1.2 Organization of the Work . . . . 3

I INTRODUCTION 1

1 General Introduction 2

1.1 Context . . . . 2

1.2 Organization of the Work . . . . 3

1.3 Main Achievements . . . . 4

2 Radioactive Waste 5 2.1 Introduction . . . . 5

2.2 Definition . . . . 5

2.3 Origin . . . . 5

2.3.1 Introduction . . . . 5

2.3.2 Waste from the Nuclear Fuel Cycle . . . . 6

2.3.3 Waste from the Production and Use of Radionuclides . . . . 6

2.3.4 Waste from the Decommissioning of Nuclear Facilities . . . . 7

2.3.5 Waste Not Deriving from Nuclear Activities . . . . 7

2.4 International Classification . . . . 7

2.5 Belgian Situation . . . . 8

2.5.1 Classification . . . . 8

2.5.2 Description . . . . 10

2.5.3 Belgian Inventory . . . . 12

2.6 HLW Management . . . . 14

2.6.1 Introduction . . . . 14

2.6.2 HLW Management Options . . . . 14

2.6.3 HLW Repository Characterization . . . . 16

2.6.4 HLW-SFA Repository Example . . . . 17

2.7 Conclusions . . . . 20

3 Nuclear Criticality Risk 21 3.1 Introduction . . . . 21

3.2 Nuclear Fission Reactions . . . . 21

3.2.1 Isotopes . . . . 21

3.2.2 Examples . . . . 22

3.2.3 Fission Products . . . . 23

3.2.4 Multiplication Factor . . . . 24

3.2.5 Feedback Mechanisms . . . . 26

3.3 Risk . . . . 27

3.3.1 Definitions . . . . 27

3.3.2 Nuclear Risk . . . . 27

Contents

3.3.3 Radiological Consequences . . . . 28

3.3.4 Nuclear Criticality Risk . . . . 29

3.4 Conclusions . . . . 31

II SCENARIOS DEVELOPMENT 32 4 Scenarios Development Procedures 33 4.1 Introduction . . . . 33

4.2 Definitions . . . . 33

4.2.1 Features, Events, and Processes . . . . 33

4.2.2 Scenarios . . . . 34

4.2.3 Scenarios Development . . . . 35

4.3 Aims of Scenarios Development . . . . 35

4.4 The Bottom-Up Procedure: The Sandia/NRC Procedure . . . . 37

4.4.1 Introduction . . . . 37

4.4.2 Identification of FEPs . . . . 37

4.4.3 Classification of FEPs . . . . 38

4.4.4 Screening of FEPs . . . . 38

4.4.5 Scenarios Construction . . . . 38

4.4.6 Screening of Scenarios . . . . 40

4.4.7 Use of Expert Judgment in Scenarios Selection Procedure . . . . 40

4.5 The Top-Down Procedure: The Joint SKI/SKB Investigations . . . . 41

4.5.1 Introduction . . . . 41

4.5.2 System Elements Identification . . . . 41

4.5.3 Element States Identification . . . . 41

4.5.4 Incompatible States Identification and Screening . . . . 41

4.5.5 Scenarios Formation and Final Screening . . . . 42

4.6 Conclusions . . . . 42

5 Criticality Scenarios Development: Examples 44 5.1 Introduction . . . . 44

5.2 Yucca Mountain Repository Project (USA) . . . . 44

5.2.1 Introduction . . . . 44

5.2.2 U.S. Design . . . . 44

5.2.3 U.S. Waste . . . . 46

5.2.4 U.S. Waste Packages . . . . 46

5.2.5 U.S. Inventory . . . . 49

5.2.6 First Approach to Criticality Scenarios Development . . . . 49

5.2.7 In-Package Critical Configurations . . . . 50

5.2.8 Scenarios Classification . . . . 53

5.2.9 Conclusions . . . . 54

5.3 KBS-3 Repository Project (Sweden) . . . . 55

5.3.1 Introduction . . . . 55

5.3.2 KBS-3 Repository Design . . . . 55

5.3.3 Swedish Spent Nuclear Fuel . . . . 55

5.3.4 Spent Fuel Canisters . . . . 57

5.3.5 Swedish Inventory . . . . 58

5.3.6 Plutonium Criticality Scenarios . . . . 58

5.3.7 Uranium Criticality Scenarios . . . . 58

5.3.8 Conclusions . . . . 59

5.4 Conclusions . . . . 59

6 In-Package Criticality Scenarios Development: SAFIR2 60

6.1 Introduction . . . . 60

6.2 SAFIR2 Repository Design . . . . 60

6.2.1 Introduction . . . . 60

6.2.2 ZAGALC Waste Repository Design . . . . 61

6.2.3 ZAGALS Waste Repository Designs . . . . 62

6.3 Comparison Between Yucca Mountain and SAFIR2 Designs . . . . 63

6.3.1 Introduction . . . . 63

6.3.2 Comparative Approach . . . . 63

6.3.3 Disruptive FEPs Identification . . . . 64

6.4 Bottom-Up Scenarios Development . . . . 65

6.4.1 Introduction . . . . 65

6.4.2 FEPs Listing and Screening . . . . 65

6.4.3 Scenarios Formation . . . . 66

6.4.4 Scenarios Screening . . . . 68

6.4.5 Bottom-Up Criticality Scenarios List . . . . 69

6.5 Top-Down Scenarios Development . . . . 71

6.5.1 Introduction . . . . 71

6.5.2 System and Element States . . . . 71

6.5.3 Combination of System States and First Screening . . . . 72

6.5.4 Second Screening and Top-Down Criticality Scenarios List . . . . 75

6.6 Conclusions . . . . 75

7 In-Package Criticality Scenarios Development: Supercontainer Designs 76 7.1 Introduction . . . . 76

7.2 Supercontainer 1 . . . . 76

7.2.1 Introduction . . . . 76

7.2.2 Design . . . . 76

7.2.3 Bottom-Up Scenarios . . . . 77

7.2.4 Top-Down Scenarios . . . . 79

7.2.5 Conclusions . . . . 80

7.3 Supercontainer 2 . . . . 81

7.3.1 Introduction . . . . 81

7.3.2 Design . . . . 81

7.3.3 Bottom-Up Scenarios . . . . 81

7.3.4 Top-Down Scenarios . . . . 83

7.3.5 Conclusions . . . . 84

7.4 Supercontainer 3 . . . . 84

7.4.1 Introduction . . . . 84

7.4.2 Design . . . . 84

7.4.3 Bottom-Up Scenarios . . . . 84

7.4.4 Top-Down Scenarios . . . . 85

7.4.5 Conclusions . . . . 86

7.5 Conclusions . . . . 86

III CRITICALITY CALCULATIONS 87 8 The MCNP Computer Code 88 8.1 Introduction . . . . 88

8.2 Monte Carlo Methods . . . . 88

8.3 Introduction to MCNP Features . . . . 89

8.3.1 Nuclear Data and Reactions . . . . 89

Contents

8.3.2 Neutron Thermal S(α, β) Tables . . . . 89

8.3.3 Source Specification . . . . 89

8.3.4 Output . . . . 89

8.3.5 Estimation of Monte Carlo Errors . . . . 90

8.3.6 Variance Reduction . . . . 90

8.3.7 Tally Choice . . . . 90

8.3.8 Nonanalog Monte Carlo . . . . 90

8.3.9 Variance Reduction Tools in MCNP . . . . 91

8.3.10 MCNP Geometry . . . . 91

8.3.11 MCNP Input . . . . 92

8.3.12 MCNP Plotter . . . . 92

8.4 Criticality Calculations . . . . 92

8.4.1 Introduction . . . . 92

8.4.2 Criticality Program Flow . . . . 92

8.4.3 Estimation of k eff Confidence Intervals . . . . 93

8.4.4 Recommendation for Making a Good Criticality Calculation . . . . 96

8.5 Conclusions . . . . 97

9 In-Package Criticality Calculations: SAFIR2 99 9.1 Introduction . . . . 99

9.2 Modelling and Hypotheses . . . 102

9.2.1 FAs . . . 102

9.2.2 Fuels . . . 102

9.2.3 Canisters . . . 102

9.2.4 Disposal Gallery and Host Rock . . . 103

9.3 Results . . . 103

9.3.1 Acceptation Criterium . . . 103

9.3.2 Comparison with Previous Results . . . 103

9.3.3 Geometry Simplification . . . 104

9.3.4 Water Moderation Effects . . . 106

9.3.5 FAs Geometry Alteration Effects . . . 106

9.3.6 Gallery Geometry Alteration Effects . . . 106

9.4 Conclusions . . . 107

10 In-Package Criticality Calculations: Supercontainer 1 112 10.1 Introduction . . . 112

10.2 Modelling and Hypotheses . . . 112

10.2.1 FAs . . . 112

10.2.2 Fuels . . . 113

10.2.3 Overpacks . . . 113

10.2.4 Supercontainer . . . 113

10.2.5 Disposal Gallery and Host Rock . . . 114

10.3 Results . . . 115

10.3.1 Water Moderation and Burn-up Effects . . . 115

10.3.2 SFAs Geometry Alteration Effects . . . 117

10.3.3 Supercontainer Internal Geometry Variations Effects . . . 121

10.4 Comparison with Scenarios . . . 125

10.5 Conclusions . . . 126

11 In-Package Criticality Calculations: Supercontainer 2 127

11.1 Introduction . . . 127

11.2 Modelling and Hypotheses . . . 127

11.2.1 FAs . . . 127

11.2.2 Fuel . . . 128

11.2.3 Overpack . . . 128

11.2.4 Supercontainer . . . 129

11.2.5 Disposal Gallery and Host Rock . . . 129

11.2.6 Additional Informations . . . 130

11.3 Results . . . 132

11.3.1 Introduction . . . 132

11.3.2 Overpack Water Density Variation . . . 132

11.3.3 Overpack Water Volume Fraction Variation . . . 135

11.3.4 Influence of the Overpack Material . . . 140

11.4 Comparison with Scenarios . . . 141

11.5 Conclusions . . . 142

12 In-Package Criticality Calculations: Supercontainer 3 143 12.1 Introduction . . . 143

12.2 Modelling and Hypotheses . . . 144

12.2.1 FAs . . . 144

12.2.2 Fuels . . . 144

12.2.3 Overpack . . . 144

12.2.4 Supercontainer . . . 145

12.2.5 Disposal Gallery and Host Rock . . . 145

12.2.6 Additional Informations . . . 145

12.3 Results . . . 148

12.3.1 Introduction . . . 148

12.3.2 SC3 Internal Geometry Variation . . . 148

12.3.3 FAs Geometry Variation . . . 151

12.3.4 Evolution in Time . . . 157

12.4 Comparison with Scenarios . . . 182

12.5 Conclusions . . . 182

IV CONCLUSIONS AND PERSPECTIVES 183 13 General Conclusions and Perspectives 184 13.1 Context . . . 184

13.2 Scenarios Development . . . 185

13.3 Criticality Calculations . . . 186

13.4 Consequences . . . 186

13.5 Perspectives . . . 187

APPENDICES 188 A Bowman and Venneri 189 A.1 Introduction . . . 189

A.2 Studied Configurations . . . 189

A.2.1 Introduction . . . 189

A.2.2 Case A: Water Ingress in TFMs and Rock Systems (Negative Feedback) . 190

A.2.3 Case B: TFMs Migration to Wet Rock Systems (Negative Feedback) . . . 190

Contents

A.2.4 Case C: TFMs Migration to wet rock Systems (Positive Feedback) . . . . 191

A.2.5 Case D: TFMs Migration to Wet Rock Systems (Positive Feedback) . . . 191

A.2.6 Case E: Drying-Out of TFMs Deposits in Rock (Positive Feedback) . . . 191

A.2.7 Case F: Small Volume Systems (Positive Feedback) . . . 191

A.3 Summary of the Results . . . 191

A.4 Conclusions . . . 192

B The Oklo Natural Fission Reactors 194 B.1 Introduction . . . 194

B.2 Situation . . . 194

B.3 The Oklo Phenomenon . . . 194

B.3.1 Uranium Accumulation at Oklo . . . 194

B.3.2 Criticality at Oklo . . . 195

B.3.3 Cyclic Time Evolution at Oklo . . . 195

B.4 Conclusions . . . 196

C Yucca Mountain Out-Package Criticality Scenarios 197 C.1 Introduction . . . 197

C.2 Near-Field Critical Configurations . . . 197

C.2.1 Failure of the Waste Package Bottom after Failure of the Top . . . 197

C.2.2 Failure of the Waste Package Bottom First . . . 198

C.3 Far-Field Critical Configurations . . . 201

C.3.1 Unsaturated Zone . . . 201

C.3.2 Saturated Zone . . . 202

C.4 Conclusions . . . 203

D NEA FEPs Database Screening 205 D.1 Introduction . . . 205

D.2 Assessment Basis (IFEP 0) . . . 206

D.3 External Factors (IFEP 1) . . . 208

D.3.1 Repository Issues (IFEP 1.1) . . . 208

D.3.2 Geological Processes and Effects (IFEP 1.2) . . . 210

D.3.3 Climatic Processes and Effects (IFEP 1.3) . . . 211

D.3.4 Future Human Actions (Active) (IFEP 1.4) . . . 213

D.3.5 Other (IFEP 1.5) . . . 215

D.4 Disposal System Domain: Environmental Factors (IFEP 2) . . . 215

D.4.1 Wastes and Engineered Features (IFEP 2.1) . . . 215

D.4.2 Geological Environment (IFEP 2.2) . . . 222

D.4.3 Surface Environment (IFEP 2.3) . . . 225

D.4.4 Human Behavior (IFEP 2.4) . . . 226

D.5 Radionuclide/Contaminant Factors (IFEP 3) . . . 228

D.5.1 Contaminant Characteristics (IFEP 3.1) . . . 228

D.5.2 Contaminant Release/Migration Factors (IFEP 3.2) . . . 229

D.5.3 Exposure Factors (IFEP 3.3) . . . 231

D.6 Conclusions . . . 232

E MCNP Input File Example 233 E.1 Introduction . . . 233

E.2 Listing of the Input File Example . . . 233

E.3 Description of the Input File Example . . . 237

E.4 Figures . . . 238

F Atomic Densities for MCNP Input 245

F.1 Introduction . . . 245

F.2 Fuel Assemblies . . . 245

F.2.1 UOX Fuels . . . 245

F.2.2 MOX Fuel . . . 246

F.2.3 Zircalloy Cladding . . . 246

F.3 Sand Filling . . . 246

F.4 Canister . . . 247

F.5 Supercontainer . . . 247

F.6 Gallery Walls . . . 247

F.7 Boom Clay . . . 248

Bibliography 249

List of Figures

2.1 A typical (Westinghouse) 17 × 17 FA. . . . 11

2.2 The KBS-3 multi-barrier design. . . . 18

2.3 The multi-barrier concept. . . . 19

3.1 Example of the thermal fission reaction of

U . . . . 22

3.2 Fission products yields for the thermal fission reaction of

U . . . . 23

3.3 Typical neutron fate in a reactor. . . . 24

4.1 Sandia scenarios selection procedure. . . . 37

4.2 Sandia scenarios formation (left) and screening (right). . . . 39

4.3 Identification of the incompatible states. . . . 42

5.1 General presentation of the Yucca Mountain site. . . . 45

5.2 Schematic view of different U.S. waste packages and the engineered barriers in a disposal gallery. . . . 47

5.3 Detailed waste package for 21 PWR uncanistered fuel assemblies. . . . 48

5.4 Top of the criticality FEPs tree. . . . 50

5.5 The criticality FEPs tree: water accumulates in waste package. . . . 51

5.6 The criticality FEPs tree: absorbers dissolution. . . . 52

5.7 The criticality FEPs tree: waste package internal structures degrade first. . . . . 53

5.8 The criticality FEPs tree: water flows through the waste package. . . . 54

5.9 The Svea 100 BWR assembly comprises four 5 × 5 arrays of pins with a 2.5 mm gap between adjacent arrays. . . . 56

5.10 F 17 × 17 PWR assembly containing no burnable poison. . . . 56

5.11 F 17 × 17 PWR assembly containing burnable poison. . . . 56

5.12 Canister design for 12 BWR SFAs. . . . 57

5.13 Canister design for 4 PWR SFAs. . . . 57

6.1 Schematic view of the SAFIR2 ZAGALC waste repository design. . . . 61

6.2 The SAFIR2 reference design for ZAGALS waste (gallery cross section). . . . 62

6.3 Bottom-up scenarios formation: initial criticality FEPs tree. . . . 67

6.4 Bottom-up scenarios first screening: incompatible combinations between FEPs are screened off. . . . 70

6.5 The 5 components of the system and their respective states. . . . 72

6.6 Incompatible system states are linked by dotted lines. . . . 73

7.1 The SC1 design (vertical cross section of a disposal gallery). . . . 77

7.2 Upper part of the SC1 in-package criticality FEPs Tree. FEPs 1, 2, and 3 are assumed to have occurred. . . . 78

7.3 The SC2 overpack holding four fuel assemblies and its cross-shaped separator. . . 81

7.4 Upper part of the SC2 in-package criticality FEPs Tree. FEPs 1, 2, and 7 are

assumed to have occurred. . . . 82

7.5 The SC3 full metal overpack of holding 4 fuel assemblies. . . . 85

9.1 The SAFIR2 reference design. . . 100

9.2 The SAFIR2 variant design . . . 101

9.3 Influence of moderation inside the canisters. . . 108

9.4 Influence of the fuel assemblies geometry (reference design) [nominal distance between the fuel rods centres = 1.26 cm]. . . 109

9.5 Influence of the fuel assemblies geometry (variant design) [nominal distance be- tween the fuel rods centres = 1.26 cm]. . . 110

9.6 Influence of the geometry of the disposal gallery (reference design) [nominal dis- tance between the disposal tubes and the gallery centres = 45 cm]. . . 111

10.1 The SC1 design (vertical cross section of a disposal gallery). . . 113

10.2 Influence of moderation inside the overpacks. . . 116

10.3 Influence of the FAs geometry (0 % vol. water inside the overpacks) [nominal distance between the fuel rods centres = 1.26 cm]. . . 118

10.4 Influence of the FAs geometry (40 % vol. water inside the overpacks) [nominal distance between the fuel rods centres = 1.26 cm]. . . 119

10.5 Influence of the FAs geometry (100 % vol. water inside the overpacks) [nominal distance between the fuel rods centres = 1.26 cm]. . . 120

10.6 Influence of the supercontainer geometry (0 % vol. water inside the overpacks) [nominal distance between the overpacks = 10 cm]. . . 122

10.7 Influence of the supercontainer geometry (40 % vol. water inside the overpacks) [nominal distance between the overpacks = 10 cm]. . . 123

10.8 Influence of the supercontainer geometry (100 % vol. water inside the overpacks) [nominal distance between the overpacks = 10 cm]. . . 124

11.1 The SC2 overpack holding four fuel assemblies and its cross-shaped separator. . . 129

11.2 MCNP cross section of a supercontainer in a disposal gallery. . . 131

12.1 The SC3 full metal overpack of holding 4 fuel assemblies. . . 143

12.2 Influence of the cross separator geometry (additional cooling time= 0 year / water density in overpack = 1.00) [nominal cross separator thickness = 8 cm]. . . 149

12.3 Influence of the burn-up (additional cooling time = 0 year / water density in overpack = 1.00 / distance between fuel rods = 1.26 cm). . . 150

12.4 Influence of the FAs geometry (additional cooling time = 0 year / water density in overpack = 0.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 152

12.5 Influence of the FAs geometry (additional cooling time = 0 year / water density in overpack = 0.25) [nominal distance between the fuel rods centres = 1.26 cm]. . 153

12.6 Influence of the FAs geometry (additional cooling time = 0 year / water density in overpack = 0.50) [nominal distance between the fuel rods centres = 1.26 cm]. . 154

12.7 Influence of the FAs geometry (additional cooling time = 0 year / water density in overpack = 0.75) [nominal distance between the fuel rods centres = 1.26 cm]. . 155

12.8 Influence of the FAs geometry (additional cooling time = 0 year / water density in overpack = 1.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 156

12.9 Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 158

12.10Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 159

12.11Influence of the FAs geometry (additional cooling time = 10

years / water density

in overpack = 0.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 160

List of Figures

12.12Influence of the FAs geometry (additional cooling time = 10

years / water density

in overpack = 0.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 161

12.13Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.25) [nominal distance between the fuel rods centres = 1.26 cm]. . 164

12.14Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.50) [nominal distance between the fuel rods centres = 1.26 cm]. . 165

12.15Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.75) [nominal distance between the fuel rods centres = 1.26 cm]. . 166

12.16Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 1.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 167

12.17Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.25) [nominal distance between the fuel rods centres = 1.26 cm]. . 168

12.18Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.50) [nominal distance between the fuel rods centres = 1.26 cm]. . 169

12.19Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.75) [nominal distance between the fuel rods centres = 1.26 cm]. . 170

12.20Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 1.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 171

12.21Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.25) [nominal distance between the fuel rods centres = 1.26 cm]. . 172

12.22Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.50) [nominal distance between the fuel rods centres = 1.26 cm]. . 173

12.23Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.75) [nominal distance between the fuel rods centres = 1.26 cm]. . 174

12.24Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 1.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 175

12.25Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.25) [nominal distance between the fuel rods centres = 1.26 cm]. . 176

12.26Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.50) [nominal distance between the fuel rods centres = 1.26 cm]. . 177

12.27Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 0.75) [nominal distance between the fuel rods centres = 1.26 cm]. . 178

12.28Influence of the FAs geometry (additional cooling time = 10

years / water density in overpack = 1.00) [nominal distance between the fuel rods centres = 1.26 cm]. . 179

12.29Variation of k eff ± 2σ with time (water density in overpack = 1.00 / distance between the fuel rods centres = 1.26 cm). . . 180

12.30Evolution in time of the k eff (Swedish case. . . 181

A.1 Criticality curves for different radii in spherical geometries. . . 190

B.1 Schematic geological profile across the western margin of the Franceville Basin. . 195

B.2 Idealised cross section of a fossil reactor zone at Oklo. . . 196

C.1 The criticality tree: near-field scenarios. . . 198

C.2 The criticality tree: near-field scenarios. . . 199

C.3 The criticality tree: near-field scenarios. . . 200

C.4 The criticality tree: near-field scenarios. . . 200

C.5 The criticality tree: far-field scenarios. . . 202

C.6 The criticality tree: near-field scenarios. . . 203

C.7 The criticality tree: near-field scenarios. . . 204

E.1 Fuel, fuel rods, control and instrument tubes (cells). . . 239

E.3 Fuel assembly (cells). . . 241

E.4 Canisters inside the supercontainer (cells). . . 242

E.5 Gallery lateral cross section (cells). . . 243

E.6 Gallery vertical cross section (cells). . . 244

List of Tables

2.1 UOX fresh fuel assemblies characteristics. . . . 10

2.2 Typical 1450 days irradiated (45 GWd/tHM) UOX SFA radionuclide inventory. . 12

2.3 Typical 1450 days irradiated (45 GWd/tHM) MOX SFA radionuclide inventory. . 13

2.4 Belgian radioactive waste inventory. . . . 13

2.5 Number of SFAs foreseen for the Belgian repository. . . . 13

2.6 Composition of residues from reprocessing of 1,000 kg of SFAs. . . . 15

4.1 Illustration of consequences on the barrier states caused by individual FEPs. . . 42

5.1 Approximate inventories of U.S. nuclear waste destined for geological disposal and quantities planned for Yucca Mountain. . . . 49

6.1 First scenarios screening: incompatible system elements states are screened off. . 74

9.1 Atomic densities of the UOX and MOX fuels. . . 102

9.2 Reference design: UOX modelling validation. . . 104

9.3 Variant design: UOX modelling validation. . . . 104

9.4 Reference design: UOX geometry simplification. . . 105

9.5 Variant design: UOX geometry simplification. . . 105

9.6 Reference design: MOX geometry simplification. . . 105

9.7 Variant design: MOX geometry simplification. . . 105

10.1 Atomic densities (in 10

atom/m

) of the UOX and MOX fuels as a function of the burn-up. . . 114

11.1 Zircalloy-4 mass composition. . . 128

11.2 UOX fuel isotopic composition. . . 128

11.3 Overpack materials compositions and densities. . . 129

11.4 Void overpack. . . 133

11.5 Water density inside the overpack = 0.25 g/cm

. . . 133

11.6 Water density inside the overpack = 0.50 g/cm

. . . 133

11.7 Water density inside the overpack = 0.75 g/cm

. . . 134

11.8 Water density inside the overpack = 1.00 g/cm

. . . 134

11.9 Pure sand filled overpack (no water). . . 135

11.10Water volume fraction in overpack = 10 %. . . 136

11.11Water volume fraction in overpack = 20 %. . . 136

11.12Water volume fraction in overpack = 30 %. . . 137

11.13Water volume fraction in overpack = 40 %. . . 137

11.14Water volume fraction in overpack = 50 %. . . 137

11.15Water volume fraction in overpack = 60 %. . . 138

11.17Water volume fraction in overpack = 80 %. . . 138

11.18Water volume fraction in overpack = 90 %. . . 139

11.19Overpack material influence on k eff ± 2σ. . . 140

12.1 UOX fuel isotopic composition (additional cooling time = 0 years). . . 145

12.2 UOX fuel isotopic composition (additional cooling time = 10

years). . . 146

12.3 UOX fuel isotopic composition (additional cooling time = 10

years). . . 146

12.4 UOX fuel isotopic composition (additional cooling time = 10

years). . . 147

12.5 UOX fuel isotopic composition (additional cooling time = 10

years). . . 147

12.6 Isotopic contribution to k eff (additional cooling time = 0 year). . . 163

12.7 Isotopic contribution to k eff (additional cooling time = 10

years). . . 163

F.1 UOX fuels atomic densities composition in 10

atom barn

cm

. . . 246

F.2 MOX fuel atomic densities. . . 247

F.3 Stainless steel weight fractions and atomic densities. . . 247

F.4 Supercontainer concrete composition. . . 247

F.5 Supercontainer concrete atomic densities. . . 248

F.6 Gallery walls atomic densities. . . 248

F.7 Boom Clay weight composition. . . 248

F.8 Boom Clay atomic densities. . . 248