Analysis of Transient Overpower Scenarios in Sodium Fast Reactors

Transcription

1 Analysis of Transient Overpower Scenarios in Sodium Fast Reactors Thesis Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Graduate School of The Ohio State University By David Grabaskas, B.S. Nuclear Engineering Graduate Program The Ohio State University 2010 Thesis Committee: Dr. Richard Denning, Advisor Dr. Tunc Aldemir

2 Copyright by David Grabaskas 2010

3 ABSTRACT The objective of this research was the demonstration of a methodology to handle epistemic and aleatory uncertainties within an unprotected transient overpower (TOP) scenario in a sodium fast reactor. This study included a comparison of the risk of TOP scenarios to safety limits that are being considered by the U.S. Nuclear Regulatory Commission for future reactor designs. An analysis of the relative importance of uncertainties was also made. The results of this experiment demonstrated that the core damage frequency for an unprotected transient overpower scenario fell well below the proposed safety limits, even without taking credit for the reliability of the reactor protection system. The control rod driveline feedback and Doppler feedback mechanisms were found to be the most important epistemic uncertainties. ii

4 ACKNOWLEDGEMENTS I would like to thank Dr. Richard Denning for all his guidance and assistance throughout my time in the BS/MS program and as a graduate student. I would finally like to thank all of the professors and students in the nuclear engineering department for their contributions to my education. I would like to thank the Nuclear Regulatory Agency which provided the funding for the fellowship which made my research possible. I would like to thank the Department of Energy for the larger NERI project which included this research. I would like to thank Argonne National Lab for their assistance with past sodium reactor experience and their willingness to help with SAS4A/SASSYS-1. iii

5 VITA December 18, Born Youngstown, Ohio 2008.B.S. Mechanical Engineering The Ohio State University OSUNE Fellow (NRC Funded) The Ohio State University MAJOR FIELD: Nuclear Engineering FIELDS OF STUDY iv

6 TABLE OF CONTENTS Page ABSTRACT... ii ACKNOWLEDGEMENTS... iii VITA... iv LIST OF FIGURES... vi LIST OF TABLES... vii CHAPTER 1 INTRODUCTION... 1 CHAPTER 2 BACKGROUND Accident Analysis for Sodium Fast Reactors Uncertainty Analysis Regulatory Application of Uncertainty Analysis Risk Informed Approach NRC Guidance for the Treatment of Uncertainties Sodium Reactor History and ABR CHAPTER 3 METHODOLOGY Approach Epistemic Uncertainties Aleatory Uncertainties CHAPTER 4 COMPUTER MODELS, RESULTS & ANALYSIS SAS4A Model Experiment Procedure Epistemic Values Chosen SAS4A Runs Conducted for Combination of Aleatory Cases Core Damage Frequency Without Time in Cycle Results Analysis Comparison with Safety Goals Importance Measures CHAPTER 5 CONCLUSIONS & FUTURE WORK Conclusions Limitations Future Work LIST OF REFERENCES APPENDIX A: Raw Experiment Results v

7 LIST OF FIGURES Page Figure 2.1 Illustration of CSAU Method [4]... 7 Figure 2.2 Elements of Risk-Informed Integrated Decision Making Process Figure 2.3 TNF Frequency-Consequence Curve Figure 2.4 Pool Type Sodium Fast Reactor Design [15] Figure 2.5 Loop Type Sodium Fast Reactor Design [15] Figure 3.1 Reactivity Insertion Rate Bins Figure 3.2 Total Reactivity Insertion Amount Bins Figure 3.3 Total Reactivity Insertion Amount Frequency Figure 3.4 Time in Cycle Binning Structure and Probabilities Figure 3.5 Reactivity Insertion Amount Partitioning Between BOC and 14.5% of the Reactor Cycle (Black indicates Area Where Core Disruption Accident is not Possible) Figure 3.6 Reactivity Insertion Amount Partitioning Between 14.5%-29% of the Reactor Cycle Figure 3.7 Reactivity Insertion Amount Partitioning Between 29%-43.5% of the Reactor Cycle Figure 3.8 Reactivity Insertion Amount Partitioning Between 43.5%-58% of the Reactor Cycle Figure 3.9 Reactivity Insertion Amount Partitioning Between 58%-72% of the Reactor Cycle Figure 3.10 Reactivity Insertion Amount Partitioning Beyond 72% of the Reactor Cycle Figure 4.1 SAS4A ABR1000 Model Figure 4.2 Core Damage Frequency Over Time in Cycle Figure 4.3 Core Damage Frequency Figure 4.4 Doppler Feedback, CDF Correlation Figure 4.5 Axial Feedback, CDF Correlation Figure 4.6 Coolant Feedback, CDF Correlation Figure 4.7 CRDL Feedback, CDF Correlation Figure 4.8 Radial Feedback, CDF Correlation Figure 4.9 Doppler Feedback, Failure Correlation Figure 4.10 Axial Feedback, Failure Correlation Figure 4.11 Coolant Feedback, Failure Correlation Figure 4.12 CRDL Feedback, Failure Correlation Figure 4.13 Radial Feedback, Failure Correlation Figure 4.14 Residuals for Full Quadratic Model Figure 4.15 Residuals for Fully Reduced Model vi

8 LIST OF TABLES Page Table 2.1 F-C Curve Limits for Dose/Frequency to Public Table 3.1 Epistemic Feedback Uncertainty Distribution Table 3.2 Total Reactivity Insertion Amount Frequencies and Source Table 4.1 SAS4A Model Channels Table 4.2 Example Epistemic Uncertainty Draw From Realization Table 4.3 Example Aleatory Combination From Realization Table 4.4 Final Core Damage Frequencies 100 Realizations Table 4.5 Exponential Fits for CDF for Epistemic Uncertainties Table 4.6 Linear Fit for Pin Failure Time for Epistemic Uncertainties Table 4.7 Sum of Squares Values for Epistemic Uncertainties vii

9 CHAPTER 1 INTRODUCTION As part of a joint Nuclear Energy Research Initiative (NERI) project between The Ohio State University, the Massachusetts Institute of Technology, and Idaho State University, an investigation was launched regarding sodium reactor accident transient behavior. The goal of this project was to establish a methodology that could be used to discover ways to reduce the costs of the reactor while ensuring that it will meet future safety and non-proliferation requirements. One task of this project has been to conduct safety analyses of selected accident scenarios with a detailed treatment of the associated uncertainties, as will be required in future license applications. A realistic assessment of uncertainties is a critical aspect of assuring that appropriate safety margins are maintained in the design. This is particularly important in a risk-informed design approach in which the designer may intentionally reduce unnecessary margin for economic reasons. The primary objectives of this study were to develop methodologies to support the application of risk tools in the design process and to examine the 1

10 characteristics of severe accidents in metal-fueled, sodium-cooled fast reactors. Because of the conceptual nature of the design, a number of assumptions were made about the design features of the plant analyzed and the frequencies of accident initiators. 2

11 CHAPTER 2 BACKGROUND 2.1 Accident Analysis for Sodium Fast Reactors Accident analysis for sodium-cooled fast reactors (SFRs) needs to focus on different kinds of accident scenarios than for light water reactors. Light water reactor safety concerns are primarily associated with loss-of-coolant accidents leading to core uncovery, heatup, and release of radioactive fission products. Reactivity insertion accidents in light water reactors are generally not of primary concern because of the inherent feedback effects, in particular due to a rapid and strong negative Doppler reactivity feedback, a negative moderator temperature coefficient and negative void coefficient. Because these reactors operate near the optimum reactivity configuration, any change in geometry or loss of coolant is likely to shut the reactor down, rather than to lead to a more reactive configuration. Nevertheless, reactor protection system reliability can be an issue in light water reactor transients, which has led to special regulatory consideration of anticipated transients without scram [1]. Loss of coolant accidents have not been the focus of regulatory concerns for sodium-cooled fast reactors because the reactor coolant system pressure is 3

12 nominal, flashing of sodium would not occur in a loss of coolant event, and guard vessels or guard pipes can be used to provide an additional level of defense in the event of a breach of the reactor coolant system. The regulatory issues with SFRs have historically been associated with the potential for reconfiguration of the core in a severe accident resulting in a more reactive condition and an energetic power excursion. Before the ability to model core heatup mechanistically, very conservative analyses were performed, called Bethe-Tait analyses, to assess the potential energy release and associated mechanical damage that could result from a hypothetical core disruptive accident [2]. Although some SFRs have been licensed world-wide, the licensing processes have been difficult. The Clinch River Breeder Reactor Project, which was to construct the first large demonstration unit in the U.S., undertook a major licensing effort prior to cancellation of the project. The other feature of fast reactors that impacts licensability is the positive void coefficient that could potentially lead to accidents in which core geometry is affected. The two most likely paths to core damage in an SFR are transient overpower or a loss of coolant flow. Flow blockage led to fuel damage in the Fermi 1 reactor but good fuel assembly design can substantially reduce the likelihood of substantial blockage of an assembly [3]. In general, SFR designs are able to accommodate rod withdrawal accidents without core damage if the reactor protection system functions and 4

13 control rods are rapidly inserted into the core. For this reason, SFR accident analysis has given more attention to scenarios in which the reactor control rods fail to insert. These are the so-called unprotected sequences. This thesis examines unprotected transient overpower (UTOP) accidents. The UTOP scenarios considered for this analysis are ones initiated by a control rod(s) withdrawal, followed by a failure to SCRAM. Transient overpower could be initiated by other mechanisms, such as the introduction of a gas bubble in the core or by core distortion. However, the control rod withdrawal accident is one that can be anticipated to occur with some frequency in a large population of reactors, at least with regards to very small reactivity insertions, since the control rods have both human and mechanical failure mechanisms. The maximum reactivity inserted is limited by the amount of excess reactivity of the operating reactor. 2.2 Uncertainty Analysis Regulatory Application of Uncertainty Analysis Traditionally, in the performance of regulatory analyses, the U.S. Nuclear Regulatory Commission (NRC) required conservative assumptions to be used to allow for uncertainties in the understanding of physical processes. The most familiar example is Appendix K to 10 CFR 50, which describes an approach to 5

14 the calculation of peak clad temperature in light water reactor loss of coolant accidents. Non-physical selections are made in the calculational method to assure that the calculated temperature is greater than would occur under realistic conditions. There was a growing recognition, however, that it isn t always clear what the impact is of a presumably conservative assumptions (those believed to over-estimate the consequences) and that conservative calculations do not necessarily lead to good regulatory decisions. An evaluation method called Code Scaling, Applicability and Uncertainty (CSAU) was developed by NRC staff, which provided an approach to the use of best estimate analysis plus consideration of uncertainties as an alternative to conservatism in models. As Figure 2.1 shows, the importance of uncertainties and biases, of input parameters and coding practices, plays an integral part in the CSAU analysis [4]. 6

15 Figure 2.1 Illustration of CSAU Method [4] 7

16 2.2.2 Risk Informed Approach The first major risk study, WASH-1400, was issued in Initially, the response of the NRC Commissioners was cautious with regards to the use of risk results in reactor regulation. The review of the Three Mile Island Unit 2 accident, which occurred in 1978, indicated that many of the design and operating weaknesses identified in WASH-1400 contributed to the accident [5]. The subsequent NUREG-1150 study substantially advanced the methods of risk assessment, particularly with regards to the treatment of risk uncertainties [6]. The first major commitment by the NRC to risk-informed regulation was the requirement for each plant to perform a Level I risk assessment in the Individual Plant Evaluation program and subsequently the Individual Plant Evaluation of External Events program [7]. In 1994 the NRC began the PRA Implementation Plan, which expanded the use of PRA in the agency [8]. This was followed by the Risk-Informed Regulation Implementation Plan (RIRIP), which began in 2000 [9]. This project prioritized which practices should become risk-informed. The Risk-Informed and Performance Based Plan (RPP) followed RIRIP and continues to present day [10]. With the RPP and its components, such as the white paper Risk-Informed and Performance-Based Regulation and Regulatory Guide (RG) An Approach for Using Probabilistic Risk Assessment in Risk-Informed Decisions on Plant-Specific Changes to the Licensing Basis, the 8

17 NRC has laid the framework for a risk-informed regulatory decision-making process NRC Guidance for the Treatment of Uncertainties The treatment of uncertainties in a PRA has changed substantially from the cursory treatment used in WASH One of the major improvements in PRA methodology undertaken in NUREG-1150 was the treatment of uncertainty. In NUREG-1150, risk assessment is inherent to the process. Rather than undertaking a best-estimate analysis and applying uncertainties to those results, in NUREG-1150, distributions of results are obtained from which a central estimate can be derived by averaging over the distribution [6]. The NRC published Regulatory Guide (RG) 1.200, An Approach for Determining the Technical Adequacy of Probabilistic Risk Assessment Results for Risk-Informed Activities, in early 2007 [11]. This document outlined an approach to determine the quality of a risk-informed analysis and the level of confidence which should be placed in its results. This approach included guidance from the Advisory Committee on Reactor Safeguards (ACRS), which recommended a sensitivity analyses within the process. The ACRS noted the following: 9

18 a systematic treatment should include rigorous analyses for parametric uncertainties, sensitivity studies to identify the important epistemic uncertainties, and quantification of the latter. In a risk-informed environment, the proper role of sensitivity study is to identify what is important to the results, not to replace uncertainty analysis. The influence of ACRS can be seen within RG 1.200, which states, An important aspect in understanding the base PRA results is knowing what are the sources of uncertainty and assumptions and understanding their potential impact. [11] In early 2009, the NRC published NUREG -1855, Guidance on the Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making [12]. This document outlined the procedure to treat uncertainties within a decision-making process. Due to the recommendations and guidance of RG 1.200, NUREG deals not only with the treatment of uncertainties within the experiment, but the assessment of uncertainties and their role within, what is called, an integrated decision. An overview of the process detailed in NUREG can be seen in Figure

19 Figure 2.2 Elements of Risk-Informed Integrated Decision Making Process Element 3 and Element 4 describe the treatment of uncertainties within the analysis and are the focus of NUREG The probabilistic analysis segment of Element 3 consists of the following steps: 1) Identifying the risk measures to be used in evaluating the impact of the decision on risk 2) Identifying the numerical guidelines used to determine the acceptability of the risk impact 3) Constructing a PRA model to generate those results 4) Comparing the results to the acceptance guidelines 5) Documenting the conclusions From there, the importance of each uncertainty can be assessed using a sensitivity analysis, as described in RG The experiment conducted in this thesis used 11

20 the guidelines set forth by NUREG In this experiment, the results of Element 3 are as follows: 1) The risk measure is core damage frequency (CDF) 2) The safety goals are those set in the technology neutral framework guidelines* 3) The PRA model is described in Chapter 3 and used SAS4A/SASSYS-1 4) A comparison to the safety goals is in Chapter 4 of this thesis 5) The conclusions are documented in Chapter 5 of this thesis * Technology Neutral Framework The Technology Neutral Framework (TNF) is outlined in NUREG 1860 [13]. It is the concept of a risk-informed, performance based regulatory structure that could be applicable to advanced reactor designs and serve as an alternative to 10 CFR 50 for the licensing of future nuclear power plants. Within this framework, licensing basis events are defined that must satisfy safety limits imposed by a frequency-consequence (F-C) curve. This curve can be seen in Figure 2.3 with a description of the limits in Table 2.1. As seen on the figure, these limits are derived from previous licensing documents such as 10 CFR 50 and EPA Protective Action Guides [13]. 12

21 Figure 2.3 TNF Frequency-Consequence Curve 13

22 Dose Range Frequency (per year) 1 mrem 5 mrem 1E+0 5 mrem 100 mrem 1E mrem 1 rem 1E-3 1 rem 25 rem 1E-4 25 rem rem 1E rem rem 1E rem 500 rem 5E-7 > 500 rem 1E-7 Table 2.1 F-C Curve Limits for Dose/Frequency to Public There is another important limit of the F-C curve not featured on the figure. If an event has a point estimate frequency below 1E-8 per year, it does not have to satisfy a consequence limit and may be dropped from the list of licensing basis events. For the UTOP study performed in this thesis, only a Level 1 type of PRA analysis is conducted with focus on the frequency of core damage. Within the context of the (TNF), the 1E-8 per year threshold provides a guideline to the designer for the reliability of the reactor protection system. If the assessed frequency of core damage exceeds the frequency threshold, the designer could choose to add an additional, diverse protection system. Conversely, if the assessed frequency is far below the threshold, the designer could relax 14

23 requirements. This type of tradeoff must continue to assure adequate safety margin and defenses in depth, however. Two key elements to the UTOP scenario analysis in this report are the margin to the safety limit curve and the individual contributions of uncertainties. The margin is important because it may allow for tradeoffs to be made between the margin to the safety goals and other factors, like economics. This possibility was foreseen by the NRC and in 2003 they released NUREG-CR-6833, Formal Methods of Decision Analysis Applied to Prioritization of Research and Other Topics [14]. This document details how to formulate a hierarchy of objectives and how to assess the results of an analysis, with uncertainties, and how they pertain to the set objectives. While the possible tradeoffs that can be made from the UTOP analysis results are not described in detail in this report, they were part of the larger joint NERI project. Calculating the relative importance of the various uncertainties does not only have benefits in the reactor design process, but also the licensing process. As RG stated, a sensitivity analysis conducted in order to determine the most influential uncertainties will also play an important in the licensing process. This is the case since it can be used a metric to determine the quality of a PRA analysis. As the analyst becomes more aware of the role that each uncertainty plays within the PRA, the quality of the PRA, and the confidence in the results, should also increase. NUREG-CR-6833 also provides guidance for this process 15

24 through its Code Scaling, Applicability, and Uncertainty Evaluation Methodology (CSAU), as discussed earlier. 2.3 Sodium Reactor History and ABR1000 Sodium Reactor Types There are several different varieties of SFRs. The two main design types are the loop and pool configurations. Pool designs consist of a large sodium pool in which the reactor core and intermediate heat exchanger sit. Figure 2.4 shows an example of a pool type sodium fast reactor [15]. A benefit of the pool type reactor design is the large thermal inertia of the pool. Due to the size of the pool, the time needed to heat up the sodium is increased. The size and the cost of the reactor pool is a potential drawback of the design. 16

25 Figure 2.4 Pool Type Sodium Fast Reactor Design [15] The loop type reactor design consists of a much smaller sodium pool and a separate intermediate heat exchanger. Figure 2.5 shows an example of the loop type design [15]. While the reactor vessel is smaller, and therefore less costly, than the pool type reactor, the operating pressure is higher and there is far more piping which increases the chance of sodium leaks. 17

26 Figure 2.5 Loop Type Sodium Fast Reactor Design [15] Many SFRs can also act as either a breeder or burner reactor. The breeder reactor fuel configuration is designed to produce more fissile material than it consumes. The burner reactor fuel configuration is used to convert actinides and plutonium to more desirable elements. One major difference between the two configurations, which is of particular interest to this analysis, is the amount of excess reactivity present. Since the blanket of a breeding reactor is absorbing some of the neutrons in order to create more fissile material, the reactor operates with a lower excess reactivity than a similar burner configuration. This would limit the possible reactivity insertion amount from a control rod misalignment. A major point of contention in the evolution of sodium fast reactor design has been the option of using oxide or metal fuel. Oxide fuel is a composite of 18

27 uranium, transuranics, and oxygen, while metal fuel is a mix of uranium, transuranics, and zirconium. Oxide fuel can withstand much higher temperatures than its metallic counterpart; however, oxide fuel has much lower heat conductivity and a smaller thermal expansion coefficient. As a result, in a transient, oxide fuel will not expand to the extent that metallic fuel will. The greater the fuel expansion, the greater the inherent negative reactivity feedback effect in a fast reactor. The tradeoff between the lower melting point of metallic fuel and its inherent feedback qualities has long been a point of dispute. Metallic fuel has also demonstrated an interesting characteristic in sodium reactor transient experiments. During the 1980 s, metal fuel experiments were conducted at the Transient Reactor Test (TREAT) facility at ANL [16]. These tests were conducted to verify metallic fuel s inherent feedback mechanisms along with establishing its margin to pin failure. In the tests, it was observed that metal fuel pins, during heating, would elongate in the axial direction before failing at the top of the pin. Since the melting point of the clad (HT-9) is higher than the melting point of metal fuel, the fuel would liquefy and rise to the top of the pin before breaching the clad and being swept out of the core. Since pin failure would occur at the top of the pin and the released fuel was swept away from the core, it would result in a negative reactivity feedback on the reactor. There are several other types of sodium fast reactor fuel, although they are far less popular than oxide and metal fuel. Uranium nitride fuel is a ceramic fuel 19

28 which uses 15 N. It has better thermal conduction than oxide fuel and a higher melting point than metal fuel. However, it is a very expensive fuel to manufacture and difficult to reprocess. Uranium carbide is another ceramic fuel with higher thermal conductivity than oxide fuel. It has had a resurgence of popularity as a nuclear fuel in small TRISO particles [17]. However, there is a potential for sodium and uranium carbide to react at higher temperatures. Due to the low operating pressure of sodium reactors, there has been some debate of the necessity of a containment structure. Instead, some have suggested the use of a confinement structure. In light water reactors, the design of the containment is based on the possible containment pressure during a reactor blowdown. Since sodium reactors operate near atmospheric pressure, the necessary design pressure of the containment is not clear. One possible design basis would be the pressure increase from a sodium spray fire. It is becoming more likely that the need for a containment will not come from internal threats, but external ones, like aircraft crashes [18]. Since a shield building will most likely be mandatory for licensing to protect the plant from external threats, the potential cost savings from using a confinement system rather than a hardened containment may be minimal. 20

29 American Sodium Reactor History The first liquid metal fast reactor built, and the first nuclear reactor to create electrical power, was Experimental Breeder Reactor (EBR) I at Idaho National Laboratory [19]. EBR-I was a 1.4 MWth, 200 kwe loop type reactor, which used a sodium-potassium (NaK) coolant. The main purpose of EBR-I was the validation of the breeder reactor concept. It operated successfully from 1951 to 1955, when it suffered a partial meltdown. The reactor was repaired and continued to operate until EBR-I was followed soon after by EBR-II, which went online in 1965 [20]. EBR-II was a 63.5 MWth, 19 MWe pool type reactor which was designed to test metallic fuel. One of the most important experiments carried out at EBR-II was an unprotected loss of flow test. The reactor was brought to full power, then the main primary pumps were shut off and the reactor shutdown systems were deactivated. Due to the thermal expansion of the metal fuel, plus other inherent feedback mechanisms, reactor power dropped to approximately zero within 300 seconds. This was a vital step in the demonstration of the sodium reactor s inherent safety features. The success of EBR-II led to the development of the Clinch River Breeder Reactor Project (CRBRP) and the Advanced Liquid Metal Reactor (ALMR) project (later renamed the Integral Fast Reactor (IFR)). CRBRP was a planned 21

30 1000 MWth, 380 MWe loop type plant [21]. As mentioned earlier, budget issues along with licensing problems resulted in the cancellation of the CRBRP in ALMR/IFR began in 1984 at Argonne National Lab (ANL) [22]. GE was also involved in the process with their commercial reactor design The Power Reactor Inherently Safe Module (PRISM) [23]. PRISM was to be a small (840 MWth), modular, pool type reactor design which could be built offsite and transported to its operating location. It also included a reactor vessel auxiliary cooling system (RVACS) which provided passive decay heat removal by using natural circulation around the reactor guard vessel. PRISM lacked a traditional containment building, instead relying on a small metal containment dome above the reactor. A pre-application review was submitted to the NRC for PRISM in 1986, and the NRC completed its review in Despite the licensing progress, no PRISM reactors have been built. PRISM evolved into SuperPRISM (S-PRISM) in the late 1990 s [24]. S- PRISM is very similar to PRISM, but uses a small concrete containment building instead of the metal dome. S-PRISM is still under development and has been proposed by GE-Hitachi as the nuclear plant for future fuel recycling efforts in the U.S. The Advanced Burner Reactor (ABR) 1000 reactor design is the latest sodium fast reactor concept from ANL [25]. It was original proposed as a demonstration of transmutation technology as part of the Global Nuclear Energy 22

31 Partnership (GNEP). It was designed using almost all proven technology and components. It embodies the accumulation and culmination of past ANL sodium reactor designs, such as ALMR/IFR. ABR1000 is a 1000MWth, 380 MWe reactor that could use either metal or oxide fuel. It is a similar design to S-PRISM, but it also has a hardened, light water reactor type containment and uses a direct reactor auxiliary cooling system (DRACS). DRACS is a passive system that uses natural circulation to remove heat directly from the sodium in the pool. The ABR1000 reactor design is the plant used for the analysis in this report. ABR1000 is not a complete reactor design. Many systems, such as the control rod mechanism, have not been explicitly detailed. This makes a full analysis of the reactor performance in a transient difficult. Because of this limited information, certain assumptions about reactor systems were made based on previous sodium reactor designs. In order to satisfy the objectives of this study, it was not necessary to proceed beyond Level 1 PRA considerations. 23

32 CHAPTER 3 METHODOLOGY 3.1 Approach In order to properly model the uncertainty within the UTOP scenario, the uncertainties were split into two categories: aleatory and epistemic uncertainties. Epistemic uncertainties are those that arise from a lack of knowledge or understanding in the modeling of a phenomenon. For the cases analyzed, the uncertainty in the feedback coefficients is the result of both a lack of understanding of the design of the system being analyzed (since the design is only conceptual) and from modeling uncertainties for the estimation of feedback effects given a specific design. Aleatory uncertainties, on the other hand, are an aspect of the inherent randomness of the timing and conditions under which an accident could be initiated. In this case, the time in cycle when the transient occurs, along with the magnitude and rate of the transient were considered aleatory uncertainties. 24

33 3.1.1 Epistemic Uncertainties Five epistemic uncertainties were included in the analysis. These are the five reactivity feedback mechanisms with the greatest effect on reactor transient behavior. The feedback mechanisms, along with their standard deviations, are shown in Table 3.1. The epistemic uncertainty distributions are assumed to be normal distributions. The form of the distribution and standard deviations were developed by Argonne National Laboratory [26]. Feedback Mechanism Standard Deviation Control Rod Driveline 20% Fuel Axial Expansion 30% Fuel Radial Expansion 20% Doppler 20% Coolant Void 20% Table 3.1 Epistemic Feedback Uncertainty Distribution 25

34 Doppler Feedback As the temperature of the fuel increases, the increased vibrational motion of the 238 U molecules results in an effective broadening of the absorption resonances and increased parasitic absorption. As a result, the effect on reactivity is negative. While the Doppler feedback is a dominant in light water reactors, the effect in a fast reactor is much smaller. Control Rod Driveline Feedback As the reactor temperature increases during the transient, the outlet temperature of the core will also increase. This causes the control rod lines, above the core, to be heated. As the control rod lines increase in temperature, thermal expansion will cause the lines to elongate downward, inserting the control rods further into the reactor. This results in a negative reactivity feedback effect. Since this analysis is assuming a transient overpower due to control rod withdrawal, there would be some correlation between the control rod driveline feedback and the amount of reactivity inserted. Depending on the time in cycle, and the amount of control rods withdrawn, the potential feedback effects of control rod driveline expansion would differ. However, since the control rod system is not fully designed, it was not a correlation which could be derived for 26

35 this analysis. Instead, control rod driveline feedback is treated as a separate mechanism. Fuel Axial Expansion Feedback During the transient, the metallic fuel pins will increase in temperature. This will cause them to elongate and expand the core. This expansion results in a less compact configuration and a negative reactivity feedback effect. Fuel Radial Expansion Feedback Similar to the fuel axial expansion, the fuel will also expand in the radial direction. This will always cause the fuel core to be less compact, resulting in a negative feedback effect. Fuel radial and axial expansion are inherently correlated. However, in this analysis they are treated as separate phenomena so that the importance of each effect can be determined. Sodium Coolant Density Feedback Sodium coolant density is the only feedback of the five epistemic uncertainties that provides a positive feedback effect as temperature increases. As the sodium increases in temperature, it becomes less dense and its moderation effects lessen. In this region of the energy spectrum, a harder spectrum results in 27

36 an increase in reactivity. Decreased density of the sodium also results in more leakage of neutrons and a decrease in reactivity but this effect is only larger than spectral hardening effect near the periphery of the core. If the accident proceeds to the point at which the sodium begins to boil, the amount of reactivity insertion can be substantial Aleatory Uncertainties Three aleatory uncertainties were included in the analysis. These uncertainties are associated with the reactivity insertion rate, the total reactivity insertion amount, and the time in cycle in which the UTOP occurs. In concept, these parameters are treated as if there is a known frequency distribution for each variable and that accidents occur at random, effectively selecting a value randomly according to the associated frequency distributions. Thus, the associated risk is representative of the expected outcome of a large number of accidents from a population of reactors of essentially identical design. It is recognized that lack of knowledge of these frequency distributions could also be treated as having an associated epistemic uncertainty, adding an additional level of complexity. 28

37 Reactivity Insertion Rate A simplified approach was taken for the reactivity insertion rate. Realistically, the reactivity insertion rate magnitude and probability would depend on the design and potential failure modes of the control rod system. If one knew the control rod worths, control rod withdrawal control logic, and the possible control rod withdrawal rates, a more plant specific assessment could be made. However, since the analysis was made on a reactor type without a fully designed control rod system, the probability of the different reactivity insertion rates was assumed to be uniform over the range of rates considered. Figure 3.1 shows the binning structure used for the reactivity insertion rates and the associated probabilities. The reactivity insertion rate was taken to be a value between 0.0 /s and /s. The maximum of /s was determined by using the methodology in the ALMR PRA via the following steps: 1) Determine the average reactivity ramp rate of a single rod by dividing the total excess reactivity by the length of the rods in the core and multiplying that value by the speed of the control rod drive (assuming withdrawal rate from ALMR PRA) 2) Multiply the average ramp rate by the number of rods being withdrawn to determine the ramp rate 29

38 The interval of possible insertion rates was split into five equal bins. The midpoint of these intervals was used in the analysis. Figure 3.1 Reactivity Insertion Rate Bins Total Reactivity Insertion Amount The total reactivity insertion amount also depends on the design of the control rod system. Figure 3.2 shows the binning structure used for the total insertion amount. Since this analysis focused on challenging transients which could possibly lead to core disruption, a lower bound of $0.90 was used. This was determined to be the threshold of UTOP transient that could possibly lead to immediate fuel pin failure. A maximum of $3.30 was used based on the maximum rod worth for the conceptual design of the reactor. 30

39 Figure 3.2 Total Reactivity Insertion Amount Bins To determine the frequencies to apply to each total insertion amount bin, the probability distribution of rod worth from the Advanced Liquid Metal Reactor (ALMR) was extrapolated to higher insertion amounts. As seen in Table 3.2, an ALMR probability distribution had been developed up to a maximum reactivity insertion of $0.90. These data were extrapolated using a logarithmic fit for each axis. Figure 3.3 shows the original ALMR data and the extended fit graphically. This curve describes the frequency associated with a reactivity insertion amount greater than or equal to the amount on the abscissa. In this experiment, a SCRAM failure probability of 1 is assumed. Realistically, for a well designed system, the SCRAM failure probability could be between 10-4 and 10-5 per demand. 31

40 Source Bin Frequency (/yr) <$ E-2 $0.06-$ E-3 ALMR $0.30-$ E-5 $0.50-$ E-6 $0.70-$ E-7 $0.90-$ E-08 $1.38-$ E-10 Extended Log Fit $1.86-$ E-11 $2.34-$ E-12 $2.82-$ E-13 Table 3.2 Total Reactivity Insertion Amount Frequencies and Source 32

41 Exceedance Frequency (/yr) Frequency of Exceeding a Level of Reactivity Insertion Insertion Amount ($) E E E E E E-05 Extended Fit 1.000E-06 ALMR 1.000E E E E E E E-13 Figure 3.3 Total Reactivity Insertion Amount Frequency Time in Cycle At the beginning of cycle (BOC), the reactor has an excess reactivity of $3.30. At the end of a 12 month cycle (EOC), the excess reactivity decreases to effectively $0.00. This results in an average rate of reduction in core reactivity of /day due to burnup of the fuel. Due to this decrease in available excess reactivity, the maximum possible reactivity insertion also decreases over time. To handle this effect, the time in cycle was partitioned into bins that coincide with the bins designed for the total reactivity insertion amount. Figure 3.4 shows the 33

42 probability of falling within each bin during the cycle and the maximum excess reactivity possible for that bin. Figure 3.4 Time in Cycle Binning Structure and Probabilities Figure 3.5 shows the probability for each total reactivity insertion bin if the transient falls within the first time-in-cycle bin (between BOC and 14.5% of reactor cycle). As the figure shows, a maximum insertion of $3.30 is possible since the reactor cycle has just started and the maximum excess reactivity is available. 34

43 Figure 3.5 Reactivity Insertion Amount Partitioning Between BOC and 14.5% of the Reactor Cycle (Black indicates Area Where Core Disruption Accident is not Possible) As the reactor cycle continues, the higher insertion amounts are no longer possible. Figure 3.6 shows the possible reactivity insertion amounts when the time in cycle is between 14.5% and 29%. As the figure shows, a reactivity insertion greater than $2.82 is no longer possible. Figure 3.6 Reactivity Insertion Amount Partitioning Between 14.5%-29% of the Reactor Cycle Figure 3.7, Figure 3.8, Figure 3.9, and Figure 3.10 show the possible reactivity insertion amounts as the reactor cycle continues. Once the reactor reaches 72% of 35

44 its cycle, a reactivity insertion greater than $0.90, as the result of rod withdrawal, is no longer possible. Figure 3.7 Reactivity Insertion Amount Partitioning Between 29%-43.5% of the Reactor Cycle Figure 3.8 Reactivity Insertion Amount Partitioning Between 43.5%-58% of the Reactor Cycle 36

45 Figure 3.9 Reactivity Insertion Amount Partitioning Between 58%-72% of the Reactor Cycle Figure 3.10 Reactivity Insertion Amount Partitioning Beyond 72% of the Reactor Cycle 37

46 CHAPTER 4 COMPUTER MODELS, RESULTS & ANALYSIS 4.1 SAS4A Model SAS4A/SASSYS-1 is a sodium reactor, severe accident analysis, computer code developed by Argonne National Lab (ANL). As part of the ABR1000 project, ANL developed a SAS4A model for ABR1000 in order to run a simplified safety analysis. The model used in this thesis involved adaptations to the ANL model. The SAS4A model has 4 channels, listed in Table 4.1. The model contains a single heat exchanger with the secondary side, plus a direct reactor auxiliary cooling system (DRACS). Figure 4.1shows their configuration. 38

47 Channel Representing Number of Assemblies 1 Inner Core 78 2 Outer Core Reflector 81 4 Peak Channel 1 Table 4.1 SAS4A Model Channels Figure 4.1 SAS4A ABR1000 Model 39

48 The SAS4A model obtained from ANL did not include the necessary modules to investigate transients which entered sodium boiling or fuel melting regimes. This was the case because the safety analysis conducted by ANL involved transients in which the consequences did not enter these regimes. For the challenging UTOP analysis to be performed, it was necessary for these modules, which are part of SAS4A but which were not activated, to be added. This was done with the guidance of ANL personnel. 4.2 Experiment Procedure Epistemic Values Chosen The first step in the experiment was to choose the epistemic values for that realization. This meant choosing the multiplier for the five feedback coefficients. The experiment included 100 different draws of epistemic values. These values were chosen using a Monte Carlo, Latin Hypercube sampling technique. Table 4.2 shows a sample epistemic draw from realization 7. These multipliers were then used to find the new input values for the SAS4A model. Realization Doppler Axial Coolant CRDL Radial Table 4.2 Example Epistemic Uncertainty Draw From Realization 7 40

49 4.2.2 SAS4A Runs Conducted for Combination of Aleatory Cases For each set of epistemic values, 25 SAS4A runs were conducted in order to cover the space of aleatory uncertainties. The matrix of 25 runs was created from a full factorial experiment design using the five possible insertion rate bins and the five possible total insertion amount bins. Table 4.3 shows this matrix of runs for realization 7. The complete set of results, for all 100 epistemic draws, is available in Appendix A. Insertion Rate ( /s) Total Insertion Amount($) X X X X X 4.95 X X X X (61.00) 8.25 X X X (32.50) (32.50) X X (19.50) (19.49) (19.50) X X (14.49) (14.49) (13.49) X No Pin Failure (XX:XX) Time of Pin Failure (secs) Table 4.3 Example Aleatory Combination From Realization 7 41

50 4.2.3 Core Damage Frequency Without Time in Cycle With a matrix of 25 aleatory runs completed for each of the 100 epistemic draws, a core damage frequency was found for each draw. This core damage frequency takes into account two of the aleatory uncertainties, total insertion amount and the insertion rate, but not the time in cycle. Figure 4.2 shows these results over different times in the cycle. Figure 4.2 Core Damage Frequency Over Time in Cycle 4.3 Results For each of the five times during the cycle, a set of 100 core damage frequencies was generated. Each of these time periods in the cycle has equal 42

51 probability. Thus, the five sets of core damage frequencies could be combined into an overall core damage frequency with uncertainties. Figure 4.3 shows the final core damage frequency. The plot has 100 data points, one for each epistemic draw. The distribution in values shows the spread in the epistemic uncertainties, while each point contains the aleatory uncertainties. Table 4.4 shows the mean, median, and 95 th and 5 th percentiles. Figure 4.3 Core Damage Frequency 43

52 Frequency (/yr) 5 th 2.85E-14 Median Mean 8.15E E th 5.85E-12 Table 4.4 Final Core Damage Frequencies 100 Realizations 4.4 Analysis Comparison with Safety Goals As the results have shown, the frequency of these events falls well below the threshold of 1E-8 per year, which was formed as a derivative of the technology neutral framework goals. However, that figure is largely dependent on the frequency assigned to the total insertion amount. There is no mechanistic basis for the extrapolation that was performed to extend the ALMR rod withdrawal density function for the probability of reactivity insertion amounts to the regime of challenging reactivity insertions. It is presumed that challenging reactivity insertions are the result of unlikely circumstances associated with rod withdrawal accidents. At the very low frequencies being considered, it is difficult to exclude other types of initiating mechanisms, such as the collapse of core structures. This case provides an example of how to perform an uncertainty 44

53 analysis considering aleatory and epistemic uncertainties. The results indicate that for the conceptual design analyzed and with the constraints placed on rod withdrawal rates, transient overpower accidents do not represent a significant challenge to the required reliability of the reactor protection system. That does not mean that other accident scenarios would not impose significant reliability requirements on the reactor protection system, or that all metal-fueled SFR designs have the large margin to fuel failure indicated in this study. As indicated in Figure 4.2, core damage frequency decreases as a function of time in cycle as the amount of excess reactivity decreases. Because core damage accidents are very rare events, the cycle-averaged value of the core damage frequency is the more meaningful value from a risk viewpoint. However, if the results of the analysis were closer to perceived safety limits, it is quite possible that the safety analyst might want to establish tighter controls for a specific range of an aleatory parameter, such as time in cycle or constraints on the simultaneous withdrawal of multiple rods Importance Measures Conducting the analysis using the methodology in this experiment also allows the experimenter to make inferences about the most important contributing factors. This would permit the designers to find which uncertainties, if reduced, could have the greatest benefit in the analysis. As a demonstration of this, an 45

54 CDF (/yr) investigation was made into the importance of each of the five epistemic uncertainties. Simplified Approach First, a simplified approach was used to measure the effect of each the epistemic uncertainties. Each epistemic uncertainty value was first plotted against the core damage frequency for each of the 100 cases. Figure 4.4 shows this plot for Doppler feedback. Doppler Feedback Multiplier Correlation Doppler Feedback Multiplier 1E E-11 1E-12 1E-13 1E-14 y = 4E-11e -4.28x Figure 4.4 Doppler Feedback, CDF Correlation An exponential function was then fit to the data to see if there was a trend between that epistemic value and the core damage frequency. The number in the 46

55 CDF (/yr) exponential power function provides a comparable value for each of the epistemic uncertainties. Figure 4.5, Figure 4.6, Figure 4.7, and Figure 4.8 show this same procedure for the four remaining epistemic uncertainties. Axial Feedback Multiplier Correlation Axial Feedback Multiplier 1E E-11 1E-12 1E-13 1E-14 y = 3E-12e x Figure 4.5 Axial Feedback, CDF Correlation 47

56 CDF (/yr) CDF (/yr) Coolant Feedback Multiplier Correlation Coolant Feedback Multiplier 1E E-11 1E-12 1E-13 1E-14 y = 1E-13e x Figure 4.6 Coolant Feedback, CDF Correlation CRDL Feedback Multiplier Correlation CRDL Feedback Multiplier 1E E-11 1E-12 1E-13 1E-14 y = 5E-11e x Figure 4.7 CRDL Feedback, CDF Correlation 48

57 CDF (/yr) Radial Feedback Multiplier Correlation Radial Feedback Multiplier 1E E-11 1E-12 1E-13 1E-14 y = 2E-12e x Figure 4.8 Radial Feedback, CDF Correlation The results of this analysis can be seen in Table 4.5. As the results show, the most prominent trends appear with the control rod driveline and Doppler feedbacks. Epistemic Uncertainty Power of Exponential Fit Control Rod Driveline Doppler Axial Expansion Coolant Radial Expansion Table 4.5 Exponential Fits for CDF for Epistemic Uncertainties 49

58 Failure Time (s) A similar approach was also used to investigate the correlation between the epistemic uncertainties and the time of pin failure. Only one case, of the matrix of 25 cases runs for each epistemic draw, failed every time. This case was the highest insertion amount, $3.06, with the highest insertion rate, /s. Figure 4.9 shows the plot of the Doppler feedback value versus the time of pin failure for the case in question. 22 Doppler Feedback Multiplier Correlation y = x Doppler Feedback Multiplier Figure 4.9 Doppler Feedback, Failure Correlation As in the core damage frequency analysis, a function was fit to the data to see if a trend appeared. In this case, a simple linear function was fit, and the value of the slope indicated the correlation. Figure 4.10, Figure 4.11, Figure 4.12, and Figure 4.13 show the same analysis for the remaining epistemic uncertainties. 50

59 Failure Time (s) Failure Time (s) 22 Axial Feedback Multiplier Correlation y = x Axial Feedback Multiplier Figure 4.10 Axial Feedback, Failure Correlation Coolant Feedback Multiplier Correlation 22 y = x Coolant Feedback Multiplier Figure 4.11 Coolant Feedback, Failure Correlation 51