Parametric Study of Reactivity for the University of Florida Training Reactor

Using MCNP

Requirement for Completing Summa Cum Laude Honors Thesis

Daniel E. Lago, Undergraduate Student

Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, FL 32611

For correspondence contact:

Daniel E. Lago

Undergraduate Student

Department of Nuclear and Radiological Engineering

University of Florida, Gainesville, Florida 32611-8300

Phone: (407) 443-7352 Email: dlago89@gmail.com

Short Title:

Improved modeling of UFTR reactivity.

Word Count: 3,673

APA Format

Table of Contents

ABSTRACT .................................................................................................................................... 1

INTRODUCTION .......................................................................................................................... 2

BACKGROUND ............................................................................................................................ 2

University of Florida Training Reactor (UFTR) ........................................................................ 2

MCNP Model of UFTR ............................................................................................................... 5

Six-factor Formula ...................................................................................................................... 6

Reactivity..................................................................................................................................... 8

Boron Content of Graphite ......................................................................................................... 9

Neutron Moderation and the Porosity of Graphite................................................................... 10

Fuel Box Size............................................................................................................................. 12

RESULTS AND DISCUSSION ................................................................................................... 13

Benchmark of Original Input .................................................................................................... 13

Boron Content of Graphite ....................................................................................................... 15

Porosity of Graphite ................................................................................................................. 16

Fuel Box Size............................................................................................................................. 18

CONCLUSIONS........................................................................................................................... 19

ACKNOWLEDGMENTS ............................................................................................................ 20

REFERENCES ............................................................................................................................. 21

1

ABSTRACT

This study was catalyzed by the unexpectedly low reactivity observed when the University of

Florida Training Reactor (UFTR) was refueled in the summer of 2010. Three parameters – the

boron content, the porosity of the graphite, and the fuel box size – were investigated with a

Monte Carlo N-Particle (MCNP) model of the UFTR. The results indicated that all three likely

decrease the reactivity, with the most significant factor being the graphite density. It was also

acknowledged that this study is theoretical, and needs to be supported by future experiments.

Keywords: MCNP, Reactor, Reactivity, Boron, Graphite

2

INTRODUCTION

In the summer of 2010, the University of Florida Training Reactor was refueled by the

reactor staff and the students involved in the Digital Upgrade of the UFTR Protection and

Control Systems. The project is an effort led by the University of Florida (UF) Nuclear and

Radiological Engineering (NRE) Department, in conjunction with Areva and Siemens, to license

the first fully digital reactor protection system for a nuclear reactor in the United States. The

project had progressed to the point where the reactor needed to be operational, which required

rebuilding the reactor and reinserting the fuel back into the core.

Computational models were developed to predict criticality as a safety precaution. A

model was created in MCNP for the Highly Enriched Uranium (HEU) to Low Enriched Uranium

(LEU) conversion that took place in 2005. This model was modified for the refueling analysis to

predict criticality for the core arrangement in 2010. Results from the MCNP model implied

criticality with only two safety blades up and the last safety blade and the regulating blade only

partially withdrawn. When all of the fuel was placed in core, the reactor needed all of the safety

blades and a substantial portion of the regulating blade to be fully removed in order to achieve

criticality.

Three parameters were examined for their effects on reactivity: the boron content in the

graphite moderator, the fuel box size, and the porosity of the graphite. The purpose of this study

is to determine which parameters affect the reactivity.

BACKGROUND

University of Florida Training Reactor (UFTR)

The UFTR is a 100 kWth non-power research reactor on the University of Florida

campus. The reactor is graphite and water moderated, water cooled, and based on a modified

Argonaut design; several experimental facilities surround the core, including the three vertical

ports, beam tubes, and the pneumatic rabbit port. Fig. 1 shows a cutaway view of the UFTR

including the experimental port facilities [1].

3

Fig.1. Isometric cutaway view of the UFTR [1].

Graphite moderator surrounds the fuel boxes on all sides; the concrete and shield tank

provide additional shielding outside the core. The fuel is a plate design made of U3Si2-Al powder

with Al cladding and a nominal enrichment of 19.75 wt% 235U. Fuel bundles are comprised of 14

plates; each fuel box is filled with four fuel bundles. Design parameters of the fuel are shown in

Table I. Fig. 2 illustrates the configuration of the fuel boxes in-core [2].

4

Table I Design Parameters of UFTR Core [1]

DESIGN DATA

Fuel Type U3Si2-Al

Fuel Meat Size

Width (cm)

Thickness (cm)

Height (cm)

5.96

0.051

60.0

Fuel Plate Size

Width (cm)

Thickness (cm)

Height (cm)

7.23

0.127

65.1

Cladding 6061 Al

Cladding Thickness (cm) 0.038

Fuel Enrichment (nominal) 19.75%

“Meat” Composition (wt% U) 62.98

Mass of 235U per Plate (nominal) 12.5 g

Number of Plates per Fuel Bundle 14

Number of Full Fuel Bundles (current) 22

Number of Partial Fuel Bundles 1 (10 fuel plates + 3

dummy plates)

Number of Dummy Bundles 1

Fig.2. Horizontal cut-through view of UFTR core [1].

Fuel bundle

Fuel box

Graphite

Graphite

N

5

The UFTR control system consists of 3 safety blades and 1 regulating blade all in-core.

Control blade drives rotate the blades in and out of the core along a vertical arc. Cadmium at the

tip of the control blades provide the neutron absorption needed for control and magnesium

shrouds protect the blades from obstruction.

MCNP Model of UFTR

MCNP is a Monte Carlo continuous energy transport code that simulates the paths and

interactions of neutrons, photons, and electrons in a three-dimensional Cartesian geometry [3].

The Monte Carlo method applies nuclear data to probabilistic methods of tracking a particle. To

achieve adequate statistics, millions of particles are tracked through the geometry created in

MCNP.

The MCNP model used in this study was created by Dr. Gabriel Ghita for use during the

HEU-to-LEU fuel conversion in 2005. The input is a highly detailed representation of the fuel,

boxes, surrounding graphite, and control blades. Fig.3 depicts the reactor geometry of the MCNP

model as provided via the MCNP Visual Editor Computer Code (VisEd). The model was

modified slightly for the reactor refuel, as updated dimensions for the fuel boxes and higher

boron content in the graphite were added. The three parameters under investigation were

manipulated by changing the surface cards (fuel box size), material cards (boron content) and

cell cards (graphite porosity).

6

Fig.3. Vertical cross-sectional view (left) and horizontal cross-section view (right) of UFTR core

model in MCNP [4].

Six-factor Formula

The key for a nuclear reactor to produce power is sustaining a desired eigenvalue, or k;

the variable describing the rate of change of the neutron population is the criticality constant, k,

described as

𝑘 =# 𝑜𝑓 𝑛𝑒𝑢𝑡𝑟𝑜𝑛𝑠 𝑖𝑛 𝑛𝑡ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛

# 𝑜𝑓 𝑛𝑒𝑢𝑡𝑟𝑜𝑛𝑠 𝑖𝑛 (𝑛−1)𝑠𝑡 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛=

𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒

𝐿𝑜𝑠𝑠 𝑟𝑎𝑡𝑒 . (1)

The three possible ranges of value for k are as follows:

1. The reactor is sub-critical. k < 1.

2. The reactor is critical. k = 1.

3. The reactor is supercritical. k > 1.

Research and power reactors are designed to be critical (k=1), so the fission reaction is sustained

but controlled. Slight fluctuations below and above 1 are still well controlled. The criticality

constant can be found through the six-factor formula,

𝑘 = 𝜂𝑓𝑝𝜀𝑃𝑇𝑁𝐿𝑃𝐹𝑁𝐿 = 𝑘∞𝑃𝑇𝑁𝐿𝑃𝐹𝑁𝐿 . (2)

Control Blade Graphite Central Hole

Horizontal

Through-port

Fuel Box Control

Blades

7

The terms of the six-factor formula, for a homogenous reactor, are described as followed:

η = average number of neutrons produced per absorption in fuel = νσf/σa

o ν = number of neutrons produced per fission.

o σf = microscopic fission cross section.

o σa = microscopic absorption cross section.

f = thermal utilization = probability neutron is absorbed in fuel, given it is absorbed.

= ΣFa/Σa

o ΣFa = macroscopic absorption cross section of the fuel.

o Σa = macroscopic absorption cross section of the system.

p = resonance escape probability = fraction of fission neutrons that manage to slow down

from fission to thermal energies without being absorbed.

ε = fast fission factor =

Total number of fission neutrons (from both fast and thermal fission)

Number of fission neutrons from thermal fissions

PTNL = Probability of thermal neutrons not leaking.

PFNL = Probability of fast neutrons not leaking

k∞ = criticality constant assuming an infinite assembly (no leakage) [5].

Fig. 4 explicitly details all six factors that determine the critical state of the reactor via an

example of the neutron life cycle with a keff = 1.

The factors η and ε are determined by the fuel (fissile isotope and enrichment) and the energy

distribution of the neutron flux. The two variables highly dependent on the overall design (size,

reflection, etc.) and the fuel-to-moderator ratio are f and p. An increase in the boron content

decreases the thermal utilization, f, since there is another strong thermal neutron absorber in the

system. The fuel-to-moderator ratio directly affects the resonance escape probability, p, since

fission neutrons are less likely to thermalize before being absorbed by the resonance peaks in

238U.

8

Fig. 4. Example neutron life cycle of a nuclear reactor [6].

Reactivity

Reactivity, used to measure the subcritical or supercritical nature of a reactor system, is

mathematically defined as

𝜌 =𝑘−1

𝑘 , (3)

where k is the criticality constant and ρ is the reactivity [7]. This study will investigate reactivity

in terms of Δk/k, which comes out explicitly from Eqn. 3. Most reactor cores are designed to be

inherently supercritical and have excess reactivity – but this reactivity is suppressed through the

use of control rods or blades.

9

Boron Content of Graphite

The raw material used to create the graphite moderator in reactors is laced with trace

amounts of some elements whose nuclei have a very high cross section for absorption of thermal

neutrons [8]. The most prominent of these impurities is 10B. Table II provides the cross sections

of 10B and 235U.

Table II. Comparison of cross sections of 10B and 235U [9].

Total Cross Sections 235U 10B

Thermal (0.0253 eV) 698.2 b 3840 b

Fast (14 MeV) 5.865 b 1.467 b

The 10B poses a serious issue for thermal reactors, especially if the total amount of boron

in the materials of the reactor is unknown. Fig. 5 shows the competing absorption cross sections

of 235U, 238U, and 10B. The 10B clearly dominates at lower energies, allowing its use as a “fission

poison” in a thermal reactor.

Fig. 5. Absorption cross sections for 235U (red), 238U (blue), and 10B (green) [9].

= 10B

= 235U

= 238U

10

Neutron Moderation and the Porosity of Graphite

Neutrons born from fission are produced at a wide range of energies, characterized by the

Watt fission spectrum χ(E), shown in Fig. 6.

Fig. 6. Fission spectrum, χ(E), for thermal neutron-induced fission in 235U [7].

Inspection of Fig. 5 shows that the fission of a 235U nucleus is most efficient at low

energies, specifically thermal energies. The most probable initial energy for a fission-born

neutron is approximately 1 MeV, many orders of magnitude greater than desired for an efficient

thermal reactor. Consequently, neutrons must be slowed down, or “moderated”, via elastic

scattering with a light nucleus. Neutron elastic scattering is characterized by the following

equations:

𝐸′ = 𝐸(1+𝛼)+(1−𝛼)cos𝜃

2 , (4)

𝛼 = (𝐴−1

𝐴+1)

2 , (5)

where E is the initial neutron energy, E’ is the neutron energy after the elastic collision, θ is the

angle of incidence in the center of mass system, and A is the mass number of the scattering

medium [5]. Commercial reactors generally use water as a moderator because of its hydrogen

(A=1) content; on average, neutrons lose half of their energy when colliding with a hydrogen

nucleus. The UFTR uses graphite and water as moderators because of their low absorption and

low mass numbers (A=12 for graphite and A=1 for the hydrogen in water).

11

The probability of a neutron scattering with a nucleus per unit length is characterized by

the macroscopic neutron scattering cross section, Σs. Macroscopic cross sections are derived

from microscopic cross sections, σs, via the relation

𝛴𝑠 = 𝑁𝐶𝜎𝑠 , (6)

𝑁𝐶 =𝜌𝑁𝐴

𝑀 , (7)

where NC is the number density in atoms/cm3, ρ is the mass density in g/cm3, NA is Avogadro’s

number, and M is the molar mass of the atom [7]. Microscopic cross sections, σ, are defined as

the effective area the nuclide presents to the incident neutron in barns (10-24 cm2). The

macroscopic cross section is directly proportional to the mass density of the medium. A decrease

in the density has a significant impact on the reactivity of the core through the resonance escape

probability. Fig. 7 shows the absorption cross section for 238U, which is the more prominent

isotope of uranium in the UFTR fuel. The resonance region spans a significant energy range,

encompassing most of the epithermal region (1eV – 100 keV). Neutrons may be absorbed by the

resonance peaks in 238U before they have the chance to thermalize and fission a 235U nucleus, an

effect enhanced in an undermoderated core.

Fig.7. Total absorption cross section for 238U [9].

Radiation damage to graphite in high temperature reactors (HTR) is generally not an

issue, because high temperatures (~500°C and higher) largely repair damage through thermal

annealing [8]. In the UFTR, the graphite moderator never reaches a high enough temperature to

12

resolve radiation damage. As a result, degradation of the graphite may cause a minute change in

the average density of the material.

Fuel Box Size

Although graphite is considered a moderating medium for the UFTR, water pumped

through the fuel boxes still plays a considerable role in thermalizing the neutrons born from

fission.

During the reactor refuel, a possible issue arose when the fuel was packing tighter than

expected in the fuel boxes. This suggests the fuel boxes are smaller than the recorded

dimensions, or the fuel is bigger than recorded. This poses a neutronics problem, as the effect on

the fuel-to-moderator ratio is non-trivial. Fig. 8 is a visualization of the northwest fuel box in

MCNP. Manipulation of the sizes of the fuel boxes was limited to the error on the specifications

of the boxes, which was less than ± 1/16th of an inch.

Fig. 8. Visual depiction of northwest fuel box in MCNP.

Somewhat analogous to the porosity of graphite discussed earlier, decreasing the size of

the fuel boxes also decreases the resonance escape probability. Unlike the former problem,

where density is the driving factor, shrinking the fuel boxes decreases the moderator-to-fuel

ratio. Although shrinking the fuel boxes likely leads to under-moderation of the system, over-

Fuel Bundle (4) Fuel Box

Water

13

moderation is still possible in a poorly designed core. Fig. 9 illustrates the effects of an over-

moderated and under-moderated system on k. Reduction of k in an under-moderated system is

driven by the resonance escape probability and the thermal utilization factor in an over-

moderated system.

Fig. 9. Effect of over-moderation and under-moderation on k[6].

RESULTS AND DISCUSSION

Benchmark of Original Input

The original input from the HEU-to-LEU conversion and the modified input for the 2010

refuel were run. Results of these runs are shown in Table III.

14

Table III. Results of benchmark criticality runs.

Run Description keff

Standard

Deviation Cycles

Skipped

Cycles

Histories

Per

Cycle

1

Original input from

HEU/LEU conversion 1.00175 0.00013 800 100 50000

2 Modified input (refuel) 1.00162 0.00014 800 100 50000

Although little justification is provided for the changes made, the modified input was

used in the rest of the simulations for this project Fig. 10 is a full, energy independent flux

profile of the UFTR core. The values above, as well the flux profiles agree with the values

presented in the HEU-to-LEU fuel conversion report [1]. As expected, the flux peaks in the

center fuel boxes and follows a cosine shape for a symmetric core.

Fig. 10. Total flux profile of UFTR core from Run 1, showing all six fuel boxes. View is cross-

sectional cut of x-y plane on center boxes.

15

Boron Content of Graphite

Table IV displays the results of the criticality runs with varying boron content in the

graphite. Fig. 11 shows the relationship between the criticality constant and the content of 10B in

the UFTR graphite. Figs. 11 and 12 detail the changes in k and reactivity with varying 10B

content. 1 ppm of 10B is worth 0.0026 Δk/k.

Table IV. Results of criticality runs with varying boron content.

10B Content (ppm) keff

Standard

Deviation Δk/k

0.8 ** 1.00162 0.00014 0.001617

0.5 1.00211 0.00013 0.002106

1 1.00102 0.00013 0.001019

1.5 1.00012 0.00013 0.00012

2 0.99876 0.00013 -0.00124

2.5 0.99761 0.00013 -0.0024 *All runs completed with 800 cycles, 100 skipped cycles, 50000 histories per cycle.

** Original model.

Fig. 11. Relationship between 10B content in graphite and keff. Error bars are encompassed by the

data points.

0.997

0.998

0.999

1.000

1.001

1.002

1.003

0.000 0.500 1.000 1.500 2.000 2.500 3.000

keff

10B (ppm)

16

Fig. 12. Relationship between 10B content in graphite and reactivity. Error bars are encompassed

by the data points.

As expected, the reactivity decreases approximately linearly with increasing boron

content. The core does not reach subcriticality until 2ppm of 10B, a substantial amount for high

purity reactor graphite. Increments of 0.5ppm 10B cause changes in reactivity on the order of

0.1%.

Porosity of Graphite

Table V shows the results of the criticality runs with varying density of graphite. Figs. 13

and 14 detail the changes in k and reactivity with varying density of the surrounding graphite of

the UFTR.

Table V. Results of criticality runs for varying graphite density.

Density of Graphite (g/cm3) keff

Standard

Deviation Δk/k

1.6 ** 1.00162 0.00014 0.001617

1.59 1.00055 0.00013 0.00055

1.58 0.999 0.00013 -0.001

1.57 0.99786 0.00013 -0.00214

1.56 0.99649 0.00013 -0.00352

1.55 0.995 0.00013 -0.00503 *All runs completed with 800 cycles, 100 skipped cycles, 50000 histories per cycle.

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.000 0.500 1.000 1.500 2.000 2.500 3.000

Rea

ctiv

ity

(Δ

k/k

)

Boron content (ppm)

17

** Original model

Fig. 13. Relationship between the density of the graphite and keff. Error bars are encompassed by

the data points.

Fig. 14. Relationship between the density of the graphite and reactivity. Error bars are

encompassed by the data points.

Decreasing the graphite density has a dramatic effect on the core, causing a subcritical

condition at 1.58 g/cm3, only a 1.25% decrease in density. Despite this decrease being

numerically feasible, an actual decrease of 1% or greater in the density is substantial. Although

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.002

1.003

1.540 1.560 1.580 1.600 1.620

keff

Density of Graphite (g/cm3)

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

1.540 1.550 1.560 1.570 1.580 1.590 1.600 1.610

Rea

ctiv

ity (

Δk

/k)

Density of Graphite (g/cm3)

18

1.6 g/cm3 is purely a theoretical density, significant fluctuations from this density should not be

assumed without some experimental measurements.

Fuel Box Size

Table VI shows the results of the criticality runs with varying fuel box sizes. Figs. 15 and

16 show the relationship between the moderator-to-fuel ratio, k, and reactivity. Moderator-to-fuel

ratio was calculated by taking the ratio of the volume of water in each fuel box to the volume of

fuel. The ratio was manipulated by changing the length and width of the fuel boxes.

Table VI. Results of criticality runs for varying moderator-to-fuel ratios.

Moderator-to-Fuel Ratio keff

Standard

Deviation Δk/k

1.18645 ** 1.00162 0.00014 0.001617

1.17710 1.00166 0.00013 0.001657

1.16496 1.00128 0.00014 0.001278

1.15468 1.00121 0.00014 0.001209

1.14441 1.00097 0.00013 0.000969

1.13039 1.00087 0.00013 0.000869 *All runs completed with 800 cycles, 100 skipped cycles, 50000 histories per cycle.

** Original Model

Fig. 15. Relationship between the moderator-to-fuel ratio and keff. The error bars represent one

standard deviation.

1.00060

1.00080

1.00100

1.00120

1.00140

1.00160

1.00180

1.00200

1.100 1.120 1.140 1.160 1.180 1.200

keff

Moderator-to-Fuel Ratio

19

Fig. 16. Relationship between the moderator-to-fuel ratio and reactivity. The error bars represent

one standard deviation.

Large error bars in Fig. 13 are due to the small range of the data. Even with the largest

decrease in fuel box size possible, k only changes a minute amount, much less than 0.1%. The

core never reaches a subcritical condition, which is expected since water is not the primary

moderator. One data point of interest in run 1, the small increase in reactivity, is likely a data

fluctuation well within the recorded uncertainty; it may also indicate some slight overmoderation

with the original fuel box size.

CONCLUSIONS

Of the three parameters investigated, the most dramatic change in reactivity was observed

when the graphite density was changed. The likelihood of this phenomenon being physically

accurate is low, but the effect is significant enough to warrant attention. One way to evaluate the

feasibility of degradation of the graphite is through chemical analysis, specifically an analysis of

indicator elements. The ideal element for such an analysis is boron through the 10B/11B ratio [11].

Investigating this ratio would provide information about the overall accumulated fluence over the

lifetime of the reactor, the condition of the graphite moderator, and the boron content.

The effect on reactivity is likely not due to one variable, but a combination of the three

factors investigated above or others not considered in this report. It is important to recognize the

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

1.100 1.120 1.140 1.160 1.180 1.200

Rea

ctiv

ity (

Δk

/k)

Moderator-to-Fuel Ratio

20

limitations of a purely theoretical study and the limitations of a tool like MCNP. An MCNP

model is only as accurate as the user makes it, and the physical correspondence of a model with

reality can only be confirmed with experiments. Unfortunately, the UFTR was not operational

for the purposes of this study. Nonetheless, the results suggest all three parameters investigated –

the boron content, the porosity of the graphite, and the fuel box size – are contributing to the

unanticipated loss in reactivity.

ACKNOWLEDGMENTS

The author would like to acknowledge Dr. Alireza Haghighat for his guidance, Dr.

Gabriel Ghita for the use of his original MCNP model of the UFTR, and Dr. Ce Yi for his help in

learning MCNP.

21

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[2]. PATEL A.D. Detailed neutron flux characterization of the experimental shield tank facility

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TEAM, MCNP5 —, LA-UR-03-1987, Los Alamos National Laboratory, Los Alamos,

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[6]. DOE FUNDAMENTALS HANDBOOK. NUCLEAR PHYSICS AND REACTOR

THEORY. Volume 2 of 2. DOE-HDBK-1019/2-93.

[7]. STACEY, W.M., 2001 Nuclear Reactor Physics / Weston M. Stacey, Jr . Wiley, New York.

[8]. CARTER, R.L., EGGLESTON, R.R., Moderator Graphite for High Temperature Reactors.

Nuclear Engineering and, Manufacturing, North American Aviation, Inc., Downey,

California. August 1, 1955.

[9]. Table of Nuclides. Web. 17 Feb. 2011. .

[10]. SJODEN, G.E., MOCK, T.A., ENU 4103/6937 Nuclear Reactor Analysis & Computation I

– Statics. Course Notes. Spring 2010.

[11]. GESH, C.J., A Graphite Isotope Ratio Method Primer—A Method for Estimating

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