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Environmental Management and Health, Vol. 11 No. 2, 2000, pp. 118-132.#MCB University Press, 0956-6163
Submitted 3 April 1999 Accepted 21 June 1999
Uncertainty associated with
radioactive waste chacteristics
Branko Kontic and Matjaz Ravnik
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 policy-making, 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.
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 facilityfor radioactive waste in the country. An attempt to acquire a disposal site in the early1990s 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, especiallythe quantities and activity of different categories of waste, was not provided in a consistent manner during the process. Moreover, the interpretation of uncertaintyassociated with the predictions, including dose and risk evaluation for the anticipated repository, was not clear or was biased.
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The Slovene Agencyfor Radwaste Management (AgencyRAO) began creating a new strategyfor radioactive waste management in 1998. The strategyfocuses on low- and intermediate-level waste disposal due to the urgencyof 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 strategyare 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 validityof safetyevaluations for repositories for the distant future (more than 102years), and unresolved ethical issues appearing in regulatory decision-making 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. theyneed to be systematicallydocumented so that theycan 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 uncertaintyin the methodology of drawing up an EIA, focusing on the uncertaintyof expert opinion (Kontic and Kross, 1999). The case studywe used was radioactive waste disposal in Slovenia. We discovered that dose and risk assessments, as health impact indicators, maybe 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
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Approach to the analysis
The main purpose of the analysis, as we have already indicated, was to clarify the issues raised bythe Green movement, particularlythe issue of uncertainty associated with the quantityof radioactive waste produced byKrsko NPP in its anticipated operational time, the radionuclide inventoryof 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. repositorytype. The dilemma is whether to build a shallow land repositoryfor 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 uncertaintyassociated 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 variabilityand accuracyof data on quantity, the radionuclide inventoryand the activityof different types of waste.
. Then, based on this information, a best estimate in terms of what we
mayexpect (with regard with these waste characteristics) bythe end of the anticipated operational period of Krsko NPP, i.e. 2023 was performed. The ORIGEN2 computer code was used for calculating isotope generation, activitybuild-up and depletion, and the decayheat 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 identifyand clearlypresent the longevityof certain waste categories.
. Given the concerns of decision-makers, as well as the criticisms
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a certain category, is based on this parameter. In this way, i.e. by knowing the time evolution of the specific activityof the LILW, it is possible to clearlydetermine 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 mainlycontribute to the activityin long timeframes, were used instead of a specific activityas 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. Approximately2000m3of this waste was stored at Krsko NPP at the end of 1998, mainlyin 210-litre standard steel drums with a total activityof around 67TBq (NPP Krsko, 1999; Biurrunet 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 activityof alpha emitters is about 0.2 per cent of total beta-gamma activity (NPP Krsko, 1999).
Other users of radioactive materials (medicine, industryand research institutions) produce minor amounts of LILW. The total amount of this waste is about 50m3(SNSA, 1998) with an activityof 5.6TBq. The waste is stored in a central temporaryfacilitylocated 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.
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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 byKrsko 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 onlyprediction of the quantityand activityof LILW at Krsko NPP was made byWestinghouse (FSAR, 1981). However, these predictions are rather obsolete. Theywere 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 safetyanalysis report. The latest revision of the updated safetyanalysis report still includes the same information (USAR, 1996).
Recent data show that the quantityof different types of LILW at Krsko NPP mayvarywithin 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 quantityand activityof the waste which would be collected by2023, and for the calculation of changes in the activityduring later periods. Estimates are based on measurement data (monitoring and control of the packed waste). Uncertaintyin 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 bySlovene 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 activitywill drop below the prescribed
Table I.
Specific activityof selected radionuclides in LILW of the NPP Krsko (best estimate)
Specific activityof selected radionuclides in the waste collected in one year (Bq/m3)
Waste type Co-58 Co-60 Cs-134 Cs-137
SR 2.3*1011 2.7*1010 9.5*1010 1.4*1011
CW 1.9*108 2.3*108 8.6*106 2.3*107
EB 1.4*109 1.7*108 5.8*108 8.5*108
F 1.8*1011 2.1E10 7.4*1010 1.1*1011
O 3.9*107 2.5*108 6.2*107 1.9*108
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level. With conservative estimates, the adopted variability(uncertainty) in the assessed specific activityof 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 activityof all LILW will drop below the required level of 1*102MBq per m3(Slovene legislation) in 341 years. This time period is determined primarilybythe content of Cs-137 in spent resins (SR); other radionuclides have shorter half-lives and diminish earlier. In the event that the initial activityof 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 primaryimportance in this sense. The evaluated total activityof long-lived radionuclides in 2023 is summarised in Table II.
Spent fuel. The keyinput data for calculations associated with spent fuel, especiallyburn-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 activityof activation products (AP), actinides (ACT), fission products (FP) and total activityper fuel batch are presented in Figure 2. The illustration is for model Batch 6; however, the
1.00E+07
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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 activityis constant at a level of 1.9*106MBq (the activityof approximately16 tonnes of non-irradiated fuel). During irradiation, this activityrises slightlyfrom 1.23 to 1.28*1014 MBq, while during the cooling period of 45 days it drops to approximatelytwo 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
Figure 2.
Activityof model batch 6 over a million years
Table II.
Anticipated total activityof selected long-lived radionuclides in LILW (IBE, 1997)
Isotope Half-life (years) Total activity (Bq)
C-14 5,730 8.1*1012
Ni-59 75,000 4.4*1013
Ni-63 96 6.6*1015
Mo-93 3,500 2.1*1010
Nb-94 20,300 2.6*1011
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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 activityand decayheat for all spent fuel at selected time-points are summarised in Table III.
These results were obtained based on the assumptions presented in the Appendix. The model adequatelyrepresents 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 keyoperational elements in future cycles, maynot remain constant, since an
Figure 3.
Total activityof all the spent fuel
Table III.
Total activityand decayheat of all the fuel from the Krsko NPP at selected time-points over a million years Time (years) Total activity (MBq) Decayheat (W)
1 5.30*1012 5.55*105
2 6.72*1012 7.19*105
3 7.92*1012 8.71*105
4 8.70*1012 9.54*105
5 9.23*1012 1.01*106
10 1.09*1013 1.13*106
15 1.21*1013 1.22*106
20 1.31*1013 1.31*106
25 1.40*1013 1.38*106
30 1.48*1013 1.45*106
35 2.69*1013 2.72*106
75 2.63*1012 3.08*105
100 1.46*1012 2.23*105
300 1.08*1011 8.44*104
1,000 4.11*1010 3.52*104
10,000 1.04*1010 8.23*103
100,000 1.28*109 6.82*102
300,000 8.12*108 3.80*102
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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 inventoryof 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 presentlyapplied, 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 theycan be neglected, since theyare 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 immediatelyor operated for almost a further 25 years.
Figure 5.
Influence of extended or shortened operation of the Krsko plant on the activityof actinides in the complete spent fuel (basic estimate is that the plant will operate 35 cycles)
Figure 4.
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Summary of results and a discussion of the radioactive wastemanagement strategy
The results of the modelling show that the main contributors to fuel activity during the period approximately200 years after irradiation are the fission products; after that, actinides will prevail. The total expected activityof the spent fuel after one million years is 4,8*1014Bq. The main contributors to this activityare the radionuclides of U- and Np-chains. Residual thermal power is about 1.0*105W approximately200 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 categoryat Krsko NPP is spent resins. The critical radionuclide in this waste is Cs-137 with a half-life of approximately30 years. According to calculations, the activityof this waste will drop below the level prescribed by Slovene regulations after approximately340 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 longevityof the waste (content of long-lived radionuclides) is one of the keycharacteristics in terms of establishing a strategyfor radwaste management.
The strategybeing prepared bythe RAO Agencyfocuses on the determination of the type of the final repository ± shallow land burial or deep geological disposal ± as well as on the repositorysite-selection process with its overall approval (bythe regulators, the public, scientists and others). According to the results of the calculations performed, and the poor possibility of accuratelypredicting 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 primarilylong-lived, intermediate and high-level 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 onlyfor
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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 safetyin 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 territoryand strong public opposition), it seems reasonable to plan onlya deep geological repository. On the other hand, the siting and the construction period will probablylast longer for such a repositorythan for shallow land disposal. This fact maycause 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 necessarywhich would enable the safe storage of operational waste from Krsko NPP. The strategyshould envisage this as well.
. Confidence building. With regard to confidence-building connected to
radioactive waste disposal, we stronglyrecommend the prompt, clear and complete informing of all interested parties and the general public. It should be clearlystated 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 safetyassessments 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 strategycan rely.
Conclusion
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References
ARAO (Agencyfor Radwaste Management) (1998),Radioactive Waste in Krsko NPP, Ljubljana
(in Slovene), Matjaz Stepisnik, 27 January, available at the ARAO.
Biurrun, E., Filbert, W., Ziegenhagen, J., Navarro Santos, M., Garcia Quiros, J.M. and O'Sullivan, P. (1998), ``Studyon radioactive waste management schemes in Slovenia'', PHARE ZZ 9423/0301, ZZ 9528/0301, Final Report, Peine, pp. 3-27.
Bozic, M. (1998),Calculation of the Activity and Decay Heat for the First 13 Cycles at Krsko NPP Based on Operational and Reactor Core Design Data(in Slovene), available at the Krsko NPP, Ljubljana.
Bragg, K.A. (1996), ``International trends in regulatoryprinciples, criteria and compliance'',
Proceedings of the 1996 International Conference on the Deep Geological Disposal of Radioactive Waste, Canadian Nuclear Society, Lac du Bonnet, pp. 9.1-9.9.
Croff, A.C. (1983), ``Origen2: a versatile computer code for calculating the nuclide compositions and characteristics of nuclear materials'',Nuclear Technology, No. 62, pp. 335-52.
FSAR (Final SafetyAnalysis Report for Krsko NPP) (1981),Chapter 11.5: Solid Waste Processing System, Westinghouse and Krsko NPP (available at Krsko NPP).
IAEA (International Atomic EnergyAgency) (1994),Issues in Radioactive Waste Disposal, IAEA-TECDOC-909, Vienna.
IAEA (International Atomic EnergyAgency) (1997),Regulatory Decision Making in the Presence of Uncertainty in the Context of the Disposal of Long-Lived Radioactive Wastes, IAEA-TECDOC-975, Vienna, pp. 22-3.
IBE (Inzenirski Biro Elektroprojekt) (1997),Long-Lived Radioactive Waste in Slovenia, No. B052/ 23, (in Slovene), available at Inzenirski Biro Elektroprojekt, Ljubljana.
IJS (Institute Jozef Stefan) (1996), A Report on Monitoring Krsko NPP, No. IJS-DP-7375 (in Slovene), available at the Institute Jozef Stefan, Ljubljana.
IJS (Institute Jozef Stefan) (1998),Time Changes of the Activity of Spent Fuel from Krsko NPP and LILW in Slovenia, No. IJS-DP-7858 (in Slovene), available at the Institute Jozef Stefan, Ljubljana.
Kontic, B. and Kross, B.C. (1999), ``Critical review of credibilityand validityof EIAs made in Slovenia from 1981 to 1997'' (under review for publication in theEnvironmental Impact Assessment Review).
Kontic, B. and Ravnik, M. (1998), ``Uncertainties in environmental impact assessments due to expert opinion. A case study: radioactive waste in Slovenia'',Proceedings Nuclear Energy in Central Europe 98, ISBN 961-6207-10-5, Ljubljana, pp. 503-09.
Kontic, B., Kross, B.C. and Stegnar, P. (1999), ``The role of environmental impact assessment in the licensing process in Slovenia; a discussion from the perspective of the validityof long-term evaluations and in reference to radioactive waste disposal'', (under review for publication inThe 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 SafetyAdministration.
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).
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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 SafetyAdministration) (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 SafetyAdministration) (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 SafetyAdministration) (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 SafetyAdministration) (1998), A Report on Nuclear and Radiological Safety in Slovenia in 1997, No. RUJV-RP-026, (in Slovene), available at the SNSA, Ljubljana.
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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 roughlycorresponds to these assumptions. Being aware of the differences between this assumption and the real operational data for Krsko NPP, a screening calculation of the activityof 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 verylittle 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.
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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.
Table AI.
Mass of uranium isotopes in the fuel (per batch) Isotope (kg)
Batch enrichment (%) U-234 U-235 U-236 U-238
2.1 2.44 341.04 2.11 15894.25
2.6 3.25 422.24 2.59 15811.91
3.1 3.89 503.44 3.09 15729.58
3.4 4.22 551.67 0.81 15683.29
3.6 4.55 584.64 0.65 15650.49
3.9 5.36 633.36 1.30 15599.82
4.0 5.85 649.60 2.03 15581.96
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Table AII.
Time-point (cycle/year) Time (days)
Characteristics summed over batches
26 9,490 1!26
27 9,855 1!27
28 10,220 1!28
29 10,585 1!29
30 10,950 1!30
31 11,315 1!31
32 11,680 1!32
33 12,045 1!33
34 12,410 1!34
35 12,775 1!37
