Monte Carlo Characterization of PWR Spent Fuel Assemblies to Determine the Detectability of Pin Diversion

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2 Monte Carlo Characterization of PWR Spent Fuel Assemblies to Determine the Detectability of Pin Diversion A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Nuclear Engineering Program of the Department of Mechanical Engineering of the College of Engineering by James S. Burdo B.S. Wright State University, M.S. University of Kentucky M.A. Kent State University, M.S. University of Cincinnati December 2009 Committee Chair: John M. Christenson, Ph.D.

3 ABSTRACT This research is based on the concept that the diversion of nuclear fuel pins from Light Water Reactor (LWR) spent fuel assemblies is feasible by a careful comparison of spontaneous fission neutron and gamma levels in the guide tube locations of the fuel assemblies. The goal is to be able to determine whether some of the assembly fuel pins are either missing or have been replaced with dummy or fresh fuel pins. It is known that for typical commercial power spent fuel assemblies, the dominant spontaneous neutron emissions come from Cm-242 and Cm-244. Because of the shorter half-life of Cm-242 (0.45 yr) relative to that of Cm-244 (18.1 yr), Cm-244 is practically the only neutron source contributing to the neutron source term after the spent fuel assemblies are more than two years old. Initially, this research focused upon developing models of PWR fuel assemblies, modeling their depletion using the MONTEBURNS code, and by carrying out a preliminary depletion of a ¼ model 17x17 assembly from the TAKAHAMA-3 PWR. Later, the depletion and more accurate isotopic distribution in the pins at discharge was modeled using the TRITON depletion module of the SCALE computer code. Benchmarking comparisons were performed with the MONTEBURNS and TRITON results. Subsequently, the neutron flux in each of the guide tubes of the TAKAHAMA-3 PWR assembly at two years after discharge as calculated by the computer code was determined for various scenarios. Cases were considered for all spent fuel pins present and for replacement of a single pin at a position near the center of the assembly (10,9) and at the corner (17,1). Some scenarios were duplicated with a gamma flux calculation for high energies associated with Cm-244. For each case, the difference between the flux (neutron or gamma) for ii

4 all spent fuel pins and with a pin removed or replaced is calculated for each guide tube. Different detection criteria were established. The first was whether the relative error of the difference was less than 1.00, allowing for the existence of the difference within the margin of error. The second was whether the difference between the two values was big enough to prevent their error bars from overlapping. Error analysis was performed both using a one second count and pseudo- statistics for a projected 60 second count, giving four criteria for detection. The number of guide tubes meeting these criteria was compared and graphed for each case. Further analysis at extremes of high and low enrichment and long and short burnup times was done using data from assemblies at the Beaver Valley 1 and 2 PWR. In all neutron flux cases, at least two guide tube locations meet all the criteria for detection of pin diversion. At least one location in almost all of the gamma flux cases does. These results show that placing detectors in the empty guide tubes of spent fuel bundles to identify possible pin diversion is feasible. iii

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6 ACKNOWLEDGMENTS First, I would like to thank Dr. Young S. Ham of Lawrence Livermore National Laboratory for the initial technical concept and providing the opportunity to work on the particular aspect developed in this dissertation. Special thanks are due to my advisors at the University of Cincinnati. During his time here, Dr. Ivan Maldonado introduced me to the Safeguard project and arranged for me to have access to the Beowulf computer cluster both here and its new location at the University of Tennessee. Dr. John Christenson took over in the middle of an unfamiliar project and provided me with continued support and advice to complete this dissertation. I would also like to thank Dr. Henry Spitz and Dr. Adrian Miron for serving on my dissertation committee. I have received valuable assistance from fellow students in University of Cincinnati Nuclear and Radiological Engineering Graduate Program. Dr. Chukai Yin performed the initial Monteburns and MCNP calculations that guided this work. Jack Galloway helped with any questions about Beowulf and Tom Griefenkamp gave feedback on inputs for MCNP. Likewise, Dr. Scott Ludwig and Dr. Ian Gauld of Oak Ridge National Lab quickly responded to inquiries about ORIGEN2 and TRITON. I would like to dedicate this work to my parents, Michael and Joy, for their support during the long time it took to finish this dissertation. v

7 TABLE OF CONTENTS ABSTRACT... ii ACKNOWLEDGMENTS... v TABLE OF CONTENTS... 1 LIST OF TABLES AND FIGURES... 2 SYMBOLS, ABBREVIATIONS AND ACRONYMS... 7 INTRODUCTION BACKGROUND AND MOTIVATION RESEARCH OBJECTIVES LITERATURE REVIEW METHODOLOGY The Monte Carlo Technique MONTEBURNS ORIGEN SCALE ORIGEN-ARP ORIGEN-S TRITON COMPUTER HARDWARE The UCNRE Beowulf Cluster Desktop PC Notebook PC EXAMPLE CALCULATIONS Estimate Calculation Threshold 1 Calculation Threshold 2 (T2) Calculation PRELIMINARY RESULTS RESULTS AND CONCLUSIONS Takahama-3 Verification and Results Beaver Valley Plant Results Conclusions BIBLIOGRAPHY

8 LIST OF TABLES AND FIGURES Tables Table 1: Neutron Energy Bins with the Watt Fission Spectrum Table 2: Neutron Results with Fresh Fuel Pin at (10,9) Table 3: Gamma Results with Fresh Fuel Pin at (10,9) Table 4: Summary of Neutron Results Table 5: Summary of Gamma Results Table 6: Summary of Neutron Results with Pin Removed Table 7: Summary of Neutron Results with Stainless Steel Pin Table 8: Summary of Gamma Results with Pin Removed Table 9: Summary of Gamma Results with Stainless Steel Pin Table 10: Cm-244 C/E-1 [%] Values Table 11: Neutron Results with Fresh Fuel Pin at (10,9) (TRITON) Table 12: Gamma Results with Fresh Fuel Pin at (10,9) (TRITON) Table 13: Summary of Neutron Results (TRITON) Table 14: Summary of Gamma Results (TRITON) Table 15: Summary of Neutron Results with Pin Removed (TRITON) Table 16: Summary of Neutron Results with Stainless Steel Pin (TRITON) Table 17: Summary of Gamma Results with Pin Removed (TRITON) Table 18: Summary of Gamma Results with Stainless Steel Pin (TRITON) Table 19: Summary of Results with Fresh Fuel Pin at 17,1 (LMOHEP) Table 20: Summary of Results with Stainless Steel Pin at 17,1 (LMOHEP) Table 21: Summary of Results with Fresh Fuel Pin at 17,1 (LM042T)

9 Table 22: Summary of Results with Stainless Steel Pin at 17,1 (LM042T) Table 23: Summary of Results with Fresh Fuel Pin 17,1 (LM046R) Table 24: Summary of Results with Stainless Steel Pin 17,1 (LM046R) Table 25: Summary of Results with Fresh Fuel Pin 17,1 (LM043Y) Table 26: Summary of Results with Stainless Steel Pin 17,1 (LM043Y)

10 Figures Figure 1: Threshold 2 Illustration Figure 2: Dominance of Cm-244 Spontaneous Fission Neutrons After 2 Years Figure 3: Alpha Neutrons Two Orders of Magnitude Lower Figure 4: Dominance of Cm-244 Actinide Group 18 Gamma Rates Figure 5: Relative Cm-244 Accumulation Used to Establish Neutron Source Figure 6: Neutron Flux with the Watt Fission Spectrum Figure 7: Neutron Flux Differences with the Watt Fission Spectrum Figure 8: Diverted Pins Considered in this Study and Guide Tubes Figure 9: Graph of Table Figure 10: Graph of Table Figure 11: Graph of Table Figure 12: Graph of Table Figure 13: Graph of Table Figure 14: Graph of Table Figure 15: Position of the SF97 spent fuel in the NT3G Figure 16: Takahama-3 C/E Values Figure 17: Takahama-3 C/E-1 [%] Values Figure 18: TRITON C/E-1 [%] Values Figure 19: SF97-4 C/E-1 [%] Values Figure 20: SF96-4 C/E-1 [%] Values Figure 21: SF95-4 C/E-1 [%] Values Figure 22: Symmetric Comparison

11 Figure 23: Diversion Detectability Using Differential Neutron Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 10,9 (TRITON) Figure 24: Diversion Detectability Using Differential Neutron Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (TRITON) Figure 25: Diversion Detectability Using Differential Gamma Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 10,9 (TRITON) Figure 26: Diversion Detectability Using Differential Gamma Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (TRITON) Figure 27: Graph of Table Figure 28: Graph of Table Figure 29: Graph of Table Figure 30: Graph of Table Figure 31: Graph of Table Figure 32: Graph of Table Figure 33: Diversion Detectability Using Differential Neutron Fluxes for 9 Diversion Scenarios: Diverted Pin Location 10, Figure 34: Diversion Detectability Using Differential Neutron Fluxes for 9 Diversion Scenarios: Diverted Pin Location 17, Figure 35: Diversion Detectability Using Differential Gamma Fluxes for 5 Diversion Scenarios: Diverted Pin Location 10, Figure 36: Diversion Detectability Using Differential Gamma Fluxes for 5 Diversion Scenarios: Diverted Pin Location 17, Figure 37: LMOHEP Bundle Depletion

12 Figure 38: Diversion Detectability Using Differential Neutron Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LMOHEP) Figure 39: Diversion Detectability Using Differential Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LMOHEP) Figure 40: Diversion Detectability Using Differential Neutron Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM042T) Figure 41: Diversion Detectability Using Differential Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM042T) Figure 42: Diversion Detectability Using Differential Neutron Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM046R) Figure 43: Diversion Detectability Using Differential Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM046R) Figure 44: Diversion Detectability Using Differential Neutron Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM043Y) Figure 45: Diversion Detectability Using Differential Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (LM043Y) Figure 46: Diversion Detectability Using Differential Neutron and Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: FFP Location 17, Figure 47: Diversion Detectability Using Differential Neutron and Gamma Fluxes for Beaver Valley Nuclear Plant Diversion Scenarios: SSP Location 17,

13 SYMBOLS, ABBREVIATIONS AND ACRONYMS BWR Boiling Water Reactor C/E Calculated to Expected CENTRM Continuous ENergy TRansport Module FENOC FirstEnergy Nuclear Operating Company FFP Fresh Fuel Pin GT Guide Tube GWd Giga Watt days IAEA International Atomic Energy Agency LANL Los Alamos National Laboratory LLNL Lawrence Livermore National Laboratory LWR Light Water Reactor MCNP Monte Carlo Neutral Particle MeV Million electron-volts MTU Metric Ton of Uranium MW Megawatt NEA Nuclear Energy Agency NEWT NEW Transport Algorithm NITAWL Nordheim Integral Treatment NRC Nuclear Regulatory Commission OECD Organization for Economic Co-operation and Development ORIGEN Oak Ridge Isotope GENeration ORIGEN-ARP Oak Ridge Isotope GENeration Automatic Rapid Processing 7

14 ORNL Oak Ridge National Laboratory PIE Post Irradiation Examination Ppm parts per million PWR Pressurized Water Reactor RE Relative Error RSICC Radiation Safety Information Computational Center SCALE Standard Computer Analysis for Licensing Evaluation SFP Spent Fuel Pin SSP Stainless Steel Pin T1 Threshold 1 T2 Threshold 2 TFTP Trivial File Transfer Protocol TRITON Transport Rigor Implemented with Time-dependent Operation for Neutronic depletion UCNRE University of Cincinnati College of Engineering's Nuclear and Radiological Engineering WABA Wet Annular Burnable Absorber 8

15 INTRODUCTION This report outlines the research pursued by the author to fulfill the Ph.D. dissertation requirements at the University of Cincinnati s Nuclear and Radiological Engineering Program. The research was carried out in collaboration with Dr Young S. Ham of Lawrence Livermore National Laboratory (LLNL). This introductory section first describes the detection of pin diversion from Pressurized Water Reactor (PWR) spent fuel assemblies, and then is followed by six sections that elaborate on the following topics: Description of the background and motivation of the proposed research. Identification of the scope and objectives of the research. Prior studies identified and preliminary literature review on this subject. Description of the methodology to be employed in the research. Results and description of the research carried out to determine the detectability of pin diversion from PWR spent fuel assemblies. Results and conclusions. For decades, a technical safeguards challenge for the International Atomic Energy Agency (IAEA) has been to identify possible diversion of nuclear fuel pins from Light Water Reactor (LWR) spent fuel assemblies. Various attempts have been made in the past two decades to develop a technology to identify a possible diversion of pin(s) and to determine whether some pins are missing or replaced with dummy or fresh fuel pins. None of the previous attempts was able to satisfy the IAEA s requirements. 9

16 Currently there exists no safeguards instrument that can detect a possible pin diversion scenario. The FORK detector, although it can characterize spent fuel assemblies using operator declared data, was never sensitive enough to detect missing pins from spent fuel assemblies. In fact, it could not even detect 50% of the fuel pins removal either with the conventional FORK detector or the enhanced FORK detector without making use of the operator s declared data [1]. Emission computed tomography system has also been used to detect missing pins from a spent fuel assembly [2]. The attempts showed some potential for showing possible missing pins but were never able to demonstrate its capabilities. In addition, the instrument was cumbersome, expensive, difficult to handle, the results were difficult to interpret and probably too complex to employ for the field application. 10

17 1. BACKGROUND AND MOTIVATION Dr. Young S. Ham of Lawrence Livermore National Laboratory has proposed a novel safeguards verification method to detect possible nuclear fuel pin diversion. The new measurement methodology that he proposed uses multiple tiny neutron and gamma detectors in a form of a cluster (detector cluster) to make underwater neutron measurement possible on PWR spent fuel assemblies stored in a reactor spent fuel pool. The data obtained from a detector cluster should provide an accurate measure of the spatial distribution of neutron and gamma flux (particles per second) within a spent fuel assembly. The expectation is that the 3-dimensional neutron and gamma data, when obtained in the presence of missing pins, will have data profiles distinctly different from the profiles obtained without missing pins. With proper modeling and benchmarking, analysis of the neutron and gamma profiles should be able to provide quantitative information about whether spent pins are missing from the assembly. The detector data should also provide an independent means of verifying the reactor operator s declaration about the length of time the assembly has been in the spent fuel pool [commonly called the cooling time ]. It is known that for typical commercial power spent fuel assemblies, the dominant neutrons come from Curium 242 and Curium 244. Because of the short half-lives of Cm-242 (half-life of 0.45 year), Cm-244 (half-life of 18.1 year) is practically the only neutron source contributing to the neutron measurements when the spent fuel assemblies are more than two years old. The ORIGEN-ARP (Oak Ridge Isotope Generation Automatic Rapid Processing) computer module of the SCALE (Standardized Computer Analysis for Licensing Evaluation) computer program from Oak Ridge National Laboratory was used to analyze the flux from an example of a PWR assembly. The calculations confirmed that neutrons from spontaneous fission 11

18 of Cm-244 dominated by at least two orders of magnitude the neutron source term in spent fuel assemblies that had cooling times of more than two years. Gamma ray peaks unique to Cm-242 and Cm-244 were found in three groups with mean energies of 5, 7, and 9.5 MeV (Million electron Volts). The Monte Carlo Neutral Particle (MCNP) computer code was used to simulate the neutron and gamma fluxes from Cm-242 and Cm-244 inside a benchmark spent fuel assembly. Different cases where a fresh fuel pin was removed entirely, replaced with a fresh fuel pin and with a stainless steel pin were analyzed. The preliminary results demonstrated that the resulting differences in the neutron and gamma profiles were large enough to be detected [3]. 12

19 2. RESEARCH OBJECTIVES The objective of this project was to further analyze the proposed verification methodology by performing more detailed depletion of a real world 17x17 PWR assembly. (Boiling Water Reactor (BWR) bundles were not considered because of the lack of guide tubes to place the detector cluster in.) The benchmark assembly was depleted using SCALE for the different diversion scenarios and at different cooling pool boron concentrations. In addition, the Department of Energy (DOE) database of discharged nuclear fuel as reported on the form RW [4] was surveyed to find the most common type of assembly. Upper and lower initial uranium enrichments and burnup times for a selected bundle type were used to see if missing pins would still alter the neutron and gamma profiles enough to be detected. Bundles from the FirstEnergy Nuclear Operating Company (FENOC) Beaver Valley 1 and Beaver Valley 2 plants were used since their information was readily available to the University of Cincinnati. 13

20 3. LITERATURE REVIEW Because this is a new approach, relatively little equivalent research has been published. A literature review has discovered similar work in characterizing the spent nuclear fuel inventory and other methods of detecting pin diversion. Characterization of spent nuclear fuel discharges in 1993 was based on Form RW-859 [4]. In addition to the previously mentioned attempts using the FORK detector [1] and emission computed tomography system [2], other papers dealing with the FORK detector have been found [13], [14]. 14

21 4. METHODOLOGY The Monte Carlo computations were performed using the codes described in this section. Calculations were performed using a configuration-controlled latest released version of the codes and data libraries. 4.1 The Monte Carlo Technique Particle transport analysis using the Monte Carlo technique consists of following each particle (such as a neutron, gamma, or electron, for example) from birth, throughout its life, and to its death by either absorption or escape. Probability distributions are randomly sampled using continuous energy cross-sectional data. These distributions are used to determine the type of interaction the particle will undergo, the number of neutrons produced if a fission event occurs, the energy of particles when they scatter, the loss of particles if leakage occurs, etc. The outcome of these calculations is, in essence, an approximate solution to the Boltzmann Transport Equation - where the accuracy of the approximation improves as the number of particle histories is increased. The most widely used and proven code to do this is MCNP [5]. 4.2 MCNP is a 3D general-purpose Monte Carlo N Particle code that can be used to simulate coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems. Version 5 of MCNP is the latest release of this code that includes some of the most significant (and modern) advancements to this program that is maintained by Group X-5 at Los Alamos National Laboratory (LANL). In recent times, has been tested at LANL as well as at other laboratories and institutions and it is increasingly being used on PCs, Linux 15

22 clusters, and Unix-based ASCI computers. The code was modernized to meet requirements of portability and standards-based coding (F90+MPI+OpenMP and PVM). MCNP calculations are performed using the HFV4.0 model; the model is a threedimensional (3-D) rendition that uses continuous energy neutron ENDF/B-VI crosssection data libraries from the National Nuclear Data Center at Brookhaven National Laboratory. The particular version of used is 1.2, obtained from the Radiation Safety Information Computational Center (RSICC). 4.3 MONTEBURNS Monteburns [6] is an automatic-cyclic coupling of the MCNP [5] and the ORIGEN2 [7] codes. Monteburns uses MCNP to calculate the neutron spectra for each region. It then calls ORIGEN2 to calculate a set of one-group cross sections for each material. ORIGEN2 [7] then calculates the core inventory and Monteburns rewrites the resulting material composition (after irradiation and/or decay) from ORIGEN2 back to MCNP in a repeated, cyclic fashion. Thus the depletion of a high burn-up core can be calculated over relatively small time steps, and not averaged over a complete cycle. One of the main advantages of the Monteburns code is that it can use the most modern neutron cross sections from different nuclear data libraries available in MCNP format. 4.4 ORIGEN 2.2 ORIGEN2 [7] performs burnup calculations using the matrix exponential method in terms of time-dependent formulation, destruction and decay concurrently. These calculations require: (1) The initial compositions and amounts of material, (2) One-group microscopic cross-sections for each isotope, (3) Material feed and removal rates, 16

23 (4) The length of the irradiation periods, (5) The flux or power of the irradiation. 4.5 SCALE SCALE [9] is a modular code system that was developed by Oak Ridge National Laboratory (ORNL) at the request of the U.S. Nuclear Regulatory Commission (NRC). It is maintained and enhanced under joint sponsorship of the NRC and the DOE. The SCALE system utilizes well-established computer codes and methods within standard analysis sequences that (1) provide an input format designed for the occasional user and/or novice, (2) automate the data processing and coupling between modules, and (3) provide accurate and reliable results. System development has been directed at problem-dependent cross-section processing and analysis of criticality safety, shielding, depletion/decay, and reactor physics problems. This proposal uses Version 5 [8] of the SCALE system for ORIGEN-ARP and Version 5.1 [9] for the TRITON (Transport Rigor Implemented with Time-dependent Operation for Neutronic depletion) module ORIGEN-ARP ORIGEN-ARP [9] is a SCALE depletion analysis sequence used to perform pointdepletion calculations with the ORIGEN-S code using problem-dependent cross sections. Problem-dependent cross section libraries are generated using the ARP module using an interpolation algorithm that operates on pre-generated libraries created for a range of fuel properties and operating conditions. Methods are provided in SCALE to generate these libraries using one-, two-, and three-dimensional transport codes. The interpolation of cross sections for uranium-based fuels may be performed for the variables burnup, enrichment, and water density. 17

24 4.5.2 ORIGEN-S ORIGEN-S [9] computes time-dependent concentrations and radiation source terms of a large number of isotopes, which are simultaneously generated or depleted through neutronic transmutation, fission, and radioactive decay. Provisions are also provided to simulate input feed rates, and physical or chemical removal rates from a system. The calculations may pertain to fuel irradiation within a nuclear reactor, or the storage, management, transportation, or subsequent chemical processing of spent fuel elements. ORIGEN-S is widely used in nuclear reactor and processing plant design studies, design studies for spent fuel transportation and storage, burnup credit evaluations, decay heat and radiation safety analyses, and environmental assessments. The matrix expansion model of the ORIGEN code is unaltered in ORIGEN-S. In addition, the code will perform integration of actinide or fission product decay energies and radiation sources over any decay interval TRITON The TRITON [9] control module was originally developed in tandem with the NEWT (NEW Transport Algorithm) functional module of SCALE to support two-dimensional (2-D) transport and depletion calculations. Beginning with the Version 5.1 release of SCALE, threedimensional (3-D) depletion based on the Monte Carlo transport codes KENO V.a and KENO- VI are supported within TRITON (KENO V.a) and the new module TRITON6 (KENO-VI). TRITON can be used to provide automated, problem-dependent cross-section processing followed by calculation of the neutron multiplication factor for a 2-D configuration using NEWT. Additionally, this functionality can be iterated in tandem with ORIGEN-S depletion calculations to predict isotopic concentrations, source terms, and decay heat as a result of timevarying fluxes calculated in a 2-D deterministic fashion or in a 3-D stochastic approach. 18

25 4.6 COMPUTER HARDWARE The UCNRE Beowulf Cluster The University of Cincinnati College of Engineering s Nuclear and Radiological Engineering (UCNRE) Beowulf cluster includes one server processor and ten computing processors, totaling 22 nodes. The server node is equipped with dual Intel Xeon processors with 512k L2 cache at 2.4 GHz, and 2 Gigabyte PC2100 ECC RAM. Each computing node has dual Xeon processors at 2.4 GHz, 1 GB RAM and a 40 GB IDE drive. The operating system Red Hat 9 (Linux kernel ) is installed on the server node, with the file system residing only on the server node. Thus, the computing nodes mount the file system through the TFTP (Trivial File Transfer Protocol) service, and the local hard drive on each node is mounted as a temporary directory. After January 2009, only the server processor was available for computations Desktop PC A desktop PC located at Room 600 in Rhodes Hall at UC (later moved to Room 408 in the Old Chemistry Building), it is a 2.4 GHz computer with Windows-XP platform that is basically dedicated to the author of this dissertation Notebook PC The author s notebook PC, a HP-Compaq 1.6 GHz computer with a Windows Vista platform, was used for later calculations. 4.7 EXAMPLE CALCULATIONS These types of calculations are performed repeatedly in this paper. 19

26 4.7.1 Estimate Calculation Assume flux reported by is the true flux and multiply by 60 s to get the actual count at one minute and use statistics for the error. This provides an estimate of how the error would change with a one minute count. Ex. The total neutron flux in the Takahama-3 bundle at the guide tube in position (9,9) with the spent fuel pin at position (10,9) replaced by a fresh fuel one is calculated by to be n/s. Assume that a one minute count will have the result equal to (60)(234917) with an AE of ±[(60)(234917)] 1/2 and a RE of ± (60)(234917)/ SQRT[(60)(234917)] 1/2 = ±1/SQRT[(60)(234917)] 1/2 = ± Threshold 1 Calculation If the relative error (RE) of the difference between the flux with all pins present and with one removed or replaced is less than 1.0, it can be assumed with reasonable confidence that it exists. Ex. The total neutron flux in the Takahama-3 bundle at the guide tube in position (9,9) is calculated to be n/s and RE ± with all spent fuel pins (SFP) present. With the SFP at position (10,9) replaced with a fresh fuel pin, it is calculated to be n/s and RE ± The difference is = 1261 n/s. The RE of this difference is ±{[(0.0012)( )] 2 + [(0.0012)( )] 2 }/1261 = ± The difference is therefore between 1661 n/s and 861 n/s and meets threshold 1 for existence. The total neutron flux in the Takahama-3 bundle at the guide tube in position (14,4) is calculated to be n/s and RE ± with all SFP present. With the SFP at position (10,9) replaced with a fresh fuel pin, it is calculated to be n/s and RE ± The difference is = 226 n/s. The RE of this difference is±{[(0.0011)( )]

27 [(0.0011)( )] 2 }/226 = ±2.07. The difference is therefore between 694 n/s and -242 n/s. This includes the possibility of it being zero, so it doesn t meet the first threshold for existence Threshold 2 (T2) Calculation If the lower bound of the flux with all SFP present is still greater than the upper bound of the flux with a SFP removed or replaced, threshold 2 is met. Ex. The total neutron flux at the guide tube in position (9,9) with all SFP present in the example in A1.2 has a lower bound of (0.0012)(236178) = n/s. With the SFP replaced with a fresh fuel one, the total neutron flux has an upper bound of (0.0012)(234917) = n/s. This is a difference of 696 n/s beyond the margins of error, so threshold 2 is met (see Fig.1). The total neutron flux at the guide tube in position (14,4) with all SFP present has a lower bound of (0.0011)(301520) = n/s. With the SFP replaced with a fresh fuel one, the total neutron flux has an upper bound of (0.0011)(301294) = n/s. This is a difference of -437 n/s, so the difference can be accounted for by the margins of error and threshold 2 is not met. 21

28 Figure 1: Threshold 2 Illustration Flux with all pins present Non-Overlap Region Flux with missing pin 22

29 5. PRELIMINARY RESULTS Considerable preliminary work was done to confirm the validity of the basic tenets of the verification proposal methodology. Some of these results have been submitted as two conference papers, as listed in references [3] and [10]. The first step was to confirm the dominance of Cm-244 spontaneous fission neutrons at times greater than two years. This was done using the ORIGEN2 V2.2 computer code with a simple point model in which one metric ton of 3.5% enriched fuel was burned in a 1 MW PWR for 880 days, then cooled for 5 years. Figure 2 illustrates the spontaneous fission neutron emission after 2 years of cooling. Alpha particle induced neutrons are illustrated in Figure 3, showing their rate is lower by two orders of magnitude. Figure 2: Dominance of Cm-244 Spontaneous Fission Neutrons After 2 Years Spontaneous Fission Neutron Source at 2 yrs 3.00E E E+08 neutrons/s 1.50E E E E+00 PU238 PU240 PU242 CM242 CM244 CM246 23

30 Figure 3: Alpha Neutrons Two Orders of Magnitude Lower Alpha Neutron Source at 2 yrs 2.50E E+06 neutrons/s 1.50E E E E+00 PU238 PU239 PU240 AM241 AM243 CM242 CM243 CM244 ORIGEN2 V2.2 was also used to output the gamma spectrum into 18 discrete energy groups, from 0 to 11 MeV. Sources were divided into activation products, actinides and their daughters, and fission products. At times greater than 1 year, fission product gamma rays in energy groups 16 (4-6 MeV), 17 (6-8 MeV), and 18 (8-11 MeV) decline dramatically (E+11->E- 5) and actinides (Cm-244) dominate. This is illustrated in Figure 4 with actinide group

31 Figure 4: Dominance of Cm-244 Actinide Group 18 Gamma Rates Actinide Group 18 (9.5 MeV) Release Rates 2.00E E E E E+05 photons/s 1.00E E+04 PU240 CM242 CM E E E E yrs The next step in the simulation process was to construct a realistic model of a modern PWR fuel assembly. This was achieved by employing an Organization for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) benchmark specification of a Takahama-3 17x17 PWR fuel assembly loaded with 248 UO2 fuel pins, 4.1%wt U235 enriched, 16 UO2-GD2O3 pins (2.6% wt U235 and 6% wt Gd) and 25 water rods. The assembly was irradiated for three cycles with a power of 38.6 W/gU [11]. Subsequently, that study was followed by the depletion of the assembly using Monteburns to approximate the isotopic distribution at EOC and after two years of cooling [3]. ORIGEN-ARP determined total neutron and gamma flux for the same time. Separate cases were run for neutron and gamma studies, and these employed 10^7 histories to confirm adequate statistics. X and y outer boundaries were set to specular reflection to simulate the effect of being surrounded by similar assemblies. According to the initial finding above, the neutron source strengths were established in the bundle in proportion to the Cm-244 relative accumulation illustrated in Figure 5. 25

32 The neutron flux was calculated by the Watt fission spectrum and divided in 23 groups between 1.0E-05 and 20MeV, plus a total count as the 24 th group as shown in Table 1. The Watt fission spectrum is expressed as a sinh function, with the flux at the higher energies approaching zero (Fig. 6). The differences in flux with a SFP gone is correspondingly smaller, leading to dramatic rises in the RE of the higher energy groups (Fig. 7). (It is doubtful neutrons with energies ~15-20 MeV could be detected.) Because of this, the total flux is used for analysis instead of the individual groups. Figure 5: Relative Cm-244 Accumulation Used to Establish Neutron Source Cm-244 Relative Distribution Relative Fraction Row Column

33 Group Energy (MeV) E E E E E E E E E E E E E E E E E E E E E E E total Table 1: Neutron Energy Bins with the Watt Fission Spectrum Figure 6: Neutron Flux with the Watt Fission Spectrum 27

34 Figure 7: Neutron Flux Differences with the Watt Fission Spectrum To determine the limits of detection, a single pin from the spent fuel assembly was removed and replaced with a fresh fuel pin. Two cases were considered: a pin replaced near the center of the assembly at row 10, column 9, and a pin replaced at the corner at row 17, column 1. Figure 8 shows these locations and the guide tubes. The flux results from pin-diverted cases were compared against runs done with all spent fuel pins present, and the differences were calculated. Using standard error propagation [12], relative errors were calculated for the differences. Both the error reported by and that calculated by estimation (see section 4.7.1) were used. Whether the differences and their relative errors met thresholds 1 and 2 (see section and 4.7.3) was determined. Initial gamma groups were the ones dominated by Cm-244 (as determined by ORIGEN2): 4-6 MeV, 6-8 MeV, and 8-11 MeV. The flux output also included a total count. 28

35 Figure 8: Diverted Pins Considered in this Study and Guide Tubes Fuel Pin (17,1) Fuel Pin (10,9) Legend Guide Tube UO2 + Gd2O3 Pin 10 9 (14,4) Guide Tube 8 7 UO2 Fuel Pin Studied 6 5 Guide Tube UO2 Fuel Pin (9,9) Table 2 illustrates the number of energy groups with relative error < 1.0, both for the MCNP results and with statistics, and if the total neutron flux has relative error < 1.0 and if it is greater than the margins of error (T2). This is assessed at each guide tube for the case of the fresh fuel pin substituted into location (10,9). The equivalent process was applied to the gamma flux differences, as shown in Table 3. 29

36 Table 2: Neutron Results with Fresh Fuel Pin at (10,9) r.e.<1 total<1 tot > overlap GT (3,6) 0 5 no no no no GT (3,9) 2 5 no yes no no GT (3,12) 3 3 yes yes yes yes GT (4,4) 1 5 no yes no no GT (4,14) 2 6 no yes no no GT (6,3) 3 4 no yes no yes GT (6,6) 5 6 yes yes no yes GT (6,9) 2 5 yes yes no yes GT (6,12) 3 5 yes yes no yes GT (6,15) 3 4 no no no no GT (9,3) 3 5 yes yes no yes GT (9,6) 5 8 yes yes yes yes GT (9,9) 9 10 yes yes yes yes GT (9,12) 3 9 yes yes yes yes GT (9,15) 5 10 yes yes yes yes GT (12,3) 2 7 no no no no GT (12,6) 3 9 yes yes yes yes GT (12,9) 6 11 yes yes yes yes GT (12,12) 0 2 no no no no GT (12,15) 0 1 no no no no GT (14,4) 0 1 no no no no GT (14,14) 1 4 yes yes no yes GT (15,6) 1 3 no no no no GT (15,9) 0 5 no no no no GT (15,12) 0 1 no no no no 30

37 Table 3: Gamma Results with Fresh Fuel Pin at (10,9) r.e.<1 total<1 tot > overlap GT (3,6) 1 0 yes no no no GT (3,9) 0 0 no no no no GT (3,12) 1 1 no no no no GT (4,4) 0 0 no no no no GT (4,14) 0 0 no no no no GT (6,3) 0 0 no no no no GT (6,6) 0 0 no no no no GT (6,9) 2 1 yes yes yes yes GT (6,12) 0 0 no no no no GT (6,15) 0 0 no no no no GT (9,3) 0 0 no no no no GT (9,6) 3 3 yes yes yes yes GT (9,9) 3 3 yes yes yes yes GT (9,12) 3 3 yes yes yes yes GT (9,15) 0 0 no no no no GT (12,3) 2 2 yes yes no no GT (12,6) 4 4 yes yes yes yes GT (12,9) 3 3 yes yes yes yes GT (12,12) 3 3 yes yes yes yes GT (12,15) 0 0 no no no no GT (14,4) 0 0 no no no no GT (14,14) 0 0 no no no no GT (15,6) 0 0 no no no no GT (15,9) 0 0 no no no no GT (15,12) 1 1 yes yes no no These preliminary Monte Carlo simulation studies showed that indeed two dimensional neutron and gamma data, when obtained in the presence of missing pins, have data profiles distinctly different from the profiles obtained without missing pins. Replacing a single spent fuel pin in the assembly resulted in detectable differences in the neutron flux greater than the designated threshold in at least three guide tubes, as summarized in Table 4 and Figure 9. Pin replaced Table 4: Summary of Neutron Results rel. err. < 1 (10,9) in 9 tubes (17,1) in 11 tubes rel. err. < 1 in 13 tubes in 13 tubes in 5 tubes in 3 tubes in 9 tubes in 5 tubes 31

38 Figure 9: Graph of Table 4 Similar results are shown in Table 5 and Figure 10, for the gamma flux. Pin replaced Table 5: Summary of Gamma Results rel. err. < 1 (10,9) in 9 tubes (17,1) in 8 tubes rel. err. < 1 in 9 tubes in 8 tubes in 4 tubes in 2 tubes in 2 tubes in 2 tubes 32

39 Number of GT Meeting Threshold Figure 10: Graph of Table 5 Summary of Gamma Results, T1, T1, T2, T2 (10,9) (17,1) SFP Replaced with Fresh Fuel Pin A 60 second count provides statistics that are adequate; using a neutron detector in each of the guide tubes should be able to determine possible pin diversion. Gamma detection could possibly be used in the central tube to verify operator supplied decay times. Further studies were done in which a pin was removed entirely and in which it was replaced with a stainless steel rod. (Because removal of a pin would be detected by visual inspection, the scenario is included here for comparison.) Results are summarized below in Tables 6, 7, 8 and 9 and Figures 11, 12, 13, and 14. Pin replaced Table 6: Summary of Neutron Results with Pin Removed rel.err. < 1 (10,9) in 18 tubes (17,1) in 13 tubes rel. err. < 1 in 23 tubes in 13 tubes in 11 tubes in 7 tubes in 20 tubes in 9 tubes 33

40 Figure 11: Graph of Table 6 Summary of Neutron Results 25 Number of GT Meeting Threshold (10,9) (17,1), T1, T1, T2, T2 SFP Removed Pin replaced Table 7: Summary of Neutron Results with Stainless Steel Pin rel.err. < 1 (10,9) in 25 tubes (17,1) in 13 tubes rel. err. < 1 in 25 tubes in 13 tubes in 23 tubes in 11 tubes in 25 tubes in 11 tubes 34

41 Number of GT Meeting Threshold Figure 12: Graph of Table 7 Summary of Neutron Results, T1, T1, T2, T2 (10,9) (17,1) SFP Replaced with Stainless Steel Pin Pin replaced Table 8: Summary of Gamma Results with Pin Removed rel.err. < 1 (10,9) in 2 tubes (17,1) in 5 tubes rel. err. < 1 in 2 tubes in 5 tubes in 2 tubes in 1 tubes in 2 tubes in 1 tubes 35

42 Figure 13: Graph of Table 8 Summary of Gamma Results 6 Number of GT Meeting Threshold (10,9) (17,1), T1, T1, T2, T2 SFP Removed Pin replaced Table 9: Summary of Gamma Results with Stainless Steel Pin rel.err. < 1 (10,9) in 4 tubes (17,1) in 7 tubes rel. err. < 1 in 4 tubes in 7 tubes in 2 tubes in 1 tubes in 2 tubes in 1 tubes 36

43 Number of GT Meeting Threshold Figure 14: Graph of Table 9 Summary of Gamma Results, T1, T1, T2, T2 (10,9) (17,1) SFP Replaced with Stainless Steel Pin Removal and replacement both led to dramatic increases in the number of guide tubes where the neutron flux was above the designated threshold. In contrast, the gamma flux in most of the guide tubes remained below the threshold. 37

44 6. RESULTS AND CONCLUSIONS 6.1 Takahama-3 Verification and Results A depletion of the Takahama-3 bundle was performed using the TRITON computer code. A quarter model of the bundle was used, with a burnup of GWd/MTU. This is equal to cycles 5, 6, and 7 with a power of 35 MW for 385 days and a downtime of 88 days, 38 MW for 402 days and a downtime of 62 days, and 33 MW for 406 days. The isotopic composition of the Takayama-3 PWR as calculated by TRITON was compared to results from Monteburns at the end of burnup and other codes and actual experimental data. The sample examined was the SF97-4 sample located at core mid-height in the NT3G24 assembly, row 1, column 9 or position I-Q (Fig. 15). This was the one used in the benchmark paper, Depletion Calculation Benchmark Devoted to Fuel Cycle Issues [11]. In addition to Monteburns, comparison was done for the selected isotopes calculated by the codes JENDL-3.2, JENDL-3.3, JEF-2.2, and JEFF-3.0. Results for these codes with this benchmark were found in the presentation, PIE Analysis for Minor Actinide [15]. Actual experimental measurements are found in the PIE (Post Irradiation Examination) database for the Takayama-3 PWR maintained in France [16]. Expected results were expressed in both kg/mtu and in the form of a ratio of one isotope to another, usually U The calculated results were similarly treated. A ratio of calculated to expected results (C/E) and percent difference of this ratio (C/E-1) were calculated and graphed (Figs. 16 and 17). The TRITON percent difference of the C/E ratio is in Fig. 18. As can be seen from the graphs, TRITON agreement with expected values was good. The isotope of interest in Safeguard, Cm-244, had a 0.97 ratio of calculated to expected, as compared to 0.75 for JENDL-3.2 and JENDL-3.3 and for Monteburns. Percent difference was , compared to and for JEF-2.2 and JEFF-3.0 and for Monteburns. 38

45 Figure 15: Position of the SF97 spent fuel in the NT3G 39

46 Figure 16: Takahama-3 C/E Values C/E Values: PIE Data from Takahama-3 PWR C/E JENDL-3.2 JENDL-3.3 Monteburns TRITON Am243/Am241 Cs137/U238 Nd148/U238 Pu239/U238 Pu240/Pu239 Pu241/Pu239 Pu242/Pu239 U235/U238 U236/U238 Cm242/U238 Cm243/U238 Cs134/U238 Eu154/U238 Nd143/U238 Nd145/U238 Nd148/U238 Sm147/U238 Sm150/U238 Isotopes Sm151/U238 Sm152/U238 U234/U238 Np237/U238 Pu238/U238 Pu239/U238 Pu240/U238 Pu241/U238 Pu242/U238 Am241/U238 Am243/U238 Cm244/U238 Cm245/U238 Figure 17: Takahama-3 C/E-1 [%] Values C/E-1 [%] Values: PIE Data from Takahama-3 PWR C/E-1 [%] 0-50 Am243/Am241 Cs137/U238 Nd148/U238 Pu239/U238 Pu240/Pu239 Pu241/Pu239 Pu242/Pu239 U235/U238 U236/U238 Cm242/U238 Cm243/U238 Cs134/U238 Eu154/U238 Nd143/U238 Nd145/U238 Nd148/U238 Sm147/U238 Sm150/U238 Sm151/U238 Sm152/U238 U234/U238 Np237/U238 Pu238/U238 Pu239/U238 Pu240/U238 Pu241/U238 Pu242/U238 Am241/U238 Am243/U238 Cm244/U238 Cm245/U238 JEF-2.2 JEFF-3.0 Monteburns TRITON Isotopes 40

47 Figure 18: TRITON C/E-1 [%] Values TRITON C/E-1 [%] Values: PIE Data 150 Am-241 Am-242m 100 Am-243 Ce-144 Cm Cm-243 Cm-244 Cm-245 C/E-1 [%] 0 TRITON Cm-246 Cm-247 Cs-134 Cs Eu-154 Nd-142 Nd Nd-144 Nd-145 Nd More TRITON depletions were done using different parameters and different benchmark samples. Because the CENTRM (Continuous ENergy TRansport Module) self-shielding methodology has a temperature dependent systemic bias in depletion calculations (U-238 capture bias), the NITAWL (Nordheim Integral Treatment) module was used without subdividing the pins, which can t be done properly using NITAWL. To examine this, depletions of the representations of the SF97-4 pin and the middle section of a gadolinium enriched pin in the NT3G24 assembly in the PIE database, SF96-4 at position C-M, were performed using the NITAWL module, NITAWL with the pins divided into four equal volume axial rings, and the CENTRM module. Monteburns results were also included for the SP96-4 pin. The percent difference of the calculated to expected ratios of the nuclides were again graphed (see Figs. 19 and 20). The Cm-244 C/E-1 results are summarized in Table 10. The NITAWL and CENTRM values are close, and the U-238 capture bias of CENTRM led to the decision to use NITAWL for 41

48 subsequent calculations. Error in Cm-244 amounts due to NITAWL calculations should not affect results much. Figure 19: SF97-4 C/E-1 [%] Values SF97-4 C/E-1[%] Values: PIE Data from Takahama-3 PWR C/E-1 [%] Values NITAWL Nw/Rings CENTRM Am243/Am241 Cs137/U238 Nd148/U238 Pu239/U238 Pu240/Pu239 Pu241/Pu239 Pu242/Pu239 U235/U238 U236/U238 Cm242/U238 Cm243/U238 Cs134/U238 Eu154/U238 Nd143/U238 Nd145/U238 Nd148/U238 Sm147/U238 Sm150/U238 Sm151/U238 Sm152/U238 U234/U238 Np237/U238 Pu238/U238 Pu239/U238 Pu240/U238 Pu241/U238 Pu242/U238 Am241/U238 Am243/U238 Cm244/U238 Cm245/U238 Isotopes 42

49 Figure 20: SF96-4 C/E-1 [%] Values SF96-4 C/E-1 [%] Values: Monteburns Included C/E-1 [%] Values NITAWL Nw/Rings CENTRM Monteburns 0 Am-243/Am- Cs-137/U-23 Nd-148/U Pu-239/U- 238 Pu-240/Pu- 239 Pu-241/Pu- 239 Pu-242/Pu- 239 U-235/U-238 U-236/U-238 Cm-242/U-23 8 Cm-244/U Isotopes Table 10: Cm-244 C/E-1 [%] Values Sample NITAWL NITAWL w/rings CENTRM Monteburns SF SF SF Further comparison of the Monteburns values with NITAWL results was done with a depletion of the pin corresponding to sample SF95-4 in the PIE database at position A-Q. C/E-1 values are in Fig. 21 and Table 10. Although the Monteburns values are more accurate for SF97-4, they are wildly inaccurate for the other two samples in regards to Cm-244. Another comparison was to show that changing the Sn quadrature value from 8 to 2 had only a % difference. 43

50 Figure 21: SF95-4 C/E-1 [%] Values SF95-4 C/E-1 [%] Values: Monteburns Included C/E-1 [%] Values NITAWL Monteburns 0-50 Am-243/Am- Cs-137/U-238Nd-148/U-238Pu-239/U-238 Pu-240/Pu Pu-241/Pu- 239 Pu-242/Pu- 239 U-235/U-238 U-236/U-238 Cm-242/U-23 8 Cm-244/U Isotopes Symmetry of the one quarter assembly depletion was tested by independently depleting regular pins at positions (1,9) (assigned material 1) and (9,1) (assigned material 2) and gadolinium enriched pins at positions (5,7) (material 541) and (7,5) (material 542). The percent differences of the isotopic composition of the symmetric pins are graphed in Fig. 22. Although the regular pins have the same composition, the gadolinium enriched ones differ so much (43% for Cm-244) that they will have to be independently depleted. 44

51 Figure 22: Symmetric Comparison Symmetric Comparison % Difference 20 % 1, 2 % Gd Nuclides With these values, a TRITON depletion of one quarter of the Takahama-3 bundle was done with a decay time of two years after the end of burnup. Using the OPUS module of SCALE with a VFUEL fuel volume equal to the middle 20 cm of the pin, data extraction of the results was performed to obtain the numerical densities of the isotopes. These were used in the MCNP inputs with the same scenarios as in the preliminary results section. Neutron results for a fresh fuel pin replacing a spent one at location 10,9 are in Table 11 and the guide tubes meeting one or all of the detectability criteria are graphed in Fig. 23. Fig. 24 graphs the scenario with a FFP at location 17,1. Summaries of the neutron results for all the scenarios are in Tables 13, 15 and 16 and associated Figs. 27, 29 and 30. Gamma results for the same conditions are in Table 15 and Figs. 25 and 26, with summaries in Tables 14, 17 and 18 and associated Figs. 28, 31 and

52 The preceding scenarios with done with pure water assumed to be in the cooling pool. Actually, a boron concentration of ~2600 ppm is the industry standard. To determine whether the boron concentration affects the number of guide tube locations meeting the detection thresholds, scenarios with the same pin replacement and varying concentrations of boron (pure water, moderator value of ~500 ppm, 2000 ppm and 3000 ppm) in the cooling pool and with the spent fuel rods in air were constructed. Results are in Figs. 33, 34, 35 and 36. Table 11: Neutron Results with Fresh Fuel Pin at (10,9) (TRITON) r.e.<1 total<1 tot > overlap GT (3,6) 2 6 no yes no no GT (3,9) 4 8 yes yes yes yes GT (3,12) 2 5 no yes no no GT (4,4) 3 4 no no no no GT (4,14) 0 2 no no no no GT (6,3) 1 5 no no no no GT (6,6) 3 4 yes yes yes yes GT (6,9) 4 7 yes yes yes yes GT (6,12) 1 3 no no no no GT (6,15) 5 8 no no no no GT (9,3) 0 3 no no no no GT (9,6) 3 5 no yes no no GT (9,9) 6 9 yes yes yes yes GT (9,12) 1 6 no yes no no GT (9,15) 6 9 yes yes no yes GT (12,3) 1 5 no no no no GT (12,6) 2 6 no no no no GT (12,9) 6 10 yes yes yes yes GT (12,12) 1 5 no yes no yes GT (12,15) 0 3 no no no no GT (14,4) 4 6 no no no no GT (14,14) 2 6 no no no no GT (15,6) 1 3 no no no no GT (15,9) 0 5 no no no no GT (15,12) 2 4 no no no no 46

53 Figure 23: Diversion Detectability Using Differential Neutron Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 10,9 (TRITON) Legend GT Meets All Detectability Criteria GT Meets At Least One Detectability Criterion 9 8 GT Does Not Meet Criteria 7 6 UO2 Fuel Pin Diverted Figure 24: Diversion Detectability Using Differential Neutron Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (TRITON) Legend GT Meets All Detectability Criteria GT Meets At Least One Detectability Criterion 9 8 GT Does Not Meet Criteria 7 6 UO2 Fuel Pin Diverted

54 Table 12: Gamma Results with Fresh Fuel Pin at (10,9) (TRITON) r.e.<1 total<1 tot > overlap GT (3,6) 0 0 no no no no GT (3,9) 0 0 no no no no GT (3,12) 1 0 no no no no GT (4,4) 0 0 no no no no GT (4,14) 0 0 no no no no GT (6,3) 0 0 no no no no GT (6,6) 0 0 no no no no GT (6,9) 1 1 yes yes no no GT (6,12) 0 0 no no no no GT (6,15) 0 0 no no no no GT (9,3) 0 0 no no no no GT (9,6) 2 2 yes yes no no GT (9,9) 3 3 yes yes yes yes GT (9,12) 2 2 yes yes no no GT (9,15) 0 0 no no no no GT (12,3) 0 0 no no no no GT (12,6) 3 2 yes yes no no GT (12,9) 2 2 yes yes yes yes GT (12,12) 2 2 yes yes yes no GT (12,15) 0 0 no no no no GT (14,4) 0 0 no no no no GT (14,14) 0 0 no no no no GT (15,6) 0 0 no no no no GT (15,9) 0 0 no no no no GT (15,12) 2 1 yes yes no no 48

55 Figure 25: Diversion Detectability Using Differential Gamma Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 10,9 (TRITON) Legend GT Meets All Detectability Criteria GT Meets At Least One Detectability Criterion 9 8 GT Does Not Meet Criteria 7 6 UO2 Fuel Pin Diverted Figure 26: Diversion Detectability Using Differential Gamma Fluxes for Takahama-3 Nuclear Plant Diversion Scenarios: Diverted Pin Location 17,1 (TRITON) Legend GT Meets All Detectability Criteria GT Meets At Least One Detectability Criterion 9 8 GT Does Not Meet Criteria 7 6 UO2 Fuel Pin Diverted

56 Pin replaced Table 13: Summary of Neutron Results (TRITON) rel.err. < 1 (10,9) in 6 tubes (17,1) in 7 tubes rel. err. < 1 in 11 tubes in 10 tubes in 5 tubes in 5 tubes in 7 tubes in 7 tubes Number of GT Meeting Threshold Figure 27: Graph of Table 13 Summary of Neutron Results (TRITON) (10,9) (17,1) SFP Replaced with Fresh Fuel Pin, T1, T1, T2, T2 Pin replaced Table 14: Summary of Gamma Results (TRITON) rel.err. < 1 (10,9) in 8 tubes (17,1) in 4 tubes rel. err. < 1 in 8 tubes in 4 tubes in 3 tubes in 2 tubes in 2 tubes in 2 tubes 50

57 Number of GT Meeting Threshold Figure 28: Graph of Table 14 Summary of Gamma Results (TRITON) (10,9) (17,1) SFP Replaced with Fresh Fuel Pin, T1, T1, T2, T2 Table 15: Summary of Neutron Results with Pin Removed (TRITON) Pin replaced rel.err. < 1 (10,9) in 21 tubes (17,1) in 9 tubes rel. err. < 1 in 24 tubes in 13 tubes in 17 tubes in 7 tubes in 23 tubes in 12 tubes 51

58 Number of GT Meeting Threshold Figure 29: Graph of Table 15 Summary of Neutron Results (TRITON) (10,9) (17,1) SFP Removed, T1, T1, T2, T2 Table 16: Summary of Neutron Results with Stainless Steel Pin (TRITON) Pin replaced rel.err. < 1 (10,9) in 25 tubes (17,1) in 22 tubes rel. err. < 1 in 25 tubes in 23 tubes in 25 tubes in 18 tubes in 25 tubes in 23 tubes 52

59 Number of GT Meeting Threshold Figure 30: Graph of Table 16 Summary of Neutron Results (TRITON) (10,9) (17,1), T1, T1, T2, T2 SFP Replaced with Stainless Steel Pin Table 17: Summary of Gamma Results with Pin Removed (TRITON) Pin replaced rel.err. < 1 (10,9) in 3 tubes (17,1) in 1 tubes rel. err. < 1 in 2 tubes in 1 tubes in 2 tubes in 1 tubes in 2 tubes in 1 tubes 53

60 Number of GT Meeting Threshold Figure 31: Graph of Table 17 Summary of Gamma Results (TRITON) (10,9) (17,1) SFP Removed, T1, T1, T2, T2 Table 18: Summary of Gamma Results with Stainless Steel Pin (TRITON) Pin replaced rel.err. < 1 (10,9) in 4 tubes (17,1) in 2 tubes rel. err. < 1 in 4 tubes in 2 tubes in 2 tubes in 1 tubes in 2 tubes in 1 tubes 54

61 Number of GT Meeting Threshold Figure 32: Graph of Table 18 Summary of Gamma Results (TRITON) (10,9) (17,1), T1, T1, T2, T2 SFP Replaced with Stainless Steel Pin 55

62 Figure 33: Diversion Detectability Using Differential Neutron Fluxes for 9 Diversion Scenarios: Diverted Pin Location 10,9. The coding for the replacement medium in each scenario is A=air,W=pure water, M=moderator boron concentration (~500 ppm), U=under average boron concentration (~2000 ppm),and O=over average boron concentration (~3000 ppm). (10,9) is the location of the pin removed or replaced by a fresh fuel pin (ff), a stainless steel dummy pin (ss), or water. The neutron flux is indicated by w for the Watt fission spectrum. 56

63 Figure 34: Diversion Detectability Using Differential Neutron Fluxes for 9 Diversion Scenarios: Diverted Pin Location 17,1. Same coding as in Fig. 21. (17,1) is the location of the pin removed or replaced. 57

64 Figure 35: Diversion Detectability Using Differential Gamma Fluxes for 5 Diversion Scenarios: Diverted Pin Location 10,9. Same coding as in Fig. 21. Fewer scenarios were used because the gamma fluxes are relatively indifferent to boron concentration, as seen by W10,9ffrpg and M10,9ffrpg Number of Guide Tubes total<1 tot > overlap Max > overlap A10,9ffrpg W10,9ffrpg M10,9ffrpg M10,9ssrpg M10,9waterrpg 58

65 Figure 36: Diversion Detectability Using Differential Gamma Fluxes for 5 Diversion Scenarios: Diverted Pin Location 17,1. (17,1) is the location of the pin removed or replaced. 6 5 Number of Guide Tubes total<1 tot > overlap Max > overlap Beaver Valley Plant Results The Beaver Valley WW17WL bundles were found to be the most numerous. The ones with the extremes of initial enrichment and maxburn (maximum burnup time) that have been depleted with TRITON are LMOHEP with an initial enrichment of 3.263% and a maxburn of GWd/MTU, LM042T with an initial enrichment of 2.105% and a maxburn of GWd/MTU, LM046R with an initial enrichment of 3.099% and a maxburn of GWd/MTU, and LM043Y with an initial enrichment of 2.105% and a maxburn of GWd/MTU. None of these bundles have gadolinium enriched pins. LMOHEP has a WABA (Wet Annular Burnable Absorber) rod in a center guide tube in each quadrant (see Fig. 37), specifications of which were found in a paper, Parametric Study of the Effect of Burnable 59

66 Poison Rods for PWR Burnup Credit [17]. The WABA rod was assumed to be removed prior to the assembly being placed in the cooling pool. The same OPUS data extraction was performed. For this report, the results were used in the MCNP scenarios with the spent fuel pin replaced by a fresh fuel or a stainless steel pin at location 17,1, the scenario with the lowest number of locations that met the different detection thresholds. The boron concentration in the cooling pool was set at the industry average, 2600 ppm. The results are in Tables and Figures

67 Figure 37: LMOHEP Bundle Depletion 61