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Abstract:

The following report specifies a design for a Generation IV nuclear seawater desalination plant. Process heat from two fluoride-salt-cooled, high-temperature reactors (FHR) is to be used to power a large, multi-effect distillation unit. The FHR, also known as the Advanced High Temperature Reactor or AHTR, uniquely combines four existing and proven technologies; the liquid salt coolant of molten salt reactors, the coated particle tristructural-isotropic (TRISO) fuel of high-temperature gas-cooled reactors, the pool configuration and passive safety system of sodium-cooled fast reactors, and the open air Brayton power cycle technology of high efficiency natural gas plants. With a core power density of 27.9 MW/m3 and a total peaked power of 312 MW(t) per reactor, the plant will be able to desalinate an estimated 414,178 m3 of seawater daily.

The FHRs innovative combination of high-temperature, coated-particle type fuel pebbles, and a low-pressure, fluoride-salt primary coolant system enables the reactor to easily deliver heat at temperatures of 700°C or higher. The process heat for desalination will not require these high operating temperatures; however, it allows for coupling with a more efficient thermal cycle. An open, air-Brayton cycle with optional natural gas co-firing will be used for power conversion. The FHR coupled with a nuclear air-Brayton combined cycle (NACC) is projected to have a baseload efficiency between 40% and 47%; significantly higher than the efficiencies of today’s nuclear power plants. The NACC turbines will power the plant compressors and generators, rejecting the hot air at around 280°C to the distillation unit which takes the place of a regenerator.

To allow power peaking, natural gas is injected after the last stage of nuclear air heating. The increased inlet temperature into the last turbine stage allows for higher power output to distillation effects. There is also the longer-term option of using biofuels or hydrogen for peaking power. Because hot air is the heat transfer media to the distillation effects, the steam plant is decoupled from the nuclear plant such that the steam plant can be independently optimized. Multiple, independent PB-FHR reactors can then be used to provide steam to the distillation plant taking advantage of the decreasing capital cost of subsequent iterations of a design observed when building consecutive reactors. The deployability and efficiency of this system make it highly suitable for this application; even in harsh, high temperature heat rejection environments where fresh water is needed most.

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Table of Contents

Chapter 1 – Introduction

1.1 Project Motivation 7

1.2 Regional Background 9

1.3 Objective 11

1.4 Scope 11

Chapter 2 – Project Description

2.1 Site 12

2.1.1 Location 12

2.1.2 Topology 12

2.1.3 Meteorology 12

2.1.4 Seismology 13

2.1.5 Neighboring Populations 14

2.1.6 Dubai – Ghweifat International Highway E11 14

2.1.7 Railway Access 14

2.2 Reactor Description 15

2.2.1 Plant Overview 15

2.2.2 Reactor Core Description 15

2.2.5 Control and Shutdown 18

2.2.6 Power Conversion System 18

2.2.7 Safety Features 18

2.3 Advanced Multi-Effect Distillation Coupling Description 19

2.3.1 Desalination Technology Decision Basis 19 2.3.2 MED Concept 19

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Chapter 3 – Economic Analysis

3.1 Plant Capital Cost 20

3.2 Additional Cost 20

3.2.1 Operating and Maintenance Costs 20

3.2.3 Fuel Costs 20

3.2.4 Decommissioning Costs 20

3.3 Economic Advantages 21

Chapter 4 – Thermodynamic Analysis

4.1 Plant Layout 22

4.2 Distillation Capacity Scaling 24

4.3 Modeling 24

4.3.1 Coiled Tube Air Heater System 25

4.3.2 Turbines & Compressor 25

4.3.3 Salt Pump System 27

4.4 Power Conversion System Specifications 28

Chapter 5 – Neutronics Analysis

5.1 Modeling Process 29

5.2 The MCNP6 Model 29

5.3 Criticality Values and Neutron Fluxes 30

5.3.1 Fully Withdrawn Scenario 30

5.3.2 Critical Bank Scenario 32

5.3.3 Fully Inserted Scenario 33

5.3.4 Shutdown Scenario 35

5.4 Fuel Depletion Calculation 36

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Chapter 6 – Thermal Hydraulics

6.1 Fuel Element Thermal Analysis 37

6.1.1 Model Verification 37

6.1.2 Average Power Pebble Analysis 40

6.2 Natural Circulation

6.1.2 Natural Circulation Summary 40

6.1.3 Modeling in Comsol 41

6.2 T/H Coupling to Neutronics and Thermodynamics 42

Chapter 7 – Accident Analysis

7.1 Power Increase Accident 43

7.1.1 Control Rod Withdrawal/Ejection Accident 43

7.1.2 Cold Loop Startup Accident 43

7.2 Flow Decrease Accident 44

7.2.1 Flow Blockage Accident 44

7.2.2 Primary Coolant Leak Accident 44

7.3 Risk Assessment 44

Chapter 8 – Conclusions and Future Work 45

Appendix A – Temperature Dependent Thermophysical Properties of Flibe 46

Appendix B – Mathematica Thermal Hydraulic Verification Code 47

Appendix C – MCNP6 model code 53

References 60

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Chapter 1: Introduction“Water is the driving force of all nature.”

~Leonardo da Vinci

1.1 Project Motivation

In many parts of the world, concern over drought and drinking water shortage has become a primary, existential concern; however, this problem will soon be of critical importance to every living person. Only 2.5% of the world's water is freshwater; 68.7% of which is tied up in glaciers and ice caps [11]. Due to the overwhelming importance of a sustainable supply of freshwater and its limited supply; seawater desalination plants are going to be ubiquitous by the end of the century. Since the water crisis is, at its core, an environmental issue; large, efficient desalination plants must be designed and built to operate without unnecessarily polluting the environment and exacerbating the problem.

It is estimated that 1 in 5 people on Earth lack access to safe water, a basic requisite for survival [15]. It is difficult to estimate just how many people die every second because they don’t have access to clean drinking water. This is because dehydration is not always the direct cause of death in these situations. Lack of freshwater can be lethal in many ways including disease, famine, and war.

In developed nations we often take for granted the ability to turn on a faucet and have access to clean drinking water. It is easy not to think about how much we actually need clean drinking water and the grim consequences of long term freshwater shortage. Chronic dehydration reduces the effectiveness of the immune system; which is often lethal in combination with the intake of unsanitary water. The World Health Organization estimates that 90 percent of the 30,000 people who die every week from diseases related to low water quality and an absence of adequate sanitation are children under 5 years old. Two million people die every year from waterborne diseases, with many millions more becoming permanently debilitated, in fact, The WHO reports that over 3.6% of the total global disease burden could be prevented simply by improving water supply and sanitation. The death toll for disease related to poor water supply can only be expected to grow dramatically as water shortages increase in coming decades since it is the poorest areas of the world who are most vulnerable to these deadly diseases that will dry up first.

Like disease, famine has been a major contributor to human mortality with nearly every continent experiencing major periods of famine throughout history. In many cases, famine can be linked to drought since crops cannot be raised without a steady supply of freshwater. Famine leads to malnutrition and starvation; leading causes of death among children. In 2014, Action Against Hunger, an international organization to prevent and treat child malnutrition and illness, estimated that 17 million children around the world suffer from severe acute malnutrition, a deadly condition

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if not treated. At least 1 million of these malnourished children die every year because they do not receive the necessary treatment [12].

Perhaps the most frightening consequence of freshwater shortage is war. Many have suggested water to be the source of the next major global conflict, but in reality the Water War has already begun. Water scarcity, though often overlooked, is a key factor in almost every global conflict today. From the Israelis diverting the River Jordan leading to the Six Day War of 1967 to the decades old conflict in Kashmir which is largely over control of the headwaters of the River Indus, to the damming of the Euphrates and more recently the Tigris River in Turkey to deprive ISIS held Syria and Iraq of water; water scarcity is a major source of tension and conflict at flashpoints around The world [14].

There exists a widely-held scientific conviction that the global climate change we are currently experiencing is in part a result of anthropogenic influence. Overwhelming evidence has concluded with a high level of certainty that human activities have exerted a substantial net warming influence on the global climate since 1750. Climatological studies have found that the global surface air temperature has increased from 1850 to 2005 by 0.76ºC, with a strong linear warming trend of 0.13ºC per decade over the last 50 years [1]. The increase in terrestrial surface air temperature directly affects the dynamics of global evapotranspiration, the movement of water from surface to atmosphere through evaporation and transpiration. Scientists expect the amount of land area affected by drought to grow by mid-century and water resources in these areas to decline by as much as 30% [2].

This desertification is driven in part by an expanding atmospheric circulation pattern known by climatologists as the Hadley Cell. There are three main categories of jet stream wind cells that are responsible for a majority of atmospheric circulation; Polar Cells, Ferrel Cells, and Hadley Cells. Hadley Cells are the low-latitude, overturning circulation currents driven by warm, moist air rising from the tropics at the equator, then cooling in the upper atmosphere and losing moisture to tropical thunderstorms. The cool, dry air then sinks at around 30° latitude in both the Northern and Southern Hemispheres, taking moisture with it as it moves back towards the equator. Hadley Cells are responsible for the trade winds in the Tropics and control low-latitude weather patterns as well as being a major contributor to widespread desertification. The heterogeneous increase in surface air temperature increases the

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Figure 1: Atmospheric Circulation Currents [3]

driving force behind this circulation causing the jet streams to shift to higher latitudes. Storm patterns shift along with the jet streams causing longer, more frequent droughts and forcing desert and semi-arid areas to expand towards the poles [3].

The problem of global freshwater scarcity is a serious one that will kill millions of people in the coming years. A World Economic Forum report in January 2015 highlighted the issue of global freshwater scarcity stating that the shortage of fresh water may be the main global threat in the next decade. Another 2015 report, this one by the IAEA stated that "Only nuclear reactors are capable of delivering the copious quantities of energy required for large-scale desalination projects." Water shortage is a serious and immediate problem that will test the resilience, fortitude, and adaptability of our species. It is critically important we as human beings give this issue the respect it deserves and invest in advanced seawater desalination technology immediately.

1.2 Regional Background

The Arab World consists of 22 States spanning roughly 10 million square kilometers of arid and semi-arid regions of Northern Africa and the Middle East. Over 370 million people call this region home; a number which has been growing by roughly 2.6% over the past 20 years. This area was once a vast ocean that dried up millions of years ago into vast expanses of desert; and indeed continues to dry out even today [4]. While the region boasts an abundance of natural resources like oil and minerals, it lacks sustainable fresh water resources. The Middle East and North Africa have by far the least current freshwater availability in the World with some countries, including the United Arab Emirates, having less than 100 m3 per capita of freshwater in reserve. From 2012 to 2014, The World Bank estimated the UAE to have the 3rd least freshwater reserves per capita of 16 m3 after Bahrain who had 3m3 and Kuwait who was estimated to have less than 1m3 of potable water per capita in reserve [9].

Seawater desalination is the only realistic option for nations like these who have plenty of wealth, yet see only a few centimeters of precipitation annually. According to a 2013 study by The Arabian Water and Power Forum, seawater desalination plants supply 98.8 percent of Dubai’s freshwater, with only 1.2 percent coming from groundwater and other sources [10]. With the main obstacle of seawater desalination being the vast thermal power requirements; coupling modern, high efficiency seawater desalination technology with an advanced, Generation IV Nuclear Reactor System would be a logical solution for the UAE. Nuclear Seawater Desalination Plants could be built along the coast of the Arab Gulf to supply all 7 Emirates with a renewable source of fresh water, store freshwater for emergencies, and sell excess water to neighbors. Investing in “clear gold” is clearly the way for the UAE to solve its most immediate problems, diversify its economy, and secure its bright future.

Located on the Arabian Peninsula, the UAE is well known for its luxurious cities filled with lavish resorts, shopping, and attractions. Driven by strong economic and industrial growth, an increasing

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population, and urbanization trends, the energy consumption of UAE has expanded rapidly. From 1990 to 2010 the energy consumption of the UAE as a whole quadrupled and is expected to double again by 2020 [8]. In 2006 the roughly 4.4 million people in the UAE used 56.6 terawatt*hours of electricity making them the highest per capita energy consumer in the world [6]. A 2009 report by the Dubai Chamber of Commerce and Industry called for $8 billion in investment to the electricity sector of Dubai over the next six to eight years to meet the growing demand. Even though energy consumption in the UAE is already high, it will continue to rise due to economic necessity. Renewable energy has become a top priority of the UAE who was one of the first major oil-producing countries to demonstrate a commitment to emissions reduction by ratifying the Kyoto Protocol to the UN Convention on Climate Change in 2005 [6].

Renewable energy initiatives in the UAE are still unmatched in the region. Of particular note is Masdar City, slated to be the clean energy capital of the world. This revolutionary city in Abu Dhabi has received billions of dollars of investment in sustainable technologies. The city is designed as a 50,000-inhabitant zero-carbon and zero-waste community. Essentially, Masdar City will be an ecosystem running on solar power and providing information and expertise for the rest of the world.

The high standard of living of these extravagant emirates does not mean that water scarcity is not a problem for oil rich states like the UAE, who are confronted with a serious depletion of their available water resources. A report from the Emirates Industrial Bank in 2005 said that the UAE had the highest per capita consumption of water in the world; 550 Liters per capita per day [5]. A 2008 survey conducted by the Environmental Agency - Abu Dhabi (EAD) to indicate the level of environmental awareness and conservationist behavior among the public in Abu Dhabi revealed that citizens of Abu Dhabi were most concerned about energy, while water ranked as their least concern. As a result of this misuse of water, the water table of the region has dropped by approximately one meter per year for the last 30 years. At this rate, the UAE will deplete its natural freshwater resources in about fifty years. Even with a robust desalination infrastructure relative to the rest of the world to reduce their freshwater deficiency, the UAE desperately needs to increase its water consumption efficiency before its energy consumption doubles in 2020 as a result of urbanization [8].

Driven by strong economic and industrial growth, an increasing population, and urbanization trends, the electricity consumption of UAE has also been expanding rapidly. From 1990 to 2010, the energy consumption of the UAE as a whole quadrupled and is expected to double again by 2020 [8]. In 2006 the roughly 4.4 million people in the UAE used 56.6 terawatt*hours of electricity making them the highest per capita energy consumer in the world [6].

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1.3 Objective

Interest in using nuclear energy to produce potable water has been growing worldwide in the past decade. The inspiration for this interest is especially strong in regions where freshwater reserves are nearly spent. Motivated by energy supply diversification and conservation of limited fossil fuel resources, the UAE will likely spend billions of dollars in the coming years on seawater desalination in the pursuit of a sustainable water supply. The objective of this project is to offer a cost efficient, environmentally friendly solution to the water shortage problem in the UAE by presenting a design for an advanced nuclear seawater desalination plant.

1.4 Scope

The scope of this project will be to design a plant which takes heat from two independent pebble bed fueled, molten fluoride salt cooled high temperature reactors and uses this heat to power the effects of a multi effect distillation apparatus to desalinate seawater. The plant will be designed to operate in high temperature heat rejection environments like the UAE with an off peak capacity of over 150,000 m3 of freshwater per day. An overview of the plant will be presented with discussion of the economics of a PB-FHR MED plant. Reactor neutronics will be evaluated in MCNP and coupled to the core thermal hydraulics model in Comsol and plant thermodynamics model in Aspen Plus to validate heat removal predictions. Finally, design basis accidents will be discussed on a probabilistic basis

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Chapter 2: Project Description

2.1 Site

2.1.1 Location

The proposed plant is to be sited adjacent the Barakah nuclear power plant site in Abu Dhabi, UAE to make further use of existing infrastructure and equipment. Barakah is a $20 billion, 5.6 GW nuclear plant consisting of 4 Korean APR-1400 reactors currently under construction to be completed by 2020. Recognizing that regional volatility is a major concern in this part of the world, physical security is a primary concern; however, it is outside the scope of this project and the expertise of the students to specifically address plant security issues.

2.1.2 Topology

The Barakah site is located on the western UAE Gulf Coast, 53 km west of Ruwais and 300 km west of Abu Dhabi city, a little closer to Qatar than to the Capital. It is a rural and remote area, yet has the existing infrastructure for construction and operation of a nuclear plant. The temperature of the seawater at Barakah is about 35°C, which makes it difficult to reject heat and drives down conversion efficiency and raises the cost of heat exchangers and condensers. Conversely, this warm water will reduce the energy required to heat the water for distillation.

2.1.3 Meteorology

The high temperatures and low precipitation levels in UAE are a tough combination for groundwater retention. Temperatures regularly reach up to 40°C in the summer months when there is little precipitation. Below is a chart showing the average monthly temperatures and rainfall in the UAE from 1990 to 2009 [9]. As described in Chapter 1 the precipitation in the region is steadily decreasing while the average surface temperature increases disproportionately to the rest of the world. In summary, the UAE cannot afford to rely on the natural replenishment of groundwater resources for much longer and needs to supplement their water supply with additional seawater desalination capacity.

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Figure 2: Barakah Nuclear Site [18]

Figure 3: Average Monthly Temperature and Rainfall in UAE from 1990-2009 [9]

2.1.4 Seismology

The area selected to site our plant is not near any major sources of seismic activity. According to Khamis Al Shamsi, Acting Head of Seismology at the National Centre of Meteorology and Seismology; "The ones [sources of seismic activity] that we can lay claim to are 'very, very low sources in the Masafi region in the northern parts of UAE that have a potential of maximum 3-3.5 magnitude event" [18]. Southern Iran on the other hand experiences a large amount of seismic activity. The main seismological concern would be an extremely energetic, shallow focus quake caused by interactions between the Arabian and Eurasian tectonic plates, which meet below the Arabian Gulf. The probability of a quake strong and shallow enough to cause significant damage to our plant hundreds of kilometers away is low enough to be beyond the design basis for this project.

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Figure 4: Observed Seismicity of Gulf Nations from 1964 to 2006 (ISC data) [18]

2.1.5 Neighboring Populations

Excluding a few small villages such as Al Hamra, the only significant population near the planned site is the small industrial town of Al Ruwais, around 53 km East of Barakah. Once a small, seasonal fishing headland, Al Ruwais today is one of the most modern industrial complexes in the Middle East. Centered around Takreer’s Ruwais Refinery, the industrialization of Al Ruwais began in the 1970s, when plans were laid to transform the remote desert site into a self-contained industrial town specifically created to fulfil the downstream requirements of Abu Dhabi’s booming oil and gas industry. Currently the refinery supplies the city with electricity; however, as the population (currently estimated around 20,000) continues to explode, the refinery will be increasingly unable to meet the growing demand [21]. Based on the aforementioned estimate by the Environmental Agency - Abu Dhabi (EAD) that the per capita daily consumption of freshwater in UAE is 550 L, our plant should be able to supply potable water to around 230,000 people [5].

2.1.6 Dubai – Ghweifat International Highway E11

The International Highway E11 is a massive highway that runs from the city of Ghweifat at the Saudi Arabian border, along the Gulf coast all the way to Dubai. The highway grants vehicles easy access to the site for faculty transportation as well as shipping.

2.1.7 Railway Access

The FHR is designed so that all components; including the reactor vessel, gas turbines, and building structural sub-modules can be transported by rail to enable modular construction. The design constraint of rail transport limits the width of components to 3.6 m, which is what constrains the reactor vessel diameter and thermal power to a value corresponding to the largest rail-shippable gas turbines commercially available today. Etihad Rail’s 1,200 km railway network, scheduled to be finished by 2021, will extend across the United Arab Emirates, from the border of Saudi Arabia to the border of Oman. Stage 2 of the network will connect Ghweifat to Ruwais, Abu Dhabi, Dubai and the Northern Emirates with access to our site along the way.

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Figure 5: Etihad Rail's 1,200 km rail network to be completed by 2021 [32]

2.2 Reactor Description

2.2.1 Plant Overview

Table 1 below shows an overview of the thermodynamic and thermal hydraulic specifications of the PB-FHR MED plant design.

Reactor Thermal power (MWt) 292.25

Total Plant Thermal Power (MWt) 623.86

Power Conversion efficiency (%) 48.06

Core power density (MW/ cubic m) 27.9

Plant Capacity (cubic m/ day) 414,400

Fuel full-power residence time in core (yr) 1.38

Fuel average surface heat flux (MW/ square meter) 0.189

Table 1: Plant Overview

2.2.2 Reactor Core Description

The PB-FHR core design combines robust, coated-particle fuel elements with advanced molten salt coolant to easily reach temperatures exceeding 700 °C. The fuel pebbles are 3cm in diameter, slightly smaller than a ping pong ball and only half the diameter of pebbles used in conventional helium-cooled pebble bed reactors. Along with the more effective heat transfer provided by salt cooling, the pebble design enables operation with significantly higher power density and smaller reactor sizes than helium cooled reactors. Modern gas cooled pebble bed reactors offer power densities on the order of 10 MW/m3 compared to the power density of 27.9 MW/m3 calculated for our reactor design. The pebble fuel elements can safely reach temperatures of 1400°C at which point diffusion of fission products becomes a concern.

The fuel pebble contains a 1.25 cm diameter, low density, spherical graphite core to make the pebble buoyant in the salt. Surrounding the pebble core is a graphite matrix of roughly 4730 suspended TRISO particles less than 1mm in diameter. The TRISO particles consist of a 200 μm radius Uranium carbide fuel kernel surrounded by a buffer layer of porous carbon 100 μm thick encased in two pyrocarbon shells separated by a layer of silicon carbide, each 35 μm thick.

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An advanced cooling system is needed to operate at these high temperatures. The coolant selected for this design is a beryllium-based fluoride salt known as flibe (7Li2BeF4). The selection of a beryllium-based coolant involves a tradeoff between fuel utilization, neutronics, activation, corrosion, chemical safety, and salt cost. Flibe is the only fluoride salt that has sufficiently low parasitic neutron capture, and enough moderating capability to allow the design of solid-fueled, salt-cooled reactor cores with negative void and temperature reactivity feedback coefficients. Flibe is a eutectic mixture of lithium fluoride and beryllium difluoride in a roughly 2:1 stoichiometric ratio by molar percentage. At this composition, the melting point of the salt is 459.1°C and the boiling point is on the order of 1400°C, yielding immense thermal safety margins. In fact, lithium fluoride and beryllium difluoride form a dieutectic system that has two eutectic compositions. The mixture is eutectic both at a composition of 32.8% BeF2 and at 53.1% BeF2 by molar percent. The 53.1% beryllium difluoride mixture is not considered due to its high viscosity and vapor pressure.

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Figure 6: Fuel Pebble and TRISO particle diagram [20]

Figure 7: LiF-BeF2 System Phase Diagram [33]

The 470,000 fuel pebbles in the core are surrounded by a layer of 120,000 pure graphite reflector pebbles of the same average density. Pebbles are loaded in the bottom of the core and removed from the top, with flibe slowly circulating passively through the reactor at low pressure in a natural circulation loop. Shown at the right, the annular core, which surrounds a cylindrical axial graphite reflector, bulges radially in the center to form a critical fuel configuration. The axial reflector contains 16 channels for control elements. Surrounding the core is another large outer graphite reflector encased in the 60 cm thick 316 Stainless steel reactor vessel.

Figure 8: Solidworks Drawing of the mk-1 FHR Core Geometry showing fuel pebbles (green) and reflector pebbles (yellow) [20]

2.2.3 Control and Shutdown

The reactor contains 16 boron carbide control rods inside the central reflector as well as shutdown blades with an uneven cruciform cross section that actually penetrate the core to reach the highest possible worth when shutting down the reactor. Both of these systems are capable of independently shutting down the reactor.

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2.2.4 Power Conversion System

An open, air-Brayton cycle with optional natural gas co-firing will be used for power conversion. The FHR coupled with a nuclear air-Brayton combined cycle (NACC) is projected to have a baseload efficiency between 40% and 47%; significantly higher than the efficiencies of today’s nuclear power plants. The NACC turbines will power the plant compressors and generators, rejecting the hot air at around 280°C to the distillation unit which takes the place of a regenerator. To allow power peaking, natural gas is injected after the last stage of nuclear air heating. The increased inlet temperature into the last turbine stage allows for higher power output to distillation effects. There is also the longer-term option of using biofuels or hydrogen for peaking power. Because hot air is the heat transfer media to the distillation effects, the steam plant is decoupled from the nuclear plant such that the steam plant can be independently optimized.

2.2.5 Safety Features

The Direct Reactor Auxiliary Cooling System (DRACS) is a passive heat removal system derived from the Experimental Breeder Reactor-II (EBR-II). The system was improved in later fast reactor designs and is the passive decay heat removal system proposed for the FHR. The DRACS consists of three fully coupled natural circulation salt loops. Two heat exchangers; the DRACS Heat Exchanger (DHX) and the Natural Draft Heat Exchanger (NDHX) are used to couple these natural circulation loops. A fluidic diode is employed to restrict parasitic flow of coolant to the DRACS during normal operation of the reactor. The diode restricts flow in one direction until it is passively activated in an accident scenario to allow flow to the DRACS. A buoyancy driven air circulation cooling system called the Reactor Vessel Air Cooling System is then activated to passively cool the reactor vessel with air and adding decay heat removal as shown below.

2.3 Advanced Multi-Effect Distillation Coupling Description

2.3.1 Desalination Technology Decision Basis

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Figure 9: Schematic of combined RVACS and DRACS system for the FHR core

There are two industrial scale methodologies widely employed for seawater desalination today. The first is reverse osmosis (RO), which works by pushing the water through a semipermeable membrane to remove the salt. The membrane acts as a filter the water can easily pass through while the salt remains behind. Membrane life is a significant factor in RO plant costs. 1990 energy prices would require a membrane life of at least 5 years to be competitive with other desalination technologies. The alternative method is thermal desalination which uses distillation to remove solubles from the condensate. The drawback of thermal desalination is that the high specific heat capacity and latent heat of vaporization of water make this method extremely energy intensive, much more so than RO. At high energy prices RO is substantially cheaper; however, with a source of cheap thermal energy, distillation becomes the more competitive option [29]. Our design will attempt to minimize the required energy input by employing multiple effects or distillation stages to effectively reuse the energy given off by the condensing steam to heat feed water traveling to subsequent effects. Adding more stages and upscaling the size of the distillation effects decreases the required energy input per unit volume of water. An industrial scale, single effect distillation system has a conversion factor of roughly 180 MJ/m3 potable water recovered. Further optimization of the distillation system is required as future work; however, existing 3 stage MED plants in Saudi Arabia have demonstrated conversion factors of 125 MJ/m3 potable water recovered.

2.3.2 MED Concept

An MED system consists of multiple stages or effects which are essentially just specialized countercurrent steam-water heat exchangers. In each stage the feed water is sprayed on the top of a bank of horizontal steam tubes, dripping from tube to tube and being heated by the condensing steam in the tubes until it collects at the bottom of the stage. Some of the water is vaporized in this process. This vaporized steam then flows into the steam tubes of the next effect, heating and vaporizing more water to be sent to the next stage of the distillation system. The goal is to increase efficiency by reusing as much energy as possible in subsequent effects. The products of this process are distilled water and saturated brine which can be processed into a number of products including sea salt and refrigerant fluid.Chapter 3: Economic Analysis

3.1 Plant Capital Cost

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Figure 10: Schematic of MED process [34]

Researchers at MIT have attempted to estimate the cost of building an FHR compared to advanced LWR’s that currently exist, and whose capital costs are well researched and understood. Their estimate is based on the required inventories of various structural materials such as concrete, steel, and other plant materials. The conclusion of this study is that the direct capital cost of building an FHR is 30% less than an LWR of the same power [22].

3.2 Additional Cost

3.2.1 Operating and Maintenance Costs

Several groups have estimated FHR operating and maintenance costs to be less than those of LWRs based on the low pressure of the system, improved efficiency, and the characteristics of the salt as a highly effective heat transfer fluid. No FHR has ever been built, and there has been no regulatory review of these studies. At this time a reasonable conclusion is that the operating and maintenance costs will be similar to other types of nuclear plants [30].

3.2.2 Fuel Costs

The fabrication costs of TRISO fuel pebbles are highly speculative and are the greatest source of uncertainty in the cost analysis of our plant. This is a key issue for proposed nuclear systems that use coated particle fuel. Estimates for TRISO fuel fabrication costs range from 1,650 to 10,000 $/kgU. Assuming fabrication costs of 10,000 $/kgU, fuel fabrication can account for 41% of the total fuel costs, about 0.58 cents/kWh(e) [23]. Since the planned enrichment for our fuel kernels is only 8.0% U235, less than half the mk-1 design specification of 19.9%, it is reasonable to assume our fuel costs will be towards the lower end of this cost range.

3.2.3 Decommissioning Costs

The FHR decommissioning process starts with the defueling of the core, followed by removal of the center reflector. The main salt pipes are then drained and the salt is sent to storage. The primary salt is pumped from the vessel using a submersible salt pump. Following the draining of the salt, the electrical heating of the vessel and main-salt piping would cease, allowing the vessel and core internals to cool to near room temperature. The reactor vessel is then flooded with water to improve radiation protection during disassembly and removal of the core internals and graphite components. The circulation of this water through filters and ion exchange columns has been found to be highly effective in removing beryllium contamination since flibe is soluble in water, as well as radioactive contamination with the exception of tritium [26]. Next, the hot and cold leg nozzles are severed and the reactor vessel is cut into segments. The reactor cavity segments are then crane lifted from the reactor and placed into a transfer cask for removal and replacement while keeping the reactor cavity flooded with water.

The IAEA has developed a useful summary of experience with the processing and disposal of graphite components, including a review of methods used in the decommissioning of the Fort St. Vrain High Temperature Gas-cooled Reactor [25]. Fort St. Vrain (FSV) nuclear power plant was a 330 MW high temperature gas-cooled reactor that Public Service Company of Colorado permanently closed in August 1989. In their evaluation of decommissioning options, the company decided to pursue immediate dismantlement to remove all significant radioactive material and

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meet the radiological limits for unrestricted use of the site [26]. This operation took place on a fixed-price, $195 million contract; therefore, costing less than 1 cent/kWh despite only a 16-year operating life with a 15% average capacity factor [27]. The project proceeded on schedule and budget to clear the site and relinquish its license early in 1997. It was the first US power reactor of this size to achieve this [28]. Based on the fact that this reactor is around the same power as one of our FHR units, yet has a much larger core due to the low power density of gas cooled reactors, it is reasonable to assume the cost to decommission one of our FHR units would be less than that of FSV. Based on these numbers it we estimate the total cost to decommission our PB-FHR MED plant would be around $400 million.

3.3 Economic Advantages

Our reactor design has a number of significant economic advantages over other plant designs. Chief among these is the variable power schedule allowed by natural gas co-firing. Being able to easily control the power output to the MED plant by adjusting the natural gas injection rate allows optimization of the power schedule based on the demand for water and the current price of natural gas. Since the infrastructure for extracting, liquefying, and transporting natural gas is still in the relatively early stages of development, the price of liquefied natural gas (LNG) is highly volatile. When the market is saturated and the price is low, peaking can be used to increase production. Since unlike electricity water can be easily stored, overproduction it is not a concern for our plant like it would be for a power plant. Furthermore, if additional freshwater capacity is needed for some emergency, the natural gas can be used to temporarily increase production.

Chapter 4: Thermodynamic Analysis

This chapter provides an overview of the thermodynamic analysis of nuclear desalination plant design. Aspen plus is the market-leading thermal process optimization software chosen for thermodynamic modeling in this project.

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4.1 Plant Layout

The power source for our plant consists of two FHR units feeding an MED plant system to distill sea water from the Arabian Gulf to be used in the United Arab Emirates. The hot air, rejected from the final turbine stage at a temperature of 280°C would power the MED plant. The reactors are identical and fully decoupled; the flow diagram for a single FHR unit is shown below. For each FHR unit, there are two gas turbines; one is a GE 7FB gas turbine and the other is an Alstrom GT24 LNG injected co-firing turbine. An air compressor is needed to compress the filtered air at the beginning of the NACC cycle. Each unit has two coiled tube air heater (CTAH) type salt to air heat exchangers which transfer the thermal energy from the hot salt to the NACC cycle. The rest of the mechanical work extracted from the cycle that doesn’t go to the compressor or the MED thermocompressor goes to a generator to power plant electrical systems.

Figure 11: FHR for desalination flow schematic [20]

Further studies have been conducted using aspen plus software to analyze the power produced in each FHR unit. For each component in the cycle, input and output flows have been implemented along with the pressure ratios through the turbines and the compresses to calculate the exact power needed and produced at each component, as shown in figure 11.

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The output power of the unit is shown in figure 12 with a value of 140 MW which could be converted to an electrical power of 46.8 MW(e) for each unit. The total electrical power combined for both units would reach 100 MW(e), approximately. This power would feed the electricity needed for the plant’s need from safety systems to the lighting of the site, along with the diesel generators. The most important output from the NACC is the air hot steam with a high temperature hot air which would feed the MED system.

4.2 Distillation Capacity Scaling

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Figure 12: Flow Diagram in Aspen Plus

Existing 3 stage MED plants in Saudi Arabia have demonstrated conversion factors of 125 MJ/m3 distilled water recovered. The power efficiency of the NACC employed by our plant is around 48% yielding a conversion factor of 260.42 MJ/m3 distilled water. This conversion factor allows for estimation of the distillation capacity of our plant. The total peaked thermal power from both units plus the LNG co-firing energy of 623.86 MW(th) which corresponds to 414,178 cubic meter of distilled water per day at 100% capacity. The main goal was to reach the range of water production of the largest desalination plants around the world. This daily production rate of over 400,000 cubic meters of water is comparable to other large desalination projects in the region. Figure 13 below shows the power distribution to the various plant systems.

Figure 13: Blue is used for distillation, Grey is extracted as mechanical work by the NACC, and Orange is electrical work generated from excess mechanical work not used in compressors and thermocompressor

4.3 Modeling

In this section, the thermodynamic modeling of one of the two identical FHR units in Aspen Plus will be discussed in depth with design parameters given for each major component in order to give detailed thermal hydraulics analysis for the plant. The detailed information for the following components were calculated using the internal thermodynamic code of Aspen Plus software in terms of pressure, temperature and power or which it refers to as duty.

4.3.1 Coiled Tube Air Heater System

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The baseline FHR design has two CTAHs which transfer the thermal heat from the primary salt flibe to compressed air for the NACC system. The CTAHS are immediately adjacent to the FHR reactor cavity. These Air heater system are similar to the heat exchanger design patented by Gilli et at. in 1973 [2E]. In figure E-6 shown below, the diameter of the CTAH model is around 3.5 meters along with the coiled tube bundle that includes the hot flibe. Worth to mention that the tube contains hot flibe which is the heat source and the air flow through the bundle transfer the thermal heat to the NACC system. After using Aspen Plus to analyze the Duty of each heat exchanger, the results are shown in table 2 showing the power in MW depends on the cold outlet pressure and the surface area, since the surface area is the same for both CTAHs. The only difference that change the Duty for the first heat exchanger to the second one is the air pressure outlet. The low pressure gives the air more time to absorb more heat which is noticeable in the table below.

4.3.2 Turbines & Compressor Two different Turbines are used in this plant project. The first is an Air Turbine and the other is a co-firing turbine with a natural gas injection. Both Turbine produced almost the same amount of power, the only difference is that the co- firing turbine has a higher inlet temperature which compensate the lower air flow inlet pressure for the co-firing turbine. The tables below list the important design parameters of the turbines and compressors.

Alstrom GT24 (Co-fired)GE 7FB (Air turbine)

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Figure 14: FHR CTAH vessel

Table 2: CTAH design parameters

CTAH 1 CTAH 2

Exchanger area (m2) 5041 Exchanger area (m2) 5041

Cold outlet pressure (bar) 18.52 Cold outlet pressure (bar) 4.99

Q (MW) 64.95 Q (MW) 227.29

Pressure ratio 18.52

Inlet Mass Flow (kg/s) 418.5

Outlet Mass Flow (kg/s) 418.5

Inlet Temp. ( C ) 670

Outlet Temp. ( C ) 418.7

Inlet Pressure ( bar ) 18.76

Isentropic efficiency (%) 80

Power produced (MW) 190.27

Pressure ratio 18.52

Inlet Mass Flow (kg/s) 418.5

Outlet Mass Flow (kg/s) 418.5

Inlet Temp. ( C ) 1371

Outlet Temp. ( C ) 418.7

Inlet Pressure ( bar ) 4.99

Isentropic efficiency (%) 80

Power produced (MW) 190.47

Table 3: Alstrom GT24 (Co-fired) design parameters

Air Compressor

Pressure ratio 18.52

Inlet Mass Flow (kg/s) 418.5

Outlet Mass Flow (kg/s) 418.5

Inlet Temp. ( C ) 35

Outlet Temp. ( C ) 418.59

Inlet Pressure ( bar ) 1.01

Outlet Pressure ( bar ) 18.58

Isentropic efficiency (%) 70

Power requirement (MW) 240.27

Table 5: Air compressor design parameters

4.3.3 Salt Pump System

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Table 4: GE 7FB Air Turbine design parameters

The FHR salt pumps have smaller size but similar requirements to the vertical-shaft, single-stage centrifugal pump designs that were developed in the early 1970’s for the MSBR, shown in figure E6.5. There are 2 loops in the FHR design, compared to 4 loops are in the MSBR design. The pump capacity is much smaller compared to the MSBR pumps as the flow is driven by natural circulation with the pumps off in normal operation.

Figure 15 : MSBR pump design [24]

4.4 Power Conversion System Specifications

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The following configuration of the NACC system is used:1- Air intake occurs through a filter bank, and the air is compressed to a pressure ratio of 18.5. The air exits the compressor at a temperature of 418 C.

2- After the compressor outlet, the air passes through a high pressure CTAH and is heated up to a turbine inlet temperature of 670C.

3- The air is then expanded to the almost the same temperature as the compressor outlet temperature of 418.

4- The air is then reheated back up to 670 C by passing the low pressure CTAH.

5- After the low pressure CTAH, the air is above the auto-ignition temperature of natural gas. A fuel such as natural gas can be injected and burned to increase the turbine inlet temperature and the power output.

6- The heated air is then expanded down to nearly atmospheric pressure at 280°C.

Figure 16: T-S diagram of the plant’s 2 turbine open air-Brayton air power conversion cycle

Chapter 5: Neutronics Analysis

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5.1 Modeling Process

The core neutronics have been modeled by Monte Carlo N-Particle 6 code (MCNP6). Initially material buckling and geometrical buckling equations were used to determine the size of the reactor by homogenizing the materials used in the core. From there, a ‘garbage can’ reactor was modelled in MCNP6 to compare to the hand calculations from the buckling equations. Once verified, the MCNP6 model was improved through a series of updates:

● First update: Added outer and inner reflector and had a homogenized core of fuel and FLIBE

● Second update: Added the core inlet, outlet, converging region, cylindrical region, expansion region and the reactor vessel. This allowed to separate the core into 5 major regions each with their own homogenized material composition of fuel pebbles, graphite pebbles and FLIBE differentiating by void fractions.

● Third update: Added sub-regions to each major region separating the fuel pebbles from the graphite pebbles. Sub-regions are homogenized either with graphite pebbles and FLIBE or fuel pebbles and FLIBE along with void fractions depending on the major region.

● Fourth update: Added control rods and control rod channels with FLIBE running through them

● Fifth update: Added shutdown blades.●

5.2 The MCNP6 Model

The complete model on MCNP6 represents the whole reactor with a detailed core that includes multi regions to model the void fractions in separate sections of the core as shown in a radial view in Figure 17. An axial view through the center of the reactor is also provided in Figure 18 showing the positions of control rods as well as the different layers of core, reflectors and reactor vessel.

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Figure SEQ Figure \* ARABIC 1s: Axial View of the Model in MCNP6. Light blue, green and blue represents material

Figure 17: Radial view of MCNP6 core model

5.3 Criticality Values and Neutron Fluxes

This section shows the results of using the MCNP6 model at different scenarios. Four scenarios are going to be presented, where one scenario has the rods inserted for 50 cm deep to ensure that the pebbles leaving the reactor are not critical, and this scenario will represent rods in a fully withdrawn case. Other scenarios will include rods being on the critical bank, fully inserted rods, and shutdown.

5.3.1 Fully withdrawn scenario

When the rods are fully withdrawn, an effective criticality value of 1.02309 is calculated by the MCNP6 model. Along with this criticality value, 90.22% of the neutrons were at thermal energies, 9.36% were at intermediate or epithermal energies, and 0.43% were in the fast energy range. This distribution remains fairly the constant in all the scenarios. Figure 19 shows the axial neutron flux distribution in this scenario, where the bottom of the core represents the height of 0 cm and the top of core represents a height of 850 cm; therefore, the rods are banked at a height of 800 cm. The neutron flux peaks axially at a value of 1.40E+14 neutrons/cm2-sec and though it might be unclear from the graph, the control rods dropped the neutron flux down to values around 1.0E+12 neutrons/cm2-sec. Figure 20 shows a radial neutron flux distribution from the center of the core with a peaking value of 2.75E+13 neutrons/cm2-sec. Note that there is a high neutron flux of 4.0E+13 neutrons/cm2-sec or larger hitting the inner reflector (<90cm in radius).

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Figure 18: MCNP6 core model axial view

Figure 19: Axial Neutron Flux Distribution with rods banked at height 800cm

Figure 20: Radial Neutron Flux Distribution with bank height of 800cm; inner reflector radius is 90 cm

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5.3.2 Critical bank scenario

In order to achieve criticality for this reactor, the rods had to be inserted for 735 cm at the height of 115 cm from the bottom of the core. Figure 5s shows an axial distribution of the neutron flux when the rods are at critical bank, showing a peak of 8.5E+13 neutrons/cm2-sec a little above the center (120 cm in radius). This peak is significantly less than the peak observed in the fully withdrawn scenario. Figure 6s shows a radial distribution of the neutron flux from the center of the core, with a peaking value 3.1E+13 neutrons/cm2-sec. This peaking value for the radial distribution is larger than the one observed in the fully withdrawn scenario. Inserting the control rods ‘squeezed’ the flux in the radial direction but reduced the flux in the axial direction. Furthermore, the neutron flux in the inner reflector has drastically dropped to values around 1.0E+12 neutrons/cm2-sec, which should reduce the thermal stress on the inner reflector.

Figure 21: Axial Neutron Distribution with rods banked at height 115 cm

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Figure 22: Radial Neutron Distribution with rods banked at height 115cm

5.3.3 Fully inserted scenario

Inserting the rods completely produces a criticality value of 0.99830. Figure 7s shows the axial neutron flux distribution with rods fully inserted, which shows a similar peak to the critical bank scenario, but has no perturbations in bottom of the core and shows a smooth curve. Figure 8s shows the radial neutron flux distribution at the center of the core with the rods fully inserted. More interestingly the flux in this Figure shows a lower peak than the peak in the critical bank scenario, but the same peak shown in the fully withdrawn scenario since the rods are no longer ‘squeezing’ the flux. This means that the peaks in both the radial and axial distributions have been reduced to its lowest values. Though unclear in Figure 8s, the neutron flux in the inner reflector has also decreased down to values around 8.00E+11 neutrons/cm2-sec which is lower than the flux observed in the critical bank scenario.

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Figure 23: Axial Neutron Flux Distribution with rods banked at height 1cm

Figure 24: Radial Neutron Flux Distribution with rods banked at height 1cm

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5.3.4 Shutdown scenario

With the addition of four shutdown blades cutting through the center of the core horizontally along with the control rods fully inserted as shown in Figure 9s, the criticality value is 0.98466. These shutdown blades have a radius of 4 cm and are 90 cm long. They will be located within the inner reflector and will be ejected slowly into the reactor through a small channel. These channels are horizontally located in the center of the inner reflector and extend to the end of the inner reflector between the vertical control rod channels. The blades’ ejection will be due to forces from springs that are coiled up mechanically from outside where such mechanism could be controlled via computer software and has a manual release of the coils in case of station black out. Figure10s shows the axial neutron flux distribution and the perturbation caused by the shutdown rods. Figure 11s shows the radial neutron flux distribution. Both figures show significant decrease in the neutron flux, especially at the center of the core.

Figure 25: Axial Neutron Flux Distribution fully shut down

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Figure 26: Radial Neutron Flux Distribution fully shut down

5.4 Fuel depletion Calculation

By approximating that the reactor is fueled with only a single isotope (U-235) with an atomic number density of 2.4004E+22 atoms/cm3 and one absorption cross section of 752 barns (the cumulative of the absorption cross sections of the fuel and FLIBE), one can use the constant flux approximation provided in Equation 1 below to determine the time it takes for the fuel to deplete. By approximating the number density at time t to be 0.1 and a constant neutron flux of 3.5E+14 (the highest observed from all scenarios), calculating time using Equation 1s results having around 2367 days before our fuels deplete. Though this is a very rough approximation, it shows that there is plenty of time for a pebble to reach the top of the core without depleting and the option of reprocessing.

Equation 1

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Chapter 6: Thermal Hydraulics

This chapter presents the thermal hydraulics for the packed pebble beds for the pebble fuel. The Pebble fuel allows for continuous and fast throughput refueling. The pebbles are circulated several times through the core of the reactor before they reach full burn-up. The fuel pebbles are three centimeters in diameter; they have an internal structure consists of 3 layers. The inner layer contains low density graphite which allow the fuel pebbles to flow adequately through the lithium beryllium- fluoride coolant. The annular fuel region consists of coated particle fuel embedded in a graphite matrix. The coated fuel particles have a diameter of around one millimeter in diameter; they consist of fuel kernel coated with several layers of graphite and silicon carbide. In this chapter, Section 6.1 provides and fuel temperature analysis using Mathematica software, which is a computational software used to solve the fuel conduction equations. Section 6.2 studies the natural circulation of the primary salt loop.

6.1 Fuel Element Thermal Analysis

6.1.1 Model Verification

● This section verifies the thermal hydraulics calculation from the mk-1 reactor along with the thermal hydraulics approach that adopted from modeling of gas-cooled reactor fuel.

● The highest total temperature rise from the the bulk temperature of the flibe coolant (650C) and the highest temperature point in the kernel particle was calculated by adding the temperature difference in four different materials ( from flibe to the uranium kernel).

● This can be done with heat conduction calculations based on the core local power density and local fluid flow conditions

● The convection rise through the coolant calculated by evaluating the following equations :

Equation 2

● The heat conduction equations was implemented in the Mathematica software to calculate the rise from the average kernel temperature in the fuel pebble to bulk temperature of the flibe coolant. The following equations are listed along with their region of interest :

1- Temperature rise across the outer graphite layer of the fuel pebble:

Equation 3

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2- Temperature rise from the outer surface of the fuel layer to the average temperature of the fuel layer:

Equation 4

−k fuel∇2❑T=

qpebble

6 k fuel∗V 2∗r2−

C1

r+C2

−k fuel∇❑❑T (0.0125)=

qpebble

k fuel∗V 2∗¿¿

T av=∫r1

r2

❑T (r )r 2dr

∫r 1

r 2

❑r 2d

ᐃT av=T av−T (0.014)

3- Temperature rise across the buffer layer of the TRISO particle.

Equation 5

∇2T=0⇒T (r )=C1

r+C2⇒ ΔTbuf =T (3.00E-4 )−T (2.00E-4)=C❑1(1/3.00E-4−1/2.00E-4 )

−k buf∇❑T (2.00E-4)=

qkernel

Ak⇒C1=

−qkernel

8 π∗kbuf

● Table 6 provides the important temperatures points for the fuel pebble along with the highest temperature rise through the fuel pebble.

Tpeakkern - Tsurf (C) Tavfuel (C) Tpeakkern (C) Tavkern (C)62.79 715.32 752.63 744.87

T coolant (C) Tsurf (C) r1 (cm) r2 (cm)650 689.84 1.25 1.4

Table 6: Fuel element design parameters

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Figure 27: Temperature distribution inside a fuel pebble

The modeling of the fuel pebble in this project is similar to that adopted from the modeling of gas-cooled reactor fuel. For both models, the primary temperature drop takes place within the TRISO particle which is shown in Figure E-1 as ΔTbuf. The reason behind that is the porous buffer layer has much lower thermal conductivity then the pyrocarbon and silicon carbide layers. Shown in figure 27, the temperature profile for gas reactor has lower temperature rise through the fuel pebble due to the higher power density of the FHR fuel.

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Figure 28 : Temperature profile for gas reactor pebble fuel ( TIMCOAT ) [35]

The major important difference between the thermal models for the gas reactor fuel and the FHR fuel is the pebble fuel has a graphite core with the fuel in an annular region in the pebble fuel. FHRs cores have higher power densities than gas cooled reactors. Moreover, the inner graphite core helps keep the fuel temperatures low and enables high power density operation through the coolant.

6.1.2 Average Power Pebble Analysis

As explained in the Reactor Description section 2.2, there are approximately 470,000 fuel pebbles in the core. The Mathematica thermal calculations given in Appendix B show that the average fuel pebble produces a power of 657.39 watts. The total thermal power would be produced based on the assumptions used above would reach 308,973,300 thermal watts from the total amount of fuel pebbles used in the core.

6.2 Natural Circulation

6.1.2 Natural Circulation Summary

Natural circulation is buoyancy driven fluid flow from a low elevation heat source to a high elevation heat sink relative to the source. As the low elevation fluid is heated by the source, in our case the reactor core, it becomes less dense and rises. Conversely, the high elevation fluid

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Figure 29: Initial conditions of NC loop at constant temperature

Figure 30: Temperature distribution after 10 mins of circulation

rejecting heat to the sink, the coiled tube air heater in our system, becomes more dense and sinks [37]. This countercurrent motion induces a passively driven flow in the loop. A passively driven cooling system like the one employed in the FHR design is far safer than actively circulating coolant systems where pump failure is a major concern.

Examples of natural circulation systems in nature range from magma flows in the cores of planets to water circulation patterns in oceans and lakes. The liquid magma comprising the Earth’s mantle flows in a circuit from the hot inner core, to the cold outer crust. The magma flows interact with the tectonic plates affecting seismic and volcanic activity. Similar phenomena occur on other planets as well; the effectiveness of natural circulation in magma oceans on Mars after high-intensity asteroid impact determines the time to magma crystallization. It is possible this phenomenology played a significant role in determining the geological structure of Mars [37].

6.1.3 Modeling in Comsol

A simplified version of one of our natural circulation salt loops was modeled in Сomsol using the parameters for pipe diameter, heat exchanger elevation, and heating rate.

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Figure 30: Temperature evolution at different points in the loop

6.3 T/H Coupling to Neutronics and Thermodynamics

The thermal hydraulics and neutronics coupling could be calculated based on power equation 6 shown below. Multiplying the reaction rate by the volume of the reactor results in the total fission rate for the entire reactor. Dividing by the number of fissions per watt-sec results in the power released by fission in the reactor in units of watts.

Equation 6

P=❑❑Ф❑ ΣV∗[1/3.12E10( fissions/watt−sec)](1 E)

Equation 7

P is power in watts, Φ is the thermal neutron flux in neutrons/cm^2 -sec), Σ is the macroscopic cross section for fission (cm^-1) and V is the volume of the core (cm^3).

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Chapter 7: Accident Analysis

Accident analysis for reactors dealing with molten salt coolant were investigated at Oak Ridge National Lab in the 1960s during the Molten Salt Reactor Experiment. Since then, safety guidelines have not been defined for any molten salt related accident analysis. In this section some possible accidents will be discussed along with transient analysis and safety protocols.

In the current procedure for light water reactor licensing, there are two main guidelines for accident analysis. The first is the ‘General Design Criteria” which consists of a guide for safe design of the reactor at a conceptual stage. The second guideline defines the accident analysis along with the studies of an in-depth analysis to the post-accident procedures. For the current categorization of accidents, all abnormal events are categorized in three types; abnormal operating trainsets (AOT), design basis accidents (DBA), and severe accidents (SA).

In this chapter, three types of accidents will be evaluated and analyzed in the framework of safety guidelines. Over pressure or over-heat accidents are caused by a power increase accident or flow decrease accident. These are the main first two accidents which will be discussed in this chapter. Besides these two accidents, loss of coolant (LOCA) or salt leakage accident may be caused by some mechanical failures of the primary loop. All of these accidents are considered in our project and will be discussed further in this chapter.

7.1 Power Increase Accident

7.1.1 Control rod withdrawal/ejection accident

Since we are using mechanical control rods made of neutron absorbing material, and when a failure happens with the equipment that control the control rods along with a smaller chance that human error cause the accident. If a withdrawn scenario happens, insertion of control rod would initiate a reactivity accident.

7.1.2 Cold-loop startup accident

If salt pump is inadvertently restarted from rest mode, and the cold salt injected into the core. That would make damages to the core cavity which lead to more severe accidents. Besides cold-loop startup accident, similar consequences will occur if the salt goes below the freezing point of the flibe (459°C).

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7.2 Flow Decrease Accident

7.2.1 Flow blockage accident

If blockage occurs at anywhere in the primary loop, same consequence will occur similar to pump trip or seizure accident. Based on a [E31] testing, 20 flow channels are blocked among totally 100 flow channels, so this kind of accidents should be highly considered. An additional concern associated with coolant freezing and blocking flow is that a solid piece of coolant would break off from the inner tubes of the coiled tube air heater and make its way back to the core. The crystalline lattice of solid flibe becomes unstable in a high neutron field causing radiolysis of the salt and corrosion of reactor internals due to the liberation of fluorine gas.

7.2.2 Fuel-salt Leak Accident

If rupture or break of the primary salt loop occurs by any chance, then the integrity of primary loop is lost, and the high temperature salt will leak out to some degree. Leaked salt is caught by a catch-pan, and collected in a drain-tank or emergency drain-tank. Worth to mention, the freezing point of the flibe is 459.1°C degrees so it will interact with the ambient air in the core causing some degree of freeze healing and preventing a full on LOCA.

7.3 Risk Assessment

The passive cooling of our reactor through natural circulation and high thermal margins to failure of our fuel make our reactor design theoretically much safer than that of an LWR. The group has confidence in the ability of the system to meet all NRC and IAEA requirements for safety.

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Chapter 8: Conclusions & Future Work

No new reactor design will be developed unless there is a compelling short term and long term case for its development. For the LWR, that compelling case was the need for a nuclear submarine that could stay underwater for months. The technology was transferable to commercial power plants because submarines and utility fossil plants used steam power cycles. For the FHR the compelling case could be seawater desalination. Further studies could increase the number of units to add more distillation capacity. The design of this plant sacrificed a certain amount efficiency for the sake of cycle simplicity so future work could include designing reheat and intercooling components to boost cycle output. Extensive thermodynamic optimization analysis outside the scope of this project to combine FHR’s with the corresponding MED equipment in the most perfect way will be required as future work before any reactor would be built.

Authors Note:

Since the application of seawater desalination is one of immediacy, it may be more appropriate to use proven LWR technology for near term seawater desalination instead of FHR. The basis of selecting an FHR power source was the combined group interest in the progress of advanced Generation IV reactor technology as opposed to a claim of competitiveness with LWR technology.

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Appendices:

Appendix A: Temperature –Dependent Thermophysical properties for Flibe Salt simplified correlations for flibe temperature dependent thermos-physical properties in the range of 600 to 800 C along with the Prandtl number and Reynolds number correlations for the thermal conduction calculations in the fuel pebble.

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Appendix B:

The thermal hydraulic Mathematica code used for the thermal temperature profile analysis of the fuel pebble along with the fuel particle. Based on the Doctoral thesis [UCB P. Raluca Scarlat 2012], after the verification of the previous fuel model some parameters were changed to design a fuel pebble needed for our project.

(*geometry*)

r1 = 1.25/100; r2 = 1.4/100; r3 = 1.5/100;

V2 = Pi*4/3*(r2^3 - r1^3); A2 = 4*Pi*r2^2;

A3 = 4*Pi*r3^2; Vpebble = Pi*4/3*r3^3;

V1 = Pi*4/3*r1^3; V3 = Pi*4/3*(r3^3 - r2^3);

(*rT=4.3*10^-4;rk=2*10^-4;rbuf=3.2*10^-4;*)

rk = 1.5*10^-4; rbuf = rk + 1*10^-4; rT = rbuf + 3*0.35*10^-4;

ripic = rbuf + 0.35*10^-4; rsic = ripic + 0.35*10^-4; ropic =

rsic + 0.35*10^-4;

VT = Pi*4/3*rT^3; Ak = 4*Pi*rk^2; Vk = Pi*4/3*rk^3;

Vbuf = Pi*4/3*(rbuf^3 - rk^3); Vipic = Pi*4/3*(ripic^3 - rbuf^3);

Vsic = Pi*4/3*(rsic^3 - ripic^3); Vopic = Pi*4/3*(ropic^3 - rsic^3);

(*material properties*)

k = 15; kgr = k;

kfluid = 1;

kbuf = 0.5; kk = 3.7;

(* density calculation *)

\[CapitalRho]core = 500; \[CapitalRho]gr = 1740;

\[CapitalRho]k = 10500; \[CapitalRho]buf = 1000; \[CapitalRho]pic = \1870; \[CapitalRho]sic = 3200; \[CapitalRho]mtrx = 1600;

\[CapitalRho]T = (\[CapitalRho]k*Vk + \[CapitalRho]buf*Vbuf + \[CapitalRho]pic*(Vipic + Vopic) + \[CapitalRho]sic* Vsic)/(Vk + Vbuf +

47

(Vipic + Vopic) + Vsic);

\[CapitalRho]fuel = trisoPF*\[CapitalRho]T + (1 - trisoPF)*\[CapitalRho]mtrx;

\[CapitalRho]pebble = (\[CapitalRho]core*V1 + \[CapitalRho]fuel*V2 + \[CapitalRho]gr*V3)/(V1 + V2 + V3);

(*CHM calculation*)

trisoPF = 0.11;

MWU = 235*0.2 + 238*0.8;

mk = \[CapitalRho]k*(Vk/VT)*trisoPF*V2;

mHM = mk*MWU/(MWU + 0.5*12 + 2*16);(* (UC0.5O2) *)

mSi = \[CapitalRho]k*(28/(28 + 12))*(Vsic/ �VT)*trisoPF*V2;

mT = \[CapitalRho]T*V2*trisoPF;

mC = \[CapitalRho]core*V1 + \[CapitalRho]gr*V3 + V2*(1 - trisoPF)*\[CapitalRho]mtrx + (mT - mk - mSi);

CHM = (mC/ �12)/(mHM/ �MWU);(* 20% enriched *)

(*density=1700,\[CapitalRho]core=500*)

Clear[trisoPF, \[CapitalRho]core]; ClearAll[trisoPF, \

\[CapitalRho]core];

\[CapitalRho]gr = 1740;

\[CapitalRho]k = 10500; \[CapitalRho]buf = 1000; \[CapitalRho]pic = \1870; \[CapitalRho]sic = 3200; \[CapitalRho]mtrx = 1600; \[CapitalRho]T =

(\[CapitalRho]k*Vk + \[CapitalRho]buf* Vbuf + \[CapitalRho]pic*(Vipic + Vopic) + \[CapitalRho]sic*Vsic) /. (Vk + Vbuf + (Vipic +Vopic) +

Vsic);

\[CapitalRho]fuel = trisoPF*\[CapitalRho]T + (1 - trisoPF)*\[CapitalRho]mtrx;

\[CapitalRho]pebble = (\[CapitalRho]core*V1 + \[CapitalRho]fuel* V2 + \[CapitalRho]gr*V3)/(V1 + V2 + V3);

(*thermal mass of the pebble=\[CapitalRho]*cp=sum(m.i*cp.i)/Vpebble*)

cp = 1725; \[CapitalRho]cppebble = \[CapitalRho]core*cp;

48

(* C/HM=300,trisoPF=0.11;*)�MWU = 235*0.199 + 238*0.801;

mk = \[CapitalRho]k*(Vk/VT)*trisoPF*V2;

mHM = mk*MWU/(MWU + 0.5*12 + 2*16);(* (UC0.5O2) *)

mSi = \[CapitalRho]k*(28/(28 + 12))*(Vsic/VT)*trisoPF*V2;

mT = \[CapitalRho]T*V2*trisoPF;

mC = \[CapitalRho]core*V1 + \[CapitalRho]gr*V3 + V2*(1 - trisoPF)*\[CapitalRho]mtrx + (mT - mk - mSi);

CHM = (mC/12)/(mHM/MWU);(*20% enriched*)

(*goal seek trisoPF and \[CapitalRho]core*)

sol = Solve[{CHM == 300, \[CapitalRho]pebble == 1700}, {trisoPF, \[CapitalRho]core}];

trisoPF = trisoPF /. sol[[1]];

\[CapitalRho]core = \[CapitalRho]core /. sol[[1]];

(*power*)

(*power-inputs*)

qcore = 27.9*10^6;(* MW/m3,core power density*)�decay = 1;(* 1=full power,0.06=6% power*)

(*power-derived values*)

q3 = decay*qcore/(0.6*V2/Vpebble)(*power density in fuel zone,W/m3*)

qpebble = q3*V2;(*power per pebble*)

q3T = q3/trisoPF;(*power density in TRISO*)

qT = q3T*VT;(*power per triso*)

q3k = qT/Vk;(*power density in kernel*)

(*convection at pebble surface*)

Ren = decay*950;(*30oC cone:Re=950*)

49

Pr = 17; Tfluid = 650;

Nu = 2 + 1.1*Pr^(1/3)*Ren^0.6;

dp = 2*r3;

h = Nu*kfluid/dp;

DTconv = (q3*V2/A3)/h;

Tsurf = Tfluid + DTconv;

\[CapitalTau] = h*(6/dp)/\[CapitalRho]cppebble;

Bi = h*dp/k;

(*graphite layer in pebble*)

C1gr = -q3*V2/A2/kgr*r2^2;

C2gr = Tsurf + C1gr/r3;

Tgr[r_] = -C1gr/r + C2gr;

DT23 = Tgr[r2] - Tgr[r3];

Tavgr = NIntegrate[Tgr[r]*r, {r, r2, r3}]/NIntegrate[r, {r, r2, r3}] -Tsurf;

(*fuel layer in pebble*)

C1 = q3/k*r1^3/3;

C2 = Tsurf + DT23 + q3/k*r2^2/6 + C1/r2;

T[r_] = -q3/k*r^2/6 - C1/r + C2;

DT12 = T[r1] - T[r2];

DTpebble = DT12 + DT23;

Tavfuel = NIntegrate[T[r]*r^2, {r, r1, r2}]/NIntegrate[r^2, {r, r1, r2}] - Tsurf;

(*TRISO buffer*)

C1buf = -q3T*VT/Ak/kbuf*rk^2;

C2buf = T[r1] + C1buf/rbuf;

Tbuf[r_] = -C1buf/r + C2buf;

50

DTbuf = Tbuf[rk] - Tbuf[rbuf];

DTfuel = DTbuf + DTpebble;

Tavbuf = NIntegrate[Tbuf[r]*r^2, {r, rk, rbuf}]/NIntegrate[r^2, {r, rk, rbuf}] - Tsurf;

(*TRISO kernel*)

C2k = Tbuf[rk] + q3k/kk*rk^2/6;

Tk[r_] = -q3k/kk*r^2/6 + C2k;

DTk = Tk[0] - Tk[rk];

DTfuel2 = DTfuel + DTk;

Tavk = NIntegrate[Tk[r]*r^2, {r, 0, rk}]/NIntegrate[r^2, {r, 0, rk}] -T[r1];

(*outputs*)

Grid[{{"Tavfuel-Tsurf", "Tavker-Tsurf", "Tpeak_kern,C",

"Tavkern,C"}, {Tavfuel + Tsurf, Tavfuel + Tavk, Tk[0],

Tavfuel + Tavk + Tsurf}, {"Tcoolant", "Tsurf", "r1,cm",

"r2,cm"}, {Tfluid, Tsurf, r1*100, r2*100}, {"~~", "q_pebble,W",

"q_core,MW �/m3", "~~"}, {"~~", qpebble, qcore/10^6, Tbuf}}, Frame -> All]

(*plot*)

Pfuel = Plot[{T[r] - Tsurf}, {r, r1, r2}, AxesOrigin -> {0, 0}, Filling -> Axis, FillingStyle -> Red];

Pavfuel = Plot[{Tavfuel}, {r, r1, r2}, AxesOrigin -> {0, 0}, PlotStyle -> {Opacity[0.8], Thick, Purple}];

Pgr = Plot[Tgr[r] - Tsurf, {r, r2, r3}, AxesOrigin -> {0, 0}, Filling -> Axis];

Pcore = Plot[T[r1] - Tsurf, {r, 0, r1}, AxesOrigin -> {0, 0}, Filling -> Axis];

Pbuf = Plot[Tbuf[r - (r1 + r2)/2] - Tsurf - (T[r1] - Tsurf - Tavfuel), {r, (r1 + r2)/2 + rk, (r1 + r2)/2 + rbuf}, AxesOrigin -> {0, 0}, Filling -> Axis,

FillingStyle -> Directive[Red, Opacity[0.6]], PlotStyle -> {Opacity[1]}];

Pbufref = Plot[Tbuf[-(r - (r1 + r2)/2)] - Tsurf - (T[r1] - Tsurf - Tavfuel), {r, (r1 + r2)/2 - rbuf, (r1 + r2)/2 - rk}, AxesOrigin -> {0, 0}, Filling ->

Axis, FillingStyle -> Directive[Red, Opacity[0.6]], PlotStyle -> {Opacity[1]}];

51

Pk = Plot[Tk[r - (r1 + r2)/2] - Tsurf - (T[r1] - Tsurf - Tavfuel), {r, (r1 + r2)/2 - rk, (r1 + r2)/2 + rk}, AxesOrigin -> {0, 0}, Filling -> Axis,

FillingStyle -> Directive[Red, Opacity[0.6]], PlotStyle -> {Opacity[1]}];

Pavk = Plot[ Tavk + Tavfuel, {r, (r1 + r2)/2 - rbuf, (r1 + r2)/2 + rbuf}, AxesOrigin -> {0, 0}, PlotStyle -> {Opacity[0.8], Thick, Purple}];

Pcoolant = Plot[Tfluid - Tsurf, {r, 0, r3}, AxesOrigin -> {0, 0}, Filling -> Axis, FillingStyle -> Directive[Opacity[0.1]], FillingStyle -> Green,

PlotStyle -> {Green}];

Show[ Pbuf, Pbufref, Pk, Pavk, Pcore, Pfuel, Pavfuel, Pgr, Pcoolant, PlotRange -> {{0, r3}, {-45, DTfuel*1.1}}, GridLines -> Automatic,

GridLinesStyle -> Opacity[0.3], TicksStyle -> Directive[10]]

52

Appendix C: MCNP6 model code

-*-mcnpgen-*- 300MWth pebble bed FHR, homo major comps w/ regions, control rodscc   -rods are banked at 735 cmc   -16 rods in totalc   -8% enrichment c   -mesh tallies and kcode c c     cell cards1     1 -1.6 -4 9 -10 32 33 34 35 52 53 54      55 56 57 58 59 95 96 97 98 imp:n=1   $ inner reflectorc   2     5 .0822156 -17 9 -7 4 imp:n=1        $ core inlet3     6 .0905432 -1 9 -7 17 imp:n=1     4     2 .0820234 -18 5 -6 4 imp:n=1        $ cylindrical region5     6 .0905432 -2 5 -6 18 imp:n=16     5 .0822156 -19 8 -10 4 imp:n=1       $ core outlet7     6 .0905432 -3 8 -10 19 imp:n=1 8     4 .0821195 -20 6 -8 4 imp:n=1        $ converging region9     6 .0905432 -11 6 -8 20 imp:n=110    4 .0821195 -21 -5 7 4 imp:n=1        $ expanding region11    6 .0905432 -12 -5 7 21 imp:n=1c 12    1 -1.6 -13 -14 15 2 imp:n=1          $ outer reflector13    1 -1.6 -2 11 6 -8 imp:n=114    1 -1.6 -2 3 8 -14 imp:n=115    1 -1.6 -3 10 -14 imp:n=116    1 -1.6 -2 12 -5 7 imp:n=117    1 -1.6 -2 1 -7 15 imp:n=118    1 -1.6 -1 -9 15 imp:n=1c 19    3 .085960 13 -16 -14 15 imp:n=1         $ reactor vesselc 20    3 .085960 22 -32 imp:n=1                $ control rod chnl 1    ss316 pipes21    3 .085960 23 -33 imp:n=1                $ control rod chnl 222    3 .085960 24 -34 imp:n=1                $ control rod chnl 323    3 .085960 25 -35 imp:n=1                $ control rod chnl 424    3 .085960 42 -52 imp:n=1                $ control rod chnl 525    3 .085960 43 -53 imp:n=1                $ control rod chnl 626    3 .085960 44 -54 imp:n=1                $ control rod chnl 727    3 .085960 45 -55 imp:n=1                $ control rod chnl 828    3 .085960 46 -56 imp:n=1                $ control rod chnl 929    3 .085960 47 -57 imp:n=1                $ control rod chnl 1030    3 .085960 48 -58 imp:n=1                $ control rod chnl 1131    3 .085960 49 -59 imp:n=1                $ control rod chnl 12

53

32    3 .085960 91 -95 imp:n=1                $ control rod chnl 1333    3 .085960 92 -96 imp:n=1                $ control rod chnl 1434    3 .085960 93 -97 imp:n=1                $ control rod chnl 1535    3 .085960 94 -98 imp:n=1                $ control rod chnl 16c 36    7 .137222 -71 imp:n=1            $ control rod 1  B4C37    7 .137222 -72 imp:n=1            $ control rod 238    7 .137222 -73 imp:n=1            $ control rod 339    7 .137222 -74 imp:n=1            $ control rod 440    7 .137222 -75 imp:n=1            $ control rod 541    7 .137222 -76 imp:n=1            $ control rod 642    7 .137222 -77 imp:n=1            $ control rod 743    7 .137222 -78 imp:n=1            $ control rod 844    7 .137222 -79 imp:n=1            $ control rod 945    7 .137222 -80 imp:n=1            $ control rod 1046    7 .137222 -81 imp:n=1            $ control rod 1147    7 .137222 -82 imp:n=1            $ control rod 1248    7 .137222 -83 imp:n=1            $ control rod 1349    7 .137222 -84 imp:n=1            $ control rod 1450    7 .137222 -85 imp:n=1            $ control rod 1551    7 .137222 -86 imp:n=1            $ control rod 16c 52    8 .0826 -22 71 imp:n=1   $ flibe around control rod 153    8 .0826 -23 72 imp:n=1   $ flibe around control rod 254    8 .0826 -24 73 imp:n=1   $ flibe around control rod 355    8 .0826 -25 74 imp:n=1   $ flibe around control rod 456    8 .0826 -42 75 imp:n=1   $ flibe around control rod 557    8 .0826 -43 76 imp:n=1   $ flibe around control rod 658    8 .0826 -44 77 imp:n=1   $ flibe around control rod 759    8 .0826 -45 78 imp:n=1   $ flibe around control rod 860    8 .0826 -46 79 imp:n=1   $ flibe around control rod 961    8 .0826 -47 80 imp:n=1   $ flibe around control rod 1062    8 .0826 -48 81 imp:n=1   $ flibe around control rod 1163    8 .0826 -49 82 imp:n=1   $ flibe around control rod 1264    8 .0826 -91 83 imp:n=1   $ flibe around control rod 1365    8 .0826 -92 84 imp:n=1   $ flibe around control rod 1466    8 .0826 -93 85 imp:n=1   $ flibe around control rod 1567    8 .0826 -94 86 imp:n=1   $ flibe around control rod 16c 100   0 16:14:-15 imp:n=0                     $ outside worldc

c     surface cards1 cz 1602 cz 2403 cz 120

54

4 cz 90c5  pz -1506  pz  1507  pz -286.568  pz  2679  pz -436.5610 pz  420c11 TRC 0 0 150 0 0 117 240 12012 TRC 0 0 -150 0 0 -136.56 240 160c13 cz 30014 pz 50015 pz -500c16 cz 360c17 cz 14018 cz 19019 cz 110c 20 TRC 0 0 150 0 0 117 190 11021 TRC 0 0 -150 0 0 -136.56 190 140c 22 RCC 75 0 -430 0 0 850 13.5 $ cylinders to define control rod channel pipes23 RCC -75 0 -430 0 0 850 13.524 RCC 0 75 -430 0 0 850 13.525 RCC 0 -75 -430 0 0 850 13.532 RCC 75 0 -430 0 0 850 1433 RCC -75 0 -430 0 0 850 1434 RCC 0 75 -430 0 0 850 1435 RCC 0 -75 -430 0 0 850 14c 42 RCC 28.7013 69.2910 -430 0 0 850 13.5 $ cyls to define control rod channel pipes43 RCC 53.0330 53.0330 -430 0 0 850 13.544 RCC 69.2910 28.7013 -430 0 0 850 13.545 RCC 69.2910 -28.7013 -430 0 0 850 13.546 RCC 53.0330 -53.0330 -430 0 0 850 13.547 RCC 28.7013 -69.2910 -430 0 0 850 13.548 RCC -28.7013 -69.2910 -430 0 0 850 13.549 RCC -53.0330 -53.0330 -430 0 0 850 13.591 RCC -69.2910 -28.7013 -430 0 0 850 13.592 RCC -69.2910 28.7013 -430 0 0 850 13.593 RCC -53.0330 53.0330 -430 0 0 850 13.594 RCC -28.7013 69.2910 -430 0 0 850 13.5

55

c52 RCC 28.7013 69.2910 -430 0 0 850 14 $ cyls to define control rod channel pipes53 RCC 53.0330 53.0330 -430 0 0 850 1454 RCC 69.2910 28.7013 -430 0 0 850 1455 RCC 69.2910 -28.7013 -430 0 0 850 1456 RCC 53.0330 -53.0330 -430 0 0 850 1457 RCC 28.7013 -69.2910 -430 0 0 850 1458 RCC -28.7013 -69.2910 -430 0 0 850 1459 RCC -53.0330 -53.0330 -430 0 0 850 1495 RCC -69.2910 -28.7013 -430 0 0 850 1496 RCC -69.2910 28.7013 -430 0 0 850 1497 RCC -53.0330 53.0330 -430 0 0 850 1498 RCC -28.7013 69.2910 -430 0 0 850 14c c to adjust control rods edit zorigin and zheight for surf71-86 (3rd and 6th entry)c    3rd entry should be (420-rodinsertionlength)c    6th entry should be (rodinsertionlength) note: max should be <850c  rodinsertionlength=73571 RCC 75 0 -320 0 0 735 12 $ cylinders to define control rods72 RCC -75 0 -320 0 0 735 1273 RCC 0 75 -320 0 0 735 1274 RCC 0 -75 -320 0 0 735 1275 RCC 28.7013 69.2910 -320 0 0 735 1276 RCC 53.0330 53.0330 -320 0 0 735 1277 RCC 69.2910 28.7013 -320 0 0 735 1278 RCC 69.2910 -28.7013 -320 0 0 735 1279 RCC 53.0330 -53.0330 -320 0 0 735 1280 RCC 28.7013 -69.2910 -320 0 0 735 1281 RCC -28.7013 -69.2910 -320 0 0 735 1282 RCC -53.0330 -53.0330 -320 0 0 735 1283 RCC -69.2910 -28.7013 -320 0 0 735 1284 RCC -69.2910 28.7013 -320 0 0 735 1285 RCC -53.0330 53.0330 -320 0 0 735 1286 RCC -28.7013 69.2910 -320 0 0 735 12

c     data cardsmode n $ transport neutrons onlycc materialscm1      6000.73c -1 $ C-12 graphite matrix rho=1.6 g/cm3mt1 grph.16t $ Graphite s(a,b) card for 1000K (~726.85C)c m2              3007.73c  0.0094399973981320        4009.73c  0.0047199986990660

56

       6000.73c  0.0482177945554625   8016.73c  0.0000813735127055

       9019.73c  0.0188799947962639   14028.73c 0.0004811693198563    14029.73c 0.0000243636639242    14030.73c 0.0000161728818340

       92235.73c 0.0000131529841555       92238.73c 0.0001493467341014  $ 0.6/0.4 void frac. tad=.08202336c m3       14028.73c   0.001567910       14029.73c   0.000079390       14030.73c   0.000052700       24050.73c   0.000677386       24052.73c   0.013062705       24053.73c   0.001481206       24054.73c   0.000368704       25055.73c   0.00174       26054.73c   0.003244520       26056.73c   0.051308168       26057.73c   0.001230680       26058.73c   0.000156632       28058.73c   0.006637508       28060.73c   0.002556743       28061.73c   0.000111150       28062.73c   0.000354315       28064.73c   0.000090285       42092.73c   0.000184016       42094.73c   0.000114700       42095.73c   0.000197408       42096.73c   0.000206832       42097.73c   0.000118420       42098.73c   0.000299212       42100.73c   0.000119412      $ lanlss316 rho=7.92 tad=.085960002cm4              3007.73c  0.0117999967476650        4009.73c  0.0058999983738325        6000.73c  0.0401814954628854

   8016.73c  0.0000678112605879        9019.73c  0.0235999934953299

   14028.73c 0.0004009744332135    14029.73c 0.0000203030532702    14030.73c 0.0000134774015284

       92235.73c 0.0000109608201295       92238.73c 0.0001244556117511 $ 0.5/0.5 void frac. tad=.08211946

57

cm5              3007.73c  0.0141599960971979        4009.73c  0.0070799980485990        6000.73c  0.0321451963703083

   8016.73c  0.0000542490084704        9019.73c  0.0283199921943959

   14028.73c 0.0003207795465708    14029.73c 0.0000162424426161    14030.73c 0.0000107819212227

       92235.73c 0.0000087686561036       92238.73c 0.0000995644894009 $ 0.4/0.6 void frac. tad=.08221557c m6              3007.73c  0.0112430369011752        4009.73c  0.0056215184505876        6000.73c  0.0511925403182162       9019.73c  0.0224860738023503 $ Copper pebble region tad=.090543169c m7       5010.73c  0.021861641914759        5011.73c  0.087995855144331        6000.73c  0.027464374264772 $ Boron Carbide tad=.13732187c m8       3007.73c  0.0235999934953299        4009.73c  0.0117999967476650       9019.73c  0.0471999869906598 $ Flibe tad=0.082599977 (100% Li-7)c c c talliesc c MCNP doesn't know the source strength or normalization, it provides tally resultsc in terms of per source particle, we must supply the source strength c (e.g. neutrons/sec)c      We know this approximately from the power level and basic fission physics:c For a power level of 300 MW:c source strength=c 300e6watt*2.4neut/fiss*1fiss/180.88MeV*1MeV/1.602e-13 wattsec=2.48e19 neut/secc c   We may need to iterate on some of these numbers using MCNP for consistencyc          (e.g. neutrons emitted/fission and MeV/fission)c c       from keff box e.g. final estimated combined...keffc            average number of neutrons produced per fission = 2.436c       use an f7 tally to get MeV/fission

58

c c fc4 neutron flux (active fuel region)f4:n 2 10 4 8 6 $ neutron flux  e4 0.625e-6 0.1 20 $ bin flux into 3 energies (thermal,intermediate,fast)fm4 2.48e19 $ norm (neut/sec)fq4 f e $ change tally printout cell/surf down, ebins across topc c mesh tally flux (cylindrical mesh i=r,j=z,k=theta in revolutions)fmesh104:n geom=cyl origin=0,0,-439 axs=0,0,1 vec=1,0,0         imesh=240.0 iints=30         jmesh=859.0 jints=30         kmesh=1.0 kints=1c mesh tally multiplierfm104 2.48e19 $ norm (neut/sec)c  c print tables of useful informationprint 40 98 $ mcard compositions, constants including fissionQ values by isotopec c     Criticality Control Cardskcode 20000 1.0 75 250ksrc             125 0 0 -125 0 0 0 125 0 0 -125 0        125 0 100 -125 0 100 0 125 100 0 -125 100        125 0 -100 -125 0 -100 0 125 -100 0 -125 -100         125 0 200 -125 0 200 0 125 200 0 -125 200        125 0 -200 -125 0 -200 0 125 -200 0 -125 -200        125 0 400 -125 0 400 0 125 400 0 -125 400        125 0 -400 -125 0 -400 0 125 -400 0 -125 -400 $ initial source locations   

59

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