INVESTIGATION AND DESIGN OF A SECURE,
TRANSPORTABLE FLUORIDE-SALT-COOLED
HIGH-TEMPERATURE REACTOR (TFHR) FOR ISOLATED
LOCATIONS
By
MASSACHUSETGS NSWTMfUTE
OF TECHNOLOGY
OCTE
2014
By
Ruaridh R. Macdonald
B.S., Nuclear Science and Engineering (2012)
LIBRARIES
Massachusetts Institute of Technology
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SEPTEMBER 2014
@ 2014 Massachusetts Institute of Technology
All rights reserved
Signature redacted
Signature of Author:
Ruaridh R. Macdonald
Deparment of Nuclear Science and Engineering
Signature redacted
21, August 2014
Certified by:
Dr. Charles Forsberg
Senior Research Scientist
Certified by:
Signature redacted
Thesis Supervisor
Dr. Michael Driscoll
Professor Emeritus of Nuclear Science and Engineering
Accepted by:
Signature redacted
Thesis Reader
Dr. Mujid Kazimi
TEPCO Professor of Nuclear Engineering
Chair, Department Committee on Graduate Students
1
INVESTIGATION AND DESIGN OF A SECURE,
TRANSPORTABLE FLUORIDE-SALT-COOLED
HIGH-TEMPERATURE REACTOR (TFHR) FOR ISOLATED
LOCATIONS
By
Ruaridh R. Macdonald
Submitted to the Department of Nuclear Science and Engineering
on August 26, 2014 in Partial Fulfillment of the Requirements
for the Degree of Master of Science in Nuclear Science and Engineering
ABSTRACT
In this work we describe a preliminary design for a transportable fluoride salt cooled high temperature
reactor (TFHR) intended for use as a variable output heat and electricity source for off-grid locations. The
goals of the project were to design an economic reactor:
a) Sized for the average load of a site but able to increase output to provide peaking power
b) With safety, security and safeguard requirements met by the choice of materials and form as opposed
to relying on security forces and infrastructure.
Powering remote sites such as mining stations, military bases, communities or even large ships could be
a significant long term market for small nuclear reactors. However, the design basis is very different. The
increased cost of transporting goods to the site and maintaining a large population of specialists means a
reactor must be simpler to operate and able to defend itself against attackers and proliferators without a
large security force. On the other hand, the increased cost of electricity in remote places means more can
be spent to meet these goals. This report discusses these issues of operating at a remote site and a general
strategy for meeting the resulting design criteria. The TFHR design puts these decisions into practice.
The TFHR described is a 125MWth, thermal spectrum reactor using SiC-matrix coated particle fuel which
can achieve single batch discharge burnups of up to 70MWd/HMkg over an 8 year cycle. Higher burnups
are possible for larger cores. The neutronics properties of SiC-matrix coated particle fuel are explored in
detail and various means by which they can be incorporated into a reactor are detailed. The TFHR uses
a nuclear air Brayton combined cycle (NACC) for electricity generation, adapted from an off the shelf GE
aero-derivative gas turbine. The NACC incorporates a combustible fuel injection port between the high and
low pressure turbines which can be used to raise the temperature of the working fluid and boost the power
extracted from the system by up to 50%. This increase of electric output occurs without changing the power
drawn drawn from the reactor, avoiding any transients. The ability to peak the power output removes the
need for a second power system or for the reactor to be sized for the maximum power demand, which is a
significant cost saving. However, using an air Brayton cycle requires a high temperature reactor. A TFHR
is a better match for this purpose than a gas cooled reactor as it operates at atmospheric pressure, making
it easier to meet the security goals described above.
Thesis Supervisor: Dr. Charles Forsberg
Title: Senior Research Scientist
2
Acknowledgments
I would like to thank my family and friends who have supported me during these past two years.
It's been a great learning experience and one I hope to build on moving forward.
I would like to thank all the faculty and staff who gave me advice or help, especially those in
the FHR group. In particular thank you Professor Driscoll for reading through my un-spellchecked
drafts and providing incisive feedback.
Thank you Dr.
Forsberg for being my advisor through
the project. I've greatly enjoyed our discussions and appreciate having learnt how to more open
mindedly identify and solve problems.
3
Contents
7
Project Motivation and Introduction
1.1
Small Modular Reactors .......
1.2
Scaling SMR Costs With Output
1.3
Organization of the Thesis Report
7
.................................
8
. . . . . . . . . . . . . . . . . . . . . . . . . .
10
.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
.
1
2 TFHR Design Basis
11
2.2
Minimal Infrastructure and Capital Equipment
. . . . . . . . . . . . . . . . . . .
13
2.3
The High Cost of Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.4
Summary of System Requirements
15
.
.
.
Small Expert Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
. . . . . . . . . . . . . . . . . . . . . . . . . .
16
3.1
Providing Peaking Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
3.2
Fluoride-Salt-Cooled High-Temperature Reactor Overview . . . . . . . . . . . . .
19
3.3
Design Goals of Inert-Matrix Coated Particle Fuel
. . . . . . . . . . . . . . . . .
20
3.4
Fuel C ycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
.
.
.
.
Meeting the System Requirements
TFHR Fuel
4.3
23
4.1.1
Experimental Envelope.....
. . . . . . . .
25
Matrix Material . . . . . . . . . . . .
. . . . . . . .
26
4.2.1
Silicon Carbide . . . . . . . .
. . . . . . . .
27
4.2.2
Tungsten Carbide . . . . . . .
. . . . . . . . 29
4.2.3
Zirconium Compounds.....
. . . . . . . . 30
. . . . . . .
. . . . . . . . 31
.
.
. . . . . . . .
.
4.2
Coated Particle Fuel . . . . . . . . .
.
4.1
23
Explosion Performance
.
4
2.1
4.3.1
Modeling Fuel Failure.....
. . . . . . . . 32
4.3.2
Modeling Matrix Failure
. . . . . . . . 33
4.3.3
Modeling TRISO SiC Fracture
.
.
3
11
. . . . . . . . 34
4
5
6
Core Design
38
5.1
Remaining TFHR Design Space ..............................
38
5.2
Methods ..........
38
5.3
Unit Cell Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.4
Thermal Reactor Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
5.4.1
TFHR Geometry and Materials . . . . . . . . . . . . . . . . . . . . . . . . . .
44
5.4.2
Neutronics Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
5.4.3
Core Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4.4
Reactivity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
6.1
Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
6.2
Storage Technology Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
6.2.1
Pool storage
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
6.2.2
In-Core Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
6.2.3
Shallow borehole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
6.2.4
Transport away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
Recommendations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Future Work
7.1
8
51
Spent Nuclear Fuel Storage
6.3
7
...........................................
G eneral
61
62
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
7.1.1
Economics of Remote Sites
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2
Modeling Material Failure
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.1.3
TRISO Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
62
7.2
Thermal TFHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3
Alternate Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
7.3.1
Non-Traditional Matrix Materials
. . . . . . . . . . . . . . . . . . . . . . . .
64
7.3.2
Alternative Coolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
Conclusions
65
References
67
5
A Full Core Results
A. 1
71
Increasing Core Moderation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
A.1.1
M oderator Block Size
A.1.2
Thickness or Axial and Radial Moderating Reflector
. . . . . . . . . . . . . .
76
A.1.3
Identifying Suitable Moderator Materials . . . . . . . . . . . . . . . . . . . . .
76.
A.1.4
Pin Diameter and Pitch to Diameter Ratio
. . . . . . . . . . . . . . . . . . .
81
A.1.5
Cycle Length and EOL Burnup Optimization . . . . . . . . . . . . . . . . . .
84
..............................
B Mean Chord Through Cylinder Calculation
6
. 71
91
1
Project Motivation and Introduction
1.1
Small Modular Reactors
In the face of continued concern over the safety and economics of large nuclear reactors in developed
countries, the nuclear industry will have to look for new users, applications and technologies in
order to maintain and improve its share of the electricity generation market as the generation of
reactors built before the 1980's are decommissioned over the next 30 years. Small modular reactors
(SMRs), reactors with power outputs less than 300MWe per unit, are an increasingly promising
complement to traditional reactors as they increase the variety of projects available to utilities
and operators. Hitachi[1], Westinghouse[2], Babcock & Wilcox[3], NuScale[4 and others are in the
process of developing SMRs[5], the latter two with the support of US Department of Energy (DOE)
funding. Two main use cases are commonly envisioned:
1. Multiple reactors (12+ in some cases) can be built at a single site so that at a grid level the
plant operates like a traditional reactor. Uniquely however, the plant could be constructed
in stages and operate almost continuously by staggering the refueling of the individual units.
These clusters of reactors would mostly be useful in developed countries where there is the
capital and grid infrastructure to support large projects.
2. Single or very small groups of reactors could be built to meet the needs of developing nations
and niche energy consumers in remote, high cost environments where there is little or no
grid connection. SMRs could provide a source of stable, relatively cheap electricity and the
capacity could be grown organically as demand and the necessary infrastructure developed.
It is still unclear as of July, 2014, how the decreased cost of manufacturing many small, factory
assembled SMR components will ultimately compare with the increased marginal cost ($/MWe) of
building and operating a small reactor but it is expected that an SMR will cost tens or low hundreds
of millions of dollars as compared to a few billion dollars for a typical large reactor. The overall
cost and build time of the SMR may be reduced by enough to make investment in an SMR viable
for new, smaller investors and mean that the failure of a project does not bankrupt the companies
involved.
7
Off-grid and new-grid applications could be a significant second market for SMRs, particularly
in the long term. Clusters of SMRs (option 1 above) may do well in the short to medium term but
if they are successful at increasing the use of nuclear power and existing utilities and operators grow
larger instead of new ones entering the market, utilities may eventually have the capital necessary to
mitigate the risk of building large reactors. At this point, it will make most sense for them to switch
to the lower marginal cost, larger reactors. This is not a necessary outcome of building clusters of
SMRs as part of developed power grids but it is a possibility. On the other hand, it is likely that
there will always be a need for the second SMR use case, especially if the reactors can be designed
to provide a variable total power solution, i.e. variable amounts of both heat and electricity. It may
never make economic sense to connect all remote population centers and industrial or military users
to the central power grid, even though they require significant amounts of power. This makes arctic
bases, mining stations, mid-sized islands, military bases and large civilian ships potential users of
off-grid SMRs. Large countries like China and Brazil have growing cities which are a long distance
from the central grid and it may remain impractical to have a unified power infrastructure for a
long time [6-8]. SMRs could provide a solution to some or all of these challenges.
1.2
Scaling SMR Costs With Output
For SMRs to be successful as a power source for a diverse range of remote users, they must be a
flexible power source, able to scale to the needs of the user and be affordable. To do this, costs
must scale as linearly as possible with reactor output and the reactor size and power output must
be minimized for a given set of community requirements. Sizing a reactor for peak electricity and
heat demand raises capital costs and lowers plant utilization. Instead, the reactor and power cycle
should be designed to provide a variable output and the reactor sized close to the average demand.
Large fixed costs which do not scale with reactor power rating are a principal barrier to a
successful remote SMR design. Safety, security and safeguards are important examples of expenses
which do not currently scale with the reactor output [9].
This makes single SMRs at isolated
sites expensive. Current regulations result in similar levels of security personnel and infrastructure
for a large 1.5GWe plant as for a small plant. While physical security infrastructure is likely to
scale closely with the size of a reactor site, the number of security personal will not as current
regulation requires does not change the size of the minimum force it must be possible to repel. This
8
is qualitatively described in Equation 1.
Cost of security ($) = I.A.O + P(1 + c.A.0).W
Where I
(1)
cost of infrastructure per km^2 ($/km^2); A = km^2/MWth; 0 = power output of site
(MWth); P = number of security personnel required to resist design basis attack; W = wages per
security personnel ($) and c is a small constant to account for the increase difficulty of defending a
large site.
Very little is published about security costs, however Sandia estimates that a trained security
employee is paid $175k/year [101 and NEI reports 9000 guards are employed between the 62 US
nuclear power plant sites [11], suggesting up to $25M is spent per site on personnel alone. NEI also
found that an average of $35M in capital costs and over $0.59M in operating costs was spent per
site to meet the post 9/11 physical protection upgrades mandated by 10 CFR 73.55 [12]. These
are large sums of money and will hurt the profitability and economic viability of an SMR unless a
change in design means the costs scale with power output.
This project will explore whether it is possible to design a reactor with a higher level of integral
security in order to lessen the need for traditional guns, gates and guards defenses. The project
aims to leverage some of the unique design possibilities of SMRs and Fluoride-Salt-Cooled HighTemperature Reactors (FHRs) to create a transportable FHR (TFHR) to meet these goals. This is
part of the wider integrated research project (IRP) between MIT, UC Berkeley, the University of
Wisconsin Madison and the national laboratories [13] to develop FHR technology.
9
1.3
Organization of the Thesis Report
This document is organized as follows, listed by section number. The author has attempted as much
as possible to only include results in the main body of the thesis in order to make it a shorter read,
especially in sections 4 and 5. The process to find these results is detailed in the appendices.
2. TFHR Design Basis - A discussion of the remote site operating environment and the capabilities necessary for a remote SMR to be successful.
3. Meeting System Requirements - Which systems are required to meet the deliverables set out
in the design basis.
4. TFHR Fuel - An explanation of inert matrix coated particle fuels and a search for matrix
materials which meet the TFHR requirements.
5. Core Design - Overview of the TFHR design and performance.
6. Spent Nuclear Fuel Storage - A discussion of strategies for dealing with spent fuel at remote
sites.
7. Future Work
8. Conclusions
Appendices:
A - Full core design results
B - Geometry optimization and chord length method
10
2
TFHR Design Basis
The TFHR design is driven from the top-down by two objectives:
1. Produce an SMR for small remote markets which can meet all variable energy and heat needs
during normal operations while minimizing the reactor peak output.
2. Design safety, security, and safeguards (S3) into the system so that the associated capital
and operating costs scale with the power rating and do not dominate the price of a small
isolated reactor.
That implies safety systems which minimize maintenance and operations
challenges, security features such that even reactor destruction will not result in major offsite consequences and fuel designs which make the fuel intrinsically unattractive for fissile
materials recovery or dispersal as a dirty bomb (radiation weapon).
This project intended to meet these objectives through the design of the core and power plant as
opposed to using typical 'bolt-on' additions to the reactor design.
Reducing the risk of nuclear
material proliferation through fuel material selection as opposed to employing a large security force
is an example of an S3 solutions which is less personnel and capital intensive and helps make S3 a
marginal as opposed to fixed capital and operating cost.
Remote locations are a unique operating environment for power generation. They are characterized by their isolation and the consequences of it: small expert populations, minimal infrastructure
/
capital equipment and slow and expensive transport to and from the site, to name a few. The
effects and interplay between these features means that some of the basic design assumptions for
nuclear power plants must be revisited and gives the TFHR a unique design basis. The causes of
these changes to the design basis are discussed here and potential solutions in the following chapter.
2.1
Small Expert Population
Remote sites are hundreds or thousands of miles away from large cities or ports and may not have
any large roads or transport infrastructure connecting them to the outside word. This is especially
true for small islands and thus it is expensive and slow for people and supplies to travel to and from
the remote site. This remoteness and the small population of such sites also means they are less likely
to cost-effectively support a large population of experts, whether it is an island nation or a mining
11
site. The cost of having a full team of reactor operators, maintenance staff and security personnel
would be overwhelming for a large dispersed network of SMRs; not to mention the difficulty of
finding and training enough experts. It is hence preferable for a remote nuclear reactor to be able
to operate with a small staff, particularly advanced technical and security staff, during both normal
operations and during an accident or attack. Assistance may take a day or more to arrive so the
reactor must be designed to either have many passive
/
personnel unintensive safety and security
features or it must be robust enough to suffer damage without radiation release to the environment
for a few days. It is also important that information about an attack or accident can promptly and
reliably reach outside helpers, but this was not a focus of this project and will not be discussed.
A reduction in security staff may also make a remote SMR a target for forceful fuel theft. Large
nuclear reactors are 'hard' targets as they have security forces sufficient to repulse most attacks or
attempts at direct theft. An SMR with a small staff in a remote environment cannot be assumed
to be able to do the same, so when thinking about how to manage the risk of attack it must be
assumed that an attacker will ultimately gain free access to the SMR. The priority then becomes
to design the reactor such that causing damage or theft of fissile material for use in a radiological
weapon, even with access to the SMR, entails very significant technical difficulty or requires a long
time. This should dissuade most groups and give friendly security forces time to find the material
and recover it. The level of difficulty should be beyond any non-state actor and sufficiently difficult
that a non-weapon-state actor would prefer an alternative route to obtain fissile materials. This will
mostly be achieved through the design and choice of fuel materials so that the solution will scale
with the application and presumably be impossible to circumvent. Note that preparing the core to
resist physical attack directly is a significant change to the typical design basis of a nuclear reactor.
There is also a risk of fissile material being discretely diverted or overtly stolen from a reactor
during refueling and this risk must be mitigated. While there is a relatively small amount of fuel in
an SMR, verifying that each assembly contains the material it is meant to is a time and manpower
intensive process. The simplest solution is to have a mobile centralized group be responsible for
fueling and unfueling the reactor so that there will be a full complement of technical and security
personnel present to check and protect each assembly while they are outside the core. This introduces a rate limiting step as the number of these teams determines the reloading schedule of a given
fleet of SMRs and imposes a large relative fixed cost on the first few reactors (as a few reactors
12
support the entire central team). These issues could be mitigated if the cycle time of the reactors
was long enough that the team could be 'rented' from another country or the reactor vendor and
refueling staggered sufficiently for one team to refuel an entire fleet. A long cycle time will also improve the economics of a reactor in an area with significant fuel transportation costs. Having some
on-site fuel storage capacity will be necessary to allow spent nuclear fuel (SNF) to cool and would
also allow a central team to go directly between SMRs for refueling without having to transport
SNF back to a central facility until a sufficient inventory has built up to justify such an operation.
2.2
Minimal Infrastructure and Capital Equipment
The high cost of transport to an isolated site and sustaining an expert population makes capital
equipment and infrastructure very expensive to construct, maintain and operate. In principle, major
cost savings can be found by reducing the amount of power generation equipment required at remote
sites. Reducing the number of redundant systems too much risks reducing the reliability of a system
below acceptable levels so there is an optimization to be done for each case.Two key ways to reduce
redundant equipment are to produce both heat and electricity from the same source and to safely
handle peaking demand using a single power train.
A total power solution (i.e. both heat and
electricity) reduces the need for separate water boilers and could also allow for high temperature
air or steam to be used in industrial processes, a synergy which provides a further cost saving. A
nuclear system which can change its power output quickly in response to changes in power demand
would reduce the need for a secondary peaking power cycle, such as an oil or diesel generator.
However, it is unclear how a typical nuclear power plant would continue to provide power during
refueling or maintenance. Also, if this system only uses nuclear power, the reactor must be sized
for the peak demand of the site.
Energy storage technologies may be an easy way to reduce these problem by allowing for power
produced during periods of low demand to be used during periods of high demand, though the
economics of doing so will depend on the site geography and geology, especially if the storage must
provide power for an entire refueling period. However, given how low the cost can be under the right
circumstances, it will be beneficial to make sure the TFHR is able to interface with energy storage
technologies. It would be preferable to find a way to avoid these issues and to size the reactor for
the average power demand while still minimizing the number of components.
13
2.3
The High Cost of Alternatives
When designing a full sized reactor for grid power, competing energy technologies create a pressure
to reduce the levelized cost of electricity as much as possible. These pressures are less for a remote
SMR. For example, cheap natural gas in the USA has made almost all other grid-scale power
production uneconomic (in the short term at least) and squeezed the profits of nuclear plants which
already exist. Designing more of the S3 features into the reactor will raise the marginal cost of the
core which is untenable for a grid reactor facing significant competition. It may be acceptable for
an SMR in a remote location as the high cost of transport to site makes any power source which
requires regular fueling, such as diesel or oil generators, more expensive. This gives remote SMRs
more financial room to play in when designing for their uniquely challenging design environment.
A simple attempt to quantify how much more expensive a remote SMR could be follows. It is
difficult to directly calculate the effects of remoteness on the levelized cost of energy (LCOE) while
also accounting for the differences in lifestyle, climate and power use. As a first pass, the LCOE and
cost of gasoline were compared between the fifty US states, accounting for the differences in taxes.
Hawaii, the most remote state without oil resources, pays a relatively similar amount for gasoline
(though it is a few percent higher as a fraction of income) but three times more for it's electricity
[14]. The price of gasoline is kept down by local refining plants and nearby military bases but 93%
of all energy is imported. Overall, the EIA reports Hawaii as having the highest price of energy [151.
Alaska, a similarly remote state, has energy prices which are much closer to the US average, between
25%-50% greater. However, rural Alaskans rely almost entirely on diesel generators which raises their
energy costs 500% above the Alaska average (i.e. 600% the US average)[16]. This scenario is what
the TFHR is being designed for and suggests a price of around $1/kWhe. International literature on
rural electrification offers more comparisons: rural South African communities pay $1.07/kWhe for
electricity from diesel generators (20 year life, 7.5kW total) compared to $0.05/kWhe from the grid
[17]. The LCOE of grid-scale nuclear reactors is often estimated as being $0.07/kWhe [18] so even
accounting for the difference between consumer and wholesale prices of electricity (for example, the
New York Independent System Operator, which governs electricity sales in New York State, quoted
wholesale electricity at $0.016/kWhe in early August 2014 v.s.
an average NY industrial power
price of $0.055/kWhe) there is substantial room for remote nuclear reactors to have a higher LCOE
14
and still be profitable.
2.4
Summary of System Requirements
To move forward, it is important to summarize the considerations above into a list of requirements
which will broadly meet the needs of a remote SMR.
The reactor must:
e Operate with a reduced staff of technical and security experts to reduce the burden and cost
on the remote community.
9 Use fuel which is difficult to extract fissile material from, either because it is difficult to
handle, reprocess or has a distinct and easily detectable signature. This will dissuade wouldbe attackers and proliferators.
e Be toughened to reduce the radiation release from a physical attack if it does happen, given
that there will be relatively few security staff.
* Have a long cycle time to reduce refueling frequency. This will improve fuel cycle economics
and potentially allow for centralized refueling.
e Provide variable amounts of electricity and heat from a single power cycle. Optimize the
number of redundant systems by trading-off between the complexity and the reliability of the
system.
e Have a power output close to the mean power demand rather than the peak demand to
minimize the costs for a given set of community requirements.
e Be able to couple to energy storage technologies.
15
3
Meeting the System Requirements
This section outlines how each system requirement was met. To meet the TFHR design objectives
efficiently, the system requirements were prioritized from power generation back to the fuel choice
and technologies which could meet multiple requirements simultaneously were looked for. This order
was chosen because there are the fewest options for meeting the variable power output requirements
and hence it is the most restrictive and dictates the type of reactor that must be used.
3.1
Providing Peaking Power
As discussed in section 2.2, a nuclear power system able to respond to peaks in power demand will
reduce the number of power systems at a site and increase component utilization. Modern nuclear
power plants are capable of altering their power output rapidly, by as much as 5% per minute[191.
However, sizing the reactor to the peak power demand is not a good way to achieve the TFHR
objectives. The cost, accident source term, safety system size and other parameters of a reactor are
tightly coupled to its maximum power output. It would be preferable to size the reactor near to the
mean power demand and find non-reactor methods to respond to increases in power demand. Energy
storage, particularly heat storage in nearby bedrock, is a possible solution as the reactor could be
sized below peak power and the technology is relatively cheap.
Alternatively, co-firing methods
using mostly off the shelf components are also promising as they allow for sustained peaking power
without requiring previous periods of low demand.
The economics of potential solutions will be
heavily dependent on the transport costs to the site and the local geography (i.e. permeable v.s.
impermeable rock nearby at useful depths), making abstract comparison difficult.
However, the
ability of co-firing methods to increase power output without requiring demand to have been low
beforehand makes it the more flexible technology and the primary focus of this project.
One promising co-firing technology for use in the TFHR is an air-Brayton power cycle with a
fuel-injection reheat stage. This concept, when used with a nuclear reactor, is commonly called
a Nuclear Air-Brayton Combined Cycle (NACC)[20].
By injecting and combusting a fuel such as
jet fuel in the working fluid between the high and low pressure turbines the power output of the
system can be increased without changing the power output or temperature of the core, avoiding
core power transients.
16
Figure 1 shows a general NACC system schematic. Air is compressed, heated using nuclear
heat with salt-to-air heat exchangers, expands through a high pressure turbine, is reheated and has
fuel injected into it, expands through a second turbine and is exhausted to a heat recovery steam
generator. It is important that the compressed air is hot enough to auto-combust the fuel when
coming out of the reheater. The exhausted air can be used for heating or process heat. In the
current design, the maximum power output is 150% of the reactor output and the injected fuel is
jet fuel. Details of this design can be found in recent project reports [201.
Process
Heat
Frtered
! Compre
sr
TurbkKn5
Pwer
Gas
cm-ftring
nt
vete
Satt-to-air
Figure 1: NACC system overview including steam bottoming cycle. Modified from [20]
The NACC is being developed as part of a joint MIT, University of California Berkeley and
University of Wisconsin FHR project. In that design, the full sized FHR utilizes graphite-matrix
coated particle fuel and liquid fluoride salt coolant.
600 0 C and 700 0 C, respectively.
The core inlet and outlet temperatures are
The NACC is based on the GE F7B gas turbine, the largest
rail-transportable gas turbine currently available from GE. The TFHR would use a smaller aeroderivative air turbine. Because the exhausted air does not need to be cooled, open aero-derivative
turbines use up to 60% less water per MWth than an LWR which is useful at a remote site with
17
limited water supplies.
For an air-Brayton to operate efficiently, it requires a hot-side temperature of at least 7000C.
For a nuclear system, this typically means that only high temperature gas reactors such as an FHR
or Very High Temperature Reactor (VHTR) are appropriate. However, the high pressure and low
power density of a VHTR do not make them suitable as remote-site power sources because it is
difficult to make the design integrally secure. A high operating pressure also implies a heavy pressure
vessel that may present major logistical challenges. An FHR, on the other hand, can provide the
same high temperature working fluid at a low pressure with a higher power density and thinner,
lighter heat exchangers, pressure vessel and other components. In either case, a high temperature
reactor will require a high temperature fuel.
The NACC system is more economic than having a separate air-Brayton cycle for rapid peaking
because it does not have an idling turbine. In most natural gas systems, idling the turbine still
requires 20-40% fuel consumption to allow for fast power changes[21].
While operation of two
separate systems may be simple, the construction, maintenance and fueling of a NACC will be
cheaper. A NACC can also function when the nuclear reactor is down for maintenance or refueling.
The jet fuel injection is throttled up as much as possible to maintain the maximum load possible.
This should be a simple means of sustaining the power supply during an outage, though a custom
ignition will need to be added in case the low pressure temperature ever drops below the autoignition temperature.
The NACC may include a Rankine bottoming cycle [201 depending on the demand and economics
of a given site. A bottoming cycle would draw heat from the exhausted air (shown in Figurel) to
produce steam to drive a turbine, as heating or as industrial process heat. A remote site may have
limited supplies of water so it may not always be prudent to run a bottoming cycle. However it will
increase the thermal efficiency of a the overall system and may allow the NACC to output more
power during an outage.
One question raised by the NACC is whether a remote site will always have a supply of jet fuel or
diesel to use. All current remote sites must have access to a supply of fuel, otherwise they would not
currently exist, so this is not a concern for them. However, the cost of such fuel is often extremely
high. Economics and risk analysis will determine the cost/benefit of using a slightly larger TFHR
versus occasionally being without NACC capability.
18
A supplemental option for the NACC system which may solve this fuel problem is to use hydrogen that is created on site as the injectable fuel.
During periods of low electricity demand,
hydrogen could be created by electrolysis and stored for use during peak periods. Storing hydrogen
securely may be challenging and the best solution in each case will depend on the particulars of a
site, especially the local infrastructure. Three possible storage methods are: bags, gas tanks and
pressurized cylinders.
1. Pressurized Cylinders - a very dense means of storage may be useful for space limited sites or
those with sea access where boats are able to deliver the cylinders. Gas cylinders are heavy
so there may be logistical difficulties bringing in many cylinders. Hydrogen can only be safely
stored outside which may make them a vulnerability to attack.
2. Gas Tanks - tanks, typically tens of meters in diameter and 20+ meters high, with free
moving, sealed lids were used in many cities to store fuel gases. This is a very easy technology
to maintain and any leaking gas safely escapes to the atmosphere but the equipment requires
significant space as the gas is kept only slightly above atmospheric pressure. This would be
suitable at a site where a construction is relatively easy but otherwise may be impractical.
3. Gas Bags - while easily the cheapest of three options presented here, gas bags are the most
modern solution as they require flexible hydrogen-impermeable plastics. In the developing
world, natural gas is often stored in large bags on top of buses or structures as a secondary
fuel supply. They have a good safety record as any escaping gas quickly rises and disperses.
The same could be true of hydrogen at a remote nuclear site but there is a question of whether
it might be a security risk to leave exposed. This would be a good option for sites where this
is considered an acceptable risk or supplies may only arrive by air and so only the lightweight
bags can be delivered.
3.2
Fluoride-Salt-Cooled High-Temperature Reactor Overview
Using the NACC solves many of the power demand problems of a remote community, both during
peak demand and when the reactor is undergoing maintenance. However, it also dictates that we use
a high temperature reactor such as a VHTR or FHR. This project does not make a full comparison
of the two reactors but it was thought that the higher power density and low operating pressure
19
of an FHR made it the better choice. Below is a general description of FHR technology and what
options it has for toughening and protecting the core.
The FHR is a promising technology which brings together existing concepts in a novel way
to solve many of the problems of the Molten Salt Reactor (MSR) and nuclear reactors generally.
It's key selling point is that an FHR can provide high temperatures (>700*C) while operating at
atmospheric pressure by using a high boiling point molten salt coolant. The current leading coolant
choices are F-Li-Be and F-Na-Zr salts (a.k.a FLiBe and NaFZrF). Unlike an MSR, the fuel is solid
rather than being dissolved in the salt coolant.
This makes chemistry control much simpler as
there are many times fewer radionuclide partial pressures to control. These fluoride salts have good
thermal performance but are corrosive to many materials which limits structural and fuel materials
choices. Most existing designs have taken their fuel design from the VHTR reactor: using either
pebble bed or prismatic tristructural isotopic (TRISO) fuel in an inert matrix. TRISO technology
will be described in more detail in the next section but is generally taken to be the best understood
high temperature nuclear fuel.
Further practical benefits of the FHR are that the salt is transparent when kept pure, allowing for
visual maintenance of many systems - something which is not possible with many high temperature
coolants such as liquid metals. Also, the low operating pressure and high specific heat of the coolant
allows for very small heat exchangers. Taken together with a thinner pressure vessel, the capital cost
of an FHR may be 30% less than that of an equivalent light water reactor (LWR). A containment
structure is still necessary, as it will be for the TFHR, as a barrier against radionuclide release and
to protect from threats such as an airplane or missile strike.
However the low internal pressure
means that the containment can also be thinner as a reactor pressure vessel rupture will not create
a large shock wave. It may be possible for the TFHR to simply be buried with a thick top cover to
protect it from airplane strikes.
3.3
Design Goals of Inert-Matrix Coated Particle Fuel
As has been discussed, the design of the TFHR is focused around suitability for remote environments;
this must start with the fuel. Coated particle fuel is a more general term for TRISO and other similar
fuels and the two terms will be used interchangeably here. Any attempt to damage the core, steal
fissile material or disrupt the operation of the reactor must ultimately involve the fuel. Designing
20
safety and security barriers into the fuel means that despite having fewer security staff and less
S3 infrastructure (a.k.a guns,gates and guards) the TFHR will have some protection and would-be
attackers will be deterred.
To this end, the fuel must provide the following design goals, in this order of importance:
" Proliferation Resistance:
- A chemically inert matrix will be be difficult to reprocess and remove fissile material
from. If the extraction process is either slow, requires expensive or scarce reagents or
has many steps it is likely that the level of difficulty will dissuade most proliferators.
Either the process will be very slow or the necessary chemical facility should also be
easily detectable.
- It will be difficult to quantify exactly how much a given matrix material will be a deterrent because a lot will depend on the exact details of the situation. However, we only
need the TFHR to be less of a proliferation risk than alternatives, accounting both for
technical difficulty and the chance of detection (which is a function of the time a process
takes). As centrifuge enrichment has become technically feasible for more nations, this
is (unfortunately) becoming easier.
- Preferably, the fuel will have a U-235 enrichment well below 20% to reduce the proliferation risk of the fresh fuel. The low fuel packing density will likely preclude the reactor
from having a fast spectrum.
" Physical Protection:
- If the reactor is physically attacked, it is important to reduce the release of radionuclides,
especially the fission gases and volatiles such as iodine and cesium. TRISO fuel is an
effective way to do this because each kernel of fuel (on the order of 1mm in diameter)
effectively has it's own spherical SiC pressure vessel which retains the fission gases. Many
thousand or tens of thousands of these particles must fail to release a significant amount
of fission gas. This contrasts with a typical metal clad fuel pin which only requires one
cladding failure to release a large amount of fission gases.
21
- To protect these TRISO particles, the core geometry, assembly geometry and fuel matrix
material should be chosen to disperse or absorb kinetic energy.
This is primarily a
protection against explosions and pressure waves which might be used to damage the core.
This complexity of this analysis will vary based on the materials chosen. High toughness
materials are the most obvious choice as they can absorb energy before fracture but
composite or porous materials made of hard, brittle materials can also be very effective.
The chosen material must also be chemically stable in fluoride salts and radiation tolerant.
e Reactor Performance:
- Lastly, the fuel must provide good neutron economy. Meeting the requirements above
will place constraints on the choice of materials and geometry but the TFHR must also be
economically viable as a reactor. This means the fuel, in particular the matrix material,
must be either a good neutron moderator or neutron transparent.
3.4
Fuel Cycle
As discussed in the previous section, the fuel cycle length of the TFHR will have an effect on the
security and economics of the plant. While the exact economics of different fuel cycles will vary
depending on the particular details of a remote site, it is fair to assume that transport costs will
dominate the costs of refueling. As such, maximizing the cycle length is a priority. The reactor
should be able to operate for two years or more so that it has a longer typical lifetime than an LWR.
It may also be possible to use staggered batch recycling in order to increase fuel discharge burnup.
22
4
TFHR Fuel
As discussed previously, many of the TFHR design goals are tied to the fuel. This section will go
through the details of how the fuel was thought about and designed.
4.1
Coated Particle Fuel
TRISO fuel consists of a kernel of fissile material, typical U02 or UCO, encased in multiple layers of
graphite, pyrolytic carbon (PyC) and silicon carbide which together form a miniature pressure vessel
and fission product catcher [22]. This fuel has been used in gas cooled reactors for several decades.
Figure 2.a shows a cross section and Figure 2.b shows an SEM image of an example particle.
Adherent
pyrolytic
graphite
Fuel particle
Pourous
pyrolytic
graphite
Silicon
carbide
Adherent
pyrolytic
graphite
:4lo
0 1996 Ademi Aomic Engines, Ic.
Figure 2: TRISO particle a. cross section; b. SEM image
The low density graphite absorbs the recoil energy of the fission products and is a plenum
for fission gases. The PyC layers support the SiC layer and protect it and the kernel during the
manufacturing process. The SiC is the primary structural and fission gas trapping layer. Table 1
gives example dimensions.
23
Material
Outer Radius (pm)
Fuel Kernel
Porous Graphite
250
345
Inner PyC
SiC
385
420
Outer PyC
460
Table 1: Example TRISO dimensions
To make these useable in a reactor, the particles are dispersed in a matrix material and compressed to form solid compacts. These compacts are commonly cylinders (prismatic fuel) or larger
spheres (pebble bed). The manufacturing process is reliable, producing a beginning of life fuel failure probability of around 10-8 [22, 231, though the end of life performance can deteriorate at high
temperatures [22, 23]. Testing has found that overall particle failure is on the order of 10-5[23].
Through-wall cracks of the SiC and IPyC layers allows for fission gas escape and so can be considered the point of fuel failure, though the solid fission products are retained by the fuel kernel
[22].
While coated particle fuels have been shown to be a reliable fuel form, there are some outstanding
issues currently under investigation which appear to deteriorate fuel performance.
These issues
include: the anisotropic response of the PyC layers to irradiation resulting in large local stresses
on the SiC layer, fuel kernel migration along temperature gradients in the particle which puncture
the SiC layer, noble metal fission products attack of the SiC layer, silica evaporation at very high
temperatures (around 2000C) which leaves a weak, porous structure and the build up of oxygen in
the particle which increases the internal pressure and accelerates corrosion as the fission fragments
fail to bond with all of the oxygen released by the fuel kernel during irradiation [24].
Solutions
have been proposed for some of these problems, such as doping the particles with an oxygen getter
or using UCO fuel as opposed to U0 2. Some researchers have also suggested replacing the SiC
shell with ZrC (resulting in TRIZO particles) as ZrC is much less susceptible to fission product
attack and can operate at higher temperatures (above 3500*C) which allows for hotter operating
and manufacturing conditions [24]. These are still under development and were not considered in
this project.
24
4.1.1
Experimental Envelope
TRISO fuels have been trialled in a handful of test reactors, most noticeably the German AVR and
ThTR [25], the Japanese HTTR [26] and Chinese HTR-10 [27] reactors. The USA has also tested a
sizable TRISO population in a variety of environments [25]. While the German tests almost always
showed very good results, there has been variability in the US results. This may have been due
to the known differences in the manufacturing processes or as-yet unrecognized phenomena. The
TFHR was designed using TRISO operating parameters within or near this test envelope. Table 2
and Figure 3 shows a range of the experimental parameters.
[USA
[Germany
Japan [South Africa
France
China
Burnup (% FIMA)
15-20
8
4
8-10
10-15
8
Temperature (00)
1250
1100
1200
1100
1100-1200
1100
Fast Fluence (10 25 rn/m2 )
Packing Fraction (%)
Power Density (W/cc)
4
< 35
6
3.5
10
3
4
30
3-6
3.5
10
3
4
10-15
3-6
3.5
10
3
Table 2: Comparison of TRISO experimental results
Packing Fraction
Power De nsity
50
(W/cc
Tem erature
C)
10
"
1250
110
GeNm
-NGNP
25
10
R
5.0
Burnup (% FIMA)
Fast Fluence
)
(x 102s n/rn 2
Figure 3: Comparison of US (NGNP) and German TRISO experiments
25
It is sometimes difficult to predict power/cc when designing a core so instead power per particle
was used. Experiments have tested power per particles of up to 105 mW/particle and simulations
have taken that further. PARFUME [28] simulations by Maki at al. [29]suggest that most TRISO
problems are exacerbated by higher powers per particle. For this study, 200mW/particle was chosen
as a an upper limit. This typically equates to a power density of around 10kW/cc. While this was
outside the experimental envelope, simulations[29] suggest that there will be acceptable performance.
In the future, when designing the fuel to be resistant to explosions or attack, the power
/
burnup
per particle will need to be revised so that the internal pressure at all points in the life cycle is
within acceptable levels and the amount of fission gas contained in each particle doesn't become
high enough that a significant volume will be released during a design basis attack or accident.
4.2
Matrix Material
To decide the suitability of a given matrix material the following questions were asked in order and
any material which failed to meet one was discounted. Graphite matrix was the base case which
had to be surpassed. The answers were taken from the literature as well as sometimes making use
of calculations or codes for verification.
Was the material:
" Chemical inert enough to make fission product removal difficult?
" Able to withstand temperatures above 1200*C?
" Physically tough, i.e. the material had a high fracture toughness or could disperse energy
from a shock?
" Stable under long term radiation?
" A poor neutron absorber at a large range of energies?
" A good neutron moderator at a large range of energies?
" Fluoride salt compatible? John Stempien's fluoride corrosion and chemical stability code [30]
was used to check the results. Salt compatible casing could be used to protect materials which
failed to meet this criteria.
26
Asking the questions in this order resulted in diminishing lists of materials which could be used for
a variety of purposes in the core, from making the fuel tougher to improving proliferation resistance
to increasing the level of neutron moderation. It was also decided to avoid extravagantly expensive
materials. One material appeared to meet all of the criteria reasonably well: silicon carbide (SiC).
Table 3 shows some of the best results. Other ceramics containing large amounts of oxygen or other
isotopes with high moderating power and efficiency were also trialled to see if the core could be
thermalized more.
Some ceramics or composites had one or two very impressive characteristics.
For example, SiC-reinforced lithium aluminosilicate has a fracture toughness of 25 MPa-m 0 .5 at
1000*C and graphite-epoxy composites have been produced with fracture toughness's of 34 MPam0 .5. However, SiC had the best combination of properties for a high temperature reactor
Material
p (g/cc)
k (W/m/K)
C (J/kg/K)
T-max ('C)
Graphite
SiC
WC
1.75
3.18
15.5
Si3 N 4
ZrC
A12 0 3
ZrO 2
BeO
3.29
6
3.69
5.68
3.02
50-100
120
60
30
2
18
2
300
850
750
240
170
350
880
400
1200
1000-1500
1650
1100
1000
1500-2400
1700
2400
~2200
[ T-melt
(9C)
3550
2700
2900
1900
3150
2050
2715
2500
Kic (MPa-mo 5 )
BOL Keff
1.23
4.6
15
6.1
2.5
3.5
8-13
3.7
1.31
1.22
0.11
0.76
1.12
1.19
1.14
1.29
Table 3: Key materials investigated as fuel matrix materials. BOL K-eff results come from core
with pin D, pin P/D = [1.4cm, 1.2] and BeO internal moderator assemblies and reflector.
4.2.1
Silicon Carbide
SiC was chosen as the matrix material based on its good chemical properties, reasonable neutronic
and mechanical performance and its long experimental history. SiC is used in a variety of industries
because it is a very hard, inert and light material. These applications include use as a protective
layer on aerojet engines and as the intermediate layer in bullet proof vests and vehicle armor. SiC
has a hardness of 9 on the Mohs scale (steels are typically 4-5 and diamonds are 10) but like most
ceramics is brittle, with a fracture toughness around 3-5 MPa-m 0 . 5 (compared to 50 MPa-mO. 5 for
a typical steel).
It is able to withstand very high temperatures and is stable under irradiation,
27
making it a suitable choice for a high temperature reactor matrix. Carbon is an excellent neutron
moderator while silicon is relatively transparent except for some epithermal to fast resonances. This
is somewhat of a concern because of the large amount of Doppler broadening expected at the TFHR
fuel temperatures (~1000*C) will damage the neutron economy. However it will also give a negative
moderator temperature coefficient, making the reactor more stable. Figure 4 shows the silicon and
carbon microscopic elastic and capture cross sections.
104
10 3
2
10 2
-m
--
.10
e3io I
-scat-
____C
a
00
Si - scat
-A
~~010
0
J4Ja.
-2
L->102
11111 I II111 I111 111 I II 111 I II111
II
IIIII
I II111
-
-~~~~~~
165
9
1
167
166
:165
164
1,53
162
1
8
Energy (MeV)
Figure 4: Silicon and carbon microscopic capture and elastic cross sections from ENDF/B-6.0 A
300K
SiC is a very inert material, much more so than graphite or other common matrix materials.
This made it a better choice to meet the non-proliferation criteria set out in the TFHR objectives.
A would-be proliferator would like to remove all of the matrix material from a TRISO fuel assembly
with one process, crack the TRISO particles using a roller and then dissolve the fissile material into
a useful solution which can be manufactured into weapons or fuels materials. SiC-matrix TRISO
28
fuel makes this difficult.
Unlike a graphite matrix, which can be combusted to remove it from
the TRISO particles, sintered SiC (though not necessarily bonded SiC) is much more difficult to
react away. The only common agents strong enough to dissolve SiC also react with uranium and
plutonium, meaning all the fuel assembly materials, including the matrix and TRISO particles, are
dissolved together. Typically, less than 10% of the fuel assembly is fissile material at beginning
of life so almost the entire fuel assembly will need to be dissolved.
If the proliferator attempts
to separate the TRISO particles mechanically, they will require very hard rollers which can crack
millimeter scale SiC pieces and it will still be very laborious (and hazardous given the fission gas
inventory of any cracked particles) to separate the fuel from the matrix material.
Whether the chemical or mechanical method is pursued, the proliferator will need either a large
and expensively equipped facility to reprocess the fuel to recover fissile material or the patience
to run many small batches. Either outcome will either make the facility easy to detect based on
off-gases and equipment orders or give investigators a long enough time to find a smaller, more
discrete facility. This should be a significant deterrence to proliferators and make the TFHR less of
a proliferation challenge. One caveat is that relying on SiC in this way will make it very important
to control the manufacturing process of the matrix to ensure that it remains proliferation resistant.
For example, some SiC layering methods allow gases to travel the length of an SiC body unless
properly sealed at the ends. This may allow chlorine or fluorine gases which leach fissile material
(as well as SiC) to be remove the uranium and plutonium in an assembly without needing to react
away a significant amount of SiC.
There was some concern that the brittle nature of SiC would mean it would provide minimal
physical protection to the fuel but further research into its performance as an armor material
suggested that careful design and pairing with protective metals could overcome these issues. This
is because the hard SiC plates have a high initial resistance to damage and after rapidly fracturing
the debris field disrupts blast waves. This phenomena is described in more detail below.
4.2.2
Tungsten Carbide
Tungsten carbide (WC) was investigated as a second matrix option because it has similar chemical
inertness to SiC but a fracture toughness of 8 - 20 MPa-m 0 .5 . This would significantly improve the
physical protection of the fuel. Tungsten metal itself was also investigated as at high temperatures
29
it has been measured to have a fracture toughness as high as 100 MPa-m 0 .5. However, a metal
matrix is unlikely to have the same dimensional stability as a ceramic at high temperatures and
neutron fluences.
A problem for both tungsten and tungsten carbide is the significant thermal
neutron capture of tungsten, shown in Figure 5. This means both materials are only tenable in a
fast reactor. A fast spectrum TFHR was considered a possibility at this stage and so was pursued
tangentially but was eventually found to be an inferior design.
4.2.3
Zirconium Compounds
Zirconium carbide (ZrC) and Zirconium dioxide (ZrO 2 ) were both promising as matrix materials,
primarily due to their high scattering cross sections, very high hardness, chemical inertness and very
high melting point. ZrO 2 was particularly interesting as a matrix material which would efficiently
provide neutron moderation because of its oxygen content.
Also, it can be manufactured to be
transparent which might allow for interesting optical methods for inspecting the TRISO particles.
However, the higher absorption cross section and large number of Zr epithermal resonances caused
greater parasitic absorption which dropped the performance below that of SiC matrices. Also, both
Zr compounds have very low thermal conductivity which might also prove a problem and at high
temperatures (1000*C+) it is reported that ZrO 2 is permeable to many ion species which may create
unexpected interactions with the fluoride salts. It is possible that thin shells of other materials could
be used to mitigate these problems but given what is available off the shelf at present, SiC offers
better performance.
30
-
""I
~
11111
iLA~4ii-Sa
'I
10 3
W -capt
102
Zr - scat
'103
0 0
Si -scat
0
Zr - capt
1
1,53
16
Si - capt
-9
18
167
166
65
4
13
Energy (MeV)
102
161
18
Figure 5: Silicon (Si), tungsten (W) and Zirconium (Zr) microscopic capture and elastic cross
sections from ENDF/B-6.0 (0 300K
4.3
Explosion Performance
Based on the ways SiC and similar ceramics are used today and discussions with armor experts,
it was thought that a carefully designed ceramic or ceramic composite matrix fuel assembly could
provide significant physical protection to interred TRISO particles. Toughened fuel is an important part of the TFHR design because it is a marginal cost replacement for traditional fixed-cost,
personnel intensive S3 methods. This made it very important to be able to predict the failure of
composite SiC materials under large mechanical shocks. This is a complicated and computationally
intensive field which involves shock wave dynamics and ceramic fracture. Ultimately, this project
was unsuccessful in producing a model which could be used to iterate the fuel rod, assembly and
core design to optimize physical protection while also maintaining neutronic performance within
acceptable bounds. Simulating liquid shock waves proved too time intensive and matrix fracture
could not be modeled with sufficient confidence for the system to work.
There were also some
problems getting access to established SiC modelling codes. For future work, Sandia's CTH code
31
seems a very strong, export controlled, choice [31]. However, multiple methods were investigated
and this work should provide a good basis for a future, focused project to either tie multiple existing
codes together or develop a new system to automatically iterate between physical and neutronic
performance.
4.3.1
Modeling Fuel Failure
The processes by which ceramic materials protect vehicles or buildings were investigated to help
understand what was important to model.
A blast or projectile will require a large amount of
energy to initially damage an SiC plate because of its high hardness but once a crack forms it will
propagate rapidly due to the low fracture toughness, most often leading to catastrophic failure of
the component. Some tanks have armor consisting of a layer of SiC discs sandwiched between two
thick steel plates.This is called Chobham or composite armor. The exterior steel plate absorbs a
large amount of energy as it fractures due to its high fracture toughness before the blast wave or
projectile reaches the SiC. This then fractures rapidly, creating a field of debris. This debris breaks
up and disrupts the passage of any remaining blast wave, reducing the maximum overpressure
on the second steel plate and protecting the tank.
The development of the new blast front is
analogous to the development of Couette flow from the mouth of a pipe and has a development
length. The overpressure on the second metal plate is significantly reduced if the SiC debris field is
shorter than the blast wave development length. Because SiC cracks will propagate long distances
through a component, many small SiC discs are used to prevent the entire SiC layer from being
destroyed by one strike. This suggests that TFHR fuel assemblies will preferably be made of sub
units, both radially using triangles to form hexagons and axially using multiple short blocks. This
will prevent a fuel failure cascade. Also, high fracture toughness materials should be sandwiched
between the assemblies, most likely metals. For a low power reactor, it may be possible for this
metal superstructure to double as heat fins
/
pipes.
Shaping the entire core to resist explosive
damage will be determined by blast wave dynamics. If the core is buried this becomes simpler as
only one direction of approach must be considered. In any case, shaping the core and reactor to be
robust will have to trade off with safety systems, particularly in ensuring adequate cooling in the
case of site power loss or other accidents where pumps may be difficult to operate.
32
From this research, it was decided to divide modeling core damage from blast waves into two
parallel problems: matrix failure based on a non-isotropic pressure at the edge of the core and
TRISO failure based on a given isotropic pressure on its surface.
This assumes that the TRISO
particles are small enough that any shock wave passing through and fracturing the matrix material
can be assumed to exert a roughly uniform pressure on nearby TRISO particles. A typical TRISO
particle diameter is on the order of a millimeter or less so this seemed a reasonable assumption. It
could be possible for this assumption to be reversed and for it to be said that the TRISO particles
can be homogenized with the matrix material when looking at how a blast wave passes through an
assembly but this depends on the method used. This is described below.
4.3.2
Modeling Matrix Failure
The major difficulty of the problem is predicting the pressure at any point within a fuel assembly
due to a blast wave approaching from a given direction. The principle challenges in this calculation
are understanding how a shock wave will pass through a given core geometry and how the resulting
wave fronts will move through the matrix-TRISO composite. Without experimental evidence, it is
difficult to know whether it is acceptable to homogenize the TRISO particles and matrix material.
If not, it becomes necessary to explicitly model the entire fuel again, from core to fuel kernel
level, as the TRISO particles contain a mix of low density graphite and high density fuel materials
which will distort the blast wave. A middle road would be to model the assembly as a sequence
of slabs of TRISO and matrix material. The thickness of the matrix slabs would depend on the
packing fraction of TRISO particles or a range of thickness could be sampled in order to account for
the random arrangement of particles, with the distribution proportional to the expected distances
between TRISO particles . This is all complicated further by the fact that the matrix material may
fracture as the shock wave passes through it, changing the stresses on the interior TRISO particles
and changing the shape of the blast front again as it simultaneously moves through coolant and
fuel.
The random nature of both the initial TRISO placement and flaw distribution in the matrix
material mean a statistical treatment of this problem is necessary. Ceramic materials have little
ability to deform plastically so failure is mostly determined by the largest pre-existing defect or
crack when a force is applied.
Statistical methods can be applied to both parts of the physical
33
modeling. The Weibull distribution is commonly used to model the distribution of initial defects
in ceramics. It defines the probability of survival based on a threshold stress below which failure
is considered impossible, a characteristic stress where failure is estimated to occur 63.2% of the
time and a Weibull modulus which determines the skew of the distribution. These variables are
estimated from experimental data using a volume term which scales the results. For this project,
the values were taken from a survey of studies at ORNL into the fracture of monolithic CVD SiC
[32]. However, Weibull-based models are very sensitive to the particulars of the data used so while
this training data may be useful for predicting the failure of TRISO SiC, which is a continuous
shell of SiC, it is unclear how accurate the results for matrix material failure will be due to the
large number of interstitial TRISO particles. A better training set would be experimental data of
SiC-matrix TRISO fuel failure, even with surrogate TRISO particles, or perhaps SiC composites
consisting of SiC fibers surrounded by an SiC matrix. A completely reliable solution will not be
possible till experimental data using the actual fuel is trialled, even on a small scale.
In addition to the Weibull model, Johnson-Holmquist models have been successfully employed to
predict the behavior of ceramics under high strain rates and partial or complete fracture. The JH-1
[33]and JH-2 [34] models take the effect of damage to ceramics into account, making assumptions
about whether failure will abruptly or gradually change the mechanical properties of the SiC in JH-1
and JH-2 respectively. The models are most commonly used for ballistics modeling and have been
integrated into commercial and national lab FEA codes for ceramic fracture, including LS-DYNA
[35]. While not used in this project, the JH models could be very useful in the future for modeling
time dependent body and surface damage of fuel assemblies.
4.3.3
Modeling TRISO SiC Fracture
In his recent thesis, Youho Lee developed a set of equations to predict the failure of SiC cladding
in LWRs based on pressure, temperature and burnup effects using the Weibull model approach [36].
These relationships were adapted to estimate the probability of SiC shell fracture given an inner
and outer pressure. The relationships are given in Equations 2 through 5. Vtt is the total volume of
the shell. The V(r)/Vtt term allows the relationship to be scaled to the volume of interest, whether
V(r) is a whole body or a fraction around radius r. amin is the minimum stress at which a sample
has been seen to fracture in experiments while Go bounds 62.3% of cases. M is a Weibull modulus
34
collected from experiments.
SRouter
(2)
Rinner
+ Pinternai(1
-3)
r)
--
_
r3
-Pexternal
o
(
ext
+ 3) +
3ext
internal (1
+
r
+
R
t
(3)
)
Pexternal(r
Ur =
(4)
S- 1
FailureProb(r). = exp
[r1 tot
- amin)
\\
(
0/
+
Oo
)m)](5)
U0
The model is relatively simple and was not integrated with the Serpent depletion module to
calculate the strain in the TRISO layers based on the build up of fission gases in the TRISO
particle.
Instead, the code calculates the failure probability of a TRISO particle for a range of
internal pressures and backs out the equivalent volume of fission gases. This can then be checked
against the Serpent result to see if too much gas collects. An external pressure can also be added to
represent the effects of an approaching blast wave or squeezing from neighboring TRISO particles.
While not sophisticated, the model gives an impression of what magnitude of accident or attack
the TFHR could withstand with different internal pressures, i.e. at different points in its burnup
history without failure.
Figures 6 and 7 show the failure probability of an AGR TRISO particle with a range of pressure
differentials. The particle is expected to begin failing at pressures greater than 27.51MPa. 10- 8 was
considered the maximum failure probability with no external pressure, i.e. at steady state. This
would equate to roughly 2.45 mol of fission gas being released at 900"C. Given a typical TFHR core
contains 0.5 to 1 billion TRISO particles, this means ten or fewer failures, which is a suitably small
number.
35
1
..................
..........
0.8
........................................
0.7
..................................
.......
. .. . . . .. . . ..
0.6
..................................
. .. . . . .. . . ..
.......
0.5
. ....
..........
0.4
.. .. . . . . . . . . . . . . .. . .... . . .. . . .. . . .. . .. . .. . . .
0.3
0.2
0.1
.
. . . .. . . .
.
. . . . .. . . . . .. . . .
.
.
. . . . .. . .... . . . . .. . . .. . . . . . . . . .. . . . .. . . . .
................I. . .. . . .
.* ................
.. . . . .
.................................
............
.
70
0.9
................ ................
.
co
-0
0
. . . .. . . .... . . . .. . . .. . .
........
..........
............... ....... .........................................
..................
. ....
................
0
10 7.432
107.435
.: ........
.......................
10 7.438
10 7.441
Pressure Differential (Pa)
10 7.444
Figure 6: TRISO survivial probability, steady state
36
107.447
100
10'2
...................
............ ......................................................
..............................
.
.
................
.......
10'4
........ ........
0
L-
CL
10-8
10- 10110 7.
.................
...... ...........
........................... ....................
43 94
10 7.4397
10 7.44
.......
10 7.4403
10 7.441DO
Pressure Differential (Pa)
Figure 7: TRISO survivial probability, zoomed
37
.
: .......... ...... .............
10,6
.........
10 7.409
5
5.1
Core Design
Remaining TFHR Design Space
Having constrained many of the fuel and material choices based on the high temperature, physical
and proliferation resistance requirements, it was left to see how safe and economically competitive
a reactor could be designed with the remaining choices. The open parameters are:
" Fluoride salt type and composition
" Power and size of the reactor
" Assembly and cooling channel geometry (to be improved on by a shock wave
/
mechanical
accidents model in the future)
" Non-salt facing and fuel-containing materials (i.e. neutron reflector, moderator, control material)
" Type of nuclear fuel
This still left many design choices for the TFHR to meet its fuel cycle objectives. A 10kW/L thermal
reactor using FLiBe coolant and internal moderator blocks was found to be the most tenable design
and will be the focus of the discussion below.
5.2
Methods
Serpent 1 was used for most of the core simulation in this project [37]. This Monte Carlo code was
chosen because of its very efficient depletion model and tools for modeling the double heterogeneity
of coated particle fuels.
One drawback of Serpent 1 is that it can only use one processor for
calculations. Serpent 2 [38]can be used with multiple parallel cores but was only swapped to later
in the project. The unit cell criticality calculations were found to be in agreement with MCNP5
[39] calculations but the results are not shown here.
A short sensitivity study was performed to discern a suitable number of particles per cycle and
burnup steps to use. Given the large design space it was important to be able to rapidly iterate
on the core design, especially when using Serpent 1 on a single processor. It was found that 5000
particles could be used per cycle without more than 2% loss in K-eff, end of life (EOL) burnup and
38
cycle time when compared to a 100,000 particle per cycle benchmark. Such a low required particle
count was not very surprising given the small size and highly symmetric TFHR design, both of
which typically reduce the dominance ratio of the power shape. All significantly successful designs
were checked again using 50,000 particles.
The calculation was more sensitive to the burnup step schedule, especially near beginning of
life (BOL). Setting the depletion steps at 0.1, 0.25, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 5, 7.5, 10, 12.5,
15, 17.5, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80 MWd/HMkg was found to be successful and in
cases without significant breeding the intervals can be 1OMWd/HMkg past 20MWd/HMkg as the
reactivity decrease was mostly linear. Using longer intervals near BOL was found to overestimate
the core life. For quick calculations without much breeding all the fuel was treated as one fuel zone.
When checking successful results or using burnable poison or thorium, four radial and one axial fuel
regions were used. This change rarely created a greater than 2% change in EOL burnup.
No parts of the core were homogenized but different depletion groups were used based on the
type of calculation being performed. For quick calculations without much breeding all the fuel was
treated as one fuel zone. When checking successful results or using burnable poison or thorium, four
radial and one axial fuel regions were used. This change rarely created a greater than 2% change in
EOL burnup. The fuel assemblies cannot be homogenized without a large decrease in calculation
accuracy because of the relatively low fuel loading. Previous work showed that homogenizing the
layers of the TRISO particles [40] might only slightly change K-eff but this was not done when
modeling the TFHR to be conservative and because Serpent 1 includes a particle object which
easily handles the large number of cells that make up a significant number of TRISO particles (5
layers each for billions pf particles).
Thermal calculations were mostly performed using pen and paper methods to allow for frequent
changes in the cooling channel and moderating material placement. Otherwise, rebuilding computational models would have become onerous, particularly given that the change in the results were
minimal.
5.3
Unit Cell Investigation
To start, a unit cell of the core with periodic boundary conditions was created to investigate the
basic properties of the core. The cell consisted of one full and eight IthTRISO spheres in a body
39
centered cubic arrangement in a cube of matrix material. The fuel was 19.9% U-235 enriched. The
quantitative results showed little relation to the eventual core results but the qualitative lessons
were useful in getting an impression of the main neutronic design issues facing the TFHR. Principle
amongst these was that using SiC as a matrix material with a high TRISO packing fraction (35%+)
resulted in a core which has a very slightly fast spectrum. Figure 8 shows K-infinite (K-inf) for
various TRISO packing fractions. TRISO packing fraction is representative of the inverse of the
moderator to heavy metal isotope ratio, meaning that a higher packing fraction results in less
neutron moderation and a faster core. Due to the hard spectrum, i.e. poor moderation, the SiC
unit cells showed significant resonance absorption, which held down K-inf.
calculation was used to investigate the results.
A 4-factor formula
The resonance escape probability was 0.4 and
decreased with increasing TRISO packing fraction while the thermal utilization factor was around
0.8 which suggesting relatively efficient use of thermal neutrons and that inserting a low atomic mass
material to assist neutrons to leapfrog the epithermal energy range might significantly improve core
performance.
1.8
1.6
1.4
1.2
*~1
0.8
0.6
0.4
0.2'
0
5
10
15
20
25
30
35
40
TRISO packing fraction ()
Figure 8: BOL K-inf for 20% enriched U0 2 TRISO fuel in a unit cube of SiC (lower line) or graphite
(upper line) surrounding matrix at various packing fractions with periodic boundary conditions
From this plot it appears that minimizing moderation will produce the best TFHR initial reactivity. However this was not borne out when the same test was performed for a full reactor as
40
the unit cell calculations did not take into account leakage effects (which are significant for a fast
spectrum SMR) or the extra moderation created by the reactor structure. The effect of extra moderation was tested by doping the unit cell with graphite particles. Figure 9 shows K-inf vs. fuel
particle packing fraction for 20% enriched TRISO fuel.
-
1.2
1
0.8
C
0.6
0.4
0.2
0
5
10
15
20
25
30
TRISO packing fraction (%)
35
40
Figure 9: K-inf vs. TRISO packing fraction for 20% enriched TRISO fuel with added graphite
moderator. In ascending order, the lines show cases with 0%, 5%, 10% and 20% packing fractions
of graphite particles and the x-value is the fuel particle packing fraction
In ascending order, the lines show cases with 0%, 5%, 10% and 20% packing fractions of graphite
particles and the x-value is the fuel particle packing fraction. Doping with a stronger moderator
/
increased the low packing fraction / thermal spectrum result above K-inf for the fast spectrum
high packing fraction. This suggested that the original unit cell in Figure 8 was still undermoderated
for packing fractions below 5% and the drop in K-inf is due to the mean distance between TRISO
particles becoming too large, meaning that adding more moderator increased K-inf. Due to a lack
of Pu breeding in the core, BOL K-inf was a good indicator of cycle time. This result suggested
that a thermal reactor was definitely the best choice. However, methods of moderation other than
reducing the fuel particle packing fraction needed to be found to maintain the TFHR power density.
Lastly, the size of the TRISO particle was varied to see the neutronic impact.
Given how
few TRISO geometries have been tested experimentally, there is a risk that using a significantly
different TRISO geometry may unexpectedly change the performance of the fuel.
41
However, the
TRISO particles are a significant proportion of the TFHR volume so it is important to understand,
if only for postulation, how the core would react to different kernel radius and layer thicknesses. In
order to stay as close as possible to the TRISO particles used in the experiments, it was assumed
that the key performance limit of TRISO fuel was the build up of fission gases in the porous graphite
region. The fission gas determines the internal pressure of the particles as well as having an effect
on the fission product flux on the SiC layer. Assuming that gas build up is linear with the volume
of the fuel, for a given burnup, it was decided that the TRISO dimensions could be changed as long
as the ratio of the fuel and porous graphite volumes (and hence the maximum pressure) stayed the
same and the SiC layer thickness changed so that it's Von Mises maximum hoop stress stayed the
same. The PyC layer thicknesses were kept the same as it was presumed that this parameter was
determined by the minimum thickness needed to protect the SiC during manufacturing. Table 4
shows the outer radii, volumes and fuel volume fractions of the various trialled particles. For a given
TRISO packing fraction the core fuel packing fraction changes linearly with the TRISO fuel packing
fraction, increasing as the fuel kernel grows. Figure 10 shows K-inf and the 4-factor formula results
for the various TRISO sizes. Increasing the TRISO particle size hardens the spectrum which causes
%
resonance escape to decrease and thermal utilization to increase. This makes sense as a smaller
of the core is carbon as the fuel kernel grows. For a thermal reactor, there is a trade-off to make
between shrinking the TRISO particles to increase the moderator to fuel ratio versus growing the
TRISO particles to increase the fuel density in the core. This is a result of assuming that the PyC
layer thickness remains constant. If the TRISO particles are made too large, extra moderator must
be added to the reactor, displacing entire fuel assemblies.
This makes an optimization difficult
without calculating every case. This tradeoff also makes it likely that the choice which maximizes
discharge burnup of the fuel will not maximize cycle lifetime for a given core geometry.
42
Kernel rad. (cm)
Graphite rad. (cm)
iPyC rad. (cm)
SiC rad. (cm)
oPyC rad. (cm)
0.005
0.0069
0.0109
0.0116
0.01
0.0138
0.0178
0.0192
0.015
0.0207
0.0247
0.0268
0.0308
1.22e-4
11.55
0.02
0.0276
0.0316
0.0344
0.0384
2.37e-4
14.13
0.025
0.0345
0.0385
0.0420
0.0460
4.08e-4
16.05
0.03
0.0414
0.0454
0.0496
0.536
6.45e-4
17.53
0.035
0.0483
0.0523
0.0572
0.0612
9.60e-4
18.7
0.04
0.0552
0.0592
0.0648
0.0688
1.36e-3
19.65
0.045
0.0621
0.0661
0.0724
0.0764
1.87e-3
20.43
0.05
0.069
0.073
0.08
0.084
2.48e-3
21.09
Vol (ml)
Fuel vol. fract. (%)
0.0156
1.59e-5
3.29
0.0232
5.23e-5
8.01
Table 4: TRISO geometry for various kernel sizes
1.04
1.035
Kinf
- --p
1.03
-f
W
- - --
1.025
eta
ep silon
t5
M
117
LO
1.02
1.015
0.01 0.015
&.02
n
0.025 0.03 0.035 0.04 0.045
0.01
Fuel kernel radius
0.02
0.03
Fuel kernel radius
0.04
0.05
Figure 10: K-inf and 6-factor results for a 1ml cube of SiC with embedded TRISO particles A 20%
packing fraction
5.4
Thermal Reactor Design
Using the qualitative lessons from the unit cell calculations, work began on a thermal reactor design.
Some additional attempts were made at developing a fast reactor because it was thought the harder
spectrum might increase Pu-239 breeding and increase the batch lifetime. A search for inert ceramic
materials which do not contain a significant moderator such as carbon or oxygen was carried out
and found materials such asSi3N4 , but none hardened the spectrum sufficiently to increase the
core lifetime to two years or more.
It seems unlikely that a viable fast reactor can be designed
using TRISO or TRIZO particle fuel, with their high carbon content, unless the fuel kernel is made
43
very large.
Given the vital benefits inert matrix TRISO particle fuel has for proliferation and
security protection, this suggested that increasing the core moderation in the TFHR was the only
path forward. Multiple methods of increasing core moderation were explored to extend the batch
lifetime past two years. The key findings are detailed below. A full discussion of the methodology
and results, including a parameter sweep of core designs judged by EOL burnup and cycle lifetime,
can be found in Appendix A.
5.4.1
TFHR Geometry and Materials
Figure 11 shows a plot of the TFHR core. Table 5 gives a description of the dimensions.
The
initial design drew on the unit cell results above and the Fluoride-Salt-Cooled High-Temperature
Test Reactor (FHTR) design
*SiC
141].
BeO
FLiBe
*
Hf CR position
N
Fuel Compact
Figure 11: TFHR core (x-y and x-z) and assembly (x-y) with control rods inserted
44
# Compact rings
# Cooling channels
#
Moderating compacts
Height
Assembly radius
Assembly pitch
0.40
1.20
2.88
cm
cm
-
-
cm
cm
cm
Unit
0.25
1.66
2.5
cm
cm
m/s
6
73
2.25
18
1.25
134.1
154.9
50
-
cm
Cooling Channel
Channel radius
Channel pitch
Coolant velocity
Core
# Assembly rings
# Fuel assemblies
Fuel volume fraction
# Moderating assemblies
Control rod radius
Core apothem
Core radius
Ax. & rad. reflector thickness
Value
-
0.04
6
200
16
250
14.06
28.36
Parameter
Unit
%
Fuel Compact
TRISO kernel radius
see Table 4 for other dim.
TRISO packing fract.
Compact radius
Compact pitch
Fuel Assembly
Value
-
Parameter
cm
cm
cm
cm
Table 5: TFHR core geometry description. Note: the apothem is the length of the line from the
center of a regular hexagon to the midpoint of one of its sides.
The outer dimensions of the reactor were chosen based on the maximum width of a regularlicense commercial truck on USA highways: 2.6m [42]. This presumed that the fuel would travel
in transport casks and not in the core so the reactor could be broken down into key components
such as the reactor head, reactor pressure vessel, reflector segments and so on. For reasons outlined
in Appendix A, the core grew slightly to be larger than the limit. However, it was found that the
low neutron leakage meant adding or subtracting one ring of assemblies had a negligible effect on
discharge burnup so it is simple to anticipate the change in batch lifetime that would result from
shrinking the core to fit a regular flatbed truck. Naturally, discharge burnup will change if any of
the other parameters are changed.
Efforts were made to reduce the amount of fuel displaced by moderator, coolant and control material but the reactor still has relatively low power density, 10.7kWth/L versus ~100kWth/L for a
typical PWR, principally because of the low fuel packing fraction of coated particle fuel. The assemblies are quite large, with a radius of 32cm, almost three times that of a PWR assembly. SiC has a
relatively low moderating power so the average slowing down and thermal travel distances are quite
large: 31.9cm and 18.8cm respectively. Having some large moderator blocks made of a very efficient
neutron moderator in which neutrons can thermalize before re-entering the fuel assemblies improved
the neutron economy significantly. Distributing small moderator blocks
/
compacts throughout the
core also improves discharge burnup but with a lower marginal effectiveness. However, having too
45
many large moderator blocks led to control difficulties as the core became decoupled so a combination of large and small compacts was used. This result and a general approach to optimizing core
geometry are explored in Appendix B. The large assembly size incorporates large moderator blocks
into a regular pattern and allowed the coolant channels to be placed between the fuel compacts. The
moderator compacts and assemblies are arranged to be as homogeneously distributed as possible.
The reflector and moderator materials were chosen using an approach based on the nuclear shell
model. BeO then MgO were found to be the best moderators. Bismuth (Bi) and BeO were the
best reflector materials found. While BeO was more effective as a material, the greater thermal
expansion of liquid Bi improved the temperature reactivity coefficient of the core.
However, Bi
leads to polonium breeding which can be a health risk. For the purposes of this study, this fact was
ignored. Tin (Sn) was another option for a liquid metal reflector, with high albedo and temperature
reactivity coefficient but it provides less moderation than Bi and hence cycle lifetime was less. The
radial area is 61% larger than the axial area so the radial reflector thickness is much more important
than the axial reflector. Using a strong moderator as the reflector cuts fast neutron leakage almost
to zero at the cost of thermal neutron efficiency. Given the significance of the moderating assemblies,
the control rods were placed in the moderating assemblies to maximize rod worth and again reduce
the volume of displaced fuel.
5.4.2
Neutronics Performance
Table 6 gives the key TFHR neutronic performance results for a once-through cycle. Figures 12 and
13 show the TFHR performance.
Value
unit
Discharge burnup
70.88
MWd/HMkg
-
Cycle lifetime
8.0
years
1/cm^2/s
kg
%
pcm
U-235 mass
Pu-239 mass
Pu-239/Pu-total purity
Peff
550
65
75
573
kg
kg
Peff
2e14
904
19.9
665
Prompt lifetime
Core Temperature coeff.
Coolant void coeff.
159
-4.33
~0
is
pcm/K
Prompt lifetime
198
Value
unit
K-eff
1.273
-
K-inf
1.309
Mean flux
U-235 mass
U-235 enrichment
Parameter
EOL State Parameter
$
BOL State Parameter
Table 6: TFHR neutronic performance with no burnable poison
46
%
Parameter
pcm
s
1.41
-
1.3
-
* 12
1.1
1
0
10
20
30
BU (MWd/kg)
40
50
60
1.4
1.3
1.2-
0
1
2
3
4
5
6
7
Years
Figure 12: TFHR Keff vs burnup and cycle time. Note, the final burnup and lifetime are linearly
extrapolated from these plots.
47
S4000
U-235
U-238
Pu-239
C2000
0)
M
0
0
10
20
30
BU (MWd/kg)
40
50
6C
100
Q-
Pu-239
Pu-240
PU-241
a)
0
!50
----
0
0
10
20
30
BU (MWd/kg)
40
50
R
30
BU (MWd/kg)
40
50
60
1
Pu-239/Pu-all
Pu-239/U-235
Pu-240/U-23Pu-241 /U-235
n 0.5
(n
CU
n
0
10
20
Figure 13: TFHR material history vs burnup
5.4.3
Core Cooling
The main priority when designing the core cooling was to reduce the amount of displaced fuel,
regardless of the necessary pressure drop.
Natural circulation during full power operation was
unlikely given the short core height. The cooling channels were placed between the fuel compacts
48
which limited their diameter to 0.5cm but ensured at least 200 cooling channels. This is very narrow
and later analysis incorporating SiC fracture models may show that the fuel matrix is weakened
too much to provide adequate protection. For now it was assumed that this was a viable cooling
geometry.
The following correlations were used to calculate the convective heat transfer coefficient. The
FLiBe thermophysical properties were taken from an unpublished report produced by the MIT FHR
group[43].
Value
Parameter
Parameter
Unit
Value
Unit
Flow Properties
Cooling Geometry
50
MWe
Flow velocity
0.7
m/s
125
MWth
Mass flow rate
525.2
kg/s
Mean thermal efficiency
0.4
-
Pressure drop
9.90
kPa
10.7
kWth/L
Reynolds number
2622.9
6.68
kWth
Nusselt number
16.64
# Coolant channels per assembly
200
-
Heat transfer coefficient
3.66
Coolant channel radius
0.25
cm
Density
1694
kg/m
Dynamic visocity
2.261
mPa-m-s
k
1.1
W/m/K
C
2380
kJ/kg/K
FLiBe Properties (0 1200K,
-
Core power density
Reactor power density
-
Rated power
Thermal power
kW/m 2 /K
0.1MPa)
3
Table 7:
Pr - cP/p - 4.892 [@1200K, 0.lMPa]
k
pDLVflow
Re =pD;po
(6)
(7)
Re < 2100
(8)
f
0.79(ln(Re) - 1.64)2
49
Re > 2100
Re <2100
4
Nu =
(Re - 1000)
Pr
8
(1+12.7(Pr U -1)(L)0.5)
0.023Re 0 8 Pr0 4
2100 < Re < 10000
(9)
Re > 10000
MSR literature showed that FLiBe had successfully been used in core up to velocities of 2.6m/s.
This was taken as the flow velocity upper limit. The constraints on the channel diameter created
by the fuel compact geometry limited the Reynolds number but flow in a 0.5cm diameter channel
remained turbulent down to flow velocities of 0.5m/s. Iteration showed that 125MWth of cooling
could be provided with an average coolant velocity of 0.7m/s. Given the 2.6m/s ceiling, this leaves
plenty of margin for power peaking.
The greater worry is that slower flow speeds in low power
assemblies will induce laminar flow and not be able to sustain sufficient heat removal.
Table 7
shows the thermal properties of the coolant and core.
The pressure drop through the core was calculated using Equation 10.
It assumes that the
gravity head loss is balanced elsewhere in the primary loop. The natural circulation pressure was
estimated to be about 1kPa, based on the density change across the core height, providing a flow
velocity of 0.22m/s.
AP = 1pLfV2
2D
(10)
Thermal transport through the assembly was modelled using an equivalent unit cell approximation. Figure 14 shows the geometry. The thermophysical properties of the fuel compact were
approximated by linear interpolation of the SiC and UCO properties based on the relative volume
fractions. Table 8 gives the results. The high thermal conductivity of SiC reduces the temperature
increase across the assembly, meaning the maximum fuel compact temperature is around 1000"C,
leaving up to 1700"C in thermal margin for the peak pins and accident situations. Keeping all other
parameters equal, the linear power would have to increase x30 to melt the fuel compact. Radiative heat removal is significant for large FHRs given the high surface temperature [44]. However,
accurately modelling this phenomena using a gray body model taking account of view factors was
unnecessary. As an estimate, taking SiC emissivity as 0.87, the core emits 3.16kW/m 2or 97.38kW
total. This is probably an underestimate as it neglects the contribution of the inner assemblies but
50
also suggests that radiation heat removal will be negligible overall.
Parameter
Value
SiC Thermal Properties
Density
3.02
kg/3
k
100
W/m/K
Unit Cell Geometry
Fuel compact radius
Coolant channel pitch
Coolant channel radius
Average Pin Result
1.2
2.88
0.25
cm
cm
cm
q'
Bulk FLiBe temp.
22.5
700
kW/m
C
Center line temp.
717
Unit
C
Table 8: SiC thermal properties and unit cell geometry
SiC
Matrix
Fuel
Compactm
1.44cm
FLiBe
Channel
2.94cm 2.9---m
3.01cm
2.4m~5m
------
1.66cm
Figure 14: Assembly unit cell and equivalent cell
5.4.4
Reactivity Control
While the core performance is quite strong, the large initial reactivity means that unless burnable
poisons are incorporated into the fuel, the control rod heights will have to be changed almost
continuously, risking transients and increasing the operator work load. Drawing power from only
half the core will also increase the already high average flux.
To reduce this issue, Gd2 0 3 and
thorium were introduced to the core to act as burnable poisons. While thorium is not typically
used as a reactivity control it has respectable neutron absorption across a wide range of energies
(~0.5b at high energies and ranging from 0.5-10b at thermal energies) and high density. U-233 has
51
similarly high neutron absorption. While the thorium absorption cross section is many orders of
magnitude less than the thermal neutron absorption cross section of Gd-155 ond Gd-157 (~1E5b)
they are more comparable at fast energies and importantly the absorptions create fissile U-233,
potentially increasing cycle length. Thorium may be an interesting prospect for all reactors as a
replacement or supplement for Gd pins.
Initially it was assumed that Gd would be blended into the UCO fuel of the TRISO particles,
similar to how it is used in an LWR. These TRISO particles would then be distributed in an entire
assembly.
This resulted in relatively low Gd %'s, 3% at most, as it was distributed widely but
also reduced the fuel load by the same amount. It is possible that the results would be somewhat
different if higher Gd content was used in only some of the fuel assemblies.
To reduce the effect
on fuel load and cycle lifetime, it was decided to place the burnable poison into the moderator
assemblies, which have very high thermal neutron flux. This will maximize the marginal use of
the Gd and reduce the amount of fuel or moderator that needed to be displaced. If used carefully,
it was thought that a molten salt soluble moderator might also be used through these assemblies,
though that may complicate the plumbing of the core. Figure 15 shows where the burnable poison
is placed, with the control rods retracted. In reality the bp positions would be rotated 60
so that
they are between the control rod positions. Figure 16 shows the altered performance over the life
of the core using Gd pellets. The case with the bismuth (Bi) reflector is included for comparison.
52
Figure 15: TFHR core Gd 2 0
3
burnable poison positions in light blue
53
-
1.3
BeO-BeO-OGd
Bi-BeO-0Gd
BeO-BeO-3Gd
1.25
1.2-
BeO-BeO-5Gd
BeO-BeO-BGd
--
1.15-
BeO-BeO-1BGd
1.05
0
10
20
30
40
Burnup (MWd/HMkg
50
60
70
-
1.3
1.25
BeO-BeO-OGd
Bi-BeO-0Gd
BeO-BeO-3Gd
BeO-BeO-5Gd
BeO-BeO-BGd
BeO-BeO-10Gd
-
1.2
1.15 -
1 .05 1
0
. ...........
1
2
3
4
Lifetime (years)
5
6
7
8
-
Figure 16: TFHR K-eff versus burnup and batch age with various amounts of Gd2 03 in the identified
moderating assemblies. The cases are listed in order of BOL Keff. Syntax is:reflector material
internal moderator material - Gd 20 3 % in bp compacts.
Figure 16 shows the typical behavior expected when using Gd. With a 10% Gd load, which is
quite high, the control rods would barely need to be utilized. Using hafnium control rods, at the
red positions shown in 11, Keff is reduced by 0.247 when the control rods are fully inserted. That is
almost enough to bring the core without Gd subcritical and is more than enough when any of the
54
Gd assemblies are used. Figure 17 shows the change in Keff depending on the fraction of the CR
rod inserted in the core.
-
0
-0.054.-
a)
-0.1
CD
ca
-0.15
-
-0.2
-0.25 L
0
0.2
0.4
0.6
0.8
1
Fraction of core length that CR rods are inserted
Figure 17: Change in Keff from inserting hafnium control rods into the TFHR for different fractions
of the core length
Thorium could not be used as a direct replacement for the Gd in the moderator blocks because
the U-233 produced will eventually fission and produce fission gases, meaning the ThO 2 must be
placed in TRISO particles.
This placed an inherent limit on the maximum concentration in an
assembly based on the maximum TRISO packing fraction (40%) of an assembly and kernel fraction
of a TRISO particle (19.6% for a 0.04cm radius kernel), capping the ThO 2 content below 7.84%.
Given the lower absorption cross section, much more thorium will need to be used than Gd in order
to see a similar reactivity hold down. Using the same pattern as in Figure 15, the BOL Keff hold
down was only around 0.05. Figure 18 shows an example of the number of Thorium pins which
must be inserted to hold down BOL Keff below 1.05.
55
BeO
I\
UCO Compacts
SiC Matrix
\
ThO2 Compacts
Figure 18: An example of Th compact placements which reduced BOL Keff below 1.05. The Th
compacts are filled with 0.04cm fuel kernel ThO 2 TRISO particles at 40% packing fraction in a
1.25cm radius x 3m long SiC matrix compact at a 3.5cm pitch.
Interestly, replacing BeO in the moderating assemblies with thorium TRISO particles in SiC
compacts had negligble effect on reactivity, which is why so much had to be replaced to see a
drop in reactivity. This may be a avenue for reducing the BeO material in the core, though to a
less extreme degree. The case in Figure 18 only lasted to 11 MWd/HMkg. The thorium breeding
reached a transient equilibrium which prevented the U-233 from contributing much reactivity. This
is a promising idea but was not taken further in this project.
56
104
Es12
10"
102
10
'2
-
L
C/
0
10
10"81
0
10
20
30
40
50
60
70
Burnup (MWd/kg)
Figure 19: TFHR material evolution over core lifetime using the ThO 2 TRISO compacts shown in
Figure 18. Curves in order of EOL mass (high->low): U-238, U235, Pu-239, Pu-240, Pu-241, U-233
57
6
Spent Nuclear Fuel Storage
6.1
Motivations
While not the primary focus of this project, it will be important for a remote reactor, such as
the TFHR, to have a secure means of storing spent nuclear fuel (SNF) without requiring a strong
security force.
The question of how long SNF is stored for is one of economics: the longer the
SNF is stored the less radioactive it becomes, increasing the number of assemblies that may be
transported per cask and reducing the shielding on each cash, allowing smaller trucks, boats, trains
or airplanes to carry it. The longer SNF is stored for, the larger the inventory that can be removed
from intermediate storage all at once, reducing the number of trips that must be made.
Similar to the strategy taken with the fuel itself, it is important to increase the technical difficulty
or time required to remove the fuel to ensure that a central security force could respond or another
method of obtaining fissile material becomes more attractive to a would-be proliferator. There are
five main locations for on-site storage: in the core, in the containment building, in a neighboring
building, in the open or underground. Dry casks are commonly used to store SNF above ground at
grid scale light water reactor sites. This is unsuitable for a remote site as the casks could relatively
easily be removed unless there was a large local security force. Storing the fuel in a second building
is possible at a remote site but extending the reactor building will most likely be cheaper than
building a second nuclear-grade building, so this was not considered.
This section reviews some
remaining options, where they have been previously employed and how they compare.
6.2
6.2.1
Storage Technology Options
Pool storage
The most common choice for SNF storage is to hold it in a spent fuel pool. This is a large pool, at
least ten meters deep, filled with the same coolant as the reactor and equipped with fuel assembly
racks on its floor. LWR SNF pools are connected to a second pool which houses the reactor pressure
vessel by a canal or transfer tube, allowing SNF to be transferred while completely submerged. A
TFHR SNF pool would have to be filled with salt in order to avoid either boiling an atmospheric
pressure water pool or the fuel would have to be cooled for a longer period inside the core, reducing
58
reactor utilization. A fluoride salt SNF pool is impractical for at least two reasons: filling an SNF
pool with fluoride salt would be prohibitively expensive and the relatively high melting temperature
of fluoride salts (~400C) means the pool may freeze if not stirred or the SNF inventory was too
small. If there is partial pool freezing that stopped full salt circulation, the SNF temperature would
increase and freeze-thaw dimensional changes could damage the storage facility. However, given the
1000*C or more margin to the melting temperature of the fuel matrix. it is unlikely that the SNF
will melt. A small transfer pool may be necessary to hold SNF assemblies until they can be loaded
into transfer casks but this would be much smaller and easier to manage than a full SNF pool.
6.2.2
In-Core Storage
Given the thin TFHR pressure vessel, it may be cost effective to increase the pressure vessel diameter
and store the SNF around the outside of the core, at least for short term cooling. This might remove
the need for even the SNF holding pool described at the end of the last paragraph. This strategy
has been used by sodium fast reactor designers; which is also an atmospheric pressure design. Core
storage reduces the amount of plumbing and heaters required to keep the salt liquid but increasing
the radius of a large cylinder (i.e. the reactor pressure vessel) will often require more volume than
creating a second small one. A given remote site will have to decide the economics of this decision
based on the cost of construction at their site.
6.2.3
Shallow borehole
Shallow borehole storage involves placing SNF in vertical lined holes, a few tens of meters long,
drilled using standard oil well equipment and covered with a large concrete and steel cap. This
solution is relatively technically simple, borrowing from and somewhat simplifying the work done
on permanent deep borehole storage [45, 46].
Shallow borehole technology is promising for the
TFHR and other remote reactors because it is a modular system which can be expanded as needed,
does not rely on much extra on-site plumbing or infrastructure and makes it very technically difficult
and time intensive to steal SNF. A field of boreholes can also be monitored remotely using satellite
or airplane passes, further managing the risk of theft. Shallow borehole storage has been successfully
used by ORNL to store radioactive material, including SNF and HEU material and was considered
a safe and secure solution.
59
Fuel assemblies are lowered into boreholes in unshielded metal canisters and can be recovered
using a transfer cask. To make the system secure, a sealed borehole must be very difficult to break
open through the cap. The next easiest option for an attacker, if social engineering is excluded,
will be to excavate the entire cap or dig deep enough to penetrate the walls of the borehole. While
doing either is technically relatively simple, both are time intensive and very likely to be noticed.
This deterrence should provide relatively passive protection to SNF.
While in the boreholes, the SNF has a high degree of thermal and mechanical protection, not to
mention the significant radiation shielding provided by the surrounding earth. The SNF is thermally
grounded to the earth through the borehole walls to ensure cooling. This and the high melting point
of the materials in the fuel means that the fuel might be able to be transferred from the reactor
vessel / a spent fuel pool earlier than usual, while the fuel is still warmer. Blast waves and other
attacks are ineffective through 30m of earth other than a large earthquake or a direct explosion
above the entrance, which again requires the cap to be removed to be effective. An earthquake can
only be protected through careful site selection and means that not every environment will be able
to employ shallow boreholes. In cases where it can work and as long as the top caps can be made
secure, the simplicity and modularity of shallow boreholes is very appealing.
6.2.4
Transport away
Removing SNF as it is produced was discussed earlier and is probably the most secure and least
practical of the three options. Removing fuel from the site as soon as it has cooled sufficiently means
there is only SNF on site for a short period and it remains in the core, reducing the risk of attack
or diversion. However, rapid removal at multiple, spread out sites would be a significant logistics
challenge and would require a strong central body with multiple operational groups to allow for
delays, technical hitches and mistakes.
The main difficulty of this option is paying for these groups and making efficient use of them. A
nation with only one or a few remote SMRs will pay more per reactor for a dedicated fuel removal
team.
If a group of nations have only a few TFHRs each it may be possible for them to share
collection teams, as long as they can collaborate on establishing the necessary institutions. A large
nation is more likely to afford having a dedicated collection team but as its fleet of remote reactors
grows it will be difficult to efficiently schedule and coordinate the operation.. Fuel collection could
60
also be sold as a service by a reactor vendor or other private company which would allow for
specialization.
A collection group could either shuttle between a sequence of remote reactors and a permanent
waste storage site or take a 'road show' of different reactors in need of fuel removal. The economics
of this decision will be decided by the refueling schedule of the whole core and distances that need to
be traveled between sites. A typical dry cask container stores 12 20x20x400-500cm LWR assemblies.
The TFHR assemblies have a 32cm radius and are 2.5m long. Optimistically, this suggests 10-12
TFHR assemblies could be fit in a typical dry cask and 4-5 casks would be sufficient to transport
the core. This is not a large number but if transport is a significant fraction of the fuel costs it may
be sensible to shrink the TFHR assemblies to allow for better packing and fewer trucks.
6.3
Recommendations
The four options each make different trade offs between security, technical difficulty and expense.
Pool storage would be easy to implement given the wealth of experience with the technology but
will probably be too expensive. If a user prefers to maximize security, prompt removal of the fuel
from the site minimizes the amount of time it is exposed on site. However, shipping short-cooled
SNF implies high decay heat and higher radiation levels.
That implies less SNF per cask for a
given cask size. This increases the costs of running a small fleet and the complexity of running a
large one, particularly given the expense of transport to remote sites. Shallow borehole storage is a
middle ground which, unlike pool storage, doesn't require the designers to plan for very eventuality
and can be built in stages if preferred. It provides the option to build a significant SNF inventory
before initiating SNF transport. Because of this and the other reasons described, shallow boreholes
seem the best remote SNF storage choice.
61
7
Future Work
While this project has shown that a viable TFHR can be designed using SiC matrix fuel, there is
lots still to be done. This section describes recommended future work, divided by what it applies
to.
7.1
7.1.1
General
Economics of Remote Sites
One of the key premises of this project is that the increased cost of operating a power plant at
a remote or otherwise off-grid site will accomodate the higher up front capital cost of a nuclear
reactor and make them more appealing as a power source. In particular, it is assumed that higher
transportation costs will make forms of power which require regular refueling uneconomic, unlike
nuclear power. A first order calculation estimated the price of electricity at a remote site as $1/kWhe,
up to six times the regular US grid price. This number needs to be investigated in more detail and
the costs broken down into the individual components so that an estimate of maximum LCOE can
be calculated for any given site. For example, how do operating costs and hence the maximum
price of electricity vary between a coastal remote site and an inland one. Some work was done
on this topic: one of the best resources is to look at government documents which discuss rural
modernization programs as they can be compared reasonably well between different locales and
then compared to the same work done in a city / non-remote location.
7.1.2
Modeling Material Failure
The two primary reasons for having a security at a reactor are to prevent core damage which leads
to offsite release of radionuclides and to prevent fuel theft and nuclear material proliferation. Using
SiC matrix fuel is inherently a good deterrant
/
protection against the latter but requires careful
design to protect against the first. As discussed in section 4.3, modeling ceramic composite fracture
is a difficult task however methods already exist to do so. Either lumped statistical methods, such
as the Weibull model, can continue to be used but then experiments on SiC coated particle fuel
compacts must be performed to improve the training data. Otherwise, it is possible to use FEA
simulations or use one of the export-controlled codes discussed in section 4.3.
62
Whichever approach is taken, it will be useful to couple the mechanical simulation to a neutronics lattice or depletion code so that an optimizer can use a fitness function to optimize both
the toughness, resistance to shockwaves and the neutronic performance. To constrain this problem, it would be useful to make some high level design choices beforehand, for instance whether
all TFHR will be buried. This choice would make mechanical optimization a ID problem but a
better understanding of the economics of remote sites needs to be had to understand whether it is
worthwhile.
7.1.3
TRISO Dimensions
TRISO particles make up around 40% of the reactor so optimizing their performance for a given
type of reactor is a high priority. Ideally this work would involve using a depletion code and TRISO
models, such as PARFUME or TIMCOAT, to explore the cost/benefit of various TRISO geometries
in different reactor environments and then in-core testing to confirm the performance.
It would
be also be interesting to explore the performance of unjacketed TRISO particles (i.e. fuel kernels
with one or no layers) which capture fission gases in the surrounding matrix or in a traditional pin
/
assembly cladding.
The increase in fuel density using unjacketed particles is significant, often
x5-xlO and may be very useful for a high temperature grid scale reactor where physical durability
is less of a priority.
7.2
Thermal TFHR
To continue to develop the thermal TFHR design presented in this paper, it would be useful to take
a tight parameter sweep around the current maximum performance geometry to further optimize
the design. More thermal and themohydraulic analysis of the core should be done to see how it
performs under a range of conditions and accidents. Protocols will also need to be developed to
prevent the salt freezing during outages or systems designed to allow the salt to be easily reheated.
It would also be useful to reduce the BeO load, mainly because it is expensive but also because
it can be toxic when mishandled. MgO and PbO are two good, though less effective alternatives.
Hydrogen containing compounds, if they can be found with sufficiently high boiling points (a liquid
moderator may preferable due to the stronger moderator temperature coefficient but it should not
boil during normal operation) will be effective and will allow the moderating blocks to be shrunk due
63
to the higher moderating power. Alternatively, parts of the BeO compacts could be replaced with
another material, as shown with the thorium compacts in Subsection 5.4.4. Lastly while the Gd
scheme discussed in Subsection 5.4.4 showed good performance, significantly reducing the maximum
reactivity, it is likely that better schemes may be found and this should be explored.
7.3
7.3.1
Alternate Designs
Non-Traditional Matrix Materials
As well as continuing to pursue SiC as a matrix material it will be interesting to investigate some
of the more exotic materials which where found. Recent developments in SiC with various materials may also open up options that have much superior capabilities to withstand explosive shock
waves and other extreme events. Iterating between fuel design, core design, and shock resistance
may further reduce S3 requirements. SiC-reinforced lithium aluminosilicate and some of the other
ceramics had one or two exceptional properties and while they may not be suitable as or there may
not be enough data to justify them as a primary matrix material, they could be used to reinforce
an SiC matrix. Si 3 N4 , MgO and other materials which are poor moderators may also be useful for
use in a fast reactor, though only if the graphite content in the TRISO particles can be reduced.
7.3.2
Alternative Coolants
There are alternative fluoride salt coolants with somewhat different properties and hazards. Some
of the alternative coolants may offer ease of operations or other advantages. These options have not
been investigated
64
8
Conclusions
This work has presented a viable first pass design of a TFHR for use in remote environments. Single
or very small groups of SMRs have a long term future in power generation as a means to provide a
stable power supply to regions which are isolated from a central grid either due to underdevelopment
or remoteness. They look to be a manageable stepping stone up to larger reactors which are cheaper
per MW but more capital intensive. The TFHR core has been designed using materials which are
reported in the literature to be very resistant to typical fissile material extraction techniques and
potentially very durable, in an effort to make the reactor proof against attacks, accidents and
attempts to proliferate nuclear material. This will reduce the need for a significant S3 protection,
an otherwise fixed cost which does not scale much with reactor size. The use of the NACC gives the
reactor operational flexibility, able to provide variable amounts of heat and electricity, even while
the core is refueling.
The core performs comparably to an LWR, with discharge burnups between 60-70MWd/HMkg.
The use of coated particle fuel in an SiC matrix gives the core significant accident margin but also
reduces the power density by a factor of 10. Internal moderator blocks, which the core relies on
to remain critical, mean the reactor can be well controlled using burnable poisons and control rods
without displacing fuel. The core is still relatively undermoderated, mainly due to the number of
materials with large absorption resonances, making it susceptible to changes in spectrum.
This
increases the worth of the various control mechanisms. The low number of thermal neutrons also
makes the reactor easy to control using Gd and other burnable poisons due to their significant
thermal neutron absoption cross sections.
This minimizes the need for control rod movement,
especially near the beginning of the cycle.
The TFHR is worth further investigation and using this work as a platform the design can be
carried forward and developed in more detail. This is somewhat contingent on a more thorough
economic analysis of the potential use cases and the development of the business case for using
nuclear power at remote sites.
However, SiC matrix coated particle fuel and the idea of non-
graphite matrix coated particle fuels in general are a very promising platform for reactor design and
may be the most valuable take away from this project. The high radiation and thermal tolerance
of ceramics and the ability to tweak their composition to tune their properties gives lots of thermal
65
margin and may allow new, interesting ideas to be pursued.
66
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[33] T.J.Holmquist G.R.Johnson. Jh-1 model. In Proceedings of EXPLOMET Conference, 1999.
[34] T.J.Holmquist G.R.Johnson. High Pressure Science and Technology. AIP, New York, 1993.
[35] D.Cronin. Implementation and validation of the johnson-holmquist ceramic material model in
ls-dyna. In 4th European LS-DYNA
Users Conference, 2003.
[36] Y.Lee. Safety of Light Water Reactor Fuel with Silicon Carbide Cladding. PhD thesis, Massachusetts Institute of Technology, 2013.
[37] J.Leppanen. Serpent 1. http://montecarlo.vtt.fi.
[38] A.Isotalo J.Leppanen. Burnup calculation methodology in the serpent 2 monte carlo code. In
PHYSOR-2012, 2012.
[39] LANL. Mcnp5. https://mcnp.lanl.gov/.
[40] W.Ji
et
al.
Reactor
physics
analysis
of
vhtgr
core,
2004.
URL
http://web.ornl.gov/sci/nsed/outreach/presentation/2004/VHTRORNL_3Dec04.pdf.
[41] S.Don R.Romatoski L.Hu C.Forsberg J.Richard, M.Short. Preliminary design of a prismatic
core fluoride-salt-cooled high-temperature test reactor (fhtr). In Proceedings of ICAPP 2013,
number 243. ICAPP, 2013.
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[42] U.S.DOT.
Federal
size
regulations
for
commercial
motor
vehicles.
http://ops.fhwa.dot.gov/FREIGHT/publications.
[43] L.Hu R.Romatoski. Fhr primary coolant properties. Unpublished draft paper.
[441 M.Minck. Preventing fuel failure for a beyond design bases accident in a fluoride-salt-cooled
high temperature reactor. Master's thesis, Massachusetts Institute of Technology, 2013.
[45] E.Bates. A Drop-in Concept for Deep Borehole CanisterPlacement. PhD thesis, Massachusetts
Institute of Technology, 2011.
[46] R.Lester B.Arnold E.Bates, M.Driscoll.
Can deep boreholes solve america's nuclear waste
problem. Energy Policy, 72:186-189, 2014.
[47] J.Kloosterman W.Kruijf. On the average chord length in reactor physics. Annals of Nuclear
Energy, 30:549-553, 2003.
70
A
Full Core Results
A.1
Increasing Core Moderation
Comparison studies were performed, looking at the placement of different moderating and reflecting
materials in various parts of the core to reduce the negative impacts of thermalizing the core and
increase the cycle time by as much as possible. It was important to optimize the placement and
effectiveness of the moderator material in order to minimize the amount of fuel that had to be
displaced.
It was found that replacing whole assemblies with moderating material- and using a
strongly moderating reflector increased EOL burnup the most.
Using a more traditional, high
atomic number, low absorption material as the reflector was also a successful alternative. Typically,
the thickness of the radial reflector was more significant than the thickness of the axial reflector,
even for a square-cylinder reactor.
The main options for adding moderator to the core were replacing fuel compacts with moderator
pins, replacing whole assemblies with moderating material or using radial and axial reflectors which
were either a good moderator or which could have some moderator inserted. While BeO was used
in most of the geometry tests because it was already known to be a good moderator, multiple moderating and reflecting materials were investigated in different core positions in order to thermalize
the core even more efficiently and maintain the fuel load
A.1.1
Moderator Block Size
To ball park the effectiveness of different geometry options, the average number of collisions and total
path length for a neutron to thermalize or collide with fuel was estimated for each of the common
materials in the core using homogenized cross sections and number densities. The calculation used
the 1MeV cross section so the result was a rough but conservative estimate. Many of the materials
in the core have long neutron mean path lengths; for example, SiC was estimated to have a mean
path length of 5.97cm. The same calculation for water estimated a 2cm mean free path. Some other
results are given in Table 9. A neutron is unlikely to travel in a straight line though so a Monte
Carlo simulation was run to see the expected distance (as opposed to path) for a neutron to fall
from 10MeV to 1eV. Figure 20 shows the an example results for BeO. The 95% certainty results are
in Table 9.
71
BeO thermalization cumulative probability
C*
1
2
>0.8
-
M
S0.7CD
-
~ 0.6
~-0.5
-.
-
t 0.4
4D
0.3-
~0.32
0 0.20.1
E
O
'0
45
50
55
60
65
70
Distance travelled (cm)
Figure 20: Mean distance through BeO for a neutron to fall from 10MeV to 1eV
Next, the mean chord length through an arbitrary cylinder was calculated for comparison with
the required path length in different materials. For an isotropic flux, the mean path length through
a circle is L and a similar though much longer formula can be produced for a finite cylinder. This
calculation is given in Appendix B. Figure 21 shows the mean chord through a cylinder of radius:
r and height: 2.5m. While the expected distances in Table 9 are overestimates, as the 1MeV cross
section is typically lower than the average cross section, calculations like this or combinations of
these calculations at a variety of energies were useful for estimating suitable moderator pin and
assembly diameters (presuming that a large hexagon can be approximated by a cylinder). The large
total path lengths required for moderation suggested that relatively large moderator blocks would
be most effective as neutrons would be more likely to completely thermalize, past the resonance
energy region, before returning to the fuel. Adding very large moderator blocks runs the risk of
decoupling different parts of the core, creating control issues, but was predicted to require the most
benefit per cm 3 of fuel which needed to be replaced.
72
Material
A
p
SiC
40
3.18
Water
18
1
[Et(1/cm)
Avg. path to collision (cm)
# Collisions
Avg. path. to thermalize (cm)
0.168
5.968
281
1677
1658
0.491
2.038
129
263
270.1
95%. dist. to collision (cm)
BeO
27
3.02
0.337
2.969
191
567
537.3
Bi
209
10.05
0.289
3.454
1448
5003
5032
Table 9:
#
of collisions and total path length estimates for TFHR assemblies and materials
80
70
E
60
50
a)
40
0
0
30
-2
r_
0
20
01
0
'
10
5
10
15
20
25
30
Cylinder radius (cm); Height = 250cm
35
40
Figure 21: Mean chord through a 2.5m cylinder of radius r in an isotropic flux
Different moderator pin and assembly configurations were trialled to test this prediction. Figure
22 shows the BOL K-eff and K-inf as a function of the number of moderating assemblies. There
were 91 assemblies in total of which up to 22 were replaced with BeO. Some of the patterns have
moderating assemblies bordering the reflector which clearly have lower marginal value. This was
done to test how local the moderating effect was and whether the increase in reactivity was a pure
function of the amount of moderator rather than being geometry dependent. The results show the
latter is true and that the moderator is most effective when relatively homogeneous. The multi-plot
in Figure 23 shows a visualization of the thermal flux in each pattern as well as the patterns used.
Each white dot is a thermal neutron collision. It is clear from the bright patches that the thermal
73
1.4
-
1.35
1.3
-
CD
".! 1.25
.
.-
-
1.2 -+1.2
-
1.05
0
5
10
15
20
25
# BeO assemblies
Figure 22: K-eff and K-inf for TFHR with different number of BeO moderator assemblies
flux is greatest in and around the moderator assemblies and that a large number of neutrons are
thermalized in the reflector.
Figure 24 shows the results of replacing different numbers of fuel pins with moderating pins,
without also adding any pure moderator assemblies. As can be seen, the reactor remains under
moderated even when a quarter of the fuel positions are given over to BeO pins and K-eff continues
to increase. Adding moderator assemblies produces a greater increase in K-eff than using moderating
pins. Replacing a quarter of the assemblies with moderating materials gave a 1500pcm increase in
BOL reactivity while replacing a quarter of the fuel pins only gave a 600pcm increase. This is not
a completely fair comparison as replacing an assembly replaced the matrix material as well as the
fuel pins but from a practical point of view they are equivalent and confirms the prediction that
using large moderating assemblies is more effective than using moderating pins. However both are
useful, especially as adding too many moderating assemblies was found to make it difficult to keep
the flux symmetric across the core when a small number of control rods were added.
74
Figure 23: Thermal flux visualization for TFHR with various moderating assembly patterns
1.2
1.15
-o
II
1.1 [
0)
-
1 .05
1
-I0
5
15
10
20
25
# BeO pins per assembly
Figure 24: K-eff and K-inf for TFHR with different number of moderator pins
75
A.1.2
Thickness or Axial and Radial Moderating Reflector
Neutron reflectors are an important part of SMR design as the smaller size of the core leads to a
larger surface to volume ratio and more leakage. The marginal benefit of thicker axial and radial
reflectors was studied because of this. Three comparisons were performed using BeO reflectors.
While BeO is not a traditional reflector as it has a relatively low atomic mass and hence thermalizes
neutrons, it has a low absorption cross section and in the TFHR's case the extra moderation is
useful. The trial core had 18 internal BeO moderating assemblies.
The study consisted of first
increasing the radial or axial reflector thickness while holding the other value constant and then a
third run where both reflector thicknesses were varied together. Figure 25 shows the results of the
runs. A true optimization is not possible without knowing the cost of an extra layer of reflector
versus the 'cost' of the leaked neutrons. However, from these plots the radial reflector appears more
important than the axial one. This is not so surprising as the square hexagon design means that
the radial surface area is roughly double the axial area. Based on the K-inf results, the moderating
reflector should be around 2 assemblies (~46cm) thick. Other, more traditional reflectors such as
MgO, PbO, Bi and Sn were trialled in combination with BeO to reduce leakage further but none
produced better discharge burnup or lifetime. Figures 26 and 27 show a comparison the performance
of various reflector choices.
A.1.3
Identifying Suitable Moderator Materials
To further improve the core, multiple moderating and reflecting materials were investigated in
order to thermalize the core even more efficiently and maintain the fuel load. A successful neutron
moderator must have a high moderating efficiency and preferably a high moderating power. The
former indicator is the ratio of the macroscopic scattering cross section of an isotope
/
material to
its macroscopic absorption cross section, weighted by the mean logarithmic reduction in energy per
collision:
(11)
76
M 1.2
II
1.1
1
1.5
2
2.5
3
3.5
4
4.5
E
4
4. 5
6
rad and ax thickness
II
1.4
OD
1.2
-
1
1
a)
1.5
2
2.5
3
3.5
ax thickness w/ rad = 2
.
1 3
1.2l
-
....
-.
.
.
1.3
1.1
1
1.5
2
2.5
3
3.5
4
4.5
rad thickness w/ ax = 2
Figure 25: K-eff and K-inf for increasing 1) radial and axial, 2) axial, 3) radial reflector thickness
77
This is a measure of moderation per neutron absorbed.
Moderating power is the numerator of
Equation 1 and indicates the amount of material required for an equivalent amount of moderation.
Common moderator materials, such as beryllium, were included as well as materials chosen based
on a survey of isotopes using the nuclear shell model to identify materials which should have a low
absorption cross section. This seemed more rigorous than looking at cross section values as in theory
it should account for the cross section behavior across the energy spectrum. Figure 26 compares the
K-eff and K-inf results for a list of materials trialed as a moderator, either as an internal moderator,
reflector or both. The hyphenated materials refer to 50/50 (atom %) homogeneous mixtures of
two materials. K-eff is roughly an indictor of how effective a moderator a material is whereas the
difference between K-eff and K-inf gives an impression of the core albedo.
Figure 27 shows the
EOL burnup when using the material as a reflector and BeO as a moderator. When the material of
interest was used as the internal moderators, only BeO and a BeO/MgO mixed achieved criticality,
achieving 44.9 and 23.3MWd/HMkg respectively.
When no internal moderator assemblies at all
were used only a BeO reflected core was critical, achieving 0.93MWd/HMkg discharge burnup.
Some of the materials, such as Pb, Bi and Sn were chosen because they would be liquid at TFHR
operating temperatures. This would have multiple safety advantages:
1. A liquid moderator will have a greater thermal expansion coefficient than a solid meaning the
thermal-reactivity coefficient is likely to be much more negative.
2. In the case of an accident or emergency, the reflector of moderator could be dropped out of
the core to give a large negative reactivity insertion. This could use melt-plugs so that the
system would activate passively if the core, reflector or moderator got too hot.
Beryllium oxide (BeO) was found to be the most effective moderator choice. It was assumed that
it would be encased in a SiC or metal container to protect it from dissolving in the fluoride salt.
Ceramic BeO is relatively safe to handle, with a toxicity rating of 2 or 3 depending on the MSDS
used. The dust created by machining it can be dangerous however so approaching the site after an
accident or attack where the BeO is cracked may be dangerous.
78
1.4
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
1.3 [
1.2
0)
1.1
1iL
1
2
3
4
5
6
7
a
9
Al, BeOMgO, BeOPbO, BeOSn, SeO, Bi, MgO, PbO, Pb, Sn
10
0.25
0.2 F
CD
0. 15 [
C
Y
0.1
0.05
I
1
I
I
I
I
I
I
2
3
4
5
6
7
8
9
Al, BeOMgO, BeOPbO, BeOSn, SeO, Bi, MgO, PbO, Pb, Sn
10
Figure 26: K-inf and K-eff for 6 ring TFHR with BeO internal moderator assemblies, 2 assembly
thick reflector and 20cm axial reflector.
79
45
I
I
I
I
I
I
I
I
a
I
I
I
40
m35
30
25
20
101
9
2
4
6
8
10
12
BeO/Sn,
BeO,
Bi,
MgAI
0
,
MgO,
PbO,
Pb, SiC, Sn
2 4
A1203' Al, BeO/MgO, BeO/PbO,
Figure 27: Discharge burnup for 6 ring TFHR with BeO internal moderator assemblies, 2 assembly
thick reflector and 20cm axial reflector using different reflector materials
80
Magnesium oxide (MgO) was the second best moderator choice. Like BeO, it is an effective
moderator and so is particularly effective as a reflector material where it can thermalize and return
any fast neutrons attempting to stream out of the core.
and is significantly cheaper and safer to work with.
MgO is used as fire brick in furnaces
However, calculations at MIT suggest that
MgO will dissolve into a fluoride salt. Other magnesium compounds, especially those bonded to
hydrogen, showed strong performance, due to their higher moderating power, but their higher cost
and questions of their stability in FLiBe make them less suited as matrix material.
Tin (Sn) was very promising as a reflector choice because of its low melting point and relatively
high moderating efficiency.
Tin has a variety of even isotopes with full valence neutron shells.
The even neutron number isotopes have absorption cross sections less than silicon but the density of energy levels creates a lot of epithermal resonances, depressing the core reactivity at high
temperatures.
Bismuth (Bi) was similarly interesting due to its low melting point and the fact that it only had
one natural isotope, Bi-209, which has a magic number of neutrons: 126 and hence low absorption.
However its high atomic number means that Bi is a relatively poor moderator (though a good
reflector) and the large number of energy levels in the 7th nuclear shell also means that it has many
epithermal resonances. Also, as mentioned in Section 4, Bi breeds polonium which may be a health
hazard.
These materials were trialled independently as well as in pairs, for example using BeO internal
moderators and a Sn reflector. The loss of thermalization near the periphery of the core reduced
K-eff and increased peaking so it was important to have many BeO assemblies distributed through
the core. One promising combination was BeO and Bi, shown in Figure 222.
A.1.4
Pin Diameter and Pitch to Diameter Ratio
Given that the core was still under-moderated despite a large drop in fuel loading caused by replacing
fuel compacts and/or assemblies, it was decided to study the effect of increasing the pin pitch and
pin pitch to diameter ratio to see if this could boost moderation without removing fuel. Figures
28 and 30 show the results of varying the two values, with and without interior BeO moderating
blocks, using BeO reflectors in each case.
81
1.15
1.3
1.28
1.2
124
t
12
140
(A)
160
180
200
2
240
pin D(cm/100)
260
280
140
300
(B)
180
180
202
220
240
260
280
300
pin 0(cm/lED
Figure 28: K-eff, K-inf v.s. pin D (A) without interior moderating assemblies (B) with interior
moderating assemblies
Increasing the pin diameter reduced K-inf while mostly increasing K-eff as the spectrum softens
and the core became larger. Figure 29 (A) shows the 6-factor formula breakdown of the 28 (B)
result. Figure 29 (B) shows the ratio of the fast and thermal fluxes for the same case. Increasing
the pin diameters when BeO assemblies are already providing moderation eventually causes the core
to become over-moderated and the resonance escape probability decreases. Figure 29 (B) shows the
ratio of fast fissions to thermal fissions (epsilon) increasing despite the spectrum softening as the
thermal neutron economy decreases. This is likely because the distance between fuel pins increases
with pin D, increasing the probability of resonance absorption in SiC or due to the onset of self
shielding.
Figures 30 and 31 show the equivalent results when varying the P/D ratio. It is important to
note that the assembly P/D ratio was held constant meaning the internal BeO assemblies grew in the
second case, eventually leading to over-moderation. Figure 31 shows the 6-factor breakdown of the
P/D results. This is more as expected than the pin diameter 6-factor results. As the matrix space
82
-- Keft
Kinf
2.5
eta
epsilon
Lt
34
1.5 1-
3.2
3
1
2.8
2.6
0.5f
24
2.2
140
160
180
200
220
240
260
280
300
160
(A)
180
(B)
200
240
220
pin D (cm/100
260
280
300
Figure 29:
1.15
1.35
-0
a)
1.1
F
1.3
-
1.25
II
a)
1.05
.......
.......-..-
1
(A)
1.15
1
1.2
1.4
1.6
pin P/O ratio
1.8
2
(B)
1
1.2
-
1.2-
1.4
1.6
pin P/D ratio
1.8
2
Figure 30: K-eff, K-inf v.s. pin P/D (A) without interior moderating assemblies (B) with interior
moderating assemblies
83
___Kefi
Kint
p
f
2.5 --
eta
-
epsilon
Lf
Ll
2 --
2.5 -
Keff
Kinf
2
eta
epsilon
Lf
1.5 --1.5
0.5
0
1.1
1.2
1.3
1.4
Lt
0.5
1.5
1.6
pin PD ratio
1.7
1.6
1.9
2
0
11
(A)
(B)
1.2
1.3
1.4
1.5
1 6
1.7
1.8
1.9
pin PlO ratio
Figure 31: 6-factor formula results for TFHR with varying P/D ratio and (A) without interior
moderating assemblies (B) with interior moderating assemblies
between fuel compacts grows, the neutrons are thermalized, decreasing epsilon and fuel utilization
decreases as more thermal neutrons are captured while traveling.
A.1.5
Cycle Length and EOL Burnup Optimization
From these comparisons and studies, a small set of options have been developed to moderate and
thermalize the core, including various internal moderators, a moderating reflector and the fuel
geometry. It is clear that the efficacy of each technique is affected by the existing level of moderation
in the core. Using the options together, it is possible to moderate the core enough to see overmoderation. It would have been useful to find a means of directly comparing the different techniques,
i.e.
to find a way to say how much thicker of a radial reflector is equivalent to making the pin
diameter 0.1cm larger?
The closest method would be to compare equivalent added moderating
power but this ignores the effects of geometry and the flux contribution to the reaction rate, which
changes with any addition of moderation and hence can't be assumed constant between designs.
To find a final core design and test whether the observations made in this section were consistent
between multiple reactor designs, a parameter sweep was performed to find the TFHR design with
the longest cycle length and EOL burnup. The pin diameter and pitch to diameter ratio were varied
around the maxima found above. Some extra cases with much larger and small numbers were also
84
run to double check that the local space being searched was close to the thermal spectrum maximum.
In theory, it would have been best to compare cores with the same fuel loading and surface to volume
ratio so that leakage and other effects were normalized. However, this was impractical given the
range of core sizes that it would create (lm 3 to 1OM 3 ) and would require the large cores to be very tall
and narrow. Instead, an engineering comparison was made, setting a constant height and diameter
for the reactor and filling the volume with fuel assemblies (or as close to it as possible using complete
hexagonal rings of fuel). The EOL burnup (when K-eff dropped below 1.0) was used to make a
normalized comparison between designs instead.
Based on the maximum width of a commercial
truck on US highways (2.6m) [42] a D-2.5m x H-2.5m reactor was used. This is probably too big
still for a road-transportable reactor but allowed the large pin D and pin P/D cores to still have a
few rings of assemblies.
In the sweep, BeO was used as an internal reflector in most cases and BeO and Bi were trialled
as reflectors. A typical core picture is shown in Figure 11. The internal moderating assemblies were
distributed as evenly as possible. Three TRISO types were trialled: regular TRISO with 0.02cm
and 0.04cm fuel kernels and then 0.04cm fuel kernel TRISO with all of the coating layers and buffer
removed to see how much they were affecting the core performance.
This last case had a much
larger fuel load due to the increase in fuel volume fraction and saw up to a x1O increase in cycle
length.
Figures 32 and 33 give multi-plots of the results, excluding the case using only the fuel
kernels rather than full TRISO particles. A table with the dimensions of each of the cores is given
in Section 4. Table 10 shows the best four results based on burnup then cycle time. The naming
convention in the left column describes each core as: pin diameter-pin pitch/diameter ratio-reflector
material-internal moderator material-TRISO fuel kernel radius.
The burnup performance of the core is relatively flat, mostly increasing with the pitch to diameter
ratio before entering the over-moderation regime and falling. This means that cycle length is almost
entirely determined by the initial fuel loading of the core. This decreases almost exponentially with
85
E
E
5
E
r'4,
E
cy
C)
C3
6
.. L
MMM
E0
W
~
-L
M
C
8
C3
.2.
E
E-
-1
CP
Qja
mcoMflOM
6
8
1-1
ER
E
CC)
(BVpMINJ) dngn 10:1
E
coM
L
C)
LO
CD
io
q
- ED~ NC -f -l
~~~~~
CDN
ED
C
Ca
CD
I
~
C4 NC'
N
~t
-C.
E
UL
~
tof
D
LP.2CD
W~~N
C
(N
C)
-
N
C
r
N
(siA) OW!IOJ!1
86
&
CD
-
,
IC
CD
-l
Csual) peoi sEz-n 109
C3
C
M
E
.2
CL
CD
C4~
Figure 32: Discharge burnup, cycle length and initial U-235 load for various TFHR cores with
varying pin diameters and pitch to diameter ratios. The core has 6 rings of pins in each assembly,
6 rings of assemblies in the core and a 45cm axial and radial relflector.
66
a)
a)
C)
.43
.45 .4..
66mmflm
~)
E
CL
C1
LO
CN
Ln
LO
-
if-I
a
0
E
r4
C
?
~~k
C)
Ii:
(Nj
A
;~8Cit
t52
63
LO
Nr
CN
0
a'
a)
8~
0
LO
8
~
C4
C0
aPC=
CL
0D
(B~vpmkA
dnuing -10:4
10 -
10
-
6
M
j
(suoi) Peoi %-l 102
Figure 33: Discharge burnup, cycle length and initial U-235 load for various TFHR cores with
varying pin diameters and pitch to diameter ratios. The core has 6 rings of pins in each assembly,
6 rings of assemblies in the core and a 45cm axial and radial relfiector. This is the same data as in
87
Figure 32 but with axes flipped.
Case (pin D-PD-refl-mod-TRISO)
1.9-1.6-BeO-BeO-0.04
0.9-1.8-Bi-BeO-0.04
0.9-1.8-BeO-BeO-0.04
1.4-1.4-Bi-BeO-0.04
JEBOL BU (MWd/HMkg) ] Cycle Time (yrs)
2.4-1.1-BeO-BeO-0.04
2.4-1.2-Bi-BeO-0.04
2.4-1.2-BeO-BeO-0.04
2.4-1.1-Bi-BeO-0.04
76.95
76.56
76.23
75.52
4.62
3.127
3.114
4.705
70.94
70.88
70.85
70.15
7.130
7.124
7.121
7.051
Table 10:
increasing pitch to diameter ratio. Removing all of the internal reflectors increases the fuel loading
but the loss of moderation and reduction in EOL burnup is not made up for.
In comparison,
removing the TRISO layers gave a five times increase in fuel loading and a corresponding increase
in cycle length. In one case where pin D = 2.9 and P/D = 1.1, i.e. with a very fast spectrum, the
reduced TRISO had an EOL BU of 77MWd/HMkg and a cycle time of 41.33 years. This would
be excellent performance.
However, these reduced TRISO particles are useable in the TFHR as
without the graphite buffer and SiC layer the fission gases would migrate out of the kernel and into
the fuel matrix of the RPV where they could be easily released in the case of an attack. In a safer
environment though, these simplified TRISO particles offer a very interesting fuel option.
Choosing which core design is best can not be decided just using Figures 32 and 33; other
proliferation and engineering concerns play a role. Figure 34 shows the calculated EOL Pu-239
content and purity in the various cores. In all cases the Pu-239 purity is below 90% which makes it
more difficult to directly use in a nuclear weapon. Relatively large amounts are being produced and
in a typical reactor this would be a proliferation concern. However, given the predicted difficulty of
reprocessing SiC matrix fuel, none of Pu-239 content or purity here was considered a game-breaker.
The next consideration was how cool-able the geometry was. The smaller the pin diameter, the
greater the surface to volume ratio of the cooling channels which replace them and the less volume
is lost to coolant. Wider channels lose more volume until the gaps between them are large enough
to have coolant channels drilled between them. Wider channels also require less pumping pressure
for a given pressure drop, improving natural circulation cooling.
Ultimately it was decided to pursue the 2.4-1.2-Bi-BeO and 2.4-1.2-BeO-BeO designs. These
88
cores showed the longest cycle length, low Pu-239 breeding and have large gaps between fuel compacts where coolant channels may be placed. Also, the average flux in these cores was lower due to
the higher fuel load and these reactors contain very large internal BeO assemblies which might be
shrunk or otherwise optimized.
89
8
0D
E
U
E
E
II
E
E
0
1
6 6
M
m
o
6CDae
0
i
6Q)
m6mmm~
6
mmcommm
p
PO WWO
66Z-n
-10
C3
.
a)
CE
C)
OD
8
88
/0
8
8
/
/1
~CD
C3
9
a9
(N.0
~01
LOJ
hi>'
Apn 8 E-n 8 10= 8
Figure 34: EOL Pu content and purity for various reactor configurations trialled
90
B
Mean Chord Through Cylinder Calculation
To estimate how large moderating elements must be to thermalize a neutron, required path lengths
were calculated in section 5.4.1. Ideally, the mean chord length of the moderating elements will be
a large fraction of this distance. Below are the required mathematics to calculate the mean chord
length of an isotropic flux through a cylinder.
Mean Chord Through Circle
To start, the 2D case was calculated. For an isotropic flux, there is an equal chance of the neutron
entering a circle at any point and angle. Figure 35 shows the general situation.
Figure 35: 2D Case: if the probability of a particle entering the circle anywhere on the perimeter is
equal (uniform flux) then the probability of all chord lengths is equal.
(12)
s = 2rcos(9)
f 27 s dO
4r
(13)
dO
S_11
2
Towards the edge of the core, especially if there is not an effective reflector, the isotropy assumption is probably not a good one. In that case a directional flux assumption can be made. The
solution to that problem can be found in Reference [47].
91
Mean Chord Through Cylinder
The 3D problem may be broken down into two 2D problems: finding the maximum chord through
a circle for a given radial angle and finding the mean chord length through a rectangle whose width
is the same as the maximum radial chord. Figure 36 shows this breakdown. The 3D mean chord
length is the average chord length through these rectangles.
D
I
H
x
Figure 36: 3D Case: a cylinder is divided into thin rectangles each if width S, based on the 2D
calculation.
92
This calculation is more complicated as no single formula can be used to calculate the chord
length through both the right hand and bottom edges. Let qcrit be the angle at past which the
neutron will leave through the bottom of the rectangle.
D
=
#criti
=
2rcos(O)
(14)
tan- ()
(15)
Ort
(1-sin2(o))1
D
0
(1-cos(4)).'
otherwise
=
s
ff sdqd~dx
(18)
fff d$d~dx
Solving these integrals analytically is complicated and results in long formulas due to integrating
[1 + tan2
.
Note, the third form of s should not be simplified further as it actually contains two
cases, depending on whether
#
I or not. The result is only the same for r cos2 (0). For very tall
and thin structures, such as a nuclear fuel pin, it was thought the first two cases could be neglected
but this is only for cases where D<<H as s increases exponentially with
4 so
the first two cases make
large contributions to the mean result. In any case, this problem is much easier to solve numerically
using an if statement to handle the three formulas for the chord length. Unfortunately this means
we do not know the exact relationships between 9, D and H but it is very quick to calculate. Figure
shows an example result for H = 250cm, D = 2.4 cm. The three columns of result are each the 0.25,
0.5 and 0.75 points along the unlabeled variable, i.e. the top row shows the results for
x
=
,t iand
3
H
93
#
and 0 at
(W3)
SCL
(w3) I~U~ P1013
-
Li
3
Ua
ca
0)
Ed
10
4116u81 PJO3O
(we)qi~eI
0I
CL
(wo) qi5ual pioq5
.0
-L
E
E
0
E
E
E
C30-
F-
ca
CD
(wo) 416usI P10(13
0
250cm, D = 2.4cm for various angles and
i
...... E
pJoL;5
*IO
(wo) ql5BIe
Figure 37: Chord length through cylinder with H
heights of entry
94
95