AN ABSTRACT OF THE THESIS OF. Justin R. Mart for the degree of Master of Science in Nuclear Engineering presented on June 14, 2013.

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2 AN ABSTRACT OF THE THESIS OF Justin R. Mart for the degree of Master of Science in Nuclear Engineering presented on June 14, Title: Feasibility Study on a Soluble Boron-Free Small Modular Reactor Abstract approved: Andrew C. Klein The elimination of soluble boron creates several advantages for Small Modular Reactor (SMR) operation. Most of these advantages are realized through significant core simplification (removal of pipes, pumping, and purification systems), the removal of the corrosive effects of soluble boron, and from improved safety effects. However, removing soluble boron creates its own set of specific challenges that must be overcome. Traditional pressurized water reactors employ soluble boron for uniform power suppression throughout the core. Thus any boron-free SMR design requires increased dependence on control rods and burnable poisons, where both are discrete neutron absorbers that locally impact the core where they are inserted. Since control rods are partially inserted, their presence negatively impacts the axial power profile and this distortion creates undesirable power peaks, leading to a reduced operating margin and a significant economic burden. Thus, the main challenge in any boron free design concerns excess reactivity suppression and active reactivity control while maintaining a proper axial power profile and reduced power peaks. The goal of the feasibility study is to investigate the physical effects of removing soluble boron, and to investigate and identify an effective strategy for containing power peaks in a boron-free SMR. Studsvik's CASMO-4E was employed to solve 2-D Transport equation for infinite lattice analysis, and SIMULATE-3K was employed to solve 3-D nodal diffusion equation for full core analysis.

3 The study identified improved reactivity feedback mechanisms associated with the removal of soluble boron, arising from a softened neutron flux and a decreased production of plutonium. An analysis of strategies for soluble boron-free operation that involved axially grading burnable poisons and U 235 enrichment percentages was found unable to be able to control the axial power profile throughout core lifetime. The inherent limitations in the lifetime of burnable poisons resulted in an inability to control the axial power profile through middle and end of cycle. Investigations of additional strategies involving an advanced control rod algorithm produced significantly improved results that met the prescribed criteria for success. The advanced control rod algorithm is thus recognized as a viable strategy for boron-free operation for SMRs.

4 Copyright by Justin R. Mart June 14, 2013 All Rights Reserved

5 Feasibility Study on a Soluble Boron-Free Small Modular Reactor by Justin R. Mart A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented June 14, 2013 Commencement June 2014

6 Master of Science thesis of Justin R. Mart presented on June 14, APPROVED: Major Professor, representing Nuclear Engineering Head of the Department of Nuclear Engineering and Radiation Health Physics Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. Justin R. Mart, Author

7 ACKNOWLEDGEMENTS I would like to express sincere thanks to my advisor, Dr. Andrew Klein, for his immense patience, guidance, and support through the scope of this project, helping me become a better student and person. I would also like to thank Dr. Alexey Soldatov for his specific help in navigating and analyzing the reactor analysis software. The faculty members of Oregon State University deserve credit for providing immense knowledge and support in the several aspects of this project, as do the members of Dr. Klein s Fringe group of Nuclear Engineering students for their moral encouragement and technical help. Lastly, I would like to acknowledge and thank all the people in my life that have encouraged and supported me. My family in friends in particular, as without their support I would never have found myself in this position.

8 TABLE OF CONTENTS Page Chapter 1 - Introduction Overview of Nuclear Reactor Physics and Key Concepts Criticality and Multiplication Factors Prompt Neutron Lifetime and Delayed Neutron Fractions Power Peaks and Pin Peaking Factors Survey of the Different Methods of Excess Reactivity Compensation Advantages and Disadvantages to Soluble Boron-Free Operation Differences between Small Modular Reactors and Typical Light Water Reactors Advantages of Soluble Boron-Free Operation in Small Modular Reactors Disadvantages to Soluble Boron-Free Operation in Small Modular Reactors Chapter 2 Literature Review Survey of Current SMR Designs Babcock and Wilcox mpower NuScale Power SMR Westinghouse SMR Relevant Soluble Boron-Free Research and Development Feasibility Studies of a Soluble Boron-Free 900-MWe PWR Elimination of Soluble-Boron for a New PWR Design A Soluble Boron-Free Core Design for the IRIS Nuclear and Thermal Hydraulic Design Characteristics of the SMART Core Chapter 3 - Methodology Definition of research goals Criteria for Success Criteria for Axial Offset Criteria for Maximum Pin Peaking Factors Available Tools for Reactor Design and Analysis Chapter 4 Reactor Design and Analysis The Selected SMR Design with Fuel Assembly Geometry and Characteristics Physical Effects of Soluble Boron-Free Operation Multiplication Factor with and without Burnable Poisons... 40

9 TABLE OF CONTENTS (Continued) Page Fuel Depletion and Plutonium Production Neutron Flux and Energy Spectra Effective Fraction of Delayed Neutrons Reactivity Feedback Mechanisms Conclusion Development and Analysis of Fuel Assemblies for use in Full Core Environment Burnable Poison Search Description and Analysis of Initial Strategies for Soluble Boron-Free Operation in the Selected SMR Design Full Core Radial Loading Geometry Full Core Axial Loading Geometry Chapter 5 - Results First Group of Axially Graded SMR Cores First Axially Graded SMR Core Further Axially Graded SMR cores from the First Group Second Group of Axially Graded SMR Cores First Core from Second Group of Axially Graded SMR cores Further Axially Graded SMR cores from the Second Group Third Group of Axially Graded SMR Cores First Core from Third Group of Axially Graded SMR Cores Further Axially Graded SMR cores from the Third Group Fourth Group of Axially Graded SMR Cores First core from Fourth group of axially graded SMR cores Further Axially Graded SMR cores from the Fourth Group Fifth Group of Axially Graded SMR Cores First Core from Fifth Group of Axially Graded Cores Further Axially Graded SMR Cores from the Fifth Group Conclusion Chapter 6 Further Strategies for Soluble Boron-Free Operation Feasibility of the Advanced Control Rod Algorithm

10 TABLE OF CONTENTS (Continued) Page 6.2 Final Advanced Control Rod Algorithm Chapter 7 Conclusions Future Work Further Control Rod Algorithms and Axial Loading Strategies Gadolinia-Oxide Burnable Poison Pellets Partial Elimination of Soluble Boron Bibliography General Publications International Atomic Energy Agency Documents and Publications Software Manuals and Descriptions Regulatory Documents Appendix

11 Figure LIST OF FIGURES Page Figure 1: Axial power profile of a hypothetical boron-free reactor core Figure 2: Averaged axial power profile of two hypothetical boron-free cores vs core height (axial node) Figure 3: Full core radial geometry Figure 4: k inf vs burnup for 5.0% U 235 assemblies with varying amounts of soluble boron Figure 5: k inf vs burnup for poisoned 5.0% U 235 fuel assemblies with varying amounts of soluble boron Figure 6: Weight percent of total Plutonium (Pu Pu 241 ) vs burnup for 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron Figure 7: U238 neutron absorption cross section (barns) vs energy (MeV) Figure 8: Total uranium and plutonium fission rate vs burnup in 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron Figure 9: Weight percent of U 235 vs burnup in 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron Figure 10: Total neutron flux vs burnup for 5.0% U 235 enriched fuel assembly Figure 11: Fast neutron flux vs burnup for 5.0% U 235 enriched assemblies Figure 12: Thermal neutron flux vs burnup for 5.0% U 235 enriched assemblies Figure 13: Effective delayed neutron yield vs burnup for 5.0% U 235 fuel assemblies Figure 14: Fuel temperature coefficient vs burnup for hot full power, cold full power, and cold zero power with and without soluble boron Figure 15: Moderator temperature coefficient for hot full power, cold full power, and cold zero power with and without soluble boron Figure 16: k inf vs burnup for a poisoned and non-poisoned fuel assembly Figure 17: Burnable poison loading geometry for each of the 5 major groups. Red indicates a control rod, blue is a poisoned fuel pin, and white is a regular fuel pin Figure 18: k inf vs burnup for fuel each major burnable poison loading geometry Figure 19: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with variations of all 5 BP geometries and with individually varied Gd 2 O 3 weight percentages Figure 20: k inf vs burnup for BP geometry 1 and 3, with 12% and 2% w/o Gd 2 O Figure 21: k inf vs burnup for final 5 fuel assemblies that exhibit a flat burnup profile Figure 22: Poisoned pin geometry for fuel assemblies with strong initial reactivity compensation and quick Gd 2 O 3 depletion Figure 23: k inf vs burnup for 5.0% U 235 fuel assemblies with 64 poisoned pins Figure 24: Burnable poison loading geometry with 52 and 64 poisoned pins

12 Figure LIST OF FIGURES (Continued) Page Figure 25: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with 52 and 56 pins poisoned with 5.0% and 6.0% w/o Gd 2 O Figure 26: Five different burnable poison loading geometries for fuel assemblies with strong initial reactivity compensation and slow depletion Figure 27: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins at 5.0% w/o Gd 2 O Figure 28: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins at 6.0% w/o Gd 2 O Figure 29: Five different burnable poison loading geometries for fuel assemblies with extraordinarily large initial reactivity compensation Figure 30: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 2.0% w/o Gd 2 O Figure 31: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 3.0% w/o Gd 2 O Figure 32: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 4.0% w/o Gd 2 O Figure 33: 2-Dimensional U 235 Enrichment Loading Geometry Figure 34: Relative power fraction for the U 235 enrichment loading geometry Figure 35: Natural power profile for soluble boron-free core at BOC and EOC Figure 36: Full core symmetry Figure 37: Burnable poison loading and average U 235 enrichment vs core height for the first core in the first group of axially graded cores Figure 38: 5.0% U 235 enriched Flat burn fuel assemblies that were employed in the first group of axially graded cores Figure 39: Average burnable poison loading (grams) per node for the first axial core Figure 40: Fuel assembly U 235 enrichment per node for the first axial core Figure 41: Axial offset and control rod insertion vs burnup for the first core Figure 42: Maximum total peaking factor vs burnup for the first core and soluble boron core Figure 43: Burnable poison loading vs core height for all cores in the first group of axially graded cores Figure 44: Average U 235 enrichment vs core height for the first group of axially graded cores Figure 45: Axial power offset vs burnup for the first group of axially graded cores Figure 46: Control rod insertion vs burnup for the first group of axially graded cores

13 Figure LIST OF FIGURES (Continued) Page Figure 47: Maximum total peaking factor vs burnup for the first group of axially graded cores Figure 48: Burnable poison loading and average U 235 enrichment vs core height for the 9th core Figure 49: Average burnable poison loading (grams) per node for the 9th core Figure 50: Fuel assembly U 235 enrichment per node for the 9th core Figure 51: Axial offset and control rod insertion percentage vs burnup for the 9th core Figure 52: Maximum total peaking factor vs burnup for the 9th core Figure 53: Burnable poison loading vs core height for the 2nd group of axially graded cores Figure 54: Average U 235 enrichment vs core height for the 2nd group of axially graded cores Figure 55: Axial power offset vs burnup for the 2nd group of axially graded cores Figure 56: Control rod insertion for the second group of axially graded cores Figure 57: k inf vs burnup for fuel assemblies used in cores 11 and Figure 58: Maximum total peaking factor vs burnup for the second group of cores Figure 59: k inf vs burnup for fuel assemblies used in the third group of cores Figure 60: Burnable poison loading and average U 235 enrichment vs core height for the first core in the third group of axially graded cores Figure 61: Average burnable poison loading (grams) per node for the 14th core Figure 62: Assembly U 235 enrichment per node for the 14th core Figure 63: Axial offset and control rod insertion percentage vs burnup for the 14th core Figure 64: Maximum total peaking factor vs burnup for the 14th core and a soluble boron core Figure 65: Burnable poison loading vs core height for the third group of cores Figure 66: Average U 235 enrichment vs core height for the third group of cores Figure 67: Axial power offset vs burnup for the third group of cores Figure 68: Control rod insertion vs burnup for the third group of cores Figure 69: Maximum total peaking factor vs burnup for the third group of cores Figure 70: Burnable poison loading and average U 235 enrichment vs core height for the 23rd core Figure 71: k inf vs burnup for the fuel assemblies used in the fourth group of cores Figure 72: Average burnable poison loading (grams) per node for the 23rd core

14 Figure LIST OF FIGURES (Continued) Page Figure 73: Fuel assembly U 235 enrichment per node for the 23rd core Figure 74: Axial offset and control rod insertion vs burnup for the 23rd core Figure 75: Maximum total peaking factor vs burnup for the 23rd core and a soluble boron core Figure 76: Burnable poison loading vs core height for the fourth group of cores Figure 77: Average U 235 enrichment vs core height for the fourth group of cores Figure 78: Axial power offset vs burnup for the fourth group of cores Figure 79: Control rod insertion vs burnup for the fourth group of cores Figure 80: Maximum total peaking factor vs burnup for the fourth group of cores Figure 81: k inf vs burnup for fuel assemblies used in the fifth group of cores Figure 82: Burnable poison loading and average U 235 enrichment vs core height for the 30th core Figure 83: Average burnable poison loading (grams) per node for the 30th core Figure 84: Fuel assembly U 235 enrichment per node for the 30th core Figure 85: Axial offset and control rod insertion vs burnup for the 30th core Figure 86: Maximum total peaking factor vs burnup for the 30th core Figure 87: Burnable poison loading vs core height for the fifth group of cores Figure 88: Average U 235 enrichment vs core height for the fifth group of cores Figure 89: Axial power offset vs burnup for the fifth group of cores Figure 90: Control rod insertion vs burnup for the fifth group of cores Figure 91: Relative power fraction and average exposure at 11 MWd/Kg for core Figure 92: Maximum total peaking factor vs burnup for the fifth group of cores Figure 93: Depletion stages for an initial control rod algorithm designed to contain the axial power profile Figure 94: Axial offset and control rod insertion vs burnup for the initial control algorithm. 147 Figure 95: Maximum total peaking factor vs burnup for the initial control rod algorithm Figure 96: k inf vs burnup for the fuel assembly used in the final control rod algorithm Figure 97: Fuel assembly U 235 enrichment and burnable poison loading profile for the final advanced control rod algorithm Figure 98: Depletion stages for the final advanced control rod algorithm Figure 99: Axial offset and control rod insertion percentage vs burnup for the final control rod algorithm

15 Figure LIST OF FIGURES (Continued) Page Figure 100: Maximum pin peaking factor vs burnup for the final control rod algorithm Figure 101: Axial offset vs burnup for the boron-free core with axially graded burnable poisons, the boron-free core with the final control rod algorithm, and for a soluble boron core Figure 102: Maximum pin peaking factor vs burnup for the boron-free core with axially graded burnable poisons, the boron-free core with the final control rod algorithm, and for a soluble boron core Figure 103: Average burnable poison loading (grams) per node for the 1st core Figure 104: Fuel assembly U 235 enrichment per node for the 1st core Figure 105: Average burnable poison loading (grams) per node for the 2nd core Figure 106: Fuel assembly U 235 enrichment per node for the 2nd core Figure 107: Average burnable poison loading (grams) per node for the 3rd core Figure 108: Fuel assembly U 235 enrichment per node for the 3rd core Figure 109: Average burnable poison loading (grams) per node for the 4th core Figure 110: Fuel assembly U 235 enrichment per node for the 4th core Figure 111: Average burnable poison loading (grams) per node for the 5th core Figure 112: Fuel assembly U 235 enrichment per node for the 5th core Figure 113: Average burnable poison loading (grams) per node for the 6th core Figure 114: Fuel assembly U 235 enrichment per node for the 6th core Figure 115: Average burnable poison loading (grams) per node for the 7th core Figure 116: Fuel assembly U 235 enrichment per node for the 7th core Figure 117: Average burnable poison loading (grams) per node for the 8th core Figure 118: Fuel assembly U 235 enrichment per node for the 8th core Figure 119: Average burnable poison loading (grams) per node for the 9th core Figure 120: Fuel assembly U 235 enrichment per node for the 9th core Figure 121: Average burnable poison loading (grams) per node for the 10th core Figure 122: Fuel assembly U 235 enrichment per node for the 10th core Figure 123: Average burnable poison loading (grams) per node for the 11th core Figure 124: Fuel assembly U 235 enrichment per node for the 11th core Figure 125: Average burnable poison loading (grams) per node for the 12th core Figure 126: Fuel assembly U 235 enrichment per node for the 12th core Figure 127: Average burnable poison loading (grams) per node for the 13th core

16 LIST OF FIGURES (Continued) Figure Page Figure 128: Fuel assembly U 235 enrichment per node for the 13th core Figure 129: Average burnable poison loading (grams) per node for the 14th core Figure 130: Fuel assembly U 235 enrichment per node for the 14th core Figure 131: Average burnable poison loading (grams) per node for the 15th core Figure 132: Fuel assembly U 235 enrichment per node for the 15th core Figure 133: Average burnable poison loading (grams) per node for the 16th core Figure 134: Fuel assembly U 235 enrichment per node for the 16th core Figure 135: Average burnable poison loading (grams) per node for the 17th core Figure 136: Fuel assembly U 235 enrichment per node for the 17th core Figure 137: Average burnable poison loading (grams) per node for the 18th core Figure 138: Fuel assembly U 235 enrichment per node for the 18th core Figure 139: Average burnable poison loading (grams) per node for the 19th core Figure 140: Fuel assembly U 235 enrichment per node for the 19th core Figure 141: Average burnable poison loading (grams) per node for the 20th core Figure 142: Fuel assembly U 235 enrichment per node for the 20th core Figure 143: Average burnable poison loading (grams) per node for the 21st core Figure 144: Fuel assembly U 235 enrichment per node for the 21st core Figure 145: Average burnable poison loading (grams) per node for the 22nd core Figure 146: Fuel assembly U 235 enrichment per node for the 22nd core Figure 147: Average burnable poison loading (grams) per node for the 23rd core Figure 148: Fuel assembly U 235 enrichment per node for the 23rd core Figure 149: Average burnable poison loading (grams) per node for the 24th core Figure 150: Fuel assembly U 235 enrichment per node for the 24th core Figure 151: Average burnable poison loading (grams) per node for the 25th core Figure 152: Fuel assembly U 235 enrichment per node for the 25th core Figure 153: Average burnable poison loading (grams) per node for the 26th core Figure 154: Fuel assembly U 235 enrichment per node for the 26th core Figure 155: Average burnable poison loading (grams) per node for the 27th core Figure 156: Fuel assembly U 235 enrichment per node for the 27th core Figure 157: Average burnable poison loading (grams) per node for the 28th core Figure 158: Fuel assembly U 235 enrichment per node for the 28th core

17 LIST OF FIGURES (Continued) Figure Page Figure 159: Average burnable poison loading (grams) per node for the 29th core Figure 160: Fuel assembly U 235 enrichment per node for the 29th core Figure 161: Average burnable poison loading (grams) per node for the 30th core Figure 162: Fuel assembly U 235 enrichment per node for the 30th core Figure 163: Average burnable poison loading (grams) per node for the 31st core Figure 164: Fuel assembly U 235 enrichment per node for the 31st core Figure 165: Average burnable poison loading (grams) per node for the 33rd core Figure 166: Fuel assembly U 235 enrichment per node for the 33rd core Figure 167: Average burnable poison loading (grams) per node for the 34th core Figure 168: Fuel assembly U 235 enrichment per node for the 34th core

18 LIST OF TABLES Table Page Table 1: SMR Fuel Assembly Specifications Table 2: SMR Full Core Specifications... 39

19 Feasibility Study on a Soluble Boron-Free Small Modular Reactor Chapter 1 - Introduction The world s energy sector is currently driven by a majority of fossil fuel power plants. In order to address and meet national and global requirements for clean, efficient, and consistent energy production designed to meet a growing demand for energy from developing nations, new and innovative nuclear reactor technologies will need to be developed. Part of this initiative includes the potential for smaller, modular nuclear reactors (SMRs) [6, 32, 33]. These SMRs possess inherent safety advantages, and have the potential to be deployed in developing nations without the infrastructure needed for traditional nuclear power plants [44]. In this vein, any improvement to the inherent safety features and overall reactor operation in SMRs is of value. The presence of soluble boron diluted in the coolant is typical in most current SMR designs [46], despite the inherent safety and reliability advantages that could be realized upon its removal [15, 24, 43]. While removing soluble boron brings inherent advantages, it also significantly complicates the manner in which the nuclear core is operated. These complications make effective operation of a soluble boron-free core difficult. This study aims to design an effective soluble boron-free SMR and investigate how the removal of soluble boron from normal operations impacts core behavior. State of the art tools used for modeling traditional LWRs was employed to evaluate different design strategies, and to generate data for analysis of boron-free operation. The study is organized in the following manner: 1) Overview of nuclear reactor physics and key concepts 2) Description of advantages and disadvantages for soluble boron-free operation 3) Literature review of current SMR designs and previous boron-free research 4) Investigation on the physical effects of soluble boron-free operation 5) Search for a soluble boron-free SMR core design that meets design criteria 6) Conclusions

20 2 1.1 Overview of Nuclear Reactor Physics and Key Concepts Nuclear reactor operation is centered on ensuring the chain reaction maintains criticality while providing sufficient heat removal to avoid meltdown. The operations involving heat removal are relegated to the thermal hydraulic discipline, while concerns about criticality involve neutronic calculations within the reactor core. This distinction provides an effective divide between two largely separate disciplines. This study focuses primarily with the nuclear core and issues relating to its operation and behavior. It is assumed that normal operating conditions exist, i.e. that there will always be sufficient heat removal for the operating specifications provided Criticality and Multiplication Factors A working definition of criticality involves a quick survey of neutron behavior in a nuclear reactor. In traditional Light Water Reactors (LWRs), so named for their use of light water as both a moderator and coolant, U 235 is employed as fuel. When a neutron is absorbed in U 235, it undergoes a fission process that splits the atom in two, creating two smaller elements. As it turns out, this process is exothermic, releasing the bulk of excess energy through kinetic energy in the smaller fission products. But it also releases an assortment of gamma rays, anti-neutrinos, and neutrons themselves. On average, for reactions typical to LWRs, each fission event produces 2.4 extra neutrons. If properly engineered, these neutrons can be absorbed in another U 235, creating a chain of fission reactions that is the backbone of nuclear reactors. In mathematical terms, criticality is defined by the rate of change of the neutron population in the core. This rate of change equation begins as: d n(t) = # of source neutrons produced # of neutrons lost dt For nuclear reactors, the only significant process producing neutrons are fission events within the fuel. Additionally, the only methods by which neutrons are lost are absorption events that do not produce fission events, and neutrons leaking from the system. Reflecting this, the rate of change of neutrons can be defined as:

21 3 d n(t) = # of fission neutrons produced (# of neutrons absorbed dt + # of neutrons leaking from the system) While this definition is useful on a technical scale, it is more useful to employ the concept of a multiplication factor, describing the balance between neutron production and neutron loss: k 0 = Rate of neutron production in reactor Rate of neutron loss in reactor = G(t) L(t) In this manner, it is easy to see that if the value of k 0 < 1 then the number of neutrons will decay to 0, representing a situation where less than one neutron (on average) produces a fission event, and the neutron economy logarithmically declines until no neutrons are left in the system and the chain reaction dies. Conversely, if k 0 > 1 then a situation where more than one neutron (on average) produces a fission event and the neutron economy exponentially grows until some other process prohibits more fission events. Appropriately, for steady-state reactor operation the target is to engineer a system where k 0 = 1, with exactly one neutron (on average) from each fission event producing another fission event. The moment this ratio is met, the reactor is said to be critical [26]. Any amount above or below is respectively dubbed subcritical or supercritical. Accordingly, if the number of neutrons in the system at time t = 0 is N 0, then the number of neutrons after the first generation will be: N 1 = K 0 N 0 If we further define the mean neutron lifetime as: l = # of neutrons in the system at time (t) Rate of neutron loss in the system at time (t) = N(t) L(t)

22 4 Then we can reformulate the neutron rate of change as: d dt n(t) = G(t) L(t) = k 0L(t) L(t) This is to say that the rate of change of neutrons in the system can be expressed as the difference between the rate of neutron production and the rate of neutron loss. Here, the rate of neutron production is put in terms of the multiplication factor and the rate of neutron loss, and the equation simplifies to: d dt n(t) = k 0L(t) L(t) = (k 0 1)L(t) = (k 0 1) N(t) l where N(t) represents the number of neutrons in the system at time t. The solution to this differential equation is: N(t) = N(0)e (k 0 1) t l if k 0 and l are independent of time. This final equation expresses the neutron population as a function of time by employing both the multiplication factor and the mean neutron lifetime. Provided that there is a nonzero number of initial neutrons, the only steady-state solution exists when the reactor is critical (k 0 = 1) Prompt Neutron Lifetime and Delayed Neutron Fractions The final equation for the neutron population with respect to time through the multiplication factor and the average neutron lifetime highlights how the overall neutron economy in the core is impacted by the mean neutron lifetime. Specifically, the rate of neutron growth is inversely proportional to the value of the mean neutron lifetime. In reactors with a small mean neutron lifetime, small perturbations in k 0 will quickly influence the overall neutron population. On a physical level, a thermal neutron is defined as a neutron in thermal equilibrium with its surroundings [13]. At room temperature and atmospheric conditions, thermal neutrons

23 5 possess an average energy of ev and travel at approximately 2200 m/s [26]. Nuclear reactors operate at much higher temperatures and pressures, which only increases the velocity of thermal neutrons. Neutrons at such speeds will rapidly interact with reactor core material through either scattering collisions or absorption events, resulting in an effective neutron total lifetime from birth to death on the order of 10-6 seconds [13]. With such a quick neutron lifetimes, this would ordinarily make any nuclear reactor far too responsive to control. If any amount of reactivity is added, the reactor would respond far too fast for any human or mechanical intervention. The saving grace comes in the form of delayed neutron fraction, or the fraction of neutrons that are emitted after the initial fission event. Most neutrons are produced instantaneously upon fission, and are hence referred to as prompt neutrons. However, small portions of the overall fraction of neutrons are produced after the initial fission, when some fission products are initially unstable and decay through the emission of a neutron. These delayed neutrons account for approximately 0.27% of all neutrons produced in a fission event for typical U 235 fueled reactors [13]. Since the half-lives of these various unstable fission products widely vary, so do individual delayed neutron lifetimes. On average, the lifetime for delayed neutrons is on the order of seconds, not microseconds. Thus, even though they only account for a tiny fraction of all neutrons, their longer lifetime accounts for a significant increase in the overall average neutron lifetime. This overall impact on the neutron economy creates a situation where reactor operators and core designers can control reactor criticality through just the delayed neutron fraction, making it possible to control criticality through human and mechanical intervention. This places particular importance on the delayed neutron percentage throughout the lifetime of the reactor. This value is impacted by several nuanced factors. Delayed neutrons are born from fission products, and the fission products are functions of neutron energy incident on U 235. This neutron energy is in turn impacted by the overall neutron flux spectrum within the core, which is in turn a function of several different variables. The exact nature of how the delayed neutron fraction changes throughout burnup is difficult to define with specificity, but its value is undoubtedly an important factor for the nuclear reactor engineer.

24 Power Peaks and Pin Peaking Factors As part of LWR safety regulations, core designers must ensure specific temperature limits are not surpassed in any postulated operating condition including anticipated accident scenarios. The critical temperature limit in LWRs occurs at the center of the fuel pin, where if temperatures exceed 2200K melting is likely to occur [38]. As part of a conservative design analysis, several other constraints arise to ensure this one temperature limit is not exceeded. One constraint involves the maximum power density for any specific fuel rod, and the maximum power density for any specific fuel volume. Said mathematically, if P signifies reactor power and V signifies core volume, then: P = P V which defines the core-averaged power density. Appropriately, the ratio of maximum power density for any specific fuel volume to the core-averaged power density supplies a power peaking factor: F q = P max P The value of this peaking factor signifies the general power density profile throughout the reactor core. A large peaking factor signifies at least one hot spot in the reactor where the power density is significantly larger than the core-average power density. Since power density is directly related to neutron flux and fuel temperature, power peaking factors directly correlate to fuel temperature design constraints. And since no part of a reactor core can exceed the established temperature limits, a primary concern for the reactor design engineer is the value of the maximum hot spot within a reactor core at all postulated operating conditions [38]. A higher peaking factor must therefore drive down the overall power density of the core in order to ensure this hot spot does not exceed the design constraints. This limits the efficiency of the reactor and represents a significant economic loss to the utility. As a result, limiting power peaking factors are a primary focus for core designers. Minimizing the peaking factors is primarily a function of reactor physics, since non-uniform

25 7 distributions of fuel enrichment, the position of control rods and burnable poisons, and other neutronic concerns largely influence the power density profile. Since removing soluble boron from reactor operations involves a greater dependence on control rods and burnable poisons, the effect on peaking factors must be carefully evaluated and minimized Survey of the Different Methods of Excess Reactivity Compensation Nuclear Power Plants (NPPs) are typically engineered to operate for years before requiring refueling [13]. During that period the amount of U 235 is gradually depleted as each fission event removes a fuel element from the core (neglecting the production of Plutonium and other fissile effects). To combat this burnup effect, a fresh new fuel assembly is loaded with an excess amount of U 235. Without any compensation for this excess U 235, a reactor would go supercritical, requiring some amount of control material to be inserted into the core to combat the extra reactivity. The amount of control material required to bring the core from supercritical to critical is dubbed excess reactivity [13]. Compensation of excess reactivity is therefore one of the primary concerns for safe operation of nuclear power plants. Fuel assemblies of typical LWRs contain excess U 235 to facilitate extended core lifetimes [26]. In these LWRs the arrangement of the fuel pins and the presence of water as a moderator are optimized for criticality. Without any mechanism to break the neutron chain reaction, these reactor cores would go supercritical. To compensate for this, LWRs employ three main methods of compensating for this excess reactivity. The first is the presence of fuel pins that contain strong neutron absorbing materials instead of fuel. These neutron poisons significantly reduce the thermal neutron economy when inserted into the core as a function of distance inserted, the absorber material, and the density of said material. These control rods provide active control of the neutron chain reaction, as the reactor operators are able to manually adjust the insertion distance. The second method of excess reactivity compensation involves the presence of strong neutron absorbing materials mixed into the fuel itself. The amount and resultant density of the fuel and absorber mixture is carefully engineered beforehand to compensate for an appropriate amount of excess reactivity. This use of this method employs burnable poisons, since these strong neutron poisons will slowly deplete as more and more neutrons are absorbed and the poisons are burned up. This effect allows engineers to compensate for the excessive initial

26 8 reactivity, without significantly influencing core behavior later in life. However, this method only provides passive control over reactivity. Once the fuel pins are fabricated with the burnable poisons, they cannot be altered. The last form of reactivity compensation comes from diluting a strong neutron absorber within the moderator. In LWRs, all fast neutrons are thermalized within the moderator, and the presence of a strong neutron absorber within the moderator serves to control the thermal neutron economy. Typically, concentrations of this soluble-absorber (typically Boron) are in the order of 800 to 2000 parts-per-million (ppm) [13]. This method allows for active control of the neutron economy through the presence of a Chemical Volume Control System, which purges or adds absorbing material in the coolant, among other functions [38]. These three methods of compensation all involve the presence of strong neutron poisons. However there are different ways to suppress the excess reactivity, but they must be engineered into core and plant design up front. Since the dynamics of a chain reaction involve multiple different variables that are functions of one another, the ability to influence some of these key variables results in an additional method to suppress excess core reactivity. To demonstrate this effect, it would be a useful exercise to consider what may happen if all three main methods of compensation were absent. In this scenario, the core would go supercritical due to the previously mentioned criticality-optimized core environment. Recall the definition of supercritical is an environment where the number of neutrons increases from one generation to the next. Since LWRs only contain one dominant neutron source (U 235 ), the increase in neutrons must come from the fission of U 235. These fission events release on average approximately 200 MeV of energy, with 95% coming in the form of kinetic energy, or heat [38]. These fission events increase proportionally with the number of thermal neutrons present, resulting in a rapid increase in temperature within the fuel pins and extending into the moderator. The rate of increase is governed by the average neutron lifetime, which in LWRs is on the order of 10-6 sec. At this point, the heat produced in the fuel pins quickly begins to affect other variables that influence the neutron chain reaction. Most notable is the moderator temperature, and thus density. As the temperature rapidly increases, the density of water surrounding the fuel pins quickly decreases, which in turn results in fewer thermal neutrons due to a decrease in the number of neutron scattering events within the moderator.

27 9 This loss of thermal neutrons due to a decrease in moderator density provides a natural mechanism to combat the fission chain reaction, specifically known as the Moderator Temperature Coefficient (MTC). Other effects similar to this one comprise additional, physical methods used to naturally control a runaway chain reaction. But these effects cannot be actively controlled by reactor operators and must be engineered beforehand, and only effect operations in accident scenarios. For these reasons, the three main methods of compensating for excess reactivity are important factors for safe operation of nuclear reactors. Removing one of the three involves a detailed discussion on the resulting safety and operational impacts Strengths and weaknesses of the different methods of excess reactivity compensation Control rods are absolutely essential in any LWR design, due to their ability to provide active reactivity control. Reactor operators retain the ability to manually and quickly insert control rods into the core, providing both an effective way to immediately shut the chain reaction off, and a way to fine-tune the level of reactivity within the core as reactor transients fluctuate. Typically, the fine tuning ability is left to automated devices, in part since typical LWR periods (total time required for the reactor to increase by a factor of e) are too small for manual human operation [13]. Manual human operation would also be tedious and create room for mistakes, whereas automated functions provide a higher level of certainty and reliability. However, in contrast to control rods the other two main methods of reactivity compensation are even slower. The devices that physically insert and remove control rods are known as control rod drive mechanisms (CRDM), and can be prone to operational issues since their presence in a highly radioactive environment leads to occasional malfunction [26]. In some LWRs, these CRDMs exist outside the main containment vessel to shield them from these effects, but that carries a rod ejection risk due to the pressure differential between the inside and outside of containment [45, 49]. However, these risks are necessary evils since the control rods represent the only active means of controlling the neutron economy. Additionally, control rods have a disturbing impact on the neutron flux profile within the core. Since specific locations in each individual fuel assembly are reserved for control rods instead of fuel pins, their effect on the neutron economy is localized to that specific area. Imagine a neutron flux profile in a well-designed LWR as a water bed. Without any objects

28 10 resting on the bed, the profile would be flat and undisturbed. In this example, control rods are represented by bowling balls. Toss a few balls onto the bed and the neutron flux profile would be greatly suppressed in the areas localized to the bowling balls, but also pushed up in the undisturbed areas. In this respect, control rods create imbalances in the neutron flux, which in turn creates larger pin-peaking and hot-rod factors. Furthermore, control rod banks are inserted together at the same axial depth. If control rods are partially inserted into the core, the absorbing effects will only be axially felt in the area where control rods are present. The resulting global effect on the neutron flux yields an axially skewed neutron profile. The neutron flux in the top half of the core would be suppressed, while the bottom half would be increased. Once again, this axial flux imbalance creates larger pin-peaking and hot-rod factors. Mitigating these effects on the neutron flux profile is a motivation for the introduction of the other two methods of reactivity compensation. However, another motivation arises from a safety standpoint, where reactor engineers must demonstrate the ability to properly shut down the reactor in its most reactive state and with the most reactive control rod stuck in a position withdrawn from the core (the stuck rod criteria) [62]. Using only control rods, this criterion would be difficult to achieve with a fresh core at the beginning of its cycle (BOC), and at cold, room temperature conditions (since the excess reactivity is greatest with a fresh core that has not experienced any depletion). In typical LWRs, the amount of excess reactivity at BOC exceeds the total amount of reactivity compensated by control rods, requiring the presence of additional compensation methods [26]. Additionally, the regulatory framework within the Nuclear Regulatory Commission (NRC) requires reactors to meet defense-in-depth criteria. For LWRs, this criteria can be summarized as requiring reactors to possess redundant layers of defense to compensate for potential human and mechanical failures so that no single layer, no matter how robust, is exclusively relied upon [65]. These factors necessitate the presence of additional methods of reactivity compensation. Burnable poisons function primarily to reduce the initial excess reactivity to more manageable levels. Since they burn out over time, their effect is only felt from the BOC to the middle of cycle (MOC), making their presence relatively benign. However, there are a vast number of factors that engineers must keep in mind when designing a burnable poison arrangement. The location and total amount of burnable poisons within each fuel assembly

29 11 should be carefully selected in order to minimize the effect they will have on the neutron flux distribution, due to their localized effect on the neutron population (similar to control rods). Additionally, shadowing and shielding effects within poisoned fuel pins will preserve some U 235, leaving a slightly higher and more reactive fuel pin once the poisons have depleted. This additional reactivity can also carry flux distribution implications. Finally, soluble boron represents the third part of a diverse, independent and redundant scheme for reactivity control, and its main advantage lies in the ability to suppress the neutron population uniformly over the radial and axial profile of the core. If the neutron profile within a reactor is analogous to a water bed, control rods and burnable poisons could be represented by bowling balls tossed on to the bed, while soluble-boron is more analogous to a blanket uniformly depressing the neutron flux everywhere. This is not a perfect example since its effect is only localized to the moderator, but since the moderator covers such a large portion of the core, the analogy largely holds. This allows reactor operators to control the reactivity within the core in a uniform manner, reducing pin-peaking and hot-rod issues associated with control rods and burnable poisons. Unfortunately, soluble Boron carries with it a number of issues. First, Boron is corrosive. Its presence in the core will increase corrosion on the primary loop and the reactor pressure vessel, and corrosive elements will become mixed in with the moderator [43]. Controlling this requires the presence of a CVCS to clean these corrosive and dislodged elements from the coolant, and to purify and control the level of Boron diluted in the moderator. The operation of a CVCS and the presence of corrosive elements in the core add to the operation and maintenance burden, and the additional piping increases the risk of loss of coolant accidents (LOCAs) [15, 43]. Soluble boron also introduces an inadvertent boron dilution accident (BDA) risk [15, 16, 42]. While boron is seen to be uniformly mixed into the coolant, there carries a statistically small chance that one area of the coolant becomes saturated or void of boron. As this section of coolant passes through the core, the reactor will experience a large insertion of positive or negative reactivity. As a result, too much positive reactivity will occasionally be added and the core will automatically be shut down. Lastly, altering the concentration of Boron can be adjusted for burnup, reactor dynamics, and even for load-follow operation. However, it is too slow to compensate for reactor kinetics, but fast enough to control reactor dynamics.

30 Burnable poison materials Large amounts of excess reactivity are undesirable because they require large amounts of control material to be inserted into the core. With more control material in the core, the consequences of a rapid removal of control material through either dilution accidents or control rod ejection become more disastrous, and potentially capable of bringing the reactor to prompt criticality [13]. As a result, limitations are placed on the amount of reactivity that can be present in a single control rod and in a bank of control rods [62]. Thus if more reactivity compensation is required, more control rods and control rod banks must be employed, increasing the mechanical complexity of the system and occupying additional valuable space within the core. All of this adds up to an additional economic impact, and should therefore be avoided if possible. To avoid excessive use of control rods, reactors today employ both soluble boron and burnable poisons as additional methods of excess reactivity compensation. In eliminating soluble boron more dependence is placed on burnable poisons and care should be taken to select the proper type of poison for use in a small LWR. There are generally three different types of burnable poisons with their own advantages and disadvantages: Gadolinia Oxide (Gd 2 O 3 ), Erbia Oxide (Er 2 O 3 ), and Integral Fuel Burnable Poisons (IFBA) [13, 26, 38]. Gadolinia Oxide, comprised of Gd 155 and Gd 157, is homogeneously mixed with UO 2 to create UO 2 -Gd 2 O 3, without any alterations to the physical fuel pin dimensions. The amount of Gd 2 O 3 present in UO 2 -Gd 2 O 3 fuel pins largely depends on the amount of reactivity compensation necessary, and thus gives flexibility to the core designer. Gd 2 O 3 also has a larger absorption cross section for thermal neutrons compared to Er 2 O 3 and IFBAs, which correlates to a smaller number of pins necessary for excess reactivity compensation. Furthermore, self-shielding effects in UO 2 -Gd 2 O 3 pins creates excess U 235 at middle of cycle (MOC) and end of cycle (EOC), usually resulting in a decision to reduce the initial amount of U 235 in UO 2 -Gd 2 O 3 pins. However, this purposely reduced enrichment (and other degradation of material properties) creates a slightly lower thermal conductivity. In order to ensure the maximum fuel temperature design criteria is never exceeded, a further purposeful reduction of U 235 enrichment may be necessary [13, 17, 18].

31 13 Er 2 O 3 is also a homogeneously mixed burnable poison, similar to Gd 2 O 3. The chief difference lies in the relatively small absorption cross as a primarily resonance absorber. This requires a larger number of Er 2 O 3 rods to suppress initial excess reactivity when compared to Gd 2 O 3. Similar to Gd 2 O 3 is the reduction in thermal conductivity, and self-shielding effects, which will again produce underburned fuel pins at MOC and EOC, requiring a reduction in initial enrichment of U 235 in UO 2 -Er 2 O 3 pins. IFBAs operate on a different design principle, placing a thin layer of Zirconium Diboride (ZrB 2 ) coating on the fuel pellets. This coating approach results in a longer overall burnup of fuel assemblies employing IFBAs because there is no fuel reduction displacement by IFBA pins [26]. As an added benefit, IFBA pins burn out completely when compared to homogeneously mixed burnable poisons like Gd 2 O 3 and Er 2 O 3 since the coating leaves essentially no residual absorption penalty. However, a significant drawback arises due to the neutron-alpha reaction with Boron-10, in which B 10 absorbs a neutron and decays via alpha emission, producing helium. This excess helium can exert additional pressure on the cladding boundary, and care must be taken to ensure the pressure limits are maintained [26]. This ultimately results in a global limit on the total IFBA loading amount. Further burnable poison arrangements include the use of lumped poisons instead of homogeneous arrangements. The strong self-shielding characteristics of lumped poisons result in a smooth burnup profile and a longer effective poison lifetime. However, the impact of discrete pellets is very difficult to model. The use of such lumped poisons represents a deviation from normal operating PWR fuel assemblies, and will not be explored in this feasibility study. 1.2 Advantages and Disadvantages to Soluble Boron-Free Operation Removing soluble boron from normal operations in a prototypical SMR introduces several inherent benefits, and creates a few key challenges. Before exploring the breadth of these benefits and issues, a brief survey of the differences between typical LWRs and SMRs is required.

32 Differences between Small Modular Reactors and Typical Light Water Reactors Small Modular Reactors represent a different business model than traditional LWRs. Since the first commercial Nuclear Power Plants (NPPs), reactor designs have steadily grown larger and larger to take advantage of an economy of scale. Unfortunately, among other things, the initial investment in both capital and time has grown disproportionately burdensome [45, 50]. The gigantic cost and the inability to determine when a plant would be licensed and built brought the industry to a point where large NPPs were rarely economically feasible. While the industry is seeing promising signs of growth, including the recent certification of the Westinghouse AP1000, the traditional NPP business model carries some serious roadblocks to long term commercial success [34, 40, 45, 50]. The Small Modular Reactor (SMR) business model addresses these roadblocks and introduces a new path to commercialization [34, 40]. The definition of SMRs depends on who you ask. In some contexts, it refers to Small to Medium Reactors, while in others it signifies a Small Modular Reactor one that can be built off-site. Traditionally, the line between SMRs and typical LWRs blurs around the MWe range [55]. Most SMRs in design today are less than 300 MWe, which is close to one third the power output of traditional LWRs [48, 54]. For these SMRs to overcome traditional economies of scale, they employ a few specific design goals: Create a reactor with far less prohibitive initial investments and a quicker return on capital; Certify standard designs that could be fabricated off-site and shipped by barge or train; Employ Safety-by-Design to create a passively safe reactor with less operation and maintenance costs; and employ an economy of multiples instead of an economy of scale [47]. In order to accomplish these goals, a major design simplification must occur. SMRs adopt standard PWR technology and condense the entire primary loop to a single containment vessel. The reactor core, control ride drive mechanisms, steam generator, pressurizer, and reactor coolant pumps are housed in a single cylindrical shell [45]. The only external elements in some designs include pressurized valves for emergency core cooling system (ECCS) mechanisms and the secondary loop running from the steam generator to the turbine and condensers. This simplification makes several of these goals possible. First, the simplified design will, once certified, enable vendors to certify and construct the reactor itself off-site, vastly reducing the construction and regulatory burden of typical LWRs. Additionally, the

33 15 simplified design features several distinct safety advantages that can be engineered to become passively safe. First, incorporating all the primary circuit elements into one containment vessel eliminates the large connecting loop of piping between component pressure vessels and the steam generators, eliminating LOCAs as design-basis events. Second, integrating the steam generator inside containment allows for some revolutionary designs that are capable of accommodating thermal expansion without excessive mechanical stress and with a high resistance to flow induced vibrations. Third, incorporating the reactor coolant pumps within containment eliminates the chance of leakage. Fourth, the pressurizer carries a potentially larger volume-to-power ratio and can potentially eliminate the need for pressurizer sprays. And finally, inserting the CRDM into the containment vessel eliminates the potential for an inadvertent rod ejection accident, and reduces the number of penetrations in the vessel head. Together, these advantages significantly reduce the manufacture and installation costs [45]. This is by no means a comprehensive list of advantages, but the cursory list demonstrates how a revolutionary simplification can bring several unique safety advantages. SMRs in design today incorporate a safety-by-design approach, where the underlying principle is that potential accidents should be intrinsically eliminated by design, rather than coping with their consequences through safety systems. The remaining inescapable accident scenarios can be dealt with through passive safety systems in part due to the lower power density and smaller core volume. Designs in certification today boast a much smaller core damage frequency (CDF) and large early release frequency (LERF), potentially reducing the off-site emergency planning zone [31, 44, 45, 47] Advantages of Soluble Boron-Free Operation in Small Modular Reactors All of the above advantages are accomplished by stringent design simplification. Any additional piping, pumps, and moving parts carry maintenance and operation implications, along with additional safety and regulatory hurdles. Returning to the initial discussion on the advantages and disadvantages of running a soluble boron-free SMR, the biggest advantage is realized in the elimination of the CVCS and any purification systems from normal operation. The elimination of this additional piping and of operational oversight bring a significant economic and safety benefit.

34 16 While most designs that incorporate soluble-boron free operation still retain boric solutions in accumulator tanks or other Emergency Core Cooling System (ECCS) functions [45], their elimination from normal operation still significantly reduces the operations cost. Consider a scenario where multiple SMR units are bundled together at a single plant with just a few reactor operators. With each reactor running a different concentration of boron at different power levels, the potential for confusion appears to be high. Running soluble boronfree will, at the least, allow a smaller team of reactor operators to oversee multiple units safely and effectively. Furthermore, the elimination of corrosive effects from boron, and problems linked to waste removal that have periodically plagued the industry represent another significant advantage [11, 15]. Corrosive elements that find themselves in the coolant are easily activated in the high flux environment, and represent an additional dose to reactor personnel that would be avoided with soluble boron-free operation. Other advantages are realized in the safety aspects of operation. Boron Dilution Accidents are completely eliminated and any potential loss of coolant accident will not be affected by the loss of soluble boron. Removing boron also creates a stronger negative moderator temperature coefficient due to density differences between pure water and a boricwater solution [43]. In typical LWR operations, the presence of soluble boron is accounted for in the neutron economy, and the density of a boric-water solution is slightly increased from a pure water solution. In an accident scenario, the overall density of the moderator is what drives the negative MTC. By removing boron, the density is automatically reduced, creating a more negative MTC. Along the same lines, some typical LWRs have a positive MTC at BOC, owing partially to a stronger boric solution at BOC. In this scenario, the moderator density at BOC is too high, creating non ideal conditions for reactivity, where a decrease in density enhances the thermalizing effect of the moderator. This of course has implications for safety and regulation that must be sufficiently dealt with, and removing boron completely eliminates this potential. In sum, the various advantages offered by boron-free operation help create a safer, more reliable SMR. Eliminating pumps, piping, overpressure transients, boron dilution accidents, and introducing a safer MTC all carry strong benefits that significantly improve the ability to create a passively safe reactor [15, 43].

35 Disadvantages to Soluble Boron-Free Operation in Small Modular Reactors For all its benefits, boron-free operation is not without disadvantages. Removing soluble boron as one of the three main methods of reactivity compensation fundamentally changes normal operating procedure. Typical LWRs use soluble boron to reduce the excess reactivity to levels manageable through limited control rod involvement. So while all reactors employ control rods to handle daily reactor kinetics, soluble-boron allows these control rod movements to be limited to the very top portion of the reactor. In this manner, the neutron flux profile is minimally affected, and does not produce an undesirable axial power profile. Without soluble boron, control rods must compensate for any excess reactivity left from the burnable poisons. This requires their direct and significant involvement in daily operations, where the active control rod bank at BOC is almost completely inserted, and is slowly withdrawn as the core depletes. This effect creates a skewed axial power profile for the lifetime of the core. Left unaddressed, this will create adverse pin-peaking factors and ultimately lower the reactor's operating margin [24, 37]. It must be noted that the overall impact of peaking factors can be reduced by lowering the overall power density of the core, and suggests that smaller reactors stand to benefit more from boron-free operation since they are better suited for small power densities that blunt the impact any adverse axial power profile may have. Nevertheless, significant engineering effort must be given to maintain a proper axial power profile. While there a few useful techniques to achieve this, it is still a cost-intensive exercise and leaves less control for operators to use in normal operations. The most obvious solution to the axial power profile issue is to attempt to mimic the effect of soluble-boron on the neutron flux. That is to say, design the discrete neutron poisons in such a manner as to mimic the effect of a unified neutron absorber. In this manner, the overall axial and radial flux profile over the life of the core will remain as smooth as possible and thereby minimize any pin-peaking issues. With only burnable poisons and control rods as viable methods to control excess reactivity, there are four main techniques that can be used to accomplish this. First, any burnable absorber arrangement can be axially graded. Higher enriched Gd 2 O 3 at the bottom of the fuel pins, in the areas that will first be exposed to higher neutron flux concentrations, can blunt the effect of control rod movement. Second, separating the

36 18 active control rods into two or more control rod banks that operate at different depths can serve to offer a step reduction in reactivity compensation, instead of the sudden cliff between axially rodded and unrodded locations. If different control rod materials are used for the different banks, a further step reduction can be achieved. Third, lowering the enriched U 235 in the fuel pins that contain burnable poisons will compensate for any shadowing and shielding effects. Finally, axially grading the enrichment of U 235 for entire fuel assemblies can adjust the amount of reactivity present at desired locations. One technique by itself might not be enough to completely overcome the axial power profile issue, but employing all four in conjunction could potentially create a suitable axial power profile throughout the lifetime of the core. The difficulty arises by the fact that none of these methods are independent variables. Their effect on the axial neutron flux profile will also affect the impact of other techniques on the flux profile. Any single manipulation of the neutron flux will ultimately change the effectiveness and overall impact of other methods of controlling the neutron flux. Thus, any optimization study would be exceedingly difficult. Other disadvantages to soluble boron-free operation carry safety implications. Any rod ejection, rod withdrawal, or stuck rod event can be much more severe due to the additional control rod worth [26, 43]. Furthermore, any refueling activity must be carefully analyzed due to increased criticality concerns. Without soluble boron, depleted fuel assemblies in cold zero power conditions carry a much lower criticality margin. Adding soluble boron for these activities might be prudent. Finally, because control rods are a discrete rather than uniform absorber, any shadowing effects caused by the insertion or removal of control rods will have a greater propensity to induce xenon oscillations. Since boron-free cores use active control rods, care must be taken to prevent these events. Overall, the removal of soluble boron carries significant advantages toward the safety and reliability of reactor operations. But its removal also brings distinct challenges, most notably in controlling the axial power profile. A complete discussion on the exact nature of these challenges will be provided later, along with an examination of potential strategies that could mitigate the challenges.

37 19 Chapter 2 Literature Review 2.1 Survey of Current SMR Designs This thesis concerns soluble-boron free operation in Small Modular Reactors. The state of the industry today involves several competing designs, some of which employ boronfree operation. The motivations for moving to boron-free have been previously discussed, and this thesis aims to further inform any decision to move to soluble-boron free based specifically on core size and power density. With this in mind, a brief survey of the three main SMRs being designed in the United States is in order Babcock and Wilcox mpower The Babcock and Wilcox (B&W) mpower reactor design [21] is a passively safe advanced light water reactor with a below-ground containment structure. Employing a competitive approach to plant operations that emphasizes safety, the mpower reactor will be a 180 MWe reactor with a passive safety that eliminates emergency power requirements, incorporates a 4-year core lifetime with standard U 235 fuel, and a 60-year plant lifetime with spent fuel storage on-site. The mpower reactor is a descendant of the B&W maritime reactor program, notably incorporating four key features of the nuclear-powered merchant ship Otto Hahn: incorporating all NSSS components within a single vessel, use of an integral, once-through steam generator, use of PWR-type fuel assemblies, and boron-free reactor coolant. The mpower design also improves upon the Otto Hahn design by introducing a higher reactor power and an improved efficiency, placing control rod drive mechanisms within the single containment vessel, and incorporating passive safety systems [21]. Notable features of the core design include a 48-month operating cycle at 95% capacity with shorter versions of standard commercial 17 x 17 PWR fuel assemblies in a closely packed square-pitch lattice. A significantly reduced average linear power density (compared to commercial PWRs) results in improved thermal margins, increased operational flexibility and longer fuel cycles. The non-borated coolant necessitates use of several different control rod banks which control excess reactivity and axial power shape. Several reactor

38 20 coolant pumps supply forced convection through the primary circuit, with a standard electrically-heated pressurizer above the steam generator. Notable differences in mpower s design compared to NuScale and Westinghouse designs include the use of boron-free coolant, a below-ground containment structure, 69 assemblies for 180 MWe operation, and a 4-year core lifetime with no refueling. Most other aspects are largely similar in design, with an integral containment vessel that allows for typical SMR advantages like advanced passive safety features and modular, scalable designs. While B&W is designed for boron-free operation, information pertaining to the operation and effectiveness of their boron-free reactor is strictly proprietary. The only public knowledge of their current design is simply that it is boron-free, but nothing further can be said of the strategies and designs used to create a suitable boron-free reactor NuScale Power SMR The NuScale Plant represents an innovative approach to SMR design by introducing a scalable plant comprised of up to 12 factory-fabricated 45 MWe power modules. Each module consists of an integrated PWR surrounded by a second, high strength containment vessel. Each vessel shares a common concrete pool that resides underground, housed in a seismic category I building, which provides 30 days of passive core and containment cooling. After 30 days, the core decay heat generation is small enough for natural convection heat transfer to provide sufficient cooling for an unlimited period [31]. This unique design represents superior passive safety, providing decay heat removal for an indefinite period of time without the need for external power or water. Owing to each module s 45 MWe power output, a smaller integrated PWR vessel with a core comprised of 37 half-height standard 17 x 17 assemblies operates on natural convection, further eliminating the need for external power. A helicoil steam generator optimized for natural circulation provides heat removal from the primary cicuit, and an integral pressurizer with heating elements and a spray system maintains the pressure at 1850 psia. Each module operates on a 2-year refueling cycle. The smaller core with a relatively lower power density and flow rate make NuScale stand out from B&W and Westinghouse. The use of a common pool and a scalable plant

39 21 further distinguished their design. However at present their design incorporates soluble boron as a primary method of excess reactivity compensation Westinghouse SMR Westinghouse s Small Modular Reactor incorporates proven design technologies realized in the AP1000 plant to create a passively safe integral pressurized water reactor. Similar to B&W and NuScale, the integral reactor containment sits below grade and houses all elements of the primary loop, including a once-through steam generator and integral pressurizer. The reactor is designed for >225 MWe operation by incorporating 89 robust 17 x ft active height PWR fuel assemblies. This larger size sets the Westinghouse design apart from both B&W and NuScale, offering the greatest energy output with a 2 year refueling cycle. Westinghouse s proven ability to design, license and deploy reactors and the experience gained through the design and certification of the AP1000 plant lends credibility to their SMR design. Some of these AP1000 features enable a passively safe design that allows for 7 days of passive core heat removal before human intervention would be required. This exceeds the current NRC regulations requiring 72 hours of passive safety, but falls short of both B&W and NuScale, owing to the larger core and greater power output. This larger design necessitates extra complexity in plant operation and safety systems, and reflected in this is the use of borated coolant through the primary loop. Of specific concern for this thesis the core size and power density of each design. As B&W, with a moderate size and power density being the only design that has pursued boronfree operation, perhaps other larger or smaller designs would be well suited to revisit a boronfree approach. Nevertheless this thesis employs a SMR design with a power density roughly in the middle of these three designs in an effort to provide research on a typical, universal SMR design.

40 Relevant Soluble Boron-Free Research and Development While some current SMR designs employ a boron-free core design, the information related to their specific design and operation are kept strictly proprietary. There are very few publicly available research papers and relevant reactor designs on soluble boron-free operations in LWRs. Nevertheless, a handful of notable and significant papers and their contributions to boron-free research are outlined and discussed below Feasibility Studies of a Soluble Boron-Free 900-MWe PWR In 1999 the French Commissariat a l Energie Atomique conducted a feasibility study on an Advanced 900-MWe PWR aiming at the partial or total elimination of soluble boron during normal operations [12, 15, 37]. Their study comprised three parts: consequences of the partial or total elimination of soluble boron on plant safety; core physics including assembly design and core control; and core physics including control rod follow and load following. Their motivations for the study involve several factors previously discussed in the introduction, with a specific eye on two main objectives: the improved safety taking into account the principle of defense in depth, and an increased simplification in the design and control. The first part concerns the safety systems and the consequences of eliminating or reducing soluble boron. The implications linked to the use of soluble boron in the coolant are described, as well as the consequences for the reactor in terms of demands for reactivity control reinforcement and for the need for defense-in-depth requirements [15]. As described, the greater the elimination of soluble boron, the greater the simplifications. All this makes operation easier (reduction or elimination of maintenance), reduces the doses received by maintenance staff (less piping in contact with coolant), simplifies accident transients, reduces the risk of human errors, and reduces maintenance costs. The second part details the various neutronic consequences of eliminating boron, including increased dependence on neutron poisons, moderation ratio, and cluster systems for control rods [37]. A specific assembly geometry is optimized by taking these consequences into account, where it was found that a 19x19 assembly lattice with 36 poisoned rods could sufficiently suppress excess reactivity. Gd 2 O 3 was selected due to its strong absorption characteristics, with 16 rods at 5% and 20 rods at 14%. Selecting such a high loading percentage for Gd 2 O 3 introduces a longer burnup period for Gd 2 O 3 and stronger self-shielding

41 23 characteristic, at the expense of slightly higher peaking values. Careful selection of the loading geometry optimized the assembly s power peaking factors, maintaining a satisfactory value of 1.16 at the beginning of cycle and 1.07 at the end of cycle. During the core design, further care was taken to select a proper loading pattern for a three-batch refueling scheme, and to optimize the Rod Control Cluster (RCC) arrangement. Several important design modifications arose as part of this first core physics study: A 19x19 lattice was designed to accept an increased number of absorber rods, and to increase the moderator-to-fuel ratio. Further axial zoning of the burnable poisons improved the axial power profile, and multiple control rod banks provide sufficient reactivity to ensure hot and cold shutdown. The last core physics study addressed control algorithms to define control rod movements so as to minimize the imposed power peaks at each instant [12]. These peaks are the inevitable result of primarily compensating for excess reactivity through control rods. Further optimization of the axially graded burnable poison profile, along with introducing both grey and black control rod clusters, allowed for a smoother power profile over the whole cycle. These specific strategies mirror what was discussed earlier in this study. Additionally, such a dependence on control rods increases the consequences of reactivity-induced accidents linked to accidental removal of rod clusters and necessitated further study on the associated safety implications. Final conclusions determined that soluble-boron free operation in a 900-MWe PWR significantly simplified the core control and improved operational flexibility. However, soluble-boron free operation creates a specific difficulty in properly controlling the power distribution at the end of cycle and during load follow operations [12]. Since the Commissariat a l Energie Atomique directed their study on the effects of removing soluble boron on a large 900-MWe reactor, their findings were concerned with all aspects of operation. SMRs reduce and simplify the traditional PWR layout to a single containment, creating several distinct differences that in turn impact the benefits and advantages to removing soluble boron. With this in mind, much of work performed by the Commissariat does not translate directly to SMRs. While many of their operating characteristics like an increased dependence on burnable poisons and additional control rods with multiple banks will be employed and expanded in this thesis, other aspects will be of no concern due to this distinct difference between traditional PWRs and SMRs.

42 Elimination of Soluble-Boron for a New PWR Design The Combustion Engineering study on soluble-boron free feasibility [43] was motivated by two main factors: the corrosion effects from boric acid, and the large contribution on the effluent volume. With these two objectives in mind, the methodology employed four steps: identification of the needs for reactivity control, lattice effects, new poisons and increased use of burnable poisons, and safety and economic analysis within an 18 month cycle. Their results covered soluble-boron free operation with commonly used technologies and standard lattices and poisons, while doubling the current number of control rods compared to standard PWRs. They also found improved performance in terms of safety and an equivalent cost when optimization is performed. However soluble boron free operation was attained at the cost of restrictions on the cycle length and on the operating margin due to peaking factors. In the end, EPRI concluded that eliminating soluble boron would allow for a greater simplification in control and maintenance through the elimination of pipes and circuits and to reducing several waste management activities. Finally, removing the corrosion effects and eliminating problems linked to overpressure transients are reflected in safety improvements. Their conclusions found that the few drawbacks linked to boron-free operation can be reduced through optimization and are less restrictive for smaller PWRs. They additionally concluded that the advantages are particularly beneficial for passive small and medium reactors [43]. Where the EPRI study ends is where this study begins. They perform their analysis with respect to traditional LWRs, but find smaller designs might be better suited for soluble boron-free operation. Many of their findings are reiterated in the advantages and disadvantages outlined earlier, but unfortunately the combustion engineering study does not contribute significantly to specific strategies for overcoming difficulties in operations A Soluble Boron-Free Core Design for the IRIS-50 The IRIS-50 was a prototypical design under development by Westinghouse as a 50 MWe integral PWR, based on the well-known 335 MWe IRIS design [16]. The larger 335 MWe IRIS design incorporates soluble boron in the coolant, in large part because additional control rod requirements would become economically burdensome [7]. However in smaller

43 25 designs like that of the IRIS-50 a soluble-boron free design could become economical. This study shows that control rod banks can be effectively used as an alternative to soluble boron for both long term and short term reactivity compensation in all plant operating conditions. Main features of the IRIS-50 include 37 fuel assemblies with a single batch, zoned fuel management arrangement. The IRIS-50 incorporates the use of 6.0 ft standard 17 x 17 Westinghouse PWR fuel assemblies with UO 2 fuel for a 4 year cycle length. Er 2 O 3 acts as an integral burnable absorber for further reactivity compensation [16]. The smaller core leads to an increase in neutron leakage, and therefore a less reactive configuration. However, this also introduces tighter coupling of the core, reducing the impact of localized events like control rod insertion. This adds to the viability of soluble boron-free operation due to an increased dependence on control rods. To demonstrate that control rod banks can be effectively used as an alternative to soluble boron, multiple control rod banks are selected for different purposes. Four banks of rodded assemblies function as primary reactivity control banks. A separate bank exists independently and functions to balance the axial power distribution. Two further banks provide shutdown margin for hot and cold conditions. The Four primary reactivity control rod banks are moved to compensate for reactor kinetics and to maintain criticality. Two insertion patterns for the different banks are proposed to ensure that different depths of insertion for each bank effectively balance any shadowing and shielding effects from protracted insertion of a control rod in a given fuel assembly. As the fuel is depleted, the two configurations are periodically alternated. Further optimization incorporates the axial offset bank to counterbalance the effect on axial power of the partial insertion of the primary reactivity control rod banks [16]. Altogether, a functional scheme for reactivity compensation in a small PWR is proposed and analyzed. The results demonstrate a 4-year effective cycle length that possesses higher relative power peaks that are still within all design limits. Further optimization of fuel loading patter and control rod design is expected to further reduce the associated power peaks. While this IRIS-50 design did not explicitly incorporate advanced burnable poison schemes, the selection of multiple control rod banks demonstrates the feasibility of depending heavily on control rods to compensate for excess reactivity. It is important to note that the IRIS-50 control rod algorithm incorporated multiple banks that are each partially inserted in the core. Unfortunately, complete information on the axial power profile, the neutronic

44 26 characteristics, peaking factors, and other relevant operational data is kept proprietary. While this thesis will adopt general strategies outlined in the IRIS-50 design, the lack of complete core data necessitates starting from scratch and building an independent strategy for soluble boron-free operation Nuclear and Thermal Hydraulic Design Characteristics of the SMART Core The System-integrated Modular Advanced ReacTor (SMART) is a 330 MWth SMR in development through the Korea Atomic Energy Research Institute (KAERI). Since its inception in the early 2000s up to today, the design has undergone significant modifications [1, 2, 23, 48], with early designs incorporating soluble boron-free operation. The details on the proposed soluble boron-free operation are provided in a 2003 paper on SMART s nuclear and thermal hydraulic design characteristics [8]. The SMART reactor employs 57 fuel assemblies in a circular array with 17x17 fuel assembly geometry. Fuel rods employ UO 2 with 4.95% U 235 for a 3-year operation cycle, with a 2 meter active core height. Burnable poisons and control rods are used to compensate for excess reactivity, with 49 total control rod elements present in the core. These 49 control rod elements are also capable of maintaining a subcritical condition at 20ºC without soluble boron. The strategy for soluble boron-free operation utilizes a combination of burnable poisons and control rod banks. With regard to burnable poisons, three main fuel assembly types are employed, each with different burnable poison characteristics. Specifically, one fuel assembly type consists of 28 Al 2 O 3 -B 4 C shim rods, and 12 Gd 2 O 3 poisoned rods. A second type contains 20 Al 2 O 3 -B 4 C shim rods and 4 Gd 2 O 3 poisoned rods, and a third type contains 24 Al 2 O 3 -B 4 C shim rods and 4 Gd 2 O 3 poisoned rods. These three different fuel assemblies provide different depletion profiles, and since neutron fluxes are higher in the core central region than in the outer peripheral region, fuel assemblies with more poisons are placed in the central region of the core. Further axial grading is also employed to compensate for control rod insertion [8], although no detail is provided on the exact nature of the axial loading. Control rod banks employ Ag-In-Cd and are grouped into 4 regulating banks and 2 startup banks. The startup banks are at the fully withdrawn position during power operation, whereas the regulating banks are used in normal operation to control core excess reactivity. The 49 control rod banks are capable of controlling core excess reactivity at all operating

45 27 conditions [8]. Furthermore, the critical rod position of each of the 4 regulating banks during normal operation is designed with a staggered profile. One critical rod bank is inserted far into the core, while another is inserted slightly less. This staggered insertion limits the impact on the axial power profile. The critical rod position for all regulating banks does not change much during the cycle because the core excess reactivity does not change much as a result of the careful selection and distribution of the fuel assembly types. This relatively constant control rod position is important for ensuring shutdown margin and power distribution control [8]. The results obtained from the above strategies produced an axial offset between and 0 throughout the entire cycle, and a maximum power peaking factor of The strategies employed by the SMART design are similar to the strategies that are employed in this study. The results obtained from SMART show significant promise for acceptable soluble boron-free operation. However, once again detailed information on the exact axial loading of burnable poisons and on control rod insertion behavior is not provided. Information on the weight percent of B 4 C in the shim rods and Gd 2 O 3 in the poisoned rods is also not provided. Furthermore, the SMART design employs Al 2 O 3 -B 4 C shim rods in addition to Gd 2 O 3 poisoned rods. This study does not employ Al 2 O 3 -B 4 C shim rods in an attempt to produce soluble boron-free operation through industry standard fuel assembly designs. Specifically, through fuel assemblies with only UO 2 fuel rods and Gd 2 O 3 poisoned rods. It should also be noted that each Al 2 O 3 -B 4 C shim rod used in the SMART design essentially creates a fully inserted control rod with limited self-shielding characteristics. This study instead employs a control rod algorithm that places fully inserted banks into the core for extended periods of time.

46 28 Chapter 3 - Methodology 3.1 Definition of research goals SMR design incorporates several fundamental design changes. Most notably, the design simplification into a single containment vessel and the reduced size associated with modular designs. These simplifications bring some inherent advantages if soluble boron is removed in normal operations. However, removing soluble boron also introduces significant complications. Thus, this study arises from a desire to remove soluble boron in normal operations for a prototypical SMR. The purpose of this study is twofold: 1) Identify a soluble boron-free SMR design that meets design requirements (to be listed below); and 2) To examine the fundamental differences in operations with and without soluble boron in an SMR. With respect to the first purpose, different strategies for operating boron-free will be explored. If a core is found to meet the design requirements, no further improvements will be attempted, since the fundamental goal of this study is to demonstrate the feasibility of boronfree operation. In this respect, this study will not seek to define or establish an ideal core. The second purpose of the study involves comparing the behavior of an SMR with and without soluble boron. Key aspects include the neutron multiplication factor without leakage effects (k inf ) vs burnup, fuel depletion and plutonium production, neutron flux and energy spectra, effective fraction of delayed neutrons, and reactivity effects (moderator and fuel coefficients). These aspects will be examined on an infinite-lattice level as a means of comparing the physical effects of removing boron. 3.2 Criteria for Success Removing soluble boron places increased dependence on control rods and burnable poisons, and requires control rods to be actively inserted in the core to maintain criticality. This principle difference in operations directly impacts the axial power profile. In an ideal PWR, the axial power profile will resemble a chopped cosine, with a natural peak in power at the midplane [13]. Since a chopped cosine naturally limits any spikes or significant peaks in power output, any deviation from this normal chopped cosine contains the potential for these peaks, and the resultant peak will have a direct impact on peaking factors within the core.

47 29 For this reason, the primary factor of concern in developing a soluble boron-free SMR revolves around the maximum peaking factor throughout depletion. Of similar interest will be the axial power profile throughout depletion, since this profile will provide insight on the peaking factors. Strategies designed to contain the axial power profile should also be helpful in containing the maximum peaking factors. However, even if maximum peaking factors are at an acceptable level, a skewed axial power profile is still less than ideal. A consistently skewed profile will result in uneven exposure axially throughout the core, along with further complications. A power profile with a peak that deviates from the center of the core also results in a neutron flux profile that deviates from the center. This shifting neutron flux profile will primarily impact exposure, where locations that experience high flux will deplete quicker. This uneven exposure throughout the core will ultimately shorten core lifetime, representing an inefficient use of fuel in the core. Beyond impacts on exposure, a skewed axial power profile will also produce shifting samarium and xenon poisoning concentrations. The effect these poisons have on operation could further complicate the axial power profile and exacerbate attempts to contain the power profile. In the end, designing a SMR that possess a skewed axial power profile is less than ideal Criteria for Axial Offset As discussed above, the axial power profile in an ideal core with soluble boron closely resembles a chopped cosine, where the core possesses inherent symmetry. The amount of power produced above the core centerline is balanced by that produced below the core centerline, with a natural peak occurring at the center. In order to quantify how close a core s power profile is from this ideal chopped cosine, a metric known as the axial offset is used [26]. In general, a positive value indicates a power profile that is skewed toward the top of the core where more power is produced above the centerline than below the centerline. Conversely, a negative value indicates more power produced below the core centerline. An axial offset of 0 indicates a perfect balance between power produced above centerline vs below. To determine the exact value of the axial offset, consider the axial power profile in Figure 1. While the power profile still clearly resembles a chopped cosine, it has been shifted

48 30 toward the bottom of the core. To calculate the axial offset value for this core, the normalized amount of power produced in each node throughout the core is first calculated, represented by the blue line. These values are produced by taking the averaged power level in each node and dividing it by 25, the total number of axial nodes in the core [59]. This produces a total percentage of power produced in each node. Then, the sum of these normalized amounts of power is taken for all the axial nodes both above centerline and then again below centerline. For this example, the nodes above centerline produced 18% of the total power, while the nodes below centerline produced 82%. 21 Axial Node Normalized Power Averaged Power Normalized Power Level Figure 1: Axial power profile of a hypothetical boron-free reactor core. Therefore, the reported axial offset value is the difference between the total average power produced above centerline and below centerline. In this example, the reported axial offset would be = In this manner, the total range of axial offset values can vary between 1 and -1. A high positive value does not necessarily equate to the locus of power being produced at the very top of the core, just that the majority of power is being produced somewhere throughout the top of the core. In other words, the difference between the integral

49 31 of power produced above centerline and below centerline is what constitutes the value of the axial offset. To demonstrate this, Figure 2 shows two different axial flux profiles that both result in a very similar axial offset value. The blue line contains an axial flux profile that more dramatically deviates from the ideal chopped cosine, with peak power production occurring very close to the bottom of the core Axial Offset = Axial Offset = Axial Node Normalized Power Level Figure 2: Averaged axial power profile of two hypothetical boron-free cores vs core height (axial node). While the two axial offset values are very similar, the axial power profile associated with the -0.6 axial offset produces a maximum peaking factor much higher (5.40) than the profile associated with the axial offset (3.34). This is due to the higher maximum average power level (at around node 8) of 2.75, whereas the blue line produces a peak (around node 4) of only 2.1. The important point is to remember that the reported axial offset value is derived from a measurement of the total amount of power produced above and below core centerline. It does not paint a definitive picture of what the actual axial power profile is, which will more accurately correlate to high or low peaking factors.

50 32 However, since the shape of the axial flux profile will change dramatically throughout burnup for a soluble boron-free core, the best simple representation of the axial power profile is the axial offset value. For this reason, graphs of the axial offset value vs burnup will be used to determine the behavior of the axial power profile throughout the lifetime of the core. But it is important to keep in mind that it is not the axial offset itself that directly correlates to peaking factors, but rather the shape of the actual axial power profile. With this in mind, a successful soluble boron-free SMR will maintain the axial offset throughout burnup at ±0.4. This band would ensure that no more than 60% of the total core power is produced either above or below the core centerline, and would therefore represent a largely uniform axial power profile Criteria for Maximum Pin Peaking Factors Thermal hydraulic disciplines in nuclear engineering revolve around one critically important factor: The reactor cannot be subject to any condition that would result in meltdown [13, 26, 62]. Among several other potential issues, fuel failure would result hydrogen production in the cladding, increasing the potential for hydrogen explosions within containment and greatly increasing the risk of fission product release. Fuel melting would also only occur in scenarios with limited heat transfer, and the resultant liquid fuel would burn through containment and cause significant environmental damage [26]. As such, this simple requirement is of critical importance, and it carries several implications. In order to ensure there is no fuel failure in PWRs, the NRC has identified that the average clad temperature during any postulated accident scenario cannot exceed 2000ºF [62]. This prevents cladding failure and the subsequent fuel melt. In order to maintain this requirement, the NRC further requires the surface heat flux for fuel pins during any postulated accident scenario does not fall below a specific ratio known at the Minimum Departure from Nucleate Boiling Ratio (MDNBR) [26, 62]. The MDNBR is a ratio that defines a critical heat flux as the heat flux at which cladding failure is likely to occur [26]. It is given as follows: MDNBR = q crit q f

51 33 Where q represents the local maximum heat flux in a reactor core, and f represents engineering uncertainties. Generally, the engineering uncertainties are owed to both overpower factors (the possibility of the reactor core operating or subject to power levels above its rated level) and a general engineering uncertainty factor (uncertainties involved with modeling and analyzing reactor behavior). Together, a total overpower factor of 1.05 and an engineering uncertainty factor of 1.15 is sufficient for the purposes of this thesis [26]. The specific requirements enforce a MDNBR > 1.3 for all postulated reactor conditions. Owing to this, thermal hydraulic demands on reactor engineers revolve around maintaining q under a specific value at which the MDNBR will be compromised. To accomplish this, the only factor of concern would be the local maximum heat flux. Wherever the heat flux is greatest throughout the reactor s entire lifetime would be the heat flux used in the MDNBR calculation. Thus, avoiding any significant spikes in power production is critical, and sheds further light on why maintaining a proper axial power offset (Section 3.2.1) is important. However, the axial power profile is not the specific item of concern. Rather, the only item of concern in relation to the MDNBR is the specific maximum pin peaking factor. This maximum pin peaking factor occurs at the fuel pin where the heat flux is at a maximum for the entire core. The value of the pin peaking factors are normalized to one, therefore the value of the maximum pin peaking factor represents how far above average that pin s heat flux is [13, 26]. Subsequently, tracking the value of the maximum peaking factor throughout burnup gives a quantifiable metric by which power spikes can be measured. However, requiring a specific maximum pin peaking factor to remain below a certain level does not certify that MDNBR limits are kept. The only value that certified MDNBR limits are kept is the specific heat flux within the maximum fuel pin (q ). Therefore, the limits imposed on maximum pin peaking factors will follow engineering judgment. Any final design must incorporate a specific examination on the actual maximum heat flux inherent to that design. Nevertheless, using engineering judgment, a pin peaking factor above a certain value that is likely to result in a MDNBR that has been exceeded can be identified. To examine this, first we must determine q crit. Several methods have been postulated since the physics behind two phase flow is exceedingly complicated [19, 20, 26]. As such, an empirical solution has not been identified, and experimental approximations are instead employed.

52 34 The selected method employs Groeneveld s critical heat flux tables [20]. Using only reactor pressure, mass flux, and thermodynamic quality, values for the critical heat flux in 8mm cylindrical tubes is estimated. Since these values are known, the Groenveld lookup tables will be employed at a final determination on the value of q crit. By employing conservatism, the as yet unknown thermodynamic quality can be set to (subcooled liquid), and a q crit value of 3335 kw/m 2 is identified. Using this value, and the above engineering uncertainties results in a total calculation of: MDNBR = 3335 KW/m q = 2762 KW/m2 q Following this equation, a value of q that exceeds 1973 KW/m 2 will result in a MDNBR that is below 1.4. This value will be used as the MDNBR heat flux criteria that must not be exceeded at any point of operation. Furthermore, from a plot of several data points correlating the maximum pin peaking factor to the associated power density gives a general pin peaking factor of 4.2 that is likely to result in a value of q that exceeds 1973 KW/m 2. Although this number was found through correlations and engineering judgment, and will therefore be used as a guideline and not a deterministic limit. 2.3 Available Tools for Reactor Design and Analysis The regulatory structure of the nuclear industry requires any design and analysis of nuclear reactors to be performed on qualified computational software [26, 62]. This feasibility study will require analysis of lattice calculations to model the behavior of fuel assemblies with and without soluble boron. These fuel assemblies and the appropriate cross sectional data will further need to be packaged into full-core geometry and model the depletion of a full-scale SMR. The software should be flexible and powerful enough to accurately simulate the complex behavior of nuclear reactors, and must be an industry recognized standard and verified for reactor analysis. While there are several options available, Oregon State University provided access to Studsvik Scandpower s suite of neutronic codes. Their code held unique advantages through

53 35 the ability to model all aspects of reactor design, from pin-cell calculations and infinite lattice studies, to 3-D full core depletion and analysis. Further benefits include the ability to couple other industry standard thermal hydraulic codes like RELAP5 for detailed analysis of the entire primary circuit. While this study does not incorporate thermal hydraulic calculations, future work may incorporate a complete analysis of the primary circuit, in which case selection of a code that easily couples with thermal hydraulic codes is beneficial. Studsvik s codes are widely recognized as an industry standard, being used by utilities, vendors, research labs, and universities in the United States and worldwide [35, 55, 59]. For the above reasons, this code was selected for use in this study to analyze boron-free behavior in a SMR. The specific codes utilized were CASMO 4E and SIMULATE 3K. CASMO 4E is a 2-D multigroup transport theory code for calculation over the entire burnup of LWR fuel in typical fuel assembly geometries or simple pin cells. The primary function of CASMO is to provide neutronic and cross sectional data for cylindrical fuel rods in a square pitch array [55]. The code contains the ability to include typical burnable poisons homogeneously mixed in the fuel pin, which is a crucial requirement for the study at hand. CASMO can also take spacer grids, instrument tubes, water channels, and other typical reactor configuration. At its core, CASMO solves the 2-D neutron transport equation for use with LWR fuel, with the provided data simulating neutronic behavior throughout the whole exposure cycle. A nuclear data library with 70 energy groups is coupled with the geometrical and physical properties supplied in the input file to generate macroscopic cross sections. Resonance integrals are approximated using an equivalence theorem and used to calculate effective absorption and fission cross sections. Shielding and shadowing effects present with fuel and control pins are calculated using Dancoff factors [35, 55]. CASMO also retains the ability to generate cross sectional and neutronic data suitable for 3-D nodal codes (SIMULATE) at several possible state points. This data and the associated cross sections are then bundled in appropriate libraries for use with SIMULATE. Additionally, several functions are automatically performed (thermal expansion of densities and dimensions) or have set default values for typical fuel and geometric parameters. The Linux based code was written exclusively in Fortran 77 and runs on UNIX and Linux workstations, along with P.C. s.

54 36 While CASMO will be used for 2-D lattice analysis and fuel assembly preparation, SIMULATE 3K will be used for 3-D full core analysis. SIMULATE 3K is an advanced code for the analysis of LWRs, specifically BWRs and PWRs. It employs a 2-group nodal code based on the QPANDA neutronics model, in which a 4 th order polynomial is used to represent both thermal and fast flux distributions [35, 59]. At its core, SIMULATE performs pin power reconstruction and can be employed to analyze fuel management, load follow, xenon and samarium transients, startup predictions, criticality searches, and several other reactor analysis data. It is a flexible and strong code capable of simulating the complex physical effects typical of LWRs [98]. Due to its position as an industry standard code and the qualification process inherent to its approval from the NRC for reactor analysis, no validation study will be performed.

55 37 Chapter 4 Reactor Design and Analysis Owing to the organizational structure of this study, the methodology and analysis is split into five main sections. First, an overview of the selected SMR design Second, a study on five key physical effects of soluble boron-free operation in a 2-D infinite lattice. Third, development and analysis of several fuel assemblies with different neutronic and depletion characteristics in preparation for a soluble boron-free full core design. Fourth, a description and analysis of different strategies for containing pin peaking factors and axial offset in a soluble boron-free reactor core through axially grading both burnable poisons and U 235 enrichment. In this manner, a foundation will be laid upon which the results from these different strategies of soluble boron-free operation can be analyzed. Chapter 5 will therefore discuss and analyze the actual results from implementing these different strategies. 4.1 The Selected SMR Design with Fuel Assembly Geometry and Characteristics The purpose of this study is to investigate the operational and physical effects involved with removing soluble boron in normal operations. With that in mind, an SMR design that follows industry standards would best capture the inherent changes induced from boron-free operation. With this in mind, the selected SMR design followed industry standards where possible. Table 4.1 and 4.2 contain the fuel assembly and full core geometry and specifications for the selected core. Westinghouse PWR fuel assembly geometry was selected since they represent an industry standard. The one significant change from normal Westinghouse fuel assemblies is the active core height. Our SMR was designed with a 200 cm active height, in order to represent a smaller, compact reactor core designed to fit in a single comprehensive containment shell typical of current SMR designs.

56 Table 1: SMR Fuel Assembly Specifications 38 Table 4.1 SMR Fuel Assembly Specifications Fuel Assembly Specifications Fuel Temperature 824 K Moderator Temperature 563K A total of 57 fuel assemblies comprise the full core in a circular array (Figure 3). This value is slightly less than Pressure 2175 PSI B&W mpower and Westinghouse (69 and Power Density 68.5 kw/l 80 fuel assemblies, respectively), while Assembly Geometry 17 x 17 larger than NuScale s SMR (37 fuel Pin Pitch 1.26 cm assemblies). The selected design Fuel Composition UO 2 Fuel Density g/cm 2 incorporates 57 fuel assemblies in order to Spacer Material 57% Inconel-718, incorporate a single central fuel assembly, 43% Stainless Steel while still retaining a symmetrical circular Spacer Density 7.9 g/cm 2 array. Spacer Mass per Axial 20.5 g/cm Core power is a function of power Unit Length Fuel Radius Fuel Pin Geometry cm density, core fueled area, and active core height. The chosen metrics provide Cladding Thickness cm Guide Tube Geometry MWth, placing this design in the same Inner Shroud Radius 0.57 cm category as the M&W mpower and Shroud Thickness 0.04 cm Westinghouse SMR designs. NuScale s Inner Shroud Composition Moderator design is significantly lower, but also Control Rod Geometry Inner Shroud Radius 0.57 cm operates on a different design philosophy Shroud Thickness 0.04 cm that incorporates natural circulation Inner Shroud Composition Ag-In-Cd throughout the core [31]. This selected design provides forced convection through the primary loop in order to retain industry standard characteristics, and to avoid particularly egregious thermal hydraulic performance issues related to natural circulation [50]. The specific coolant mass flux is proportional to the mass flux in the mpower design, and again represents industry averaged values. The same can be said for the operating pressure, coolant inlet temperature, and fuel composition. In the end, simulating the chosen design with soluble boron results in typical depletion characteristics. This provides a good foundation to compare operating characteristics with and without soluble boron.

57 Table 2: SMR Full Core Specifications Table 4.2 SMR Full Core Specifications Full Core Geometry Fuel Assemblies 57 Active Core Height 200 cm Core Volume 5272 liters Core Fueled Area cm 2 Core Loading MT Fuel Assembly Pitch cm Axial Nodes 25 Node Height 8 cm Reflector Assembly 2.0% U 235 in UO 2 Axial Reflector Length 8 cm Full Core Operating Conditions Power Density 68.5 kw/l Thermal Power MWth Pressure 2175 PSI Coolant Mass Flux kg/cm 2 hr Coolant Temperature In 543 K Relative Power 100% Relative Flow 100% Core Inlet Temp 543 K Boron 0 ppm 39 The initial infinite lattice study on the physical effects of soluble boron-free operation was conducted in CASMO to model reactor assemblies. Each infinite lattice was modeled using Westinghouse PWR geometry, with design specifications listed in Table 4.1. CASMO performs thermal expansion calculations automatically, so that a relatively simple list of input cards can be used to model a complete infinite lattice. Fuel, guide tube, and control rod geometry is also included in Table 4.1. Radial Reflector Fuel Assembly Figure 3: Full core radial geometry.

58 Physical Effects of Soluble Boron-Free Operation A study on the physical effects of soluble boron-free operation in a 2-D infinite lattice compared to normal operation with 2000 and 1000 ppm boron will be presented below. This study was conducted using Studsvik s CASMO reactor simulation software [55, 56], which solved the 2-D transport equation in an infinite lattice [54, 55]. Each lattice was set up with typical Westinghouse PWR geometry as outlined in section 4.1. These physical effects were analyzed with 5.0% U 235 enriched fuel assemblies. This study encompassed five different sections: Infinite multiplication factor, k inf, with and without burnable poisons. Fuel depletion and Plutonium production Neutron flux and energy spectra Prompt neutron lifetime and effective fraction of delayed neutrons Reactivity effects: Fuel and Moderator Temperature Coefficients Multiplication Factor with and without Burnable Poisons In normal PWR reactor operations, soluble boron is dissolved in the coolant at specific concentrations, providing strong neutron absorption characteristics in the moderator. All other neutron poisons exist either in the fuel (burnable poisons) or in discrete locations (control rods). Since boron is dissolved in the coolant, its suppressive effects on the neutron flux are felt globally throughout the reactor, acting as a uniform suppressant, since the coolant exists in a large volume of the reactor core. Elimination of this suppressant will naturally increase the value of k inf. Figure 4 displays the multiplication factor, k inf, for a boron-free fuel assembly vs 1000 and 2000 ppm boron.

59 k inf Boron Free 1000 ppm Boron 2000 ppm Boron Burnup (MWd/Kg) Figure 4: k inf vs burnup for 5.0% U 235 assemblies with varying amounts of soluble boron. As expected, k inf is linearly proportional to the boron concentration. Additional boron suppresses the neutron flux in the core in a linearly increasing fashion. Throughout burnup, the effects of soluble boron slowly decrease. At around 60MWd/Kg the difference between the boron free assembly and 2000ppm boron is markedly less than at BOC. This is attributed to the varying rates of depletion between boron and U 235. Additionally, increasing the boron concentration decreases the cycle length. The 2000 ppm assembly reached k inf = 1 at 25 MWd/Kg, which corresponds to the point at which the reactor becomes subcritical. The boron-free core reaches k inf = 1 at 43 MWd/Kg, an increase of 72%. However, this does not mean a boron-free core will have a longer cycle length, as the initial excess reactivity must be compensated for in some form anyway. A full core operating with soluble boron will exhibit a boron burnup curve where the concentration of boron slowly decreases during burnup. Conversely, a boron-free core will compensate for excess reactivity with burnable poisons that naturally deplete, and with control rods than are actively removed from the core. All forms of reactivity compensation allow for a variable amount of compensation, such that a maximum cycle length can be achieved. Thus, any difference in actual cycle length must be attributed to other physical effects. Figure 5 shows the multiplication factor vs burnup for a similar group of assemblies with nominal burnable poisons. These assemblies contain 16 fuel pins poisoned with 8% Gd 2 O 3 weight percent, and 12 pins with 4% Gd 2 O 3. These poisoned assemblies demonstrate

60 42 the effect combining burnable poisons with soluble boron will have to be compared to a soluble boron-free assembly. k inf Boron Free with Poisoned Pins 1000 ppm Boron with Poisoned Pins 2000 ppm Boron with Poisoned Pins Burnup (MWd/Kg) Figure 5: k inf vs burnup for poisoned 5.0% U 235 fuel assemblies with varying amounts of soluble boron. At 2 MWd/Kg, the difference in k inf between the boron-free assembly and 1000 ppm Boron is 0.060, and from 1000 ppm to 2000 ppm it is When the poisons are fully depleted, at 20 MWd/Kg, the differences are and respectively an increase of around 0.01 in k inf after the poisons are depleted. This unexpected increase arises from the increased shielding and shadowing from the additional poisons. This shielding decreases the effectiveness of the poisons, producing tighter coupling at BOC. Once the poisons are depleted there is less shielding, which increases the difference in k inf between each assembly Fuel Depletion and Plutonium Production Light water reactors fueled with enriched U 235 contain two primary effects that contribute to energy production: fission of U 235 and the production and fission of Pu 239 and Pu 241. While the fission of U 238 from fast neutrons does occur, its contribution is negligibly low, around 5-8%.

61 43 Figure 6 displays the weight percent of total fissile Plutonium (Pu 239 and Pu 241 ) as a function of burnup. During operation, plutonium will continue to be produced due to neutron capture in U 238 and the subsequent decay chain into Pu 239. Once Pu 239 absorbs a neutron, it either fissions or transmutes into Pu 240. Following one more neutron absorption, Pu 240 becomes fissile Pu 241. Weight Percent of Total Plutonium ppm Boron, Pu Pu ppm Boron, Pu Pu-241 Boron Free, Pu Pu Burnup (MWd/Kg) Figure 6: Weight percent of total Plutonium (Pu Pu 241 ) vs burnup for 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron. Since Boron is a resonance absorber, its presence has little direct effect on the fast neutron population. An examination of the U 238 neutron absorption cross section (Figure 7) shows that U 238 has a pronounced resonance structure beginning at approximately 10 ev and extending to approximately 10 KeV [26, 40]. These resonance integrals create favorable conditions for neutron absorption in the epithermal and fast neutron spectra. Thus, the presence of soluble boron would have no direct effect on fissile Plutonium production.

62 44 Figure 7: U238 neutron absorption cross section (barns) vs energy (MeV). However, soluble boron does have an indirect effect on plutonium production. Since Soluble boron suppresses the thermal neutron flux, a higher total neutron flux is required if a constant power density is to be achieved. Power density is directly correlated to fission events in the core, and at BOC the only available means of fission is through thermal interactions with U 235 (neglecting the low percentage of U 238 fission evens). Thus a higher overall neutron population, reflected in a lower multiplication factor when compared to a boron-free assembly, is achieved for a constant power density. This higher total neutron flux primarily impacts the fast neutron flux profile, since boron absorbs thermal neutrons. A higher fast neutron flux will lead to increased absorption in U 238 which in turn produces plutonium. Figure 8 demonstrates how this accumulation of plutonium ultimately affects the total fission rate balance between uranium and plutonium isotopes. Near BOC, U 235 dominates fission events, but the steady production of plutonium coupled with the depletion of uranium ultimately results in an assembly that is driven by fission from plutonium at approximately 40 MWd/Kg. However this balance is not affected by the presence of absence of soluble boron.

63 45 Fission Rate (Fissions / cm 3 sec) 1.20E E E E E E+10 Uranium ppm Boron Uranium ppm Plutonium ppm Boron Uranium - Boron Free Plutonium ppm Boron Plutonium - Boron Free 0.00E Burnup (MWD/Kg) Figure 8: Total uranium and plutonium fission rate vs burnup in 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron. Figure 9 displays the weight percent of U 235 vs burnup. There is no appreciable difference between a soluble boron-free core and a core loaded with 2000 ppm boron. While there is a difference, it is largely negligible due to the large total amount of U 235. Thus, even though the soluble boron-free core is subject to a slightly higher thermal flux and U 235 fission rates, this impact on the total weight percent of U 235 is statistically insignificant even at 60 MWd/Kg.

64 46 Weight Percent Burnup (MWD/KG) ppm Boron 1000 ppm Boron Boron Free Burnup (MWd/Kg) Figure 9: Weight percent of U 235 vs burnup in 5.0% U 235 enriched fuel assemblies with varying amounts of soluble boron Neutron Flux and Energy Spectra The neutron flux spectrum is an important characteristic in determining the behavior of the reactor core and understanding the isotopic composition and the contributions from Plutonium. For the purposes of this study, a two-group model is implemented defining thermal and fast neutrons as follows: Group Number Name Lower Boundary Upper Boundary Group 2 Thermal 0.0 ev ev Group 1 Fast ev 10 MeV In order to determine the differences between operating a core with and without soluble boron, a characterization of the total, fast and thermal neutron fluxes must be provided. Figure 10 provides the total neutron flux required to maintain a constant power density of 68.5 KW/L for the specified SMR. Increasing U 235 enrichment would result in a decrease in the overall flux level due to increasing U 235 loading in the core. As a general rule, lowing the amount of U 235 in the core increases the necessary neutron flux level is a constant power

65 47 density is to be maintained. As Figure 10 shows, the total neutron flux steadily increases throughout burnup, reflecting the need to compensate for steady U 235 depletion. Additionally, the total neutron flux increases with increasing levels of soluble boron. This is a reflection of the need to overcome increased thermal absorption in soluble boron, which limits the thermal neutron flux available for fission interactions. Total Neutron Flux 9.0E E E E E E E E E E E ppm Boron 2000 ppm Boron Boron Free Burnup (MWd/Kg) Figure 10: Total neutron flux vs burnup for 5.0% U 235 enriched fuel assembly. Figure 11 displays the total fast neutron flux in the reactor core. The fast neutron flux contains 90% of all neutrons in the core, and thus mirrors the total neutron flux, since any thermal neutron effect is not noticeable in the total neutron flux because of the large fast neutron population. Since boron is most notably a thermal absorber, the addition of boron only affects the thermal neutron population. In this manner, the fast neutron spectrum mirrors the total neutron flux.

66 48 Total Fast Neutron Flux 7.5E E E E E E E E E E ppm Boron 2000 ppm Boron Boron Free Burnup (MWd/Kg) Figure 11: Fast neutron flux vs burnup for 5.0% U 235 enriched assemblies. However, the thermal neutron flux is clearly impacted by the presence of boron (Figure 12). At BOC, the total thermal neutron population remains constant despite the presence of boron. This is because nearly all fission events occur in U 235, which requires thermal neutrons. In order to maintain a constant power density, the amount of fissions must also remain constant. However, since the presence of boron increases the initial fast neutron flux, plutonium production increases (as described in Section 4.2.2). Total Thermal Neutron Flux 1.0E E E E E E E E E E E ppm Boron 2000 ppm Boron Boron Free Burnup (MWd/Kg) Figure 12: Thermal neutron flux vs burnup for 5.0% U 235 enriched assemblies.

67 49 Plutonium production results in an increased percentage of fast neutron fission events, due to its relatively large fast neutron fission cross section. This increase in fast neutron fissions reduces the requirements on thermal neutron population, and results in an overall reduction in the thermal neutron population for increasing concentrations of boron, when compared to a boron free assembly. However, the total thermal population gradually increases throughout depletion. This effect is due to the steady depletion of U 235, requiring higher thermal neutron population to maintain a steady amount of fission events. Since the overall mass of U 235 loading still greatly outweighs plutonium for typical PWRs, an increase in thermal neutron flux is required to continue to make use of the depleting U 235 population Effective Fraction of Delayed Neutrons Delayed neutrons perform an essential function in nuclear power reactors. The average lifetime of prompt neutrons, those neutrons emitted from the fission event itself, is on the order of milliseconds. Any impact these neutrons have on the reactor core and the multiplication factor is therefore extremely fast. If these prompt neutrons were the only contribution to the total neutron flux, any addition of positive reactivity, no matter how small, would result in a transient too quick for any human or mechanical system to control. In such a scenario, the only basis for controlling a reactor would lie in physical reactor feedback mechanisms such as moderator and fuel temperature coefficients. In any practical sense, a controllable nuclear reactor would be physically impossible. Thankfully, prompt neutrons are not the only source of neutrons. Delayed neutrons are not emitted from the fission event itself, but rather from fission fragments with varying halflives. The numerous radioactive elements that decay via neutron emission are typically collected in 6 main groups based on their general half-life [13]. These groups contain elements whose half-lives range anywhere from 10-3 seconds to almost 1 min. While this is still relatively quick, it is on average several orders of magnitude longer than the prompt neutron lifetime. Thus, even though only 0.65% of the overall neutron flux is comprised of these delayed neutrons, their relatively long half-lives push the average neutron lifetime to levels that are manageable for both human and mechanical control.

68 50 In this manner, an investigation on the impact boron-free operation has on the fraction of delayed neutrons and the average neutron lifetime is crucial. Figure 13 shows the fraction of delayed neutrons vs burnup Effective Delayed Neutron Yield ppm Boron 1000 ppm Boron Boron Free Burnup (MWd/Kg) Figure 13: Effective delayed neutron yield vs burnup for 5.0% U 235 fuel assemblies. As can be seen, the elimination or addition of boron has no appreciable effect on delayed neutron contributions. Different fertile isotopes have different fission product yields, and these fission products result in different contributions of delayed neutrons. Nevertheless, the increase in plutonium production (Section 4.2.2) and the resultant increase in fast fission events in plutonium for fuel assemblies with soluble boron does not result in any measurable different in the total effective delayed neutron yield Reactivity Feedback Mechanisms Several reactor parameters that determine the reactivity of a reactor are also functions of temperature [13]. Of most significance is the effect that fuel and moderator temperature have on reactivity, as any increase or decrease in fuel and moderator temperature will naturally follow any increase or decrease in reactor power. Such temperature effects on reactivity must be defined due to their significant contribution toward the inherent stability of the reactor.

69 51 All coefficients are defined by the simple relation: α = dρ dt where α represents the feedback coefficient. As defined, the simple derivative of reactivity divided by the change in temperature for fuel, moderator, etc, defines the temperature coefficient of the reactor at that state point. It follows that, if α is positive, any increase in temperature will result in a further increase in reactivity through the temperature coefficient. This increase in reactivity further increases the temperature, and the reactor power exponentially increases until some other mechanism stops the process. Conversely, if α is negative, any increase in reactivity will result in a subsequent decrease in reactivity through the temperature coefficient, and the reactor will naturally stop increasing through physical effects alone. In this manner, the inherent stability of the reactor is largely defined by these temperature coefficients. The NRC recognizes the importance of these inherent stability factors and will not license any reactor with a positive fuel or moderator temperature coefficient in all conceivable reactor state points [25]. There are two main reactor feedback coefficients of primary concern for PWRs: Fuel temperature coefficient, moderator temperature coefficient, and void coefficient. Each fuel assembly was sampled at a chosen state point. For the purposes of this thesis, three state points comprise the reactor conditions of most interest: At full power and normal operating conditions, during startup, and at cold shutdown. These three conditions cover the range of reactor conditions in which a transient is most likely to occur. The relevant fuel and moderator temperatures for each condition are given below: Reactor State Point Average Moderator Average Fuel Temperature (K) Temperature (K) Hot Full Power Cold Full Power Cold Zero Power

70 52 Calculating both MTC and FTC requires a simple ratio: RFM(depletion) = k dep 0 k 0 1 T 0 T 1 Where the Reactor Feedback Mechanism value (RFM) as a function of depletion is equal to a ratio of the difference in the multiplication factor at the initial state point temperatures (k 0 ) and a slightly higher state point temperature (k 1 ), and the difference in the actual initial state point temperatures (T 0 and T 1 ). For example, consider the Moderator Temperature Coefficient (MTC) at BOC and with hot full power conditions. The MTC value would therefore be: MTC(0 MWd/Kg) = k 0 MWd/Kg 563 K fuel temp 0 MWd/Kg k 583 K fuel temp 563 K 583 K Appropriately, the units for such a calculation are reflected as a change in the multiplication factor per degree Kelvin ( δk inf ). However traditional MTC and Fuel K Temperature Coefficients (FTC) are expressed in units of reactivity, ρ [13] (where ρ = k 1 k ). In order to convert the current units δk inf K performed: to the traditional δρ, the following operation is K MTC(0 MWd/Kg) = 0 MWd/Kg k 563 K fuel temp k 563 K fuel temp 0MWd Kg 1 0 MWd/Kg k 583 K fuel temp K 583 K 0MWd Kg k 583 K fuel temp Fuel temperature coefficient The most important feedback mechanism concerns the fuel temperature coefficient (FTC). The reactor fuel temperature will be first to respond to any increase in power since there is no need for any heat removal effects to take place before the fuel increases in temperature. The fission events occur in the fuel itself, so any increase in power almost

71 53 instantaneously increases the fuel temperature as well. Thus, if the fuel temperature coefficient is positive, the feedback loop will be inherently fast and lead to greater instability. For this reason, a careful examination of the fuel temperature coefficient in boron-free reactors must be performed. Figure 14 demonstrates the fuel temperature coefficients vs burnup for each of the three state point conditions, both with and without soluble boron. 8.0E-05 Fuel Temperature Coefficient (δρ/k) 6.0E E E E E E-05 Burnup (MWd/Kg) Hot Full Power ppm Boron Hot Full Power - Boron Free Cold Zero Power ppm Boron Cold Zero Power - Boron Free Cold Full Power - Boron Free Cold Full Power ppm Boron Figure 14: Fuel temperature coefficient vs burnup for hot full power, cold full power, and cold zero power with and without soluble boron. Generally speaking, the behavior of the fuel temperature coefficient reflects the impact of resonance absorption in U 238, and the Doppler broadening of the resonances with increases in temperature. Additionally, the increasing presence of Plutonium and its unique cross section and resonance characteristics produce variations in the value of the FTC throughout burnup. To explain the behavior of the FTC in relation to boron concentration, it is important to note that the presence of soluble boron results in an increased fast thermal neutron flux. As the temperature of the fuel is increased, so too is the resonance absorption cross section for U 238. Fast neutrons which require no thermalization are absorbed in this resonance absorption cross

72 54 section, and thus a larger fast neutron population will result in a more positive FTC. This primary effect produces the more negative FTC with the removal of soluble boron. Figure 14 shows that a fuel assembly with soluble boron possesses a positive FTC during cold full power, a possible condition at reactor startup. This creates inherent safety risks and a full safety analysis report would be required to exhaustively investigate this effect. However, the removal of soluble boron not only decreases the FTC in all selected reactor state points, but produces a negative FTC at cold full power. Additionally, while the FTC does become positive as burnup progresses due to the accumulation of plutonium in the core, soluble boron-free fuel assemblies do not become positive until 45 MWd/Kg, at which point the multiplication is below 1, and is therefore a condition that is unlikely to arise Moderator temperature coefficient The second feedback mechanism of significance is the MTC. While the FTC provides the fastest feedback mechanism due to its close proximity to the fission events, the MTC also plays an important role due to its necessary moderation capabilities. The feedback loop associated with the MTC will be slower than the FTC due to the required heat transfer from fuel to coolant before any reactivity effect will materialize. Figure 15 demonstrates the MTC for the above three state points with varying amounts of soluble boron.

73 55 6.0E-04 Moderator Temperature Coefficient (δρ/k) 4.0E E E E E E-04 Burnup (MWd/Kg) Hot Full Power ppm Boron Hot Full Power - Boron Free Cold Zero Power ppm Boron Cold Zero Power - Boron Free Cold Full Power ppm Boron Cold Full Power - Boron Free Figure 15: Moderator temperature coefficient for hot full power, cold full power, and cold zero power with and without soluble boron. As can be seen, a decrease in soluble boron results in a stronger negative MTC during hot full power, increasing the inherent stability of the reactor. This effect can be partly attributed to the density differences resulting from the addition of boron. Since boron is a strong neutron absorber, and since the presence of boron in the moderator takes away space that would be occupied by a strong neutron moderator (H 2 O), any addition of boron results in a decrease in moderation potential. But beyond that simple effect, temperature and density are inversely proportional, and any decrease in moderator density by definition reduces the amount of moderator atoms in a given volume. This decrease fundamentally impacts the ability to moderate neutrons, and results in a lower resonance escape probability, and therefore a decrease in the multiplication factor. This effect is shown in the negative MTC. Figure 15 shows how the MTC at BOC for a fuel assembly with soluble boron is slightly positive at hot full power conditions. This condition is very likely, since reactors generally operate at full power to enhance efficiency, and the positive MTC would require extensive safety analysis. Thus, removing soluble boron not only increases the inherent

74 56 stability of the reactor at BOC and for the other selected reactor state points, but also prevents a possibly exhaustive and expensive safety analysis associated with the positive MTC Conclusion Impacting any aspect of operation in a nuclear reactor will affect several other variables due to the inherently complex physical mechanisms involved. Something as seemingly innocuous as removing soluble boron from the coolant was found to carry significant implications on several key parameters. While this was not a comprehensive evaluation on all the aspects impacted by soluble boron-free operation, a few effects with significant safety implications were confirmed. Most notably, removing soluble boron was found to harden the neutron spectrum in the reactor core. A hardened spectrum results in increased neutron absorption in U 238, leading to greater quantities of plutonium. While some reactors are designed to produce plutonium as a way to increase the core lifetime, plutonium production in SMRs carries significant safety implications. The fuel temperature reactivity coefficient was found to be directly impacted by plutonium production due to its increased resonance absorption capabilities. Any increase in plutonium fundamentally increases the FTC, reducing the inherent stability of the reactor. In fact, removing soluble boron changed a previously positive FTC for cold full power conditions to a negative value. This dramatic reduction would not only increase inherent safety of the reactor during startup scenarios, but it would also carry the potential of eliminating exhaustive and expensive safety analysis reports. Similar to the fuel temperature coefficient, removing soluble boron was found to fundamentally reduce the moderator temperature coefficient. This also carries significant safety implications, and is identified as one of the primary motivations for removing soluble boron in normal operations. In the end, while some physical effects remain unchanged by the removal of soluble boron, several key factors were found to be beneficially impacted. While this study is not exhaustive, the above findings help confirm motivations for soluble boron free operation.

75 Development and Analysis of Fuel Assemblies for use in Full Core Environment The development and analysis of fuel assemblies for use in a full core environment was conducted in CASMO-4E. Technically CASMO models an infinite lattice that contains a 17 x 17 grid of fuel assemblies with specifications listed in section 4.1. CASMO then solves the 2- D neutron transport equation and provides detailed data on neutron behavior, generates cross sections for every conceivable reactor state point, and returns the eigenvalue solution for each depletion state point, among other things [57]. This data can then be supplied to SIMULATE- 3K and be used as the basis for reactor fuel assemblies in a full core environment. In the soluble boron-free core the unique requirements on burnable poisons and control rods for reactivity suppression necessitate the need for a comprehensive search to find ideal burnable poison and control rod placements. The initial phase of this study must keep three things in mind: First, initial ideas for soluble-boron free operation include complex axial grading of burnable poisons to compensate for any skewed axial power profile. Since such axial grading would ultimately be dependent on specific reactivity suppression needs over the lifetime of the core, the development of several different fuel assemblies with multiple levels of reactivity suppression through burnable poisons is required. These levels also incorporate three elements: o Initial reactivity compensation o Rate of burnable-poison depletion o Burnable poison effective lifetime. Second, initial ideas for soluble-boron free operation also include axial grading of U 235 enrichment. Therefore, each burnable poison arrangement must also be performed for different overall U 235 enrichments. Finally, several fuel assemblies with different values for each of the above elements are required in order to provide a comprehensive set of fuel assemblies for use in fullcore analysis. In this manner, any necessary fuel loading arrangement can be provided.

76 Burnable Poison Search The ability to provide any necessary fuel loading arrangement requires a comprehensive set of fuel assemblies that possess unique burnup characteristics. These unique burnup characteristics fall into three types: 1) Fuel assemblies with partial to moderate initial reactivity compensation with a flat burnup profile. 2) Fuel assemblies with moderate to strong initial reactivity compensation with a peaked burnup profile. 3) Fuel assemblies with different burnable poison effective lifetimes. Types 1 and 2 are mutually exclusive, but both Type 1 and Type 2 can be coupled with different burnable poison effective lifetimes (Type 3). In this manner, a comprehensive set of fuel assemblies can be provided Fuel Assembly Type 1: Fuel assemblies with partial to moderate initial reactivity compensation with a flat burnup profile. In order to find fuel assemblies that match type 1 requirements, an ideal burnable poison loading geometry for a flat burnup profile must be determined. To create a flat burnup profile, a look at the physics involved is required. Since burnable poisons are strong neutron poisons, their presence in fuel pins strongly influences the local thermal neutron flux. This results in a marked depression of the local multiplication factor, which diffuses out to ultimately inf luence the overall multiplication factor for the entire fuel assembly. The presence of even relatively small amounts of these strong poisons has a large impact on the multiplication factor, so only a small fraction of fuel pins within the fuel assembly are loaded with burnable poisons. Even then, the enrichment of burnable poisons in the fuel pin rarely exceeds 10%. By way of example, consider a fuel assembly with only 40 out of the 264 fuel pins poisoned with 4% Gd 2 O 3. The burnup characteristics of such a sparsely poisoned fuel assembly are seen in contrast to those for a non-poisoned fuel assembly in Figure 16. It can clearly be seen how the initial multiplication factor of the poisoned assembly is markedly

77 59 suppressed from the non-poisoned assembly. However, the high flux environment quickly depletes the available Gd 2 O 3 and its neutron absorption capabilities gradually deplete with time, resulting in a smooth increase in the initially depressed multiplication factor. Eventually all of the Gd 2 O 3 is transmuted by neutron capture, and the fuel assembly mirrors the nonpoisoned assembly. This occurs at a burnup of approximately 14 MWd/Kg K inf Non-Poisoned Assembly 40 Pins Poisoned with 4% Gd2O Burnup (MWd/Kg) Figure 16: k inf vs burnup for a poisoned and non-poisoned fuel assembly. If a flat burnup profile is desired, the depletion of Gd 2 O 3 must match the natural depletion of U 235, so the overall multiplication factor remains constant until all the Gd 2 O 3 has been depleted. To accomplish this, the fuel assembly must be engineered by altering three variables: The number of poisoned fuel pins. The amount of Gd 2 O 3 in each poisoned fuel pin. The geometric arrangement of each poisoned fuel pin. To accomplish this, five typical PWR burnable poison geometric loading arrangements were identified. These five typical arrangements formed five major groups of fuel assemblies. The loading geometry for each group is given in Figure 17. As can be seen, each different loading arrangement contained a different overall amount of poisoned fuel pins.

78 60 BP Geometry #1: 16 Poisoned Pins BP Geometry #2: 16 Poisoned Pins BP Geometry #3: 28 Poisoned Pins BP Geometry #4: 24 Poisoned Pins BP Geometry #5: 20 Poisoned Pins Figure 17: Burnable poison loading geometry for each of the 5 major groups. Red indicates a control rod, blue is a poisoned fuel pin, and white is a regular fuel pin.

79 61 Several fuel assemblies with varied Gd 2 O 3 weight fractions were modeled for each group. An initial study in which all poisoned pins were kept at the same Gd 2 O 3 weight fraction (4%) was performed. These fuel assemblies are shown in Figure k inf Poisoned Loading #1 Poisoned Loading #2 Poisoned Loading #3 Poisoned Loading #4 Poisoned Loading # Burnup (MWd/Kg) Figure 18: k inf vs burnup for fuel each major burnable poison loading geometry. The difference in reactivity compensation is attributed to a few different effects. First, the total amount of poisoned material and the number of poisoned pins varies for each fuel assembly type. This is best seen between Burnable Poison geometry (BP geometry) #1 and #3, where the k inf at BOC is 1.24 and 1.1 respectively, a difference of However, even between #1 and #2, which both contain 16 poisoned pins, a k inf difference of 0.04 at BOC can be seen. This is attributed to differences in the radial neutron flux profile, which creates natural hot spots where k inf is larger. In fuel assemblies with 17x17 geometry, the central fuel pins that are not immediately surrounded by a control rod tube will be most reactive. Thus, absorber material placed in these regions will have a large effect on the neutron flux, and therefore the value of k inf. BP geometry #1 has poisoned pins further from the center, which appropriately have less of an

80 62 effect on the neutron flux. Conversely, BP geometry #2 has more pins closer to the center, and this has a larger effect on the neutron flux. This effect produces the 0.04 difference in k inf between the two assemblies at BOC. An important effect to take note of is the initial sharp reactivity drop exhibited in each fuel assembly. This is produced from the buildup of Samarium and Xenon, natural fission products. Being strong neutron poisons, as more and more are produced they begin to have an appreciably large effect on reactivity. But since they both possess relatively short half-lives with respect to the length of a cycle, an equilibrium steady-state concentration is quickly reached. It is also important to note that this infinite lattice study, while retaining shroud tubes for both instrumentation and control rods, is not modeled with any control material in the control rod positions. Instead, moderator exists in the open control rod tubes. During normal operation in a 3-D fuel assembly we may expect control rods to be fully or partially inserted. In this scenario, shadowing and shielding effects would have a pronounced effect on the worth associated with poisoned pins right next to the control rods. The depression in the neutron flux produced from the insertion of the control rods reduces the worth associated with both the control rods and any poisoned pins nearby, while increasing the neutron flux in areas that do not have any control material. As can be seen in Figure 18, simply varying the overall BP geometry does not produce a flat burnup, and increasing or decreasing the Gd 2 O 3 weight fraction would not significantly alter the behavior of k inf over burnup. Therefore, a further study that individually varies the Gd 2 O 3 weight fractions is required. While this burnable poison loading will change individually from one pin to the next, care was taken to maintain symmetry across the entire fuel assembly. A large number of fuel assemblies were modeled, with several different poison loading patterns for each BP geometry type. Some of these fuel assemblies are shown in Figure 19, where each different enrichment loading pattern clearly provides unique burnup characteristics.

81 K inf Burnup (MWd/Kg) Figure 19: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with variations of all 5 BP geometries and with individually varied Gd 2 O 3 weight percentages. As can be seen, any sort of burnup profile can be attained by altering the BP weight fraction loading geometry. A few general trends can be seen. First, 5 overall groups of assemblies can be identified by their relative initial k inf levels. Fuel assemblies where k inf begins between belong to assemblies of BP geometry type 1 and type 2. Similarly, belongs to type 5, belongs to type 4, and belongs to type 3. This grouping effect can be attributed to the differences in the overall number of poisoned fuel pins. To examine why, consider four different fuel assemblies: Two from BP geometry type 1, one loaded with all 16 fuel pins at 2% Gd 2 O 3, and the other with 12% Gd 2 O 3 ; and Two from BP geometry type 3, again with all 28 pins 2% and 12%. Figure 20 shows k inf vs burnup for these assemblies.

82 BP Geometry 3 with 12% Gd2O3 BP Geometry 3 with 2% Gd2O3 BP Geometry 1 with 12% Gd2O3 BP Geometry 1 with 2% Gd2O3 k inf Burnup (MWd/Kg) Figure 20: k inf vs burnup for BP geometry 1 and 3, with 12% and 2% w/o Gd 2 O 3. As can be seen, the initial excess reactivity suppression provided by the assemblies is driven by the total number of poisoned fuel pins, and not the overall amount of absorber material. Comparing BP Geometry 3 with 2% Gd 2 O 3 with BP Geometry 1 with 12% Gd 2 O 3 demonstrates this effect. The 12% assembly has almost 3.5 times the amount of absorber material, yet the 2% assembly provides more initial reactivity suppression. The reason is due to shadowing and shielding effects. The 12% poisoned fuel pins provide such a drop in the neutron flux that they limit their effectiveness. There comes a point where adding more absorber material to the same fuel pin produces diminishing returns, reducing the overall effectiveness of the absorber material. On the other hand, this effect does improve the lifetime of the poison. Additionally, the total amount of poison in the assembly is the driving force behind the effective lifetime of the poisons. The 2% Gd 2 O 3 assemblies both demonstrate significantly quick burnup rates, as they burn out relatively quickly and behave like non-poisoned assemblies around 7 MWd/Kg. This is due both to a relatively small total amount of poisons, and to the lack of shielding and shadowing which increases the effectiveness of the absorber material. Meanwhile, the 12% assemblies demonstrate no appreciable increase in k inf, maintaining the same overall

83 65 effectiveness due to strong shadowing and shielding effects. They finally completely burn out at around 25 MWd/Kg. As these two effects demonstrate, mixing and matching different Gd 2 O 3 weight fractions and total absorber loading amounts produces the various burnup characteristics demonstrated in Figure 19. Since a flat burnup profile is desired, each fuel assembly in Figure 19 that exhibited a relatively flat burnup was identified and further modified. In this manner, a group of 5 final fuel assemblies each with a relatively flat burnup profile were selected. These are shown in Figure K inf Burnup (MWd/Kg) Figure 21: k inf vs burnup for final 5 fuel assemblies that exhibit a flat burnup profile. Clearly, different total concentrations of Gd 2 O 3 in the various fuel assembly designs, and dissimilar numbers of poisoned fuel pins in each assembly, provides a varying amount of total excess reactivity compensation and contrasting effective burnable poison lifetimes. These five fuel assemblies were selected for potential use in a full core environment, so iterations of each of the five fuel assemblies were also modeled with different U 235 enrichments (from 2.50% to 4.95% by 0.5%). These fuel assemblies are provided in the Appendix.

84 Fuel Assembly Type 2: Fuel assemblies with moderate to strong initial reactivity compensation with a peaked burnup profile A flat burnup profile will be useful in certain environments, but the ability to have a peaked profile will be useful in other environments. Specifically, anything from a strong initial reactivity suppression that quickly depletes to moderate initial reactivity suppression with a long Gd 2 O 3 lifetime will be potentially useful in a full-core environment. To model these fuel assemblies, three different variables were independently altered: 1) Total loading amount of Gd 2 O 3 2) Specific enrichment percentages in different fuel pins (while maintaining symmetry) 3) BP Geometry type As discussed above, altering these three variables produces a wide variety of burnup profiles Fuel Assembly Type 2: Fuel assemblies with strong initial reactivity compensation with quick depletion Creating fuel assemblies that provide strong initial reactivity compensation with quick depletion requires fuel assemblies with a large amount of poisoned pins that contain a low Gd 2 O 3 enrichment percentage. The large number of poisoned pins will provide the strong initial suppression, while the low Gd 2 O 3 percentage ensures a quick depletion. Figure 22 shows the poisoned pin geometry in the 17x17 fuel assembly for fuel assemblies with these depletion characteristics. 64 out of the 264 total fuel pins are poisoned with 2%, 3%, and 4% weight percent Gd 2 O 3. Figure 23 demonstrates k inf vs burnup for these 5.00% U 235 enriched fuel assemblies. As can be seen, the numerous poisoned pins provide strong initial reactivity suppression, while the low Gd 2 O 3 weight percent allows for a quick burnup. The quick burnup results in a smooth increase in k inf until the all the Gd 2 O 3 has been burned at which point a natural depletion curve is seen. In this case, 2% Gd 2 O 3 results in an initial k inf of 0.95, far from its natural non-poisoned state of Around 10 MWd/Kg all Gd 2 O 3 has depleted, and the fuel assembly resembles a non-poisoned assembly.

85 67 64 Poisoned Pins Figure 22: Poisoned pin geometry for fuel assemblies with strong initial reactivity compensation and quick Gd 2 O 3 depletion K inf Non-Poisoned Assembly 2% Gd2O3 3% Gd2O3 4% Gd2O Burnup (MWd/Kg) Figure 23: k inf vs burnup for 5.0% U 235 fuel assemblies with 64 poisoned pins.

86 68 To provide a complete set of fuel assemblies for use in a full core environment, the 2%, 3% and 4% Gd 2 O 3 fuel assemblies were paired with different U 235 enrichments (from 2.50% - 5.0% by 0.5% increments). A graph of k inf vs burnup for these fuel assemblies is provided in the appendix. Another possibility for strong initial reactivity compensation with a quick Gd 2 O 3 depletion could be found in a slightly lower number of poisoned fuel pins coupled with a slightly higher Gd 2 O 3 weigh percentage. In such a configuration, a small increase in Gd 2 O 3 lifetime would provide more initial reactivity compensation. Two different geometrical BP layouts, with 52 and 64 poisoned pins respectively, are shown in Figure Poisoned Pins 56 Poisoned Pins Figure 24: Burnable poison loading geometry with 52 and 64 poisoned pins. Both of these assemblies are loaded with 5% and 6% Gd 2 O 3, and k inf vs burnup is displayed in Figure 25.

87 K inf Burnup (MWd/Kg) Non-Poisoned Assembly 52 Poisoned Pins with 5.0% Gd2O3 52 Poisoned Pins with 6.0% Gd2O3 56 Poisoned Pins with 5.0% Gd2O3 56 Poisoned Pins with 6.0% Gd2O3 Figure 25: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with 52 and 56 pins poisoned with 5.0% and 6.0% w/o Gd 2 O 3. These fuel assemblies create additional burnup characteristics that might be useful in a full core environment. Identical assemblies for each of the above 4 assembly types with different U 235 enrichments were also created (2.50%-5.0% by 0.5%), and those graphs are available in the appendix Fuel Assembly Type 2: Fuel assemblies with strong initial reactivity compensation with slow depletion To create fuel assemblies with strong initial reactivity compensation and slow depletion there must be a large number of poisoned pins with a higher Gd 2 O 3 weight percent. Figure 26 shows the different burnable poison loading patterns. The number of poisoned pins steadily increases from 44 to 64 out of 264. Each burnable poison geometry was modeled with both 5% and 6% Gd 2 O 3. Figure 27 shows the behavior of k inf vs burnup for 5.0% U 235 enriched assemblies by burnable poison loading geometry.

88 70 44 Poisoned Pins 48 Poisoned Pins 52 Poisoned Pins 56 Poisoned Pins 64 Poisoned Pins Figure 26: Five different burnable poison loading geometries for fuel assemblies with strong initial reactivity compensation and slow depletion.

89 K inf Poisoned Pins 48 Poisoned Pins 52 Poisoned Pins 56 Poisoned Pins 64 Poisoned Pins Non-Poisoned Assembly Burnup (MWd/Kg) Figure 27: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins at 5.0% w/o Gd 2 O 3. As expected, initial reactivity compensation is linearly proportional to the number of poisoned fuel pins. Also, Gd 2 O 3 depletion is largely irrespective of the number of poisoned pins all 5 fuel assemblies resume a normal burnup curve around 15 MWd/Kg. Figure 28 reinforces these findings by showing k inf vs burnup for 5.0% U 235 enriched assemblies with 6.0% Gd 2 O 3. There is slightly more initial reactivity compensation, but the largest difference is in the Gd 2 O 3 lifetime, which completely depletes around 17 MWd/Kg.

90 K inf Poisoned Pins 48 Poisoned Pins 52 Poisoned Pins 56 Poisoned Pins 64 Poisoned Pins Non-Poisoned Assembly Burnup (MWd/Kg) Figure 28: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins at 6.0% w/o Gd 2 O 3. A final group of fuel assemblies were created to provide an extraordinarily large amount of initial reactivity suppression. These assemblies were not designed for realistic use in a full-core environment; rather they were created for use in hypothetical scenarios to see how inserting a severely depressed fuel assembly in some axial part of a full-core environment would affect core operations and the axial power profile. In this manner, they could provide insight into the upper limit to the impact of poisoned assemblies in a full core environment. Figure 29 shows the five different burnable poison geometrical loading arrangements that were used to create these fuel assemblies. The number of poisoned pins linearly increases, containing 64, 100, 136, 172, and finally 264 poisoned pins. Obviously such dramatically poisoned pins will exhibit very strong shadowing and shielding effects, along with a highly suppressed neutron flux.

91 73 64 Poisoned Pins 100 Poisoned Pins 136 Poisoned Pins 172 Poisoned Pins 264 Poisoned Pins Figure 29: Five different burnable poison loading geometries for fuel assemblies with extraordinarily large initial reactivity compensation.

92 74 Each of these fuel assemblies were loaded with 2%, 3% and 4% weight percent Gd 2 O 3. Anything above 4% Gd 2 O 3 was observed to provide diminishing returns, since the 4% poisoned fuel assemblies would already take a relatively long time to deplete due to the strong shielding and shadowing effects. Figures 30, 31, and 32 show k inf vs burnup for 2%, 3%, and 4% Gd 2 O 3 assemblies. Kinf Poisoned Pins 100 Poisoned Pins 136 Poisoned Pins 172 Poisoned Pins 264 Poisoned Pins Burnup (MWD/KG) Figure 30: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 2.0% w/o Gd 2 O 3. Kinf Poisoned Pins 100 Poisoned Pins 136 Poisoned Pins 172 Poisoned Pins 264 Poisoned Pins Burnup (MWD/KG) Figure 31: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 3.0% w/o Gd 2 O 3.

93 75 Kinf Poisoned Pins 100 Poisoned Pins 136 Poisoned Pins 172 Poisoned Pins 264 Poisoned Pins Burnup (MWD/KG) Figure 32: k inf vs burnup for 5.0% U 235 enriched fuel assemblies with various numbers of poisoned fuel pins (from Figure 29) at 4.0% w/o Gd 2 O 3. As expected, increasing the number of poisoned pins dramatically decreases the value of k inf. Increased shielding and shadowing also decreases Gd 2 O 3 burnup. For 4% Gd 2 O 3, a fuel assembly with 64 poisoned pins resumes a normal burnup curve around 12 MWd/Kg, whereas 264 poisoned pins depletes at 16 MWd/Kg Conclusion In the end, over 80 fuel assemblies were modeled in CASMO, each with unique burnup characteristics. These differing burnup characteristics provide a wide range of options for use in a full core environment. Certain burnup characteristics may be required to manage the axial power offset that arises from partial control rod insertion in a soluble boron-free core.

94 Description and Analysis of Initial Strategies for Soluble Boron-Free Operation in the Selected SMR Design As previously discussed, removing soluble boron in a full core environment challenges the axial power profile due to the dependence on discrete poisons. This challenge must be met by carefully considering each factor that affects the axial power profile. The main factor arises from increased dependence on control rods when soluble boron is removed. These rods will be partially inserted in the core during normal operations, and will thus impact the axial power profile negatively. To combat this, axially grading both burnable poisons and 235U enrichment percentage, if done properly, can minimize and negate the impact from active control rods. For example, since any partial insertion of control rods will leave the bottom of the core unsuppressed, loading this region of the core with strong burnable poisons can create a more uniform reactivity suppression profile throughout the core and therefore a more uniform axial flux profile. But the nature of a full core burnup cycle is not steady-state. This initial arrangement of strong poisons at the bottom to overcome the partial insertion of control rods would only work properly for a few MWd/Kg of burnup. As the U 235 naturally depletes, the control rods are slowly removed, which alters the impact the control rods have on the axial power profile. Additionally, as their name suggests, the burnable poisons slowly deplete as well, reducing their effectiveness as the core is burned. This dynamic situation creates challenges for the reactor engineer to discover an arrangement that will properly balance the axial flux profile throughout the lifetime of the core. This chapter will explore different methodologies to contain this dynamic environment, and contains two main sections: First, establishing a proper radial geometry that minimizes the radial peaking factors. Second, searching for a proper axial arrangement of burnable poisons and U 235 fuel enrichment to create as uniform an axial power profile as possible Full Core Radial Loading Geometry Before jumping into axially grading a full core environment, a foundational 2-D U 235 enrichment loading geometry must be selected. This loading arrangement will serve as a

95 77 template upon which only axial variations in burnable poisons will be altered. In this manner, a 2-D profile that minimizes radial peaking factors will be maintained throughout the core. To achieve this, multiple geometrical loading arrangements were analyzed. In the first search, only the U 235 enrichment was varied, with no burnable poisons present anywhere in the core. The idea was to determine which enrichment loading geometry would perform best with respect to the 2-D radial power profile. Figure 33 shows the final geometrical loading arrangement that appears to demonstrate a preferred performance Figure 33: 2-Dimensional U 235 Enrichment Loading Geometry. The outer ring of fuel assemblies was deliberately kept at 4.95% U 235 for the duration of the search. Since smaller cores are more sensitive to neutron leakage, the idea was to minimize the effects of leakage by placing highly enriched assemblies on the outer ring. While the current full core geometry makes use of a reflector segment around this outer ring, the leakage effects still have a dramatic influence on the overall neutron flux and thus the relative power production in the outer ring. So while this arrangement does not lend itself to an efficient use of fuel, it is beneficial from a neutron economy perspective. Figure 34 displays the 2-D relative power fraction at the center of the core and at BOC for the above loading geometry.

96 Figure 34: Relative power fraction for the U 235 enrichment loading geometry. Due to the symmetry of the core, the center fuel assembly is prone to high relative power fractions and therefore higher peaking factors. To combat this, the center of the core contains slightly lower enriched assemblies. An effort was made to select a 2-D loading geometry that contained as many high enriched assemblies as possible, since the total plutonium loading mass will play a large role in the overall cycle limit of the core. The above arrangement produced a 2-D relative power fraction that contained a standard deviation of just Since reactor power level is proportional to the neutron flux, this relatively flat relative power distribution equates to a relatively flat radial flux profile, which will help lower the overall peaking factors throughout the core. However, this arrangement was selected without any burnable poisons present. Since the main purpose behind the use of burnable poisons is reactivity suppression, the presence of any poisoned assemblies will have a marked impact on the radial flux profile. And since this full core analysis seeks to find a comprehensive axially poisoned core, it would be inefficient to conduct an optimization of the radial flux profile for each axial node. Furthermore, the overall peaking factor for a core is a combination of the radial and axial peaking factors. As will later be demonstrated, the radial peaking factor is routinely far lower than the axial peaking factor, minimizing the importance of the radial peaking factor.

97 79 For these reasons, this optimization study on the radial enrichment loading geometry is of little importance moving forward. Instead, the results demonstrated in figure 34 provide general guidelines that will produce lower radial peaking factors. Namely, the importance of placing assemblies with relatively lower reactivity in the center and those with higher reactivity on the outside. But even these guidelines become difficult to enforce in light of the full cycle length of a typical core. While one loading arrangement may be ideal for the beginning of the cycle, the depletion of burnable poisons and the movement of control rods, both of which significantly impact the overall reactivity of each assembly, will render any attempts at optimizing the radial flux profile over the lifetime of the core useless. There are simply too many variables in play to prioritize the radial flux profile. Instead, a focus on optimizing the axial flux profile and the associated axial peaking factors is desired. For a soluble boron-free core, this peaking factor will be the largest determining factor behind the overall peaking factor for the core, so it should be highlighted. In this manner, only general guidelines discovered in this radial flux profile study will be kept in mind Full Core Axial Loading Geometry As mentioned above, the search for a proper axial loading geometry will require balancing several different variables at once, and adjusting for their changes through the lifetime of the cycle. It is expected to be difficult to find a full core loading arrangement that produces an ideal burnup profile. But this is not an optimization study, so any loading arrangement that meets the design criteria will be accepted as a final design. The strategy involved with discovering a suitable full core environment revolves around balancing the reactivity compensation in such a way that limits the axial flux profile offset. With this is mind, each different factor that influences the axial flux profile will be examined and analyzed in relationship to every other factor. There are four main factors that influence the axial flux profile: 1) Number of active control rods and the collective control rod movement 2) Burnable poison loading, placement, and depletion 3) U 235 enrichment percentage and their collective loading geometry 4) Fission product poisoning

98 Factors influencing the axial flux profile: Number of active control rods and the collective control rod movement The active control rod bank in normal operations possesses the largest amount of reactivity worth, and therefore has the largest influence on the axial flux profile. Partially inserting such a large amount of reactivity in the core must be overcome through some combination of factors 2-4. Furthermore, any change in the amount of excess reactivity will result in further active control rod movement. This dynamic situation continually impacts the axial flux profile and creates a significant challenge in maintaining a proper profile. There are a few strategies that can be employed to overcome this strong disturbance on the axial flux profile. The first would be to load the bottom of the core with strong burnable poisons. If engineered properly, the poisons would contain enough negative reactivity to match the partial insertion of control rods, and restore a proper axial flux balance. However, this ideal situation would not last long. As the core depletes, the amount of excess reactivity is reduced and the control rods are slowly removed to compensate. This results in a further disturbance in the axial flux profile, and the burnable poison loading strategy that previously worked becomes less effective. To manage this, the burnup of poisons must match the depletion of the core, such that the overall amount of excess reactivity that must be compensated for by the control rods is kept relatively constant. In this manner, the control rod movement would be minimized until the burnable poisons are depleted. Unfortunately, at this point there would be nothing to further counter balance the partially inserted control rods, and the axial flux profile would be adversely affected. This creates a need for burnable poisons that would last throughout the life of the core. Since there is a set amount of total excess reactivity that must be compensated, any increase in burnable poisons would affect the amount of reactivity compensated for by control rods, and thus affect the overall control rod insertion depth. Any change in control rod insertion depth would affect the axial flux profile unless it is carefully matched by burnable poisons. This iterative process would require a careful balance of the reactivity compensation strategy between control rods and burnable poisons. Additionally, several other factors play a role in control rod insertion depth, such as fission product poisoning, shielding and shadowing effects, and other smaller reactor transients. This creates a situation that is very difficult to optimize. Additional complications

99 81 introduced through axially grading the U 235 enrichment percentages would further increase the complexity Factors influencing the axial flux profile: Burnable poison loading, placement, and depletion Unlike control rods, burnable poisons are not actively controlled. Their placement within the core is determined before operation, and cannot be altered in any way. For the soluble boron-free core that is dependent on careful engineering of excess reactivity compensation strategies, there is limited room for error. For example, if a large transient knocks the control rods from their expected location in the core, the axial flux profile would be altered. This creates locations of higher than expected flux, which would increase the rate of burnup in that specific area and decrease the rate of burnup in a different area. Over time, this has the potential to significantly alter the depletion characteristics within the core, and compromise the careful and extensive work of the reactor engineers. In other words, the soluble boron-free core is sensitive to large reactor transients, and there is little room for error. All of this places increased importance on developing a robust core that resists and manages the unwanted effects of reactor transients. But this engineering must be done beforehand, and it must be reflected in the final burnable poison loading arrangement Factors influencing the axial flux profile: U 235 enrichment and their collective loading arrangement As discussed in section 4.4.1, it is necessary to carefully balance the excess reactivity compensation strategy between control rods and burnable poisons. Altering the U 235 enrichment percentage presents a different impact by reducing or increasing the overall excess reactivity in the core. Even a simple alteration to the U 235 enrichment will require reengineering the careful balance between burnable poisons and control rod movement, let alone axially grading the U 235 enrichment in individual fuel assemblies. The natural burnup behavior in a soluble boron-free core exhibits an axial power offset skewed toward the bottom of the core at BOC (Figure 35). If no corrections are made, this increased neutron flux and power density at the bottom of the core leads to increased depletion

100 82 of U 235. Eventually, this loss of fuel ultimately drives the axial offset upward, where the presence of control rods have previously shielded the U 235 in the top of the core from depletion. This creates relatively high U 235 loads at the top of the core at EOC. This effect is driving force behind the positive axial power offset at EOC (Figure 35). Figure 35: Natural power profile for soluble boron-free core at BOC and EOC.