideration:
.
Disposal. Deep geological disposal offers more confidence in waste
isolation for longer periods of time and from the perspective of potential
human contact with disposed waste in the future. Such repositories
should, therefore, accept primarily long-lived, intermediate and highlevel waste. In Slovenia, it is expected that this will be decommissioned
waste (reactor vessel, steam generators) and spent fuel from Krsko NPP.
.
Burial. Shallow land burial should be a disposal method only for shortlived LILW. This is justifiable from the perspective that the safety of
such a waste repository cannot be accurately evaluated (or ensured) for
longer periods due to uncertainties connected with the future use of the

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characteristics
127

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128

.

.

environment and human habits. Since human habits form the basis for
exposure and dose assessment, this indicator does not seem to be
appropriate for interpreting safety in the distant future due to associated
uncertainty. Recent evaluations in connection with this suggest that
even within timeframes shorter than 102 years, predictions of safety
regarding radioactive waste repositories are uncertain (IAEA, 1994;
Bragg, 1996; Kontic and Ravnik, 1998). For longer periods, safety
evaluations in terms of the repository's performance assessment should
not even be called predictions, but rather illustrations and/or hypotheses
only (IAEA, 1997).
Geological repository. Since it is difficult to believe that there could be
two repositories built in Slovenia (due to insufficient territory and strong
public opposition), it seems reasonable to plan only a deep geological
repository. On the other hand, the siting and the construction period will
probably last longer for such a repository than for shallow land
disposal. This fact may cause Krsko NPP to stop its operation earlier
because there will be neither more interim storage capacities nor a final
disposal site. In this situation, a kind of intermediate solution is
necessary which would enable the safe storage of operational waste
from Krsko NPP. The strategy should envisage this as well.
Confidence building. With regard to confidence-building connected to
radioactive waste disposal, we strongly recommend the prompt, clear
and complete informing of all interested parties and the general public.
It should be clearly stated that the spent fuel from Krsko NPP, and a part
of the decommissioned waste, will remain radioactive above today's
prescribed levels for hundreds, thousands or even a million years from
now. Consequently, a strategy built upon waiting for the activity to
``disappear'' cannot be effective. Doubts and uncertainties regarding
safety assessments in a timeframe of a million years should also be
revealed. At the same time, efforts should be made to present the concept
of reasonable assurance (IAEA, 1997) as the most reliable method, and
as the basis upon which a waste management strategy can rely.

Conclusion
The problem of uncertainty and its influence on the credibility of predictions
upon which regulatory decisions and radwaste management policy ± as a
whole ± are based, were discussed in relation to long-term estimates of the
quantity and activity of radioactive waste. It was recognised that the basic
characteristics of this waste can be accurately predicted, since all the sources of
uncertainty are well defined, understandable and therefore controllable.
Residual uncertainty does not change the overall picture of the waste, which
would mean that the predictions could clearly be used as a basis for policy
making, i.e. creating a strategy for radioactive waste management, decisionmaking and also for communication with the public.

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the licensing process in Slovenia; a discussion from the perspective of the validity of longterm evaluations and in reference to radioactive waste disposal'', (under review for
publication in The Journal of Environmental Assessment Policy and Management)
NPP Krsko (1997), A Report on Packed Waste in 1997, No. KM-11/97/8772, Krsko (in Slovene),
available at Krsko NPP and Slovenian Nuclear Safety Administration.
NPP Krsko (1999), A Report on LILW at the Interim Storage Facility at NPP Krsko, No. INZ11/99
(in Slovene), available at Krsko NPP and IJS Krsko.
Official Gazette (1986), National Regulation on Radioactive Waste Categorisation, No. 40/86,
Ljubljana, (available in Slovene).
ORNL (Oak Ridge National Laboratory) (1987), RSIC Computer Code Collection, Origen2 Isotope
Generation and Depletion Code, Radiation Shielding Information Center, Oak Ridge.

Radioactive
waste
characteristics
129

EMH
11,2

130

Ravnik, M. and Zeleznik, N. (1990), Calculation of Radionuclide Inventories of Krsko NPP Fuel
Elements, No. IJS-DP-5851 (in Slovene) available at the Institute Jozef Stefan, Ljubljana and
NPP Krsko.
SNSA (Slovene Nuclear Safety Administration) (1995), A Decree on Required Monitoring at
Krsko NPP, No. 318-35/94-8425/SA (in Slovene), available at the SNSA, Ljubljana.
SNSA (Slovene Nuclear Safety Administration) (1996), A Report on Nuclear and Radiological
Safety in Slovenia in 1995, No. RUJV-RP-022 (in Slovene), available at the SNSA,
Ljubljana.
SNSA (Slovene Nuclear Safety Administration) (1997), A Report on Nuclear and Radiological
Safety in Slovenia in 1996, No. RUJV-RP-024 (in Slovene), available at the SNSA,
Ljubljana.
SNSA (Slovene Nuclear Safety Administration) (1998), A Report on Nuclear and Radiological
Safety in Slovenia in 1997, No. RUJV-RP-026, (in Slovene), available at the SNSA,
Ljubljana.
USAR (Updated Safety Analysis Report for Krsko NPP) (1996), Chapter 11.5 Solid Waste
Processing System, Rev. 3, Westinghouse and Krsko NPP (available at Krsko NPP).

Appendix. Basic assumptions in modelling spent fuel characteristics at Krsko NPP
The basic assumptions for modelling spent fuel characteristics are as follows:
.

35 fuel cycles are assumed for the operational period of Krsko NPP.

.

The average cycle burn-up is 12,000 MWd/tU. >This value was adopted based on the
following: The average number of effective days of full power operation per cycle is 324.
Using 1,876 MW as the nominal power of the plant, and 48.7 t of uranium per cycle, one
obtains 11,857 MWd/tU. When this is rounded off, 12,000 MWd/tU for burn-up and 320
effective days of operation at full power is obtained.

.

A 12-month cycle was assumed (i.e. the cycle lasts 365 days); the operational period is
320 days and the cooling (decay) period between cycles is 45 days (actually used for
refuelling and maintenance).

.

One batch of fuel consists of 40 elements, containing 16.24 tonnes of uranium, and on
average represents one-third of the total amount of fuel in the cycle (there are three
different batches in the reactor during operation). Each batch is in the reactor for three
subsequent cycles, except the first, the second, the penultimate and the last. The real
situation was more complicated but roughly corresponds to these assumptions. Being
aware of the differences between this assumption and the real operational data for Krsko
NPP, a screening calculation of the activity of spent fuel for the first 13 cycles was made,
for the purpose of further calibrating the model. Comparison between the model results
and the results based on more precise operational data (Ravnik and Zeleznik, 1990;
Bozic, 1998) showed very little discrepancy.

.

The content (mass) of uranium isotopes per fuel batch is given in Table AI.

.

The mass of zircaloy (Zr-40) per batch is 4012.5 kg; the mass of oxygen (O-16) is 2183.5 kg.

.

The average power per tonne of uranium is 37.5 MW; the average power of the batch is
609 MW.

Calculations were made for each batch separately during an operation of 35 assumed cycles/
years. Each year the activity and other characteristics were added to specific batches according
to the production of spent fuel. After this period, calculations were performed for all batches (37
batches altogether). The total calculation period was one million years. The selected time points

for the presentations of results are 75; 100; 300; 1,000; 10,000; 100,000; 300,000; and 1 million
years. The approach of the calculation is depicted in Table AII. The notation of the form 1!5
was used to facilitate the presentation, and indicates the sum over the first, second, third, fourth
and fifth batches.

Radioactive
waste
characteristics
131

Batch enrichment (%)

U-234

2.1
2.6
3.1
3.4
3.6
3.9
4.0

2.44
3.25
3.89
4.22
4.55
5.36
5.85

Isotope (kg)
U-235
341.04
422.24
503.44
551.67
584.64
633.36
649.60

U-236

U-238

2.11
2.59
3.09
0.81
0.65
1.30
2.03

15894.25
15811.91
15729.58
15683.29
15650.49
15599.82
15581.96

Time-point (cycle/year)

Time (days)

Characteristics summed over
batches

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

365
730
1,095
1,460
1,825
2,190
2,555
2,920
3,285
3,650
4,015
4,380
4,745
5,110
5,475
5,840
6,205
6,570
6,935
7,300
7,665
8,030
8,395
8,760
9,125

1
1+2
1+2+3
1+2+3+4
1!5
1!6
1!7
1!8
1!9
1!10
1!11
1!12
1!13
1!14
1!15
1!16
1!17
1!18
1!19
1!20
1!21
1!22
1!23
1!24
1!25
(continued)

Table AI.
Mass of uranium
isotopes in the fuel (per
batch)

Table AII.
Time-points and
summation model for
the calculation of the
spent fuel
characteristics

EMH
11,2

132

Table AII.

Time-point (cycle/year)

Time (days)

Characteristics summed over
batches

26
27
28
29
30
31
32
33
34
35

9,490
9,855
10,220
10,585
10,950
11,315
11,680
12,045
12,410
12,775

1!26
1!27
1!28
1!29
1!30
1!31
1!32
1!33
1!34
1!37

Note: in all subsequent time-points (75,100,300, 1,000, 10,000, 100,000, 300,000, 1,000,000
years) the characteristics were calculated for complete spent fuel, i.e. 1!37