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A methodology for a risk-based approach to complex scenarios in a long-term safety assessment of a radioactive waste repository
Nuclear Engineering and Design 268 (2014) 58–63
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Short communication
A methodology for a risk-based approach to complex scenarios in a long-term safety assessment of a radioactive waste repository Jung-Woo Kim ∗ , Dong-Keun Cho, Jongtae Jeong Radioactive Waste Disposal Research Division, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea
a r t i c l e
i n f o
Article history: Received 6 February 2013 Received in revised form 20 November 2013 Accepted 21 November 2013
a b s t r a c t A methodology for a risk-based approach to complex scenarios in a long-term safety assessment of a radioactive waste repository was developed using a Monte Carlo sampling method. The methodology consists of event characterization, influence evaluation, scenario combination, scenario assessment, and a convergence check. The methodology was applied to a hypothetical repository system considering earthquake events for illustration. Since two independent impacts by earthquakes were considered in the illustration, the complex scenarios could be categorized into 5 types including the simultaneous occurrence of impacts. From the assessment results, the total risk computed by the new methodology involved the occurrence probabilities of the complex scenarios, and these probabilities were reasonably converging to pseudo-theoretical probabilities. For further study, the characterizations of events and their impacts on a repository system must be preliminarily determined for a successful assessment. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The long-term safety assessment of a geologic repository system for high-level radioactive wastes and spent fuels has been widely studied to improve the confidence in the safety of the system (e.g., Campbell and Cranwell, 1988). During about 30 years of Yucca Mountain Project in US, for instance, several performance assessments were continuously conducted to evaluate feasibility of the site and to demonstrate compliance (Sinnock et al., 1987; Barnard et al., 1992; Wilson et al., 1994; DOE, 1998, 2008). Recently, SKB published their final safety assessment report of the SR-Site project to support SKB’s license application for a final repository at Forsmark site in Sweden (SKB, 2011). From the point of view of a long-term safety assessment, various scenarios related to the release and migration of radionuclides can be occurred. The various scenarios include (1) reference or normal scenarios in which all systems work naturally without any unexpected physical interruptions and (2) alternative or disruptive scenarios in which natural disasters like earthquakes and uncontrolled human intrusions can impede the repository system (Campbell and Cranwell, 1988). US US DOE (2008) considered 3 types of natural events, such as seismic, igneous, and early waste package and drip shield failure, and human intrusion, such as exploratory drilling for groundwater, to be included in
∗ Corresponding author. Tel.: +82 42 868 2547; fax: +82 42 868 2035. E-mail address: jw [email protected] (J.-W. Kim). 0029-5493/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.11.086
the scenario formation in the performance assessments of Yucca Mountain Project. Due to the local climate conditions of Sweden, SKB (2011) considered glacial cycle and global warming in the reference scenario. And, potential loss of safety functions, such as canister failure due to shear load, and human actions, such as boring intrusion, were included in the additional scenarios. For the safety assessment to be comprehensive, it is inevitable to assess complex scenarios that combine both reference and alternative scenarios with the aleatory uncertainty. The assessment methodology of the complex scenarios can be classified into disaggregated and aggregated approaches. Unlike the disaggregated approach in which the exposure dose rate to the representative person is calculated for each scenario, in the aggregated approach, the risk or mean dose rate is calculated from the exposure dose rates from all possible scenarios considering their occurrence probability (ICRP, 2000). It is advantageous that the aggregated approach or risk-based approach is capable of considering the various scenarios in a single assessment. In practice, SNL (2008) submitted the total mean and median annual doses in the performance assessment of the Yucca Mountain repository for the license application, and the total mean and median annual doses were calculated by simply summing up the expected annual doses for each normal and alternative scenario sets multiplied by their occurrence probabilities. In addition, Seo et al. (2010) suggested a theoretical methodology of an integrated approach to a risk-based long-term safety assessment, and Seo et al. (2012) applied the methodology to a case study dealing with seismic events and human intrusion. In their methodology, the exposure dose rates to the representative person
J.-W. Kim et al. / Nuclear Engineering and Design 268 (2014) 58–63
were individually computed for each scenario. After each individual computation, the exposure dose rates were multiplied by the occurrence probability of the respective scenario. The computation results for all scenarios were then summed to obtain the final value of the risk. In the previous practices described above, it was impossible to cover all possible scenarios due to the aleatory uncertainty. That is, for example, the number of scenarios will be the product of the number of event features and the number of time steps which is a huge number even when just a single event was considered. If more events are considered, the number of scenarios for the safety assessment will become much bigger. Practically speaking, it is very difficult and time-consuming to cover all possible scenarios. In addition, the methodologies used in the previous practices ignored the complex impacts of two or more events which can occur simultaneously and/or sequentially. Actually, even a single event can give different impacts on the different parts of the repository system (e.g., a seismic event will differently impact on the engineered barrier system including waste packages and the fractures in the far-field host rock). To resolve the drawbacks, the objective of this study is the development of a new methodology for a risk-based approach to complex scenarios, in which the complementary impacts on the repository system are considered, in a long-term safety assessment of a radioactive waste repository. The methodology employed a Monte Carlo method considering the probability of quantitative and/or qualitative properties of events as well as their occurrence probability. Finally, the methodology was applied to a Korea’s hypothetical repository system for pyroprocessed wastes (Choi et al., 2011) considering earthquake events for the illustration.
2. Methodology 2.1. Procedure of the risk assessment of the complex scenario The new methodology of risk-based safety assessment consists of (1) a characterization of events, (2) an evaluation of the influence on the repository system, (3) a determination of the criteria to generate scenarios, (4) a scenario combination through Monte Carlo sampling, (5) an assessment of the scenario using a safety assessment model, and (6) a computation of risk. The final three processes are repeated until the predefined convergence criteria are met. The flowchart of the overall procedure is depicted in Fig. 1. For the safety assessment, as mentioned above, various external events can be considered independently and/or simultaneously in a complex scenario. The external events include natural disruptive events, such as earthquakes, and human intrusion events. In the event characterization process, the properties of those events related to the performance of the repository system are digitized and represented by probability density functions (PDFs). In the case of an earthquake, for example, the properties can be the occurrence rate, magnitude, distance from the hypocenter, etc. The PDFs of each property have to be carefully determined based on the historical records, a statistical analysis, expert judgments, etc. The PDFs of each property are converted into cumulative density functions (CDFs) for a scenario combination process. In the influence evaluation process, how the external events will affect the repository system is defined. The external events will discriminatorily affect each part of the repository system, such as an engineered barrier system including a canister, natural barrier in the far-fields, and the biosphere. The impacts on the repository system are also dependent on the properties of the external events. Some impacts can be irreversible so that the influence continues during the period of assessment, and some impacts can be reversible so that the disrupted parts are recovered after some time,
59
Start Event Characterization
Influence Evaluation
Preliminary Process
Criteria
Scenario Combination (Monte Carlo Sampling)
Scenario Assessment
MainProcess (Risk Assessment)
Risk No
Convergence Check Yes
End Fig. 1. Flowchart of the overall procedure for a risk-based safety assessment of complex scenarios in a radioactive waste repository system.
or the influence of some repeating impacts can be increased gradually. This process also has to be carefully conducted based on the analogical interpretations of the experimental results and the relevant field data. In the end of the preliminary process, the criteria that determine (1) which property of the external event will be influential, (2) which part of the repository system will be affected, (3) how severely the part will be impacted, etc. are set up. The criteria defined in the previous process are utilized to generate a complex scenario. In the scenario combination process, Monte Carlo sampling method is utilized as random numbers are independently generated and converted into the occurrence times and/or the values of the properties using the predefined CDFs for each property of the external events. The types of impacts by the external events are then determined based on the criteria. As all impacts on the repository system are arranged in the process of time, a complex scenario is finally completed. The overall flowchart of the scenario combination process is shown in Fig. 2. For every iteration of scenario assessment process, a new complex scenario is preliminarily generated through the scenario combination process. In the scenario assessment process, each complex scenario developed in the scenario combination process is simulated using the user-defined safety assessment model. As the results of the scenario assessments, the exposure dose rates to the representative person are computed for each scenario. Because the complex scenario was randomly generated based on the criteria and their probabilities, the resulting exposure dose rates already involve the probability of the scenario. In other words, if an exposure dose rate is obtained often from the iterations of scenario assessments, it implies that the scenario related to the exposure dose rate has a high occurrence probability. After each iteration, the exposure dose rates are cumulatively averaged and converted into the total risk using a dose-to-risk conversion factor, and the occurrence probabilities of each scenario are computed and compared with those at the previous iteration step. If the difference is less than the user-defined
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J.-W. Kim et al. / Nuclear Engineering and Design 268 (2014) 58–63
Fig. 2. Flowchart of the scenario combination process.
convergence criteria, it is assumed that the iteration of Monte Carlo sampling is satisfactory and all possible scenarios are exhaustively considered. As the number of scenarios increased, the results will be statistically stabilized. 2.2. Safety assessment model In this study, the scenario assessment was conducted by a safety assessment model, GoldSim-based Total System Performance Assessment (GSTSPA), developed at the Korea Atomic Energy Research Institute (KAERI) (Lee and Hwang, 2009; Hwang and Kang, 2010). GSTSPA was originally developed to assess Korea’s hypothetical repository system, an Advanced Korea Repository System (A-KRS), in which the pyroprocessed waste is supposed to be disposed (Choi et al., 2011). The domain of GSTSPA consists of an engineered barrier system including waste packages, far-field host rock, and the biosphere. Two types of waste packages are considered in GSTSPA: one is metallic waste disposed of in a tunnel at a level of −200 m, and the other is ceramic waste disposed of in a bore hole at a level of −500 m. GSTSPA explains the radionuclide release from a waste package (metallic waste) or canister (ceramic waste), diffusive transport through buffer material, sorption, precipitation, and radioactive decay in the EBS. In the far-field host rock, GSTSPA explains the radionuclide transport through the fractured rock. In the biosphere, finally, GSTSPA explains the groundwater pathway in the subsurface, groundwater utilization for cultivation, a surface water pathway, and a sink into the marine water. 3. Application The new risk-based safety assessment methodology described above was illustrated by applying to a simple hypothetical case for which an earthquake was considered as a single external event. 3.1. Complex scenario In the event characterization process as the first step of the preliminary process (Fig. 2), an earthquake was characterized in terms of the occurrence time, magnitude, and distance from the hypocenter. Since the repository site is not determined yet in Korea and
there are still many lacks of knowledge to predict earthquake in the future, the characteristics of earthquake in this study were highly simplified to the hypothetical case. Earthquake sequences were generally characterized by Poisson random distribution (Rydelek and Sacks, 1989). Although it was not always correct, it seemed to be appropriate for the simple hypothetical case. Typical Poisson distribution is in terms of the number of event occurrence during a time period. However, the interest here is the intervals between events, and GoldSim (GTG, 2010) employed the alternative CDF of the Poisson distribution which was used to explain the occurrence time of the earthquake in this study. F(t) = 1 − exp(−t)
(1)
where F(t) is the probability that the time to the next earthquake will be less than or equal to t, and is the mean occurrence rate of the earthquake. In this study, was assumed to be 1/10,000 yr−1 . The occurrence time of the earthquake was computed using the inverse function of Eq. (1) as follows: t=−
ln(1 − F(t)) ln(1 − ) =−
(2)
where is the random number between 0 and 1 generated from Monte Carlo sampling. Since the distribution of the historical earthquakes in the Korean Peninsula during about last 1900 years (data not shown) was similar to the log-uniform distribution with respect to the earthquake magnitude, the truncated log-uniform distribution for the magnitude of the earthquake, M, seemed to be appropriate for the simple hypothetical case. The CDF of the truncated log-uniform distribution is (GTG, 2010)
F(M) =
⎧ 0 ⎪ ⎪ ⎨
ln M − ln m1
ln m2 − ln m1 ⎪ ⎪ ⎩ 1
(M ≤ m1 ) (m1 ≤ M ≤ m2 )
(3)
(M≥m2 )
where m1 and m2 are the minimum and maximum values of the magnitude of the earthquake, respectively. In this study, m1 and m2 were assumed to be 5.5 and 8, respectively. The magnitude of the earthquake was computed by the inverse function of Eq. (3) as
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Table 1 Categories of complex scenarios generated and their occurrence probabilities obtained by the risk assessment and by a pseudo-theoretical computation. Scenario category
Occurrence sequence of impacts
Occurrence probability
1 2 3 4 5
Impact #1 → Impact #2 → Impact #2 Impacts #1 and #2 → Impact #2 Impact #2 → Impact #1 → Impact #2 Impact #2 → Impacts #1 and #2 Impact #2 → Impact #2 → Impact #1
Assessment
Pseudo-theory
0.07 0.25 0.02 0.15 0.51
0.041 0.184 0.033 0.141 0.601
follows: M = exp(ln m1 + F(M) · (ln m2 − ln m1 )) = exp(ln m1 + · (ln m2 − ln m1 ))
(4)
Due to the lack of knowledge about the repository site location, the distance from the hypocenter, D, was arbitrarily determined by the tri-angular distribution function. The CDF of the tri-angular distribution is (GTG, 2010)
⎧ 2 (D − d ) ⎪ ⎪ ⎨ (d − d )(d1 − d ) 2 1 3 1 F(D) = 2 ⎪ (d3 − D) ⎪ ⎩1−
(d3 − d2 )(d3 − d1 )
(d1 ≤ D ≤ d2 ) (5) (d2 ≤ D ≤ d3 )
where d1 , d2 , and d3 are the minimum, most, and maximum values of the distance from the hypocenter, respectively. In this study, d1 , d2 , and d3 were assumed to be 0, 5, and 25 km, respectively. The distance from the hypocenter was computed by the inverse function of Eq. (5) as follows:
D=
=
d1 + d3 −
F(D)(d2 − d1 )(d3 − d1 )
Fig. 3. Results of the risk assessment for the complex scenario (100 iterations).
(1 − F(D))(d3 − d2 )(d3 − d1 )
⎧ ⎪ ⎨ d1 + (d2 − d1 )(d3 − d1 )
≤
d2 − d1 d3 − d1
⎪ ⎩ d − (1 − )(d − d )(d − d ) ≥ d2 − d1 3 3 2 3 1
(6)
d3 − d1
In the influence evaluation process as the second step of the preliminary process (Fig. 2), two kinds of earthquake impacts were considered in this simple hypothetical case. The Impact #1 is hypothesized that the function of the far-field rock, which is the retardation of radionuclide transport, is irreversibly lost owing to an earthquake. And, the Impact #2 is hypothesized such that the groundwater flowrate at the MWCF is increased 10 times by earthquake. The Impact #2 could be occurred up to 2 times. That is, the maximum numbers of occurrence times of Impacts #1 and #2 are 1 and 2, respectively. As the final step of the preliminary process (Fig. 2), the criteria for classification of earthquake impacts were determined. For the first criterion, if the magnitude of an earthquake is larger than 7.5, the Impact #1 will be applied to the repository system. For the second criterion, if the ratio of the earthquake magnitude to the distance from the hypocenter (M/D) is larger than 0.5/km, the Impact #2 will be applied. As expected, if both criteria #1 and #2 are met, both Impact #1 and #2 will be occurred at the same time. Otherwise, there will be no impact on the repository system by the earthquake. In the following main process (Fig. 2), scenario was firstly generated by Monte Carlo sampling for the aleatory uncertainty. There may be many earthquakes during the simulation period which is 1,000,000-year in this study (the outbreak times are determined by Eq. (2)). Once an earthquake is occurred, the properties of
earthquake (randomly generated by Eqs. (4) and (6)), will be judged by the criteria above and then it will be determined which impact will be applied to the repository system. Based on the occurrence sequence of the impacts, therefore, the complex scenarios can be categorized by 5 types including the simultaneous occurrence of Impacts #1 and #2 (Table 1). Following is a possible scenario of Scenario Category #1 for example. The magnitude of the first earthquake is larger than 7.5 and the M/D is smaller than 0.5, and thus the function of the far-field rock is failed. The magnitude of the second earthquake is smaller than 7.5 and the M/D is larger than 0.5, and thus the flowrate at the MWCF is increased by 10 times. At this time, the function of the far-filed rock is still remained as failed, so that the both Impact #1 and #2 will influence to the repository system. Finally, the following earthquake meets the second criterion again, and thus the flowrate at the MWCF is increased by 10 times again (100 times in total). And, any additional earthquakes are not influential to the repository system since then. After a scenario was generated, the scenario was assessed by GSTSPA, and the main process (Fig. 2) was iterated for 100 times. 3.2. Risk assessment results The results of the risk assessment for the complex scenario designed above are depicted in Fig. 3. The black lines are the temporal distribution of the each exposure dose rates resulted from the 100 iterations, and the purple line is the averaged exposure dose rate. The red dots and blue circles indicate the magnitudes of the
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J.-W. Kim et al. / Nuclear Engineering and Design 268 (2014) 58–63
earthquakes which induce Impacts #1 (far-field fail) and #2 (MWCF flowrate increase), respectively. The red dots and blue circles at the same locations indicate that the earthquakes induced both Impact #1 and #2 at the same time: these events must be the elements of the scenario which is categorized as Category #2 and #4 in Table 1. The influence of Impact #2 (MWCF flowrate increase) seemed to be insignificant since any changes of exposure dose rates correlated with the blue circles were not observed in Fig. 3. The result corresponds with the preliminary sensitivity analysis (Lee and Jeong, 2012, Table 2) in which the Darcy velocity and plume width of the MWCF were known to be insignificant parameters. On the other hand, Impact #1 (far-field fail) induced the distinct increase of dose rate as the step-up of the exposure dose rates had correlation with the red dots in Fig. 3. The largest increase of the exposure dose rate by Impact #1 was almost 1-order difference at about 10,000 years. The result also corresponds with the highly ranked parameters related to the far-field hydrology in the preliminary sensitivity analysis (Lee and Jeong, 2012, Table 2). Interestingly, the influence of Impact #1 was not occurred anymore just after the exposure dose rates hit the peak (about 200,000 years). From the result, it can be carefully discussed that the function of the far-field rock is no longer valid after the exposure dose rate hits the peak. Since the effect of Impact #2 was insignificant, the difference between the results from Impact #2 (red dots) only and both Impact #1 and #2 (red dots in blue circles) was hardly detectable. Nevertheless, it can be reasonably discussed that the complex scenario was well simulated and assessed by the new methodology suggested in this study. Finally, the total risk (green line in Fig. 3) was computed by multiplying the dose-to-risk conversion factor (= 0.05/Sv; CIRRPC, 1992) to the averaged exposure dose rates. Since the convergence criteria were not defined in this assessment, the iteration number of the main process with Monte Carlo sampling was predefined as 100. Instead, the occurrence probability of the scenario category was compared with the pseudo-theoretical probability (Table 1). From each iterative simulation, the scenario was analyzed based on the sequence of events occurred and then categorized as one of the five scenario categories in Table 1. After the last iterative simulation, the numbers of scenarios for each scenario category were normalized to compute the occurrence probability of the scenario category. From the result, Scenario Category #5 had the majority (51%) of the occurrence probability and Scenario Categories #2 (25%), #4 (15%), #1 (7%), and #3 (2%) were followed in order. The pseudo-theoretical probabilities for each scenario category were separately computed by 100,000 Monte Carlo samplings, which is much bigger than the number of iterative simulations (= 100), for Eqs. (2), (4) and (6) without any scenario assessment. Comparison between the occurrence probabilities resulted from the iterative simulations and the pseudo-theoretical values in Table 1 was intended to see if the number of iterative simulations (= 100) was enough to show the convergence of the results. Although the two results were not exactly same, the proportions for each scenario category between them were almost same having the same order. Overall, the result confirms that the total risk computed by the new methodology for the risk assessment involves the occurrence probabilities of the complex scenarios and the probabilities reasonably converge into the pseudo-theoretical probabilities.
4. Conclusion A methodology for a risk-based approach to a complex scenario in a long-term safety assessment of a radioactive waste repository was developed using a Monte Carlo sampling method in this study. The robustness of the methodology could be confirmed by the results showing the occurrence probabilities of the complex
scenarios were reasonably converged into pseudo-theoretical values. The efficiency of the risk assessment can be considerably improved with the following advantages: • Not necessary to compute separately the occurrence probabilities and exposure dose rates of each scenario; - Occurrence probability of the scenario is inherent in the classification of the complex scenarios and it is determined in the Monte Carlo samplings of event properties (e.g., Eqs. (2), (4) and (6)). • Not necessary to simulate all possible scenarios (almost infinite scenarios) from Monte Carlo sampling; - Convergence of the assessment results can be monitored at the every other simulation, and the scenario which has low occurrence probability will be automatically excluded. • Capable of representing the complementary effects of more than two events on the repository system; and - The complex scenarios generated by the new methodology include the complementary conditions in which two or more events and/or two or more impacts by an event are occurred simultaneously and/or sequentially (Table 1). • Convenient to automate the assessment process. The newly suggested methodology will be efficiently capable of carrying out the risk assessment for the complex scenarios with various external events in the long-term safety assessment of a radioactive waste repository. For further study, the characterizations of the events and the impacts of the events on the repository system should be carefully determined for a successful assessment. Acknowledgments This work was supported by the Nuclear Research and Development Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP). References Barnard, R.W., Wilson, M.L., Dockery, H.A., Gauthier, J.H., Kaplan, P.G., Eaton, R.R., Bingham, F.W., Robey, T.H., 1992. TSPA 1991: An Initial Total-System Performance Assessment for Yucca Mountain. SAND91-2795. Sandia National Laboratories, Albuquerque, NM. Campbell, J.E., Cranwell, R.M., 1988. Performance assessment of radioactive waste repositories. Science 239, 1389–1392. Choi, H.-J., Lee, M., Lee, J.Y., 2011. Preliminary conceptual design of a geological disposal system for high-level wastes from the pyroprocessing of PWR spent fuels. Nuclear Engineering and Design 241, 3348–3356. CIRRPC, 1992. Use of BEIR V and UNSCEAR 1988 in Radiation Risk Assessment – Lifetime Total Cancer Mortality Risk Estimates at Low Doses and Low Dose Rates for Low-LET Radiation. Science Panel Report No. 9. Committee on Interagency Radiation Research and Policy Coordination. DOE (US Department of Energy), 1998. Viability Assessment of a Repository at Yucca Mountain: Introduction and Site Characteristics. DOE/RW-0508. Office of Civilian Radioactive Waste Management, US Department of Energy, Washington, DC. DOE (US Department of Energy), 2008. Yucca Mountain Repository License Application, Safety Analysis Report. DOE/RW-0573. Office of Civilian Radioactive Waste Management, US Department of Energy, Washington, DC. GTG (GoldSim Technology Group), 2010. GoldSim User’s Guide: Probabilistic Simulation Environment. GoldSim Technology Group LLC, Washington, DC. Hwang, Y., Kang, C.-H., 2010. The development of a safety assessment approach and its implication on the advanced nuclear fuel cycle. Nuclear Engineering and Technology 42 (1), 37–46. ICRP (International Commission on Radiation Protection), 2000. Radiation Protection Recommendations as Applied to the Disposal of Long-Lived Solid Radioactive Waste. ICRP Publication 81. Pergamon Press, Oxford. Lee, Y.-M., Hwang, Y., 2009. A GlodSim model for the safety assessment of an HLW repository. Progress in Nuclear Energy 51, 746–759. Lee, Y.-M., Jeong, J., 2012. A Probabilistic Safety Assessment of a Pyro-processed Waste Repository. Journal of Korean Radioactive Waste Society 10 (4), 263–272. Rydelek, P.A., Sacks, I.S., 1989. Testing the completeness of earthquake catalogues and the hypothesis of self-similarity. Nature 337 (19), 251–253.
J.-W. Kim et al. / Nuclear Engineering and Design 268 (2014) 58–63 Seo, E.J., Jeong, C.W., Sato, S., 2010. An integrated approach to risk-based post-closure safety evaluation of complex radiation exposure situations in radioactive waste disposal. Journal of Radiation Protection 35 (1), 6–11. Seo, E.J., Jeong, C.W., Sato, S., 2012. Application of risk-based approach to postclosure safety assessment in radioactive waste disposal: an integration of complex radiation exposure situations. Annals of Nuclear Energy 49, 96–101. Sinnock, S., Lin, Y.T., Brannen, J.P., 1987. Preliminary bounds on the expected postclosure performance of the Yucca Mountain repository site, southern Nevada. Journal of Geophysical Research 92 (B8), 7820–7842. SKB (Svensk Kärnbränslehantering AB), 2011. Long-Term Safety for the Final Repository for Spent Nuclear Fuel at Forsmark: Main Report of the SR-Site Project.
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SKB TR-11-01. Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden. SNL (Sandia National Laboratories), 2008. Total System Performance Assessment Model/Analysis for the License Application (Section 6). MDL-WIS-PA-000005. Sandia National Laboratories, Las Vegas, NV. Wilson, M.L., Gauthier, J.H., Barnard, R.W., Barr, G.E., et al., 1994. Total-System Performance Assessment for Yucca Mountain – SNL Second Iteration (TSPA-1993): Executive Summary SAND93-2675. Sandia National Laboratories, Albuquerque, NM.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Short communication
A methodology for a risk-based approach to complex scenarios in a long-term safety assessment of a radioactive waste repository Jung-Woo Kim ∗ , Dong-Keun Cho, Jongtae Jeong Radioactive Waste Disposal Research Division, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea
a r t i c l e
i n f o
Article history: Received 6 February 2013 Received in revised form 20 November 2013 Accepted 21 November 2013
a b s t r a c t A methodology for a risk-based approach to complex scenarios in a long-term safety assessment of a radioactive waste repository was developed using a Monte Carlo sampling method. The methodology consists of event characterization, influence evaluation, scenario combination, scenario assessment, and a convergence check. The methodology was applied to a hypothetical repository system considering earthquake events for illustration. Since two independent impacts by earthquakes were considered in the illustration, the complex scenarios could be categorized into 5 types including the simultaneous occurrence of impacts. From the assessment results, the total risk computed by the new methodology involved the occurrence probabilities of the complex scenarios, and these probabilities were reasonably converging to pseudo-theoretical probabilities. For further study, the characterizations of events and their impacts on a repository system must be preliminarily determined for a successful assessment. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The long-term safety assessment of a geologic repository system for high-level radioactive wastes and spent fuels has been widely studied to improve the confidence in the safety of the system (e.g., Campbell and Cranwell, 1988). During about 30 years of Yucca Mountain Project in US, for instance, several performance assessments were continuously conducted to evaluate feasibility of the site and to demonstrate compliance (Sinnock et al., 1987; Barnard et al., 1992; Wilson et al., 1994; DOE, 1998, 2008). Recently, SKB published their final safety assessment report of the SR-Site project to support SKB’s license application for a final repository at Forsmark site in Sweden (SKB, 2011). From the point of view of a long-term safety assessment, various scenarios related to the release and migration of radionuclides can be occurred. The various scenarios include (1) reference or normal scenarios in which all systems work naturally without any unexpected physical interruptions and (2) alternative or disruptive scenarios in which natural disasters like earthquakes and uncontrolled human intrusions can impede the repository system (Campbell and Cranwell, 1988). US US DOE (2008) considered 3 types of natural events, such as seismic, igneous, and early waste package and drip shield failure, and human intrusion, such as exploratory drilling for groundwater, to be included in
∗ Corresponding author. Tel.: +82 42 868 2547; fax: +82 42 868 2035. E-mail address: jw [email protected] (J.-W. Kim). 0029-5493/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.11.086
the scenario formation in the performance assessments of Yucca Mountain Project. Due to the local climate conditions of Sweden, SKB (2011) considered glacial cycle and global warming in the reference scenario. And, potential loss of safety functions, such as canister failure due to shear load, and human actions, such as boring intrusion, were included in the additional scenarios. For the safety assessment to be comprehensive, it is inevitable to assess complex scenarios that combine both reference and alternative scenarios with the aleatory uncertainty. The assessment methodology of the complex scenarios can be classified into disaggregated and aggregated approaches. Unlike the disaggregated approach in which the exposure dose rate to the representative person is calculated for each scenario, in the aggregated approach, the risk or mean dose rate is calculated from the exposure dose rates from all possible scenarios considering their occurrence probability (ICRP, 2000). It is advantageous that the aggregated approach or risk-based approach is capable of considering the various scenarios in a single assessment. In practice, SNL (2008) submitted the total mean and median annual doses in the performance assessment of the Yucca Mountain repository for the license application, and the total mean and median annual doses were calculated by simply summing up the expected annual doses for each normal and alternative scenario sets multiplied by their occurrence probabilities. In addition, Seo et al. (2010) suggested a theoretical methodology of an integrated approach to a risk-based long-term safety assessment, and Seo et al. (2012) applied the methodology to a case study dealing with seismic events and human intrusion. In their methodology, the exposure dose rates to the representative person
J.-W. Kim et al. / Nuclear Engineering and Design 268 (2014) 58–63
were individually computed for each scenario. After each individual computation, the exposure dose rates were multiplied by the occurrence probability of the respective scenario. The computation results for all scenarios were then summed to obtain the final value of the risk. In the previous practices described above, it was impossible to cover all possible scenarios due to the aleatory uncertainty. That is, for example, the number of scenarios will be the product of the number of event features and the number of time steps which is a huge number even when just a single event was considered. If more events are considered, the number of scenarios for the safety assessment will become much bigger. Practically speaking, it is very difficult and time-consuming to cover all possible scenarios. In addition, the methodologies used in the previous practices ignored the complex impacts of two or more events which can occur simultaneously and/or sequentially. Actually, even a single event can give different impacts on the different parts of the repository system (e.g., a seismic event will differently impact on the engineered barrier system including waste packages and the fractures in the far-field host rock). To resolve the drawbacks, the objective of this study is the development of a new methodology for a risk-based approach to complex scenarios, in which the complementary impacts on the repository system are considered, in a long-term safety assessment of a radioactive waste repository. The methodology employed a Monte Carlo method considering the probability of quantitative and/or qualitative properties of events as well as their occurrence probability. Finally, the methodology was applied to a Korea’s hypothetical repository system for pyroprocessed wastes (Choi et al., 2011) considering earthquake events for the illustration.
2. Methodology 2.1. Procedure of the risk assessment of the complex scenario The new methodology of risk-based safety assessment consists of (1) a characterization of events, (2) an evaluation of the influence on the repository system, (3) a determination of the criteria to generate scenarios, (4) a scenario combination through Monte Carlo sampling, (5) an assessment of the scenario using a safety assessment model, and (6) a computation of risk. The final three processes are repeated until the predefined convergence criteria are met. The flowchart of the overall procedure is depicted in Fig. 1. For the safety assessment, as mentioned above, various external events can be considered independently and/or simultaneously in a complex scenario. The external events include natural disruptive events, such as earthquakes, and human intrusion events. In the event characterization process, the properties of those events related to the performance of the repository system are digitized and represented by probability density functions (PDFs). In the case of an earthquake, for example, the properties can be the occurrence rate, magnitude, distance from the hypocenter, etc. The PDFs of each property have to be carefully determined based on the historical records, a statistical analysis, expert judgments, etc. The PDFs of each property are converted into cumulative density functions (CDFs) for a scenario combination process. In the influence evaluation process, how the external events will affect the repository system is defined. The external events will discriminatorily affect each part of the repository system, such as an engineered barrier system including a canister, natural barrier in the far-fields, and the biosphere. The impacts on the repository system are also dependent on the properties of the external events. Some impacts can be irreversible so that the influence continues during the period of assessment, and some impacts can be reversible so that the disrupted parts are recovered after some time,
59
Start Event Characterization
Influence Evaluation
Preliminary Process
Criteria
Scenario Combination (Monte Carlo Sampling)
Scenario Assessment
MainProcess (Risk Assessment)
Risk No
Convergence Check Yes
End Fig. 1. Flowchart of the overall procedure for a risk-based safety assessment of complex scenarios in a radioactive waste repository system.
or the influence of some repeating impacts can be increased gradually. This process also has to be carefully conducted based on the analogical interpretations of the experimental results and the relevant field data. In the end of the preliminary process, the criteria that determine (1) which property of the external event will be influential, (2) which part of the repository system will be affected, (3) how severely the part will be impacted, etc. are set up. The criteria defined in the previous process are utilized to generate a complex scenario. In the scenario combination process, Monte Carlo sampling method is utilized as random numbers are independently generated and converted into the occurrence times and/or the values of the properties using the predefined CDFs for each property of the external events. The types of impacts by the external events are then determined based on the criteria. As all impacts on the repository system are arranged in the process of time, a complex scenario is finally completed. The overall flowchart of the scenario combination process is shown in Fig. 2. For every iteration of scenario assessment process, a new complex scenario is preliminarily generated through the scenario combination process. In the scenario assessment process, each complex scenario developed in the scenario combination process is simulated using the user-defined safety assessment model. As the results of the scenario assessments, the exposure dose rates to the representative person are computed for each scenario. Because the complex scenario was randomly generated based on the criteria and their probabilities, the resulting exposure dose rates already involve the probability of the scenario. In other words, if an exposure dose rate is obtained often from the iterations of scenario assessments, it implies that the scenario related to the exposure dose rate has a high occurrence probability. After each iteration, the exposure dose rates are cumulatively averaged and converted into the total risk using a dose-to-risk conversion factor, and the occurrence probabilities of each scenario are computed and compared with those at the previous iteration step. If the difference is less than the user-defined
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Fig. 2. Flowchart of the scenario combination process.
convergence criteria, it is assumed that the iteration of Monte Carlo sampling is satisfactory and all possible scenarios are exhaustively considered. As the number of scenarios increased, the results will be statistically stabilized. 2.2. Safety assessment model In this study, the scenario assessment was conducted by a safety assessment model, GoldSim-based Total System Performance Assessment (GSTSPA), developed at the Korea Atomic Energy Research Institute (KAERI) (Lee and Hwang, 2009; Hwang and Kang, 2010). GSTSPA was originally developed to assess Korea’s hypothetical repository system, an Advanced Korea Repository System (A-KRS), in which the pyroprocessed waste is supposed to be disposed (Choi et al., 2011). The domain of GSTSPA consists of an engineered barrier system including waste packages, far-field host rock, and the biosphere. Two types of waste packages are considered in GSTSPA: one is metallic waste disposed of in a tunnel at a level of −200 m, and the other is ceramic waste disposed of in a bore hole at a level of −500 m. GSTSPA explains the radionuclide release from a waste package (metallic waste) or canister (ceramic waste), diffusive transport through buffer material, sorption, precipitation, and radioactive decay in the EBS. In the far-field host rock, GSTSPA explains the radionuclide transport through the fractured rock. In the biosphere, finally, GSTSPA explains the groundwater pathway in the subsurface, groundwater utilization for cultivation, a surface water pathway, and a sink into the marine water. 3. Application The new risk-based safety assessment methodology described above was illustrated by applying to a simple hypothetical case for which an earthquake was considered as a single external event. 3.1. Complex scenario In the event characterization process as the first step of the preliminary process (Fig. 2), an earthquake was characterized in terms of the occurrence time, magnitude, and distance from the hypocenter. Since the repository site is not determined yet in Korea and
there are still many lacks of knowledge to predict earthquake in the future, the characteristics of earthquake in this study were highly simplified to the hypothetical case. Earthquake sequences were generally characterized by Poisson random distribution (Rydelek and Sacks, 1989). Although it was not always correct, it seemed to be appropriate for the simple hypothetical case. Typical Poisson distribution is in terms of the number of event occurrence during a time period. However, the interest here is the intervals between events, and GoldSim (GTG, 2010) employed the alternative CDF of the Poisson distribution which was used to explain the occurrence time of the earthquake in this study. F(t) = 1 − exp(−t)
(1)
where F(t) is the probability that the time to the next earthquake will be less than or equal to t, and is the mean occurrence rate of the earthquake. In this study, was assumed to be 1/10,000 yr−1 . The occurrence time of the earthquake was computed using the inverse function of Eq. (1) as follows: t=−
ln(1 − F(t)) ln(1 − ) =−
(2)
where is the random number between 0 and 1 generated from Monte Carlo sampling. Since the distribution of the historical earthquakes in the Korean Peninsula during about last 1900 years (data not shown) was similar to the log-uniform distribution with respect to the earthquake magnitude, the truncated log-uniform distribution for the magnitude of the earthquake, M, seemed to be appropriate for the simple hypothetical case. The CDF of the truncated log-uniform distribution is (GTG, 2010)
F(M) =
⎧ 0 ⎪ ⎪ ⎨
ln M − ln m1
ln m2 − ln m1 ⎪ ⎪ ⎩ 1
(M ≤ m1 ) (m1 ≤ M ≤ m2 )
(3)
(M≥m2 )
where m1 and m2 are the minimum and maximum values of the magnitude of the earthquake, respectively. In this study, m1 and m2 were assumed to be 5.5 and 8, respectively. The magnitude of the earthquake was computed by the inverse function of Eq. (3) as
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Table 1 Categories of complex scenarios generated and their occurrence probabilities obtained by the risk assessment and by a pseudo-theoretical computation. Scenario category
Occurrence sequence of impacts
Occurrence probability
1 2 3 4 5
Impact #1 → Impact #2 → Impact #2 Impacts #1 and #2 → Impact #2 Impact #2 → Impact #1 → Impact #2 Impact #2 → Impacts #1 and #2 Impact #2 → Impact #2 → Impact #1
Assessment
Pseudo-theory
0.07 0.25 0.02 0.15 0.51
0.041 0.184 0.033 0.141 0.601
follows: M = exp(ln m1 + F(M) · (ln m2 − ln m1 )) = exp(ln m1 + · (ln m2 − ln m1 ))
(4)
Due to the lack of knowledge about the repository site location, the distance from the hypocenter, D, was arbitrarily determined by the tri-angular distribution function. The CDF of the tri-angular distribution is (GTG, 2010)
⎧ 2 (D − d ) ⎪ ⎪ ⎨ (d − d )(d1 − d ) 2 1 3 1 F(D) = 2 ⎪ (d3 − D) ⎪ ⎩1−
(d3 − d2 )(d3 − d1 )
(d1 ≤ D ≤ d2 ) (5) (d2 ≤ D ≤ d3 )
where d1 , d2 , and d3 are the minimum, most, and maximum values of the distance from the hypocenter, respectively. In this study, d1 , d2 , and d3 were assumed to be 0, 5, and 25 km, respectively. The distance from the hypocenter was computed by the inverse function of Eq. (5) as follows:
D=
=
d1 + d3 −
F(D)(d2 − d1 )(d3 − d1 )
Fig. 3. Results of the risk assessment for the complex scenario (100 iterations).
(1 − F(D))(d3 − d2 )(d3 − d1 )
⎧ ⎪ ⎨ d1 + (d2 − d1 )(d3 − d1 )
≤
d2 − d1 d3 − d1
⎪ ⎩ d − (1 − )(d − d )(d − d ) ≥ d2 − d1 3 3 2 3 1
(6)
d3 − d1
In the influence evaluation process as the second step of the preliminary process (Fig. 2), two kinds of earthquake impacts were considered in this simple hypothetical case. The Impact #1 is hypothesized that the function of the far-field rock, which is the retardation of radionuclide transport, is irreversibly lost owing to an earthquake. And, the Impact #2 is hypothesized such that the groundwater flowrate at the MWCF is increased 10 times by earthquake. The Impact #2 could be occurred up to 2 times. That is, the maximum numbers of occurrence times of Impacts #1 and #2 are 1 and 2, respectively. As the final step of the preliminary process (Fig. 2), the criteria for classification of earthquake impacts were determined. For the first criterion, if the magnitude of an earthquake is larger than 7.5, the Impact #1 will be applied to the repository system. For the second criterion, if the ratio of the earthquake magnitude to the distance from the hypocenter (M/D) is larger than 0.5/km, the Impact #2 will be applied. As expected, if both criteria #1 and #2 are met, both Impact #1 and #2 will be occurred at the same time. Otherwise, there will be no impact on the repository system by the earthquake. In the following main process (Fig. 2), scenario was firstly generated by Monte Carlo sampling for the aleatory uncertainty. There may be many earthquakes during the simulation period which is 1,000,000-year in this study (the outbreak times are determined by Eq. (2)). Once an earthquake is occurred, the properties of
earthquake (randomly generated by Eqs. (4) and (6)), will be judged by the criteria above and then it will be determined which impact will be applied to the repository system. Based on the occurrence sequence of the impacts, therefore, the complex scenarios can be categorized by 5 types including the simultaneous occurrence of Impacts #1 and #2 (Table 1). Following is a possible scenario of Scenario Category #1 for example. The magnitude of the first earthquake is larger than 7.5 and the M/D is smaller than 0.5, and thus the function of the far-field rock is failed. The magnitude of the second earthquake is smaller than 7.5 and the M/D is larger than 0.5, and thus the flowrate at the MWCF is increased by 10 times. At this time, the function of the far-filed rock is still remained as failed, so that the both Impact #1 and #2 will influence to the repository system. Finally, the following earthquake meets the second criterion again, and thus the flowrate at the MWCF is increased by 10 times again (100 times in total). And, any additional earthquakes are not influential to the repository system since then. After a scenario was generated, the scenario was assessed by GSTSPA, and the main process (Fig. 2) was iterated for 100 times. 3.2. Risk assessment results The results of the risk assessment for the complex scenario designed above are depicted in Fig. 3. The black lines are the temporal distribution of the each exposure dose rates resulted from the 100 iterations, and the purple line is the averaged exposure dose rate. The red dots and blue circles indicate the magnitudes of the
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earthquakes which induce Impacts #1 (far-field fail) and #2 (MWCF flowrate increase), respectively. The red dots and blue circles at the same locations indicate that the earthquakes induced both Impact #1 and #2 at the same time: these events must be the elements of the scenario which is categorized as Category #2 and #4 in Table 1. The influence of Impact #2 (MWCF flowrate increase) seemed to be insignificant since any changes of exposure dose rates correlated with the blue circles were not observed in Fig. 3. The result corresponds with the preliminary sensitivity analysis (Lee and Jeong, 2012, Table 2) in which the Darcy velocity and plume width of the MWCF were known to be insignificant parameters. On the other hand, Impact #1 (far-field fail) induced the distinct increase of dose rate as the step-up of the exposure dose rates had correlation with the red dots in Fig. 3. The largest increase of the exposure dose rate by Impact #1 was almost 1-order difference at about 10,000 years. The result also corresponds with the highly ranked parameters related to the far-field hydrology in the preliminary sensitivity analysis (Lee and Jeong, 2012, Table 2). Interestingly, the influence of Impact #1 was not occurred anymore just after the exposure dose rates hit the peak (about 200,000 years). From the result, it can be carefully discussed that the function of the far-field rock is no longer valid after the exposure dose rate hits the peak. Since the effect of Impact #2 was insignificant, the difference between the results from Impact #2 (red dots) only and both Impact #1 and #2 (red dots in blue circles) was hardly detectable. Nevertheless, it can be reasonably discussed that the complex scenario was well simulated and assessed by the new methodology suggested in this study. Finally, the total risk (green line in Fig. 3) was computed by multiplying the dose-to-risk conversion factor (= 0.05/Sv; CIRRPC, 1992) to the averaged exposure dose rates. Since the convergence criteria were not defined in this assessment, the iteration number of the main process with Monte Carlo sampling was predefined as 100. Instead, the occurrence probability of the scenario category was compared with the pseudo-theoretical probability (Table 1). From each iterative simulation, the scenario was analyzed based on the sequence of events occurred and then categorized as one of the five scenario categories in Table 1. After the last iterative simulation, the numbers of scenarios for each scenario category were normalized to compute the occurrence probability of the scenario category. From the result, Scenario Category #5 had the majority (51%) of the occurrence probability and Scenario Categories #2 (25%), #4 (15%), #1 (7%), and #3 (2%) were followed in order. The pseudo-theoretical probabilities for each scenario category were separately computed by 100,000 Monte Carlo samplings, which is much bigger than the number of iterative simulations (= 100), for Eqs. (2), (4) and (6) without any scenario assessment. Comparison between the occurrence probabilities resulted from the iterative simulations and the pseudo-theoretical values in Table 1 was intended to see if the number of iterative simulations (= 100) was enough to show the convergence of the results. Although the two results were not exactly same, the proportions for each scenario category between them were almost same having the same order. Overall, the result confirms that the total risk computed by the new methodology for the risk assessment involves the occurrence probabilities of the complex scenarios and the probabilities reasonably converge into the pseudo-theoretical probabilities.
4. Conclusion A methodology for a risk-based approach to a complex scenario in a long-term safety assessment of a radioactive waste repository was developed using a Monte Carlo sampling method in this study. The robustness of the methodology could be confirmed by the results showing the occurrence probabilities of the complex
scenarios were reasonably converged into pseudo-theoretical values. The efficiency of the risk assessment can be considerably improved with the following advantages: • Not necessary to compute separately the occurrence probabilities and exposure dose rates of each scenario; - Occurrence probability of the scenario is inherent in the classification of the complex scenarios and it is determined in the Monte Carlo samplings of event properties (e.g., Eqs. (2), (4) and (6)). • Not necessary to simulate all possible scenarios (almost infinite scenarios) from Monte Carlo sampling; - Convergence of the assessment results can be monitored at the every other simulation, and the scenario which has low occurrence probability will be automatically excluded. • Capable of representing the complementary effects of more than two events on the repository system; and - The complex scenarios generated by the new methodology include the complementary conditions in which two or more events and/or two or more impacts by an event are occurred simultaneously and/or sequentially (Table 1). • Convenient to automate the assessment process. The newly suggested methodology will be efficiently capable of carrying out the risk assessment for the complex scenarios with various external events in the long-term safety assessment of a radioactive waste repository. For further study, the characterizations of the events and the impacts of the events on the repository system should be carefully determined for a successful assessment. Acknowledgments This work was supported by the Nuclear Research and Development Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP). References Barnard, R.W., Wilson, M.L., Dockery, H.A., Gauthier, J.H., Kaplan, P.G., Eaton, R.R., Bingham, F.W., Robey, T.H., 1992. TSPA 1991: An Initial Total-System Performance Assessment for Yucca Mountain. SAND91-2795. Sandia National Laboratories, Albuquerque, NM. Campbell, J.E., Cranwell, R.M., 1988. Performance assessment of radioactive waste repositories. Science 239, 1389–1392. Choi, H.-J., Lee, M., Lee, J.Y., 2011. Preliminary conceptual design of a geological disposal system for high-level wastes from the pyroprocessing of PWR spent fuels. Nuclear Engineering and Design 241, 3348–3356. CIRRPC, 1992. Use of BEIR V and UNSCEAR 1988 in Radiation Risk Assessment – Lifetime Total Cancer Mortality Risk Estimates at Low Doses and Low Dose Rates for Low-LET Radiation. Science Panel Report No. 9. Committee on Interagency Radiation Research and Policy Coordination. DOE (US Department of Energy), 1998. Viability Assessment of a Repository at Yucca Mountain: Introduction and Site Characteristics. DOE/RW-0508. Office of Civilian Radioactive Waste Management, US Department of Energy, Washington, DC. DOE (US Department of Energy), 2008. Yucca Mountain Repository License Application, Safety Analysis Report. DOE/RW-0573. Office of Civilian Radioactive Waste Management, US Department of Energy, Washington, DC. GTG (GoldSim Technology Group), 2010. GoldSim User’s Guide: Probabilistic Simulation Environment. GoldSim Technology Group LLC, Washington, DC. Hwang, Y., Kang, C.-H., 2010. The development of a safety assessment approach and its implication on the advanced nuclear fuel cycle. Nuclear Engineering and Technology 42 (1), 37–46. ICRP (International Commission on Radiation Protection), 2000. Radiation Protection Recommendations as Applied to the Disposal of Long-Lived Solid Radioactive Waste. ICRP Publication 81. Pergamon Press, Oxford. Lee, Y.-M., Hwang, Y., 2009. A GlodSim model for the safety assessment of an HLW repository. Progress in Nuclear Energy 51, 746–759. Lee, Y.-M., Jeong, J., 2012. A Probabilistic Safety Assessment of a Pyro-processed Waste Repository. Journal of Korean Radioactive Waste Society 10 (4), 263–272. Rydelek, P.A., Sacks, I.S., 1989. Testing the completeness of earthquake catalogues and the hypothesis of self-similarity. Nature 337 (19), 251–253.
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