The Design of a Reduced Diameter Pebble Bed Modular Reactor for Reactor Pressure
Vessel Transport by Railcar
By
Matthew S. Everson
B.S. & M.S., Nuclear Science and Engineering (2009)
Massachusetts Institute of Technology
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND
ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
BACHELOR OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING AND
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY
0
2009 Massachusetts Institute of Technology
MASSACHUSETTS INSTfUE
OF TEm' 'LOGY
All rights reserved
AUG 1 9 2009
LIBRA RIES
Signature of Authors:
Matthew S. Everson
Department of Nuclear Science and Engineering
May 21, 2009
Certified by
Professor Andrew C. Kadak
Professor of the Practice, Nuclear Engineering
Thesis Supervisor
Certified by
Professor Benoit Forget
Assistant Professor of Nuclear Science and Engineering
Thesis Reader
Accepted by:
"/
gr7 Jacqueyn C. Yanch
Profess of Nuclear Stience and Engineering
Chair, Department Committee on Graduate Students
ARCHIVES
Acknowledgements
I would like to thank Professor Andrew Kadak of MIT for the excellent guidance and
expertise he has provided on the road to completing this thesis.
I would also like to thank Eben Mulder of North West University for contributing to my
knowledge of the inner workings of VSOP.
And I express my gratefulness for my amazing fiance, who has always been there for me
when I needed her.
-2-
The Design of a Reduced Diameter Pebble Bed Modular Reactor
for Reactor Pressure Vessel Transport by Railcar
By
Matthew S. Everson
Submitted to the Department of Nuclear Science and Engineering
on May 21, 2009 in partial fulfillment of the
requirements of the degrees of Bachelor of Science in Nuclear Science and Engineering
and Master of Science in Nuclear Science and Engineering
ABSTRACT
Many desirable locations for Pebble Bed Modular Reactors are currently out of
consideration as construction sites for current designs due to limitations on the mode of
transportation for large RPVs. In particular, the PBMR-400 design developed by PBMR
Pty of South Africa uses an RPV with an outer diameter of 6.4 meters. Since current
SCHNABEL railcars can only haul components up to 4.3 meters wide, the only other
possibility for transport is by barge, which limits construction to sites accessible by river,
lake or coast. Designing a PBMR with a core able to fit within an RPV able to be
transported by railcar would be extremely valuable, especially for potential inland sites
only accessible by railway, such as those in the Canadian Oil Sands at which the PBMR
would be utilized for oil extraction processes.
Therefore, a study was conducted to determine the feasibility of a Pebble Bed Modular
Reactor design operating at 250 MWth with a core restricted to fitting inside an RPV with
an outer diameter of 4.3 meters. After reviewing the performance of various core
configurations satisfying this constraint, an optimized PBMR design operating at this
power was found. This new design uses the same fuel management scheme as the
PBMR-400, as well as similar inlet and outlet coolant temperatures. This MPBR-250
design includes a pebble bed with an outer diameter of 2.7 meters, an outer reflector 50
cm thick and 12.5% enriched fuel. A mixture of graphite pebbles of 11.7% is also
included in the pebble bed to produce an equilibrium core with minimal excess reactivity.
This thesis shows that the MPBR-250 can perform up to the standards of the PBMR-400
design with respect to power peaking factors, peak temperatures and RPV fast fluences
and can also increase fuel burnup to nearly 110 GWd/T. In addition, the MPBR-250 is a
much more agile design, able to be deployed at a wider variety of locations because its
RPV can be transported by railcar.
Thesis Supervisor: Andrew C. Kadak
Title: Professor of the Practice, Nuclear Engineering
-3-
Table of Contents
1. INTRODUCTION
1.1.
THE PEBBLE BED MODULAR REACTOR
1.1.1. PBMR 400 MW, REACTOR
1.1.2. FUEL ELEMENTS
1.1.3. THERMAL HYDRAULICS
1.1.4. FUEL MANAGEMENT
1.1.5. NEUTRONICS
1.1.6. SUMMARY
2. METHODS
2.1. USING
2.1.1.
2.1.2.
2.1.3.
2.2.
2.3.
2.4.
VSOP 94
DATA.DAT
BIRGIT.DAT
VSOP.DAT
APPROACHING THE PROBLEM
IMPLEMENTATION
CALCULATING PEAK PEBBLE TEMPERATURE
3. RESULTS AND ANALYSIS
3.1. PBMR 400 MWTH PERFORMANCE
3.2.
OUTER REFLECTOR ONLY SCOPING ANALYSIS
3.2.1. 250 MWTH DESIGN
3.2.2.
3.2.3.
-4-
3.2.1.1. K-effective
3.2.1.2. Power Peaking Factor
3.2.1.3. Peak Temperature
3.2.1.4. RPV Fast Fluence
3.2.1.5. Fuel Burnup
3.2.1.6. Analysis
200 MW DESIGN
3.2.2.1. K-effective
3.2.2.2. Power Peaking Factor
3.2.2.3. Peak Temperature
3.2.2.4. RPV Fast Fluence
3.2.2.5. Fuel Burnup
3.2.2.6. Analysis
150 MW DESIGN
3.2.3.1. K-effective
3.2.3.2. Power Peaking Factor
3.2.3.3. Peak Temperature
3.2.3.4. RPV Fast Fluence
3.2.3.5. Fuel Burnup
8
8
9
10
12
14
15
16
16
18
20
21
23
26
27
30
32
33
39
39
40
42
45
46
49
52
53
54
55
57
58
60
61
63
63
65
66
68
69
3.2.3.6.
3.3.
Analysis
50 CM INNER DYNAMIC REFLECTOR
3.3.1. 250 MWTH DESIGN
3.3.1.1. K-effective
3.3.1.2. Power Peaking Factors
3.3.1.3. Peak Pebble Temperature
3.3.1.4. RPV Fast Fluence
3.3.1.5. Fuel Burnup
3.3.1.6. Analysis
3.4. A CRITICAL CORE WITH A 50 CM OUTER REFLECTOR
3.4.1.
3.4.2.
3.4.3.
GRAPHITE PEBBLE MIXTURE
25 CM. CENTRAL REFLECTOR
ANALYSIS
70
72
73
74
76
77
79
80
81
82
82
86
88
4. CONCLUSIONS
89
5. REFERENCES
92
APPENDIX
MPBR-250 MW BIRGIT2.DAT INPUT FILE
93
APPENDIX
MPBR-250 MW DATA2.DAT INPUT FILE
94
APPENDIX
MPBR-250 MW VSOP2.DAT INPUT FILE
95
APPENDIX
MPBR-250 VSOP OUTPUT FILE
107
APPENDIX
PBMR-400 MW BIRGIT2.DAT INPUT FILE
108
APPENDIX
PBMR-400 MW DATA2.DAT INPUT FILE
110
APPENDIX
PBMR-400 MW VSOP2.DAT INPUT FILE
111
APPENDIX
PBMR-400 VSOP OUTPUT FILE
123
-5-
Table of Figures
Figure 1 : Cross section of the PBMR 400 MWth reactor .........................................
9
Figure 2 : PBM R 400M W th Fuel Pebble Design ......................................................... 11
Figure 3 : Comparison of PBMR-400 and MPBR-250 Design Target.......................... 18
Figure 4 : A 2-D, R-Z representation of the core channels and layers in VSOP94 ......... 22
Figure 5 : Diagram of VSOP94 fuel management. ......................................................... 24
Figure 6 : Thermal conductivity for A3-3 Matrix Graphite ....................................
.35
Figure 7 : Relative power distributions in the PBMR 400 MWth VSOP94 model...........36
Figure 8 : Coolant and Peak Pebble Axial Temperature Profile for the PBMR-400........ 38
Figure 9 : K-effective for a 10% enriched core operating at 250 MWth ........................ 40
Figure 10 : K-effective for a 12.5% enriched core operating at 250 MWth .................. 41
Figure 11 : Power peaking factors for a 10% enriched core operating at 250 MWth........ 42
Figure 12 : Power peaking factors for a 12.5% enriched core operating at 250 MW.......44
Figure 13 : Peak pebble temperature for a 10% enriched core operating at 250 MWth.... 45
Figure 14 : Peak pebble temperature for a 12.5% enriched core operating at 250 MWth. 46
Figure 15 : RPV fast fluence for a 10% enriched core operating at 250 MWth ............. 48
Figure 16 : RPV fast fluences for a 12.5% enriched core operating at 250 MWth.......
49
Figure 17 : Fuel burnup for a 10% enriched core operating at 250 MWth ..................... 50
Figure 18 : Fuel burnup for a 12.5% enriched core operating at 250 MWth .................... 51
Figure 19 : K-effective for cores operating at 200 MWth................................
...... 54
Figure 20 : Power peaking factors for cores operating at 200 MWth ............................
56
Figure 21 : Peak pebble ptemperature for cores operating at 200 MWth. ...................... 57
Figure 22 : RPV fast fluence for cores operating at 200 MWth. .................................... 59
Figure 23 : Fuel bumup for cores operating at 200 MWth. ............................................ 61
Figure 24 : K-effective for cores operating at 150 MWth................................ ..... 64
Figure 25 : Power peaking factors for cores operating at 150 MWth ............................ 66
Figure 26 : Peak pebble temperature for cores operating at 150 MWth ........................ 67
Figure 27 : RPV fast fluence for cores operating at 150 MWth. ................................... 68
Figure 28 : Fuel bumup for cores operating at 150 MWth. .....................................
70
Figure 29 : Diagram comparing an outer reflector design to a central reflector design... 73
Figure 30 : K-effective for a core with a 50 cm. inner reflector. .................................. 75
Figure 31 : Power peaking factors for a core with a 50 cm inner reflector ................... 77
Figure 32 : Peak pebble temperatures for a core with a 50 c. inner reflector. ............... 78
Figure 33 : RPV fast fluences for a core with a 50 cm inner reflector .......................... 79
Figure 34 : Fuel bumups for a core with a 50 cm inner reflector. ................................. 80
Figure 35 : Graphite pebble mixture vs. k-effective for a core operating at 250 MWth.... 83
Figure 36 : Relative power distributions in the 250 MWth design with graphite .............. 84
Figure 37 : Axial Temperature Profiles for the Graphite Mixture Core ....................... 85
Figure 38 : Relative power distribution in the 250 MWth design with inner reflector..... 87
-6-
Table of Tables
Table 1 : PBMR Fuel Pebble Properties ................................................... 21
Table 2 : Tested Core Configurations - 250 MWth Core, Outer Reflector Only........... 28
Table 3 : Tested Core Configurations - All other core designs ........................................ 29
Table 4 : M ass flow rates for each core power tested .................................................... 32
Table 5 : Performance of the PBMR 400MWth from the VSOP94 Model Output........... 34
Table 6 : Comparison of the PBMR 400 MWth design and the 250 MWth design ........... 53
Table 7 : Comparison of PBMR 400 MWth design with the 200 MWth designs. ............. 63
Table 8 : Comparison of PBMR 400 MWth design with the 150 MWth designs .............. 71
Table 9 : Comparison of the PBMR-400 design to the 50 cm central reflector design .... 81
Table 10 : Comparison of the PBMR 400 MWth design and the 250 MWth designs...... 88
Table 11 : Executive summary comparing the PBMR-400 with the final MPBR-250.....91
-7-
1. Introduction
The goal of this thesis is to assess the feasibility of modifying the design of a current
Pebble Bed Modular Reactor (PBMR) such that the reactor pressure vessel (RPV) fits
within a 4.3 meter (-14 ft.) diameter space 1. This new constraint of the geometry of the
PBMR is set such that the RPV of said reactor may be transported to remote sites only
accessible by railcar. In this thesis, the end use of the PBMR is set to, but not limited to,
the extraction of oil from the Canadian Oil Sands, most of which can only be accessed by
railcar. With this new constraint applied to the reactor, the feasibility of operating a
PBMR at 250 MWth under said design constraints will be evaluated. If such an operating
power is not viable, a lower power rating and/or higher fuel enrichment may be
considered. To determine the feasibility of these designs, a pebbled bed code called
VSOP94 is used to calculate reactor physics parameters including, but not limited to,
neutron multiplication factor, power peaking factor, maximum power per pebble and
reactor vessel edge fast fluence.
1.1.
The Pebble Bed Modular Reactor
The pebbled bed reactor concept has been around for many decades and proof of
concept reactors were built in Germany and China and will soon be built in South Africa.
In general, the purpose of the PBR ranges from high efficiency power generation to
thermo-chemical hydrogen production and steam production for industrial processes,
such as oil sands extraction, all made possible by the high outlet temperatures the system
is designed to withstand 2. Whereas the light water reactor is suitable for mostly power
generation, the pebble bed design is well suited for a variety of applications.
-8-
1.1.1.
PBMR 400 MWth Reactor
The reference design for a typical pebble bed reactor is the PBMR 400 MWth
design of the South African PBMR, Pty Company.
The PBMR 400 MWth reactor
consists of three main sections: a solid graphite inner reflector, a fuel annulus and a solid
graphite outer reflector. For this particular design, the diameter of the inner reflector is 2
meters, the fuel annulus is 85 cm thick and the outer reflector is 1 meter thick. The top of
the core is covered with another reflector roughly 1 meter thick and another reflector on
the bottom about 2 meters thick. The total height of the core, excluding the top and
bottom reflectors, is 11 meters. This core is held inside a reactor pressure vessel with an
outer diameter of 6.4 meters and an inner diameter of 6.1 meters. The 15 cm thick vessel
has a total height of 16 meters 3.
Figure 1 : Cross section of the PBMR 400 MWth reactor.
-9-
Helium is used as the main coolant for in a direct Brayton cycle. No secondary
system is used in this design, meaning the Helium coolant which passes through the core
goes directly to the power turbine. The inlet temperature of the coolant is set to 500C
and the outlet to 9000 C.
The direct Brayton cycle, coupled with such high outlet
temperatures, allows for thermal efficiencies in excess of 40%. This allows the reactor,
rated at 400 MWth, to produce over 160 MWe 3.
The challenge associated with this design is that the reactor vessel diameter is too
large to easily ship in one piece by train, making it very difficult to locate these plants
anywhere but in coastal or water navigable sites. This thesis will explore how a smaller
reactor vessel with a 4.3 meter maximum outer diameter can achieve 250 MWth by
modifying the core and reflector design without exceeding peaking factors and vessel
fluence limits while also achieving desired burnups.
1.1.2.
Fuel Elements
The main feature that sets the pebble bed design apart from many other reactors is
the spherical fuel element design used in the core. These fuel elements, each 6 cm in
diameter, are comprised of an outer graphite layer 0.5 cm thick and a 5 cm inner diameter
of very small fuel particles suspended in a graphite matrix. The fuel particles inside the
pebble are made up of 9.6% enriched UO 2 kernels surrounded by a porous carbon buffer,
serving to provide room for fission product release from the kernel. This is, in turn,
surrounded by three layers of carbon called TRISO (TRiple ISOtopic) layers. The kernel
of fissile material is surrounded first by an inner layer of pyrolitic carbon (IPyC), then by
a layer of silicon carbide (SIC) and a second layer of pyrolitic carbon (OPyC). Around
-10-
15,000 of these fuel particles are deposited within the inner graphite matrix of the fuel
pebble. The individual coatings of every kernel of UO2 provide the first barrier to fission
gas release from the fuel.
FUEL ELEMVENT DESIGN FOR PBMR
Fuel Sphere
in
Half Section
Coated Particle
U~ium Dooxide
Fuel
Figure 2 : PBMR 400MWth Fuel Pebble Design 7
Theoretically, the TRISO layer on the fuel particles is able to contain fission
product buildup for burnups up to 100 GWd/T, allowing efficient use of the fuel and
more of the waste produced from radiative capture of neutrons by the primary fissile
isotope. Such a high burnup is a vast improvement upon that seen in light water reactors,
typically 35 GWd/T.
In addition to reduced waste, the TRISO layer serves as an
additional fission product barrier, which may be able to negate any need for a costly
containment building surrounding a pebble bed reactor.
If the TRISO layer is
compromised then the fission gas will be released into the helium coolant. There are
- 11 -
approximately 15,000 very small TRISO particles per pebble such that if individual
particles fail, the release of fission products into the coolant will be very small. This
chain of events differs slightly from the cylindrical fuel elements within the light water
reactor. In an LWR, the fuel element is comprised of a central column of fuel pellets
stacked one on top of the other and surrounded by a cladding material. Since the thermal
stresses within the fuel pellets are so high once the reactor is at full power, the pellets will
crack and release some amount of fission gas. The average temperature within the fuel is
therefore limited such that only 5% of the fission gas inventory is released from the
pellets. After this cracking occurs, the only barrier between the gas and the primary
coolant is the cladding. The equivalent to this in the pebble bed core is the TRISO layer,
but the failure of the silicon carbide shell releases only the contents of a microsphere as
opposed to a stack of fuel pellets approximately 12 feet long 5. Therefore the spherical
fuel elements used in the PBMR are less likely to release fission product gas and allow
increased use of fuel contents than LWRs. The steady state peak fuel pebble temperature
must be limited to 12000 C, though, in order to prevent mechanical failure while the
pebbles pass through the core 6.
1.1.3.
Thermal Hydraulics
Instead of the light water coolant predominant in current power generating
reactors, the PBMR uses helium as its coolant. The use of helium as a coolant allows for
safer operation in addition to the gains made by using spherical fuel elements. First, a
virtually non-existent microscopic cross section for radiative capture coupled with a very
low number density (since the helium coolant is in gas phase) allows the coolant to be
passed through the core with almost no neutron activation thereafter. Second, helium is
-12-
inert and therefore will not chemically interact with the carbon in the fuel pebbles, such
as the outer graphite reflector or any additional systems involved in the primary coolant
loop. Although there are no corroding forces in the PBMR via chemical reactions as
there are in LWRs, there are still concerns over whether the graphite dust generated
during mechanical interactions between pebbles with each other and the inner diameter of
the outer reflector would lead to degradation of coolant systems and combustible
conditions during an air ingress accident. Third, the helium coolant is always in gas
phase in the core and therefore will not be subject to the various two-phase flow accident
scenarios which can occur in LWRs (departure from nucleate boiling in pressurized water
reactors or dryout in boiling water reactors). Since there is no such degradation in heat
transfer of helium as is seen above critical heat fluxes in LWRs and no chemical
reactions occurring with material in the core and the coolant, the inlet and outlet
temperatures can be set much higher than those found in LWRs. Typical inlet and outlet
temperatures for the PBMR are 5000 C and 9000 C respectively allowing for higher
thermal efficiencies for power production compared to LWRs which are limited to
maximum outlet temperatures of 3400 C and peak efficiencies of 34% 5. These higher
temperatures are what allow the PBMR design to be used in a much wider variety of
applications, including high efficiency power generation and oil extraction.
In addition to the differences in coolant, the thermal properties of graphite are
very favorable during power transient scenarios in maintaining reactor safety, in
particular minimizing rapid temperature changes on the RPV. The high thermal inertia of
graphite makes it well suited for power transients because rapid changes in temperature
take longer to travel through the fuel pebble graphite and the graphite of the outer
-13-
reflector. Therefore, these rapid changes in temperature will take longer to diffuse out to
the RPV and minimize how quickly the temperature of the RPV changes during such a
transient. This should allow the RPV to be subjected to a higher fast fluence, which
would allow the lifetime of the reactor to be extended if the fast flux is fixed at the
previously designed value. It might also allow the fast flux to be increased, generally
equivalent to an increased power rating or a reduction in the thickness of the outer
reflector.
1.1.4.
Fuel Management
In LWRs, the fixed lattice of fuel rods pose an interesting and difficult problem in
how to effectively create uniform burnup among the fuel rods over their residence time
while the fission rate can vary substantially from one position in the core to another. In
order to do achieve an even burnup, the reactor must be shut down every 12 to 24 for
refueling. During the refueling operation, about 1/3 of the core is replaced with fresh fuel
while the rest is rearranged to achieve criticality for the next operating cycle and achieve
as uniform burnup as possible. Clearly, the challenge for the fixed lattice cores is that the
top and bottom of the fuel assembly is always underutilized.
The amount of time
required for such routine shutdowns corresponds to a loss of revenue for the operators of
the power plant. Typical refueling outages last about 30 days in the United States 5.
Pebbled bed reactors are refueled during operation by constantly recirculating the
fuel pebbles. Pebbles are inserted in the top of the core and removed from the bottom of
the reactor vessel. At the time of removal the pebbles are checked for burnup and if not
completely used up, they are recycled back into the top of the core.
When the fuel
reaches the maximum burnup permitted, the pebbles are discharged and channeled into
- 14-
spent fuel storage tanks. This is the main difference with respect to fuel management
between LWRs and PBMR. In addition to possible increases in capacity factor using
online refueling, the fuel pebbles can be cycled through the reactor multiple times as well
as be mixed in with fresh fuel when reinserted from the top of the core allowing for more
complete utilization of the uranium in the fuel. Given that fresh fuel is inserted when
needed to maintain criticality, there is very low excess reactivity when the equilibrium
core has been attained again maximizing productive fuel utilization.
During initial startup, the core is filled with a mixture of half fuel pebbles with
half the normal enrichment and half graphite pebbles. This start up composition is then
gradually filtered out when the full enrichment fuel pebbles are added in, eventually
leading to an equilibrium core once all graphite and half enrichment pebbles are removed
from the core. Once this process is fine tuned for a specific PBMR design, it is possible
to achieve small excess reactivity relative to LWRs, especially during the start up process.
LWRs need enough excess reactivity at the beginning of every startup to last the 12 to 18
months of operating. Since excess reactivity can be reduced for equilibrium operation in
the PBMR, either the reactivity worth of individual control rods can be reduced if the
total number is held constant or if reactivity worth is constant, the number of control rods
needed to maintain criticality can be decreased relative to the LWRs.
1.1.5.
Neutronics
Thermal reactors use the large microscopic fission cross sections of fissile
material for neutrons at thermal energies to reduce the total flux necessary to produce the
same amount of power. Reducing the fast flux near the edge of the core reduces the fast
neutron fluence of the RPV thus extending the lifetime of the reactor. From a neutronics
- 15 -
standpoint, the core must be designs to achieve equilibrium criticality without exceeding
design peaking factors, achieving the target burnup of the discharged fuel and minimizing
fast fluence on the reactor vessel. The variables under consideration include the size of
the central reflector, core annulus thickness and outer reflector dimension within the
constraint of the outer diameter of the reactor vessel of 4.3 meters.
1.1.6.
Summary
The PBMR design couples very high thermal efficiencies, increased utility and the
capability for extremely high fuel burnup to make this reactor one of the most flexible
with regards to application and waste.
The high fuel burnups achievable make this
design of special interest to nations lacking the ability or motivation to reprocess spent
fuel, which are therefore limited to storing spent fuel and waste. But, in the case of the
Canadian Oil Sands, this current design is way too large to be transported to any site by
railcar.
Therefore, this thesis endeavors to produce a modular pebble bed reactor,
operating at 250 MWth, of similar performance to the PBMR 400 MWth design that is
able to fit on a railcar for transport. This thesis will base relative performance of this new
reactor design on the following quantities: k-effective, peaking power, peak pebble
temperature, RPV fast fluence and fuel burnup.
2. Methods
Very Superior Old Program 94 (VSOP94), a software package developed in
Germany to simulate the steady state operation of a pebble bed reactor, was used to
determine key reactor physics properties to be used in optimizing a PBMR design under
the constraint that the outer diameter of the RPV must be held constant at 4.3 meters.
-16-
Since VSOP94 does not include the RPV in the thermal hydraulics or neutronics
calculations, the assumption was made that the RPV was 15 cm thick and that the spacing
between the inner diameter of the RPV and the outer diameter of the outer reflector was
15 cm. This further constrains the core of the new PBMR design to a radius of 1.85
meters, which includes the outer reflector, fuel region and central reflector. Figure 3
below is a comparison of the current design of the PBMR 400MW reactor to the size of
the design with the imposed 4.3 meter outer vessel diameter constraint.
The RPV is
shaded in gray.
-17-
6.4 meters
4.3 meters
11 meters
Figure 3: Comparison of PBMR-400 and MPBR-250 Design Target
2.1.
Using VSOP 94
VSOP 94 is a suite of separate programs used to solve a coupled neutronics
thermal-hydraulics burnup problem, including the effects of online refueling, for a welldefined PBMR design.
18-
An inner iteration of the program at each time step occurs
between the CITATION and THERMIX programs. First Citation solves the 4-group (3
fast groups and 1 thermal) neutron diffusion equation for the flux shape and neutron
multiplication factor given an initial distribution of fuel, such as the core filled up with
startup fuel pebbles, and then uses the given thermal power from the input files to
determine the magnitude of the flux. These fluxes are used to generate fission reaction
rates, which are relayed to THERMIX to solve the thermal hydraulics equations. Once
the temperatures are calculated, the information is fed back into GAM, a 68
fast/epithermal group spectrum solver, and THERMOS, a 30 thermal group spectrum
solver, to generate new multi-group cross sections which are then condensed into 4 group
cross sections for use in CITATION 8. This process is repeated until a user defined
convergence criterion is satisfied, after which the various reactor physics parameters
calculated in this process are saved to the output.
Once the inner iteration is complete, the converged flux and cross sections are
used to determine isotopic changes in the fuel under a given exposure (i.e. power and
time). The duration of this exposure is defined as a cycle. One cycle may be broken up
into multiple time steps to provide a better estimate of the new fuel composition. When
the cycle is complete, the fuel already present in the core is moved down through the
reactor, fresh fuel and recycled fuel are mixed and added in from the top and the series of
iterations in the next cycle are initiated. This process is repeated for many cycles until
the core reaches a steady state value for k-effective. A true equilibrium core reaches
steady state operation with minimal excess reactivity.
-19-
2.1.1. DATA.dat
The DATA file specifies all the material properties, composition and dimensions
of the fuel pebbles and their constitutive fuel particles.
Two main types of fuel are
defined in this file, the first being the start up fuel which consists of half fresh full
enrichment fuel pebbles and half dummy graphite pebbles.
The second type of fuel
consists entirely of fresh, full enrichment fuel pebbles to be inserted after the PBMR core
is filled with the startup mix.
The fuel dimensions are typical of many PBMR designs currently under
consideration. The graphite matrix in which the TRISO fuel particles are suspended was
set to have a 5 cm diameter and was surrounded by a 0.5 cm thick graphite layer. The
density of both the matrix and outer layer was set to 1.75 g/cm 3 . The individual fuel
particles are also defined in this file. The diameter of the U0 2 fuel kernel was defined as
0.5 mm, the thickness of the IPyC layer was set at 0.04mm, the SiC layer at 0.035 mm
and the OPyC layer at 0.04mm. The respective density of these layers, starting from the
UO 2 kernel and moving outwards, is 10.40 g/cm 3, 1.90 g/cm 3, 3.18 g/cm 3 and 1.90 g/cm 3 .
Table 1 summarizes these properties of the fuel used in the PBMR-400 design.
-20-
Table 1 : PBMR Fuel Pebble Properties
Graphite Matrix Diameter
Graphite Matrix Density
Outer Graphite Layer Thickness
Outer Graphite Layer Density
Fuel Kernel Diameter
Fuel Kernel Density
Porous Buffer Thickness
Porous Buffer Density
IPyC Thickness
5 cm
1.75 g/cm 3
0.5 cm
1.75 g/cm 3
500 jim
10.40 g/cm 3
95 jLm
1.05 g/cm 3
40 ltm
IPyC Density
1.90 g/cm 3
SiC Thickness
35 jm
SiC Density
OPyC Thickness
OPyC Density
3.18 g/cm 3
40 jim
1.90 g/cm 3
2.1.2. BIRGIT.dat
The BIRGIT files define the geometric model of the reactor, including fuel region
and reflectors, as well as the flow of fuel pebbles through the core. The flow of fuel is
defined by channels. The axial and radial positions for multiple points along the edges of
each of these channels are used to model the flow of fuel. These channels are then
divided into a certain number of layers, specified by the user, according to the velocities
of the pebbles in one channel relative to the others.
A roughly parabolic velocity
distribution is assumed in this study, the pebbles moving fastest in the center and slowest
nearest to the outer reflector. In total the core was divided into six fuel channels, the first
and second containing 13 layers, the third 14 layers, the fourth 16 layers, the fifth 18
-21-
layers and the last channel containing 22 layers. The increase in the number of layers
reflected the speed at which the pebbles move through each channel. Each of these layers
are then broken up into 6 batches of equal volume. These batches contain information
about the differing stages of fuel burnup as fuel passes through the core multiple times.
The assumption on the number of batches is derived from the number of passes required
to achieve the desired burnup - in this case 6 passes through the core. Shown on Figure 4
is a graphic of the VSOP modeling of the core with its 6 channels, layers and batches
within each layer.
VSOP Channels and Layers
E
0
O
U)
ox
0
20
40
60
80
100
120
140
160
Radial Position (cm.)
Figure 4 : A 2-D, R-Z representation of the core channels and layers in VSOP94.
The geometry of the core in the VSOP reference model is modified such that the
shape of the fuel channels is kept constant.
- 22 -
This is done by multiplying the radial
position of the points defining the channel edges by the fraction of the new radius of the
core over the previous radius. For example, if the channels were defined previously for a
core with a fuel zone radius of 155 cm and the next radius to be tested is 145 cm, then the
radial positions defining the channel edges need to be multiplied by a fraction of 145 over
155. In a similar manner the thickness of the outer reflector is defined by a set of radial
meshes, which can be modified in a similar fashion as the fuel zone radius.
2.1.3. VSOP.dat
The VSOP file defines the fuel management scheme of the PBMR, meaning that
the file dictates how the top and bottom layers of each channel are dealt with after each
time step VSOP 94 evaluates. In this study, the same multi-recycle scheme is taken as
the PBMR 400MW design calls for. This scheme calls for the fuel pebbles to be passed
through the reactor 6 times over the span of 3 years, leading to an average time of 6
months per pass. To accomplish this, all the layers in every channel were divided up into
6 batches. Each batch is able to store information for fuel at a different state of burnup.
This is implemented such that the first batch contains fuel on its first pass through the
core, essentially fresh fuel, the second batch contains fuel on its second pass and so on
and so forth for the rest of the batches. Therefore the sixth batch contains fuel on its last
pass through the core. At the end every time step is evaluated, once all flux and burnup
calculations have been completed, all the batches within each layer are stepped down in
their respective channels to the next layer location. Therefore, all the batches in the first
layer of the first channel are moved down to the second layer of the same channel, the
second layer batches are moved to the third and so on. This movement of fuel is applied
up until the last layer of each channel, the bottom of the core.
-23-
At the bottom of the core, the first batch from each bottom layer moves to the first
of six temporary storage boxes, the second set of batches to the second and so on. This
means that all of the first batches from the last layer of each channel, fuel that has passed
once through the core, are placed together into the same storage box. All of the second
batches in the bottom layers for each channel are placed together in the second storage
box. This process is repeated for the rest of the batches at the bottom of the core as well.
When placed into these storage boxes, the varying degrees of burnup experienced
through movement of fuel in the 6 channels are averaged out into a homogenous material
for each box.
This process mixes all fuel exiting the core which has already passed
through the core the same number of times. Therefore all fuel exiting the core after
passing through once are placed inside the first storage box and mixed. The same process
occurs for all fuel leaving the core that has passed through twice, three times, and so on
until fuel which has passed through the core six times is placed into the sixth storage box.
The upper half of Figure 5 below shows this process for all batch 1 fuel, fuel exiting the
core after its first pass.
Last Layer of Each Channel
Batch 1
Batch 1
Batch 1
Cycle n
Batches Mixed Together
Storage Box 1
Cycle n+1
Batch 2
Batch 2
Batch 2
First Layer of Each Channel
Figure 5 : Diagram of VSOP94 fuel management.
- 24 -
When the fuel in the storage boxes is homogenized, the individual information of
each batch placed into these storage boxes is lost. This is equivalent to mixing the fuel
before placement back in through the top of the core. Once homogenized, all fuel within
the same storage box has the same average burnup.
For reinsertion of fuel into the core, the fuel from the first storage box placed into
the second batch position in each top layer according to each batches' respective volume
as seen in the lower half of Figure 5. This ensures that the same volume of fuel exiting
each channel is replaced. The same process is applied to the second, third, fourth and
fifth storage boxes. The fuel from the sixth storage box, though, is placed into spent fuel
storage. In this way, fuel is removed after it has passed through the reactor six times as is
desired. The first batch for each top layer is filled with fresh fuel. Once the fuel is
reinserted into their respective batches within the top layer of each channel, their
individual burnups are followed as they continue down through the core until they are
placed into storage boxes when they exit the core again. The only parameter remaining
to be defined is the length of the time step, which is chosen such that after 6 passes
through the reactor the residence time of the fuel is set at 3 years.
A slightly different scheme was used to model reactor startup. At the beginning
of the program, all layers of the core are filled with a mix of half, fully enriched fuel
pebbles and half graphite pebbles. As the batches of each layer are moved down through
the reactor, the first batch within each of the top layers is filled with the second type of
fuel, fully enriched fuel pebbles with not mix of graphite pebbles, while the 5 batches
below continue to be filled with fresh fuel of the first type. Therefore, in this startup
-25-
phase, no recycling of fuel occurs. This is applied to the PBMR until the first batch of
the second fuel type reaches the last layer of the sixth channel.
Once the second type of fuel, carried down in the first batch of each layer, reaches
the bottom of the core, the fuel management transitions to the scheme previously
discussed for steady state operation.
2.2.
Approaching the Problem
In order to design an optimized, equilibrium PBMR core small enough to be
transported by rail car, many different core design needed to be tested.
The first
objective was to model the PBMR 400 MWth core based on the information of the current
design by which other design could be compared. Next, it was necessary to determine
whether a core of such smaller size than the PBMR 400 MWth design could reach
criticality at a power rating of 250 MWth.
To begin the analysis of these designs, a scoping analysis which only included an
outer reflector present was done. The maximum core dimension including reflectors was
limited to a 185 cm. radius. These designs were tested at three powers, 150 MWth, 200
MWth and 250 MWth, and using two different fuels, one 10% enriched and the other
12.5%. Every design was tested for the same fuel management scheme, 6 passes through
the core over a 3 year period before discarding occurred. K-effective, power peaking
factors, peak pebble temperatures, RPV fast fluences and fuel burnup, were obtained
directly from the VSOP output or calculated from the output and then compared with
those values found for the PBMR 400 MWth design to determine any design candidates.
Another scoping analysis including central reflectors into the design of the core
was conducted to determine if performance was enhanced with their inclusion. This was
- 26 -
done by placing a 50 cm radius central dynamic reflector in a core, initially with a 10 cm
outer reflector, for a direct comparison with the 165 cm. fuel zone radius and a 20 cm
thick outer reflector design. Both designs contain approximately an equivalent amount of
reflector material and fuel pebbles.
Once a design which matched the PBMR 400MWth standard in performance was
found, the necessary steps were taken to form an equilibrium core at or near criticality.
This was done either by mixing a certain fraction of graphite pebbles into the fuel or, as it
is later explained, by including a central reflector.
2.3.
Implementation
The three main input files described in the previous section, initially created from
a previous VSOP94 user, were modified to reflect typical values of a PBMR design along
with the new dimensions of the reactor 10. The general method used was to run VSOP94
for several possible core geometries at a fixed power, initially 250 MW, and a fixed
enrichment, initially 10% with a 4.3 meter outer vessel constraint. This limited the actual
core dimension to a 1.85 meter radius available for those three main core regions central, core and outer reflector. First calculations were done with only an outer reflector
and then a second set were conducted with a 50 cm inner dynamic reflector added, as
discussed in the previous section.
In order to find an optimized core design at each desired power and enrichment,
the first fuel zone radius tested was set to 175 cm, no central reflector and the outer
reflector thickness set to 50 cm to test the sensitivity of k-effective to the reflector
dimension. Once the program was run for this geometry, the output from the program
-27 -
was saved and the thickness of the outer reflector was decreased by 10 cm for each
proceeding run until reaching the outer reflector reached a thickness of 10 cm. After
reaching this lower limit on the reflector size, the fuel zone radius was decreased by 10
cm and the same reflector reductions from an initial thickness of 50 cm were made again.
This process was repeated until the fuel zone radius reached 125 cm, at which point the
outer reflector thickness was started at the thickness corresponding to a sum of fuel zone
radius and reflector thickness corresponding to 185 cm. At each fuel zone radius, the
calculations for all possible reflector thicknesses would only be stopped prematurely if
the neutron multiplication factor in the reactor's equilibrium state decreased significantly
below unity. All designs tested according to this process are shown below in Table 2.
Table 2 : Tested Core Configurations - 250 MWth Core, Outer Reflector Only
Fuel Radius
175 cm
165 cm
155 cm
145 cm
135 cm
Tested
125 cm
115 cm
10 cm
10 cm
Outer
20 cm
20 cm
20 cm
Reflector
30 cm
30 cm
30 cm
Thicknesses
40 cm
40 cm
40 cm
50 cm
50 cm
50 cm
60 cm
60 cm
70 cm
* Green - Criticalat 250 MWth using both 10% and 12.5% enrichedfuel
Yellow - Criticalat 250 MWth only using 12.5% enrichedfuel
Since it was found that the most favorable core designs occurred using all
possible space within the 185 cm radius constraint, all further VSOP runs were conducted
-28-
using only designs which used the entire available space. Therefore, for all core designs
tested at 200 MWth and 150 MWth with only an outer reflector, only designs in which the
fuel zone radius and outer reflector thickness summed to the 185 cm limit were used.
The various configuration tested can be seen below in Table 3.
Table 3 : Tested Core Configurations - All other core designs
FZR*
105 cm
95 cm.
ORT*
80 cm
90 cm.
* ORT - Outer Reflector Thickness, FZR - Fuel Zone Radius
Green - Criticalat 200 and 150 MWth using 12.5% enrichedfuel
Yellow - Criticalat only 150 MWth using 12.5% enrichedfuel
The second series of cases, in which a 50 cm inner reflector was added, were run
with designs that filled up the total amount of space available under the geometric
constraint as well. This means that when the outer radius of the fuel zone was decreased,
the extra space left over was filled in by the outer reflector. Similar to the first set of
VSOP runs, the outer radius of the fuel zone was decreased from 175 cm by 10 cm steps
until dropping below criticality. All possible designs were run for a reactor operating at
250MWth using 10% and 12.5% enriched fuel.
For every single case, the fuel management scheme was maintained at 6 passes
over a 3 year period until fuel was removed from the core. The goal of this was to further
match the scheme of the PBMR 400MWth design so that a direct comparison of
performance could be maintained while only the core geometry, enrichment and power
was varied.
-29-
2.4.
Calculating Peak Pebble Temperature
Since VSOP94 does not explicitly calculate the peak pebble temperature, instead
given the peak pebble power as its output, the heat equation must be solved for a fuel
pebble being driven to this peak power. A list of conservative assumptions was compiled
with which the heat equation could be solved for a fuel pebble and the peak temperature
calculated.
The first assumption was that the helium coolant surrounding the pebble
driven at the highest power would be 900C. A second assumption was made that the
power at which the pebble was being driven was uniformly distributed over the volume
of the pebble containing the TRISO fuel particles. The next assumption was that there
was an adiabatic boundary condition set upon the center of the pebble due to radial
symmetry. The last assumption was that the thermal conductivity of the fuel pebble did
not have any radial dependence. These assumptions allow the heat equation, as detailed
below, to be solved analytically.
kV2 T =-q.' which becomes
d (q,
(+r2
11
dr
r 2 dr
where k is the thermal conductivity of the pebble and q"' is the uniform heat
generation rate in the pebble, which is calculated by dividing the peak pebble power
generated by VSOP by the volume of the TRISO fuel particle region. Solving this
equation for the geometry of the fuel pebble yields the following equation for the peak
pebble temperature.
1
T~ak~1
= Peak
T Peak
peak
-30-
4rf2hHe
+
(1
4kc r
1
-
ro
+1T~
+
8kcr, )
T
In the above equation Ppeak refers to the peak pebble power, THe refers to the
temperature of the helium coolant surrounding the pebble set at 900C, ri and ro refer to
the inner and outer radius of the fuel pebble which are 2.5 cm and 3 cm respectively and
kc refers to the thermal conductivity of graphite in the pebble which is set at a
conservative value of 18 W/mK, equivalent to the thermal conductivity of graphite
subjected to a fluence of approximately 2.5x1021 n/(cm 2).
hHe, the heat transfer
coefficient of Helium in a pebble bed, was calculated using the following empirical
formula:
Nu = 1.27
NuPr0.3 3 Re0.36
1.18
+0.033
0. 03
.5Re0.86
1.07
=
hedp
kHe
where Pr is the defined as the product of viscosity and heat capacity of Helium
divided by its thermal conductivity, e is defined as the porosity which is set at .39, and
Re is defined as the product of the mass flow rate of Helium and the pebble diameter
divided by the product of cross sectional area of the core and the viscosity of Helium 8.
The mass flow rate can be found using the following equation for heat balance
QCore
= rhcp (Tout - Tin )
in which Qcore is the total thermal power produced by the core, c, is the heat capacity of
Helium at constant pressure, 5195 J/kgK, and Ti and Tout are the inlet and outlet
temperatures set to 5000 C and 9000 C, respectively 8. Calculations for the mass flow rates
for each power rating can be found in Table 4 below.
-31 -
Table 4 : Mass flow rates for each core power tested
These set of equations allow the peak pebble temperature to be calculated with all
the assumed properties provided to VSOP and the peak pebble power calculated for all of
the core designs evaluated. This analysis does not include radiative heat removal, which
may further reduce the peak pebble temperature in all cases.
Since the thermal
conductivity of graphite was taken to be extremely conservative, representative of
graphite at high fluences, this may also unnecessarily increase the peak temperature,
especially for cases in which fresh fuel is being driven to the peak pebble power. If this
analysis fails, directly comparing the peak pebble powers calculated with those of the
PBMR 400 MWth design is sufficient.
3. Results and Analysis
The results of the VSOP runs have been separated out in this section by three
different design parameters: geometry, power rating and enrichment. Geometry covers
the arrangement of reflectors and fuel within the core, distinguishing between whether
the core has an outer reflector or inner reflector. The inner reflector cases were only
evaluated along the design constraint, the sum of all constituents' thicknesses (inner
reflector, fuel zone and outer reflector) set equal to 185 cm, since it was found in the
outer reflector only case that the best reactor performance lay on this line. Within these
two categories, the power rating and enrichments were varied due to issues minimizing
power peaking factors. Three different power ratings were used: the original 250 MWth,
- 32 -
then 200 MWth and 150 MWth. At each of these powers, two different enrichments were
used: the original 10% and new 12.5% enriched fuel. All of the following sections detail
the results and analysis of the equilibrium cores established for these designs.
3.1.
PBMR 400 MWth Performance
The PBMR 400 MWth design was modeled in VSOP94 with a central reflector 2
meters in diameter, a fuel annulus 0.85 meters thick and an outer reflector 1 meter thick.
The enrichment of the fuel used was approximated as 10%. Fuel pebbles were passed
through the core 6 times over the course of 3 years, as specified for this design. The solid
graphite central reflector was modeled as a dynamic central reflector with the packing
fraction set to 0.95 instead of 0.61 to model a solid reflector. This central reflector was
formed in channel 1, while channels 2 through 6 defined the flow of fuel pebbles through
the core. A two meter thick bottom reflector and a 1 meter thick top reflector were
placed into the model as well. The total height of the pebble bed was set at 11 meters.
The performance of this design, as calculated using this VSOP94 model, is
summarized in the Table 5 below.
-33-
Table 5 : Performance of the PBMR 400MWth from the VSOP94 Model Output
Parameter
Performance
k-effective
1.0180
Number of Fuel Pebbles
452,000
Number of Graphite Pebbles
0
VSOP Power Peaking Factor
9.89
Peak Pebble Power
6.48 kW
Peak Pebble Temperature
1715.6 0C
Core Edge Fast Fluence*
4.32x10 22 n/cm2
Fuel Burnup
87.7 GWd/T
* Fast fluence occurring over a 40 year reactor lifetime.
From this data, it is clearly seen that excess reactivity has been minimized and
that a fuel burnup of near 90 GWd/T, as specified by the PBMR design, is achieved. A
few troubling observations were made, though, while reviewing this data in terms of
interpreting the results. The VSOP displayed power peaking factor and calculated peak
pebble temperature are extremely high for a reactor based on these power peaking factors.
The extremely high peak pebble temperature can also be explained by the fact that overly
conservative graphite thermal conductivity and surrounding coolant temperature values
were used in the analysis of the peak temperature. In addition to this, any radiative heat
removal was neglected in the current temperature analysis, thus removing a possibly
significant source of heat removal.
The power peaking factor calculated by VSOP94 is done in the following manner.
The fluxes in the core are calculated by homogenizing the 6 batches of each layer into
- 34 -
one material. Once the relative fluxes are found, the power is used to determine the
actual magnitude of the fluxes in each layer. The flux for every layer is thus calculated,
and once finished, is applied to each batch separately within each layer. This means that
235
batches with higher burnup and therefore less
Will contribute less power than fresh
U
fuel on its first pass through the core. This further suggests that the pebble driven to the
peak power has not been subjected to a high fluence, therefore resulting in a higher
thermal conductivity and lowering peak temperature according to Figure 6 below.
1
I
St
-
---- -
I
jX
X
I
I
1
,
I
I
i I
I
I
i
4 -- - -
i4
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I
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-
i
r
i
i
i
i-
i
calcuate te
calculate
4 i
I
4
these
power
power peaking
factors.
These
I
I
relatriv------powers
o
p
relative
i
t
peaking
To
powers
i4i
I
4
Si i
4
I
t
4
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iI I
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This
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that
t
i
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i
I
t
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f
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the
usual
--exceedingly
are
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i
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method,
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i
-35 -
PBMR 400 MWth design, all relative powers have been averaged by layer and plotted
according to their position in each channel.
3.5
3
Channel 2
Channel 3
- Channel 4
- Channel 5
Channel 6
-o 2.5
0.
0
2
.! 1.5
0
1
0.5
0
0
200
400
600
800
1000
1200
Axial Distance from Top of Core (cm.)
Figure 7 : Relative power distributions in the PBMR 400 MWth VSOP94 model.
This shows that the actual power peaking factor in the core is approximately 3.7,
rather than the 9.89 value given in the output, which is more commonly used to
determine the peak pebble power than the VSOP power peaking factors. Figure 7 also
further supports the assumption that the temperature of the coolant surrounding the
pebble driven to the peak power is much cooler, since the peak in the power distribution
occurs much closer to the coolant inlet. Since, all other things remaining constant, the
analysis contains the correct dependences on peak pebble power, mass flow rate, and core
geometry, the peak temperature found for this design, -1715 0 C, will be used as a metric
of performance for other tested designs.
-36-
A more in-depth temperature analysis was conducted using the relative power
distributions from the VSOP output. This in-depth analysis approximate the PBMR core
as one single channel with a relative power distribution the same as Channel 2, another
conservative assumption. Next, the linear and volumetric power generation rates were
taken to have the same shape as the relative power distribution of Channel 2. This was
then used to calculate both the temperature of the coolant and the temperature at the
center of a fuel pebble in the following way.
The coolant temperature was calculated by using the steady state energy equation
below:
ri
dz
= q'(z) which, following integration, becomes THe (z) - Ti,,
1 q'(z)dz 11
mcp o
As stated before, the shape of q'(z) was taken to be the same as the relative power
distribution for Channel 2 and the integration was carried out using a basic Riemann sum
approximation. The resulting function was normalized by the integral along the length of
the core so that the final temperature distribution of the coolant varied from 500oC to
900oC as would be expected. This is summarized in the equation below.
Sq'(z)dz
T
(z) - Tn =-(4oo
= (4000C) °L0
THe(Z)-I
I q'(z)dz
0
To calculate the temperature in the center of a fuel pebble at any position along
the axis of the core, the volumetric power generation distribution was calculated by
multiplying the relative power distribution of Channel 2 by the fuel averaged volumetric
power generation. This fuel averaged quantity was used because the power is not spread
-37-
evenly over the whole core since only 61% of the volume of the core is composed of
pebbles. Further, only a fraction of the volume in a fuel pebble generates power due to
the presence of the .5 cm thick graphite coating. For the PBMR-400, the fuel averaged
3
volumetric power generation rate was found to be -13.54 MW/m . Once all of the
relative powers in Channel 2 were multiplied by this quantity, the resulting values were
multiplied by the volume of the power generating region in a fuel pebble to determine the
peak pebble power at all axial positions in the core. These numbers were then used in the
same heat conduction and convection analysis discussed in Section 2.4. The results of
this analysis for the PBMR-400 design are shown in Figure 8.
The peak pebble
0
temperature calculated using this method is 1107 0C, well below the 1200 C upper limit.
Axial Temperature Profiles for PBMR-400
1200
00.
11
1100
-
Coolant Temperature (Interpolation)
Temperature (Data)
* Coolant
............................ --..n. .
Pebble Temperature (Interpolation)
-Center
F Center Pebble Temperature (Data)
500-
0
100
200
300
400
500
600
700
800
900
1000
1100
Axial Position Top to Bottom (cm)
Figure 8: Coolant and Peak Pebble Axial Temperature Profile for the PBMR-400
The PBMR neutronics-thermal hydraulics coupled steady state benchmark
predicts a temperature of 1042 0 C, which shows that the heat transfer analysis used is
-38-
conservative 9. In this thesis, we will however be consistent in comparative analysis of
these results despite the overly conservative peak temperature calculation.
Since it has been shown that the PBMR 400 MWth already satisfies the 1200 0 C
upper limit on peak temperature, new designs will be compared directly to the PBMR
400 MWth peak temperature calculated directly from the VSOP peak pebble power output,
1715 0C, for simplicity.
3.2.
Outer Reflector Only Scoping Analysis
Core designs containing only an outer reflector were first considered to determine
their effectiveness in reducing power peaking factors, edge fast fluences and satisfying
the "1200 0 C" upper limit on the peak pebble temperature. If these parameters are not
able to perform up to the PBMR 400 MWth design including whether or not the core is
able to achieve criticality, then alternative core configurations will be considered,
primarily those which include a central dynamic reflector. Inclusion of this into the core
should, in theory, reduce radial peaking factors and decrease the total power peaking
factor
3.2.1. 250 MW Design
A 250 MWth core design which fits within an RPV small enough to be transported
by railcar is the overarching goal of this study. If power peaking factors do not achieve
levels comparable to the PBMR 400MWth design, then additional core designs will be
tested, in particular, those which include an inner reflector.
-39-
3.2.1.1. K-effective
Using the same fuel enrichment that the PBMR 400MWth design uses, 10%
2 35U,
and no graphite pebbles mixed in with the fuel, the 250 MWth reactor yielded somewhat
encouraging results. As seen in the graph below of k-effective for this reactor, criticality
can be easily achieved. Critical core configurations can be attained using fuel zone radii
Unfortunately, concerns arose about
varying from 175 cm all the way to 145 cm.
whether a reflector less than 50 cm thick would fail mechanically, especially with the
inclusion of control rods in the reflector. Therefore it would be favorable to have a
design which could be made critical for a design with a 50 cm thick outer reflector and a
135 cm fuel zone radius. Using only an outer reflector with 10% enriched fuel, this
particular design was unable to reach criticality, having a k-effective of roughly 0.88. It
was postulated, though, that inserting additional reflector material into the center of the
core would be able to increase reactivity and possibly create a critical core for this case.
40
K-effective - 10% Enriched, 250 MWth, Outer Reflector Only
I
I
I
E
) 30-
K>1.25
1.25>K>1.20
1.20>K>1.15
i .15>K>1.10
.10>K>1.05
"1
1.05>K>1.00
K<1.00
-
o
"320
0 15
145
150
155
160
15
170
175
Fuel Zone Radius (cm.)
Figure 9 :K-effective for a 10% enriched core operating at 250 MWth without an
inner reflector
-40 -
In an effort to make the 250 MW design work without need for an internal
reflector, the fuel enrichment was increased to 12.5% and the VSOP program run again
for the different core configurations. These results can be seen in Figure 10.
K-effective - 12.5% Enriched, 250 MWth, Outer Reflector Only
60
SK>1.35
- 1.35>K>1.30
55
~1.30>K>1.25
.
K<1.00
1.20>K>.15
2,
O
15
1 25
130
135
140
145
150
100
155
165
170
175
Fuel Zone Radius (cm.)
Figure 10: K-effective for a 12.5% enriched core operating at 250 MWth without an
inner reflector
At this higher enrichment, the number of possible core configurations able to
achieve criticality increases substantially. Critical cores vary from a fuel zone radius of
175 cm all the way to almost 125 cm. At this enrichment, a core with a 50 cm outer
reflector thickness could become critical, negating any need of an inner reflector to
establish a critical core for this design. If power peaking factors become an issue in the
design, though, relative to the PBMR 400 MWth design, including an inner reflector into
the core may be able to reduce these factors.
This will be discussed further in Section
3.3.
-410
An equilibrium core is found for a core design with a fuel zone radius of
126.5 cm
and an outer reflector thickness of 58.5 cm. This still satisfies the 50
cm lower limit on
the outer reflector and achieves a k-effective of 1.007 in the process.
Although no
corresponding equilibrium core can satisfy the reflector thickness constraint
using lower
enriched fuel at this power, the core parameter of this 12.5% enriched
design will be
compared to the PBMR 400 MWth design.
3.2.1.2. Power Peaking Factor
Just as the K-effective results for the 10% enriched fuel designs
were not as
favorable as those for the 12.5% enriched cores, comparing the power
peaking factors
seen in Figure 11 and Figure 12 suggest that using higher enriched
fuel is favorable.
Most of the peaking factors seen in both graphs, though, are still below
the 9.89 VSOP
value calculated for the PBMR 400 MWth design.
Power Peaking Factors - 10% Enriched, 250 MWth, Outer Reflector Only
40
PPF>10
10>PPF>9
9>PPF>8
8>PPF>7
7>PPF>6
36
o
0 -o
6>PPF>5
PPF<5
25
20
0 15is
145
150
155
160
Fuel Zone Radius (cm.)
1M5
170
175
Figure 11 :Power peaking factors for a 10% enriched
core operating at 250 MWth.
-42-
In the graph above, the power peaking factor decreases as the outer reflector
thickness increases at any fixed fuel zone radius. This is what would be expected since
the presence of light atomic mass material, in this case carbon, has the effect of reflecting
the neutrons back towards the core. This reduces leakage from the core and in turn
reduces the current at the interface between the fuel zone and the reflector. Since the
neutron current is directly proportional to the gradient of the flux, a decrease in the
current produces a decrease in the rate at which the flux drops near this interface. This
causes the radial flux distribution to level off, decreasing the ratio of the peak radial flux
to the average radial flux, which is the radial power peaking factor. For very large
thicknesses, this effect begins to level off because at some point adding more material
will cause more neutrons to be absorbed than scattered back to the core.
Just as well, at a fixed reflector thickness, the power peaking factor decreases as
the fuel zone radius increases.
This is simply due to the additional volume of fuel
introduced into the core as the fuel zone increases in size. The additional fuel reduces the
total flux necessary to achieve the same overall power and in turn reduces the average
burnup experienced by the fuel as it moves axially through the core. Because of this, the
difference in the average enrichment of fuel entering and exiting the core will decrease
and cause the axial power peaking factor to drop.
-43 -
Power Peaking Factors - 12.5% Enriched, 250 MWth, Outer Reflector Only
E o50
U)
Un 45
U
C
40
r.
35
0
a30
U)
CC 25
o0
145
150
155
Fuel Zone Radius (cm.)
Figure 12 : Power peaking factors for the 12.5% enriched fuel reactor operating at
250 MW.
While the 135 cm fuel zone radius and 50 cm thick outer reflector design is
unable to attain criticality using 10% enriched fuel, using 12.5% enriched fuel, this
design is able to both achieve criticality and operate at well below the power peaking
factors seen in the PBMR 400 MWth design. Steps still need to be taken, though, in order
to reach a true equilibrium core with very little excess reactivity for this specific design.
The properties of this design will likely change in the process of achieving an equilibrium
core and will be further discussed in Section 3.4.
Without any further modification to the design, a core with a fuel zone radius of
126.5 and an outer reflector thickness of 58.5 cm. can achieve criticality. The power
peaking factors of this design are found to be 9.22, a slight improvement upon the 9.89
value seen in the PBMR 400 MWth design.
-44 -
3.2.1.3. Peak Temperature
The peak temperature within the PBMR must be kept at a temperature at or below
the PBMR-400 metric temperature during steady state operation in order to satisfy the
safety analysis requirements of the plant. Based on the discussion of peak temperature in
0
Section 3.1, the PBMR-400 metric for our analysis is 1715 C for comparative purposes.
Peak Pebble Temperature - 10% Enriched, 250 MWth, Outer Reflector Only
T>1900
1900>T>1800
1800>T>1700
1700>T>1600
1600>T>1500
1500>T>1400
36-
30
1400>T>1300
T<1300
C)
0,
O 15
45
150
155
160
165
170
175
Fuel Zone Radius (cm.)
Figure 13 :Peak pebble temperature for a 10% enriched core operating at 250
MWth.
For the 10% enriched fuel case in Figure 13, cores with a fuel zone radius from
175 cm to 145 cm fall below the PBMR-400 temperature. On the other hand, when
12.5% enriched fuel is used, any critical designs with a fuel zone radius greater than 130
cm violate this limit. This places some concern as to whether the 135 cm fuel zone radius
design with the 50 cm thick outer reflector will be able to satisfy this upper limit as well
once measures are taken to reduce excess reactivity.
The design being considered thus far for this power rating does suffer from a
substantial increase in the power peaking temperature relative to the PBMR 400 MWth
-45-
design. A core with a 126.5 cm fuel zone radius and a 58.5 cm outer reflector
thickness
is calculated to have a peak pebble temperature of 2050.70 C, more than a 300 0
C increase
upon the 1715 0 C achieved in the PBMR 400 MWth core can be seen in Figure
14 below.
Peak Pebble Temperature (oC)- 12.5% Enriched, 250 MWth, Outer Reflector
Only
T>1800
55-
- 1800>T>1500
1500>T>1300
E 5o
1300>T>1200
cn 45
45
T<1200
a-
40 -
35
0
30CC25
"20
25 130
135
140
145
150
155
100
165
170
175
Fuel Zone Radius (cm.)
Figure 14 :Peak pebble temperature for the 12.5% enriched core operating
at 250
MWth.
3.2.1.4. RPV Fast Fluence
The fast fluence, or total number of fast neutrons incident upon one square
centimeter of the RPV over an elapsed period of time, is extremely
important in
determining the lifetime of the reactor.
This is because the interaction of the fast
neutrons with the RPV material causes the ductile-to-brittle transition
temperature
(DBTT) to rise. If a metal's temperature reaches or drops below its DBTT it will
lose its
malleable properties and become more susceptible to cracking due to pressurized
thermal
shock (PTS).
PTS occurs during planned and unplanned shutdowns: essentially
whenever the temperature of the RPV drops quickly, bringing the temperature
closer to
the DBTT.
-46 -
The fast fluences at the edge of the core were calculated for all core
configurations and for a reactor lifetime of 40 years. These values are assumed to be
representative of the fast fluences the RPV will be subjected to over the same period of
time since there is little space between the outer diameter of the core and the inner
diameter of the RPV. As can be seen in Figure 15, the fast fluence is only weakly
dependent on the thickness of the outer reflector, especially within the bounds of the
geometric constraints.
The fast fluence is largely dependent on the fuel zone radius
because the total flux which the reactor needs to be operated at is almost wholly
dependent on the total volume of fuel in the core. The fast flux will increase with the
total flux as the volume of fuel in the core decreases, leading to an increase in the fast
flux at the edge of the core as this occurs. The slight decreases seen in the fast fluence
when the outer reflector thickness is increased is due to an increase in slowing down of
fast neutrons. With more carbon to scatter with, more of the neutrons slow down to
epithermal and thermal energies, leading to an overall decrease in the population of fast
neutrons.
-47 -
RPV Fast Fluence - 10% Enriched, 250 MWth, Outer Reflector Only
FF>3.0
3.0>FF>2.5
2.5>FF>2.0
2.0>FF>1.5
1.5>FF>1.0
FF<1.0
35s
o
vn
C
3o
25
o
a:
Os
45
150
155
160
165
170
175
Fuel Zone Radius (cm.)
Figure 15 : RPV fast fluence for the 10% enriched core operating at 250 MWth.
Relative to the PBMR 400 MWth design, which had an operating core edge fast
fluence of 4.32x1022 n/cm 2 over a 40 year time period, it is easily seen from Figure 15
that all critical cores are able to produce lower RPV fast fluences. The results from the
12.5% enriched fuel design, seen in Figure 16, show that some designs, again those with
a fuel zone radius below 130 cm do not perform as well compared to the PBMR 400
MWth design with respect to RPV fast fluence. Since the 135 cm fuel zone radius design
lies particularly close to this value, there is a concern that once the necessary measures
are taken to reduce excess reactivity, the fast fluence would increase.
Since most
methods considered to reduce excess reactivity involve reducing the volume of fuel in the
core, fluxes would increase and possibly push the RPV fast fluence above 4.32x1022
n/cm 2 . These worries will be addressed in Section 3.4.
-48-
RPV Fast Fluence (x10 2 2 n/cm 2 ) - 12.5% Enriched, 250 MWth, Outer Reflector Only
FF>4
O
4>FF>3
3>FF>2
2>FF>1
55-
E so0
45
C
40
T_ 25
520
15
25
130
135
140
145
150
155
160
165
170
175
Fuel Zone Radius (cm.)
Figure 16 : RPV fast fluences for the 12.5% enriched core operating at 250 MWth.
For the equilibrium core design established using 12.5% enriched fuel, an RPV
fast fluence of 5.24x1022 n/cm 2 is found. This value is much higher than that calculated
22
for the PBMR 400 MWth design, which had a calculated RPV fast fluence of 4.32x10
n/cm 2 . This further shows the need to develop a new design which can achieve the same
performance as the PBMR 400 MWth equilibrium core but at 250 MWth and under the
geometric constraints placed on the core
3.2.1.5. Fuel Burnup
One of the major advantages of the spherical fuel element design used in these
reactors is to achieve fuel burnups much higher than those found in fuel rods in light
waters reactors. Fuel burnup essentially is the reactor equivalent of fuel efficiency. It is
defined as the amount of energy, GWd, able to be extracted from one metric ton of fuel
by the reactor. Maximizing this value not only increases efficiency, but also allows the
reactor to burn more of the waste produced from radiative capture in 238U, mostly
239Pu.
-49 -
For such high burnups as the TRISO fuel particles were designed for, the amount
of
nuclear waste produced can be reduced by burning the
239
Pu produced in the previous
passes through the reactor. Since this is all self-contained within the fuel pebble, there
is
no worry about proliferation because there is no reprocessing of spent fuel involved.
Fuel burnup is almost solely dependent on the fuel zone radius, as can be seen in
the figure below. This is because the total burnup the fuel experiences as it passes
through the core is a function of the average volumetric power generation, which depends
only on the total volume of fuel in the core since the power is fixed at 250 MWth. There
is an almost unnoticeable increase in the fuel burnup as the reflector thickness increases.
This behavior may be due to slight increases in the thermal neutron population as the
reflector size increases. More thermal neutrons would be available for both fission and
radiative capture and less fast neutrons would be available for the fast fission of 238U. In
this case, more
239Pu
would be formed and thus there would be more fissile inventory.
Fuel Burnup (GWd/T) - 10% Enriched, 250 MWth, Outer Reflector Only
40
FB>85
85>FB>80
- 80>FB>75
75>FB>70
35
3o
(D70>FB>65
a 30"
FB<65
c
) 25
10
145
150
155
160
165
170
175
Fuel Zone Radius (cm.)
Figure 17 : Fuel burnup for the 10% enriched core operating at 250 MWth.
-50-
Comparing the fuel burnups calculated for the 10% and 12.5% enriched fuel cases,
it is clearly seen that the same behaviors and almost the exact same numbers are
calculated for the overlapping core designs. This further shows exactly how the fuel
burnup is entirely dependent on the volume of fuel in the core at a constant power.
Fuel Burnup (GWd/T) - 12.5% Enriched, 250 MWth, Outer Reflector Only
o
"
I
I
FB>110
-110>FB>105
105>FB>100
55
-:
- 100>FB>95
95>FB>90
so
o
90>FB>85
45
- 85>FB>80
-40
80>FB>75
- 75>FB>70
so
70>FB>65
I30
-
t
FB<65
20
15
25
130
135
140
145
150
155
10
165
170
175
Fuel Zone Radius (cm.)
Figure 18 :Fuel burnup for the 12.5% enriched reactor operating at 250 MWth.
The fuel burnups able to be achieved by the 10% enriched fuel case are limited to
approximately 85 GWd/T, according to Figure 17. This isn't too far from the near 90
GWd/T value achieved in the PBMR 400 MWth design, but still falls slightly short of the
goal. The 12.5% enriched fuel design, though, increases the number of core designs and
in turn allows the formation of critical cores with higher burnups. In particular, the 135
cm fuel zone radius core is able to achieve a burnup of just under 100 GWd/T and still
maintaining criticality.
The promise of this design is the ability to generate higher
burnup than the PBMR 400 MWth, while achieving improved performance with respect
to peaking factors, peak pebble temperature and RPV fast fluence.
-51 -
The equilibrium core design achieved using 12.5% enriched fuel is found to
achieve a burnup of 109.9 GWd/T, over a 20 GWd/T increase upon the fuel burnup
calculated for the PBMR 400 MWth design.
3.2.1.6. Analysis
Although critical equilibrium cores are able to be established using 10% enriched
fuel, the minimum outer reflector thickness of 50 cm could not be accommodated into the
core without driving it subcritical. Therefore, without any other design modifications,
12.5% enriched fuel was instead used to establish a critical core for a design at fuel zone
radius of 135 cm and an outer reflector thickness of 50 cm.
All possible core
configurations tested which achieved criticality showed promise in performing similar to
or better than the PBMR 400 MWth design. Most of these cores, though, had very high
excess reactivities relative to that of the current PBMR core, including the 135 cm fuel
zone radius design.
Additional steps will be taken in Section 3.4. to form a true
equilibrium core to be able to make a fair comparison between this specific design and
the PBMR 400 MWth design.
The equilibrium core formed with the 12.5% enriched fuel and no further
modifications performed poorly relative to the PBMR 400 MWth design. Table 6 below
compares the various core parameters of this new design and the PBMR 400 MWth
design.
- 52 -
Table 6 : Comparison of the PBMR 400 MWth design and the 250 MWth design
Parameters
PBMR 400 MWth
250 MWth - 12.5% e.
K-effective
1.0180
1.007
9.89
9.33
Peak Pebble Temp.
1715.6 0 C
2050 0 C
RPV Fast Fluence
4.32x10 22 n/cm 2
5.24x10 22 n/cm 2
87.7 GWd/T
109.9 GWd/T
Power Max./Avg.
Fuel Burnup
3.2.2. 200 MW Design
The power was downrated to 200 MWth to see if this would allow core designs to
be able to achieve criticality using 10% enriched fuel once steady state operation is
established. Again, only an outer reflector was placed in the design to determine if any
optimal reflector size existed for the 200 MWth reactor. The second goal in decreasing
the power was to reduce the difference in enrichment between the various batches in each
layer, thereby reducing the peak batch power at which fresh fuel is driven and in turn
reducing the VSOP power peaking factor.
A reduction of the peaking factors would
likely reduce the peak pebble temperatures to values below the 17150C limit set on steady
state operation by the PBMR 400 MWth design. But since the burnup is proportional to
the power times the fuel residence time, fuel burnups will be expected to decrease from
those observed in the 250 MWth case.
-53-
3.2.2.1. K-effective
The k-effective results for the 10% enriched fuel 200 MWth designs did produce a
range of critical cores similar to that of the 250 MWth design using 12.5% enriched fuel,
once steady state operation was obtained. The possible core designs ranged from a fuel
zone radius of 175 cm down to about 130 cm. This increase in k-effective relative to the
250 MWth core using 10% enriched fuel is due to an increase in the average enrichment
of fuel in the core for a given design. At a higher power, the average enrichment inside
the core, once equilibrium is reached, is lower because the higher fluxes cause more of
the fissile content to be burned. The opposite effect occurs when power is decreased,
which causes the average enrichment to increase and k-effective to increase as well.
K-effective - 200 MWth, Outer Reflector Only
At
.I
;I
I
I
1.35
. . . . . . . ..-..
. . . . . . . . .
1.3
. . . . . . . . . . .. . . . . . . . .
1.25
.-. . . . . . . . .. . . . . . . . . .
1.2
.. . . . . . . .. . . . . . . .
1.15
. . . . . . . . . .. . . .
.. ...
1.1
1.05
.
0.gs
0.16
0
110
120
I
130
-10% Enrichment (Interpolation)
* 10% Enrichment (Data)
-12.5% Enrichment (Interpolation)
* 12.5% Enrichment (Data)
140
. I
150
I.. ..
, I ... ..
, .. . . . . . . . . . . . . .
160
170
180
Fuel Zone Radius (cm.)
Figure 19 : K-effective for the 10% and 12.5% enriched reactor designs operating at
200 MWth.
As can be seen in Figure 19 above, two cores are found that can satisfy the
minimum required thickness of the outer reflector, 50 cm, and achieve minimal excess
reactivities at steady state operation.
- 54-
Using a cubic spline interpolation with the 10% enriched fuel data, this design is
found to occur at a fuel zone radius of approximately 126.8 cm and an outer reflector
thickness of 58.2 cm. K-effective for this design is approximately 1.004. For the 12.5%
enriched fuel data, the design with minimal excess reactivity occurs at a fuel zone radius
of 114 cm and an outer reflector thickness of 71 cm. The k-effective for this design was
1.007. These two equilibrium cores will be analyzed based on their performance relative
to each other and the PBMR 400 MWth design.
3.2.2.2. Power Peaking Factor
Although k-effective increased when the power was decreased from 250 MWth to
200 MWth enriched fuel, VSOP power peaking factors were found to decrease.
All
critical cores fell well below the 9.89 VSOP power peaking factors observed in the
PBMR 400 MWth design.
-55 -
Power Peaking Factors - 200 MWth, Outer Reflector Only
7
-10%
6e.5~
\
10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
* 12.5% Enrichment (Data)
Ss5.5s
L)
Enrichment (Interpolation)
U5
" 4.5
4
o 35
a)
3
2.5
15
125
135
145
155
165
175
Fuel Zone Radius (cm.)
Figure 20 : Power peaking factors for 10% and 12.5% enriched reactor designs
operating at 200 MWth.
Again, using a cubic spline interpolation to predict the values of untested core
configurations, the power peaking factors were calculated for the two equilibrium core
designs discussed in the previous section.
For the design using a 126.8 cm fuel zone radius and a 58.2 cm thick outer
reflector with 10% enriched fuel, a power peaking factor of 7.85 was obtained. For the
12.5 % enriched fuel design, having a 114 cm fuel zone radius and a 71 cm thick outer
reflector, achieved a power peaking factor of 7.83. Both of these cores have such similar
peaking factors that this along can't be used to determine the best design. In addition,
both of these design improved significantly upon the 9.89 power peaking factor found in
the PBMR 400 MWth design.
- 56 -
3.2.2.3. Peak Temperature
The decrease in reactor power from 250 MWth to 200 MWth was able to decrease
the peak pebble temperature in all critical core designs previously tested, to the point that
the peak temperature approaches the PBMR-400 metric, 1715 0 C. The trends seen in
Figure 21 reflect those seen in the 250MWth case along the upper limit of core design
sizes; improvements upon the peak temperature, calculated with the VSOP output,
occurred as fuel zone radius increases.
Peak Pebble Temperature - 200 MWth, Outer Reflector Only
1 I
I I I
I
~
I
I
I
1 I
.................................................
. - 10% Enrichm ent (Interpolation)
* 10% Enrichment (Data)
1700
......-
1800
leoo
.....
12.5% Enrichment (Interpolation) .....
* 12.5% Enrichment (Data)
:
C,
I
I
1500
E
a 1400
1300
(L
-N 1200
. ... .. .. . . .. .. ... ..
1100
. ... ....
.... ....
5
.... ....
.... ...
125
135
145
155
165
1
Fuel Zone Radius (cm.)
Figure 21 : Peak temperature for the 10% and 12.5% enrichment reactor designs
operating at 200MWth.
Cubic spline interpolation was used again to predict the peak pebble temperature
for all untested designs. As can be seen above, most of the core designs which attained
criticality produced peak pebble temperature seen well below the 1715 0 C value obtained
from the PBMR 400 MWth VSOP94 model.
The 10% enriched fuel design which achieved minimal excess reactivity was able
to achieve improved performance with respect to the peak pebble temperature. For this
-57-
design, the peak temperature was found to be 1695°C, a slight improvement upon the
PBMR 400 MWth design.
The 12.5% enriched fuel design, though, failed to reach this goal value. The peak
pebble temperature calculated for this design was 1861 0C, more than a 1000 C increase
from the PBMR 400 MWth core. Although the current analysis of the peak temperatures
is limited, this core may still be viable and produce a steady state peak temperature below
12000 C.
Since all other material properties are held constant in the temperature
calculations, the peak pebble power is still greater relative to the PBMR 400 MWth core,
making the 10% enriched fuel design more appealing.
3.2.2.4. RPV Fast Fluence
In decreasing the power of the reactor by 50 MW, the fast fluence was able to be
reduced by 30% to almost 50% in many instances. This can be seen by comparing the
graph below of the edge fast fluence with those of the 250 MWth case in Figure 15 and
Figure 16. Even though measures can be taken to mitigate the fast fluence incident upon
the RPV, such as placing a steel shroud around the core, the configuration of the core
should be made to minimize the fast fluence if at all possible.
Since reducing the fast fluence on the RPV is so essential in maximizing the life
of the reactor and optimizing its availability to the industry the core is employed within,
finding the core design which improves upon the edge fast fluence seen in the PBMR 400
MWth core is highly favorable.
-58 -
RPV Fast Fluence - 200 MWth, Outer Reflector Only
* 10% Enrichment (Data)
"
E
3 ................................
.................................
............
c\I
2 "5
12.5 % E nric hm ent (Inte rpo latio n)
* 12.5% Enrichment (Data)
x
a
I-
1.5
0.5
?15
125
135
145
155
165
175
Fuel Zone Radius (cm.)
Figure 22 : Edge fast fluence for the 10% and 12.5% enriched reactor designs
operating at 200 MWth.
For the two designs being discussed under the 200 MWth power rating, the cubic
spline interpolation used to produce the smooth lines seen in Figure 22 is also used to
predict the RPV fast fluences values of untested designs.
For the 10% enriched fuel design, the RPV fast fluence achieved was 3.71x10 22
n/cm 2 over a 40 year time period. The fast fluence calculated for the PBMR 400 MWth
core was 4.32x10
22
n/cm 2 over the same amount of time.
So far, this design is
performing just as well to the PBMR design.
The 12.5% enriched fuel design is observed to have slightly poorer performance
with regard to the RPV fast fluence. A value of 4.58x1022 n/cm 2 was calculated for this
design. Although this is slightly higher than seen in the PBMR 400 MWth design, this
fluence is close enough to be tolerable.
-59-
3.2.2.5. Fuel Burnup
Although the decrease in power resulted in substantial improvements upon many
parameters, the average fuel burnup produced for the majority of the critical designs was
reduced. In order for an optimized design to be found, a compromise needs to be reached
between the safety of the reactor, which increases as the power decreases and the volume
of fuel in the core increases, and its overall fuel performance, which decreases under
similar circumstances.
The poorer fuel performance in the 200 MWth reactor is a direct result of the
reduced flux necessary to maintain a lower power, as opposed to the 250 MWth case.
Since the amount of time the fuel spends in the core is fixed at approximately 3 years, the
total fluence the fuel is exposed to decreases accordingly.
This is easily seen when
comparing the fuel bumup performance of the 250 MWth reactor in Figure 17 and Figure
18 to the graph below of burnup for the 200 MWth reactor. While the fuel burnup varies
from around 65 to 115 GWd/T in Figure 18, the calculated burnup for the 200 MWth
reactor ranges from 50 to 110 GWd/T.
Not only does the fuel burnup depend on the power, but also the core geometry,
which leads to a significant decrease in burnup as the fuel zone radius increases from 145
cm to 175 cm. This decrease, discussed before, is the result of the decrease in the amount
of fuel over which the power is distributed. Fluxes inside the core must be higher if there
is less fuel present in the core in order to maintain the same power. In the same way, if
more fuel is present in the core, the fluxes can be reduced. But, since the time the fuel
spends in the core is fixed, if the fluxes are reduced, the average amount of fissile
- 60 -
material left over in a fuel pebble after exiting the core increases, causing the burnup to
decrease.
Fuel Burnup - 200 MWth, Outer Reflector Only
110
1
100.....
-10%
Enrichment (Interpolation)
* 10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
- 0*........................
............
I. . ......
12.5% Enrichm ent (Data)
=-
LL
60
51
415
125
135
145
155
185
175
Fuel Zone Radius (cm.)
Figure 23 :Fuel burnup for the 10% and 12.5% enriched reactor designs operating
at 200 MWth.
For the 10% enriched core, the average fuel bumup exiting the core is calculated
to be approximately 88.4 GWd/T. This value is a slight improvement upon the 87.7
GWd/T calculated for the PBMR 400 MWth design. The 12.5% enriched fuel design
produces a significantly higher burnup than that produced by the PBMR 400 MWth. The
12.5% enriched core allows for an increase in fuel burnup up to 108.6 GWd/T, over a 20
GWd/T increase on the PBMR 400 MWth design.
3.2.2.6. Analysis
Two core designs show promise in producing a critical equilibrium core with
performance on par with or greater than that of the PBMR 400 MWth design as well as
providing enough space in the core to fit an outer reflector at least 50 cm thick. The core
-61-
using 10% enriched fuel is designed with a 126.8 cm fuel zone radius and a 58.2 cm thick
outer reflector thickness. This design is able to achieve a k-effective near unity, 1.004,
with enhanced performance in all calculated quantities used to compare this design with
the PBMR 400 MWth core. A second core using 12.5% enriched fuel formed a critical
equilibrium core with a 114 cm fuel zone radius and an outer reflector 71 cm thick. This
core was able to achieve similar performance with respect to power peaking and RPV fast
fluences relative to the PBMR 400 MWth design. Unfortunately, there was a significant
increase in the peak pebble temperature beyond that calculated for the PBMR 400 MWth
core.
While VSOP power peaking factors stayed relatively the same using both
enrichments, the peak pebble power increased in the 12.5% enriched design due to the
increase in volumetric power generation associated with the decrease in total fuel volume.
This caused the temperature to increase when using 12.5% enriched fuel instead of 10%
enriched fuel. The uncertainty of the temperature analysis, though, allows no conclusions
to be made regarding whether the increase is tolerable. Although the peak pebble power
may be higher for this design, the fuel burnup is able to be increased significantly relative
to the PBMR 400 MWth design. Table 7 below provides the various core parameters for
these designs to summarize the comparisons.
- 62 -
Table 7 : Comparison of PBMR 400 MWth design with the 200 MWth designs.
Parameters
PBMR 400 MWth
200 MWth - 10% e.
200 MWth - 12.5% e.
K-effective
1.0180
1.004
1.007
Power Max./Avg.
9.89
7.85
7.83
Peak Pebble Temp.
1715.6 0 C
1695 0 C
1861 0 C
RPV Fast Fluence
4.32x10 22n/cm 2
3.71x1022 n/cm
4.58x1022 n/cm2
87.7 GWd/T
88.4 GWd/T
108.6 GWd/T
Fuel Burnup
3.2.3. 150 MW Design
3.2.3.1. K-effective
As per the 200 MWth designs suggested, an analysis was undertaken which
decreased the power 100 MW below the target to see if further enhance of performance
could be achieved relative to the PBMR 400 MWth design. Because of this reduction in
power, the average enrichment of fuel during steady state operation for all possible core
designs increases because the total flux in the core decreases.
This leads to a total
decrease in the amount of fissile material which is burned within the fuel pebbles as they
pass through the core (that is for a specific design). Although this will cause further
reduction of the burnup achieved in all possible designs tested at 200 MWth, it allows the
core to become critical at reduced fuel zone radii. The comparison of k-effective for all
tested core designs using 10% and 12.5% enriched fuel is shown in Figure 24.
A new behavior in K-effective begins to appear in the 150 MWth core. For all
previous tested designs at higher powers, k-effective was observed to increase until the
- 63 -
slop of increasing k-effective starts to decrease. For the 150 MWth core, k-effective is
seen to reach an almost constant value when using either 10% or 12.5% enriched fuel.
These values essentially represent the value of k-effective for an "infinite" reactor, or kinfinity (infinite with respect to the neutrons interacting with the reactor). Beyond these
fuel zone radii, the neutrons within the core essentially don't notice the additional fuel
because they interact with the fuel around them before reaching it.
K-effective - 150 MWth, Outer Reflector Only
1.5
1.3-
-10%
Enrichment (Interpolation)
* 1 0 % Enrichment (Data)
Enrichment (Interpolation)
-12.5%
1. ......
o3
CD
12.5% Enrichment (Data)
L*
1
I
I
I
I
135
145
155
165
0.9
115
125
175
Fuel Zone Radius (cm.)
Figure 24 : K-effective for the 10% and 12.5% enriched reactor designs operating at
150 MWth.
Using 10% enriched fuel, a reactor operating at 150 MWth can achieve criticality
along the geometric constraint for core configurations ranging from a fuel zone radius of
175 cm to approximately 110 cm. An actual equilibrium core with minimum excess
reactivity can be formed using a fuel zone radius of 111.5 cm and an outer reflector 73.5
cm thick. K-effective for this design is approximately 1.005.
Using 12.5% enriched fuel extends the full range of operable core designs from a
fuel zone radius of 175 cm to 100 cm.
-64 -
An equilibrium core with very little excess
reactivity can be established using a fuel zone radius only 1 meter thick surrounded by an
outer reflector 85 cm thick. K-effective for this design is near 1.006.
These two designs will be compared with each other and with the PBMR 400
MWth design according to their performance
3.2.3.2. Power Peaking Factor
New behavior in the power peaking factors is also observed in the 150 MWth case
as well. For a core using 10% enriched fuel, as the fuel zone radius is reduced from 175
cm to near 162 cm, the power peaking factor decreases. After reaching 162 cm peaking
factors then begin to increase. A minimum power peaking factor 2.94 is found near a
fuel zone radius of 156.7 cm and an outer reflector thickness of 28.3 cm.
Using 12.5% enriched fuel, a minimum power peaking factor of 2.58 is found at a
fuel zone radius of 150 cm and an outer reflector thickness of 25 cm. Unfortunately for
both the 10% and 12.5% enriched fuel cores, the minimum power peaking factors occur
almost exactly where the largest excess reactivities were found in the Section 3.2.3.1.
Since establishing an equilibrium core with minimal excess reactivity, these designs are
not pursued any further, as interesting as they may seem.
-65 -
Power Peaking Factors - 150 MWth, Outer Reflector Only
7
Enrichment (Interpolation)
-10%
* 10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
* 12.5% Enrichment (Data)
o
U-
05
115
125
145
135
Fuel Zone Radius (cm.)
155
185
175
Figure 25 : Power peaking factors for the 10% and 12.5% enriched reactor designs
operating at 150 MWth.
The design which minimized excess reactivity using 10% enriched fuel was able
to achieve a power peaking factor of approximately 6.55. This is nearly 2/3 the 9.89
power peaking factor seen in the PBMR 400 MWth design. The 12.5% enriched fuel
design which reached a true equilibrium core also improved upon the PBMR 400 MWth
power peaking factors. This design achieved a peaking factor of around 6.65, again,
almost 2/3 of that observed in the PBMR 400 MWth core.
Since the power peaking
factors for both of the 150 MWth cores perform equally well here, the rest of the
parameters must be taken into account.
3.2.3.3. Peak Temperature
As opposed to the 200 MWth case where only one of the various core
configurations or fuel enrichments were able to achieve a peak pebble temperature below
temperature metric, both the 10% and 12.5% enriched fuel cores operating at
the 1715'C
LL
a
the 1715C temperature metric, both the 10% and 12.5% enriched fuel cores operating at
- 66 -
if
150 MWth are able to satisfy this condition. These equilibrium cores are able to match
not reduce the peak pebble temperature from the 1715'C value observed in the PBMR
400 MWth design.
The 10% enriched core, having a fuel zone radius of 111.5 cm and an outer
0
reflector thickness of 73.5 cm, was able to attain a peak pebble temperature of 1550 C, a
significant improvement upon that seen in the PBMR 400 MWth core.
The 12.5%
enriched equilibrium core, with a 1 meter fuel zone radius and an 85 cm thick outer
reflector, was able to satisfy the upper limit set by the PBMR 400 MWth design. The
0
peak pebble temperature produced here was 1705 C, just barely reaching the upper limit,
but still satisfying it.
Peak Pebble Temperature - 150 MWth, Outer Reflector Only
16000
-10%
..................
1500 ........
.
. 1400
Enrichment (Interpolation)
10% Enrichm ent (Data)
Enrichment (Interpolation)
-12.5%
.......
* 12.5% Enrichment (Data)
o
E
1100
a,1200
100%5
I
I
115
125
I
I
I
I
135
145
155
185
175
Fuel Zone Radius (cm.)
Figure 26 : Peak pebble temperature for the 10% and 12.5% enriched reactor
designs operating at 150 MWth.
Since neither of these equilibrium core designs violated the upper limit on
the steady state peak temperature and they matched each other in power peaking factor
- 67 -
performance, the RPV fast fluences and fuel burnups must then be taken into
consideration to determine the best design.
3.2.3.4. RPV Fast Fluence
Since the fast fluence on the RPV is so crucial in determining the lifetime of the
reactor, it is desirable to minimize this quantity as much as possible. Therefore the value
of this key parameter will be compared for the two equilibrium core designs discussed
previously. If either of the two designs provide a significant improvement relative to one
another or to the PBMR 400 MWth design, this will be highly favorable for the
corresponding design.
RPV Fast Fluence - 150 MWth, Outer Reflector Only
135
145
Fuel Zone Radius (cm.)
Figure 27 : RPV fast fluence for the 10% and 12.5% enriched reactor designs
operating at 150 MWth.
For the equilibrium core utilizing 10% enriched fuel, the RPV fast fluence
calculated was roughly 3.34x10 22 n/cm 2 over the assumed 40 year lifetime of the core.
This is a significant improvement upon the PBMR 400 MWth fast fluence of 4.32x1022
-68 -
n/cm 2 over the same time.
The 12.5% enriched core was able to achieve a modest
improvement upon the PBMR 400 MWth design's fluence. This design's fluence was
found to be 4.18x10 22 n/cm 2.
3.2.3.5. Fuel Burnup
Since the power is further down rated to 150 MWth and the residence time of the
fuel pebbles in the core remains constant at 3 years, it is expected that the fuel burnups
observed for all designs previously tested for the 200 MWth case will decrease. Indeed,
further reductions in the average fuel burnups of all these designs are seen comparing
Figure 23 with Figure 28.
The lowest possible burnup decreases from around 47.8
GWd/T in the 200 MWth case to approximately 35.7 GWd/T for the 150 MWth design.
An interesting observation was made that the average fuel burnup does not change
when the fuel enrichment is increased from 10% to 12.5% when the core design is held
constant. At first it was thought that the different power peaking factors using the two
enrichments would result in higher burnups, but this turned out not to be the case. Since
VSOP calculates the volumetric average of fuel burnup as the fuel leaves the core,
information on the highest and lowest burnups of fuel taken out of the core is lost. This
leads to a dependence solely on the reactor power and volume of fuel in the core.
-69-
Fuel Burnup - 150 MWth. Outer Reflector Only
100
-10%
Enrichment (Interpolation)
* 10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
.......... .... *.........................
12.5% Enrichm ent (D ata)
80
3:
.50-
05
115
125
135
145
155
185
175
Fuel Zone Radius (cm.)
Figure 28: Fuel burnup for the 10% and 12.5% enriched reactor designs operating
at 150 MWth.
The 10% enriched fuel equilibrium core was able to reach a fuel bumrnup of
approximately 86.2 GWd/T, slightly lower than the 87.7 GWd/T burnup achieved by the
PBMR 400 MWth design, but still very close to it. The 12.5% enriched fuel core was
able to significantly increase this burnup, though, to a value of 106.4 GWd/T. Use of the
higher enrichment fuel is able to significantly increase the bumrnup of the equilibrium core
because the difference in the enrichment of fresh fuel and used up fuel exiting the core
can be increased while still maintaining an overall average enrichment in the core similar
to that using lower enriched fuel.
3.2.3.6. Analysis
For a reactor operating at 150 MWth, two equilibrium core designs are found
which perform up to or better than the PBMR 400 MWth design. The first core utilizing
10% enriched fuel consists of a fuel zone radius of 111.5 cm and an outer reflector 73.5
- 70 -
cm thick. This design is able to significantly reduce all parameters, power peaking factor,
peak pebble temperature, and RPV fast fluence while maintaining nearly the same fuel
burnup achieved by the PBMR 400 MWth design. While this core reduced the parameters
and maintained a similar burnup, the 12.5% enriched core was able to maintain roughly
the same parameters as the PBMR 400 MWth design, but significantly increase the
achievable fuel burnup in the process.
This design consists of a fuel zone radius of
exactly 1 meter and an outer reflector 85 cm thick. This design matched almost exactly
the peak pebble temperature and RPV fast fluence of the PBMR design while achieving
nearly the same power peaking factor as the 10% enriched equilibrium core.
While
performance was matched in nearly all these areas, the fuel burnup was able to be
increased to 106.4 GWd/T, significantly higher than the 87.7 GWd/T produced with the
PBMR 400 MWth core. Table 8 below summarizes this statement.
Table 8 : Comparison of PBMR 400 MWth design with the 150 MWth designs
Parameters
PBMR 400 MWth
150 MWth - 10% e.*
150 MWth - 12.5% e.*
K-effective
1.0180
1.005
1.006
9.89
6.55
6.65
Peak Pebble Temp.
1715.6 0C
1550 0 C
1705 0C
RPV Fast Fluence
4.32x10 22 n/cm 2
3.34x10 22 n/cm2
4.18x10 22 n/cm2
87.7 GWd/T
86.2 GWd/T
106.4 GWd/T
Power Max./Avg.
Fuel Burnup
* 10% e. - 111.5 cm. fuel zone radius and a 73.5 cm. thick outer reflector
12.5% e. - 100 cm. fuel zone radius and a 85 cm. thick outer reflector
-71 -
3.3.
50 cm Inner Dynamic Reflector
Initially, only an outer reflector was included into the design of the core because
of concerns that including both an inner and outer reflector would displace too much fuel
and cause the peak pebble temperature to increase. This concern was addressed in this
analysis by comparing the performance of a reactor with a central dynamic reflector with
the data obtained for reactors with only outer reflectors.
An central reflector with a
radius of 50 cm was chosen in order to match the fuel displacement achieved when the
outer reflector thickness is increased from 10 cm to 20 cm.
This dynamic reflector
consists entirely of graphite dummy pebbles which move through the core with the rest of
the fuel. By using the same volume a 20 cm outer reflector takes up in the core and
instead applying the inner 10 cm of this to form a central reflector, the effectiveness of a
central reflector can be directly compared to that of the outer reflector. The figure below
shows a simple to-scale drawing of comparing the cross sections of these two different
designs.
- 72 -
Fuel Zone
3.3 meters
1 meter
Outer Reflector
.2 meters thick
Outer Reflector
.1 meters thick
Figure 29: Diagram of an outer reflector design compared to an central reflector
design.
3.3.1. 250 MWth Design
Even though the 250 MWth design using 10% enriched fuel was not able to attain
a critical equilibrium core with a minimum outer reflector thickness of 50 cm included,
the presence of a dynamic central reflector could enable the core to reach criticality. This
was thought because this inner reflector would be placed where the fast neutron flux
would be the highest, at the center of the core. The graphite pebbles would then be able
to more effectively slow down neutrons because of their placement where the fast fluxes
were initially highest. An additional thought was that because this reflector was placed at
the center of the core, if fast or thermal neutrons passed through it, there would still be
fuel on the other side to interact with. In the case with an outer reflector, once the
neutrons passed through, there was little to no chance of these neutrons coming back.
Both of these expected behaviors relate directly to the boundary conditions applied to the
core by CITATION. At the center of the core no net neutron current can exist due to
-73-
radial symmetry, leading to the interpretation that there is no net leakage of thermal or
fast neutrons across the core centerline.
Since thermal neutrons are produced in the
reflector, leakage of them can only occur away from the core centerline and towards the
fuel. For the outer reflector, the thermal neutrons produced from thermalization of fast
neutrons can either be reflected back towards the fuel or leaked out of the core. Since the
inner reflector is expected to perform better in reflecting thermal neutrons back towards
the fuel and since thermal neutrons drive most of the fission reactions in the core, it
would be expected that k-effective would increase, possibly to the point where the core
could become critical.
3.3.1.1.
K-effective
Opposite of what would be expected, the introduction of the central reflector into
the core causes k-effective to decreases. The figure below shows that while critical cores
can still be established using either 10% or 12.5% enriched fuel with this reflector, the keffective values have decreased relative to the calculations done with the same core
designs but no central reflector. This may be due to the fact that thermalization by the
graphite already present in the fuel zone was not taken into account since most
thermalization was thought to occur within the outer reflector. It is apparent from the
results that this is not the case. Since sufficient slowing down of neutrons already exists
within the pebble bed itself, the placement of additional moderating material, in this case
either outer or inner reflector, will cause both displacement of fuel and additional
parasitic absorption of thermal neutrons which would have otherwise caused fission.
As can be seen in Figure 30, the inner reflector allowed a maximum k-effective
value of approximately 1.3 to be achieved for the core using 12.5% enriched fuel, a
- 74 -
reduction in k-effective from the original value of 1.36 when the central reflector was not
included in the design. The 10% enriched fuel case also suffered a reduction of the
maximum k-effective from roughly 1.26 to 1.2 when the central reflector was included.
The insertion of this 50 cm inner reflector thus leads to an overall Ak of approximately 0.06.
K-effective - 50 cm. Inner Reflector, 250 MWth
1.35
1.25
-10%
Enrichment (Interpolation)
1.310% Enrichment (Data)
- 12.5% Enrichment (Interpolation)
S12.5% Enrichment (Data)
1.2
m 1.15
L 1.05
1
0.
0"
6
140
145
150
15
180
15
170
175
Fuel Zone Outer Radius (cm.)
Figure 30 :Comparison of K-effective for a core with a 50 cm. inner reflector
operating at 250 MWth.
For designs with larger outer reflectors, such as the 135 cm fuel zone radius and
50 cm outer reflector thickness design, an even greater decrease in k-effective occurred.
For this design in particular, k-effective decreased from a value of approximately 1.15 to
near 0.95, a Ak of -0.2. This is due to the larger fraction of the total fuel volume which
the central reflector takes up for this design compared to the 175 cm fuel zone design.
The consequence of this is that a reactor operating at 250 MWth can't form an
equilibrium core using 10% enriched fuel in a design incorporating the 50 cm thick outer
- 75 -
reflector necessary to avoid mechanical failure. Further scoping of central reflector sizes
will be carried out in Section 3.4.
Although it may be the case that 10% enriched fuel can't be used to produce an
equilibrium core of this design, 12.5% enriched fuel can achieve a core very close to this.
At a fuel zone radius of 137.5 cm and an outer reflector thickness of 47.5 cm can produce
an equilibrium core with a k-effective of 1.003.
Therefore, the insertion of the central
reflector into the core served as a mixed blessing. It was unable to produce a critical
equilibrium core using 10% enriched fuel when a minimum outer reflector thickness of
50 cm was included but at the same time, it reduced the excess reactivity of this design
such that in the 12.5% enriched fuel case, the core achieves minimum excess reactivity
close to this design.
3.3.1.2. Power Peaking Factors
Since power peaking factors are such a great concern in reactor safety during
transients, the core design selected in the previous section needs to at least perform
similarly to the PBMR 400 MWth design with respect to this parameter. As seen in the
graph below of the power peaking factors for the various design, the 137.5 cm fuel zone
radius seem to approach the 9.89 VSOP peaking factor value of the PBMR 400MWth
design very closely. Indeed, the actual power peaking factor calculated for this particular
design operating at 250 MWth is 9.66, a slight improvement upon the PBMR.
- 76 -
Power Peaking Factors - 50 cm. Inner Reflector, 250 MWth
-10%
Enrichment (Interpolation)
* 10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
12.5% Enrichment (Data)
12-
1
S10
98
7
6
5
4
3
135
I
I
140
145
150
155
160
165
170
175
Fuel Zone Outer Radius (cm.)
Figure 31 : Comparison of power peaking factors for a core with a 50 cm inner
reflector operating at 250 MWth.
Many of the other designs in Figure 31 are able to improve upon the 9.66 peaking
factor produced with this design, but, as occurred in many of the previous core designs,
the designs achieving minimum power peaking factors also maximized excess reactivity
in the core. This excess reactivity can theoretically be controlled through addition of
more burnable poisons and control rods into the design.
The whole advantage of
designing a reactor with online fuel movement, though, is the ability to maintain low
excess reactivity while achieving high burnups. Thus the best design is still the 137.5 cm
fuel zone radius core.
3.3.1.3. Peak Pebble Temperature
Although these core designs perform considerably better with regards to power
peaking factors, if these designs do not satisfy the 1715C temperature calculated for the
PBMR 400 MWth design then it is questionable as to whether they will operate with a
- 77 -
peak pebble temperature under 1200C. This is of particular concern for the 250 MWth
case because the peak temperatures of core designs near criticality when the core only
included an outer reflector were almost all above the 1715 0C calculated for the PBMR
400 MWth design.
Peak Pebble Temperature - 50 cm Inner Reflector, 250 MWth
2200
Enrichment (Interpolation)
2100
-10%
2000-
* 10% Enrichment (Data)
-12.5%
Enrichment (Interpolation)
Sloo
* 12.5% Enrichment (Data)
l 180oo0
T 1700
E 1600oo
a)
1500
a 1400
13001200
1100
135
140
145
150
I
155
I
160
I
165
170
175
Fuel Zone Outer Radius (cm.)
Figure 32 :Comparison of peak pebble temperatures for a core with a 50 c. inner
reflector operating at 250 MWth.
The 12.5% enriched core, using a fuel zone radius of 137.5 cm and an outer
reflector 47.5 cm thick with the 50 cm central reflector violates the 1715 0 C upper limit
significantly. The peak temperature calculated for this specific design is 1928 0 C. Now
while this calculated temperature exceeds PBMR's by 2000 C, it is still uncertain as to
whether it truly lies below 12000 C because of the failure of the temperature analysis used
in this study.
Since the analysis used over conservative values for the surrounding
helium temperature as well as low thermal conductivities for graphite, it may very well
be that this design could satisfy this 12000 C limit.
-78 -
3.3.1.4. RPV Fast Fluence
In Figure 33, it is seen that the minimum edge fast fluences are achieved when the
fuel zone outer radius is 175 cm for both the 10% and 12.5% enriched fuel cases. But,
once again, these favorable values hold only for cores with high excess reactivities, and
make them poor candidates for this reactor.
RPV Fast Fluence - 50 cm. Inner Reflector, 10% & 12.5% Enrichment, 250 MWth
-10%
Enrichment (Interpolation)
* 10% Enrichment (Data)
5
-12.5%
E
Enrichment (Interpolation)
* 12.5% Enrichment (Data)
o
x
Ct-
N
140
145
150
155
100
185
170
175
Fuel Zone Outer Radius (cm.)
Figure 33 :Comparison of the RPV fast fluences for a core with a 50 cm inner
reflector operating at 250 MWth.
For the design being considered, a core comprising of a 50 cm central dynamic
reflector, an outer fuel zone radius of 137.5 cm and an outer reflector thickness of 47.5
cm, an RPV fast fluence of 4.57x1022 n/cm2 is achieved over a 40 year time period. This
is slightly worse than the PBMR 400 MWth design, which had a 4.32x10 22 n/cm 2 RPV
fast fluence. Despite the poorer performance, the increase in RPV fast fluence is still
tolerable.
-79-
3.3.1.5. Fuel Burnup
As can be seen in Figure 34 below, there is little difference between the burnups
achieved when 12.5% enriched fuel is switched out with 10% enriched fuel for any
particular design. The main difference between using these two enrichments comes from
the extension of critical cores to cores with smaller volumes of fuel, which allows for
higher burnup cores.
Now, if the 12.5% enriched fuel core with a fuel zone outer radius of 175 cm had
been chosen as the optimized core design based solely off of its minimized power
peaking factors and edge fast fluence, then the fuel burnup achieved by such a reactor
would be only 65.2 GWd/T.
Fuel Burnup - 50 cm. Inner Reflector, 10% & 12.5% Enrichment, 2 50MWth
115
I
I
110
-10%
105 -
* 10% Enriched Fuel (Data)
-12.5%
Enriched Fuel (Interpolation)
Slooz
Enriched Fuel (Interpolation)
* 12.5% Enriched Fuel (Data)
90
75
m
85
80
75
70
135
140
145
150
155
160
165
170
175
Fuel Zone Outer Radius (cm.)
Figure 34 : Comparison of fuel burnups for a core with a 50 cm inner reflector
operating at 250 MWth.
The core, though, which minimizes excess reactivity when the 50 cm central
reflector is included, achieves a fuel burnup of 107.3 GWd/T.
- 80-
This is a significant
improvement upon the 87.7 GWd/T bumup observed in the PBMR 400 MWth design.
Although power peaking factors and RPV fast fluence are nearly the same for this design
as they are for the PBMR 400 MWth design, the nearly 20 GWd/T improvement makes
these compromises worth while.
3.3.1.6. Analysis
By placing an dynamic reflector made of up of graphite pebbles into the center of
the core, the 250 MWth design was only able produce an equilibrium core using 12.5%
enriched fuel. This core using 12.5% enriched fuel minimized reactivity did not perform
as well as the PBMR 400 MWth design, especially with respect to the peak pebble
temperature. Due to the uncertainty in the analysis of the peak temperature, though, this
can't render the design as unacceptable until a more accurate analysis is conducted. In
addition to this, the performance of this design relative to the PBMR 400 MWth core with
respect to peaking factors, RPV fast fluences and especially fuel burnup, make this
design very favorable.
Table 9 below compares all the calculated parameters for this
proposed design with the PBMR 400 MWth design.
Table 9 : Comparison of the PBMR 400 MWth design to the 250 MWth design using
a 50 cm central reflector
Parameters
PBMR 400 MWth
250 MWth - 12.5% e.
K-effective
1.0180
1.003
Power Max./Avg.
9.89
9.66
Peak Pebble Temp.
1715.6 0 C
1928 0 C
RPV Fast Fluence
4.32x1022 n/cm2
4.57x1022 n/cm
87.7 GWd/T
107.3 GWd/T
Fuel Burnup
-81 -
3.4.
A Critical Core with a 50 cm Outer Reflector
After analyzing the 250 MWth core designs in Section 3.2.1., the goal was set
forth to create a design which reduced the excess reactivity of a core with an outer fuel
zone radius of 135 cm and an outer reflector 50 cm thick using 12.5% enriched fuel.
Two approaches were taken to do this. The first approach was to add a mixture of
graphite pebbles without any fuel particles inside them to reduce the total volume of fuel
in the core, thereby reducing reactivity. The second method to reduce reactivity was to
place a 25 cm radius central reflector in the core and then add a mixture of graphite
pebbles if necessary. Both of these approaches would hopefully not just reduce excess
reactivity, but also improve upon the performance of the PBMR 400 MWth design as well.
3.4.1. Graphite Pebble Mixture
12.5% enriched fuel was used in this analysis because an equilibrium critical core
with 10% enriched fuel using the PBMR 400 MWth fuel scheme and operating at a power
of 250 MWth was unable to be produced. The introduction of 12.5% fuel, though, did not
produce an exactly critical core, though, and thus various mixtures of graphite pebbles
into the fuel were tested to find the mixture which produced an equilibrium core with
minimal excess reactivity.
For a reactor with an outer reflector of 50 cm and a fuel zone radius of 135 cm,
graphite pebbles were added into the fuel 5% at a time starting initially with no graphite
pebbles mixed in. The fraction of graphite pebbles was incremented 5% at a time until
the core became subcritical. The graph below shows the results of this analysis.
- 82 -
K-effective - 12.5% Enriched, 135 cm. FZ, 50 cm. OR, 250 MWth
1.15
1.05 -
a,
0.95
0.
0.025
0.05
0.075
0.1
0.125
0.15
Fraction of Graphite Pebbles in Fuel
Figure 35 : The effect of the graphite pebble mixture on k-effective for the 12.5%
enriched core operating at 250 MWth.
In Figure 35 above, it is seen that only a small fraction of the fuel must be mixed
with graphite pebbles to obtain an equilibrium core. The exact fraction at which this
occurs is when 11.7% of all pebbles in the core are graphite and the other 88.3% consist
of fuel pebbles.
With this fraction of graphite pebbles, a k-effective of 1.0031 was obtained with
this 250 MWth design. This design also achieved a power peaking factor of 9.38, lower
than any 250 MWth equilibrium core evaluated yet. This is also an improvement upon
the 9.89 peaking factor calculated for the PBMR 400 MWth design.
Now, where as the power peaking factors provided in the VSOP94 output
provided this information according to batch relative power, the actual power peaking
factor would be defined for the individual layers, averaging the relative powers generated
by each layer's batches.
The graph of the relative powers generated by each layer
according to their channel position is seen below. The power peaking factor defined in
- 83 -
this fashion is 3.61, lower than the 3.73 peaking factor found for the PBMR 400 MWth
design.
4
3.5
3
7
Channel
-- Channel
Channel
--- Channel
-- Channel
S---
o 2.5
.
2
2
.
-- 1.5
1-"
1
2
3
4
5
Channel 6
0.5 -
0 0
200
400
600
800
1000
1200
Axial Distance
Figure 36 : Relative power distribution throughout each channel for this core design.
In addition to the improvement with respect to power peaking factors, the RPV
fast fluence achieved was almost exactly the same as that calculated for the PBMR 400
MWth design, a 4.28x10
22
n/cm 2 fluence compared to 4.32x10 22 n/cm 2.
Significant
increases in fuel burnup to a value of 109.1 GWd/T were calculated for this design, as
well.
Although the performance of the design according to these parameters improved,
the peak pebble temperature still exceeded those calculated for the PBMR 400 MWth core.
This new design was calculated, using the VSOP data, to have a peak pebble temperature
of 1930.9 0 C compared to the 1715 0 C calculated for PBMR. Since, it may very well be
the case that this new design can keep peak pebble temperatures below 1200 0 C during
- 84-
steady state operation, the in-depth temperature analysis applied to the PBMR-400 will
be used here.
By analyzing the core as a single channel with a relative power distribution
according to Channel 1 in Figure 36 and applying the same heat conduction and
convection model for the fuel pebble as before, the axial temperature profile for the
helium coolant and center pebble temperature is found. The results of this analysis are
plotted below in Figure 37.
Axial Temperature Profile for MPBR-250
1100
Coolant Temperature (Interpolation)
............... .... ........
1000
oo00
.
.
.
.
..
. .
...........................
.. . .
0
100
200
S Coolant Temperature (Data)
......... ............ Center Pebble Temperature (Interpolation)
Center Pebble Temperature (Data)
. .
.
.......-
. . . . .. . . .. . . . .
300
.
.
........
.
..
....
. . .. . . . .. . . .. . . . .
400
500
. .
. .
........
.. .. . . . .. . .
600
. .
.
.
.
.........................
. . . . .. . . .. . . .. . . .. . .. ..
700
800
000
.........
. .. . . . .. . . .. . . .
1000
1100
Axial Position Top to Bottom (cm)
Figure 37: Coolant and Peak Pebble Axial Temperature Profile for the Graphite
Mixture Core
- 85 -
The results from this analysis shows that the peak pebble temperature is 1079 0C,
satisfying the 1200 0 C upper limit on the steady state peak core temperature.
This
additional analysis therefore shows that this design still fits within this additional
constraint.
3.4.2. 25 cm. Central Reflector
The introduction of a 25 cm radius central dynamic reflector into the 135 cm fuel
zone radius and 50 cm outer reflector thickness design reduced k-effective from a value
of 1.1548 in the original design to 1.0948. Since this excess reactivity is still quite large
compared to the equilibrium cores obtained so far, the further addition of graphite
pebbles into the fuel will be necessary.
The graphite pebble mix necessary to achieve near exact criticality was calculated
first by determining the approximate Ak per percentage of graphite pebbles mixed. Using
the date from the previous section, this was found to be -.013231 Ak per % mixing. The
inverse of this was then multiplied by the excess Ak, .0948, producing an estimated 7.3%
mixing to achieve a critical design. Now, because the data taken from Figure 35 was not
exactly linear, this calculated amount overestimated the percentage of graphite pebble
mixing necessary to achieve criticality, therefore yielding a slightly subcritical core.
When the percentage was decreased to exactly 7%, an equilibrium core almost exactly at
criticality was achieved.
For this design, k-effective was found to be 1.0024 and the batch power peaking
factor calculated to be 9.87, almost exactly the same as the PBMR 400 MWth design.
The RPV fast fluence was almost an exact match as well, 4.36x10 22 n/cm 2 compared to
4.32x1022 n/cm 2 in the PBMR design. The fuel burnup achieved significantly improved
- 86 -
from 87.7 GWd/T calculated for the PBMR 400 MWth core to 109.1 GWd/T, the same
burnup seen in the previous design.
In addition to the VSOP calculated power peaking factor, the relative power
distribution in each channel was calculated and plotted in the graph below. The power
peaking factor from these calculations were found to be 3.81, higher relative to both the
3.73 value for the PBMR 400 MWth design and the 3.61 factor calculated for the design
in the previous section.
4
3.5
3
2.
---
o 2.5
w
Channel 2
Channel 3
Channel 4
-- Channel5
SChannel 6
2
1
0.5
0
0
200
400
600
800
1000
1200
Axial Distance (cm.)
Figure 38 : Relative power distribution throughout each channel of this core design.
The peak temperature was slightly higher for this design, as well, calculated to be
1984.6 0 C. Again, the same comments made about the uncertainty in the thermal analysis
in the previous section apply here. Therefore, although this peak temperature exceeds the
1715 0C limit set by the PBMR 400 MWth design, this does not necessarily mean this
design exceeds the actual 12000 C limit.
- 87 -
3.4.3. Analysis
Both of the equilibrium core designs obtained in this analysis produced relatively similar
RPV fast fluences, as well as peak pebble temperatures and fuel burnups. Both of these
cores significantly improved upon the fuel bumups achieved by the PBMR 400 MWth
design. A total increase in the fuel burnup by over 20 GWd/T was achieved with these
new designs.
Peak pebble temperatures are a concern, though, having exceeded the
PBMR 400 MWth peak temperature by over 2000 C. Although this does not necessarily
mean these designs fail to maintain a peak pebble temperature below the 1200'C steady
state limit, these concerns need to be qualified with a more accurate thermal analysis of
the fuel pebble being driven to the peak pebble power. Table 10 below summarizes this
analysis.
Table 10 : Comparison of the PBMR 400 MWth design and the 250 MWth designs
Parameters
PBMR 400 MWth
250 MWth- No IR*
250 MWth - 25 cm. IR*
K-effective
1.0180
1.0031
1.0024
Batch Peaking
9.89
9.38
9.87
Core Peaking
3.73
3.61
3.81
Peak Pebble Temp.
1715.60 C
1930.9 0C
1984.6 0 C
RPV Fast Fluence
4.32x1022 n/cm2
4.28x1022 n/cm 2
4.36x1072 n/cm 2
87.7 GWd/T
109.1 GWd/T
109.1 GWd/T
Fuel Burnup
* No IR - 11.7% graphitepebble mixture used
25 cm IR - 7% graphitepebble mixture used
-88-
4. Conclusions
Several core designs have been considered which fit within the 3.7 meter space
within the reduced diameter RPV. The first set of designs included only an outer reflector
into the core to determine if the core needs an inner reflector as the PBMR 400 MWth
design suggests. Each design was tested at three powers, 250, 200, and 150 MWth. For
each power, 10% and 12.5% enriched fuels were used and equilibrium core designs
found with each. Power peaking factors, RPV fast fluence and peak pebble temperature
were used to establish the level of performance achieved in each design relative to the
PBMR 400 MWth core. An additional constraint was put on the thickness of the outer
reflector because of worries of mechanical failures using an outer reflector less than a 50
cm thick.
Therefore, only designs were considered which used an outer reflector
thickness of at least 50 cm.
For the designs operating at 250 MWth without an inner reflector, only a core
using 12.5% enriched fuel could form an equilibrium core using an outer reflector over
50 cm thick. This core design, which included a fuel zone with a radius of 126.5 cm and
an outer reflector 58.5 cm thick, performed poorly relative to the PBMR 400 MWth
design. Therefore, further steps were taken to obtain an equilibrium core with a design
using the minimum outer reflector thickness of 50 cm.
Three different approaches were taken to reduce the excess reactivity of the 135
cm fuel zone radius and 50 cm thick outer reflector design. First, a central reflector 50
cm in radius was inserted into the core to displace fuel and lower k-effective. This
produced a core with a much improved peak pebble temperature and RPV fast fluence.
Second, a design with no central reflector but with graphite pebbles homogenously mixed
-89-
in with the fuel was considered. An equilibrium core was maintained using an 11.7%
mixture of graphite pebbles and performed slightly better than the 50 cm central reflector
design. The third design considered used both a 25 cm radius central reflector and a
mixture of graphite pebbles to achieve an equilibrium core. This core was able to achieve
near criticality using a 7% graphite pebble mixture, but performance relative to the two
previously mentioned designs declined.
Out of all the 250 MWth equilibrium cores using 12.5% enriched fuel, the design
with a fuel zone radius of 135 cm, an outer reflector thickness of 50 cm, no inner
reflector and a graphite pebble mixture of 11.7% was chosen as the overall best candidate.
This design was able to reduce both core and batch peaking factors relative to many of
the other designs as well as produce the lowest RPV fast fluence. Table 11 below
summarizes the performance of the chosen 250 MWth design relative to the PBMR-400.
- 90-
Table 11 : Executive summary comparing the PBMR-400 with the final MPBR-250
Reactor Parameters
PBMR 400 MWth
MPBR 250 MWth
Reactor Inlet Temperature
500 0 C
500 0C
Reactor Outlet Temperature
9000 C
9000 C
192.5 kg/s
120.9 kg/s
9 MPa
9 MPa
Central Reflector Radius
1.0 m
0.0 m
Pebble Bed Outer Radius
1.85 m
1.35 m
Outer Reflector Thickness
1.0 m
0.5 m
Pebble Bed Height
11.0 m
11.0 m
Volume of Pebble Bed
-84 m 3
-63 m 3
Number of Fuel Spheres
-452,000
-300,000
0
-39,700
Fuel Enrichment
9.6 %
12.5 %
K-effective
1.0180
1.0031
9.89
9.38
VSOP Peak Temperature
1715.6 0C
1930.9 0C
Modeled Peak Temperature
1107 OC
1079 OC
Mass Flow Rate
System Operating Pressure
Number of Graphite Spheres
VSOP Power Peaking Factors
RPV Fast Fluence
4.32x1022 n/cm 2
4.28xl 022 n/cm 2
87.7 GWd/T
109.1 GWd/T
Fuel Burnup
Verification of the thermal analysis applied to these designs is required, though, to
make sure that the peak pebble temperature during steady state operation remains below
the 1200 0C limit. If these results are verified, then this design achieves both improved
performance upon the PBMR 400 MWth design and is able to fit within an RPV small
enough in diameter to be transported by railcar, also improving upon design mobility and
accessibility to prospective reactor sites.
-91 -
5. References
1. Boenig, H.J.; Rogers, J.D.; McLelland, G.R.; Pelts, C.T., "Transportation of a 451
ton generator stator and a 234 ton generator rotor from Hartsville, TN, to Los
Alamos, NM," Fusion Engineering, 1989. Proceedings., IEEE Thirteenth
Symposium on , vol., no., pp. 4 3 2 -4 3 5 vol.1, 2-6 Oct 1989
2. Finan, A.; Miu, k.; Kadak, A., "Nuclear Technology & Canadian Oil Sands Integration of Nuclear Power with In-Situ Oil Extraction", ICAAP 2006, Reno,
Nevada.
3. Venter, P.J.; Mitchell, M.N., "Integrated design approach of the pebble BeD
modular reactor using models", Nuclear EngineeringandDesign, Volume 237,
Issues 12-13, July 2007, Pages 1341-1353
4. Ion, S.; Nicholls, D.; Matzie, R.; Matzner, D., "Pebble Bed Modular Reactor: The
First Generation IV Reactor To be Constructed", World Nuclear Association
Annual Symposium, London, September 2003
5. Knief, R.A., "Nuclear Engineering: Theory and Technology of Commerical
Nuclear Power Second Edition", American Nuclear Society, Inc., La Grange Park,
Illinois, 2008, pp. 247-251, 256-257
6. International Atomic Energy Agency, "Heat Transport and Afterheat Removal for
Gas Cooled Reactors Under Accident Conditions", IAEA-TECDOC-1163, IAEA,
Vienna, Austria, 2001
7. Slabber, J., "PBMR Nuclear Material Safeguards", 2 nd International Topical
Meeting on High Temperature Reactor Technology, Beijing, China, September
2004
8. Teuchert et al., "V.S.O.P ('94) Computer Code System for Reactor Physics and
Fuel Cycle Simulation", Germany Juelich, Juel-2897.
9. Reitsma, F., et. Al., "The PBMR Steady State and Coupled Kinetics Core
Thermal Hydraulics Benchmark Test Problems", 2 nd International Topical
Meeting on High Temperature Reactor Technology, Beijing, China. September
2004
10. Galloway, C., " Summary of VSOP Studies on Reactor Core and Vessel Sizing
for Modularity", MIT Nuclear Science and Engineering Department, 2007
11. Kazimi, K.S.; Todreas, N.E., "Nuclear Systems I: Thermal Hydraulics
Fundamentals", Taylor and Francis Group, LLC, New York, NY, 1990
- 92 -
Appendix A.
MPBR-250 MW Birgit2.dat Input File
25 37 0 8 0
BI-1
0 0 600 300
0.1 7 0
L.E-6
0. BI-2
0 13 6 13 0.
0.
0.
BI-3
0.0
293.93
57 9.65
751.14
792.68
834.22
BI-4
875.76
917.30
958.84 1000.39 1036.05
1070.21
BI-4
1100.0
BI- 4
34.7
34.1
32.7
29.4
25.7
21.6
BI-5
18.1
13.8
10.9
8.3
6.6
5.9
BI-5
5.5
BI-5
0 13 6 -1 0.
0.
0.
BI- 3
56.2
55.2
53.0
47.5
41.6
34.9
BI- 5
29.2
22.3
17.5
13.3
10.7
9.4
BI-5
8.9
BI-5
0 14 6 -1 0.
0.
0.
BI- 3
82.1
81.0
78.6
73.6
69.6
63.0
BI-5
54.5
44.5
36.8
28.9
23.3
18.1
BI- 5
14.3
BI- 5
0 16 6 -1 0.
0.
0.
BI-3
103.0
102.4
100.9
97.0
93.9
88.9
BI-5
80.9
69.7
56.7
46.5
37.9
29.7
BI- 5
17.3
BI-5
0 18 6 -1 0.
0.
0.
BI- 3
119.6
119.6
118.6
117.0
114.9
109.8
BI-5
104.9
95.3
84.7
70.6
55.6
38.8
BI- 5
20.0
BI-5
1 22 6 0
0.0
140.0
86.8
BI- 3
-1 0 0 0
0.0
0.0
0.0
BI- 3
0 27.0 0
7.7 0 16.6 0 16.6 0 67.1 3
1.9 BI-6
2
4.2 3
9.9 3
3.2 3 7.1 3 5.8 4 17.9 BI-6
BI-6
2 50.0 3 90.0 1 10.0 3 50.0 3 61.2 0 109.044 BI- 7
0 109.044 0 109.044 0 109.044 0 109.044 0 109.044 0 109.044 BI- 7
0 109.044 0 109.044 0 118.604 3 50.0 2 50.0 2 50.0 BI-7
2 50.0 2 25.0
BI-7
1 1 1 1 1 1 16 28 28 28 28 49
BI- 8
52 52 52 52 52 52 16 30 28 28 44 49
BI-8
52 2 2 2 2 2 16 29 29 29 44 49
BI- 8
53 3 3 3 3 10 16 30 35 40 44 49
BI-8
4 4 4 4 4 10 17 30 35 40 44 49
BI-8
0 0 0 0 0 11 18 31 36 41 45 49
BI-8
0 0 0 0 0 11 19 31 36 41 45 49
BI-8
0 0 0 0 0 11 20 31 36 41 45 49
BI-8
0 0 0 0 0 12 21 32 37 42 46 49
BI-8
0 0 0 0 0 12 22 32 37 42 46 49
BI-8
- 93 -
0 0
0 0
0 0
0 0
0 0
6 7
6 50
6 8
6 54
6 9
27.0
16.6
54.52
54.52
54.52
16.95
16.94
BI-8
0 12 23 32 37 42 46 49
BI-8
0 13 24 33 38 43 47 49
BI-8
0 13 25 33 38 43 47 49
BI-8
0 13 26 33 38 43 47 49
BI-8
0 14 27 34 39 55 48 49
BI-8
7 14 14 34 39 55 48 49
BI-8
50 51 51 51 39 55 48 49
BI-8
8 54 54 54 39 55 15 49
BI-8
54 54 54 54 15 15 15 49
BI-8
999999949
7.7 2 16.6 2 16.6 2 16.6 2 16.6 BI-9
BI-9
17.3
54.52 3 54.52 BI-10
54.52
54.52 3 54.52
54.52
54.52 3 54.52 BI-10
54.52 3 54.52
54.52
54.52 3 54.52 BI-10
54.52 3 54.52
16.95
16.95 1 16.95 BI-10
16.95 1 16.95
BI-10
Appendix B.
MPBR-250 MW Data2.dat Input File
D 1
65 1 0
678 9 10 11 12 13 14 15 16 17 133 87 160 88 35 149 D2
52 54 57 59 151 62 143 64 67 69 75 156 84 152 89 144 99 154 D2
101 102 103 104 107 148 147 108 109 155 110 111 175 112 113 116 117 118 D2
D 2
120 121 122 130 164 29 4 26 150 5 23
$ 1 1 250. 0. 0. 0. 0. 0. 3.60 0. 0. 2.20 D 3
D 4
0.
0.
23.4
FUELTYPE 1, FEED-I LOW ENRICHED 9 GR/KUGEL, FUEL ELEMENTS
D5
D6
0101 2 1 0 2
D7
1.
0.
0.
0.126394
0.085
D8
143
D9
0.025
10.40
0.
0.
D11
3.18
1.90
0.00 135
1.05
0.004
0.0095
D11
0.0040
1.90
D)12
2.5
3.0
0.0
0.0
1.0
0. 117
D 13
1.0
0.0
1.75
1.75
0.15600 1.75
D 19
150
-.293
D 19
87
0.343 E-10
FUELTYPE 1, FEED-I LOW ENRICHED 9 GR/KUGEL, START-UP ELEMENTS
D5
D6
0102 1 0 0 2
D7
0.
1.
0.
0.085
0.07589
D
19
150
-.293
D 19
87
0.343 E-10
- 94 -
FUELTYPE 2, FEED-I
0201 1 1 0 2
0.07589
0.085
0.0
2.5
3.0
1.75
1.75
0.1560
150
-.293
87
0.343 E-10
FUELTYPE 3, FEED-I
0301 1 1 0 4
0.126394
0.085
2.5
3.0
0. 0
1.75
0.15600 1.75
150
-.293
87
0.343 E-10
130
0.3500E-06
164
3.5050E-06
Appendix C.
BK = BLINDKUGELN
D6
D7
1.
0.
0.
D 12
1.0
0.5
0.0
D 13
0.0
0.0
1.75
D 19
D 19
65%BK (+NOSES)
D6
1.
0.
0.
D7
D 12
1.0
0.5
0.0
1.0
D 13
1.75
0.0
D 19
D 19
D 19
D 19
D5
D5
MPBR-250 MW VSOP2.dat Input File
*1999 MS; 0.3%BE IN MS; 265MW; 44 FISPR; 10.2G/K;
V 2
07730 0 15 20 0 25 0 0
V 3
0
0
3
36
6
3
4350
42
0
65
V 4
44 44 0 0 0 1
V10
0
1.
0.0001
1 3 1 0 1 2 0 0 0
K1 V 11
301 0 0 0 0 1
7
V11
010002
13 V11
010003
010004
19 V11
25 V11
010005
31 V11
010006
010007
37 V11
43 V11
010008
0 1 0 0 0 10
49 V 11
55 V11
010000
61 V11
010000
67 V11
010000
73 V11
010000
79 K2 V 11
010001
85 V11
010002
010003
91 V11
010004
97 V11
103
V 11
010005
010006
109 V 11
010007
115 V 11
010008
121 V11
0 1 0 0 0 10
127 V 11
0 1 0 0 0 10
V I
- 95 -
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 0 0 0 0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
- 96 -
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
4
5
6
7
8
9
10
0
0
0
0
26
27
28
29
30
31
32
33
34
35
0
0
0
0
0
0
26
27
28
29
30
31
32
33
34
35
0
0
133 V11
139 V11
145 V11
151 V 11
157K3V11
I
163 VII
169 VI1
175 V11
181 VII
187 V11
193 V11
199 VI1
205 V11
211 V11
217 Vi
223 Vi
229 V11
235 V1
241 K4 V 11
247 V11
253 V1
259 Vi1
265 Vi1
271 V11
277 V 1
283 V11
289 VI1
295 V11
301 Vi
307 V
313 V 1i
319 V 11
325 V11
331 Vi
337K5 V 11
343 V11
349 Vi
355 Vll
361 Vi
367 Vi
373 V11
379 V 1
385 V 1
391 V 1
397 Vll
403 V
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 026
0 027
0 028
0 029
0 30
0 031
0 26
0 27
0 28
0 1 0 0 0 33
0 1 0 0 0 34
0 1 0 0 0 35
64
010000
0
0 0 0 -02
0
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100-20000110000000000000
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100-2000011001 1 0
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1 0 0-1 0 0 0 0 1 1 0 0 0 0 0 0 000 0 0 0 0
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1 0 0-1 00 0 1 0 1 0 0 0000 0 00 000 0
R9
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0 Enabling Thermal Hydraulics
TX1
-10200000000000000
TX2
250 0 1100 0 0 0 0 0 0 1
T X3
3600.0 0 2.400E01
T (4
0.00000E00 1.10000E03 1 0 0 0
TX5
1 43 0
TX6
3 27.0 2
7.7 2 16.6 2 16.6 2 16.6 2 16.6 TX7
2 16.6 2 17.3
TX7
3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
1 16.95 1 16.95 1 16.95 1 16.95 1 16.95 1 16.95 TX8
1 16.94
TX8
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
11111111
TX9
- 106 -
1 111111
TX9
TX9
111 11 1
TX9
1 11 1 1 1 1
TX9
1 1 1 11 1 1
TX9
11 11111
TX9
1111 1 1
1 1 1 11 1 1
TX9
TX9
1 111111
HET 1 -1 17 36 0 0 0 .61 1.75 0 0 700 500 -1 0 TX10
TX11
0.390E00 6.000E00 4
TX12
2.500E00 17 36 1.000E00 2.000E00 17 36 1.000E00
TX12
1.500E00 17 36 1.000E00 1.000E00 17 36 1.000E00
TX14
1 0
0 0 37 0.00000E00 0.00000E00 4.36151E00 1.02102E01 7.00000E01 TX17
8.00000E00 5.00000E02 1.10000E03 0.00000E00 2.50000E00 7.589E0000 TX19
KX1
0 0
0.000E00 0.000E00 0.000E00 0.000E00 0.000E00
KX2
0.000E00 0.000E00 0.000E00 0.000E00 8.000E01 2
1 0 1 0 0 -1E00 O0.OEO 1.0E0.39E0 0.OEO 127.5 500E0 KX3
Appendix D.
MPBR-250 VSOP Output File
OPERATIONEL
SUMMARY OUTPUT OF CASE:
PERIOD:233
TIMESTEP:
1
PERFORMANCE DATA OF TIMESTEP NO.: 1
GLOBAL DATA:
K-EFF
1.0031
3.071
E+10 (FISS/WS)
FISSIONS/ENERGY
9.38
POWER PEAKING MAX./AVG.
MAX. POWER PER BALL
KW/BALL
7.29
NEUTRON DOSIS:
FAST NEUTRON EXPOSURE (>0.1 MEV)
E+21/(CM2*360D)
MAX. UPPER EDGE
E+21/(CM2*360D)
MAX. LOWER EDGE
E+21/(CM2*360D)
MAX. OUTER EDGE
THERMAL NEUTRON FLUX (<1.85 EV):
E+14/(CM2*SEC)
MAX. UPPER EDGE
MAX. LOWER EDGE
E+14/(CM2*SEC)
E+14/(CM2*SEC)
MAX. OUTER EDGE
E+14/(CM2*SEC)
AVG. THERMAL FLUX
2.24
0.00
1.07
2.26
0.00
2.35
1.31
- 107-
AVG. TOTAL FLUX
E+14/(CM2*SEC)
NEUTRON BALANCE:
FRACTIONAL FISSIONS OF
U -235
%
U -236
%
U -238
%
PU-239
%
PU-241
%
87.32
0.04
0.35
9.04
3.24
NEUTRON LOSSES IN HEAVY METALS
ESP. IN FISSILE ISOTOPES
49.80
ESP. IN U -235
%
43.23
ESP. IN U -236
%
1.16
ESP. IN U -238
%
5.55
ESP. IN NP-239
%
0.01
ESP. IN PU-239
%
5.07
ESP. IN PU-240
%
1.64
ESP. IN PU-241
%
1.49
ESP. IN PU-242
%
0.10
ESP. IN NP-237
%
0.59
IN FISSION PRODUCTS
11.97
ESP. IN XE-135
%
2.43
CORE-LEAKAGE
2.33
%
58.84
24.38
PERFORMANCE DATA OF CYCLE NO.:233
GLOBAL DATA:
AVG. ENRICHMENT
%
3.41
AVG. FUEL RESIDENCE TIME
DAYS
1146.6
AVG. BURNUP
MWD/T 109078.3
CONVERSION RATIO
0.144
SOURCE NEUTR./FISSILE ABS. ET'A*EPSIL
2.008
CAPTURE/FISSION IN FISS.MAT. ALPHA
0.238
FAST DOSIS SPENT FUEL ELEM. IE+21/CM2
2.98
Appendix E.
PBMR-400 MW Birgit2.dat Input File
25 37 0 8 0
BI- 1
0 0 600 300
0.1 7 0
1.E-6
0. BI- 2
0 13 6 13 0.
0.
0.
BI-3
0.0
417.01
834 .0)2
856.56
879.10
901.64
BI- 4
928.69
955.74
91841.59 1013.44
1042.29
1071.15
BI- 4
1100.0
BI- 4
- 108 -
BI-5
100.00
100.00
100.00
100.00
100.00
100.00
BI-5
100.00
100.00
100.00
100.00
100.00
100.00
BI-5
100.00
BI-3
0.
0.
0 20 6 -1 0.
BI- 5
110.54
111.65
112.75
109.44
109.44
109.44
BI-5
131.52
122.69
127.10
114.96
117.17
119.38
BI-5
137.04
BI-3
0.
0.
0 15 6 -1 0.
BI- 5
134.63
134.63
134.63
134.63
134.63
134.63
BI- 5
137.94
136.84
136.84
135.73
135.73
135.73
BI-5
140.15
BI- 3
0.
0.
0 13 6 -1 0.
BI-5
150.37
150.37
150.37
150.37
150.37
150.37
BI-5
148.16
147.06
149.27
148.16
149.27
149.27
BI-5
144.85
BI- 3
0.
0.
0 15 6 -1 0.
172.25
BI- 5
174.46
173.35
175.56
175.56
175.56
BI- 5
162.31
157.90
153.48
170.04
167.83
165.62
BI-5
147.96
80.26
BI-3
1 20 6 0
0.0
151.89
BI-3
0.0
-1 0 0 0
0.0
0.0
0 37.0 0 10.6 0 22.7 0 22.7 0 92.0 3
3.8 BI- 6
6.4 3 14.1 3 11.5 4 36.0 BI-6
2
8.3 3 19.9 3
BI-6
2 50.0 3 90.0 1 10.0 3 50.0 3 61.2 0 109.044 BI-7
0 109.044 0 109.044 0 109.044 0 109.044 0 109.044 0 109.044 BI-7
0 109.044 0 109.044 0 118.604 3 50.0 2 50.0 2 50.0 BI- 7
BI- 7
2 50.0 2 25.0
BI-8
1 1 1 1 1 1 16 28 28 28 28 49
BI-8
52 52 52 52 52 52 16 30 28 28 44 49
BI- 8
52 2 2 2 2 2 16 29 29 29 44 49
BI- 8
53 3 3 3 3 10 16 30 35 40 44 49
BI-8
4 4 4 4 4 10 17 30 35 40 44 49
BI-8
0 0 0 0 0 11 18 31 36 41 45 49
BI-8
0 0 0 0 0 11 19 31 36 41 45 49
BI-8
0 0 0 0 0 11 20 31 36 41 45 49
BI- 8
0 0 0 0 0 12 21 32 37 42 46 49
BI- 8
0 0 0 0 0 12 22 32 37 42 46 49
BI- 8
0 0 0 0 0 12 23 32 37 42 46 49
BI-8
0 0 0 0 0 13 24 33 38 43 47 49
BI-8
0 0 0 0 0 13 25 33 38 43 47 49
BI- 8
0 0 0 0 0 13 26 33 38 43 47 49
BI- 8
0 0 0 0 0 14 27 34 39 55 48 49
BI- 8
5 6 7 7 7 14 14 34 39 55 48 49
BI-8
6 50 50 50 51 51 51 39 55 48 49
BI-8
6 8 8 8 54 54 54 39 55 15 49
-109-
5 6 54 54
56999999
3 37.0 2
2 22.7 2
3 54.52 3
3 54.52 3
3 54.52 3
1 16.95 1
1 16.94
54 54 54 54 15
9 9
10.6 2 22.7 2
23.9
54.52 3 54.52
54.52 3 54.52
54.52 3 54.52
16.95 1 16.95
Appendix F.
65
6
52
101
120
$
15 15 49
BI-8
9 49
BI-8
22.7 2 22.7 2 22.7 BI- 9
BI-9
3 54.52 3 54.52 3 54.52 BI-10
3 54.52 3 54.52 3 54.52 BI-10
3 54.52 3 54.52 3 54.52 BI-10
1 16.95 1 16.95 1 16.95 BI-10
BI-10
PBMR-400 MW Data2.dat Input File
1 0
D 1
7 8 9 10 11 12 13 14 15 16 17 133 87 160 88 35 149 D 2
54 57 59 151 62 143 64 67 69 75 156 84 152 89 144 99 154 D 2
102 103 104 107 148 147 108 109 155 110 111 175 112 113 116 117 118 D 2
121 122 130 164 29 4 26150 5 23
D 2
1 1 250. 0. 0. 0. 0. 0. 3.60 0. 0. 2.20 D 3
23.4
0.
0.
D 4
FUELTYPE 1, FEED-I LOW ENRICHED 9 GR/KUGEL, FUEL ELEMENTS
D5
0101 2 1 0 2
D6
0.101147
0.085
1.
0.
0.
D7
143
D8
0.025
10.40
0.
0.
D9
0.0095
1.05
0.004
1.90
0.0035
3.18
D 11
0.0040
1.90
Dl
2.5
3.0
0.0
0.0
0.0
0.0
D 12
0.13751
1.75
1.75
1.75
0.0
1.0
D 13
150
-.293
D 19
87
0.343 E-10
D 19
FUELTYPE 1, FEED-I LOW ENRICHED 9 GR!KUGEL, START-UP ELEMENTS
D5
0102 1 0 0 2
D6
0.07589
0.085
1.
0.
0.
D7
150
-.293
D 19
87
0.343 E-10
D 19
FUELTYPE 2, FEED-I
BK = BLINDKUGELN
D5
0201 1 1 0 2 0.95
D6
0.101147
0.085
1.
0.
4
D7
2.5
3.0
0.0
0.0
1.0
1.0
D 12
0.00006
1.75
1.75
1.75
0.0
0.0
D 13
150
-.293
D 19
87
0.343 E-10
D 19
FUELTYPE 3, FEED-I
65%BK (+NOSES)
D5
110-
D6
0301 1 1 0 4
D7
0.
1.
0.
0.101147
0.085
0.5
D 12
1.0
2.5
3.0
0.0 0.0
D 13
1.0
1.75
1.75
0.0
0.13751
1.75
D 19
150
-.
293
D 19
87
0.3430E-10
D 19
130
0.3500E-06
D 19
164
3.5050E-06
Appendix (
PBMR-400 MW VSOP2.dat Input File
*1999 MS; 0.3%BE IN MS; 265MW; 44 FISPR; 9.OG/K;
V 2
07730 0 15 20 0 25 0 0
V 3
65 42 0 4350 42 7 3 0 3 0
V 4
44 44 0 0 0 1
V 10
1. 0
0.0001
1 3 1 0 1 2 0 0 0
I1KiV11
301 0 0 0 0 1
7 V1i
0 1 0 0 0 2
13 V11
0 1 0 0 0 3
19 VI1
0 1 0 0 0 4
25 V11
0 1 0 0 0 5
31 Vi
0 1 0 0 0 6
37 Vii
0 1 0 0 0 7
43 Vii
0 1 0 0 0 8
49 V11
0 1 0 0 0 10
55 VI1
0 1 0 0 0 0
61 VI1
0 1 0 0 0 0
67 V11
0 1 0 0 0 0
73 V11
0 1 0 0 0 0
79 K2 V 11
0 1 0 0 0 1
85 V11
0 1 0 0 0 2
91 Vi1
0 1 0 0 0 3
97 V11
0 1 0 0 0 4
103 V11
0 1 0 0 0 5
109 V1I
0 1 0 0 0 5
115 Vi
0 1 0 0 0 6
121 Vll
0 1 0 0 0 6
127 V11
0 1 0 0 0 7
133 V11
0 1 0 0 0 7
139 V1i
0 1 0 0 0 8
145 V11
0 1 0 0 0 8
151 V11
0 1 0 0 0 9
157 V I
0 1 0 0 0 9
163 V11
0 1 0 0 0 10
169 V11
0 1 0 0 0 10
V1i
175
0 1 0 0 0 0
V 1
-111-
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-112-
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
4
5
6
7
8
9
9
10
10
0
0
0
26
27
28
29
30
31
32
33
34
35
0
0
0
26
27
28
29
30
31
32
33
34
34
35
35
0
0
0
181 VII
187 V11
193 Vll
199 K3 V 11
205 V1
211 V11
217 Vll
223 VI1
229 V11
235 Vii
241 V1I
247 V1I
253 V11
259 V11
265 V11
271 V1i
277 VII
283 V11
289K4V 11
295 Vii
301 VI1
307 V11
313 Vi
319 Vi
325 V1i
331 VII
337 V11
343 VII
349 Vll
355 Vll
361 V1i
367 K5 V 11
373 V11
379 V11
385 V1i
391 V11
397 V 1
403 V1i
409 V11
415 V11
421 V11
427 Vii
433 V1i
439 Vii
445 Vi1
451 V11
0 1 0 0 0 26
0 1 0 0 0 27
0 1 0 0 0 28
0 1 0 0 0 29
0 1 0 0 0 30
0 1 0 0 0 30
0 1 0 0 0 31
0 1 0 0 0 31
0 1 0 0 0 32
0 1 0 0 0 32
0 1 0 0 0 33
0 1 0 0 0 33
0 1 0 0 0 34
0 1 0 0 0 34
0 1 0 0 0 35
0 1 0 0 0 35
0 1 0 0 0 0
0 1 0 0 0 0
0 1 0 0 0 0
0 1 0 0 0 0
2 0 0 0 0 14
63 2.30577 -02
64 7.86962 -02
4 0 0 0 0 11
58 0.0 -04
59 0.0 -03
63 2.49736 -02
64 8.52341 -02
20000
63 2.48234 -02
64 8.47225 -02
20000
63 2.22115-02
64 7.58082 -02
1 0 0 0 0 12
64 9.02479 -04
2 0 0 0 0 13
63 1.55 -02
64 5.28 -02
20000
63 2.64423 -02
64 9.02479 -02
2 0 0 0 0 14
63 2.45094 -02
64 8.36508 -02
2 0 0 0 0 15
457 K6 V 11
463 V 11
469 V 11
475 V 11
481 V 11
487 V 11
493 V 11
499 V 11
505 V 11
511 V 11
517 V 11
523 V 11
529 V 11
535 V 11
541 V 11
547 V 11
553 V 11
559 V 11
565 V 11
571 V 11
577 KON V11
V 12
V 12
1 B 1V11
V 12
V12
V 12
V 12
2B2V11
V 12
V 12
3B3V11
V 12
V 12
4B4V11
V 12
5B5VII
V 12
V 12
6B6 Vi
V 12
V 12
7B7V11
V 12
V 12
8B8 VII
-113-
63
1.93792 -02
64 6.61415-02
0 1 0 0 0
2 0 0 0 0 16
63 2.64423 -02
64 9.02479 -02
0 10 0 0 0 17
0 10 0 0 0 18
0 10 0 0 0 19
0 10 0 0 0 20
0 10 0 0 0 15
3 0 0 0 0 16
58 1.453 -06
63 1.81923 -02
64 6.20906 -02
0 16 0 0 0
0 16 0 0 0 17
0 16 0 0 0
30000
58 0.0 -06
63
1.81923 -02
64 6.20906 -02
0 20 0 0 0 18
0 20 0 0 0
0 20 0 0 0
0 20 0 0 0 19
0 20 0 0 0 20
0 1 0 0 0 21
02000
0 10 0 0 0
0 10 0 0 0 22
0 10 0 0 0 23
0 10 0 0 0 24
0 10 0 0 0 25
4 0 0 0 0 21
58 0.0 -04
59 0.0 -03
63 2.49736 -02
64 8.52341 -02
0 35 0 0 0 22
0 35 0 0 0 23
0 35 0 0 0 24
0 35 0 0 0 25
4 0 0 0 0 21
58 0.0 -04
59 0.0 -03
-114-
V 12
V 12
9 B 9 V11
10 B10 V11
V 12
V 12
11 Bll VI
12 B12 V1i
13 B13 VII
14 B14 V11
15 B15 VI1
16 B16 V1I
V 12
V 12
V 12
17 B17 V11
18 B18 V11
19 B19 V11
20 B20 V11
V 12
V 12
V 12
21 B21 V11
22 B22 V11
23 B23 V11
24 B24 V 11
27 B27 V11
28 B28 V11
29 B29 Vi1
30 B30 V 11
31 B31 VI1
32 B32 V11
33 B33 V11
34 B34 V11
35 B35 V11
V 12
V 12
V 12
V 12
36 B36 V11
37 B37 V1i
38 B38 V11
39 B39 V11
40 B40 V 11
V 12
V 12
V 12
V 12
41 B41 VI1
42 B42 V11
43 B43 V11
44 B44 V11
V 12
V 12
V12
V 12
45 B45 V11
46 B46 V11
47 B47 Vi1
48 B48 V11
49 B49 V11
V 12
V 12
50 B50 V11
V 12
V 12
V 12
V 12
51 B51 V11
V 12
V 12
V 12
V 12
52 B52 V11
53 B53 V11
54 B54 V11
-55 B55 V11
0.
0.700
V 15
V 16
V21
V 22
V 23
30 3 3 5 0 0 0
G 1
612.
637.
663.
685. G2/R19
794.
647.
0.
0. G2/R19
0.
0.
0.
0. G2/R19
0.
0.
0.
0. G2/R19
629.
681.
793. G2/R19
738.
920.
944.
927.
0. G2/R19
0.
0.
0.
0. G2
1 1 1 1 1 1 3 3 G3
3 3 3 3 3 3 3 3 G3
63 1.82734 -02
64 6.23664 -02
0 40 0 0 0 22
0 40 0 0 0 23
0 40 0 0 0 24
4 0 0 0 0 37
58 0.0 -04
59 0.0 -03
63 2.49736 -02
64 8.52341 -02
0 44 0 0 0 38
0 44 0 0 0 39
0 44 0 0 0 40
0 44 0 0 0 41
2 0 0 0 0 36
60 4.08572 -02
64 9.02479 -04
4 0 0 0 0 42
58 5.01175 -05
59 2.04286 -04
63 2.29165 -02
64 7.82771 -02
4 0 0 0 0 42
58 5.40700 -05
59 2.20397 -04
63 2.47238 -02
64 8.44504 -02
0 10 0 0 0 11
0 52 0 0 0 11
0 1 0 0 0 15
0 40 0 0 0 25
1.832329 400.+06
6 10
1 1 0 0
1 0
5015 180 515
575.
590.
702.
712.
0.
0.
0.
0.
0.
594.
844.
887.
0.
0.
1 1 1 1
3 3 3 3
-115-
3 2 2 2 2 2 2 2 2 2 2 3 G3
3 3 3 3 3 3
G 3
1 0
G4
6 901 902 903 904 905 906
G4
1 0
G4
6 901 902 903 904 905 906
G4
1 0
1 0
10000(0.
29.
1.86
G5
2 3 2 11 -1 0
T 1
1600 1601 1603 1604 1460:5 1606 1607 1608 1609 1610 1612
573.
587.
608.
633.
658.
680. T3/R20
697.
708.
788.
644.
551.
566. T3/R20
751.
883.
745.
553.
602.
702. T3/R20
780.
836.
503.
534.
541.
546. T3/R20
589.
589.
622.
670.
725.
780. T3/R20
830.
874.
909.
934.
921.
200. T3/R20
503.
534.
541.
546.
589.
883. T3
1121 1122 1123 1124 1125
T2
575.
590.
612.
637.
663.
685. T3/R20
702.
712.
794.
647.
0.
0. T3/R20
0.
0.
0.
0.
0.
0. T3/R20
0.
0.
0.
0.
0.
0. T3/R20
0.
594.
629.
681.
738.
793. T3/R20
844.
887.
920.
944.
927.
200. T3/R20
0.
0.
0.
0.
0.
0. T3
4.0 6 12 29
T4
1 4 1 1 1 1
1 1 1 1 1 T5
3 3 3 3 3 3
3 3 3 3 3 T5
3 3 3 1 1 1
1 1 1 1 1 T5
1 3 3 3 3 3
3
T5
1.5 0.61
1.
1.
-1.
1. T 6
11111111 122220000000
T7
4 01
0.0
1.
T9
6 00
-1.0
0.
0.
T9
1.
26 01
1.0
0.
0.
T9
130 01
-2.0
0.0
0.0
T9
150 01
-2.0
0.0
0.0
T9
-1001 01
-2.0
0.0
0.0
T9
1.5 0.61
0.
1.
-1.
1. T 6
11111111 122233333300 1 1
.025
.046 .14537
1.0694
2.5
3.0
3.985
T8
4 01
0.0
1.
T9
6 00
1.0
0.
T9
26 01
1.0 0.
T9
130 01
0.0
1.0
0.
0.
T9
116-
T2
T 7
T 9
0.
150 01 .24682 .17968 .57350
T 9
0.
.57350
.17968
.24682
-1001 01
0. T 6
0.
1.
0.0
1.0
1.5
T 7
10000000000000000000
T 8
1.0
T 9
1.
-4 00
1. T 6
-1.
1.
0.0
1.0
1.5
0.0 T 7
0.0
0.0
0.0
11112222220000000000 1 0
T 8
1.0466
0.375
T9
1.
0.
4 00
T 9
0.
1.
01
130
T 9
0.
1.
164 01
T 9
0.98555
01
0.01445
-1001
T 11
0.1
3.0
2.5
0.0
0.61
CO-1
120000
CO-2
*7730* MEDUL H/R=805/175; CITA 2-Z
CO-3
**KOPPLUNG: VSOP - CITATION**
CI-1
001
0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0-1 C1-2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C1-3
840 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 0 0 0 C1-4
0. C1-5
0.
0.
0.
0.
0.
C3-1
003
00 1 0 C3-2
0-1
1
00
0000
1
0
0
0
0000700
0. C3-3
0.
0.
0.
0.0001
0.0001
0. C3-4
1.
0. 3.287800-11
0.
0.
C7-1
1 1
C7-2
1 204 204
C7-3
C7-4
C7-5
0.5
0.1
185.
CX-1
14 81 18 0
0.99 R 1
0.99
0.99
0.99
0.0
0.0
0.0 R 1
0.0
0.0
0.0
0.0
0.99
0.0 R 1
0.0
0.0
0.0
1.0
0.0
0.0 R 1
0.0
0.0
0.0
0.0
0.0
0.0 R 1
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0.0
0.0
0.0 R 1
0.0
0.0
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0.0
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0.0
0.0
0.0
0.0
0.0
0.0
0.0 R 1
0.0
0.0
0.0
0.0
0.0
0.0 R 1
0.0
0.0
0.0
0.0
0.0
1.0 R 1
1.0
1.0
0.0
0.0
0.0
R 1
1.0
1.0
1.0
1.0
0. R 2
0.
0.8
365.
0.
0.
R3
1 0 0 0
R 5
1.
1 6.005536E+6 -101
-117-
2 2.658231E+6 -201
3 6.005536E+6 -301
1320 20001 103
1 0
0
554.5
571.1
595.1
698.4
717.2
799.7
0.0
0.0
0.0
0.0
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0.0 577.8
614.7
852.8
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799.7
0.0
0.0
0.0
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0.0 577.8
614.7
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940.7
0.0
0.0
0.0
1
2
2
2
3
2
4
2
5
2
6
2
73 67 7
74 68 7
75 69 7
76 70 7
77 71 7
78 72 7
79
1
80
3
81
3
82
3
83
3
84
3
193 187 1
194 188 2
-118-
2.
R5
3.
R5
000111000000 R9
R16
R17
622.8
651.0
676.3 G2/R19
630.4
0.0
0.0 G2/R19
0.0
0.0
0).0 G2/R19
0.0
0.0
0).0 G2/R19
669.4
733.1
796.2 G2/R19
968.9
955.2
0.0 G2/R19
0.0
0.0
().0 G2/R19
615.3
642.6
667.6 T3/R20
624.6
514.4
541.1 T3/R20
517.3
589.3
735.8 T3/R20
559.1
616.0
665.4 T3/R20
654.4
713.6
774.0 T3/R20
950.5
941.9
314.9 T3/R20
467.9
468.2
867.6 T3/R20
622.8
651.0
676.3 T3/R20
630.4
0.0
0.0 T3/R20
0.0
0.0
0).0 T3/R20
0.0
0.0
0).0 T3/R20
669.4
733.1
796.2 T3/R20
968.9
955.2
0.0 T3/R20
0.0
0.0
0).0 T3/R20
0.16667
R24
0.16667
R24
0.16667
R24
0.16667
R24
0.16666
R24
0.16666
R24
R24
R24
R24
R24
R24
R24
0.01453
R24
0.01452
R24
0.01452
R24
0.01452
R24
0.01452
R24
0.01452
R24
R24
R24
195 189
196 190
197 191
198 192
199
200
201
202
203
204
283 277
284 278
285 279
286 280
287 281
288 282
289
290
291
292
293
294
361 355
362 356
363 357
364 358
365 359
366 360
367
368
369
370
371
372
451445
452446
453 447
454 448
455 449
456450
457
458
459
460
461
462
3
4
5
6
0.04273
0.04272
0.04272
0.04272
0.04272
0.04272
1
2
3
4
5
6
0.03734
0.03734
0.03734
0.03734
0.03734
0.03734
1
2
3
4
5
6
0.05658
0.05657
0.05657
0.05657
0.05657
0.05657
1
2
3
4
5
6
0.01552
0.01551
0.01551
0.01551
0.01551
0.01551
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
-119-
571 565 1
R24
572 566 2
R24
573 567 3
R24
574 568 4
R24
575 569 5
R24
R24
-576 570 6
0 0000
20 0 0-2 0 0000
100000000
R9
0 0 0 0 0 0 R9
1 0 0-1 0 0001103000000
R24
1
2 1
0.16667
210007
R24
0.16667
310007
R24
0.16667
R24
410007
0.16667
510007
R24
0.16666
610007
R24
0.16666
R24
73 67 7
R24
74 68 7
R24
75 69 7
R24
76 70 7
77 71 7
R24
78 72 7
R24
R24
79
1 1
0.01452
0.08715
R24
8010001
R24
0.08715
8110002
0.08715
R24
8210003
0.08715
R24
8310004
R24
0.08715
8410005
R24
193 187 1
R24
194188 2
R24
195 189 3
R24
196 190 4
197 191 5
R24
198 192 6
R24
1 1
0.04272
R24
199
0.25633
R24
20010001
R24
20110002
0.25633
R24
20210003
0.25633
R24
0.25633
20310004
0.25633
R24
20410005
R24
283 277 1
R24
284 278 2
R24
285 279 3
R24
286 280 4
R24
287 281 5
R24
288 282 6
R24
289
1 1
0.03734
29010001
0.22401
R24
-120-
29110002
29210003
29310004
29410005
361355 1
362356 2
363357 3
364358 4
365359 5
366360 6
1
367
36810001
36910002
37010003
37110004
37210005
451445 1
452446 2
453447 3
454448 4
455449 5
456450 6
1
457
45810001
45910002
46010003
46110004
46210005
571565 1
572 566 2
573567 3
574 568 4
575569 5
-576 570 6
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
20 0 0-2 0 0 0 0
1 0 0-2 0 0 0 0
0.22401
0.22401
0.22401
0.22401
1
1
0
1
0
1
0
1
0
1
0
1
0
1
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
R24
0.05657
R24
0.33944
R24
0.33944
R24
0.33944
R24
0.33944
R24
0.33944
R24
R24
R24
R24
R24
R24
R24
0.01551
R24
0.09308
R24
0.09308
R24
0.09308
R24
0.09308
R24
0.09308
R24
R24
R24
R24
R24
R24
1 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0
R9
R9
R9
R9
R9
R9
R9
R9
R9
R9
R9
R9
-121-
20 0 0-2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0
R9
1 0 0-2 0 0 0 0 1 1 0 0 0 0 0 0 0 00 0 0 00
R9
20 0 0-2 0 0 0 0 0 1 0 0 0 0 0 0 0 00 00 0 0
R9
1 0 0-2 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
R9
20 0 0-2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
R9
1 0 0-1 0 00 0 1 1 0 0 0 0 0 0 00 0 0 0 0
R9
1 0 0-1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
R9
13212000010000000000001
R9
0 Enabling Thermal Hydraulics
TX1
-10200000000000000
FX2
400 0 1100 0 0 0 0 0 0 1
T X3
3600.0 0 0 2.400E01
T (4
0.00000E00 1.10000E03 1 0 0 0
TX5
143 0
TX6
37.0 2 10.6 2 22.7 2 22.7 2 22.7 2 22.7 TX7
22.7 2 23.9
TX7
54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
54.52 3 54.52 3 54.52 3 54.52 3 54.52 3 54.52 TX8
16.95 1 16.95 1 16.95 1 16.95 1 16.95 1 16.95 TX8
16.94
TX8
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
1111111
TX9
-122-
HET 1 -1 17 36 0 0 0 .61 1.75 0 0 700 500 -1 0 TX10
TX11
0.390E00 6.000E00 4
TX12
2.500E00 17 36 1.000E00 2.000E00 17 36 1.000E00
TX12
1.500E00 17 36 1.000E00 1.000E00 17 36 1.000E00
TX14
1 0
0 0 37 0.00000E00 0.00000E00 4.36151E00 1.02102E01 7.00000E01 TX17
8.00000E00 5.00000E02 1.10000E03 0.00000E00 2.50000E00 7.589E0000 TX19
KX1
0.000E00 0.000E00 0.000E00 0.000E00 0.000E00 0 0 0
KX2
2
8.000E01
0.000E00
0.000E00 0.000E00 0.000E00
1 0 1 0 0 -1E00 O.OEO 1.0E0.39E0 0.0E0 127.5 500E0 KX3
Appendix H.
PBMR-400 VSOP Output File
PERFORMANCE DATA OF TIMESTEP NO.: 1
GLOBAL DATA:
1.0180
K-EFF
E+10 (FISS/WS)
FISSIONS/ENERGY
€3.070
).89
POWER PEAKING MAX./AVG.
6.48
KW/BALL
MAX. POWER PER BALL
NEUTRON DOSIS:
FAST NEUTRON EXPOSURE (>0.1 MEV)
E+21/(CM2*360D)
MAX. UPPER EDGE
E+21/(CM2*360D)
MAX. LOWER EDGE
E+21/(CM2*360D)
EDGE
MAX. OUTER
THERMAL NEUTRON FLUX (<1.85 EV):
E+14/(CM2*SEC)
MAX. UPPER EDGE
E+14/(CM2*SEC)
MAX. LOWER EDGE
E+14/(CM2*SEC)
MAX. OUTER EDGE
E+14/(CM2*SEC)
AVG. THERMAL FLU)
E+14/(CM2*SEC)
AVG. TOTAL FLUX
NEUTRON BALANCE:
FRACTIONAL FISSIONS OF
%
U -235
%
U -236
%
U -238
%
PU-239
%
PU-241
1.51
0.00
1.08
2.60
0.00
3.11
1.73
2.53
86.07
0.03
0.35
10.16
3.38
NEUTRON LOSSES IN HEAVY METALS
50.49
%
ESP. IN FISSILE ISOTOPES
43.13
%
ESP. IN U -235
59.98
- 123 -
ESP. IN U -236
ESP. IN U -238
ESP. IN NP-239
ESP. IN PU-239
ESP. IN PU-240
ESP. IN PU-241
ESP. IN PU-242
ESP. IN NP-237
IN FISSION PRODUCTS
ESP. IN XE-135
CORE-LEAKAGE
%
%
%
%
%
%
%
%
0.86
6.36
0.02
5.78
1.78
1.58
0.08
0.39
%
10.88
2.50
%
%
20.20
PERFORMANCE DATA OF CYCLE NO.:213
GLOBAL DATA:
AVG. ENRICHMENT
%
2.91
AVG. FUEL RESIDENCE TIME
DAYS
840.8
MWD/T 87688.4
AVG. BURNUP
CONVERSION RATIO
0.162
SOURCE NEUTR./FISSILE ABS. ETA*EPSIL
1.980
CAPTURE/FISSION IN FISS.MAT. ALPHA
0.240
FAST DOSIS SPENT FUEL ELEM. E+21/CM2
1.75
- 124-