DEVELOPMENT OF A 37-ELEMENT FUEL BUNDLE FOR THE PRODUCTION OF

MOLYBDENUM-99 IN CANDU POWER REACTORS

By

Jawad Haroon

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Applied Science

In

The Faculty of Energy Systems and Nuclear Science

Nuclear Engineering

University of Ontario Institute of Technology

August 2014

© Jawad Haroon, 2014

Abstract

In this study, the potential use of CANDU power reactors for the production of

Mo-99 is assessed. Five different modifications of a 37-element fuel bundle that could be used for the production of Mo-99 in existing CANDU type power reactors are explored. Since Mo-99 is generated by the fission of U-235 with a fission yield of 6.1%, the proposed designs use enriched uranium in the Mo-99 producing fuel pins. The challenge lies in designing a fuel that is able to produce significant quantities of Mo-99 while having similar neutronics and thermalhydraulic characteristics to the standard

CANDU fuel.

The proposed designs, when irradiated in the peak power channel of a CANDU core, are shown to produce significant quantities of Mo-99 while maintaining the necessary reactivity and power rating limits. The total Mo-99 production activities are found to be approximately 2335, 2297, 2336, 4131 and 4268 six-day Curies per bundle for Designs 1 to 5, respectively. The yield corresponds to approximately 19% (for

Designs 1, 2 and 3) and 34% (for Designs 4 and 5) of the world weekly demand for

Mo-99. A production cycle of 6 bundles per week (for Designs 1, 2 and 3), or 3 bundles per week (for Designs 4 and 5) can meet the global demand of Mo-99 medical isotopes.

Keywords: Medical Isotopes, CANDU, DRAGON Code, Molybdenum-99, Six-Day Curies,

Infinite Multiplication Factor, Linear Heat Rating, Fuel Centreline Temperature

Page | ii

Acknowledgement

I am grateful to my research supervisor Dr. Eleodor Nichita for giving me this opportunity to research under his guidance. I sincerely thank him for his valuable advice and confidence in my abilities throughout my Masters. I thank him for all the guidance and information he provided that allowed me to start off this project, and helping me every time I felt lost.

A special thank you to Wargha Peiman, who is a PhD candidate at the University of Ontario Institute of Technology for his help with the DRAGON code and the many interesting discussions we had on deciphering code manuals.

I would like to dedicate this thesis to my mother and father, Sarwat Siddiqa and

Haroon-ur-Rashid, who from an early age encouraged me to pursue my interest in science and engineering. Thank you for all the encouragement along the way and for the value placed on family. Thank you to my wonderful sister, Saba Haroon, who was there for me throughout the writing process to help me proofread and give suggestions. I would like to thank all my family and friends for their love and support throughout my

Masters, in particular, Brooke Smyth for many years of happiness and continued love, support and inspiration.

It has been an honour and a pleasure, thank you all.

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Table of Contents

ABSTRACT ...... II

ACKNOWLEDGEMENT ...... III

TABLE OF CONTENTS ...... IV

LIST OF ACRONYMS ...... XII

CHAPTER 1 INTRODUCTION ...... 1

1.1 INTRODUCTION TO NUCLEAR MEDICINE ...... 3

1.1.1 WHAT IS NUCLEAR MEDICINE? ...... 3

1.1.2 MEDICAL ISOTOPES AND DISEASES ...... 4

1.1.3 MOLYBDENUM-99/TECHNETIUM-99M: THE MOST COMMON RADIOISOTOPE ...... 5

1.2 DEMAND FOR MOLYBDENUM-99 ...... 5

1.3 THE BIG FIVE MEDICAL ISOTOPE PRODUCING REACTORS ...... 7

1.4 INTRODUCTION TO RADIOISOTOPE PRODUCTION IN NUCLEAR REACTORS ...... 11

1.5 ALTERNATIVE METHODS FOR PRODUCING MOLYBDENUM-99 ...... 12

1.5.1 PHOTO-FISSION PROCESS 238U(Γ,F)99MO ...... 12

1.5.2 NEUTRON ACTIVATION OF MOLYBDENUM-98 ...... 12

1.5.3 NEUTRON EMISSION FROM MOLYBDENUM-100 ...... 13

1.6 RADIOACTIVE DECAY OF MOLYBDENUM-99/TECHNETIUM-99M ...... 14

1.7 CONSIDERATIONS IN THE PRODUCTION OF MOLYBDENUM-99 IN NUCLEAR REACTORS ...... 16

1.7.1 MOLYBDENUM-99 TARGET PROCESSING TECHNIQUES ...... 18

Page | iv

1.7.2 TECHNETIUM-99M GENERATORS...... 21

1.7.3 SPENT FUEL CONSIDERATIONS ...... 23

1.8 CANDU REACTORS AND THE DRAGON LATTICE CODE ...... 26

1.8.1 USING CANDU REACTORS FOR MOLYBDENUM-99 PRODUCTION ...... 26

1.8.2 THE DRAGON CODE ...... 30

CHAPTER 2 PRODUCTION OF MOLYBDENUM-99 IN NUCLEAR REACTORS: PRESENT AND

FUTURE ...... 33

2.1 CURRENT MOLYBDENUM-99 SUPPLY CHALLENGES ...... 34

2.2 CONVERSION OF MOLYBDENUM-99 TARGETS FROM HIGHLY-ENRICHED URANIUM TO LOW-

ENRICHED URANIUM ...... 35

2.3 NEW PRODUCERS OF MOLYBDENUM-99 WORLDWIDE ...... 37

2.4 MOLYBDENUM-99 PRODUCTION IN POWER REACTORS ...... 38

CHAPTER 3 METHODOLOGY FOR THE DEVELOPMENT OF A MOLYBDENUM-99

PRODUCING 37-ELEMENT FUEL BUNDLE DESIGN ...... 41

3.1 DESIGN OBJECTIVES ...... 41

3.2 DESIGN PLAN AND STRATEGY ...... 42

3.2.1 SATISFYING DESIGN REQUIREMENTS ...... 45

3.3 REACTOR OPERATING CONDITIONS AND ASSUMPTIONS ...... 51

3.3.1 REACTOR FUELLING CONSIDERATIONS ...... 52

3.4 DESIGN OPTIONS AND METHODOLOGY ...... 54

3.4.1 METHOD FOR CALCULATING THE LINEAR HEAT RATING ...... 57

3.4.2 METHOD FOR CALCULATING THE RADIAL TEMPERATURE PROFILE ...... 60

Page | v

3.4.3 METHOD FOR CALCULATING THE MASS AND ACTIVITY OF MOLYBDENUM-99 PRODUCED ...... 69

CHAPTER 4 ASSESSMENT RESULTS AND DISCUSSION ...... 73

4.1 TASK 1 - COMPARISON OF INFINITE MULTIPLICATIVE CONSTANTS ...... 78

4.2 TASK 2 - COMPARISON OF LINEAR HEAT RATING ...... 85

4.3 TASK 3 - COMPARISON OF RADIAL TEMPERATURE PROFILES ...... 92

4.4 MASS AND ACTIVITIES OF MOLYBDENUM-99 ...... 113

CHAPTER 5 CONCLUDING REMARKS AND FUTURE WORK ...... 117

REFERENCES ...... 120

APPENDICES ...... 135

APPENDIX A – POTENTIAL PRODUCERS OF REACTOR PRODUCED MOLYBDENUM-99...... 135

A.1 MULTIPURPOSE APPLIED PHYSICS LATTICE EXPERIMENT (MAPLE) ...... 135

A.2 AQUEOUS HOMOGENEOUS REACTOR (AHR) ...... 137

A.3 OPEN POOL AUSTRALIAN LIGHT-WATER (OPAL) REACTOR ...... 138

A.4 JULES HOROWITZ REACTOR (RJH) ...... 140

A.5 CHINA ADVANCED RESEARCH REACTOR (CARR) ...... 142

A.6 UNIVERSITY OF MISSOURI RESEARCH REACTOR CENTER (MURR) ...... 143

A.7 SANDIA NATIONAL LABORATORIES (SNL) ...... 144

A.8 OTHER POTENTIAL SUPPLIERS OF REACTOR PRODUCED MOLYBDENUM-99 ...... 148

A.9 NEW APPROACHES IN DIAGNOSTIC NUCLEAR MEDICINE ...... 150

APPENDIX B – MATERIALS, LATTICE SPECIFICATIONS AND IMPORTANT PARAMETERS FOR 37-ELEMENT

CANDU FUEL BUNDLE CALCULATIONS ...... 151

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APPENDIX C – INITIAL ESTIMATES OF ENRICHED FUEL REGION THICKNESS AND PIN RADIUS FOR UO2

AND U-METAL FUEL DESIGNS BASED ON URANIUM MASS BALANCING ...... 153

Page | vii

List of Figures

Figure 1-1: Approximate Global Demand for Molybdenum-99 ...... 7

Figure 1-2: Principal Decay Scheme of Molybdenum-99 ...... 16

Figure 1-3: Buildup of Molybdenum-99 Radioactivity for a Neutron Flux Typical of a CANDU-6 ...... 18

Figure 1-4: Global Supply Chain of Molybdenum-99 and Utilization Schematics ...... 20

Figure 1-5: Decay of Molybdenum-99 and Buildup of Technetium-99m Activity after Each Elution,

Calculated for 7 Days ...... 22

Figure 1-6: Generic Flow Chart of Waste Streams Generated from Molybdenum-99 Production ...... 25

Figure 1-7: CANDU Reactor Face ...... 28

Figure 1-8: A Typical CANDU Fuel Channel...... 29

Figure 3-1: A Pictorial Representation of the Proposed Designs Assessed for Molybdenum-99 Production .... 44

Figure 3-2 37-Element CANDU Fuel Bundle and the Infinite Lattice Cell Representation of Design 2...... 57

Figure 3-3: A Plot of UO2 Thermal Conductivity Showing Variation Due to Temperature ...... 65

Figure 4-1: Radial Pin Power Profile for Reference CANDU 37-Element Bundle ...... 74

Figure 4-2: Reference CANDU 37-Element Bundle Radial Temperature Profile of Ring 4 Pin Using IAEA and

Constant Thermal Conductivity for UO2 ...... 77

Figure 4-3: Design 1 Unitcell Lattice k-infinity Versus Variations in Radius of Enriched Central Target

Region (Fuel Pin Radius 6.075 mm) ...... 80

Figure 4-4: Design 2 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target

Region (Fuel Pin Radius 6.075 mm) ...... 81

Figure 4-5: Design 3 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target

Region (Fuel Pin Radius 4.266 mm) ...... 82

Figure 4-6: Design 4 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target

Region (Fuel Pin Radius 6.075 mm) ...... 83

Figure 4-7: Design 5 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target

Region (Fuel Pin Radius 4.266 mm) ...... 84

Figure 4-8: Design 1 Bundle Radial Pin Power Profile ...... 87 Page | viii

Figure 4-9: Design 2 Bundle Radial Pin Power Profile ...... 88

Figure 4-10: Design 3 Bundle Radial Pin Power Profile ...... 89

Figure 4-11: Design 4 Bundle Radial Pin Power Profile ...... 90

Figure 4-12: Design 5 Bundle Radial Pin Power Profile ...... 91

Figure 4-13: Design 1 Radial Temperature Profile of Ring 4 Pin Using IAEA Thermal Conductivity for UO2 . 97

Figure 4-14: Design 1 Radial Temperature Profile of Ring 4 Pin Using a Constant Thermal Conductivity for

UO2 (0.024 W/cm∙K) ...... 98

Figure 4-15: Design 2 Radial Temperature Profile of Ring 4 Pin Using IAEA Thermal Conductivity for

UO2 ...... 101

Figure 4-16: Design 2 Radial Temperature Profile of Ring 4 Pin Using a Constant Thermal Conductivity for

UO2 (0.024 W/cm∙K) ...... 102

Figure 4-17: Design 3 Radial Temperature Profile of Ring 4 Pin Using a Constant Thermal Conductivity for

U-Metal (0.43 W/cm∙K) ...... 105

Figure 4-18: Design 4 Radial Temperature Profile of Ring 4 Pin Using IAEA Thermal Conductivity for

UO2 ...... 108

Figure 4-19: Design 4 Radial Temperature Profile of Ring 4 Pin Using a Constant Thermal Conductivity for

UO2 (0.024 W/cm∙K) ...... 109

Figure 4-20: Design 5 Radial Temperature Profile of Ring 4 Pin Using a Constant Thermal Conductivity for

U-Metal (0.43 W/cm∙K) ...... 112

Page | ix

List of Tables

Table 1-1: Worldwide Production Capacity of Molybdenum-99 ([11], [12], [13], [14]) ...... 9

Table 1-2: Small-Scale Producers of Molybdenum-99 in 2011 ([8], [11], [14]) ...... 10

Table 1-3: Status of CANDU reactors and CANDU-Derivatives in 2014 ([28], [29]) ...... 27

Table 4-1: Reference CANDU 37-Element Bundle Data Structures for Radial Pin Power Profile

Calculations...... 74

Table 4-2: Reference CANDU 37-Element Bundle Normalized Heat Density and Linear Power Rating in Ring

4 Sub-regions ...... 75

Table 4-3: Reference CANDU 37-Element Bundle Numerical Integration Results Using IAEA and Constant

Thermal Conductivity for UO2 ...... 76

Table 4-4: Design 1 Unitcell Lattice k-infinity for Variations in Radius of Enriched Central Region ...... 80

Table 4-5: Design 2 Unitcell Lattice k-infinity for Variation in Thickness of Enriched Annular Region ...... 81

Table 4-6: Design 3 Unitcell Lattice k-infinity for Variation in Thickness of Enriched Annular Region ...... 82

Table 4-7: Design 4 Unitcell Lattice k-infinity for Variation in Thickness of Enriched Annular Region ...... 83

Table 4-8: Design 5 Unitcell Lattice k-infinity for Variation in Thickness of Enriched Annular Region ...... 84

Table 4-9: Design 1 Data for Radial Pin Power Profile Calculations ...... 87

Table 4-10: Design 2 Data for Radial Pin Power Profile Calculations ...... 88

Table 4-11: Design 3 Data for Radial Pin Power Profile Calculations ...... 89

Table 4-12: Design 4 Data for Radial Pin Power Profile Calculations ...... 90

Table 4-13: Design 5 Data for Radial Pin Power Profile Calculations ...... 91

Table 4-14: Thermophysical Properties of Coolant Using NIST REFPROP [46] ...... 94

Table 4-15: CANDU Specific Important Heat Transfer Parameters [46] ...... 94

Table 4-16: Design 1 Normalized Heat Density and Linear Power Rating in Ring 4 Sub-regions ...... 95

Table 4-17: Design 1 Numerical Integration Results Using IAEA and Constant Thermal Conductivity for

UO2 ...... 96

Table 4-18: Design 2 Normalized Heat Density and Linear Power Rating in Ring 4 Sub-regions ...... 99

Page | x

Table 4-19: Design 2 Numerical Integration Results Using IAEA and Constant Thermal Conductivity for

UO2 ...... 100

Table 4-20: Design 3 Normalized Heat Density and Linear Power Rating in Ring 4 Sub-regions ...... 103

Table 4-21: Design 3 Numerical Integration Results Using Constant Thermal Conductivity for U-Metal ..... 104

Table 4-22: Design 4 Normalized Heat Density and Linear Power Rating in Ring 4 Sub-regions ...... 106

Table 4-23: Design 4 Numerical Integration Results Using IAEA and Constant Thermal Conductivity for

UO2 ...... 107

Table 4-24: Design 5 Normalized Heat Density and Linear Power Rating in Ring 4 Sub-regions ...... 110

Table 4-25: Design 5 Numerical Integration Results Using Constant Thermal Conductivity for U-Metal ..... 111

Table 4-26: Design 1 Molybdenum-99 Production Results ...... 114

Table 4-27: Design 2 Molybdenum-99 Production Results ...... 114

Table 4-28: Design 3 Molybdenum-99 Production Results ...... 114

Table 4-29: Design 4 Molybdenum-99 Production Results ...... 115

Table 4-30: Design 5 Molybdenum-99 Production Results ...... 115

Table A-1: Potential Future Suppliers of Reactor Produced Molybdenum-99 [13] ...... 149

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List of Acronyms

ACRR Annular Core Research Reactor

AECL Atomic Energy of Canada Limited

AHR Aqueous Homogeneous Reactor

ANSTO Australian Nuclear Science and Technology Organization

B&W Babcock & Wilcox

CANDU CANada Deuterium Uranium

CARR China Advanced Research Reactor

CEA Atomic Energy Commission

CHF Critical Heat Flux

CNSC Canadian Nuclear Safety Commission

DOE Department of Energy

FDA Food and Drug Administration

HEU Highly-Enriched Uranium

HFR High Flux Reactor

IAEA International Atomic Energy Agency

Page | xii

LEU Low-Enriched Uranium

MNR McMaster Nuclear Reactor

MURR University of Missouri Research Reactor

NRU National Research Universal

NU Natural Uranium

OPAL Open Pool Australian Light-Water Reactor

RJH Jules Horowitz Reactor

SNL Sandia National Laboratories

SNM Society of Nuclear Medicine

US-NRC Unites States Nuclear Regulatory Commission

WLUP WIMS-D Library Update

Page | xiii

Chapter 1

Introduction

In nuclear medicine, radioactive nuclides are used to obtain functional information about a patient’s organs and to diagnose and treat various medical conditions [1]. The most common radioisotope used in nuclear medicine is technetium-99 (Tc-99m), which is produced through the radioactive decay of molybdenum-99 (Mo-99). Tc-99m is used in approximately 30 million procedures per year, accounting for 80% of all nuclear medicine procedures worldwide [2].

Mo-99 is most commonly and effectively generated in nuclear reactors by the fission reaction of U-235 with a yield of 6.1% [3]. Mo-99 production in fission reactors is usually achieved by irradiation of specially designed highly-enriched uranium (HEU) targets located inside irradiation rigs positioned at special high-flux sites in the core.

These HEU targets typically have a U-235 enrichment of 90 wt% or higher. Although some Mo-99 is produced in natural uranium (NU), the NU fuel composition is not suitable for producing significant quantities of Mo-99 since the ratio of Mo-99 yield to fuel volume processed is generally low. Therefore, the use of enriched fuel is desirable from the perspective of Mo-99 production.

When uranium is enriched to less than 20% by weight of U-235, it is considered low-enriched enriched uranium (LEU). Concerns over weapon proliferation and nuclear security have led to advanced discussions between experts of the field with the aim of using LEU instead of HEU as reactor fuel and target material.

Page | 1

As of 2014, the National Research Universal (NRU) reactor in Chalk River,

Ontario, produces approximately 40% of the global demand for Mo-99 [4]. The NRU is

57 years old and is scheduled to cease Mo-99 production in the year 2016. Consequently, alternative production methods and radioisotope production facilities need to be developed. One possibility is to irradiate specially designed fuel in the operating

CANDU®1 reactors; this is the main driver of the work presented in this thesis.

A CANDU reactor with its pressure channel design and its ability to fuel online has the potential to produce large quantities of Mo-99, while maintaining its power production targets. The production and extraction of Mo-99 is not possible in most other power plants due to batch fuelling. The online refuelling capabilities in CANDU, with its flexible and compact fuel design give CANDU reactors an edge over pressure-vessel light water reactors which are generally refuelled in batches every 18 to 24 months.

The goal of this thesis is to evaluate various modified 37-element fuel bundles specifically made for CANDU reactors with the intent to generate a significant portion of the world’s demand for Mo-99 without significantly changing the physics or fuel bundle safety characteristics. Several variations of the 37-element fuel bundle are analyzed using the DRAGON lattice code. Strict design acceptance criteria are used, consisting of close proximity of the fresh fuel k-infinity value to that of the reference CANDU bundle

1 CANDU is a trademark of Atomic Energy of Canada Limited used under licence by Candu Energy

Inc.

Page | 2

(Δρ < 1 mk) and maintaining existing margins to linear heat rating limits. An assessment of the fuel centreline temperature is also performed for the modified fuel bundle pins.

The strict design constraints allow the station to maintain existing operating practices and eliminate the need for supplemental fuel safety analysis or full core neutronics calculations.

1.1 Introduction to Nuclear Medicine

1.1.1 What is Nuclear Medicine?

Nuclear medicine uses small quantities of unstable nuclei administered to a patient to study the function of specific organs in the body or to treat tumours and other diseases ([1], [4]). The field of nuclear medicine can be divided into two branches: diagnostics and therapeutics.

Diagnostics: A radiopharmaceutical consisting of a radioisotope bound to a substrate is administered to a patient. The substrate is what governs the distribution of the radiopharmaceutical in the body and is chosen such that it is predominantly accumulated in the organ that needs to be investigated. The amount of accumulation in the specific organ gives information about the health and function of the organ. The gamma-emitting radioactive isotopes is what allows the distribution of the radiopharmaceutical to be visualized using an external detector which produces a diagnostic image. Images are then analyzed to detect partial or excessive absorption of

Page | 3 the isotope as an indication of organ malfunction [4]. Nuclear medicine imaging provides a view of the position and concentration of the radioisotope which depends primarily on an organ’s functioning rather than on its anatomy.

Therapeutics: Radioisotopes are injected into a patient in higher doses. The isotopes emit very energetic photons or particles which can destroy targeted cells such as cancer cells.

1.1.2 Medical Isotopes and Diseases

Medical isotopes are used routinely in the diagnosis and treatment of various diseases at hospitals and radiation clinics. The following list includes, but is not limited to some of the health conditions where various medical isotopes are used for monitoring and evaluation [2]:

 Heart disease

 Level of functioning of brain, heart, lungs, kidneys and other organs

 Tumours

 Progression of cancer – spreading to bones

 Hormonal disorders, ex. thyroid disease

Over hundreds of radiopharmaceutical products are used at hospitals and radiation clinics in North America every day. About 95% of the radiopharmaceuticals are used for medical diagnosis, while the rest are used for therapeutic purposes ([5], [6]).

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1.1.3 Molybdenum-99/Technetium-99m: The Most Common Radioisotope

The most commonly used radioisotope in diagnostic nuclear medicine is Tc-99m, which is produced directly from the radioactive decay of Mo-99 ([5], [7]). Tc-99m is used in approximately 30 million procedures per year, accounting for 80% of all nuclear medicine procedures worldwide [2].

Mo-99 and Tc-99m do not exist naturally. Mo-99 is most commonly and effectively generated by the fission of U-235 in nuclear reactors with a fission yield of

6.1% [3]. The reaction shown in Eq. (1.1) corresponds to the production of Mo-99 from the fission of U-235, which occurs for approximately 6.1% of all fission reactions.

235 99 133 92U  n42 Mo 50Sn  4n (1.1)

Mo-99 is formed from the nuclear fission of U-235 and consequently exists as a fission by-product in uranium targets. These targets are specifically irradiated for radioisotope production in nuclear reactors. The Mo-99 is then extracted in dedicated processing facilities and placed in generators that are sent to various medical institutions around the globe.

1.2 Demand for Molybdenum-99

Every week, approximately 300 therapeutic doses of medical isotopes and 30000 diagnostic treatments are performed in Canadian hospitals [2]. Over 10000 hospitals worldwide use radioisotopes of which 90% are used strictly for diagnosis [4].

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In developed countries, which account for 26% of the world population, the relative use of diagnostic nuclear medicine among all health procedures is 1.9% per year, one tenth of which involves therapy using radiopharmaceuticals [4]. In the United

States, there are approximately 18 million nuclear medicine procedures per year

(population of 311 million), and there are about 10 million procedures performed in

Europe (population of 500 million). In Australia, there are approximately 560000 procedures performed per year (population of 21 million) out of which 470000 of these procedures are done using reactor produced isotopes [4].

In North America, the demand for Mo-99 ranges from 5000 to 7000 six-day

Curies per week with an estimated annual growth rate between 3 and 5% [8]. Canada accounts for approximately 1/11 of the total North American consumption. A breakdown of the global demand of Mo-99 in 2009 is shown in Figure 1-1.

Curie is the unit of radioactivity (1 Curie = 3.7x1010 disintegrations per second or

Becquerels, Bq). A six-day Curie is a unit of measure most commonly used in the industry which equates to the amount of Mo-99 remaining in a Tc-99m generator six days after shipment from the producer’s facility. In other words, the producers usually calibrate a shipment value to the activity of the Mo-99 isotopes 6 days after it leaves the production facility [8].

The worldwide demand for Mo-99 has reached approximately 12000 six-day

Curies per week [7]. When accounting for the processing time and efficiency, 12000 six- day Curies is equivalent to about 77000 end-of-bombardment Curies which is 160 mg of

Mo-99 at the end of the irradiation stage [8]. The demand for medical isotopes for

Page | 6 diagnosis and therapy purposes is expected to grow over 10% per year worldwide ([4],

[9]).

16%

4% 44% 14%

22%

United States Europe Japan Canada Other

Figure 1-1: Approximate Global Demand for Molybdenum-992

1.3 The Big Five Medical Isotope Producing Reactors

Currently, five nuclear reactors are producing approximately 95% of the world’s supply of Mo-99 [11]. The five are the Chalk River National Research Universal (NRU) reactor in Canada, the High Flux Reactor (HFR) in the Netherlands, BR2 in Belgium,

OSIRIS in France, and the SAFARI-1 in South Africa. In addition to the production of

2 Data taken from Reference [10]

Page | 7 medical isotopes, these reactors also provide multiple services such as nuclear fuel testing and material research.

These big five industrial scale research reactors producing most of the world’s

Mo-99 supply are government-owned and funded. The global market share of these five major isotope producing reactors is shown in Table 1-1. The Canadian NRU reactor and the HFR in Netherlands, each produce approximately 30% to 40% of the global demand for Mo-99. The other two European reactors and the reactor in South Africa combined, produce approximately 36% of the Mo-99 supply. The smaller reactors around the world support approximately 4% of the world’s demand of Mo-99.

As of 2014, Canada’s NRU in Chalk River is 57 years old, HFR in Petten,

Netherlands is 53 years old, SAFARI-1 in Pelindaba, South Africa is 49 years old, BR-2 in

Mol, Belgium is 53 years old, and OSIRIS in Saclay, France is 48 years of age [12].

Table 1-1 also provides additional information on these five reactors (e.g., thermal powers and neutron fluxes, and estimated reactor stop date).

The majority of the smaller Mo-99 producing reactors around the globe accommodate local or regional medical isotope markets. Some regional producers of

Mo-99 are Australia, Argentina, Germany, Indonesia, and Poland as shown in Table 1-2.

The research reactors in the aforementioned countries do not produce the commercial quantities necessary to compensate for the closure of one or more of the big five reactors.

However, they can act as a short term make-up when one of the big five reactors experiences an outage. The regional reactors are listed in Table 1-2.

Page | 8

Table 1-1: Worldwide Production Capacity of Molybdenum-99 ([11], [12],

[13], [14])

Reactor Approximate Thermal Thermal Target Estimated Market Power Neutron Type Stop Date Share (%) (MW) Flux (n·cm-2·s-1) National 30% to 40% 135 4x1014 HEU 2016 Research Universal (NRU) (Canada) High Flux 30% to 40% 45 2.7x1014 HEU 2022 Reactor (HFR) (Netherlands) SAFARI-1 (South 15% 20 2.4x1014 HEU 2025 Africa) BR2 (Belgium) 14% 100 1x1015 HEU 2026 OSIRIS (France) 7% 70 1.7x1014 HEU 2018 Rest of the 4% - - - world

Page | 9

Table 1-2: Small-Scale Producers of Molybdenum-99 in 2011 ([8], [11], [14])

Reactor Typical Thermal Thermal Target Type Capacity (Six- Power (MW) Neutron Flux day Curies) (n·cm-2·s-1) OPAL (Australia) 20 3x1014 LEU RA-3 (Argentina) 200 5 4.8x1013 LEU MARIA (Poland) 30 3.5x1014 HEU LWR-15 (Czech 10 1.5x1014 HEU Republic) WWR-TS (Russia) 15 1.8x1014 HEU IRT-T (Russia) 6 1.4x1014 HEU FRM-II (Germany) 20 8x1014 HEU ETTR-2 (Egypt) 250 22 2.8x1014 LEU RSG-GAS 150 30 2.5x1014 HEU (Indonesia) PARR-1 20 10 1.7x1014 HEU (Pakistan) RECH-1 (Chile) 250 5 7x1013 LEU

Page | 10

1.4 Introduction to Radioisotope Production in Nuclear Reactors

Neutrons in nuclear reactors drive the nuclear reactions that must take place for the successful production of various radioisotopes. The neutron flux typically achieved in nuclear reactors is several orders of magnitude higher when compared to neutron generators and other isotopic neutron sources [7], for example ~1014 n·cm-2·s-1 for a typical nuclear reactor versus 1010 n·cm-2·s-1 for a typical neutron source. The quantity and activity of radioisotopes is directly proportional to the neutron flux. This explains why nuclear reactors that have high neutron flux values hold a strategic advantage in the production of medical radioisotopes.

Although all reactors are neutron sources; not all are suitable for Mo-99 production. The factors that determine whether a reactor is suitable for Mo-99 production are:

(i) neutron flux available for target irradiation,

(ii) volume of the irradiation rigs into which targets can be placed, and

(iii) in the case where targets are fissionable isotopes of enriched uranium, a further

consideration is heat removal from the targets [15].

Currently, nuclear reactors are producing Mo-99 and its decay product Tc-99m through irradiation of HEU targets. After spending several days in the reactors, these irradiated targets are sent for processing to dedicated processing facilities [7].

Page | 11

1.5 Alternative Methods for Producing Molybdenum-99

A nuclear reactor is not a requirement when it comes to producing Mo-99. An accelerator can also be utilized to generate Mo-99 by photo-fission of the U-238 atoms present in NU. Alternative options for the production of Mo-99 include eliminating uranium from the process by using other isotopes of molybdenum and converting them to Mo-99. This consists of four possible reactions: 98Mo(n,γ)99Mo (neutron activation) occurring inside a reactor, 100Mo(γ,n)99Mo, 100Mo(p,pn)99Mo and 100Mo(p,2n)99mTc

(neutron emission) using accelerators.

1.5.1 Photo-fission Process 238U(γ,f)99Mo

In this method, a high intensity beam of photons is generated and directed at

U-238 [16]. This reaction results in nearly the same 6.1% fission yield for Mo-99 as the fission yield of U-235 in nuclear reactors. The cross-section for this reaction is about

1000 times smaller than the neutron fission cross-section of U-235. As a result, a relatively large number of accelerators would be required to produce significant amounts of Mo-99. One estimate is that half a dozen accelerators are needed to supply

30% to 50% of North American demand [8].

1.5.2 Neutron Activation of Molybdenum-98

The reaction, 98Mo(n,γ)99Mo (neutron activation), requires thermal (~ 0.025 eV) or epithermal (0.025 – 1.0 eV) neutrons. However, only a small portion of this target is converted to Mo-99 because the cross-section of this reaction is small (σthermal ~ 0.14 barns). In addition, although neutron activation of molybdenum generates the desired

Page | 12 radionuclide with little to no waste stream, Mo-99 produced through this method is not

“carrier-free” as it contains Mo-98 (natural molybdenum contains approximately 24% of Mo-98) which is chemically identical to Mo-99 and behaves as a contaminant.

The Mo-99 produced through neutron activation has low specific activity and requires a large number of targets to produce significant quantities of Mo-99. A nuclear reactor would still be required to provide the necessary neutron flux for this method.

Furthermore, the potential exists for increased elution of undesirable Mo-98 when formulating patient dosages [8].

1.5.3 Neutron Emission from Molybdenum-100

The three neutron emission methods (100Mo(p,pn)99Mo, 100Mo(γ,n)99Mo and

100Mo(p,2n)99mTc) require accelerators that can generate very high intensity beams of protons (500 μA) or electrons, in order to create photons powerful enough to overcome the significantly smaller cross-sections for these reactions.

When the 100Mo(γ,n)99Mo reaction is used, high energy photons known as

Bremsstrahlung radiation are produced by the electron beam as it interacts and loses energy in the ‘converter’ target. The photons are subsequently used to irradiate another target material (Mo-100) placed just behind the converter to produce Mo-99 via neutron emission.

The 100Mo(p,2n)99mTc neutron emission method, results in the direct production of Tc-99m which has a significant disadvantage due to its short half-life. It is not an ideal method to produce Tc-99m because any need to ship the Tc-99m generators over

Page | 13 distances would reduce the usefulness to the end-user and by extension, to the patient

[8].

1.6 Radioactive Decay of Molybdenum-99/Technetium-99m

Mo-99 decays into Tc-99m, which is then extracted from the generators and combined with other reagents to form a radiopharmaceutical that can be given to patients. Tc-99m is an ideal radioisotope for diagnostic nuclear medicine ([7], [10], [17]) because of its physical and chemical properties. The 6.01-hour half-life of Tc-99m is neither too long nor too short for a medical procedure. Its parent radionuclide, Mo-99, has a 66-hour half-life which provides sufficient time for processing and long-distance transportation, and thus permits shipping under the form of a Mo-99/Tc-99m generator

[5].

Conversely, due to its short half-life, Tc-99m cannot be stockpiled or produced directly in nuclear reactors or through neutron activation as a final product, nor can it be shipped to hospitals and radiation clinics around the globe. Instead, Tc-99m is obtained through elution with a sterile saline solution from an alumina column containing its parent isotope Mo-99. The alumina column assembly is known as a

Tc-99m ‘generator’ [3].

Another desirable property of Tc-99m, is the energy of the emitted gamma radiation, which is in a range that allows a clear image to be produced in a gamma camera. In addition, since 89% of Tc-99m emits pure gamma radiation that is energetic

Page | 14 enough to pass through human body without significant attenuation, this keeps the total dose administered to patients low ([1], [18]).

Figure 1-2 shows the decay sequences of Mo-99 to Tc-99 with the respective half- lives and yields. Mo-99 disintegrates with a half-life of 66 hours to either Tc-99m or

Tc-99 by emitting a beta particle. The “m” in Tc-99m stands for ‘meta-stable’. The

Tc-99m radionuclide is unusual since it undergoes a gamma decay into Tc-99 ground state rather than decaying instantaneously, as is the case with most excited radionuclides produced through β- or β+ decay [19]. As depicted in Figure 1-2, Tc-99m decays by isomeric transition. The principal gamma-emission associated with the transition from the meta-stable state to the ground state of Tc-99 emits a 140-keV photon [5]. Using a scintillator that is made up of special plastic or NaI-Tl crystals, the photon is captured by the detector, and converted into visible light photons which are then converted by a photomultiplier tube into electrical pulses and counted electronically [20].

Page | 15

Figure 1-2: Principal Decay Scheme of Molybdenum-993

1.7 Considerations in the Production of Molybdenum-99 in Nuclear

Reactors

The activity of Mo-99 produced in a target is a function of irradiation time, the thermal neutron fission cross-section for U-235, the thermal neutron flux induced on the target, the mass of U-235 in the target, and the half-life of Mo-99 [22]. For a typical reactor with thermal neutron fluxes on the order of 1014 n·cm-2·s-1, irradiation times of about 15 to 20 days are sufficient to achieve the maximum possible activity of Mo-99 in the targets. Beyond this equilibrium stage, the amount of Mo-99 produced in the targets

3 Reproduced from Reference [21]

Page | 16 approximately balances the amount of Mo-99 being lost to radioactive decay [8].

Additional irradiation time is also uneconomical due to the fact that there would be additional accumulation of other undesirable fission products, adding to the radioactive fields from the targets, and the wastes that ultimately require disposal.

In theory, for a target irradiated by a thermal neutron flux inside a reactor, the rate of production can be represented by the following mathematical relationship:

dN   N  N (1.2) dt T

For Mo-99 production in U-235 targets, Eq. (1.2) can be solved to determine the specific activity of radioactive atoms at time ‘t’:

0.6 f  S  Mo99 f (1 et ) (Bq / g) (1.3) A

In Eqs. (1.2) and (1.3), NT is the total number of U-235 atoms in the target, N is

the number of Mo-99 atoms produced as a fission product, f Mo99 is the fraction of fission

products leading to the production of Mo-99 (6.1%),  f is the microscopic fission cross- section,  is the thermal neutron flux, and  is the Mo-99 decay constant. Figure 1-3 illustrates the buildup of Mo-99 activity for a target irradiated in a thermal neutron flux of approximately 2×1014 n·cm-2·s-1, which is typical of a CANDU reactor.

Page | 17

2.00E+13 1.80E+13

1.60E+13 (Bq/g)

1.40E+13

99 99 - 1.20E+13 1.00E+13 8.00E+12 6.00E+12 4.00E+12

Specific Mo of Activity Specific 2.00E+12 0.00E+00 0 100 200 300 400 500 600 700

Time (Hours)

Figure 1-3: Buildup of Molybdenum-99 Radioactivity for a Neutron Flux

Typical of a CANDU-6

1.7.1 Molybdenum-99 Target Processing Techniques

After irradiation in the reactor for several days, the HEU or LEU target is chemically processed by one of the two processes: i) acid dissolution and molybdenum separation process (Cintichem process), or ii) alkaline dissolution process.

The acid dissolution was developed by Cintichem Incorporated. The technology was later purchased by the US Department of Energy (DOE) following the decommissioning of Cintichem’s Tuxedo, NY reactor. The facility is currently focused on proposing modifications to convert to an LEU target for US supplies of medical isotopes.

Page | 18

A proprietary Nordion Incorporated acid-dissolution process is currently used for the isotope production from NRU. The process is believed to be very similar to the

Cintichem process according to available sources [20]. A brief overview of the acid dissolution process is provided below.

The alkaline dissolution process is generally used for targets that contain aluminum and is currently being used by all major isotope producers except Nordion

Incorporated (formerly known as MDS Nordion).

Following several days of irradiation, the targets are removed and allowed to cool in water for up to half a day. The targets are then transferred to an associated “hot cell” facility. The hot cells are cabins which are shielded by lead and concrete, and are able to withstand the decay heat and intense radiation fields of the targets. The time it takes for the processing of the targets in the hot cells is optimized in order to minimize Mo-99 losses due to radioactive decay. Approximately 1% of the generated Mo-99 is lost to decay per hour after end-of-bombardment inside a nuclear reactor [23]. The processing time required following irradiation inside a reactor means that a significant amount of

Tc-99m will eventually be lost.

In the hot cell facility, the cladding is punctured and volatile fission products such as Kr-85 and Xe-133 are removed. The target assembly is dissolved in hot nitric acid, forming a nitrate solution containing uranium, molybdenum, and other fission by- products. The solution is poured through an alumina (Al2O3) column that adsorbs the nitrates. The column is then washed with additional nitric acid to elute excess uranium and other fission by-products, leaving the molybdenum bounded within the column

Page | 19 matrix. Sodium hydroxide is then added to the column which elutes purified Mo-99 [5].

This process typically yields recovery greater than 85-90% of the Mo-99 in the targets

[8].

The removed Mo-99 is immediately shipped to Covidien in Mansfield,

Massachusetts or Lantheus Medical Imaging in North Billerica, Massachusetts, where they manufacture Tc-99m generators. These Tc-99m generators are used to extract the decayed daughter Tc-99m isotopes from the parent Mo-99. Finally, the generators are then shipped to destinations around the globe as depicted in Figure 1-4.

Figure 1-4: Global Supply Chain of Molybdenum-99 and Utilization

Schematics4

4 Reproduced from Reference [12]

Page | 20

1.7.2 Technetium-99m Generators

Manufacturing of a Tc-99m generator generally consists of adsorption of Mo-99 onto an alumina column. Positively charged beads are used in the alumina column to adsorb the Mo-99 as Mo99O42- [17]. When the Mo-99 decays it forms pertechnetate TcO4-.

Due to its single charge, pertechnetate is less tightly bound to the alumina. The column has a higher affinity for the Mo-99 than the Tc-99m ensuring the preferential elution of

Tc-99m when a saline solution is poured through the column. Breakthrough of small quantities of Mo-99 still occurs. The amount of breakthrough is one of the quality control parameters for manufacturing Tc-99m generators and is regularly monitored [17].

Due to the short half-life of Mo-99 (66 hour), the complete manufacturing process must take place quickly. For this reason, most nuclear medicine institutions rely on weekly shipments of Tc-99m generators to meet their demands. The supply chain is currently capable of supplying Tc-99m from reactor extraction to the patient in less than

48 hours in an ideal case.

When the supply reaches the hospital or the radiation clinic, a radiopharmacist calculates the amount of Tc-99m generated by disintegration of Mo-99 nuclides based on the transient equilibrium that exists between the two nuclides. For commercial kits such as Cardiolite®, the Tc-99m is eluted from the column with sterile saline (0.9%

NaCl), as sodium pertechnetate (Na99mTcO4), and is then mixed with other reagents into a final form that can be administered to patients. The column is re-used, or “milked”, until most of the Mo-99 has decayed and the column is exhausted [5]. Figure 1-5 shows the “milking” process of Tc-99m from its first elution.

Page | 21

TechneLite® is a Tc-99m generator that is produced by Lantheus Medical Imaging

Incorporated. Dosage from TechneLite can range from 0.08 mCi/kg for pediatric thyroid imaging to 0.28 mCi/kg for blood pool imaging of the heart [24]. Cardiolite® is another

Tc-99m generator produced by Lantheus Medical Imaging that is widely used in cardiac stress test applications.

Figure 1-5: Decay of Molybdenum-99 and Buildup of Technetium-99m Activity after Each Elution, Calculated for 7 Days5

5 Reproduced from Reference [17]

Page | 22

1.7.3 Spent Fuel Considerations

It is important to consider various concerns that generally arise in the production of Mo-99 from the perspective of waste management. Management of waste starts from the planning, designing and construction phase of the Mo-99 production facility and continues through the operational phase. Waste management strategy has to also account for the route taken by the spent targets and long-lived fission products.

Establishment and implementation of an effective and safe waste management strategy is generally a licensing requirement which is approved and regulated by the authorities.

Target fabrication, irradiation, and extraction of Mo-99 from targets generate significant quantities of chemical and radioactive waste. Waste is generated as solids, liquids, and gases, and can include material in the low, intermediate and highly radioactive waste categories [25]. Initial treatment of waste streams is usually done at the production site, from where it is transferred to short or long term storage facilities.

Treatment of gaseous waste is generally carried out in the production facility on site while treatment of solid and liquid radioactive waste can be performed off-site [25].

Figure 1-6 is a generic flow chart of waste streams generated from Mo-99 production.

The conversion from HEU to LEU targets, which is underway at most of the current Mo-99 producing facilities, would generate even larger quantities of waste. If current target dissolution processes are maintained, the existing waste storage facilities may not be able to accommodate a five-fold estimated increase in waste products.

Page | 23

A study conducted by the Nuclear Energy Agency gives an insight on the increased waste levels that are to be expected with LEU-based targets [26]. For example, the annual amount of waste corresponding to the 12000 six-day Curies per week production rate were 215 kg LEU uranium waste vs. 43 kg of HEU waste and 25 g of

Pu-239 for LEU vs. 1.2 g for HEU. These numbers are estimated annually for 20% enriched targets vs. 93% enriched targets, respectively. It is further noted from the OPAL reactor in Australia, LEU processed targets will yield increased volumes of intermediate and low-level liquid waste in comparison to HEU strategies [26]. However, the possibility remains that by converting liquid waste products to its solid form will optimize waste storage tanks that are currently operating below capacity and hence, waste storage will not be significantly impacted [8].

Page | 24

Figure 1-6: Generic Flow Chart of Waste Streams Generated from

Molybdenum-99 Production6

6 Adapted from Reference [27]

Page | 25

1.8 CANDU Reactors and The DRAGON Lattice Code

1.8.1 Using CANDU Reactors for Molybdenum-99 Production

CANDU reactors are known as pressurized heavy water reactors. The acronym

‘CANada Deuterium Uranium’ (CANDU) comes from the reactor’s use of heavy water as a moderator and NU as fuel. The moderator fills a large tank called the calandria. The calandria is penetrated by hundreds of horizontal fuel channels, each consisting of an inner pressure tubes which contains natural uranium oxide fuel in a form of fuel bundles and an outer calandria tube. The fuel is cooled by heavy water under high pressure. The pressure channel design makes it possible to refuel the reactor continuously without shutting it down. This is done by connecting in-tandem both sides of an individual channel to a fuelling machine and a fuelling machine cooling circuit. Table 1-3 gives a breakdown of the CANDU reactors and CANDU-derivatives that exist around the world.

Figure 1-7 depicts the important components of a typical CANDU reactor. A typical CANDU fuel channel is shown in Figure 1-8. The diagram shows the channel inlet/outlet end fitting and the arrangement of the fuel bundles in the pressure tube.

Page | 26

Table 1-3: Status of CANDU reactors and CANDU-Derivatives in 2014 ([28],

[29])

Country No. of Status Capacity Reactors (MWe net) Argentina 3 Operational 1627 Canada 19 Operational 13500 6 Permanent Shutdown 2143 China 2 Operational 1300 India 18 Operational 4091 4 Under Construction 2520 Republic of 4 Operational 2684 Korea Pakistan 1 Operational 90 Romania 2 Operational 1300

Page | 27

Figure 1-7: CANDU Reactor Face7

7 Reproduced from the CANTEACH website [30]

Page | 28

Figure 1-8: A Typical CANDU Fuel Channel8

8 Reproduced from the CANTEACH website [31]

Page | 29

1.8.2 The DRAGON Code

Analysis of the proposed bundle designs is performed at the lattice level using the lattice transport code DRAGON version 3.05 [32], [33], [34]. DRAGON has been developed at École Polytechnique9 de Montreal and is considered one of the recommended codes by the nuclear industry to perform lattice calculations. The code solves the integral neutron transport equation using 2-D and 3-D collision probability techniques.

DRAGON is a lattice code which is used to solve the neutron transport equation for a given geometry. DRAGON includes all of the functions that characterize a lattice cell code divided into several calculation modules. The modules are linked together by

GAN generalized driver. The exchange of information is ensured by well-defined data structures. This is done so that new calculation techniques can be implemented in the code [35].

DRAGON consists of two main components, one -group collision probability tracking modules and multigroup flux solvers. The interface-current technique is used by the JPM tracking option at the level of each homogenous region associated with a

9 The École Polytechnique de Montréal is an engineering school/faculty affiliated with the

University of Montreal in Montreal, Quebec, Canada.

Page | 30 specific geometry. In cases where a multiplicative medium is analyzed, DRAGON performs power iterations to find the effective multiplication factor.

The effective multiplication factor (keff) is defined as the ratio of the number of fissions (or fission neutrons) in one generation divided by the number of fissions (or fission neutrons) in the preceding generation. keff provides an idea of deviation of the system from equilibrium. The system can be termed critical (the production and destruction rates are equal), subcritical (the production rate is smaller than destruction rate) or supercritical (the production rate is greater than destruction rate) based on the following definition:

< 1 푟푒푎푐푡표푟 푠푢푏푐푟푖푡푖푐푎푙 푘푒푓푓 {= 1 푟푒푎푐푡표푟푐푟푖푐푡푖푐푎푙 (1.4) > 1 푟푒푎푐푡표푟 푠푢푝푒푟푐푟푖푡푖푐푎푙

The multiplication factor of an infinite lattice calculation is represented as kinf. In the case where the coefficient of reflection at the surface boundary is set to 1 everywhere, as is the case with the models analyzed in this thesis, the outgoing fluxes will be reflected back into the volume, making the neutron leakage equal to zero, and thus making keff equal to kinf. It is referred to as the reflective boundary condition.

Another important quantity in reactor neutronics is known as reactivity (ρ). It is defined as the fractional departure of a system from criticality and is calculated as:

k 1   eff (1.5) k eff

Page | 31

The system reactivity change can be positive or negative depending on the process involved. For example, addition of any form of poison, like boron in the moderator or insertion of control rods, brings about a reduction in reactivity, while removal of poison or addition of fresh fuel or enrichment of NU can bring about an increase in reactivity.

In the present study, the focus is on change in reactivity from introducing a region of enriched fuel by comparing it to that of NU. The change in reactivity ∆ρ, introduced due to enrichment can be defined as:

 1 1       x 1000mk  k natrual k enriched   eff eff  (1.6)

There are microscopic cross-section libraries that are structured according to a standard format and are accessible to DRAGON [34]. The output data stream provided by DRAGON is the source for obtaining useful information such as macroscopic cross- section, neutron fluxes, etc.

Page | 32

Chapter 2

Production of Molybdenum-99 in Nuclear Reactors: Present

and Future

Mo-99 is obtained from the fission of U-235, and is principally produced through the 235U (n,f) 99Mo  99mTc reaction using the five government-owned and funded multi- purpose reactors listed in Table 1-1. The ageing of these five research reactors has required ever growing shutdown periods for maintenance and repair. This has made the supply of Mo-99 more fragile and a topic of concern for the medical community.

Additional challenges are cast on the supply of Mo-99 due to the fact that the major Mo-99 manufacturers have been using HEU (~93%) for target material, except for

SAFARI-1 in South Africa that uses 45% [8]. Some of the regional producers of Mo-99 are using LEU targets, including for example, the RA-3 reactor in Argentina and the OPAL reactor in Australia [8].

The challenges arising from the limited number of ageing reactors and the use of

HEU, which ultimately affect the reliable supply of Mo-99 worldwide, will be explored further in this Chapter.

Page | 33

2.1 Current Molybdenum-99 Supply Challenges

Five nuclear research reactors are producing most of the worldwide supply of

Mo-99 as listed in Table 1-1. In 2007, major disruptions occurred in the global supply of

Mo-99 due to an extended shutdown of the NRU reactor. The disruptions lasted for several weeks. As a result, many of the diagnostic testing and procedures for life- threatening conditions were cancelled affecting tens of thousands of patients throughout

Canada and the US [2].

The crisis began when the NRU reactor did not return to operation for several weeks following a routine maintenance shutdown due to regulatory issues. The NRU shutdown event was followed by an extension of the planned outage at HFR-Petten due to leaks, and an unplanned shutdown of an isotope processing facility due to Iodine-131 release from the waste stream [12]. Concerns over the long term supply of medical isotopes were further exacerbated by the government of Canada’s decision to stop the development of the MAPLE reactors. These reactors were being designed and built to meet the world’s demand of medical isotopes, specifically Mo-99, I-125, I-131, and

Xe-133 [36]. There are currently no reliable long-term substitutes to NRU to ensure continuity in the supply of Mo-99 to the world.

Page | 34

2.2 Conversion of Molybdenum-99 Targets from Highly-Enriched

Uranium to Low-Enriched Uranium

The current producers of Mo-99 use HEU targets of ~93 wt% U-235 with the exception of SAFARI-1 reactor in South Africa which uses 45 wt% U-235 targets. For the

NRU reactor, HEU from Y-12 National Security Complex in Oak Ridge, Tennessee is shipped to Chalk River Laboratories in Chalk River, Canada to be manufactured into

Mo-99 targets. Published records by the United States Nuclear Regulatory Commission

(US-NRC) report shipments of 10-25 kg of HEU per year from the US to Canada for Mo-99 production ([20]).

The most pressing change in the medical isotopes industry has been surrounding the efforts to convert the fuel and the Mo-99 targets to LEU (less than 20% U-235 by weight). In the interest of nuclear security and non-proliferation, many countries around the world are making strides in the efforts to migrate from using HEU to LEU.

The movement was supported by the US House of Representatives in November of 2009 in the form of passing a legislation which would eliminate the US export of HEU for isotope production in Canada within a period of 7 to 10 years [37].

Substituting LEU directly in place of HEU targets would reduce the Mo-99 yield to approximately 20% of that generated from the HEU due to reduced number of U-235 atoms available for fission. The lower yield can be overcome by irradiating five times more targets in the reactor, however the available reactor space limitations may preclude such an option.

Page | 35

Irradiating five times more targets will also result in five times the volume of separation waste leading to storage and disposal issues. In addition, employing LEU targets will also increase the generation of fissile plutonium-239 due to neutron capture by the higher proportion of uranium-238 atoms. However, plutonium can be ultimately used to make mixed-oxide fuel for nuclear power plants as it is generally insoluble and can therefore be separated from liquid wastes during processing of the LEU targets [8].

Research is underway to yield more efficient LEU target designs. Researchers are looking at ways to alter the composition of LEU targets for the purpose of increasing the density of U-235 in the targets [8]. The Reduced Enrichment for Research and Test

Reactors program was first established in 1978 at the Argonne National Laboratory by the US Department of Energy. The primary objective of this program was to develop the technology needed to use LEU instead of HEU in the research and test reactors, without impacting the experimental performance, economics, or safety of the reactors [38].

There will have to be substantial economic incentives for any large producer of

Mo-99 to change from using HEU. Large investments would be required for infrastructure, approval of new processes and procedures and the required research.

Any new process would need to be qualified by the various regulators, which is a long and expensive process, adding to its cost. Implications regarding waste management with respect to treatment of irradiated targets and disposal should also receive high priority [39].

Page | 36

2.3 New Producers of Molybdenum-99 Worldwide

The current fleet of Mo-99 producers consisting of the big-five reactors is aging and is expected to stop the production of Mo-99 in the next decade. The NRU is scheduled for shutdown and to cease all production in the year 2016. The OSIRIS reactor is expected to shut down by the end of 2018. These two reactors account for over a quarter of the available capacity of Mo-99. This will drastically reduce the supply of

Mo-99.

Since the 2007 disruptions in the supply of Mo-99, several countries have expressed interest in building modern research reactors dedicated to Mo-99 production in order to curtail reliance on other countries for medical isotopes and to develop domestic production capabilities. Some countries have proposed new projects to initiate molybdenum production from an existing facility not originally built for that purpose.

Commissioning a new reactor for isotope production is a lengthy process. According to a European Commission study on the supply of medical isotopes, it can take ten or more years for any new project from the planning phase to become operational. If an existing facility is upgraded to supply Mo-99, these facilities can take five or more years to become operational depending on available equipment and facilities at the specific reactor site [7].

Appendix A provides a list of potential producers that have the technological resources to develop Mo-99 production capabilities. A general underlying objective of these new initiatives is to develop domestic capabilities of producing Mo-99 and reducing the dependence on foreign suppliers. In few cases where potential exists to

Page | 37 irradiate a large number of targets, exports of medical isotopes may occur from those facilities to aid in meeting the global demand for medical isotopes.

2.4 Molybdenum-99 Production in Power Reactors

Production of Mo-99 using commercial power reactors is a novel idea considering power plants are not normally used to produce radioisotopes. Other radioisotopes have been produced using power reactors, particularly in CANDU reactors. In Canada, tritium is recovered from the heavy water coolant [28]. The adjustor rods used in CANDU reactors are also processed to produce cobalt-60 sources for industrial radiation processing. However, most commercial power reactors generally restrict their use solely to the generation of electricity.

The production of medical isotopes in power reactors involves several interrelated areas such as target fabrication, neutronic analysis, thermalhydraulic calculations, safety analysis, fuelling schemes, processing and transportation of irradiated targets [28]. Another important factor is the number and volume of targets being irradiated at a time, which will determine the yield of radioisotopes. Irradiation time in reactor is another important factor in obtaining high specific activity.

The CANDU reactors and CANDU-derivatives have a pressure tube design that permits these reactors to be refuelled online by connecting in-tandem to a fueling machine. From the standpoint of Mo-99, a case can be made that irradiation of targets

Page | 38 in power reactors is similar to their irradiation in a research reactor in the sense that these targets can be recovered at any time.

It is also possible to irradiate targets in the irradiation channels that exist in some pressure tube type reactors ([26], 28]). Instrumentation channels can also be used to irradiate targets in most reactors. However, this may be a challenging task requiring reconfiguration of the reactor instrument calibration and possibly the core neutronics.

Irradiation of uranium targets in CANDU has already been proposed in recent past ([22], [40], [41]). Researchers at McMaster University have analyzed a new 37- element fuel bundle containing a combination of slightly enriched/depleted uranium pins that, when irradiated in a CANDU reactor, could yield 100% to 120% of the world demand of Mo-99 ([22], [40]). The researchers have proposed modifications to the 37- element fuel bundle that would contain 1.5% to 3% enriched uranium oxide fuel either in the second and third ring, or in the fourth ring of the fuel bundle, with the rest of fuel pins containing depleted uranium. Calculations done in the WIMS-AECL-v3.121 lattice code showed that these targets, when irradiated in the central and periphery channels, produced significant amounts of Mo-99 without adversely affecting important reactor safety parameters such as neutronics, heat rating limits, and including any significant impact on standard fuelling operations. However, the design constraints used in the

McMaster research had wide margins allowing for the Mo-99 producing bundle neutronics to deviate significantly from the reference value. For example, a reactivity difference of 10 to 15 mk from the reference CANDU bundle was deemed acceptable for

Page | 39 the Mo-99 producing bundles, potentially leaving a gap in the safety analysis and a need for confirmation of the design using full core calculations and experimental testing.

Page | 40

Chapter 3

Methodology for the Development of a Molybdenum-99

Producing 37-Element Fuel Bundle Design

3.1 Design Objectives

One of the attractive features of the CANDU reactor is its versatility in fuelling applications. Opportunity exists for evolutionary improvements in the CANDU fuel design that can produce large quantities of medical isotopes while maintaining its power production targets. The ability to refuel online while maintaining a good thermal neutron economy in the core makes CANDU reactors a strong candidate for producing significant quantities of Mo-99 to meet the global demand of medical isotopes. On-power fuelling of the CANDU reactors allows the gradual introduction of new fuel bundle designs intended for Mo-99 production.

The objective of this thesis is the development of new 37-element fuel bundles that, when irradiated in a standard CANDU reactor, are able to produce significant quantities of Mo-99, and which have neutronic and thermalhydraulic properties nearly identical to those of the standard CANDU fuel bundle. This objective translates into six design requirements:

1. The bundle shall use LEU fuel of less than 20% U-235 enrichment by

weight and produce Mo-99 in sufficient concentrations to be extracted

using chemical processes currently in use.

Page | 41

2. The hydraulic resistance of the Mo-99-producing bundle shall be identical

to that of a standard CANDU fuel bundle.

3. The bundle shall be dimensionally compatible with the fuel channel

components and with the appropriate fuel handling components.

4. The reactivity of the Mo-99-producing bundle shall be close to that of a

standard CANDU fuel bundle. A reactivity change of ±1 mk of standard

CANDU is deemed acceptable.

5. The power generation rate in the Mo-99-producing bundle shall be similar

to that of the standard CANDU fuel bundle when placed in the same

position in the core.

6. The bundle shall demonstrate that the operating and safety margins

regarding fuel sheath dryout power and fuel centreline temperatures are

maintained with the use of the new bundles in the core.

3.2 Design Plan and Strategy

The plan is to consider various design options that utilize the standard

37-element fuel bundle geometry. The proposed designs for Mo-99 production range from a fuel bundle comprised of a combination of enriched and depleted UO2 concentric fuel layers in the outer rings and NU in the centre and inner rings, to a fuel bundle with mixed fuel pins (enriched + depleted uranium) in all four rings of the 37-element bundle

Page | 42 for maximum yield of Mo-99. Other design options include a fuel-bundle comprised of uranium metal fuel, which is utilized to achieve higher margins for fuel centreline melting (due to the metal’s higher thermal conductivity compared to the ceramic) and ease of manufacturing with respect to the proposed thickness of the enriched fuel region.

Five different design options are assessed in this study. Designs 1, 2 and 3 use mixed fuel targets (enriched + depleted) in Ring 4 and natural UO2 in the centre and inner rings. Designs 4 and 5 use mixed fuel targets in all rings. Design 3 and 5 use uranium metal fuel in the target pins as a test for improved safety margins with respect to fuel centreline temperatures. A pictorial representation of the various designs options that are considered in this study is shown in Figure 3-1.

As discussed in Chapter 2, nuclear proliferation concerns have limited the enrichment in target bundles to 20 wt% of U-235. Due to the fact the ratio of Mo-99 yield to the total fuel volume processed is low for NU, from the perspective of maximizing the yields of Mo-99, use of higher enrichment is advantageous. Hence, use of 19.5 wt% of

U-235 enrichment, which is just below the HEU category, is recommended for this study.

The depleted uranium region is assumed to have 0.20% of U-235 by weight.

Depleted uranium is a by-product of the uranium enrichment process. Different fuel enrichment facilities may have different end-cycle enrichment of uranium tails. Because the enrichment of most uranium tails is typically less than 0.3% [42], 0.2 % is an easily achievable value to be used as depleted uranium fuel in the proposed designs.

Page | 43

19.5% Enriched 19.5% Enriched Natural UO2 Natural UO2 UO2 UO2

0.2% Depleted 0.2% Depleted UO2 UO2

0.2% Depleted 19.5% Enriched 19.5% Enriched U-Metal U-Metal UO2

Natural UO2 0.2% Depleted UO2

19.5% Enriched

U-Metal

0.2% Depleted U-Metal

Figure 3-1: A Pictorial Representation of the Proposed Designs Assessed for

Molybdenum-99 Production10

10 The base image of the 37-elment bundle is adapted from Reference [43]

Page | 44

3.2.1 Satisfying Design Requirements

In this section, the methodology that is adopted to satisfy the design requirements listed in Section 3.1 is presented in detail.

Requirements 2 and 3:

The new fuel bundle design is based on the standard 37-element CANDU fuel bundle. The bundle geometry is kept dimensionally identical to the standard CANDU bundle. This allows the new design to have the same hydraulic resistance as the reference bundle and, hence, be compatible with fuel channel components and the appropriate fuel handling components in order to allow online refuelling.

Requirements 2 and 3 are thus satisfied.

Requirement 4:

Fuel pins in some (or all, depending on the specific design) rings are divided into two concentric regions, one consisting of enriched uranium fuel and another consisting of depleted uranium fuel. The relative dimension and position of the enriched-fuel and depleted-fuel regions are determined from the condition that the bundle has a fresh fuel infinite-lattice k-infinity (kinf) value that is similar to the standard CANDU fuel lattice along with the condition on the fuel heating and centreline temperature limits. The cell fresh fuel kinf is determined by the DRAGON code for the specified infinite lattice model geometry. The kinf value needs to be as close as possible to the reference CANDU bundle to allow for existing operational practices and bundle safety characteristics to be maintained.

Page | 45

In order to meet the bundle reactivity criterion (Requirement 4), Task 1 has been created and addressed further in Section 4.1.

Task 1

Calculate the thickness (or radius) of enriched fuel region for the various

design options considered which yields a fresh fuel infinite-lattice kinf

value that is similar to that of the reference CANDU bundle. For this

study, a difference in reactivity (Δρ) value of ±1 mk compared to the

reference CANDU bundle is considered acceptable.

Requirement 5:

Requirement 5 is implicit in the sense that a bundle with the same kinf as the standard CANDU bundle and with identical overall bundle geometry will have average two-group cross-sections similar to the standard CANDU bundle resulting in similar power generation rates. Hence, Requirement 5 is also met by satisfying Requirements 2 and 4.

Page | 46

Requirement 6:

Fuel sheath dryout and fuel centreline temperatures are two phenomena that serve as indicators of the onset of a heat transfer crisis and deteriorating bundle safety characteristics. Heat generated in the fuel volume must be transported out through the fuel surface.

The linear power rating represents the power produced per unit length (W/m) of a fuel element. The linear heat rating of the element primarily dictates the sheath temperature rise in case of a dryout. The heat flux is defined as the heat transferred per unit surface area (W/m2). Generating excessive power from a bundle causes sheath temperature to rise and bundle critical heat flux (CHF) and fuel centreline melting margins to diminish. The CHF characteristics of a bundle are functions of bundle radial flux distribution from ring-to-ring, bearing pad height, channel creep profile, fuel string axial flux distribution. Other design features (such as end cap, end plate, etc.) also affect

CHF characteristics of a bundle.

Designs 1, 2 and 4 have the same fuel pellet and sheath diameters as the reference

CANDU bundle. This ensures the ability of the bundle to maintain the same hydrodynamic properties as the reference CANDU bundle. For a bundle that is dimensionally identical to the reference bundle with similar power generation rates, its available margins to CHF can be determined by making a comparison of the linear power ratings of the highest-power pins in both bundles.

Page | 47

Designs 3 and 5, which use uranium metal as fuel, have the same pin diameter, but a smaller fuel pellet diameter. The increase in parasitic absorption due to the thicker cladding is balanced by increasing the thickness of the enriched layer as part of the activities performed under Task 1. Similar assertions regarding the CHF margins can be made for Designs 3 and 5.

The second important safety parameter is fuel centreline temperature, which must not exceed the values specified for the standard CANDU bundle for the same bundle heat generation rates. The new fuel bundles will have non-homogenous fuel composition containing concentric fuel regions inside Mo-99 target pins. Hence, meeting the linear heat rating limits alone will not ensure adequate margins to the fuel centreline melting.

The outermost ring (Ring 4) of the 37-element fuel bundle generally has the highest linear heat rating value due to its proximity to the moderator and therefore to the highest flux of thermalized neutrons. This is especially true if the outermost ring contains a region of enriched fuel as is the case in the proposed designs (see Figure 3-1).

The enriched fuel region, due to its increased rate of fission and consequently higher power density, creates the possibility of having a higher than reference centreline temperature in the fuel.

To satisfy Requirement 6 regarding bundle safety characteristics, Task 2 and

Task 3 are created and addressed further in Sections 4.2 and 4.3.

Page | 48

Task 2

The modified bundle designs need to comply with the existing linear heat rating, bundle power and channel power limits prescribed for standard

CANDU fuel. Specifically, the new designs must maintain a maximum linear heat rating of less than 60 kW/m [44]. Ideally, the bundle must have a ring power distribution that is similar to the existing bundles.

Task 3

Produce a radial temperature profile of the fuel pin with the highest linear heat rating and compare it with the radial temperature profile of the reference fuel pin of the same ring to ensure that adequate margins to fuel centreline melting are maintained. The melting points of UO2

(2860 °C) and U-metal (1132 °C) are used as constraints here.

Page | 49

Requirement 1:

The enrichment of the enriched-fuel region is fixed at 19.5 wt% of U-235 which is sufficiently high to allow Mo-99 extraction by existing processes while being slightly below the 20 wt% limit for low-enriched fuel. According to an IAEA report [45], fuel reprocessing technologies exist for both LEU metal and UO2 targets for Mo-99 production. Beside some modification needed to accommodate the larger masses of LEU target material, the rest of the chemical processing involved for the production of Mo-99 using LEU targets is very similar to the present process for producing Mo-99 using HEU.

The expert committee report by the US National Academy of Sciences also concluded that the there are no technical barriers to producing large quantities of Mo-99 from LEU targets [8].

For the modified fuel bundles proposed in this thesis, the Mo-99 producing fuel pins are expected to be chemically processed using the modified acid dissolution technique. After irradiation, the enriched fuel pellets are removed from the cladding and processed for Mo-99 extraction. The mass and activity of Mo-99 that is expected to be produced in these pins can be calculated from the output of the DRAGON code. The code output is obtained for each specified lattice sub-region of the modified fuel bundle geometrical model. The mass and activity of Mo-99 produced is also explored as part of this thesis in Section 4.4. The expected yield of Mo-99 in six-day Curies is calculated for each new bundle design.

Page | 50

3.3 Reactor Operating Conditions and Assumptions

The modified fuel bundles with different geometrical arrangements of 19.5 wt% enriched, 0.2 wt% depleted and 0.71 wt% uranium fuels in different fuel rings are subject to the same conditions and power limits as the existing fuel bundles in an operating CANDU core. The new fuel bundle is designed to withstand irradiation in the highest power channel of the 380-channel CANDU-6 reactor with a total thermal power of approximately 2x109 Wth. A bundle power of 900 kW is used as the upper limit for a typical CANDU fuel assembly in order to meet the existing channel power limits. The maximum licensed bundle power limit for a CANDU-6 fuel-channel using 37-element fuel bundle is 935 kW. This corresponds to a linear power rating in the hottest (outermost) fuel element of approximately 60 kW/m.

Therefore, for all new designs considered, the lattice cell bundle power at

100% FP is assumed to correspond to the maximum instantaneous power of 900 kW.

The reference CANDU-6 fuel bundle contains 19.85 kg of uranium fuel. Hence, the corresponding bundle specific power is 45.34 W/g (900 kW/19.85 kg per bundle). In order to assess the safety margins of the proposed designs, the pin powers and linear ratings are scaled according to the maximum operating CANDU-6 bundle specific power.

The bundle designs are analyzed using the reactor physics code DRAGON version 3.05 ([32], [33], [34]). Transport calculations are performed using the collision probability method as implemented in the DRAGON code. The model used for this study is a single-cell infinite lattice with reflective boundaries on all sides. The effects of reactivity devices are ignored in the single-cell DRAGON model.

Page | 51

The heat generated by the bundle is conducted through the fuel rod and convected by the surrounding coolant in the fuel channel. In the current study, the fuel temperature is calculated for the fuel pin with the highest linear heat rating at various points along the radius of the pin, including the centre. The fuel temperature profile of a 4th ring pin is calculated using a numerical integration method (see Section 3.4.2) for each design and compared to the fuel melting limits.

The numerical integration method assumes a radial conduction model for a slice of fuel element based on steady-state conditions where the fuel element geometry, thermal properties, and physical characteristics are known. Axial conduction is assumed negligible and thermal conductivity of the cladding material is assumed constant.

The melting points of UO2 (2860 °C) and U-metal (1132 °C) are used as the maximum allowable fuel centreline temperatures. Steady-state cooling flow conditions are assumed in the fuel channel resulting in a constant bulk coolant temperature.

Temperature of the coolant is assumed to be 276 °C, which is 10 °C higher than the average CANDU-6 inlet temperature [46], added for conservatism in the analysis. The difference in the proposed and reference CANDU temperature profiles and the available margins to fuel melting limits provide high confidence in the adopted designs.

3.3.1 Reactor Fuelling Considerations

The use of modified fuel bundles for the production of Mo-99 will have an impact on the regular refuelling cycles at CANDU stations. As previously explained, irradiation times of about 15 to 20 days are sufficient to achieve maximum possible activity of

Page | 52

Mo-99. A burnup of 906.62 MWD/T, which corresponds to 20 days of irradiation at the specific power of 45.33 kW/kg is used in this study.

The burnup time required to reach the maximum activity levels of Mo-99 is much shorter than the normal time a regular fuel bundle spends inside the reactor (8 to 12 months depending on the location of the bundle in the core). As a consequence of the shorter irradiation period, a fuelling machine visit is needed after the peak production rate for Mo-99 is reached. To achieve steady production levels of Mo-99, two or more modified fuel bundles can be loaded together at a time. By staggering the production in multiple channels, a steady amount of Mo-99 producing bundles can be removed each day to provide a constant yield.

Researchers from McMaster University have studied the impact of shorter irradiation cycles for Mo-99 producing bundles on the standard fuelling operations [22].

This involved changing the total number of fuelling machine visits that may be required in order to produce significant yields of Mo-99. The study simulated two different fuelling scenarios consisting of 3 to 6 fuel channels containing 2 to 6 Mo-99 target bundles in a staggered manner. The study concluded that with an additional 6 to 8 fuelling operations per week, a production level of 4 bundles per week is attainable [22].

Due to the unique flexibility of fuelling arrangement in CANDU reactors, a yield of higher than 4 bundles per week is also possible. For the new designs proposed in this study, the consequent changes in the existing fuelling schemes are not studied as no difficulties are foreseen. The number of bundles to be extracted per week is assumed to

Page | 53 be a function of Mo-99 yield per bundle and the underlying commercial and medical isotope market considerations.

Once an approximate activity of Mo-99 per bundle is known, a detailed calculation based on the instantaneous channel parameters can be performed at various stages in the fuelling cycle. The bundle fuelling scheme can then be optimized to determine the most favourable irradiation times for each stage and bundle position for the Mo-99 production bundles. Using multiple channels in a staggered manner would ensure a yield of multiple bundles for a constant output of Mo-99 required for the target medical isotopes market.

3.4 Design Options and Methodology

To develop a new 37-element fuel bundle aimed at producing large quantities of

Mo-99, five different design options are assessed. They include:

Page | 54

Design 1

19.5 wt% enriched UO2 fuel in the centre of the 4th ring fuel elements encapsulated by 0.2 wt% depleted UO2 fuel. Fuel elements in the centre and inner rings contain natural UO2.

Design 2

0.2 wt% depleted UO2 fuel in the centre of the 4th ring fuel elements encapsulated by 19.5 wt% enriched UO2 fuel. Fuel elements in the centre and inner rings contain natural UO2.

Design 3 0.2 wt% depleted U-metal fuel in the centre of the 4th ring fuel elements encapsulated by 19.5 wt% enriched U-metal fuel. Fuel elements in the centre and inner rings contain natural UO2.

Design 4

0.2 wt% depleted UO2 fuel in the centre of the fuel elements encapsulated by 19.5 wt% enriched UO2 fuel in all four rings.

Design 5 0.2 wt% depleted U-metal fuel in the centre of the fuel elements encapsulated by 19.5 wt% enriched U-metal fuel in all four rings.

Page | 55

A unit lattice cell is analyzed using the DRAGON neutron-transport code. The cell is initially divided into 37 homogenous regions to represent different parts of the fuel bundle including the four fuel rings, cladding, annulus gas, pressure tube and coolant.

Depending on the design, the regions are further split into sub-regions for accuracy and higher resolution. For example, in Design 2 which contains an enriched uranium fuel region encapsulated by depleted uranium fuel in the 4th ring and NU in other rings (see

Figure 3-1), the depleted and enriched fuel regions in the fuel pellet are further split into

10 and 3 sub-regions, respectively. In the remaining rings, a total of 4 sub-regions are used to simulate the NU fuel pellet. Figure 3-2 illustrates the 46 (37 +9 additional splitting) lattice sub-regions of the DRAGON geometrical model that is used to represent the 37-element fuel bundle.

The multigroup transport equation is solved using the DRAGON code and the

69-group IAEA WIMS-D Library Update (WLUP) [34] for a single-cell lattice model to find the neutron flux and cross-sections in each of these sub-regions integrated over all energy groups. The fresh fuel kinf values are recorded for each case for assessment.

Data on lattice specifications for a 37-element CANDU fuel bundle is provided in

Appendix B.

Page | 56

Figure 3-2 37-Element CANDU Fuel Bundle and the Infinite Lattice Cell

Representation of Design 211

3.4.1 Method for Calculating the Linear Heat Rating

For the purpose of establishing the bounding linear heat rating for fuel pins of the proposed bundles for Mo-99 production, this study assumes that a fresh target bundle will be loaded in the middle of the highest power fuel channel facing a high thermal- neutron flux and irradiated there for the duration of the irradiation period. In other words, the position of the fuel bundle is assumed to be in position 6 or 7 out of a total of

12 fuel bundles in each CANDU fuel channel. This is a rather conservative case considering the bundle would initially be loaded anywhere between position 1 to 12

11 The 37-element fuel bundle image is reproduced from the CANTEACH website [31]

Page | 57 depending on the fuelling scheme adopted, and hence could initially have a lower power rating.

The maximum instantaneous bundle power located in the centre of the CANDU core is 900 kWth. The pin power ratings are scaled according to the reference CANDU-6 bundle specific power as listed in Section 3.3. The procedure used to evaluate the linear heat rating is provided within this section.

First, the density of uranium dv, U is computed, followed by the calculation of the total linear density dL, U of the initial heavy elements in the fuel.

d A d  v,UO2 U (3.1) v,U A UO2

regions

dL,U  dv,U V2Di (3.2) i1

where dv, UO2 is the density of natural uranium oxide fuel, AU is atomic mass of natural uranium, AUO2 is atomic mass of uranium oxide, and V2-Di is the 2-D volume (cm2) of each fuel region in the lattice cell.

The normalized linear heat rating QL’ for a fuel bundle is then given by

' QL  d L,U Pbundle (3.3)

where Pbundle is the normalized bundle specific power which is equal to 45.34 W/g

(based on 900 kW maximum bundle power), used for scaling with the reference

CANDU-6 bundle.

Page | 58

The unnormalized linear heat rating qi,u’ for each fuel region ‘i’ is given by:

' qeViuifiiD,,2 ˆ  (3.4)

where ei is the energy produced per fission, Σf,i is the macroscopic fission cross- section at burnup, and ˆ is the condensed neutron energy group volume-integrated flux at each region at burnup.

The total unnormalized linear heat rating QL,u’ for the entire fuel bundle is therefore:

regions ' ' QL,u   qi,u (3.5) i1

The normalized linear heat power and the unnormalized linear heat rating for a region within a fuel element are related by the following formula:

 '  ' QL ' Q i    q i,u (3.6)  '   QL,u 

In DRAGON, the multiple sub-regions (or splits) within one fuel type (enriched, depleted, or natural) can be merged to provide cross-sections and fluxes for each fuel type using volume averaging. The bundle length is also constant.

The linear power rating is important for fuel pins, but not for sub-regions inside each fuel pin. Therefore, once the linear power in each fuel type within one fuel element is known, the overall linear power for a fuel element composed of different fuel regions

(enriched + depleted) is the summation of two linear powers.

Page | 59

Finally, since there are N pins,r pins associated with a ring, the average pin heat

' rating, Qr , in ring ‘r’ can be computed by the following formula:

' ' ' Q enriched fuelregion  Q depleted fuelregion Qr  (3.7) N pins,r

3.4.2 Method for Calculating the Radial Temperature Profile

The heat generated in a fuel pin directly affects the fuel centreline temperature and the temperature profile going from the fuel centre to the fuel surface. The fuel centreline temperature and the temperature gradient are functions of thermal conduction within the fuel pellet, heat transfer through the diametral fuel-sheath gap, and conduction through the sheath, coolant temperature and sheath-to-coolant heat transfer coefficient.

The primary heat transfer mechanisms within the diametral gap are conduction through the fill gas and solid-to-solid contact conduction (fuel and sheath are in contact).

For the purpose of this work, the fuel pellet is assumed to remain in contact with the cladding making the thickness of the gap between the fuel pellet and the cladding equal to zero. This is a reasonable assumption considering that the Mo-99 producing fuel bundles will use collapsible sheaths and are expected to be irradiated for a maximum of

20 days, which is not long enough for a gap to develop.

As part of the new fuel bundle development for Mo-99 production, a radial fuel temperature profile of the 4th ring element of the proposed fuel bundles is produced and compared against the fuel melting limits. The enriched fuel region in the fuel pellets adds

Page | 60 to the possibility of having higher centreline temperatures in the pin due to the increased rate of fission and consequently higher power density in the region. Due to its proximity to a large number of thermalized neutrons, the elements of the 4th ring present the most conservative estimate for centreline calculations.

For the current study, the fuel centreline temperature is calculated using a numerical integration method described below.

Numerical Integration Method

For any new fuel design, the interface between the fuel and the coolant is centrally important to the design of the reactor because it limits the power output. The heat transfer coefficient (hc) of the coolant is dependent on the fluid properties and flow conditions. For liquid-to-wall heat transfer, the coefficient can be estimated by the use of certain dimensionless fluid mechanic numbers:

 Reynolds number

 Prandtl number

 Nusselt number

The Reynolds number is a measure of the relationship between the inertial and viscous effects of the moving fluid and can be defined as [47]:

VD Re  h  (3.8)

Page | 61

where ρ is density of the fluid, V is average fluid velocity, Dh is hydraulic radius of the flow path, and μ is dynamic viscosity of the fluid.

4A D  flow h P wet (3.9)

where Aflow is the coolant flow area through the fuel bundle, and Pwet is the wetted parameter.

The Prandtl number is a measure of the fluid thermal properties and can be defined as:

c  Pr p k (3.10)

where cp is specific heat of the fluid, μ is dynamic viscosity of the fluid, and k is thermal conductivity of the fluid. Some software such as NIST REFPROP can also provide

Prandtl number and other useful thermophysical properties of fluids at the specified fluid state.

For the specific case of convective heat transfer inside a tube, the Nusselt number is an empirical formula that is defined as:

0.8 0.4 Nu 0.023Re Pr (3.11)

where Re is Reynolds number, and Pr is Prandtl number. The relationship between the Nusselt number and the heat transfer coefficient h can be defined as [48]:

Page | 62

hD Nu  h k (3.12)

For a solid, the general thermal energy balance equation of an arbitrary volume can be expressed as:

e dV  Q'''(r,t)dV  Q''(r,t)nˆ ds (3.13)  t  

[stored] [generated] [transferred]

where ρ is the material density, e is the internal energy, V is the volume, S is the surface area, Q''' is the volumetric heat generation, Q'' is the heat flux, and nˆ  is the unit vector on the surface. The internal energy can be replaced with temperature T times the heat capacity c. Using Gauss law, the heat balance equation can be transformed into:

 Q'' Q''nˆ  ds (3.14) V S

(cT )  Q'''(r,t)   Q''(r,t) (3.15) t

Using Fourier law: Q''(r,t)  k T(r,t) , the equation governing the fuel temperature distribution can be derived.

(cT )  Q'''(r,t)    kT(r,t) (3.16) t

Page | 63

In order to calculate the fuel centreline temperature, steady-state one- dimensional heat transfer with volumetric heat source and variation of thermal conductivity with temperature is assumed.

Q'''(r,t)   k f T(r,t) (3.17)

1 ddT (())'''()kTrQrf   (3.18) rdrdr

dT dkTrQrrdr(())'''()   (3.19) f dr

Integrating both sides from the centreline to an arbitrary radius r:

dT r k( T ) r    Q '''( )  d  f dr  0 (3.20)

Since

r Q'(r) Q'''()d   2 0 (3.21)

Therefore,

dTQ r '( ) kTrf ()   dr 2 (3.22)

Qr'( ) kf () T dT dr 2r (3.23)

Page | 64

Integrating both sides again from an arbitrary radius r to the radius of the fuel pin rf:

r Ts 1'()f Q  kTdTd()   f 2 Tr (3.24)

or, equivalently:

r T 1'()f Q  kTdTd()   f 2 Trs (3.25)

100 6400 16.35 where, k f (T)  2  5 / 2 exp   (3.26) 7.5408 17.692  3.6142    

where  = T/1000, T is in Kelvin, and kf is thermal conductivity for 95% dense

UO2 in W/m∙K. The above expression for thermal conductivity is taken from the IAEA materials database [49]. The expression is plotted in Figure 3-3.

5.5 K) ∙ 5.0 4.5 4.0 3.5 3.0 2.5 2.0 Thermal Conductivity (W/m ThermalConductivity 400 600 800 1000 1200 1400 1600 1800 Temperature (K)

Figure 3-3: A Plot of UO2 Thermal Conductivity Showing Variation Due to

Temperature

Page | 65

Since the temperature dependence of thermal conductivity kf(T) is known, the left-hand side of Eq. (3.25) is a function, which can be calculated using the trapezoidal rule to approximate the integral and equate with the right-hand side. Therefore, the equation can be re-written as:

T FTTkTdT(,)()  sf Ts (3.27)

Or, equivalently:

r 1'()f Q  FTTd(,)   s 2 r (3.28)

The solution of Eq. (3.28) gives the temperature T as a function of radius r corresponding to different points on the pin. If the radius r is taken to be zero

(integration from the centreline to the outer radius of the pin), then:

r TcL 1'()f Q  kTdTd()   f 2 Ts 0 (3.29)

Or, equivalently:

r 1f Q '( ) F(,) T T d cL s 2 0 (3.30)

It is to be noted that the integrand in the right-hand side of Eq. (3.30) vanishes as the radius approaches zero. In mathematical form:

Page | 66

dQ '() Q'() d limlimlim 2'''()0 Q 0L'Hopital's Rule00 d d (3.31)

For a fuel pin that is divided into n annular regions of radii ri, the temperature at boundaries between annuli will be denoted by T(ri)=Ti, where rn=rf and r0=0, and for temperatures, T0=TcL and Tn=Ts. Each annulus will have the same index ‘i’ as its outer radius.

In what follows, discrete forms of Eq. (3.21), Eq. (3.27) and Eq. (3.28) are presented. The discrete forms of each equation are obtained by approximating the integral in the respective equation. Because DRAGON, provides the average heat generation rate for each annulus, Eq. (3.21) is approximated as:

22 i rr  jj1  Qr'()i Qi '''  (3.32) j1 22

It can be observed that the above approximation provides the values of the linear heat generation rate at the boundaries between annuli, which is at radii ri. To discretize

Eq. (3.27), kf(T) is assumed to be tabulated at discrete values Tk. using Eq. (3.26), and with T0=Ts. Using the trapezoidal rule to approximate the integral, Eq. (3.27) becomes:

k kf()() T j k f T j1 FTTTT(,)k s  j j1  (3.33) j1 2

For temperatures between the tabulation points Tk-1 and Tk, the function F can be interpolated linearly as:

Page | 67

F(,)(,) TTFksks TT 1 F(,)(,) TTFsksk TTTT 11  (3.34) TTkk 1

Because the values of the linear heat generation rate Q’ is calculated (according to Eq. (3.32)) at radii ri, the integral in Eq. (3.28) can be approximated using the trapezoidal rule:

n 1 QrQr'()'()jj1 rrjj 1  FTT(,)is  (3.35) 22 ji1 rrjj1

From a practical perspective, Eq. (3.35) is solved by finding the interval (Tk-1, Tk) such that:

n 1 Q'( rjj ) Q '( r 1 ) rrjj 1  FTTFTT(,)(,)k1 s    k s (3.36) 22 ji1 rrjj1

And then solving:

n rr F( Tk , TF sks )(, T ) T1 1 Q'( rQjj )'() r 1  jj1  F(, Tksik11 ) TT T     (3.37) Tkkjj Trr1122 ji1 

The fuel sheath (cladding) is exposed to constant heat flux. For the purpose of this study, it is assumed that no gap exists between the fuel and cladding. Also since

Q’’’clad =0, heat conduction in the clad then becomes:

1 d dT (kc  r  )  0 r dr dr (3.38)

Page | 68

n Qi ' i1 rF  tc kc  Tclad  kc (Tc Ts )   ln( ) (3.39) 2 rF

Heat transfer from the clad to coolant can be represented by Newton’s law of cooling (by convection).

n Qi '' hs (Ts  TB ) (3.40) i1

n n n 2 Qi '' Qi '''ri Qi ' i1 i1 i1 TCool  (Ts TB )    (3.41) hs hs 2(rG  tc ) hs 2(rG  tc )

The phenomenon is dominated by the presence of a thin surface layer. The temperature drop is assumed to occur over this thin layer and the bulk of the coolant is assumed to have a constant temperature of 549 K.

3.4.3 Method for Calculating the Mass and Activity of Molybdenum-99

Produced

The IAEA-WLUP library [34] does not include fission yield data for Mo-99 and, as a consequence, DRAGON cannot explicitly calculate the atomic density (or mass) of

Mo-99 produced from fission. Hence, the mass and activity of Mo-99 must be calculated based on the total fission rates calculated by DRAGON. The following methodology is used for calculating the mass and activity of Mo-99 produced.

Rate of change = Rate produced – Decay rate

Page | 69

dN  f  cˆ V  N (3.42) dt Mo99 f enriched,U 235

where N is the number of Mo-99 atoms produced as a fission product, f Mo99 is

-1 the Mo-99 fission yield,  f is the macroscopic fission cross-section at burnup (cm ), c is the DRAGON scaling multiplier, ˆ is the condensed neutron volume integrated flux in

the enriched region at burnup (n·cm/s), and Venriched,U 235 is the volume of the enriched

U-235 region in the bundle (cm3). Furthermore, the activation of Mo-99 by capturing a neutron can be neglected here due to a small cross-section value of this reaction (σabs =

2.65 barns).

Let Rprod  f Mo99  f cˆ Venriched,U 235 (3.43)

The equation then becomes:

dN  R  N (3.44) dt prod

dN  Rproddt  Ndt (3.45)

dN  Ndt  Rproddt (3.46)

Multiply both sides by eλt

t t t e dN  e Ndt  e Rproddt (3.47)

t t d(Ne )  Rprode dt (3.48)

Page | 70

Integrate both sides with-respect-to time

t t d(Net )  R et dt (3.49)   prod 0 0

The neutrons in the fuel region are not mono-energetic. There exists a spectrum of neutron energy distribution. However, an energy condensed volume integrated neutron flux is assumed here. As well, the corresponding average macroscopic cross- sections are used. Hence the rate of production in this case is a constant, and Eq. (3.49) then becomes:

t t d(Ne t )  R et dt (3.50)  prod  0 0

R R Ne t  N  prod et  prod (3.51) 0  

Multiply both sides by e-λt

R R N(t)  prod  prod et  N et (3.52)   0

N0 is the initial number of Mo-99 items at t=0, which is equal to zero.

R N(t)  prod 1et  (3.53) 

Or, equivalently:

t N(t)  (t)  Rprod 1e  (3.54)

Page | 71

t (t)  f Mo99  f cˆ Venriched,U 2351e  (Bq) (3.55)

where, (t) is activity at irradiation time t. The mass of Mo-99 produced then becomes:

R A m(t)  prod 1et . Mo99 (3.56)  6.023x1023

f Mo99  f cˆ Venriched,U 235 A m(t)  1et . Mo99 (grams) (3.57)  6.023x1023

where m(t) is the mass of Mo-99 produced due at irradiation time t, and AMo99 is the atomic weight of Mo-99.

Eq. (3.56) and Eq. (3.57) above calculate the end-of-bombardment (EOB) activity and mass of Mo-99 in fission products. The processing efficiency for Mo-99 is about 90% and takes approximately one day, resulting in a post processing total that is equivalent to 70.65% of the EOB value. The six-day Curies value is then computed as:

t (t)  f Mo99  f cˆ Venriched,U 2351e  p decay (Bq) (3.58)

 ˆ  f Mo99  f c Venriched,U 235 t AMo99 m(t)   1e . 23   p decay (grams) (3.59)   6.023x10 

Where  p is the post processing efficient of 70.65%, and decay is computed using:

N(6days) (6days)  decay   e  0.22 (3.60) N0

Page | 72

Chapter 4

Assessment Results and Discussion

This chapter provides the results obtained from the DRAGON lattice code along with the calculations of the linear heat ratings and fuel centreline temperatures for the proposed designs.

As mentioned before, five different design options are assessed in this study.

Information on these proposed variations of the standard 37-element CANDU bundle designs for Mo-99 production are provided in Sections 3.2 and 3.4. For each design, the fuel pellets in the target rings are made up of two-regions, a region of enriched fuel surrounded by a region of depleted uranium (or vice versa). Enrichment of 19.5 wt%

U-235, which is less than the threshold of HEU, was used in the modified designs. The depleted uranium was assumed to have 0.20 wt% U-235 enrichment.

A single cell infinite lattice assembly was modelled using reactor physics code

DRAGON version 3.05. The DRAGON model considers a fresh fuel bundle at the start and irradiates it for 20 days corresponding to a burnup of 906.62 MWD/T. This burn is sufficient to reach the maximum activity of Mo-99 in the target fuel.

The Mo-99 production bundles are designed to meet the same safety and design constraints as the standard 37-element CANDU fuel with respect to reactor neutronics and heat generation in the fuel elements. The standard CANDU bundle with NU fuel is used as a benchmark for new designs. The reference bundle assessment results are provided in Tables 4-1 through 4-3 and Figures 4-1 and 4-2.

Page | 73

The DRAGON calculated fresh fuel kinf for the reference CANDU unitcell with NU fuel bundle and heavy water coolant is found to be 1.1228. The kinf is greater than 1 since the effects of adjuster rods and reactivity devices are not modelled in the DRAGON unitcell lattice model. The reactivity devices absorb neutrons and result in the kinf being closer to 1.

Table 4-1: Reference CANDU 37-Element Bundle Data Structures for Radial

Pin Power Profile Calculations

Normalized Macroscopic Integrated 2-D Unnormalized Linear Linear Fission Cross- Volume, Linear Power Density, Region Flux, ˆ Power Section, Σf V2-D Rating, qi.u dL, U Rating , Q' (cm-1) (n·cm/s) (cm2) (kW/cm) (g/cm) r (kW/m) Ring 1 0.02236 0.3682 1.159 2.696E-16 10.83 37.68 Ring 2 0.02330 2.224 6.957 1.697E-15 65.00 39.53 Ring 3 0.02595 4.534 13.91 3.852E-15 130.0 44.87 Ring 4 0.03091 7.018 20.87 7.181E-15 195.0 55.76

60 Reference CANDU Fuel Bundle 55

50

45

40

35

30

LINEAR HEAT RATING (KW/M) RATING LINEAR HEAT 1 2 3 4

FUEL BUNDLE RINGS

Figure 4-1: Radial Pin Power Profile for Reference CANDU 37-Element Bundle

Page | 74

Table 4-2: Reference CANDU 37-Element Bundle Normalized Heat Density and

Linear Power Rating in Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt%) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Ring4-Disk1 0.7110 0.03757 0.03757 468.5 2.077 Ring4-Disk2 0.7110 0.03757 0.07513 469.6 8.324 Ring4-Disk3 0.7110 0.03757 0.1127 469.7 18.73 Ring4-Disk4 0.7110 0.04948 0.1622 469.9 38.81 Ring4-Disk5 0.7110 0.04948 0.2117 470.9 66.18 Ring4-Disk6 0.7110 0.04938 0.2611 472.1 100.8 Ring4-Disk7 0.7110 0.04938 0.3106 473.5 142.9 Ring4-Disk8 0.7110 0.04948 0.3601 475.4 192.5 Ring4-Disk9 0.7110 0.04938 0.4096 477.6 249.6 Ring4-Disk10 0.7110 0.04938 0.4591 480.4 314.5 Ring4-Disk11 0.7110 0.04948 0.5085 483.7 387.3 Ring4-Disk12 0.7110 0.04938 0.5580 487.8 468.2 Ring4-Disk13 0.7110 0.04948 0.6075 493.5 557.6

Page | 75

Table 4-3: Reference CANDU 37-Element Bundle Numerical Integration

Results Using IAEA and Constant Thermal Conductivity for UO2

Temperature using Temperature using Node IAEA Thermal Constant Thermal Conductivity (°C) Conductivity (°C) Fuel Centreline 1919 2197 Node1 (Ring4) 1911 2190 Node2 (Ring4) 1887 2170 Node3 (Ring4) 1847 2135 Node4 (Ring4) 1770 2069 Node5 (Ring4) 1665 1978 Node6 (Ring4) 1533 1863 Node7 (Ring4) 1380 1724 Node8 (Ring4) 1211 1561 Node9 (Ring4) 1036 1373 Node10 (Ring4) 860.9 1161 Node11 (Ring4) 689.9 924.0 Node12 (Ring4) 526.6 661.4 Node13 (Ring4) 373.2 373.2 Node14 (Sheath) 309.7 309.7 Node15 (Coolant) 275.8 275.8

Page | 76

3000 UO2 Melting Point

2500 IAEA Thermal Conductivity (Eq. 3.26) Constant Thermal Conductivity 2000

(0.024 W/cm-K) C) ° 1500

1000 Temperature Temperature ( 500

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-2: Reference CANDU 37-Element Bundle Radial Temperature Profile of Ring 4 Pin Using IAEA and Constant Thermal Conductivity for UO2

Page | 77

4.1 Task 1 - Comparison of Infinite Multiplicative Constants

Using an infinite lattice cell model, the fresh fuel kinf value of the new designs is used to evaluate the viability of the design with respect to the reference CANDU kinf value.

The goal is to change the amount of 19.5 wt% U-235 enriched fuel used in the new designs while maintaining the overall fuel bundle geometry such that the overall bundle reactivity is compatible with the reference CANDU 37-element lattice.

For Designs 1, 2 and 3, the initial estimates of the thickness (or radius) of the enriched fuel region are made based upon a simple mass balance relation with-respect- to the mass of U-235 in new designs and the standard CANDU bundle, while ignoring bundle physics related parameters such as bundle geometry, neutron flux and parasitic absorptions. These estimations are provided in Appendix C.

The initial estimates are the starting point for inputting new fuel specifications in the unitcell lattice simulations. The initial estimates are later adjusted based on their deviation from the data collected using the reference CANDU lattice specifications.

Following the first few data points collection for new designs, the later data points are synthesized through linear interpolation.

Designs 4 and 5 are slight variations of Designs 2 and 3, respectively, where the initial concept of using mixed fuel (enriched + depleted) in Ring 4 elements are extended to all rings for maximum yields of Mo-99 per bundle. Hence, the initial estimates for the thickness of the enriched part was inferred from the parent designs (Design 2 or 3), and altered accordingly based on the DRAGON simulation results.

Page | 78

Due to the higher fuel density of uranium metal compared to ceramic UO2 fuel,

Designs 3 and 5 present a challenge for balancing the mass of fuel in the pins, and avoiding any resulting dissimilarity in bundle ring power distribution. The solution is to find an optimal cladding thickness that would preserve the compatibility of bundle reactivity with the existing CANDU bundle. The proposed thickness of the cladding

(2.27 mm) was calculated through mass balancing of both U-235 and U-238 in Design 3 and Design 5 fuel elements with the reference CANDU bundle.

The addition of enriched uranium in the Mo-99 target pins causes an increase in fission rate resulting in a higher reactivity in that specific region. To compensate for this increase reactivity, the remainder of the fuel pin is composed of depleted uranium.

Multiple cases with varying thickness (or radius) of the enriched region are simulated in DRAGON for each design until a thickness (or radius) is determined with Δρ value within the acceptable range (±1 mk). These cases are summarized in Tables 4-4 through 4-8 for each design. It is apparent from DRAGON results that the lattice reactivity is very sensitive to changes in the amount of enriched region for the fixed enrichment of 19.5 wt% U-235. Small changes in the amount of the enriched fuel produce relatively large increase in reactivity.

Figures 4-3 through 4-7 illustrate the unitcell eigenvalue (k-infinity) as a function of the thickness (or radius) of the enriched fuel region for the same overall fuel pin radius as the reference bundle and compared with the kinf of the CANDU lattice.

Page | 79

Design 1

Table 4-4: Design 1 Unitcell Lattice k-infinity for Variations in Radius of

Enriched Central Region

Radius of Enriched Fresh Fuel k- Case # Central Target ∆ρ (mk) infinity Region (mm) 1 1.00 1.0874 -29.0 2 1.10 1.1158 -5.64 3 1.20 1.1418 14.7 4* 1.14 1.1263 2.72 5* 1.127 1.1229 0.0301 * Value obtained through linear interpolation of data points

1.150

1.140

1.130

1.120

1.110

INFINITY 1.100

- K 1.090

1.080

1.070

1.060 1 mm 1.1 mm 1.2 mm 1.14 mm 1.127 mm

Design 1 Reference CANDU

Figure 4-3: Design 1 Unitcell Lattice k-infinity Versus Variations in Radius of

Enriched Central Target Region (Fuel Pin Radius 6.075 mm)

Page | 80

Design 2

Table 4-5: Design 2 Unitcell Lattice k-infinity for Variation in Thickness of

Enriched Annular Region

Thickness of Enriched Annular Fresh Fuel k- Case # ∆ρ (mk) Target Region infinity (mm) 1 0.0750 1.1067 -13.0 2 0.125 1.1961 54.5 3 0.0850 1.1267 3.07 4* 0.0830 1.1228 0.00793 * Value obtained through linear interpolation of data points

1.190

1.170

1.150

1.130

INFINITY

- K 1.110

1.090

1.070 0.075 mm 0.125 mm 0.085 mm 0.083 mm

Design 2 Reference CANDU

Figure 4-4: Design 2 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target Region (Fuel Pin Radius 6.075 mm)

Page | 81

Design 3

Table 4-6: Design 3 Unitcell Lattice k-infinity for Variation in Thickness of

Enriched Annular Region

Thickness of Enriched Fresh Fuel Case # ∆ρ (mk) Annular Target k-infinity Region (mm) 1 0.0660 1.1357 10.1 2 0.0560 1.1090 -11.1 3* 0.0610 1.1227 -0.108 * Value obtained through linear interpolation of data points

1.160 1.150 1.140 1.130 1.120

1.110

INFINITY - K 1.100 1.090 1.080 1.070 0.066 mm 0.056 mm 0.061 mm

Design 3 Reference CANDU

Figure 4-5: Design 3 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target Region (Fuel Pin Radius 4.266 mm)

Page | 82

Design 4

Table 4-7: Design 4 Unitcell Lattice k-infinity for Variation in Thickness of

Enriched Annular Region

Thickness of Enriched Fresh Fuel Case # ∆ρ (mk) Annular Target k-infinity Region (mm) 1 0.0830 1.1248 1.54 2 0.0820 1.1212 -1.29 3* 0.0825 1.1230 0.128 * Value obtained through linear interpolation of data points

1.150

1.140

1.130

1.120

INFINITY 1.110

- K 1.100

1.090

1.080 0.0830 mm 0.0820 mm 0.0825 mm

Design 4 Reference CANDU

Figure 4-6: Design 4 Unitcell Lattice k-infinity Versus Variations in Thickness of Enriched Annular Target Region (Fuel Pin Radius 6.075 mm)

Page | 83

Design 5

Table 4-8: Design 5 Unitcell Lattice k-infinity for Variation in Thickness of

Enriched Annular Region

Thickness of Enriched Fresh Fuel Case # ∆ρ (mk) Annular Region k-infinity (mm) 1 0.0610 1.1201 -2.15 2 0.0620 1.1246 1.37 3* 0.0616 1.1228 -0.0325 * Value obtained through linear interpolation of data points

1.150

1.140

1.130

1.120

INFINITY 1.110

- K 1.100

1.090

1.080 0.061 mm 0.062 mm 0.0616 mm

Design 5 Reference CANDU

Figure 4-7: Design 5 Unitcell Lattice k-infinity Versus Variations in

Thickness of Enriched Annular Target Region (Fuel Pin Radius 4.266 mm)

Page | 84

4.2 Task 2 - Comparison of Linear Heat Rating

The new designs must maintain a maximum power rating licensing limit of

60 kW/m to allow for existing operational practices to be maintained. Furthermore, to avoid dissimilar power peaking effects in the bundle, the new designs are intended to mimic the existing 37-element bundle radial pin power profile.

As mentioned in the previous section, in order to deal with the increased reactivity of the fuel pins containing enriched fuel region over NU fuel, the remaining fuel material in the pins is made up of depleted uranium. Once the thickness (or radius) of the enriched region in the pins for each design is selected in Task 1 whereby the total change in reactivity is within ±1mk with-respect-to the reference CANDU lattice, the designs with those particular thicknesses (or radii) are further investigated for evaluation and calculation of the element linear heat rating and fuel centreline temperatures.

Data structures for macroscopic fission cross-sections, condensed neutron volume integrated flux, and 2-D volume etc., for each fuel region are obtained from

DRAGON and processed for calculating the bundle radial pin power profile. The linear heat rating is calculated using the methodology described in Section 3.4.1. The DRAGON data structures for linear heat rating calculations are provided in Tables 4-9 through

4-13.

Figures 4-8 through 4-12 show the power profiles of the new designs versus the reference CANDU bundle located in the highest power channel in the core. The

Page | 85 corresponding bundle specific power is 45.34 W/g (based on 900 kW bundle power). All the pin powers and linear ratings are scaled to this specific power.

As expected, the power profile is lowest in the centre and higher in the outer rings due to the corresponding neutron flux at these locations. The radial pin power profiles of Mo-99 target bundles are also very similar to the reference CANDU radial pin profile, whereby all designs meets the linear heat rating licensing limit of 60 kW/m with adequate margins.

The linear heat rating of the target elements in the modified fuel bundle designs was a priori postulated to be higher than the reference CANDU bundle due to the presence of enriched fuel region. The resemblances of the two curves is not quite unexpected. Efforts to keep the fresh fuel kinf value for a partially enriched fuel bundles as close as possible to the reference CANDU lattice resulted in a configuration which consisted of a relatively large depleted uranium region and a relatively small enriched fuel region in these pins. The volumetric ratio of enriched fuel to depleted fuel was

3.56% in Design 1, 2.79% in Design 2 and 4, and 2.92% in Design 3 and 5. Therefore, the increase in the fission rate and thus power density in the enriched region is compensated by the relative decrease of power density in the depleted region, resulting in an overall linear heat rating profile similar to the reference CANDU fuel bundle.

Page | 86

Design 1

Table 4-9: Design 1 Data for Radial Pin Power Profile Calculations

Macroscopic Unnormalized Linear Normalized Integrated 2-D Fission Cross- Linear Power Density, Linear Power Region Flux, ˆ Volume, ' Section, Σf Rating, qi.u dL, U Rating , Qr (n·cm/s) V2-D (cm2) (cm-1) (kW/cm) (g/cm) (kW/m) Ring 1 0.02232 0.3637 1.159 2.658E-16 10.83 37.14 Ring 2 0.02331 2.194 6.956 1.675E-15 65.00 39.01 Ring 3 0.02593 4.484 13.91 3.807E-15 130.0 44.33 Ring 4 0.5216 0.2538 0.7182 4.299E-15 6.711 (Enriched) 56.32 Ring 4 0.01329 6.714 20.15 2.957E-15 188.2 (Depleted)

60 Design 1 Reference CANDU 55

50

45

40

35

LINEAR HEAT RATING(KW/M) 30 1 2 3 4 FUEL BUNDLE RINGS

Figure 4-8: Design 1 Bundle Radial Pin Power Profile

Page | 87

Design 2

Table 4-10: Design 2 Data for Radial Pin Power Profile Calculations

Normalized Macroscopic Integrated 2-D Unnormalized Linear Fission Cross- Volume, Linear Power Density, Linear Power Region Flux, ˆ ' Section, Σf V2-D Rating, qi.u dL, U Rating , Q (n·cm/s) r (cm-1) (cm2) (kW/cm) (g/cm) (kW/m) Ring 1 0.02236 0.3658 1.159 2.678E-16 10.83 37.43 Ring 2 0.02327 2.211 6.956 1.685E-15 65.00 39.26 Ring 3 0.02586 4.513 13.91 3.821E-15 130.0 44.50 Ring 4 0.01337 6.771 20.30 2.999E-15 189.7 (Depleted) 56.11 Ring 4 0.6737 0.1932 0.5664 4.227E-15 5.292 (Enriched)

60 Design 2 Reference CANDU 55

50

45

40

35

LINEAR HEAT RATING(KW/M) 30 1 2 3 4 FUEL BUNDLE RINGS

Figure 4-9: Design 2 Bundle Radial Pin Power Profile

Page | 88

Design 3

Table 4-11: Design 3 Data for Radial Pin Power Profile Calculations

Normalized Macroscopic Integrated 2-D Unnormalized Linear Fission Cross- Volume, Linear Power Density, Linear Power Region Flux, ˆ ' Section, Σf V2-D Rating, qi.u dL, U Rating , Q (n·cm/s) r (cm-1) (cm2) (kW/cm) (g/cm) (kW/m) Ring 1 0.02243 0.3673 1.159 2.698E-16 10.83 37.67 Ring 2 0.02335 2.224 6.956 1.700E-15 65.00 39.58 Ring 3 0.02616 4.530 13.91 3.880E-15 130.0 45.15 Ring 4 0.02589 3.336 9.999 2.860E-15 189.4 (Depleted) 55.56 Ring 4 1.319 0.1004 0.2922 4.302E-15 5.537 (Enriched)

60 Design 3 Reference CANDU

55

50

45

40

35

LINEAR HEAT RATING(KW/M) 30 1 2 3 4 FUEL BUNDLE RINGS

Figure 4-10: Design 3 Bundle Radial Pin Power Profile

Page | 89

Design 4

Table 4-12: Design 4 Data for Radial Pin Power Profile Calculations

Normalized Macroscopic Integrated 2-D Unnormalized Linear Fission Cross- Volume, Linear Power Density, Linear Power Region Flux, ˆ ' Section, Σf V2-D Rating, qi.u dL, U Rating , Q (n·cm/s) r (cm-1) (cm2) (kW/cm) (g/cm) (kW/m) Ring 1 0.009508 0.3546 1.128 55.87 10.54 (Depleted) 37.70 Ring 1 0.4927 0.009897 0.03128 1.549 0.2922 (Enriched) Ring 2 0.009894 2.143 6.769 335.2 63.24 (Depleted) 39.52 Ring 2 0.5111 0.05991 0.1877 9.294 1.753 (Enriched) Ring 3 0.01100 4.372 13.53 670.5 126.5 (Depleted) 44.90 Ring 3 0.5686 0.1225 0.3753 18.59 3.507 (Enriched) Ring 4 0.013348 6.760 20.30 1005 189.7 (Depleted) 55.74 Ring 4 0.6729 0.1918 0.5630 27.88 5.260 (Enriched)

60 Design 4 Reference CANDU 55

50

45

40

35

LINEAR HEAT RATING (KW/M) RATING LINEAR HEAT 30 1 2 3 4 FUEL BUNDLE RINGS

Figure 4-11: Design 4 Bundle Radial Pin Power Profile

Page | 90

Design 5

Table 4-13: Design 5 Data for Radial Pin Power Profile Calculations

Normalized Macroscopic Integrated 2-D Unnormalized Linear Fission Cross- Volume, Linear Power Density, Linear Power Region Flux, ˆ ' Section, Σf V2-D Rating, qi.u dL, U Rating , Q (n·cm/s) r (cm-1) (cm2) (kW/cm) (g/cm) (kW/m) Ring 1 0.01873 0.1755 0.5553 1.089E-16 10.52 (Depleted) 38.52 Ring 1 0.9797 0.005259 0.01639 1.673E-16 0.3106 (Enriched) Ring 2 0.01945 1.057 3.332 6.811E-16 63.14 (Depleted) 39.89 Ring 2 0.9896 0.03221 0.09835 1.035E-15 1.863 (Enriched) Ring 3 0.02155 2.1509 6.664 1.535E-15 126.2 (Depleted) 45.17 Ring 3 1.110 0.06521 0.1967 2.350E-15 3.727 (Enriched) Ring 4 0.02581 3.315 9.996 2.833E-15 189.4 (Depleted) 55.40 Ring 4 1.316 0.1009 0.2951 4.315E-15 5.591 (Enriched)

60 Design 5 Reference CANDU 55

50

45

40

35 LINEAR HEAT RATING (KW/M) RATING LINEAR HEAT 30 1 2 3 4 FUEL BUNDLE RINGS

Figure 4-12: Design 5 Bundle Radial Pin Power Profile

Page | 91

4.3 Task 3 - Comparison of Radial Temperature Profiles

Another important fuel design parameter is fuel centreline temperature. The margins available for fuel melting under normal operations and various accidental scenarios play an important role in fuel bundle design and design optimization. In addition to fuel centreline temperature, the sheath temperature must also be kept below the accepted limits established by the industry.

The melting point of UO2 and U-metal is 2865 °C and 1132 °C, respectively. For the purpose of this work, it is assumed that no gap is developed between the fuel and cladding due to the short irradiation period required to reach peak activities of Mo-99.

The variation in UO2 thermal conductivity as a function of fuel temperature is accounted for by utilizing the IAEA UO2 thermal conductivity relation (Eq. 3.26). A second radial temperature profile is produced using a conservative value of UO2 thermal conductivity

(0.024 W/cm∙k). The thermal conductivity of U-metal is 0.43 W/cm∙k.

The fuel temperature calculations are greatly dependent on the heat conduction coefficient used. The intent of the analysis is to compare the radial temperature profiles of the highest power element of the new designs to the reference CANDU bundle profile, and to ensure that the fuel centreline melting criterion is satisfied. This is illustrated in

Figures 4-13 through 4-20.

Thermophysical properties of coolant obtained using NIST REFPROP are provided in Table 4-14. Table 4-15 lists the CANDU specific important heat transfer parameters required for radial temperature profile calculations.

Page | 92

Additional data on materials and lattice specifications for 37-element CANDU fuel bundle are provided in Appendix B. A numerical integration methodology as described in Section 3.4.2 is used to calculate the radial temperature profiles for all designs, and summarized in Tables 4-16 through 4-25.

Using the numerical integration method, the centreline temperatures of the

Mo-99 target bundles are calculated and found to satisfy the centreline melting criterion for all new designs with the exception of Design 1 (See Figures 4-13 and 4-14). This is not unexpected. The UO2 centreline temperature has always been a concern for the industry due to relatively low thermal conductivity of ceramic UO2. In the case of

Design 1, the 19.5 wt% U-235 enriched fuel region is located in the centre of the Mo-99 target pins. The enriched fuel region with its high power density is encapsulated by a relatively large volume of depleted fuel with much lower power density (see Table 4-16).

The power density of the enriched region is approximately 43 times higher than the depleted region. Hence, the majority of the power production takes place towards the centre of the pin resulting in significantly high centreline temperatures.

For the remaining designs, the fuel centreline temperature is lower than the reference fuel. This is due to the relatively small thickness of the enriched fuel region on the periphery of the fuel elements.

For the same steady-state channel conditions used in this analysis, the ΔT across the thicker cladding used in Designs 3 and 5 is much higher compared to the reference bundle. This is compensated by the much higher thermal conductivity of the U-metal

Page | 93

(0.43 W/cm∙K) as compared to ceramic UO2. The resulting centreline temperatures provide adequate margins to centreline melting.

Table 4-14: Thermophysical Properties of Coolant Using NIST REFPROP [46]

Temperature Pressure Density Viscosity Prandtl

(°C) (MPa) (kg/m3) (Pa∙s) x 10-6 Number

Channel 266 11.05 781.9 101.0 0.8215 Inlet Channel 312 10.29 686.5 81.41 0.9534 Outlet

Table 4-15: CANDU Specific Important Heat Transfer Parameters [46]

Parameter Value

Average Coolant Velocity through the Channel, V 10 m/s Coolant Flow Area, A 0.003507 m2 Wetted Perimeter, Pw 1.847 m Hydraulic Diameter, Dh 0.007595 m Reynolds Number, Re 305661 Nusselt Number, Nu 536.0 Coolant Heat Transfer Coefficient, HC 4.006 W/cm2∙K Thermal Conductivity of Clad, kC 0.107 W/cm∙K Thermal Conductivity of UO2 0.024 W/cm∙K Thermal Conductivity of U-Metal 0.430 W/cm∙K

Page | 94

Design 1

Table 4-16: Design 1 Normalized Heat Density and Linear Power Rating in

Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt %) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Enriched1 19.50 0.03757 0.03757 7797 34.57 Enriched2 19.50 0.03757 0.07513 8057 141.7 Enriched3 19.50 0.03757 0.1127 8659 333.7 Depleted1 0.2000 0.04948 0.1622 194.8 342.0 Depleted2 0.2000 0.04948 0.2117 198.5 353.5 Depleted3 0.2000 0.04948 0.2611 200.6 368.3 Depleted4 0.2000 0.04948 0.3106 202.0 386.2 Depleted5 0.2000 0.04948 0.3601 203.3 407.4 Depleted6 0.2000 0.04948 0.4096 204.4 431.9 Depleted7 0.2000 0.04948 0.4591 205.5 459.7 Depleted8 0.2000 0.04948 0.5085 206.7 490.8 Depleted9 0.2000 0.04948 0.5580 207.9 525.2 Depleted10 0.2000 0.04948 0.6075 209.5 563.2

Page | 95

Table 4-17: Design 1 Numerical Integration Results Using IAEA and Constant

Thermal Conductivity for UO2

Temperature Using Temperature Using Node IAEA Thermal Constant Thermal Conductivity (°C) Conductivity (°C) Fuel Centreline 4486 5862 Node1 (Enriched1) 4428 5748 Node2 (Enriched2) 4247 5398 Node3 (Enriched3) 3921 4794 Node4 (Depleted1) 3425 3962 Node5 (Depleted2) 2996 3342 Node6 (Depleted3) 2580 2837 Node7 (Depleted4) 2149 2401 Node8 (Depleted5) 1705 2012 Node9 (Depleted6) 1305 1653 Node10 (Depleted7) 987.3 1316 Node11 (Depleted8) 738.1 993.5 Node12 (Depleted9) 538.4 680.7 Node13 (Depleted10) 374.1 374.1 Node14 (Sheath) 310.0 310.0 Node15 (Coolant) 275.8 275.8

Page | 96

5000 Design 1 4500 Reference 4000 CANDU Enriched 3500 Region 3000 UO Melting Point

C) Depleted 2 ° 2500 Region

2000

1500 Temperature Temperature ( 1000

500

0 Fuel Centreline 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-13: Design 1 Radial Temperature Profile of Ring 4 Pin Using IAEA

Thermal Conductivity for UO2

Page | 97

7000

6000 Design 1 Reference CANDU 5000 Enriched Region 4000

C) Depleted ° Region 3000

UO2 Melting Point

2000 Temperature Temperature (

1000

Fuel Centreline 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-14: Design 1 Radial Temperature Profile of Ring 4 Pin Using a

Constant Thermal Conductivity for UO2 (0.024 W/cm∙K)

Page | 98

Design 2

Table 4-18: Design 2 Normalized Heat Density and Linear Power Rating in

Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt %) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Depleted1 0.2000 0.05992 0.05992 204.5 2.306 Depleted2 0.2000 0.05992 0.1198 204.6 9.233 Depleted3 0.2000 0.05992 0.1798 204.7 20.78 Depleted4 0.2000 0.05992 0.2397 205.1 36.97 Depleted5 0.2000 0.05992 0.2996 205.3 57.82 Depleted6 0.2000 0.05992 0.3595 205.7 83.35 Depleted7 0.2000 0.05992 0.4194 206.2 113.6 Depleted8 0.2000 0.05992 0.4794 206.7 148.5 Depleted9 0.2000 0.05992 0.5393 207.3 188.3 Depleted10 0.2000 0.05992 0.5992 207.8 232.8 Enriched1 19.50 0.002767 0.6020 10444 341.9 Enriched2 19.50 0.002767 0.6047 10384 450.8 Enriched3 19.50 0.002767 0.6075 10466 561.1

Page | 99

Table 4-19: Design 2 Numerical Integration Results Using IAEA and Constant

Thermal Conductivity for UO2

Temperature Using Temperature Using Node IAEA Thermal Constant Thermal Conductivity (°C) Conductivity (°C) Fuel Centreline 874.8 1178 Node1 (Depleted1) 868.8 1171 Node2 (Depleted2) 851.1 1148 Node3 (Depleted3) 822.0 1109 Node4 (Depleted4) 782.5 1056 Node5 (Depleted5) 733.4 987.1 Node6 (Depleted6) 676.1 902.7 Node7 (Depleted7) 611.9 802.9 Node8 (Depleted8) 542.1 687.5 Node9 (Depleted9) 468.3 556.5 Node10 (Depleted10) 391.7 409.9 Node11 (Enriched1) 387.3 401.1 Node12 (Enriched2) 381.3 389.1 Node13 (Enriched3) 373.8 373.8 Node14 (Sheath) 309.9 309.9 Node15 (Coolant) 275.8 275.8

Page | 100

3000 UO2 Melting Point

470 C) 2500 ° 420 Design 2

370

Reference Temperature ( Temperature 2000 320 CANDU 0.590 0.600 0.610 0.620

Radial Distance (cm) C) ° 1500

Depleted 1000 Region

Temperature Temperature ( Enriched Region 500

0 Fuel Centreline 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-15: Design 2 Radial Temperature Profile of Ring 4 Pin Using IAEA

Thermal Conductivity for UO2

Page | 101

3000 UO2 Melting Point

470 C) 2500 ° 420 Design 2

370 Reference Temperature ( Temperature 2000 320 CANDU 0.59 0.60 0.61 0.62

Radial Distance (cm) C) ° 1500

1000 Depleted Enriched

Temperature Temperature ( Region Region 500

Fuel Centreline 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-16: Design 2 Radial Temperature Profile of Ring 4 Pin Using a

Constant Thermal Conductivity for UO2 (0.024 W/cm∙K)

Page | 102

Design 3

Table 4-20: Design 3 Normalized Heat Density and Linear Power Rating in

Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt %) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Depleted1 0.2000 0.04205 0.04205 394.6 2.192 Depleted2 0.2000 0.04205 0.08410 394.8 8.772 Depleted3 0.2000 0.04205 0.1261 395.3 19.75 Depleted4 0.2000 0.04205 0.1682 396.0 35.15 Depleted5 0.2000 0.04205 0.2102 396.8 54.99 Depleted6 0.2000 0.04205 0.2523 397.6 79.28 Depleted7 0.2000 0.04205 0.2943 398.6 108.0 Depleted8 0.2000 0.04205 0.3364 400.2 141.4 Depleted9 0.2000 0.04205 0.3784 401.8 179.3 Depleted10 0.2000 0.04205 0.4205 403.0 221.9 Enriched1 19.50 0.002033 0.4225 20392 331.7 Enriched2 19.50 0.002033 0.4246 20478 442.5 Enriched3 19.50 0.002033 0.4266 20800 555.6

Page | 103

Table 4-21: Design 3 Numerical Integration Results Using Constant Thermal

Conductivity for U-Metal

Temperature Using Node Constant Thermal Conductivity (°C) Fuel Centreline 793.0 Node1 (Depleted1) 792.6 Node2 (Depleted2) 791.4 Node3 (Depleted3) 789.3 Node4 (Depleted4) 786.5 Node5 (Depleted5) 782.8 Node6 (Depleted6) 778.4 Node7 (Depleted7) 773.1 Node8 (Depleted8) 766.9 Node9 (Depleted9) 760.0 Node10 (Depleted10) 752.2 Node11 (Enriched1) 751.7 Node12 (Enriched2) 751.0 Node13 (Enriched3) 750.1 Node14 (Sheath) 309.6 Node15 (Coolant) 275.8

Page | 104

3000 UO2 Melting Point

780 2500

C) Design 3 ° 760

740 Reference CANDU 2000 Temperature ( Temperature 720 0.41 0.42 0.43 0.44

Radial Distance (cm) C) ° 1500

U-Metal Melting Point

1000 Temperature Temperature (

500 Depleted Region Enriched Region Fuel Centreline 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-17: Design 3 Radial Temperature Profile of Ring 4 Pin Using a

Constant Thermal Conductivity for U-Metal (0.43 W/cm∙K)

Page | 105

Design 4

Table 4-22: Design 4 Normalized Heat Density and Linear Power Rating in

Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt %) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Depleted1 0.2000 0.05993 0.05993 203.7 2.298 Depleted2 0.2000 0.05993 0.1198 203.8 9.199 Depleted3 0.2000 0.05993 0.1798 203.9 20.70 Depleted4 0.2000 0.05993 0.2397 204.3 36.84 Depleted5 0.2000 0.05993 0.2996 204.6 57.61 Depleted6 0.2000 0.05993 0.3595 205.0 83.05 Depleted7 0.2000 0.05993 0.4195 205.4 113.2 Depleted8 0.2000 0.05993 0.4794 206.0 148.0 Depleted9 0.2000 0.05993 0.5393 206.6 187.7 Depleted10 0.2000 0.05993 0.5993 207.1 232.1 Enriched1 19.50 0.002750 0.6020 10410 340.1 Enriched2 19.50 0.002750 0.6048 10358 448.1 Enriched3 19.50 0.002750 0.6075 10435 557.4

Page | 106

Table 4-23: Design 4 Numerical Integration Results Using IAEA and Constant

Thermal Conductivity for UO2

Temperature Using Temperature Using Node IAEA Thermal Constant Thermal Conductivity (°C) Conductivity (°C) Fuel Centreline 871.3 1175 Node1 (Depleted1) 865.4 1167 Node2 (Depleted2) 847.7 1144 Node3 (Depleted3) 818.9 1106 Node4 (Depleted4) 779.6 1052 Node5 (Depleted5) 730.8 984.1 Node6 (Depleted6) 673.8 900.0 Node7 (Depleted7) 609.9 800.4 Node8 (Depleted8) 540.6 685.5 Node9 (Depleted9) 467.1 554.9 Node10 (Depleted10) 390.9 408.8 Node11 (Enriched1) 386.5 400.2 Node12 (Enriched2) 380.6 388.2 Node13 (Enriched3) 373.1 373.1 Node14 (Sheath) 309.7 309.7 Node15 (Coolant) 275.8 275.8

Page | 107

3000

2500 Design 4

Reference 2000

CANDU C) ° 1500

Depleted 1000 Region

Temperature Temperature ( Enriched 500 Region

Fuel Centreline 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-18: Design 4 Radial Temperature Profile of Ring 4 Pin Using IAEA

Thermal Conductivity for UO2

Page | 108

3000 UO2 Melting Point

2500 Design 4

Reference 2000

CANDU C) ° 1500

1000 Enriched Depleted Temperature Temperature ( Region Region 500

Fuel Centreline 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-19: Design 4 Radial Temperature Profile of Ring 4 Pin Using a

Constant Thermal Conductivity for UO2 (0.024 W/cm∙K)

Page | 109

Design 5

Table 4-24: Design 5 Normalized Heat Density and Linear Power Rating in

Ring 4 Sub-regions

Normalized Cumulative Heat Normalized Sub-regions Enrichment Thickness Pin Radii Density, Q’’’ Linear in Ring 4 (wt %) (cm) (cm) (kW/cm3) Power Rating, Q’ (kW/cm) Depleted1 0.2000 0.04204 0.04204 390.5 2.169 Depleted2 0.2000 0.04204 0.08409 390.6 8.678 Depleted3 0.2000 0.04204 0.1261 391.2 19.54 Depleted4 0.2000 0.04204 0.1682 391.8 34.77 Depleted5 0.2000 0.04204 0.2102 392.7 54.40 Depleted6 0.2000 0.04204 0.2523 393.4 78.44 Depleted7 0.2000 0.04204 0.2943 394.5 106.9 Depleted8 0.2000 0.04204 0.3364 396.0 139.9 Depleted9 0.2000 0.04204 0.3784 397.7 177.4 Depleted10 0.2000 0.04204 0.4204 398.9 219.5 Enriched1 19.50 0.002053 0.4225 20223 329.5 Enriched2 19.50 0.002053 0.4245 20329 440.6 Enriched3 19.50 0.002053 0.4266 20653 554.0

Page | 110

Table 4-25: Design 5 Numerical Integration Results Using Constant Thermal

Conductivity for U-Metal

Temperature Using Node Constant Thermal Conductivity (°C) Fuel Centreline 791.2 Node1 (Depleted1) 790.8 Node2 (Depleted2) 789.6 Node3 (Depleted3) 787.6 Node4 (Depleted4) 784.8 Node5 (Depleted5) 781.1 Node6 (Depleted6) 776.7 Node7 (Depleted7) 771.5 Node8 (Depleted8) 765.4 Node9 (Depleted9) 758.5 Node10 (Depleted10) 750.8 Node11 (Enriched1) 750.3 Node12 (Enriched2) 749.6 Node13 (Enriched3) 748.7 Node14 (Sheath) 309.5 Node15 (Coolant) 275.8

Page | 111

3000 UO2 Melting Point

2500 Design 5

Reference CANDU

2000 C) ° 1500

U-Metal Melting Point

1000 Temperature Temperature ( Depleted 500 Region Enriched Fuel Centreline Region 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radial Distance (cm)

Figure 4-20: Design 5 Radial Temperature Profile of Ring 4 Pin Using a

Constant Thermal Conductivity for U-Metal (0.43 W/cm∙K)

Page | 112

4.4 Mass and Activities of Molybdenum-99

The proposed designs utilize 19.5 wt% U-235 enriched fuel over several target pins which can generate a large yield of Mo-99 per bundle. Tasks 1, 2 and 3 ensure that high yields of Mo-99 can be done without significantly changing the bundle physics and fuel safety characteristics.

The mass and activity of Mo-99 is calculated for each design by extension of the

DRAGON calculated fission rates as described in Section 3.4.3. The total Mo-99 production values are 2335, 2297, 2336, 4131 and 4268 six-day Curies for Design 1 to 5, respectively. This yield corresponds to approximately 19% of the world weekly demand for Designs 1, 2 and 3, and approximately 34% of the world weekly demand for Designs 4 and 5.

The activities of Mo-99 produced per bundle at EOB and six-day Curies are listed in Tables 4-26 through 4-30. The required extraction rate to meet worldwide demands of Mo-99 for each design is also specified. A production cycle of 6 bundles per week for

Designs 1, 2 and 3, or 3 bundles per week for Designs 4 and 5 would yield sufficient quantities of Mo-99 to ensure stable supply of Mo-99 to satisfy the global demand.

Page | 113

Table 4-26: Design 1 Molybdenum-99 Production Results

Weekly Extraction EOB Activity Total EOB Total EOB Total Six-Day Bundle Rate Required of Mo-99 Activity of Mass of Curies of Location to Meet (Ci) Mo-99 Mo-99 Mo-99 Worldwide Demand Ring 1 0 Ring 2 0 15006 31.26 2335 ~6 Ring 3 0 Ci/Bundle mg/Bundle Ci/Bundle Bundles/Week Ring 4 15006

Table 4-27: Design 2 Molybdenum-99 Production Results

Weekly Extraction Rate EOB Activity Total EOB Total EOB Total Six-Day Bundle Required to of Mo-99 Activity of Mass of Curies of Location Meet (Ci) Mo-99 Mo-99 Mo-99 Worldwide Demand Ring 1 0 Ring 2 0 14761 30.74 2297 ~6 Ring 3 0 Ci/Bundle mg/Bundle Ci/Bundle Bundles/Week Ring 4 14761

Table 4-28: Design 3 Molybdenum-99 Production Results

Weekly Extraction Rate EOB Activity Total EOB Total EOB Total Six-Day Bundle Required to of Mo-99 Activity of Mass of Curies of Location Meet (Ci) Mo-99 Mo-99 Mo-99 Worldwide Demand Ring 1 0 Ring 2 0 15008.21 31.26 2336 ~6 Ring 3 0 Ci/Bundle mg/Bundle Ci/Bundle Bundles/Week Ring 4 15008

Page | 114

Table 4-29: Design 4 Molybdenum-99 Production Results

Weekly Extraction Rate EOB Activity Total EOB Total EOB Total Six-Day Bundle Required to of Mo-99 Activity of Mass of Curies of Location Meet (Ci) Mo-99 Mo-99 Mo-99 Worldwide Demand Ring 1 551.8 Ring 2 3470 26547 55.29 4131 ~3 Ring 3 7894 Ci/Bundle mg/Bundle Ci/Bundle Bundles/Week Ring 4 14629

Table 4-30: Design 5 Molybdenum-99 Production Results

Weekly Extraction Rate EOB Activity Total EOB Total EOB Total Six- Bundle Required to of Mo-99 Activity of Mass of Day Curies Location Meet (Ci) Mo-99 Mo-99 of Mo-99 Worldwide Demand Ring 1 583.0 Ring 2 3606 27423 57.11 4268 ~3 Ring 3 8192 Ci/Bundle mg/Bundle Ci/Bundle Bundles/Week Ring 4 15040

Page | 115

Although the centre and middle rings provide higher margins to heating limits as depicted in Figures 4-8 through 4-12, the 4th ring provides a higher flux exposure which is a key factor for the production of Mo-99. This aspect of core neutronics is utilized in

Designs 1, 2 and 3. Furthermore, by only using the outer most rings for Mo-99 production, the post processing procedure becomes simpler since only those pins will need to be demounted for processing, and can easily be replaced with fresh Mo-99 targets for another production run. Ideally the re-use of the remaining pins should be limited to a few cycles since excessive irradiation of the NU will produce Pu-239 through neutron absorption. Build-up of small amounts of Pu-239 will also occur in the depleted fuel inside the Mo-99 producing pins. However, due to the 20-day irradiation period and the presence of only a small number Mo-99 producing bundles in the core, the effect of

Pu-239 build-up on the overall reactivity is expected to be small.

The production of Mo-99 must be balanced against the bundle power and linear heating limits. Assessment of Designs 1, 2 and 3 showed that the bundle reactivity and distribution of power resembles greatly with the standard CANDU bundle at the pin level. This resemblance made it possible to extend the design of the 4th ring elements to other rings for maximum Mo-99 yield. Tables 4-26 through 4-30 list the total six-day

Curies of Mo-99 produced for each design. As calculated in these tables, Designs 4 and 5 distribute the total power of the bundle over increased number of target elements, 37 pins in total, and therefore provide a much higher yield of Mo-99 compared to Designs 1,

2 and 3.

Page | 116

Chapter 5

Concluding Remarks and Future Work

This thesis explores the possibility of using modified 37-element fuel bundles for the production of Mo-99 in existing CANDU reactors without affecting the core properties or day-to-day operations of the plant. The tasks performed in Sections 4.1,

4.2 and 4.3 are used to evaluate the viability of the designs with respect to the existing safety margins as well as to demonstrate the similarity of the proposed target bundles to the standard 37 element bundle behavior.

As mentioned above, various designs with different amounts of 19.5 wt% U-235 enriched fuel were simulated using the DRAGON lattice code and the fresh fuel kinf values were recorded for each case. The use of 19.5 wt% U-235 enriched fuel as Mo-99 targets in different rings of a 37-element fuel bundle result in increased fission rates and hence power rating of the enriched region is increased. In order to have a high confidence in the available margins to the maximum linear power ratings and centreline temperature limits, the bundles are assumed be irradiated in the highest power channel of the CANDU reactor core corresponding to the maximum instantaneous power of 900 kWth.

In conclusion, the design of modified fuel bundles for Mo-99 production met the criteria specified in Section 3.1 of this thesis. Although the impacts of the enriched target pins on safety analysis were not directly examined in this work, the similarity in the unitcell eigenvalue (kinf) and the pin linear heat rating with the reference CANDU bundle suggest that the resultant impact on accident analysis should be small. However, direct

Page | 117 confirmation may still be required before the new design can be implemented in operating reactors.

Over the last few years, there have been a number of supply shortages of Mo-99.

The situation is to deteriorate further with the expected permanent shutdown of the

Canadian NRU reactor in 2016. The CANDU power reactors can play a large role in ensuring a stable supply of Mo-99. The feasibility of producing large and continuous quantities of Mo-99 in the CANDU power reactors has been demonstrated in this thesis.

The continuous and reliable supply of medical isotopes will ensure the availability of life- saving medical procedures for millions of patients around the globe.

Recommendations for Future Work:

During the course of this research, some areas were identified as requiring future study if the production of medical isotopes using one of the proposed bundle designs in

CANDU reactor was actually begun. These areas of potential research include:

Fuel pellet manufacturability: Designs 2, 3, 4 and 5 proposed in this thesis have very thin annular enriched fuel regions composed of either UO2 or U-metal on the periphery of the fuel pellet. Although the new fuel manufacturing methods have significantly advanced, the proposed thin layers may still challenge manufacturing feasibility. The manufacturability of the posed fuel pellets should be examined.

Use of demountable fuel bundles: The study assumes the use of demountable bundles for the proposed designs. Upon completion of the irradiation cycle, the target pins will be demounted and sent for processing. Although, this is not critical to the

Page | 118 proposed study, it will provide ease with respect to fuel reprocessing and reuse. The feasibility of demountable bundles to use in the operating CANDU reactors should be examined.

Handling and processing of medical isotopes producing 37-element bundle: Upon extraction from the reactor the pins with enriched uranium will be sent to the Mo-99 production facilities for further processing, whereas the remaining pins can either be sent away to spent fuel storage or be mounted on another target fuel bundle and reloaded into the reactor for another Mo-99 production cycle. Additional fuel handling procedures would need to be developed to remove the Mo-99 target pins from the demountable bundle and send them for processing. Handling and processing of newly designed fuel bundles would require updating the existing infrastructure and is a subject for future research.

Pilot production: The study assumes that the proposed bundle will be irradiated in the highest power channel of the CANDU reactor. The 900 kWth bundle power is the upper limit for a typical CANDU fuel bundle and the bundle power at the periphery location can be half of this value [50]. Ideally the new bundles will be first irradiated in a low-power channel on the periphery of the core to get more operational experience before moving the bundles to the high-power central channels. Therefore, from an operational standpoint, it is advisable to load the new proposed bundles in the periphery channels first to gain operational experience before loading them into the high power channels of the CANDU core.

Page | 119

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Appendices

Appendix A – Potential Producers of Reactor Produced

Molybdenum-99

Numerous projects have surfaced worldwide related to the building of new reactors dedicated to the Mo-99 production, including production of Mo-99 from an existing facility that was not originally built for that purpose. In some cases, these initiatives are expected to play a big role in the production of medical isotopes in the future, while in other cases, the projects are either cancelled or lobbying for governments to provide support for further research to be carried out.

The following is a list of potential producers of reactor-based Mo-99 that have the technological resources to play a large role in the production of medical isotopes in the future.

A.1 Multipurpose Applied Physics Lattice Experiment (MAPLE)

Designed by Atomic Energy of Canada Limited (AECL), two reactors, MAPLE I and

II were planned and constructed to supply the world’s demand for Mo-99. The MAPLE reactors were designed to generate 10 MW of heat for the sole purpose of medical isotope production [51]. Each reactor was capable of producing enough medical isotopes to supply 100% of the worldwide demand (~12000 six-day Curies per week).

The MAPLE reactors were planned to use LEU fuel and HEU targets.

Page | 135

Designed and built to replace the 54 year old NRU reactor in Canada, the project was estimated to cost $140 million but ended up costing much more due technical design flaws which were discovered during commissioning. It was discovered that these reactors have a positive power coefficient of reactivity. The reactors were designed to have a small negative power coefficient of reactivity, estimated at -0.12 mk/MW, but it was measured to be +0.28 mk/MW.

The power coefficient of reactivity describes the number of neutrons available per generation per unit change in power. A positive value indicates that there are more neutrons available in each subsequent generation as the reactor power is increased. This meant that the reactor inherently tried to increase the power during power increases, a positive feedback. The original safety systems of the reactor were inadequate and design changes were implemented to accommodate the positive power coefficient of reactivity.

Investigations by AECL and other contracted service providers were unable to explain the positive power coefficient, and in 2008, AECL and the Government of Canada announced that the project would be discontinued [52].

There has been much debate among experts on the issue of reviving the MAPLE reactors. A number of scientists believe that the reactor could have operated safety with a positive power coefficient of reactivity, after the design changes to take it into account were implemented. However, another roadblock hindering the MAPLE project was that the fuel processing facility was designed to accommodate HEU targets. Conversion to

LEU targets would have required a significant redesign of the processing facility with

Page | 136 larger waste tanks, etc. Calls to complete commissioning of the MAPLE project have not received much attention.

It is expected that a general re-revisit of the positive power reactivity coefficient problem may take up to 6 years to rectify if possible. If it is later decided that redesigning and replacing the entire core of MAPLE reactors is the only way to solve the positive power reactivity coefficient problem, those efforts may take additional 7 to 10 years and may cost tens of millions of dollars [53].

A.2 Aqueous Homogeneous Reactor (AHR)

Babcock & Wilcox (B&W) have proposed to build an aqueous homogeneous reactor (AHR), also known as a solution reactor, which will utilize an LEU fuel salt dissolved in acid and water. In this reactor, the uranium in the solution is both the reactor fuel and the target material. This system would eliminate the need to manufacture or encapsulate a target, and un-fissioned uranium can be recycled back into the reactor instead of being removed as waste. Various solution forms of fuel are possible, such as: uranyl nitrate (UO2(NO3)2), uranyl sulfate (UO2SO4), or uranyl fluoride

(UO2F2) [54]. The extraction process itself would not differ remarkably from the existing adsorption process of using an alumina column that is currently used by processing facilities.

B&W has estimated that an AHR reactor could generate approximately 18% of the North American Mo-99 demand (1100 six-day Curies per week) while assuming a 26

Page | 137 hour processing time. The proposal suggests building three to four 200 kW units for higher Mo-99 yields. They have also projected a total waste volume of less than 5 m3 each year consisting generally of alumina column wastes [54].

B&W assumes that five years will be required from conceptual design (which has begun) to commercial operation for their newly designed AHR. However, the plan is still lacking concrete budget projections derived from actual experience from building solution reactors. B&W’s own initial estimate states that less than $100 million will be required for research and development of the AHR [55].

Being first of its kind in terms of design and scale, another hurdle to the construction of AHR is lack of regulatory framework. Current nuclear reactor regulations do not specifically address AHR, so licensing under current regulations may require clarifications, or new regulations may be needed to appropriately address the safety of the solution reactors [55].

A.3 Open Pool Australian Light-Water (OPAL) Reactor

The OPAL reactor started its operation in late 2006. This multipurpose pool type reactor was built by INVAP for the Australian Nuclear Science and Technology

Organization (ANSTO). The purpose was to replace the aging High Flux Australian

Reactor.

Page | 138

OPAL is a 20 MW reactor with peak thermal neutron flux: 3x1014 n·cm-2·s-1 in the reflector vessel. The core of OPAL consists of compact 16 uranium oxide fuel assemblies interspersed with control rods. The fuel assemblies are cooled by demineralised light water, while the core is surrounded by heavy water moderator in a zirconium alloy reflector vessel at the bottom of a 13-metre-deep open pool of light water [56].

OPAL uses LEU fuel with around 20% U-235 enrichment by weight [56]. This gives OPAL a distinct advantage over other research reactors around the world in terms of nuclear security and safeguards. OPAL has the capacity to operate 340 days a year which is a significant increase over the operating levels typically achieved by comparable research facilities.

The ANSTO facility includes an onsite processing facility which produces many important radionuclides, such as Mo-99, extracted from LEU uranium-aluminium alloy targets. The processing facility was also build by INVAP with a budget of $200 Million

[57]. The facility supplies medical isotopes to meet 100% of Australia’s demand, as well as the demands of a number of overseas countries, especially in the Asia-Pacific region.

The reactor has been producing medical isotopes since May 2008, and is expected to produce medical isotopes for the next 40 years.

The reactor is currently producing Mo-99 one manufacturing run per week. If there is a need to produce for the wider market, such as North America, the manufacturing process can be run multiple times per week with multiple targets being irradiated [55]. However, before the operators of OPAL decide on expanding their manufacturing runs, appropriate approvals by the government drug oversight agencies

Page | 139 will be required in order to use Mo-99 made by ANSTO. In July 2006, the US Food and

Drug Administration (FDA) and Health Canada authorized Lantheus Medical Imaging to use Mo-99 produced by the OPAL reactor to make Tc-99m for diagnostic imaging for

North American health care facilities ([53], [58]).

Beside some political and long-distance transportation related issues, the OPAL reactor was intended to only provide medical isotopes for the local Australian and New

Zealand markets, and is only capable of providing a small fraction of the worldwide demand of Mo-99 ([53], [55]).

A.4 Jules Horowitz Reactor (RJH)

Jules Horowitz Reactor is a 100 MW material test reactor located at the Cadarache site in southern France. Built by the French Commissariat à l'énergie atomique (Atomic

Energy Commission, CEA), the reactor is expected to replace the 70 MW OSIRIS reactor when the RJH becomes operational. The reactor is projected to be operational in the second quarter of 2016, with an estimated budget of 500 million Euros and with a lifetime of 50 years ([59], [60]).

The RJH reactor core is dismountable type. Reactor fuel is inserted in the form of cylinders of six concentric curved fuel plates hot-rolled from uranium alloys. 46 cylinders can fit in the one-piece aluminum alloy core rack at a time. The fuel is enriched to 25% U-235 by weight, amounting to a total mass of 21 kg U-235. The dismountable reactor core is partly surrounded by a beryllium reflector. The reactor core between

Page | 140 coolant inlet and outlet can be replaced to accommodate scope of future research initiatives [60].

Although the facility and the related infrastructure was initially conceptualized for scientific studies dealing with material and fuel behaviour under irradiation, a recent focus on the production of medical isotopes as part of the European strategy to ensure reliable supply for use in nuclear medicine has been gaining some momentum ([61],

[62]). The plan is to coordinate the production with the isotopes processing facilities in the Netherlands to provide a back-up supply for medical isotopes for Europe.

RJH will have a thermal neutron flux of 5x1014 n·cm-2·s-1 in the reflector region

[63]. The reactor is expected to be operational for 220 days a year and can have flexible

Mo-99 production cycles. RJH is expected to produce 25% (1200 six-day Curies per week) of the European base needs, with the possibility to increase the production up to

50% of European needs (2400 six-day Curies per week) if required. This can be achieved by irradiating 32 to 48 LEU targets in the core and in the reflectors in both fixed and movable positions [61].

Design studies for Mo-99 irradiation systems based on LEU targets has been completed, and the irradiation tests of LEU targets are expected to take place in the second quarter of 2018. The reactor is expected to begin its normal level of Mo-99 production in 2019 [62].

The RJH has the capacity to increase the number of target irradiation in order to significantly contribute to the Mo-99 world market. However, the reactor is built mainly

Page | 141 for material testing purposes and is not likely to limit its activity to the production of

Mo-99 [64]. The project is expected to supply a fraction of the European medical isotope need and is unlikely to play a major role in the North American medical isotope market.

A.5 China Advanced Research Reactor (CARR)

The China Advanced Research Reactor began its construction on August 26, 2002 and on March 1st, 2012 it successfully achieved full power operations ([65], [66]). The reactor is located at the China Institute of Atomic Energy Fangshan, Beijing site. The sophisticated light-water tank type reactor with a heavy water reflector is one of the most advanced research reactors in the world, producing 60 MW at full power [66]. The core of CARR is immersed in a 15-meter pool of water. CARR has maximum thermal neutron flux of 1×1015 n·cm-2·s-1 at the centre of the reactor core, and about

8×1014 n·cm-2·s-1 at the heavy water reflector. CARR has nine tangent horizontal neutron beam channels available for experiments and 25 vertical irradiation channels [67].

The overall design objective of CARR is to enhance China’s research capabilities in fields such as nuclear physics and chemistry, neutron scattering experiments, testing of reactor materials and nuclear fuels and neutron activation analysis. The reactor is also being used to irradiate targets for the production of radioactive isotopes [65].

Mo-99 produced in CARR is sent to CIRA member companies for processing and to produce Tc-99m generators. The CARR production capacity per week is about 250 six-day Curies of Mo-99. The demand activities of Mo-99 in China are 200 six-day Curies

Page | 142 per week. Therefore, CARR is expected to supply 100% of the China’s and neighbouring countries medical isotope needs and is unlikely to play a major role in the North

American medical isotope market.

A.6 University of Missouri Research Reactor Center (MURR)

Built in 1966, the University of Missouri Research Reactor is a 10 MW tank type reactor. MURR is the largest university research reactor in North America. It is a flux- trap reactor with high intensity thermal and fast neutron flux which can be as great as

5x1014 n·cm-2·s-1 [68]. The reactor runs 24 hours a day, 7 days a week, with a scheduled

12 hour maintenance shutdown on Mondays. In 2006, the reactor was relicensed to operate for another 20 years. The MURR is attempting to establish a domestic production source of Mo-99. In 2007, the facility produced 41 different isotopes, and more than 1000 shipments were exported to 14 different countries [69].

MURR has indicated its intention to commercially produce Mo-99 and is soliciting funding for studying the design and construction of the processing facilities for post irradiation extraction of medical isotopes [70]. Overall, the objective is to develop the capability to produce Mo-99 from LEU targets, with little change to the current reactor layout.

MURR has completed a conceptual design of a processing facility which will allow the safe processing of the LEU targets. The facility is to be located adjacent to MURR to permit safe transfer of targets to the facility after irradiation. Production objectives are

Page | 143 to produce 50% of current U.S. weekly demand (3000 six-day Curies per week) [71].

MURR could also help to fill gaps for up to about 75% of the US demand when other reactors are on planned shutdowns. This can be achieved through short-term shifts in production schedules [70]. It is estimated that it will take 3-4 years for MURR to build the appropriate processing facilities to handle the anticipated volumes of Mo-99 [53].

The current status of the planned upgrades is unknown.

In March 2011, MURR entered into a contract with NorthStar to build an electron linear accelerator to produce low specific activity Mo-99. The goal is to ramp up the production to 3000 six-day Curies per week, but have only been able to produce just over

1100 six-day Curies ([72], [73]). Although the separation chemistry of the accelerator produced low specific activity of Mo-99 is very well understood, the generated doses do not fit in the current distribution stream. The low specific activity of Mo-99 requires new generating systems to utilize the products and generate Tc-99m in activity concentrations typically needed in nuclear pharmacies [73].

A.7 Sandia National Laboratories (SNL)

Home to the Annular Core Research Reactor (ACRR), the Sandia National

Laboratories are located on Kirtland Air Force Base in Albuquerque, New Mexico and are managed and operated by the Sandia Corporation, which is a wholly owned subsidiary of Lockheed Martin Corporation. Since the late 1990s, SNL has been seeking for licensing approval to produce Mo-99. The initial preparatory work included reproduction and

Page | 144 verification of the Cintichem Mo-99 production process, development of production hardware, modification of the hot cell facility, reconfiguration of the ACRR and preparation of documentation to meet FDA and US-NRC approvals [74].

The ACRR is an open tank-type reactor filled with about 10 meters of water which provides both core cooling and radiation shielding. Heat is transferred to the open water pool through natural convection. The pool itself is cooled by an external heat exchanger.

The core of ACRR consists of an annular array of UO2-BeO fuel elements. The height of the active fuel part is 52 centimetres. For target irradiation, the dry steel-lined control cavity can be removed from the centre of the core to provide a water-filled region. Two options are available for target irradiation, one with a maximum of 19 targets and the other with a maximum of 37 targets at a time. With targets inserted, only 180 or 130 conventional fuel assemblies, depending on the option selected, would be required to operate the reactor [75]. ACRR has flexibility to operate at 30000 MW in pulse mode or

4 MW in a steady state mode [55].

The SNL site which includes ACRR, hot cell facility, and other associated facilities are a promising option for the isotope production program. The characteristics of ACRR are fully compatible with radioisotope production. It is capable of being dedicated to continuous isotope production, which is necessary to meet the demands for Mo-99. The connected hot cell facility was modified in the 1990s for Mo-99 production. The ACRR site is in proximity to excellent air transportation facilities which are useful for radioisotope shipments [76].

Page | 145

The SNL facility has the capability to serve as a backup supply to provide up to

30 % of the U.S. market demand (~1800 six-day Curies per week) under normal circumstances. It also has the capability to produce 100% of US Mo-99 requirement

(~6000 six-day Curies) should the need arise [75]. The problem however, is that the reactor is currently being used by the defense programs group at the US-DOE. In order to free the ACRR for production of medical radionuclides, it would require DOE to reassign the mission of the ACRR from defense program uses, and make significant investments in the reactor and the processing facilities [55].

It is estimated that it would require $10 to $50 million to convert the ACRR into a steady state reactor and make necessary upgrades to the existing hot cell facility in order to process Mo-99 using LEU targets [55]. Furthermore, the current fuel is 35% enriched U-235, which is considered HEU. However, it is possible to convert the ACRR to use LEU fuel for the production of Mo-99.

The proposed Mo-99 project regarding changing the mission of the ACRR for

Mo-99 production has been dropped by the DOE in favour of a new LEU reactor for the production of Mo-99 at SNL. In the more recent publication coming out of SNL, the facility is proposing to build a new reactor for the sole purpose of producing medical isotopes alongside a hot cell facility ([77], [78] [79], [80]). The intention is to construct a new reactor which is capable of producing 100% of the U.S demand (~6000 six-day

Curies per week). The reactor concept is unique in that the fuel for the reactor and the targets for the Mo-99 production are the same. In other words, no driver core is required for irradiation of Mo-99 targets. The fuel pins will be irradiated on a 7 to 21 day cycle.

Page | 146

The reactor will use LEU uranium oxide fuel enriched to 20 wt% of U-235. The fuel pins will be approximately 1 cm in diameter and 30 to 40 cm in height, encapsulated in a zirconium alloy cladding. An estimated 90 to 150 fuel pins will be arranged in the core located inside a water pool about 9 meters deep [77].

The reactor power level will be between approximately 2 MW. Since the production of 6000 six-day Curies per week requires at least 1.1 MW of continuous target fission power, assuming two post-irradiation days for processing and shipping

[77], the proposed reactor is capable of meeting 100% of North American demand. The proposed facility will also have an adjacent hot cell facility which would be connected to the reactor pool by a water channel to facilitate remote transfer of irradiated targets for processing. Processing will be done using oxide dissolution and separation processes. A provisional patent for the SNL medical isotope reactor concept was filed on

September 11, 2009 [77].

Although, there are no impediments to prevent the SNL medical isotope reactor concept along with its hot cell facility, from being designed, fabricated, and licensed today, the only question is who will be funding this project. A report by US Society of

Nuclear Medicine (SNM) task group suggests that SNL should explore the possibility of partnerships with National Nuclear Security Administration and DOE [55].

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A.8 Other Potential Suppliers of Reactor Produced Molybdenum-99

Following the major disruptions in the supply of medical isotopes in 2007, the

Canadian government has initiated OECD12 meetings on radioisotope availability in Paris and again in Toronto in 2009. Also in efforts to expand Canada's isotope production capabilities, in May 2009 the provincial and federal governments announced a $22- million fund for the McMaster University research reactor to upgrade the research reactor’s infrastructure. However, the McMaster Nuclear Reactor (MNR) is a 50-year- old reactor and will use HEU targets [53]. According to a report by SNM, even with 24/7 operation, it is estimated that MNR can only supply about 30% of North American Mo-99 demands [55]. The MNR is likely to assume the role of a backup supplier rather than a primary producer of Mo-99 for North America.

In the United States, a proposal to produce Mo-99 by using LEU solution targets at the University of California at Davis in the McClellan Nuclear Radiation Center reactor could also reach the commercial production stage in 3-4 years [53].

Table A-1 provides a list of many potential reactor projects at various stages of development. Some of these projects are very well advanced, while others are still in proposal or a design phase seeking funding and/or regulatory approvals before actually advancing to the construction phase.

12 The Organisation for Economic Co-operation and Development

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Table A-1: Potential Future Suppliers of Reactor Produced Molybdenum-99

[13]

Reactor Target Expected Estimated Status Facility Normal First Full Capacity per Year of Week Production (six-day Curies) MNR LEU 1500 Project is seeking funding. (McMaster University, Canada) RIAR (Russian HEU 800-2000 2015 The facility includes three reactors. Federation) Two of which will produce Mo-99, with the third being a back-up. Currently in Phase 2 of development. INR, Pitesti LEU 900 2015 Proposal (Romania) FRM-II LEU 1950 2016 Pending LEU target design (Germany) approval. Coqui (United LEU 7000 2017 Project is seeking funding. States) BMR (Brazil) LEU 1000 2018 Project is in preliminary design stage. RA-10 LEU 200 2019 Project is in preliminary design (Argentina) stage. PALLAS LEU 7300 2023 Project is in preliminary design (Netherlands) stage. Project is also seeking funding. SAFARI-II LEU 3000 2026 Feasibility study for this project is (South Africa) underway.

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A.9 New Approaches in Diagnostic Nuclear Medicine

Going into the future, there may be a number of accelerators and nuclear-based technologies that could play a potential role in providing a stable supply of Mo-99. In addition, there are a variety of new and emerging medical imaging techniques that could possibly bypass the need for nuclear reactor based medical isotopes. Positron Emission

Tomography – Computed Tomography has already been successful in this regard.

However, there is no guarantee that any new technology will receive clinical acceptance even though it may be commercially viable. Cost, ease of use, facilities for the production and transportation may be some of the determinants [81].

Other means of producing Mo-99 include photo-fission of U-235, neutron activation of Mo-98, and photo neutron interactions of Mo-100. Even before the 2007 crisis, TRIUMF based in Vancouver, Canada, proposed a plan to produce Mo-99 by photon fission of U-238 by using photons from an electron accelerator [82]. This method of production yields low quantities of Mo-99, which requires multiple units to supply the world's demands.

Construction of new reactors or conversion of existing reactors as well as possible use of accelerators to meet increasing demands has been the focus of the medical isotope industry in recent years, including the use of alternate radionuclides and medical imaging techniques ([2], [8], [11], [81], [83], [84]).

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Appendix B – Materials, Lattice Specifications and Important

Parameters for 37-Element CANDU Fuel Bundle Calculations

Materials, Lattice Specifications and Value Other Important Parameters

Initial Uranium Composition Weight Percentage Natural UO2 U-235 0.711% U-238 99.289% Enriched UO2/U-metal U-235 19.50% U-238 80.50% Depleted UO2/U-metal U-235 0.200% U-238 99.8% UO2 fuel density 10.60 g/cm3 U-metal fuel density 18.95 g/cm3 Fuel temperature 1155 K Element radius 0.6075 cm U-metal fuel element radius 0.4266 cm Element length/bundle length 49.53 cm Number of fuel pins 37 Inner fuel ring radius (6) 1.4885 cm Middle fuel ring radius (12) 2.8755 cm Outer fuel ring radius (18) 4.3305 cm Cladding material Zircaloy Cladding radius 0.6540 cm Pressure tube Inner radius 5.1689 cm Outer radius 5.6032 Calandria tube Zircaloy Inner radius 6.4478 cm Outer radius 6.5875 cm Coolant D2O Atom purity 99.75 % Density 0.8360 g/cm3 Temperature 549 K Moderator D2O Atom purity 99.91 % Density 1.083 g/cm3 Temperature 346 K

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Fuel channel square pitch 28.575 cm Approximate burnup 906.62 MWd/MgU Mo-99 fraction in fission products 6.1% Mo-99 decay constant (λ) 0.252 d-1 Mo-99 atomic weight 99.91 g/mol

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Appendix C – Initial Estimates of Enriched Fuel Region Thickness and

Pin Radius for UO2 and U-Metal Fuel Designs Based on Uranium Mass

Balancing

Design 1

Fuel Pellet Radius = Rf = 0.6075cm

Fuel pin length = Lf = 49.5cm

Assumptions:

 The isotopic composition of Uranium includes only U-235 and U-238 isotopes. Other uranium isotopes (U-234, U-236, etc.) are ignored.  Weight percentage of U-235 in natural uranium, rnat,U = 0.71%  Weight percentage of U-235 in enriched uranium, renr,U = 19.5%  Weight percentage of U-235 in depleted uranium, rdep,U = 0.2%  Density of UO2 will remain the same irrespective of the enrichment, ρnat,U = ρdep,U = ρenr,U = 10.6 g/cm3

Atomic weight of enriched Uranium, MU, is:

1 r r r 1 r  U 235  U 238  U 235  U 235 M M M M M U U 235 U 238 U 235 U 238

Atomic weight of UO2 = MU  2*MO16, therefore:

Mass of U-235 in CANDU-6 fuel pin is:

2 MU nat mnat,U-235 = Rf Lf nat,U rnat,U MU nat  2*MO16

Mass of U-238 in CANDU-6 fuel pin is:

2 MU nat mnat,U-238 = Rf Lf nat,U (1 rnat,U ) MU nat  2*MO16

In Design 1, the enriched UO2 fuel region is inscribed inside the depleted uranium annulus. The mass of U-235 in the enriched fuel pin is therefore:

2 MU enr m’enr,U-235 = R'enrf Lf enr,U renr,U MU enr  2*MO16

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The mass of U-235 in depleted uranium annulus is:

2 2 MU dep m’dep,U-235 =  (Rf  R'enrf )Lf dep,U rdep,U MU dep  2*MO16

To calculate the radius of the enriched fuel layer in Design 1, a simple mass balance relation can be formulated based on the mass of U-235 in the reference CANDU-6 and Design 1 fuel pins.

mnat,U-235 = m’enr, U-235 + m’dep, U-235

2 MU nat 2 MU enr Rf Lf nat,U rnat,U  R'enrf Lf enr,U renr,U  MU nat  2* MO16 MU enr  2* M O16

2 2 MU dep  (Rf  R'enrf )Lf dep,U rdep,U MU dep  2* M O16

The above equation can be simplified to:

2 2 2 2 Rf nat,U nat,U rnat,U  R'enrf enr,U enr,U renr,U  (Rf  R'enrf )dep,U dep,U rdep,U

2 2 R'enrf dep,U dep,U rdep,U  R'enrf enr,U enr,U renr,U  (i) 2 2 R f dep,U dep,U rdep,U  R f nat,U nat,U rnat,U

where,

1  rnat,U 1 rnat,U     MU nat  MU 235 MU 238  nat,U   1 MU nat  2* M O16  r 1 r   nat,U nat,U      2* M O16  MU 235 MU 238 

1  rdep,U 1 rdep,U     MU dep  MU 235 MU 238  dep,U   1 MU dep  2*M O16  r 1 r   dep,U dep,U      2*M O16  MU 235 MU 238 

1  renr,U 1 renr,U     MU enr  MU 235 MU 238  enr,U   1 MU enr  2*M O16  r 1 r   enr,U enr,U      2*M O16  MU 235 MU 238 

Eq. (i) then becomes:

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2 2 R f dep,U dep,U rdep,U  nat,U nat,U rnat,U  Renrf  dep,U dep,U rdep,U  enr,U enr,U renr,U

2 Rf dep,U dep,U rdep,U  nat,U nat,U rnat,U  Renrf  (ii) dep,U dep,U rdep,U  enr,U enr,U renr,U

Assuming the densities do not change for different enrichments:

enr,U  dep,U  nat,U

Eq. (ii) can be simplified to:

2 R f dep,U rdep,U  nat,U rnat,U  Renrf  dep,U rdep,U  enr,U renr,U where,

1 1  rnat,U 1 rnat,U   0.71% 1 0.71%         MU 235 MU 238   235.044 238.051  nat,U  1  1  r 1 r   0.71% 1 0.71%   nat,U  nat,U   2*M     2*15.994   O16 235.044 238.051  MU 235 MU 238   

nat,U  0.8815

1 1  rdep,U 1 rdep,U   0.2% 1 0.2%         MU 235 MU 238   235.044 238.051 dep,U  1  1  r 1 r   0.2% 1 0.2%   dep,U  dep,U   2*M     2*15.994   O16 235.044 238.051  MU 235 MU 238   

dep,U  0.8815

1 1  renr,U 1 renr,U   19.5% 119.5%         MU 235 MU 238   235.044 238.051  enr,U  1  1  r 1 r   19.5% 119.5%   enr,U  enr,U   2*M     2*15.994   O16 235.044 238.051  MU 235 MU 238   

enr,U  0.8813

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Therefore,

0.60752 0.882*0.002  0.882*0.0071 R  enrf 0.882*0.002  0.881*0.195

Renrf = 0.098 cm ≅ 0.1 cm

Design 2

In Design 2, the depleted UO2 fuel region is inscribed inside a thin enriched fuel annulus. The mass of U-235 in the depleted uranium pin is:

2 MU dep mdep,U-235 = Rdepf Lf dep,U rdep,U MU dep  2*MO16

The mass of U-235 in the enriched fuel annulus is:

2 2 MU enr menr,U-235 =  (Rf  Rdepf )Lf enr,U renr,U MU enr  2*MO16

Again, to calculate the thickness of the thin enriched fuel layer in Design 2, a simple mass balance relation can be formulated based on the mass of U-235 in the reference CANDU-6 and Design 2 fuel pins.

mnat,U-235 = mdep, U-235 + menr, U-235

2 MU nat 2 MU dep R f L f nat,U rnat,U  Rdepf L f dep,U rdep,U  MU nat  2*M O16 MU dep  2*M O16

2 2 MU enr  (R f  Rdepf )L f enr,U renr,U MU enr  2*M O16

Based on the previous terminology for Aenr,U, Adep,U and Anat,U, the above equation can be simplified to:

2 2 2 2 Rf Lf nat,U nat,U rnat,U  Rdepf Lf dep,U dep,U rdep,U (Rf  Rdepf )Lf enr,U enr,U renr,U

2 2 2 2 Rf nat,U nat,U rnat,U  Rdepf dep,U dep,U rdep,U  (Rf  Rdepf )enr,U enr,U renr,U

2 2 2 2 Rdepf enr,U enr,U renr,U  Rdepf dep,U dep,U rdep,U  Rf enr,U enr,U renr,U  Rf nat,U nat,U rnat,U

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Separating Rdepf to one side gives:

2 2 R f enr,U enr,U renr,U  nat,U nat,U rnat,U  Rdepf  enr,U enr,U renr,U  dep,U dep,U rdep,U

2 R f enr,U enr,U renr,U  nat,U nat,U rnat,U  Rdepf  enr,U enr,U renr,U  dep,U dep,U rdep,U (iii)

Again, assuming the densities do not change for different enrichments:

enr,U  dep,U  nat,U

Eq. (iii) simplifies to:

2 R f enr,U renr,U  nat,U rnat,U  Rdepf  enr,U renr,U  dep,U rdep,U

Evaluating the above equation gives:

0.60752 cm 2 0.8813*0.195  0.8815*0.0071 R  depf 0.8813*0.195  0.8815*0.002

Rdepf  0.5994cm  0.600cm

Thickness of the enriched layer then becomes:

tenrf =0.6075 cm – 0.6 cm = 0.0075 cm

Design 3

Assumptions:

Density of uranium metal, ρdep,U = ρenr,U = 18.95 g/cm3

In Design 3, the depleted U-metal fuel region is inscribed inside a thin enriched U-metal fuel annulus. Furthermore, uranium metal is used in the modified fuel bundle for both depleted and enriched regions. The mass of U-235 in the depleted uranium pin is:

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2 MU dep mdep,U-235 = Rdepf Lf dep,U rdep,U MU dep

The mass U-238 in the depleted uranium pin is:

2 MU dep mdep,U-238 = Rdepf Lf dep,U (1 rdep,U ) MU dep

The mass of U-235 in the enriched fuel annulus is:

2 2 MU enr menr,U-235 =  (Rm  Rdepf )Lf enr,U renr,U MU enr

The mass of U-238 in the enriched fuel annulus is:

2 2 MU enr menr,U-238 =  (Rm  Rdepf )Lf enr,U (1 renr,U ) MU enr

where Rm is the new fuel pellet radius. Again, to calculate the thickness of the thin enriched U- metal fuel layer in Design 3, a simple mass balance relation can be formulated based on the mass of U-235 in the reference CANDU-6 and Design 3 fuel pins.

mnat,U-235 = mdep, U-235 + menr, U-235

2 MU nat 2 MU dep R f L f nat,U rnat,U  Rdepf L f dep,U rdep,U  MU nat  2*M O16 MU dep

2 2 MU enr  (Rm  Rdepf )L f enr,U renr,U MU enr

Based on the previous terminology for Anat,U, the above equation can be simplified to:

R2 L   r  R2 L  r  (R2  R2 )L  r f f nat,U nat,U nat,U depf f dep,U dep,U m depf f enr,U enr,U

The above equation can be further simplified by multiplying both sides by πLf.

2 2 2 2 R f nat,U nat,U rnat,U  Rdepf dep,U rdep,U  (Rm  Rdepf )enr,U renr,U

2 2 2 Rdepf (dep,U rdep,U  enr,U renr,U )  Rm enr,U renr,U  Rf nat,U nat,U rnat,U (iv)

Similarly, a simple mass balance relation can be formulated based on the mass of U-238 in the reference CANDU-6 and Design 3 fuel pins.

mnat,U-238 = mdep, U-238 + menr, U-238

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2 MU nat 2 MU dep Rf Lf nat,U (1 rnat,U ) =Rdepf L f dep,U (1 rdep,U ) + MU nat  2*MO16 MU dep

2 2 MU enr (Rm  Rdepf )Lf enr,U (1 renr,U ) MU enr

2 2 2 2 Rf Lf nat,U nat,U (1 rnat,U ) Rdepf Lf dep,U (1 rdep,U ) (Rm  Rdepf )Lf enr,U (1 renr,U )

The above equation can be further simplified by multiplying both sides by πLf.

2 2 2 2 Rf nat,U nat,U (1 rnat,U )  Rdepf dep,U (1 rdep,U )  (Rm  Rdepf )enr,U (1 renr,U )

2 2 Rdepf [dep,U (1 rdep,U )  enr,U (1 renr,U )] Rm enr,U (1 renr,U )  (v) 2 R f nat,U nat,U (1 rnat,U )

Eq. (iv) and Eq. (v) can be solved for the two unknown Rdepf and Rm by multiplying Eq. (iv) by

(1 renr,U ) and subtracting it from Eq. (v). This gives: renr,U

2 (1 renr,U ) 2 Rdepf (dep,U rdep,U  enr,U renr,U )  Rm enr,U (1 renr,U )  renr,U (vi) 2 (1 renr,U ) R f nat,U nat,U rnat,U renr,U

Subtracting Eq. (v) from Eq. (vii) gives:

2 (1 renr,U ) 2 Rdepf (dep,U rdep,U  enr,U renr,U )  Rdepf [dep,U (1 rdep,U )  enr,U (1 renr,U )]  renr,U

2 (1 renr,U ) 2 R f nat,U nat,U rnat,U  R f nat,U nat,U (1 rnat,U ) renr,U

 (1 r )  R2   r enr,U   (1 r )   (1 r )   (1 r )  depf  dep,U dep,U enr,U enr,U dep,U dep,U enr,U enr,U   renr,U 

 (1 r )  R2    (r enr,U  (1 r )) f  nat,U nat,U nat,U nat,U   renr,U 

Page | 159

  (1 r )  2   enr,U  Rdepf dep,U rdep,U  (1 rdep,U )   r    enr,U 

  (1 r )  2   enr,U  R f nat,U nat,U rnat,U  (1 rnat,U )  r    enr,U 

  (1 r )  2   enr,U  R f nat,U nat,U rnat,U  (1 rnat,U )   r  2   enr,U  Rdepf    (1 r )    enr,U  dep,U rdep,U  (1 rdep,U )  r    enr,U 

  (1 r )  2   enr,U  R f nat,U nat,U rnat,U  (1 rnat,U )  r    enr,U  Rdepf    (1 r )    enr,U  dep,U rdep,U  (1 rdep,U )  r    enr,U 

Evaluating the above equation gives:

2   (1 0.195)  0.6075 10.6*0.88150.0071  (1 0.0071)   0.195  Rdepf     (1 0.195)  18.950.002  (1 0.002)   0.195   3.3229  0.1772 18.7556

Rdepf  0.4209 cm

Thickness of the depleted Uranium metal layer would be 0.4209 cm. Substituting this value back into Eq. (iv) gives:

2 2 2 Rdepf (dep,U rdep,U  enr,U renr,U )  Rmenr,U renr,U  Rf nat,U nat,U rnat,U

2 2 2 Rm enr,U renr,U  Rf nat,U nat,U rnat,U  Rdepf (dep,U rdep,U  enr,U renr,U )

2 2 2 R f nat,U nat,U rnat,U  Rdepf (dep,U rdep,U  enr,U renr,U ) Rm  enr,U renr,U

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2 2 Rf nat,U nat,U rnat,U  Rdepf (dep,U rdep,U  enr,U renr,U ) Rm  enr,U renr,U

Evaluating the above equation gives:

0.60752 *10.6*0.8815*0.0071 0.42092 *(18.95*0.002 18.95*0.195) R  m 18.95*0.195

0.02448  (0.6479) R   0.18196 m 3.6953

Rm  0.4266 cm

Thickness of the enriched layer then becomes:

tenrf =0.4266 cm – 0.4209 cm = 0.00567 cm

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