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Modeling Radionuclide Diffusion Using Moose a Multiscale, Multiphysics Platform Jonathon Gardner University of South Carolina

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Modeling Radionuclide Diffusion Using Moose a Multiscale, Multiphysics Platform Jonathon Gardner University of South Carolina University of South Carolina Scholar Commons Theses and Dissertations 2016 Modeling Radionuclide Diffusion Using Moose A Multiscale, Multiphysics Platform Jonathon Gardner University of South Carolina Follow this and additional works at: https://scholarcommons.sc.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Gardner, J.(2016). Modeling Radionuclide Diffusion Using Moose A Multiscale, Multiphysics Platform. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/3918 This Open Access Thesis is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. MODELING RADIONUCLIDE DIFFUSION USING MOOSE A MULTISCALE, MULTIPHYSICS PLATFORM by Jonathon Gardner Bachelor of Science Georgia College & State University, 2014 Submitted in Partial Fulfillment of the Requirements For the Degree of Master of Science in Mechanical Engineering College of Engineering and Computing University of South Carolina 2016 Accepted by: Travis W. Knight, Director of Thesis Kyle Brinkman, Reader Cheryl L. Addy, Vice Provost and Dean of the Graduate School c Copyright by Jonathon Gardner, 2016 All Rights Reserved. ii DEDICATION This thesis is dedicated to my wife Rachel Gardner and my family, for their constant encouragement and support. iii ACKNOWLEDGEMENTS Funding for this project is from the U.S. Department of Energy. This material is based upon work supported by the U.S. Department of Energy Office of Sci- ence, Office of Basic Energy Sciences and Office of Biological and Environmental Research under Award Number DE-SC-00012530. Great contributions to this project were made in the form of the review and instruction of Dr. Travis W. Knight, Dr. Elwyn Roberts, Dr. Brian Powell, Dr. Lindsay Shuller-Nickles, and Dr. Kyle Brinkman. Their instruction has helped focus and direct my research. I also express deep gratitude to Dr. Travis W. Knight for providing me with the opportunity, the means and the support to conduct this research. I would also like to thank my colleagues at the University of South Carolina; Aaren Rice, Ryan Preist, Donald Shurtliff, Kallie Metzger, Austin Freeman, and David Mason. At times, they have given me good insight and advice to improve and maintain my work. iv ABSTRACT Very durable ceramic waste forms have been proposed which offer long- term stability by binding certain radionuclides in their specific crystalline net- work. Moreover, multiple such ceramic phases can be tailored to contain specific radionuclides generated in the fuel cycle. Many such candidate ceramic forms are in the early stages of development with limited data. Modeling and simulation including modeling of diffusion can inform and provide direction to ongoing fab- rication and experimental efforts. Material properties important in modeling can be obtained through laboratory measurement where available and atomistic simu- lation. Since diffusion occurs over multiple scales and follows multiple pathways, multiscale modeling is important to capture the detailed behavior from different material phases and microstructures. In light of this, a MOOSE based application (TREX) has been developed to meet these conditions. Different kernel, material, and postprocessor objects have been created in TREX to model anisotropic multi- phase, multiscale, multipath diffusion, radionuclide decay , multiphase, multiscale thermal conduction and other physics. v TABLE OF CONTENTS DEDICATION . iii ACKNOWLEDGEMENTS . iv ABSTRACT . v LIST OF TABLES . viii LIST OF FIGURES . ix LIST OF ABBREVIATIONS . xiii CHAPTER 1: INTRODUCTION . 1 1.1 MOTIVATION . 1 1.2 OBJECTIVES . 1 CHAPTER 2: REVIEW OF LITERATURE . 2 2.1 WASTEFORMS . 2 2.2 MODELING SOFTWARE . 3 2.3 FINITE-ELEMENT METHOD . 4 2.4 DIFFUSION . 9 2.5 HEAT TRANSFER . 11 2.6 RADIONUCLIDE DECAY . 12 2.7 EFFECTIVE PROPERTIES . 14 CHAPTER 3: METHODOLOGY . 20 3.1 ADDED OBJECTS . 20 3.2 VALIDATING CASES . 32 CHAPTER 4: RESULTS . 62 CHAPTER 5: CONCLUSIONS . 90 vi 5.1 CONCLUSION . 90 5.2 FUTUREWORK . 90 BIBLIOGRAPHY . 95 vii LIST OF TABLES Table 3.1 KernelTable . 38 Table 3.2 AuxKernelTable . 38 Table 3.3 InitialConditionTable . 38 Table 3.4 MaterialTable . 39 Table 3.5 PostprocessorTable . 39 Table 3.6 ActionTable . 39 Table 3.7 ExecutionerTable . 39 Table 3.8 MultiappTable . 40 Table 3.9 ThermalMaterialProperties . 40 Table 3.10 HeatOutputThermal . 40 Table 3.11 RadioactiveGenerationCaseProperties . 40 Table 4.1 ThermalPropertiesofAnalogCase . 69 Table 4.2 CsDischarge . 69 Table 4.3 IDischarge . 69 Table 4.4 ThermalPropertiesofFinalCase . 69 Table 4.5 FinalCaseProperties . 69 Table 4.6 HollanditeDiffusionCoefficientPreexponential . 69 viii LIST OF FIGURES Figure 2.1 Coupled Simulation . 18 Figure 2.2 Vacancy Diffusion . 18 Figure 2.3 Grain Boundary Diffusion . 19 Figure 2.4 Interstitials Diffusion . 19 Figure 3.1 Multi Phase Diffusion Coefficient . 41 Figure 3.2 Multi Grains . 41 Figure 3.3 Diffusion Validation a: initial and boundary conditions . 41 Figure 3.4 Diffusion Validation a: Results . 42 Figure 3.5 Diffusion Validation b: Results . 42 Figure 3.6 Side View of Canister . 43 Figure 3.7 Top View of Canister . 43 Figure 3.8 Canister . 44 Figure 3.9 Thermal Validation: Results . 44 Figure 3.10 Radionuclide Decay Validation . 45 Figure 3.11 Radionuclide Decay, Generation and Diffusion Validation . 45 Figure 3.12 AverageTimeStepForDiffusion Validation . 46 Figure 3.13 AverageTimeStepForDiffusion Concentration Validation . 46 Figure 3.14 Preferred Paths Structures . 46 Figure 3.15 1D Validation . 47 Figure 3.16 Structure One 1D Isotropic Validation . 47 Figure 3.17 Structure Two 1D Isotropic Validation . 48 Figure 3.18 Structure Three 1D Isotropic Validation . 48 ix Figure 3.19 Structure Four 1D Isotropic Validation . 49 Figure 3.20 Structure Five 1D Isotropic Validation . 49 Figure 3.21 Structure One 2D Isotropic Validation . 50 Figure 3.22 Structure Two 2D Isotropic Validation . 50 Figure 3.23 Structure Three 2D Isotropic Validation . 51 Figure 3.24 Structure Four 2D Isotropic Validation . 51 Figure 3.25 Structure Five 2D Isotropic Validation . 52 Figure 3.26 Structure One 2D Anisotropic Validation . 52 Figure 3.27 Structure Two 2D Anisotropic Validation . 53 Figure 3.28 Structure Three 2D Anisotropic Validation . 53 Figure 3.29 StructureFourTwoDACValidation . 54 Figure 3.30 Structure Five 2D Anisotropic Validation . 54 Figure 3.31 Structure One Small Domain 2D Anisotropic Validation . 55 Figure 3.32 Structure One Large Domain 2D Anisotropic Validation . 55 Figure 3.33 Structure One Small Domain 2D Anisotropic Validation Error . 56 Figure 3.34 Structure One Original Domain 2D Anisotropic Validation Error 56 Figure 3.35 Structure One Large Domain 2D Anisotropic Validation Error . 57 Figure 4.1 Heat Output . 70 Figure 4.2 Specific Heat . 70 Figure 4.3 Thermal Conductivity . 71 Figure 4.4 Thermal Diffusivity . 71 Figure 4.5 Analog Case . 72 Figure 4.6 Cesium Diffusion Coefficients . 72 Figure 4.7 Cesium 134 Mass Contianed in SiC-C Phase . 73 Figure 4.8 Cesium 134 Mass Released from SiC-C Phase . 73 Figure 4.9 Cesium 136 Mass Contianed in SiC-C Phase . 74 Figure 4.10 Cesium 136 Mass Released from SiC-C Phase . 74 Figure 4.11 Cesium 137 Mass Contianed in SiC-C Phase . 75 x Figure 4.12 Cesium 137 Mass Released from SiC-C Phase . 75 Figure 4.13 Iodine Diffusion Coefficients . 76 Figure 4.14 Iodine 129 Mass Contianed in SiC-C Phase . 76 Figure 4.15 Iodine 129 Mass Released from SiC-C Phase . 77 Figure 4.16 Iodine 131 Mass Contianed in SiC-C Phase . 77 Figure 4.17 Iodine 131 Mass Released from SiC-C Phase . 78 Figure 4.18 Iodine 132 Mass Contianed in SiC-C Phase . 78 Figure 4.19 Iodine 132 Mass Released from SiC-C Phase . 79 Figure 4.20 Diffusion Coefficient in Hollandite . 79 Figure 4.21 Cesium 134 Mass Contianed in Hollandite . 80 Figure 4.22 Cesium 134 Mass Released from Hollandite . 80 Figure 4.23 Barium 134 Mass Contianed in Hollandite . 81 Figure 4.24 Barium 134 Mass Released from Hollandite . 81 Figure 4.25 Temperature Profile of Cesium 134 Case . 82 Figure 4.26 Cesium 137 Mass Contianed in Hollandite . 82 Figure 4.27 Cesium 137 Mass Released from Hollandite . 83 Figure 4.28 Barium 137 Mass Contianed in Hollandite . 83 Figure 4.29 Barium 137 Mass Released from Hollandite . 84 Figure 4.30 Temperature Profile of Cesium 137 Case . 84 Figure 4.31 Cesium 134 Mass Contianed in Hollandite No Stainless Steel . 85 Figure 4.32 Cesium 134 Mass Released from Hollandite No Stainless Steel . 85 Figure 4.33 Barium 134 Mass Contianed in Hollandite No Stainless Steel . 86 Figure 4.34 Barium 134 Mass Released from Hollandite No Stainless Steel . 86 Figure 4.35 Temperature Profile of Cesium 134 No Stainless Steel Case . 87 Figure 4.36 Cesium 137 Mass Contianed in Hollandite No Stainless Steel . 87 Figure 4.37 Cesium 137 Mass Released from Hollandite No Stainless Steel . 88 Figure 4.38 Barium 137 Mass Contianed in Hollandite No Stainless Steel . 88 Figure 4.39 Barium 137 Mass Released from Hollandite No Stainless Steel . 89 xi Figure 4.40 Temperature Profile of Cesium 137 No Stainless Steel Case . 89 Figure 5.1 Cesium 137 Mass Contianed in Hollandite Fast Path . 93 Figure 5.2 Cesium 137 Mass Released from Hollandite Fast Path . 93 Figure 5.3 Barium 137 Mass Contianed in Hollandite Fast Path . 94 Figure 5.4 Barium 137 Mass Released from Hollandite Fast Path . 94 xii LIST OF ABBREVIATIONS DOE . Department of Energy FEM . Finite Element Method INL . Idaho National Laboratory MOOSE . Multiphysics Object-Oriented Simulation Environment xiii CHAPTER 1 INTRODUCTION 1.1 MOTIVATION The commercial nuclear fuel cycle produces nuclear waste in the form of numerous distinct and mobile radionuclides. To ensure safe disposal of nuclear waste, it is important to stabilize the radionuclides. To this end, certain ceramic materials and phases are proposed to immobilize and stabilize these radionuclides.
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