ORNL-TM-13524.txt

ORNL/TM-13524

ISOTOPIC DILUTION REQUIREMENTS FOR **U CRITICALITY SAFETY IN
PROCESSING AND DISPOSAL FACILITIES

K. R. Elam, C. W. Forsberg, C. M. Hopper, and R. Q. Wright

Oak Ridge National Laboratory”
Oak Ridge, Tennessee 37831-6495

November 1997

 

"Managed by Lockheed Martin Energy Research Corp., under contract DE-AC05-960R22464 for the
U.S. Department of Energy.
CONTENTS

LIST OF FIGURES . . .o e e e e e e e e s i i, v
LIST OF TABLES . . . e e e e e e e e e e s i i, Vil
AC R ON Y M . e, 1X
EXECUTIVE SUMMARY . .. e e e e e e s i i, X1
AB ST R ACT . .o e, XV
1. INTRODUCTION . .. . e e e e s 1
1.1 BACKGROUND .. e e, 1
1.2 GOALS OF THIS REPORT . .. .. e e, 1
1.3 REPORT STRUCTURE . . ... e i 2
1.4 METHODOLOGY . ..o e e e e i s i, 2
2. APPROACHES TO CRITICALITY CONTROL . . . ... e 3
3. BASIS FOR NUCLEAR CRITICALITY CONTROL BY ISOTOPIC DILUTION ..... 5

3.1 PRECEDENTS: THE STRATEGY FOR CRITICALITY CONTROL OF

WASTE 27U .. 5

3.2 CRITICALITY CONTROL IN WASTE PROCESSING OPERATIONS ........ 6
3.2.1 Process Options for 22U .. ... ... ...t 6

3.2.2  Characteristics of Waste Process Operations ........................ 6

3.2.3  Current Criticality Control Practices .............................. 7

3.24 2¥U Processing Example Case ... ...........uuiuieiiieiaennan. 8

3.3 CRITICALITY CONTROL IN DISPOSAL FACILITIES .................... 9
3.3.1 Concerns About Nuclear Criticality in Repositories .................. 9

3.3.2  Specific Nuclear Criticality Scenarios . .................cuiine.n... 9
3.3.2.1 Package Criticality ......... ..., 11

3322 ZoneCriticality ......... ... 11

3.3.2.3  Factors Affecting Isotopic Dilution Requirements for *°U . . . .. 13

3.3.3 Institutional and Legal Requirements for Repository Criticality Control . . 14
3.3.3.1 Current Requirements ................ ... .. .......... 14

3.3.3.2 NWTRB Recommendations . ............................ 15

334  Conclusions ... ...t e 15

111
CONTENTS (continued)

4. ISOTOPIC DILUTION OF U . ...ttt e e e e e 17
4.1 METHODOLOGY ... e e e e e e 17
4.2 RESULTS .. 18
4.3 NEUTRONIC CONCLUSIONS ... e 18
5. CONCLUSION . . e e e e e e e e e 19
6. REFERENCES ... e e e e e e 21

Appendix A: NEUTRONIC ANALYSIS OF **U CRITICALITY CONTROL
REQUIREMENTS . .. e A-1

v
Fig. 1
Fig. 2

LIST OF FIGURES

Alternative disposal facility criticality scenarios .......

Natural and man-made formation of uranium ore deposits
Table 1

Table 2

Table A.1
Table A.2
Table A.3
Table A.4
Table A.5
Table A.6

LIST OF TABLES

Allowable enrichment levels for 2°U without nuclear criticality controls . ... .. 7
Use of isotopic dilution for control of U nuclear criticality ................ 8
Computational results . .. ... e A-8
Example SCALE XSDRNPM input forresult No. 51 ...................... A-12
SCALE calculated vs regression predicted values ... ...................... A-14
Influence of ***U and U on infinite systems of *°U diluted with **U ........ A-16
Characteristics of CEUSP material ........... ... ... ... ... ... ..... A-18
k. vs water volume fraction . . ... ... ... ... e A-19

Vil
ANS
CEUSP
CFR
DOE
DU
DWPF
EBS
EIS
EPA
HEU
HLW
IAEA
LMES
LWR
NAS
NRC
NWTRB
ORNL
SNF
TRUW
WHC
WIPP

ACRONYMS AND ABBREVIATIONS

American Nuclear Society
Consolidated Edison Uranium Solidification Program
Code of Federal Regulations

U.S. Department of Energy

Depleted uranium

Defense Waste Processing Facility
Engineered barrier system
Environmental impact statement

U.S. Environmental Protection Agency
High-enriched uranium

High-level waste

International Atomic Energy Agency
Lockheed Martin Energy Systems, Inc.
Light-water reactor

U.S. National Academy of Sciences
U.S. Nuclear Regulatory Commission
U.S. Nuclear Waste Technical Review Board
Oak Ridge National Laboratory

Spent nuclear fuel

Transuranic Waste

Westinghouse Hanford Company

Waste Isolation Pilot Plant

1X
EXECUTIVE SUMMARY

BACKGROUND

With the end of the cold war, the U.S. government is examining options for disposing of excess
fissile materials, which potentially include ***U. Part of this material will be retained for research,
medical, and industrial uses. However, a portion of the inventory may be declared excess and
consequently may require disposal.

Uranium-233 has a smaller critical mass than does either U or **’Pu and has other fissile properties
that are also significantly different from other fissile isotopes. This report addresses the unique
criticality issues associated with processing and disposal of U and suggests the use of isotopic dilution

to minimize nuclear criticality control problems.

CHARACTERISTICS OF PROCESSING AND DISPOSAL OF **U

The potential quantities of ***U requiring disposition are small, and some of the ***U contains ***U
and its highly radioactive daughter products sufficient such as to require hot-cell processing of the
material to an acceptable waste form. For these relatively small quantities of material, there are strong
economic incentives to (1) use existing facilities and (2) avoid complex criticality control and other
licensing issues associated with the high-level waste (HLW)/spent nuclear fuel repository program.

Existing U.S. Department of Energy (DOE) HLW vitrification facilities and proposed transuranic
waste processing facilities may be able to process **U. However, these facilities are not designed for
significant concentrations of fissile materials. If such facilities are to be used, it is not possible to rely on
traditional geometry or chemical (e.g. neutron absorbers or fissile concentration) controls to maintain
nuclear criticality safety without substantial modifications of plant equipment and operations.

If neither geometric nor chemical control is practicable for nuclear safety in a processing facility,
1sotopic dilution (enrichment) 1s the best remaining criticality control option. Isotopic dilution is the
addition of ***U sufficient such as to lower the ***U enrichment level below that at which nuclear
criticality can occur. It is important to note that all uranium isotopes have the same chemical
characteristics; therefore, the >**U used to isotopically dilute the ***U will not separate from the fissile
uranium in any normal chemical process.

It is also difficult to rely on geometry or chemical composition alone within disposal facilities to

control criticality over geological time frames. Several mechanisms can cause changes in waste

Xi
geometry and chemistry, including groundwater transport of uranium and mechanical disturbances of the
waste. If criticality control is to be ensured for thousands of years by either geometric control or
chemical control (including neutron absorbers), system performance must be predictable for these lengths
of time. Such predictions are difficult to generate and are subject to substantial uncertainties. No such

difficulties exist when isotopic dilution is used for criticality control.

LEGAL AND INSTITUTIONAL CONSIDERATIONS

An expanding series of laws, regulations, recommendations, and actions by the U.S. government
address nuclear criticality in regard to disposal facilities. A trend is developing to use isotopic dilution as
the preferred method of criticality control for fissile materials following disposal. The environmental
impact statement (DOE, June 1996) and record of decision (DOE, July 1996) for the disposition of
excess high-enriched uranium (HEU) recommended isotopic dilution of the fissile **°U if any HEU was
disposed of as a waste. The same considerations apply to the disposition of excess **U. The U.S.
Nuclear Waste Technical Review Board (NWTRB), the Congressionally-mandated review board for the
proposed Yucca Mountain geological repository, has also recommended consideration of the use of
depleted uranium (DU) to isotopically dilute fissile materials to prevent the potential for nuclear
criticality in geological repositories containing fissile material (NWTRB, 1996). Finally, a recent U.S.
Nuclear Regulatory Commission report made similar recommendations on the use of DU for criticality

control in various disposal facilities (NRC, 1997).

CONTROL OF NUCLEAR CRITICALITY BY ISOTOPIC DILUTION

The work presented herein determined that to ensure control of nuclear criticality in >**U by isotopic
dilution with ***U, the **U concentration must be reduced to <0.66 wt %. In terms of nuclear criticality
safety, this concentration is equivalent to °U at an enrichment level of ~1.0 wt %—a level which will
not result in nuclear criticality under conditions found in processing or disposal facilities. These uranium
1sotopic concentrations avoid the need to control other parameters to prevent nuclear criticality; that is,
the U can be treated as another radioactive waste. At these concentrations, nuclear criticality will not
occur in a geological environment, over time, nor in waste processing operations that have not been
designed for fissile materials.

For mixtures of Z*U and **’U, the amount of DU (with 0.2 wt % **U) in grams (g) required to ensure

criticality control by isotopic dilution in a water-moderated system is the following:

Xii
g DU = 188 ¢ U + (EO—_Sl) - g of enriched uranium, (E.1)

where

DU
E

g of DU (0.2 wt % >U)
the wt % of **U, where the g of enriched uranium = total U - **U

In Eq. (E.1), #*U and ***U may be considered to be **U—providing the atom ratio of the (**U +
29U):*°U does not exceed 1.0. If the quantity of grams DU calculated using Eq. (E.1) is negative, the
uranium material already contains sufficient Z*U such as to ensure subcriticality; therefore, no additional

DU is needed.

REFERENCES

U.S. Department of Energy, Office of Fissile Materials Disposition, June 1996. Disposition of Surplus
Highly Enriched Uranium Final Environmental Impact Statement, DOE/EIS-0240, Washington, D.C.

U.S. Department of Energy, July 29, 1996. Record of Decision for the Disposition of Surplus Highly
Enriched Uranium Final Environmental Impact Statement, Washington D.C.

U.S. Nuclear Waste Technical Review Board, 1996. Report to the U.S. Congress and the Secretary of
Energy: 1995 Findings and Recommendations, Arlington, Virginia.

U.S. Nuclear Regulatory Commission, 1997. The Potential for Criticality Following Disposal of
Uranium at Low-level Waste Facilities, NUREG/CR-6505, Washington, D.C.

X111
ABSTRACT

The disposal of excess *’U as waste is being considered. Because *°U is a fissile material, one of
the key requirements for processing ***U to a final waste form and disposing of it is to avoid nuclear
criticality. For many processing and disposal options, isotopic dilution is the most feasible and preferred
option to avoid nuclear criticality. Isotopic dilution is dilution of fissile **U with nonfissile **U. The
use of 1sotopic dilution removes any need to control nuclear criticality in process or disposal facilities
through geometry or chemical composition. Isotopic dilution allows the use of existing waste
management facilities, that are not designed for significant quantities of fissile materials, to be used for
processing and disposing of **U.

The amount of isotopic dilution required to reduce criticality concerns to reasonable levels was
determined in this study to be ~0.66 wt % ***U. The numerical calculations used to define this limit
consisted of a homogeneous system of silicon dioxide (Si0,), water (H,0), ***U, and depleted uranium
(DU) 1in which the ratio of each component was varied to determine the conditions of maximum nuclear
reactivity. About 188 parts of DU (0.2 wt % ***U) are required to dilute 1 part of ***U to this limit in a
water-moderated system with no SiO, present. Thus, for the U.S. inventory of ***U, several hundred

metric tons of DU would be required for isotopic dilution.

XV
1. INTRODUCTION

1.1 BACKGROUND

With the fairly recent ending of the cold war, the U.S. government is examining options to dispose of
excess fissile materials, which potentially include ***U. Part of this material will be retained for research,
medical, and industrial uses. A portion of the inventory may be declared excess and, consequently, may
require disposal.

If #*U is declared a waste, there are economic incentives to use existing waste processing facilities to
prepare the material for disposal. Much of the ***U contains significant quantities of ***U and its highly
radioactive daughter products. The characteristics of these materials may require that processing for
waste management occur in hot cells. Because of the cost of such facilities and the relatively small
quantities of U (<2 t), it would be sensible to use current waste management facilities. However, these
facilities were not designed for significant concentrations of fissile materials and for addressing any
resulting nuclear criticality control issues. Therefore, criticality control is the major technical issue
associated with using these facilities for ***U processing.

Requirements for disposal of this material as waste are being identified (Kocher, 1996). Most of the
technical requirements are somewhat understood because they are similar to those required for other
wastes. The exception is nuclear criticality safety requirements for the **U wastes following their
disposal. Because fissile materials can be used for nuclear weapons, materials with high fissile
concentrations were not considered for disposal before the end of the cold war. Consequently, disposal
of such fissile materials imposes the addition of criticality control to other requirements for safe disposal.

Uranium-233 has a smaller critical mass than does either U or **’Pu and has other fissile properties
that are also significantly different from other fissile isotopes. This report addresses the unique
criticality issues associated with processing and disposal of U and suggests the use of isotopic dilution

to minimize nuclear criticality control problems.

1.2 GOALS OF THIS REPORT
The objectives of this report are to:

. Identify and describe regulatory, engineering, and other factors influencing the choice of a
criticality control strategy.
2

. Describe the basis for choosing isotopic dilution as the preferred criticality control strategy
for the disposition of **°U.

. Identify and describe the technical factors and historical experience in isotopic dilution for
criticality control.

. Determine required dilution of >**U with ***U to avoid criticality concerns during processing
or disposal.

1.3 REPORT STRUCTURE

This report addresses three issues: (1) a description of the possible approaches to criticality control
for *U (presented in Sect. 2), (2) the basis for criticality control by isotopic dilution (described in Sect.
3), and (3) a neutronics analysis of the required dilution required for ***U (provided in Sect. 4). The

appendix provides the detailed descriptions of the criticality analysis.

1.4 METHODOLOGY

The available information on criticality control for systems containing ***U is limited compared to the
extensive theoretical and experimental work done with 2°U systems. Therefore, the approach used in
this study was to use the **U experience to define criticality control requirements for analogous ***U

systems.
2. APPROACHES TO CRITICALITY CONTROL

Nuclear criticality of fissile material is controlled through the balance of neutron production (i.e.,
through the fission process) with neutron losses (i.e., leakage from the fissile material system or
nonfission neutron capture in the fissile material). Two common approaches to ensuring subcriticality
are (1) geometric arrangement of fissile material which enhances neutron leakage from the system and
(2) the use of neutron absorbers. Geometrically safe design of process equipment in a large-capacity
plant is expensive. If neutron absorbers are used to control criticality, care must be taken to ensure that
the absorbers do not chemically separate from the fissile material. Many different neutron absorbers
(e.g., boron, gadolinium, cadmium, >**U) are available. However, nuclear criticality in **U systems can
best be avoided by isotopic dilution of the ***U with the nonfissile neutron absorber 2*U. This avoids the
above constraints. Because all uranium isotopes have the same chemical characteristics, the **U will not
separate from the fissile uranium (which could be ***U or ***U) in any normal chemical process, either
before or after disposal.

If the ***U is declared waste, isotopic dilution converts the material from a fissile material for which
nuclear criticality is a major safety concern into another type of very low-enriched uranium waste for
which nuclear criticality 1s not a significant concern. This approach simplifies waste management
operations in two ways:

1. It allows the use of existing waste management facilities such as high-level waste (HLW)

vitrification plants for conversion of the uranium into an acceptable chemical form for disposal.
Waste management facilities are not typically designed to be geometrically safe for criticality

control, and chemical reactions within such processes may separate uranium from other elements
that are neutron absorbers.

2. Italso allows disposal in a geological repository without creating new, unique, and difficult
issues, such as the expected repository licensing requirements for the control of nuclear
criticality.

This simplification is important for disposition of **U, which, although a unique material, is in
quantities that are small when compared to quantities of excess plutonium or excess high-enriched
uranium (HEU). While the development of new technologies, new facilities, and new institutional
structures may be warranted for the disposition of large quantities of excess plutonium or HEU, such
costs would be excessive for disposition of the smaller quantities of ***U. Therefore, strong economic
incentives exist to use current technologies, systems, and facilities where possible. Isotopic dilution is an
acceptable nuclear criticality control in existing facilities in which neither geometric nor chemical

conditions can be tightly controlled.
3. BASIS FOR NUCLEAR CRITICALITY CONTROL BY ISOTOPIC DILUTION

The recommendation to use isotopic dilution for nuclear criticality control during the processing and
disposing of **U is based on three considerations: (1) the decision to use isotopic dilution for disposition
of 2U, (2) technical factors associated with criticality control in process operations, and (3) technical

and institutional factors associated with criticality control in disposal facilities.

3.1 PRECEDENTS: THE STRATEGY FOR CRITICALITY CONTROL OF WASTE *°U

The U.S. Department of Energy (DOE), in its environmental impact statement (EIS) on disposition of
surplus HEU (DOE, June 1996) and the subsequent Record of Decision (DOE, July 1996) has defined
preferred alternatives for disposition. The relatively pure HEU is to be blended with ***U down to 4 wt
% **U and sold for power reactor fuel. The HEU with no commercial value (because of various
impurities, including *°U) is to be isotopically diluted with ***U to eliminate safeguards and nuclear
criticality concerns and disposed of as waste. For HEU that is declared waste, the EIS recommended
blending down to 0.9 wt % ***U to eliminate criticality concerns. This conservative value was chosen to
bound the environmental impacts of uranium-processing operations. (The homogeneous nuclear
criticality limit for U is ~1 wt % ***U.) The lower the final enrichment of the waste uranium, the more
DU that must be added to the HEU, the larger the processing requirements, and the more waste there will
be to dispose of. It is also noteworthy that a recent U.S. Nuclear Regulatory Commission (NRC) report
made similar recommendations on the use of DU for criticality control in various disposal facilities
(NRC, 1997).

The decision to use isotopic dilution to below 1% **U as the preferred strategy for criticality control
in the disposition of excess HEU as waste is based on many considerations. These include:

» Historical, experimental, and theoretical information suggests that if uranium enrichments are
>1.3 wt % **°U, nuclear criticality in a geological repository is a possibility (Naudet, 1977). In
fact, the historical geological records (Brookins, 1990; Cowan, July 1976; and Smellie, March
1995) show that nuclear criticality has occurred in natural uranium ore bodies in the past. At the
Oklo, Africa, site, 15 natural nuclear reactors have been identified which operated when the *°U
enrichment of natural uranium on earth was ~3.6 wt %. When these natural reactors shut down,
the *°U enrichments were as low as 1.3 wt %—an enrichment which is equivalent to the fissile
enrichment of full-burnup light-water reactor (LWR) spent nuclear fuel (SNF). Today, natural

uranium deposits have a >**U enrichment level of 0.71 wt %. Nuclear criticality can now no
longer occur in natural uranium ore bodies because of these low enrichment levels.

e The French Atomic Energy Commission (Commissariat Francais a L’Energie Atomique) has
studied the conditions during which natural nuclear reactors formed (Naudet, 1977). Its analysis
indicates that nuclear criticality could occur at enrichments as low as 1.28 wt % **°U, but
criticality becomes more reasonably probable in some geological environments as enrichments
approach 1.64 wt % **°U.
6

* Criticality standards [American Nuclear Society (ANS), October 7, 1983] and laboratory
experiments (Paxton and Pruvost, July 1987) with the types of materials found in the natural
environment indicate that nuclear criticality could, in theory, occur with fissile enrichment
concentrations as low as 1 wt % ***U, but no experimental evidence exists that such an event has
occurred in nature. Such criticality in a natural system would require nearly incredible
conditions.

* Modeling studies for disposal of high-enriched SNF in repositories using waste packages not
filled with depleted uranium (DU) show nuclear criticality to be the major technical issue for
disposition of such fuels (Rechard, 1993; Patric and McDonell, March 6, 1992). The models
conclude that criticality may occur in a repository in a manner similar to that which has occurred
in the natural environment. The uncertainties associated with geochemical evolution of a
repository, over time, make predictions highly uncertain.

The criticality and safeguards concerns associated with disposing of ***U also apply to ***U. The
same techniques for criticality control are also applicable, and the institutional precedents set by the HEU

EIS are noteworthy.

3.2 CRITICALITY CONTROL IN WASTE PROCESSING OPERATIONS
3.2.1 Process Options for 2°U

Many options are available for preparing and processing ***U for disposal. However, no decision has
been made on the preferred option. Large waste management facilities with billion-dollar capital costs
exist, and additional facilities are being built. Because the quantities of excess ***U are small, there are
strong economic incentives to use these existing facilities. However, none are designed to handle fissile

materials for which nuclear criticality is a consideration. Examples of options include:

» HLW glass logs. DOE is vitrifying HLW into borosilicate glass logs for disposal. The Defense
Waste Processing Facility (DWPF) is operating at the Savannah River Site, and other facilities
for vitrifying HLW are under construction or are being planned. Excess **’U could be added to
the HLW tanks and converted into glass.

» Transuranic waste (TRUW) processing facility. DOE, Idaho Operations Office, has requested
proposals to process TRUW in order to minimize storage, transport, and disposal costs and risks.
Excess **U could be coprocessed with these materials.

3.2.2 Characteristics of Waste Process Operations

In most waste management operations, criticality control is not an issue because the quantities of
fissile materials in the waste streams are very low or fissile materials such as ***U are isotopically diluted
with DU before being processed for disposal to eliminate criticality concerns. For many types of waste
management operations, it is difficult or impossible to ensure criticality control by controlling the

geometry or chemical composition.
7

Wastes are usually heterogeneous, but after waste processing, a homogeneous, high-quality waste
product is often obtained by blending and mixing wastes before their treatment to obtain a chemically
uniform feed to the treatment process. For example, HLW is blended in batches of several hundred
thousand gallons before it is converted to HLW glass. Criticality control via geometry limits on
equipment is not practicable for such large-scale process operations.

Because most wastes do not have uniform chemical compositions that are well-defined, the front-end
chemistry in most waste management processes is also not well-defined. If the chemistry changes during
processing, uranium may precipitate or concentrate. Therefore, a feed material containing dilute
concentrations of uranium will not necessarily remain dilute throughout the entire process.

These intrinsic characteristics of most large-scale waste processing facilities imply that the only
viable nuclear criticality control strategy for such facilities is isotopic dilution of the fissile uranium with

238U.
3.2.3 Current Criticality Control Practices

Nuclear criticality is avoided in chemical processes that are not designed for geometric nuclear
criticality control by either not allowing fissile material into the waste management systems or by
limiting the enrichment level of uranium fed to these systems. Table 1 shows the allowable enrichment
levels for U in different facilities for which no other criticality controls are required. Table 2 shows
the allowable enrichment levels after isotopic dilution for #°U at different DOE facilities at which

1sotopic dilution is conducted as a pretreatment option before fissile wastes enter the treatment system.

Table 1. Allowable enrichment levels for 2*U without nuclear criticality controls

 

 

Site Allowable **°U Reference
Y-12¢ 1.0 Lockheed Martin Energy System (LMES),
February 1995
ETTP? 0.93 LMES, February 1995
Hanford* 1.0 Westinghouse Hanford Company (WHC), 1994
Hanford? 0.71 WHC, 1994

 

“Limits for liquid disposal systems.

*Limits for liquid disposal system, uranium enrichment facility with associated variable enrichments.
‘As homogeneous solutions, compounds, and metals.

YAny amount (except as reflectors).
8

Table 2. Use of isotopic dilution for control of **U nuclear criticality

 

 

Site Allowable U Reference
Oak Ridge National Laboratory 1.00% LMES, February 1995
Savannah River Technical Center 0.65% Westinghouse Savannah River
Company,
May 23, 1995

 

These criticality control limits are based on decades of theoretical analysis, laboratory experiments
(Paxton and Pruvost, 1987), and plant experience. Also, current industrial standards address the
requirements for criticality controls (ANS, 1983).

The allowable **°U assay chosen for criticality control by isotopic dilution depends upon a number of
technical factors. If the wastes to be disposed of are solutions, a higher assay of U can be allowed
because the **U is isotopically mixed with the waste. If the wastes contain solids, isotopic exchange of
the 2°U with the #*U will occur, over time, but the process may be slow. In such cases, added DU may

be required to compensate for mixing uncertainties.
3.2.4 U Processing Example Case

One of the vitrification options for disposition of ***U involves the use of the DWPF. This option
provides an example of the issues associated with nuclear criticality in process operations. This example
also shows the need to examine the specific issues associated with each option. Feed to the DWPF is
from an HLW tank farm. Either the tank farm or the DWPF may place mass limits on ***U feeds. In this
example, the HLW tank farm currently contains 160 t of uranium with an average enrichment of ~0.5 wt
% ***U. Most of this uranium is in only a few tanks. Because the quantities of 2*U for disposal are
relatively small, if the **U is mixed with the HLW in the high-uranium tanks, isotopic dilution would
lower the enrichment to levels sufficient to remove criticality concerns for feed to the DWPF. Thus, in
this example, the criticality issues are (1) acceptance by the tank farm of the ***U and (2) ensurance that it
is possible to mix the ***U uniformly with the existing HLW. In this case, it may be feasible to partly
isotopically dilute the 2*U, add other neutron absorbers that are required to make glass, and feed the
mixture first to the HLW tanks and then the DWPF. Such options may significantly reduce the need to
add DU to the ***U for disposition and minimize final waste volumes. Several waste streams with high

DU loadings in the DOE complex have the potential for coprocessing and disposal.
9
3.3 CRITICALITY CONTROL IN DISPOSAL FACILITIES

Several disposal options exist for **U if it is declared a waste. No decision has been made on the
choice of a preferred option. Options include, but are not limited to, the Yucca Mountain site, which is a
candidate for an HLW repository; the Waste Isolation Pilot Plant (WIPP); and special-case waste
facilities. The fundamental criticality control requirements are similar for all disposal sites, but the

specific details about how the requirements are to be achieved may differ.
3.3.1 Concerns About Nuclear Criticality in Repositories

Nuclear criticality must be avoided in any disposal site to prevent the release of radionuclides to the
environment. Evidence from nuclear reactors naturally occurring in the geological past [Cowan, July
1976; International Atomic Energy Agency (IAEA), 1975; TAEA, 1977; and Smellie, March 1995]
indicate that such events have generated both added radioactivity and heat over time periods of hundreds
of thousands of years. The heat generated creates higher disposal site temperatures that accelerate
chemical reactions which, in turn, degrade waste packages and waste forms. This added heat also causes
water movement within a disposal site that may transport radioactivity to the environment (Buscheck and
Nitao, December 1993) and contributes to large uncertainties in site performance. Water movement can
be accelerated in both unsaturated (Buscheck, Nitao, and Wilder, December 1993) and saturated
geological environments by heat. In this context, it is important to emphasize that the concern is not
necessarily that nuclear criticality may occur or that some radioactivity is added to the disposal site, but
rather that criticality may occur sufficiently and often for a long enough period of time such as to
generate significant amounts of heat, which is a driver for groundwater movement and, hence,
radionuclide transport.

If the ***U material is disposed of in a repository with SNF or HLW, there is initially significant
radioactive decay heat. To minimize the potential impacts of heat on repository performance, the waste
1s packaged in long-lived waste packages. The radioactive decay heat is expected to decrease to low
levels before the waste packages degrade significantly. Nuclear criticality, should it occur, would most
likely occur after loss of waste package integrity. Therefore, the waste package system can not be

expected to contain or prevent the added heat from affecting the repository environment.
3.3.2 Specific Nuclear Criticality Scenarios

There are two classes of repository criticality concerns (Fig. 1): nuclear criticality involving a single
waste package (package criticality) and nuclear criticality involving fissile material from multiple waste
packages (zone criticality). In both classes, there are many possible scenarios. Several of these are

described below.
10

INITIAL CONDITIONS (T = T)

    
     

XKL

  
  
 

—  WASTE
WATER PACKAGE
e e

FLOW

—_—

 

ORNL DWG 95C-555R

x NEUTRON ABSORBER
O URANIUM

Fig. 1. Alternative disposal facility criticality scenarios.
11
3.3.2.1 Package Criticality

Over time, the waste package degrades. Water selectively leaches components from the waste
package. In particular, it is known (Vernaz and Godon, 1992) that boron and certain other neutron
poisons will leach preferentially from a waste package (Fig. 1). Subsequently, if the waste package
contains sufficient fissile material, criticality could occur. This type of nuclear criticality is primarily
associated with large waste packages loaded with many critical masses of fissile material. The
probability of a nuclear criticality occurrence 1s highly dependent upon the details of the waste package

design and the waste form selected.
3.3.2.2 Zone Criticality

Once the waste package has degraded, materials within the waste package will begin to leach into the
groundwater at various rates. Chemical neutron poisons (boron, rare earths, cadmium, etc.) may separate
from the uranium, the uranium will dissolve in groundwater, migrate, and then redeposit. In the
geological environment, uranium dissolves in oxidizing groundwater and then precipitates under
chemically reducing conditions (Wronkiewicz et al., 1992; Smellie, March 1995). Uranium may also be
precipitated by the formation of less soluble uranium species in the same uranium oxidation state. These
chemical mechanisms created most of the natural uranium ore bodies. In addition, some of these deposits
are the result of placer deposit mechanisms during which high-density materials (e.g., uranium oxides
and gold) separated from other materials while in flowing water. Other deposits have formed because of
temperature differences in hydrothermal systems. In a repository, the same geological mechanisms will
operate and may concentrate and purify uranium (Fig. 2).

Some of these mechanisms may be accelerated by oxidizing groundwater conditions (which occur at
the proposed Yucca Mountain repository) and the inclusion of chemical reducing agents in the repository
(i.e., iron in waste packages) and tunnel support systems (i.e., rock bolts, etc.) that create local
chemically reducing conditions for buildup of uranium deposits. These are much longer term phenomena
(Fig. 1) than package criticality.

The potential for zonal nuclear criticality events can be eliminated by isotopic dilution. Because the
mechanisms involve transport of the uranium from the waste package, it may not always be necessary
that the DU be isotopically mixed with the enriched uranium in the waste package. It is only required
that uranium be isotopically mixed when the uranium is transported from the waste package. In some

situations, this is an important distinction.
ORNL DWG 95C-783R2
FORMATION OF URANIUM ORE DEPOSITS FROM URANIUM IN ROCK

\\\\\\\‘\ RAIN /\l
%EBEE HEB

ROLL FRONT URANIUM
\ DISSOLVE URANIUM IN DEPOSIT
OXIDIZING GROUNDWATER (U5+ —= |J4)

 

 

   
 

REDUCING GROUNDWATER REDUCING GEOLOGY

\\;\:“‘ OXIDIZING

GROUNDWATER (LITTLE URANIUM) (ORGANIC, ETC.)

 

FORMATION OF URANIUM ORE DEPOSITS FROM URANIUM WASTES

 

 

 

 

 
  

  

 

\\ \\\\‘ RAIN
VAN
OXIDIZING URANIUM
GROUNDWATER DEPOSIT
\ ¥ (U6+ _____ - U4+)
N DISSOLVED URANIUM REDUCING GROUNDWATER
\\m. e - el
IN GROUNDWATER (LITTLE URANIUM)
C DEGRADED (\-IRON (WASTE PACKAGE,
WASTE PACKAGE ROCK BOLTS, ETC.)

Fig. 2. Natural and man-made formation of uranium ore deposits.
13

Studies (Forsberg et al., November 1995; Forsberg et al., April 1996; Forsberg et al., December
1996) have been conducted on filling LWR SNF waste packages with small beads of DU oxide or DU
silicates. The same option could exist for other waste forms. The rationale is that as the waste package
degrades and groundwater flows through the waste package, the DU will isotopically mix with the
enriched uranium from the SNF. In the specific example of LWR SNF, a reasonable case can be made
because (1) the amount of isotopic dilution required is small because of the low enrichment of the SNF,
(2) the DU and SNF have the same chemical form (oxide) with similar dissolution rates, and (3) the DU
in the SNF coolant channels is mixed with the enriched uranium on a scale of 1 cm in a waste package
measured in meters.

In recent years, speculation has arisen that criticality events might occur in geological repositories
(Bowman and Venneri, 1994) in addition to those demonstrated to have occurred at Oklo. However,
these postulated criticality events appear to require special conditions that are very unlikely. Recent
studies (Kastenberg et al., September 1996) show that use of isotopic dilution with ***U eliminates these

theoretical criticality concerns.
3.3.2.3 Factors Affecting Isotopic Dilution Requirements for U

Uranium geochemistry, the characteristics of uranium ore bodies, and naturally occurring nuclear
reactors define the chemical and geometric conditions under which uranium may be found in the natural
environment. This knowledge can be used to determine the minimum fissile enrichment of uranium
required to avoid the potential for nuclear criticality in a disposal site.

There are many kinds of ore deposits. The only elements almost always associated with high-purity
uranium deposits are hydrogen, oxygen, and silicon. The hydrogen is in the form of water that may be
either free water or waters of hydration (mineralized). Oxygen is in the water, silicon oxides, and
uranium minerals. Silicon may exist as silicon oxides or uranium silicates. Silicon and oxygen are also
the dominant chemical species in the earth's crust.

Though other elements found in geological deposits may be effective neutron scatterers (e.g., silicon,
aluminum, oxygen) or somewhat effective neutron absorbers (e.g., iron, sodium, calcium), no assurance
can be provided that such elements will remain with the uranium during hydrogeochemical processes
over geological time spans.

These considerations suggest that nuclear criticality in disposal sites can be prevented if isotopic
dilution 1s sufficient such as to prevent nuclear criticality in a homogeneous system consisting of
uranium, silicon oxide, and water in its most reactive configuration. This approach is a conservative

control strategy that greatly reduces the need for addressing criticality issues in any repository setting.
14
3.3.3 Institutional and Legal Requirements for Repository Criticality Control

Until very recently, the only concentrated fissile-containing material that was considered for disposal
was LWR SNF. For this reason, most of the institutional and legal requirements addressing nuclear
criticality issues were developed in the context of LWR SNF. This will change as consideration is given
for disposal of other fissile materials. In terms of heavy metal, LWR SNF is typically 1.5 wt % fissile
materials (primarily U and **Pu) and 98.5 wt % **U.

3.3.3.1 Current Requirements

The NRC regulations in 10 Code of Federal Regulations (CFR) Part 60.113 (1995) forbid nuclear
criticality in a geological environment. Those regulations do not, however, specify the time period
during which the disposal facility must comply with this requirement. The U.S. Nuclear Waste
Technical Review Board (NWTRB) has stated that these requirements do not have a time limit.

The regulatory structure for both the candidate Yucca Mountain repository and WIPP are changing.
The 1992 amendments to the Nuclear Waste Policy Act directed the U.S. Environmental Protection
Agency (EPA) to formulate site-specific standards for protection of public health and safety for the
candidate Yucca Mountain repository. The federal law also (a) mandated that the National Academy of
Sciences (NAS) make a set of recommendations on what should be in the standard and (b) required that
the final EPA standards be consistent with the recommendations of the NAS.

The NAS report, Technical Bases for Yucca Mountain Standards (1995), made several
recommendations. The panel recommended that repository performance be considered out in time to the
period of maximum risk to the public. By definition, this point in time occurs after waste package failure
and migration of radionuclides (including uranium) through the geological environment. This time frame
for regulatory concern includes sufficient time for uranium dissolution and precipitation and, therefore,
the potential for nuclear criticality.

The NAS has not addressed the specific issue of repository nuclear criticality control. However,
several members of the NAS Board of Radioactive Waste Management have published their perspectives
on various aspects of repository design including nuclear criticality control. For example, Chris
Whipple, the Chairman of this NAS Board recently stated (Whipple, June 1996):

“While the possibility of criticality at some time far into the future cannot be completely ruled out,

simple technical fixes could render its probability negligible. The simple addition of DU to waste
canisters would be one such approach.”
15
3.3.3.2 NWTRB Recommendations

The NWTRB was created by law to review the technical design of the HLW and SNF waste
management system. Although the NWTRB has no regulatory authority, its recommendations are widely
read and usually followed by DOE, EPA, NRC, and NAS. In its Report To the U.S. Congress and the
Secretary Of Energy: 1995 Findings and Recommendations (NWTRB, 1996), the NWTRB
recommended isotopic dilution as the method to ensure nuclear criticality control for SNF in the

repository. Specifically the NWTRB stated:

Estimating the probability of criticality within an intact or damaged waste package will be less
difficult than estimating “external (zonal) criticality,” i.e., criticality that may occur due to selective
dissolution and transport of neutron absorbers and fissile materials, and their recombination outside
the waste package. Although external criticality may be highly unlikely, it can not be dismissed
without thorough analysis. The Board understands that DOE intends to use a probablistic risk
analysis methodology to address external criticality. While such an approach is appealing, it may
turn out to be costly and time-consuming to the point of impracticality in a repository context
because of the very large number of events and geometric configurations possible in a repository.
The Board suggests that DOE consider increasing the criticality control of the engineered barrier
system (EBS). Examples of increased criticality control robustness of the EBS could include a
longer waste-package lifetime; more criticality control material inside the waste package; the use of
fillers; and the use of criticality control material in packing, inverts, and backfill. In particular, the
use of DU in filler, invert, or backfill material, or in all three, is a concept the program has not yet
explored adequately. Conceivably, increasing the criticality control robustness of the EBS could turn
a potentially intractable analysis of external criticality into a comparatively easy one.

3.3.4 Conclusions

Except for the use of »**U as a neutron absorber, neither geometry nor neutron absorbers can prevent
nuclear criticality with certainty in a repository over geological time spans because of two problems:
*  Geometry. Innature, uranium migrates via groundwater and other mechanisms. Uranium is

concentrated from levels of parts per million in granite to >80 wt % uranium in some ore
deposits.

*  Neutron absorbers. In a geological environment, uranium can separate from other neutron
absorbers. However, theory, laboratory experiments, and field geology all indicate that isotopes
of a given element cannot be separated by geochemical processes. Therefore, 2**U will not
separate from **°U or #*U under these conditions.

Technical, legal, and regulatory factors indicate that isotopic dilution of ***U with >**U is the

preferred method for nuclear criticality control in a waste processing facility or a geological repository.

Isotopic dilution should be sufficient to prevent criticality in any system containing ***U and water,

regardless of the chemical composition of the surrounding materials.
4. ISOTOPIC DILUTION OF **U

4.1 METHODOLOGY

General dilution requirements, using DU (specifically, 0.2 wt % **U and 99.8 wt % ***U), were
developed to ensure the subcriticality of infinite homogeneous mixtures of **U, DU, quartz sand [silicon
dioxide (Si0,)], and water (H,0), and of infinite homogeneous mixtures of uranium enriched in *°U plus
DU. Silicon dioxide and H,O were selected as the most restrictive materials for subcriticality that occur
in large process systems and natural geological environments. Both silicon and oxygen have very small
probabilities for capturing neutrons, thereby permitting neutrons to scatter about in the material until they
are absorbed in the uranium or they are degraded in energy by scattering with hydrogen. Neutron
absorption in uranium results in either the neutron being lost from the system through a parasitic capture
process or fission occurring which results in further neutron production. The degradation of neutron
energy through hydrogen-neutron scattering can increase the probability of neutrons causing **°U fission
and can also increase the probability of neutrons being lost from the system by capture in hydrogen.
Other neutron-absorbing compounds consisting of iron, calcium, and sodium cannot be ensured to be
present in any specific proportion; consequently, they were not considered in this study. Therefore, only
combinations of **U, *°U, Si0,, H,0, and DU were evaluated. The Standardized Computer Analyses for
Licensing Evaluation (SCALE) software and neutron cross-sections (SCALE, April 1995) were used to
evaluate subcritical mixtures of these materials. The selected subcritical value for the infinite-media
neutron multiplication factor (k.) for the U mixtures was <0.95. The limiting subcritical enrichment
for °U (Paxton and Pruvost, July 1977) for optimumly moderated homogeneous aqueous systems is
well-defined to be 1 wt % ***U. This value was used to define the subcritical DU dilution relationship for
uranium enriched in #*°U. Using the results of the computational study for ***U dilution and the
knowledge about the subcriticality of aqueous homogeneous 1 wt % ***U enriched uranium, a simple
equation was developed to define the necessary DU dilution to ensure the subcriticality of a mixture of
233U and uranium enriched in Z°U. The developed relationship for the most restrictive combinations of
233U, enriched uranium, and DU is based upon the commonly accepted concept that two or more mixtures
of optimumly water-moderated, subcritical (i.e., maximum k_ <1.0), infinite-media fissile materials may
be homogeneously combined and remain subcritical if the composition of the materials remains
homogeneous [e.g., the unity rule in 10 CFR Part 71.24(b)(7)].

Because the physical and chemical conditions of **U and ***U for some types of process and disposal

options cannot be guaranteed, the results of this isotopic dilution study were reduced to the most

17
18

restrictive possible combination of materials (i.e., SiO,, H,O, DU, *°U, ***U, and #**U) that will ensure
subcriticality. This approach also ensures criticality control for typical process systems. As determined
from these computational studies and published data that are presented in the appendix to this report, the
most restrictive combination of materials is a homogeneous mixture of uranium and water. For this

study, the mixture was assumed to be a mixture of water molecules and uranium atoms.

4.2 RESULTS

A simple equation was developed to ensure the subcriticality of **U and uranium enriched in *°U by
dilution with DU, specifically 0.2 wt % **U (see Appendix A). The mass of DU is expressed in terms of

233U and enriched uranium masses as:

g DU = 188 ¢ U + (EO—_Sl) - g of enricheduranium, (1)

where

DU
E

gof DU (ie., 0.2 wt % 2°U)
the wt % of *U where the g of enriched uranium = total U - **U.

In Eq. (1), #*U and ***U may be considered to be ***U—providing that the atom ratio of the (**U +
2U):**U does not exceed 1.0. If the calculated quantity of ¢ DU using Eq. (1) is negative, the uranium
material already contains **U sufficient such as to ensure subcriticality and no additional DU is needed.

A more general equation which applies to DU of other than 0.2 wt % **U is presented in Appendix A.

4.3 NEUTRONIC CONCLUSIONS

The developed DU dilution equation provided in Sect. 4.2 is a good first approximation for diluting
233U and enriched uranium—providing the mixture is homogeneous and consists of uranium compounds
(excluding compounds of beryllium and deuterium) and water. The presence of other fissionable
materials or non-neutron-absorbing, highly neutron-moderating elements such as nuclear-grade carbon,
beryllium, or deuterium has not been considered in this work. Though other scattering or absorbing
nuclides may be present in a mixture, their effects have not been accounted for in the reduction of required
DU mass for dilution of ***U and enriched uranium.

Because the dilution equation uses DU as the diluent to approximate an equivalent 1 wt % *°U
enriched uranium and water-moderated system, the potential for an autocatalytic criticality accident
(Kastenberg et al., 1996) is rendered impossible because homogeneous systems of 1 wt % ***U cannot be

made critical as a mixture of U and H,O.
5. CONCLUSION

To avoid nuclear criticality issues in process or disposal facilities with uranium containing U, it is
recommended that the ***U be diluted with 188 parts by weight of DU (0.2 wt % **°U) per part ***U.
Because this degree of dilution with DU ensures subcriticality of optimumly water-moderated,
homogeneous mixtures of *°U, less optimumly water-moderated mixtures have further subcritical k.
values, thereby compensating for uncertain nuclear parameters for dry (less water-moderated) mixtures of
23U, #°U, and #*U. Additional DU would be required for any other fissile uranium isotopes in the
uranium-containing materials. If significant ***U is already present in the material, an evaluation should
be performed to determine if the material is already diluted sufficiently such that subcriticality can be

ensured.

19
6. REFERENCES

American Nuclear Society, Oct. 7, 1983. American National Standard for Nuclear Criticality Safety in
Operations with Fissionable Materials Outside Reactors, ANSI/ANS-8.1-1983, La Grange Park, Illinois.

Brookins, D. G., 1990. “Radionuclide Behavior at the Oklo Nuclear Reactor, Gabon,” Waste
Management, 10, 285.

Bowman, C. D. and F. Venneri, 1994. Underground Autocatalytic Criticality from Plutonium and Other
Fissile Materials, LA-UR 94-4022, Los Alamos National Laboratory, Los Alamos, New Mexico.

Buscheck, T. A. and J. J. Nitao, December 1993. “Repository-Heat-Driven Hydrothermal Flow at Yucca
Mountain, Part I,” Nucl. Tech. 104(3), 418.

Buscheck, T. A., J. J. Nitao, and D. G. Wilder, December 1993. “Repository-Heat-Driven Hydrothermal
Flow at Yucca Mountain, Part II,” Nucl. Tech. 104(3), 449.

Cowan, G. A., July 1976. “A Natural Fission Reactor,” Sci. Am., 235, 36.

Forsberg, C. W., et al., November 1995. DUSCOBS—A Depleted-Uranium Silicate Backfill For
Transport, Storage, and Disposal of Spent Nuclear Fuel, ORNL/TM-13045, Lockheed Martin Energy
Systems, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Forsberg, C. W., et al., April 29, 1996. “Depleted-Uranium-Silicate Backfill of Spent-Fuel Waste
Packages for Improved Repository Performance and Criticality Control,” pp. 366 in Proc. 1996

International High-Level Radioactive Waste Management Conference, Las Vegas, Nevada, April 29—May
3, 1996.

Forsberg, C. W., December, 1996. “Depleted Uranium Oxides and Silicates as Spent Nuclear Fuel Waste
Package Fill Materials,” in Proc. Scientific Basis for Nuclear Waste Management XX, Materials Research

Society, Pittsburgh, Pennsylvania.

Kastenberg, W. E., et al., September 1996. “Considerations of Autocatalytic Criticality of Fissile
Materials in Geological Repositories,” Nucl. Tech., 155(3), 298.

Kocher, D. C., April 1996. Draft Letter Report: Legal and Regulatory Requirements for Disposal of **U,
ORNL/MD-45, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

International Atomic Energy Agency, 1975. The Oklo Phenomenon, Proc. Symposium, Libreville,
June 23-27, 1975, Vienna, Austria.

International Atomic Energy Agency, 1977. Natural Fission Reactors, Proc. Meeting of the Technical
Committee on Natural Fission Reactors, Paris, France, December 19-21, 1977, Vienna, Austria.

Lockheed Martin Energy Systems, Inc., February 1995. Waste Acceptance Criteria for the Oak Ridge
Reservation, ES/'WM-10, Rev. 1, Oak Ridge, Tennessee.

21
22

National Academy of Sciences, 1995. Technical Basis for Yucca Mountain Standards, National Academy
Press, Washington, D.C.

Naudet, S. R., 1977. “Etude parametrique de la criticite des reacteur naturels,” p. 589 in Natural Fission
Reactors, Proc. Meeting of the Technical Committee on Natural Fission Reactors, Paris, France,
December 19-21, 1977, International Atomic Energy Agency, Vienna, Austria.

Patric, L. W. and W. R. McDonell, March 6, 1992. Action Plan No. REP-7: NPR Spent Nuclear Fuel
Disposal Studies and Program to Resolve Disposal Cost Questions, Westinghouse Savannah River
Company, Aiken, South Carolina.

Paxton, H. C. and N. L. Pruvost, July 1987. Critical Dimensions of Systems Containing *>U, **’Pu, and
3U: 1986 Revision, LA-10860-MS, Los Alamos National Laboratory, Los Alamos, New Mexico.

Rechard, R. P., et al., 1993. [nitial Performance Assessment of the Disposal of Spent Nuclear Fuel and
High-Level Waste Stored at Idaho National Engineering Laboratory, SAND93-2330, Sandia National
Laboratory, Albuquerque, New Mexico.

SCALE: A Modular Code System for Performing Standardized Computer Analysis for Licensing
Evaluation, April 1995. NUREG/CR-0200, Rev. 4 (ORNL/NUREG/CSD-2/R4), Vols. 1, II, and III,
Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Smellie, J., March 1995. “The Fossil Nuclear Reactors of Oklo, Gabon,” Radwaste Mag. 2(2), 18.

U.S. Department of Energy, Office of Fissile Materials Disposition, June 1996. Disposition of Surplus
Highly Enriched Uranium Final Environmental Impact Statement, DOE/EIS-0240, Washington, D.C.

U.S. Department of Energy, July 29, 1996. Record of Decision for the Disposition of Surplus Highly
Enriched Uranium Final Environmental Impact Statement, Washington D.C.

U.S. National Academy of Sciences, 1995. Technical Bases for Yucca Mountain Standards, National
Academy Press, Washington, D.C.

U.S. Nuclear Regulatory Commission, 1995. Code of Federal Regulations, 10 CFR
Part 60.113(a)(1)(11)(B), Washington D.C.

U.S. Nuclear Regulatory Commission, 1997. The Potential for Criticality Following Disposal of Uranium
at Low-level Waste Facilities, NUREG/CR-6505, Washington, D.C.

U.S. Nuclear Waste Technical Review Board, 1996. Report to the U.S. Congress and the Secretary of
Energy: 1995 Findings and Recommendations, Arlington, Virginia.

Vernaz, E. Y., and Godon, N., 1992. “Leaching of Actinides From Nuclear Waste Glass: French
Experience,” Scientific Basis for Nuclear Waste Management XV, ed. C Sombret, 87, Materials Research
Society, Pittsburgh, Pennsylvania.

Westinghouse Hanford Company, May 23, 1994. “Criticality Safety Control of Fissile Materials: Rev. 0,
Change 1,” Nuclear Criticality Safety Manual, WHC-CM-4-29.
23

Westinghouse Savannah River Company, 1995. Nuclear Material Control, High Level Tanks (U),
Administrative Procedure Manual L2-1, Procedure L2-1-00076A, Effective 12/21/95,
Aiken, South Carolina.

Whipple, C. G., June 1996. “Can Nuclear Waste Be Stored Safely at Yucca Mountain?”,
Sci. Am. 274(6), 72.

Wronkiewicz, D. J., et al., 1992. “Uranium Release and Secondary Phase Formation During Unsaturated
Testing of UO, at 90°C,” J. Nucl. Mater. 190, 107.
Appendix A:

NEUTRONIC ANALYSIS OF #°U CRITICALITY CONTROL REQUIREMENTS
NEUTRONIC ANALYSIS OF #°U CRITICALITY CONTROL REQUIREMENTS

A.1 INTRODUCTION

This appendix provides the bases for guidance in using depleted uranium (DU) (specifically 0.2 wt %
23U and 99.8 wt % ***U) as a diluent to ensure the subcriticality of an infinite homogeneous mixture of
233U plus quartz sand [silicon dioxide (Si0,)], light water (H,0), and uranium enriched in ***U. The
considered range of parameters defining optimum-moderation, maximum, infinite-media neutron
multiplication constant, k., was

e 0<gSi0,/g*°U <1480

e 0<gH,0/g*U <22

e 0<gDU/g*U <188

Various combinations of ***U, Si0O,, H,0, and DU were computed to define subcritical (i.e., k., <0.95)
mixtures of these materials. The computations were performed with the SCALE software and neutron
cross sections (SCALE, April 1995). Additionally, the limiting subcritical (Paxton and Pruvost, July
1987) 1 wt % **°U enrichment for optimumly moderated, homogeneous aqueous systems and about 5.1 wt
% ***U enrichment for unmoderated, homogeneous metal systems were used for establishing a subcritical
DU dilution relationship for uranium enriched in 2*U. Also, the effects of nonfissile fissionable ***U and
U were examined to demonstrate that the ***U and **°U may be considered to be ***U—providing that the
total mass of ***U plus ***U does not exceed the mass of **’U in the homogeneous mixture. Using the
results of the computational study and the knowledge about the subcriticality of aqueous, homogeneous 1
wt % **U-enriched uranium and 5.1 wt % **U-enriched uranium, simple algebraic equations were
developed to define the necessary DU dilution to ensure the subcriticality of these materials. The
developed relationships are based upon the commonly accepted concept that two or more mixtures of
optimumly water-moderated, subcritical, infinite-media (i.e., maximum k_ <1.0) fissile materials may be
homogeneously combined—provided that the composition of the materials and their combined
homogeneity can be maintained. The equation developed for DU (0.2 wt % *°U) dilution of ***U and

enriched uranium is

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sio H,0 Sio H,0
35.38 - 0.026- gm 2| 4 100.6- | £ zgi - 0.1436- gm 2. gzgi
I = g™y gy g U g =°U
Sio H,0 Sio H,0
1 +02597- | 222 4 04991 | E27 | ~ 0.000626- | 202 - | 222
g 233U g 233U g 233U g 233U

 

 

 

 

 

 

 

 

 

+ ( EO_S 1) - g of enricheduranium,

(A.1)

A-3
where

g of enriched uranium = gtotal U - g #*U

DU = DU (ie., 0.2 wt % *°U)

E = enrichment of uranium as wt % U
for

 

 

If the calculated quantity of g DU using Eq. (A.1) is negative, the uranium material already contains ***U
sufficient such as to ensure subcriticality and no additional DU is needed.
If the enriched uranium, DU, and ***U mixture is known to be unmoderated metal, the following

relationship may be used:

E - 5.1

DU = 36 - ¢ 25U +
s s ( 4.9

) - g of enricheduranium. (A.2)

If no controls are available on the range of Si0, or H,O content, then the optimization of Eq. (A.1)

with H,O moderation and no Si0, results in the following relationship that should be used:

E -1

DU = 188 - g**¥U +
: : ( 0.8

) - g of enricheduranium. (A.3)

This results in a mixture of uranium that contains <1 wt % **U and <0.53 wt % **U.
Equations (A.1) through (A.3) were derived for and are applicable only when using DU with 0.2 wt %
>U. These equations take into account that some of the ***U in the DU must be used to dilute the **°U

that is also present in the DU. A more general equation (when using DU with other enrichments) is

1

— (150.4 g2, 99 g235_ g238> ’ (A4)

DU(z) =

 
A-5

where
DU(z) = gDU with*°U content of z wt %
g3 = g *’U in material to be isotopically diluted
g = g >”U in material to be isotopically diluted
g?3® = g U in material to be isotopically diluted

The resulting mixture will contain no more than 0.66 wt % ***U and no more than z wt % **U.

The development of the relationships expressed in Egs. (A.1) through (A.4) is provided in Sect. A.2.

A.2 BACKGROUND

A need existed to develop guidance in terms of nuclear criticality safety for the processing and
disposition of fissile >**U in systems for which neither geometric nor chemical compositional controls can
be ensured. Guidance was sought particularly on how to denature ***U by diluting it with DU to a similar
state as ~1 wt % ***U optimumly water-moderated, enriched uranium or 5.1 wt % ***U-enriched uranium
as unmoderated metal. Such dilution must ensure the same level of criticality safety of the U as very-
low-enriched ***U in an infinite, homogeneous system. Any homogeneous, aqueous medium of ***U can
be denatured with DU to a limiting subcritical weight percent with a similar level of criticality safety as 1
wt % **U enriched-uranium solutions or 5.1 wt % **U unmoderated uranium metal.

Because “down-blending” of the **U may also include the use of a homogeneous fixing agent (e.g.,
borosilicate glass or concrete), it i1s necessary to consider a “surrogate” material for calculating the
denaturing guidance. Consequently, infinite-media tertiary mixtures of water, S10,, and uranium metal
(i.e., U + #°U + #*U) were evaluated to develop denaturing, “dilution equation” guidance. Though no
benchmarks of homogeneous uranium metal, water, and SO, mixtures exist, the average neutron energy
causing fission in such systems is very similar to well-moderated aqueous ***U systems, for which
benchmarks do exist. There still remains an issue regarding the adequacy of silicon cross sections. This
issue has not been addressed because of delays in the processing of the new sixth evaluated nuclear data
file (ENDF/B-VI) for the various isotopes of natural silicon. Even upon eventual completion of that
processing, no integral critical benchmarks will exist for silicon. Such processing with more current data
will provide merely greater confidence in the use of differential cross sections for computational results.

Regardless of shortfalls in the experimental data, computational studies of the referenced tertiary
systems were performed. Additionally, computational studies were performed to examine the influence of
24U and *°U on variably moderated systems having various Z°U:***U, #*°U and ***U atom ratios. The
results of those studies and an equation that was developed from a multilinear regression of the

independent variables
A-6

to estimate the dependent parameter, g of DU per g of »*°U, are provided in this appendix. Also, a term
was added to that equation to account for the required addition of DU for diluting uranium enriched in

23U so that this equation is useful in analyzing materials that contain mixtures of ***U and **U.

A.3 APPROACH

Development of guidance for DU dilution of ***U and uranium enriched in **U was based upon
standardized, subcritical neutronic computational results for >**U in combination with SiO, and H,O and
was further based upon the experimental subcritical infinite-media enrichment of homogeneously light-
water moderated *°U. The calculated subcritical infinite media neutron multiplication factor, k.,
acceptance criteria for the ***U systems was 0.95.

Silicon dioxide and H,O were selected as the most restrictive materials for subcriticality that are in
process systems and are naturally occurring in large geological environments. Both silicon and oxygen
have very small probabilities for capturing neutrons, thereby permitting neutrons to scatter about in the
material until they are absorbed in uranium or they are degraded in energy by scattering with hydrogen.
Neutron absorption in uranium results in either the neutron being lost from the system through a capture
process or fission being caused that results in further neutron production. The degradation of neutron
energy through hydrogen-neutron scattering can increase the probability of neutrons causing ***U fission,
but can also increase the probability of neutrons being lost from the system by capture in hydrogen.
Because other neutron-absorbing compounds found in many process and geological systems, including
iron, calcium, and sodium, cannot be ensured to be present in any specific proportion, they were not
considered in this study. Therefore, only combinations of **U, ***U, SiO,, H,O, and DU were evaluated.
The SCALE software and neutron cross sections (SCALE, April 1995) were used to evaluate subcritical
mixtures of these materials. The selected subcritical value for the infinite-media neutron multiplication
factor (k.) for the *U mixtures was k. <0.95. The limiting subcritical enrichment of ***U (Paxton and
Pruvost, July 1987) for optimumly moderated, homogeneous, aqueous systems is well defined to be 1 wt
% U and 99 wt % ***U. The 1 wt % **’U value was used for defining the subcritical DU dilution
relationship for uranium enriched in **U. Using the results of the computational study for ***U dilution
and the knowledge about the subcriticality of aqueous homogeneous 1 wt % *°U enriched uranium, a
simple equation was developed to define the necessary DU dilution to ensure the subcriticality of a
mixture of ***U and uranium enriched in **U. The developed relationship for the most restrictive
combinations of ***U, enriched uranium, and DU is based upon the commonly accepted concept that two
or more mixtures of optimumly water-moderated, subcritical (i.e., maximum k_ <1.0), infinite-media
fissile materials may be homogeneously combined and remain subcritical if the composition of the

materials remains homogeneous.
A-7

Because the physical and chemical conditions of **U and *U cannot be guaranteed in certain waste
management processing systems nor in subterranean storage or disposal over geological time periods, the
results of this isotopic dilution study were reduced to the most restrictive possible combination of
materials (i.e., SiO,, H,0, DU, #°U, ***U, and ***U) that will ensure subcriticality. As determined from
these computational studies and published data, the most restrictive combination of materials is a
homogeneous mixture of uranium and water. For this study, the mixture was assumed to be a mixture of

water molecules and uranium atoms.

A4 COMPUTATIONAL APPROACH AND RESULTS

The neutronic computations performed in this study used the SCALE system, AJAX, and CSAS1X
sequence (BONAMI, NITAWL, XSDRN), with the 238-energy group ENDF/B-V neutron cross-section
library. The computations were executed on the Oak Ridge National Laboratory (ORNL) Computational
Physics and Engineering Division Nuclear Engineering Applications section workstation, CAO1. The
AJAX, BONAMI, NITAWL, XSDRN, and cross-section data set identifiers and creation dates are
AJAX—09/13/95, O00008; BONAMI—09/13/95, O00002; NITAWL—09/18/95, O00001;
XSDRNPM—09/13/95; and scale.rev03.xn238—06/08/95, respectively.

Historic validation studies (Jordan, Landers, and Petrie, December 1986; Primm, November 1993)
using ENDF/B-V neutron cross sections have demonstrated that water-moderated, homogeneous, single-
and multiunit ***U critical systems have calculated k_’s >0.95 (average k., ~0.99). Therefore, the
CSASI1X sequence was executed for various combinations of SiO,, H,O, **U, and DU (0.2 wt % **U and
99.8 wt % ***U) to calculate subcritical, infinite, homogeneous, medium, multiplication factors, k_’s,
approximating 0.95 (0.98 for some systems). The use of a k. acceptance value of 0.95 for this U
scoping study is not fully justified (i.e., integral experimental data for combined SiO, H,O, ***U, and **U
mixtures is not available for data testing and validation). Additionally, specific validation and analytical
studies involving the use of configuration-controlled hardware and software relative to these systems and
materials is necessary to satisfy criteria for computational safety evaluations. Obtaining experimental
benchmark data is a primary hurdle for researchers before they can complete such a specific validation.

Because of the multiple parameters involved in this study, step-wise approaches were used to establish
the parameter space that maintains subcriticality for the combinations considered. That is, each infinite
homogeneous material was assumed to consist of a selected volume fraction of Si0O, (assumed theoretical
density = 1.5888 g SiO,/cm’ = 60% of maximum actual 2.65 g SiO,/cm?), a volume fraction of H,O
(assumed theoretical density = 0.99823 g H,0/cm?), and a volume fraction of uranium metal (assumed

theoretical density = 18.90 g U/cm?). The wt % of *°U was varied within the uranium metal, but the wt %
A-8

of 2*U remained constant (at 0.2 wt % **°U in the metal). The wt % of ***U was varied inversely with the
23U to compensate for the values of 2*U wt %. The wt % of ***U in the uranium was chosen to
approximate k. <~0.95 for any selected volume fraction of H,O moderation for given Si0, volume
fractions up to 0.6. That is to say, for a given SiO, volume fraction and ***U wt % in the uranium, any
variation in H,O volume fraction would not exceed a calculated k_ of about 0.95. The selection of the
subcritical 2**U weight fraction was an iterative process for each assumed SiO, volume fraction.
Parametric input data and results for some of the calculations are provided in Table A.1. The results
are expressed in terms of D (g of DU per g of **U), S (g of SiO, per g of ***U), H (g of H,O per g of **U),

and K (k_, of the mixture).

Table A.1. Computational results (continued)

 

 

Result D S H K
No. (gDU/g*PU) (g Si0/g 2U) (g H,0/g **U) (k.)
1 187.6792 0.0000 26.9434 0.9447
2 187.6792 0.0000 25.6252 0.9463
3 187.6792 0.0000 24.3979 0.9474
4 187.6792 0.0000 23.2525 0.9482
5 187.6792 0.0000 22.1810 0.9486
6 187.6792 0.0000 21.1764 0.9487¢
7 187.6792 0.0000 20.2327 0.9484
8 187.6792 0.0000 19.3445 0.9479
9 187.6792 0.0000 18.5071 0.9471
10 187.6792 0.0000 17.7162 0.9460
11 184.5288 7.0892 30.2877 0.9389
12 184.5288 6.7810 28.5448 0.9420
13 184.5288 6.4984 26.9471 0.9444
14 184.5288 6.2385 25.4773 0.9463
15 184.5288 5.9985 24.1205 0.9476
16 184.5288 5.7764 22.8642 0.9484
17 184.5288 5.5701 21.6977 0.9488"
18 184.5288 5.3780 20.6116 0.9488

—_—
\O

184.5288 5.1987 19.5979 0.9483
A-9

Table A.1. Computational results (continued)

 

 

Result D S H K

No. (gDU/g*PU) (g Si0/g 2U) (g H,0/g **U) (k.)
20 184.5288 5.0310 18.6496 0.9476
21 181.4818 16.1474 30.9431 0.9360
22 181.4818 15.3401 28.9141 0.9398
23 181.4818 14.6096 27.0783 0.9428
24 181.4818 13.9455 25.4094 0.9451
25 181.4818 13.3392 23.8856 0.9466
26 181.4818 12.7834 22.4887 0.9475
27 181.4818 12.2720 21.2037 0.9478°
28 181.4818 11.8000 20.0174 0.9477
29 181.4818 11.3630 18.9191 0.9470
30 181.4818 10.9572 17.8992 0.9459
31 177.5714 26.4906 29.4041 0.9372
32 177.5714 25.0189 27.2466 0.9411
33 177.5714 23.7021 25.3161 0.9439
34 177.5714 22.5170 23.5788 0.9457
35 177.5714 21.4448 22.0068 0.9467
36 177.5714 20.4700 20.5778 0.9470°
37 177.5714 19.5800 19.2731 0.9466
38 177.5714 18.7642 18.0770 0.9455
39 177.5714 18.0136 16.9767 0.9439
40 177.5714 17.3208 15.9610 0.9418
41 171.4138 41.4106 29.9206 0.9357
42 171.4138 38.6499 27.3188 0.9409
43 171.4138 36.2343 25.0423 0.9445
44 171.4138 34.1028 23.0335 0.9468
45 171.4138 32.2082 21.2480 0.9479
46 171.4138 30.5131 19.6504 0.9480°
47 171.4138 28.9874 18.2126 0.9472
48 171.4138 27.6071 16.9117 0.9455
A-10

Table A.1. Computational results (continued)

 

 

Result D S H K
No. (gDU/g*PU) (g Si0/g 2U) (g H,0/g **U) (k.)
49 171.4138 26.3522 15.7290 0.9431
50 171.4138 25.2064 14.6492 0.9400
51 165.6667 70.0529 35.2109 0.9176
52 165.6667 63.6845 31.2097 0.9284
53 165.6667 58.3774 27.8753 0.9361
54 165.6667 53.8869 25.0539 0.9413
55 165.6667 50.0378 22.6356 0.9444
56 165.6667 46.7019 20.5397 0.9457¢
57 165.6667 43.7830 18.7058 0.9455
58 165.6667 41.2076 17.0877 0.9440
59 165.6667 38.9183 15.6493 0.9413
60 165.6667 36.8700 14.3624 0.9377
61 155.2500 131.3492 46.7645 0.8743
62 155.2500 112.5850 38.9049 0.9016
63 155.2500 98.5119 33.0103 0.9207
64 155.2500 87.5661 28.4255 0.9335
65 155.2500 78.8095 24771577 0.9417
66 155.2500 71.6450 21.7568 0.9462
67 155.2500 65.6746 19.2556 0.9477¢
68 155.2500 60.6227 17.1399 0.9469
69 155.2500 56.2925 15.3262 0.9440
70 155.2500 52.5397 13.7543 0.9394
71 139.0000 250.0000 23.6428 0.8608
72 139.0000 250.0000 25.815803 0.8626
73 139.0000 250.0000 26.954066  0.8629
74 139.0000 250.0000 28.129047 0.8629
75 139.0000 250.0000 29.342552  0.8625
76 139.0000 250.0000 30.596507 0.8618
77 90.0000 499 .4865 20.191625 0.8383
A-11

Table A.1. Computational results (continued)

 

 

Result D S H K
No. (gDU/g*PU) (g Si0/g 2U) (g H,0/g **U) (k.)
78 90.0000 499 .4865 21.794135 0.8411
79 90.0000 499 .4865 23.435259 0.8428
80 90.0000 499 .4865 25.116411 0.8436
81 90.0000 499 .4865 26.839073 0.8434
82 90.0000 499 .4865 28.604802  0.8426
83 35.3640 0.0000 0.0000 0.9477¢
84 11.9870 71.3500 0.0000 0.9509¢
85 4.4600 199.0000 0.0000 0.9499¢
86 1.6596 499.0000 0.0000 0.9487¢
87 0.4400 999.0000 0.0000 0.9498“
88 0.0000 1480.4800 0.0000 0.9505¢

 

“‘Optimumly-moderated (e.g., maximum k_ for given mixtures).

Result Nos. 83 and 84 were obtained to determine the subcritical values for dry ***U as blended with
DU and as blended with DU and SiO,.
An example SCALE input for Result No. 51 of Table A.1 is provided in Table A.2.

A.5 INTERPRETATION OF RESULTS

The results of Table A.1 that are marked a [optimumly moderated (i.e., maximum k) for given
mixtures| were input into the statistical graphics program called STATGRAPHICS Plus 5.2
(STATGRAPHICS, November 15, 1991) and were statistically fit by its multiple regression program. The
calculational results demonstrate that the required dilution of ***U with DU is proportional to the volume
fraction or mass fraction of H,O or Si0O, in the homogeneous mixture. Furthermore, the plots indicate that
the proportional behavior becomes asymptotic at increased fractions of H,O and Si0,. Therefore, the
form of the regression equation was taken to be the product of two quotients, each made up of linear
relationships, for the independent variables, S (g SiO,/g ***U) and H (g H,O/g *U), resulting in the
dependent variable, D (g DU/g ***U), computational result.
A-12

Table A.2. Example SCALE XSDRNPM input for result No. 51

 

=shell
rm ft70f001
rm ft51f001
rm ft52f001
#In -s /home/rqw/scale/data/xn199.1r3 {t51f001
#In -s /home/eSa/sammy/u235bench/data/libampxfff2 {t52f001
In -s /scale/scale4.3 _ibm/data/scale.rev03.xn238 ft5 1f001
end
#ajax
0$$ 70 51 1$$ 1 ¢
288 51 6 t
3$$ 1001 8016 14000 92233 92235 92238 t
end
=csaslx  parm=size=600000
casel2 uranium/si/h2o study, 1.0 wt% uf=0.10, 02-22-96
199¢r inth*
arbmsio2 1.5888 2011 8016 2 14000 11 0.5 end
h2o0 1 den=0.99823 0.40 end
uranium
end comp

end

 

*Reference to the 199gr is an artifact of the cross-section library unit identification for the ENDF/B-V
238-energy group library.
A-13

That 1s

a+ b-S d + eeH
D=—-—|' |———— (A.5)
1 + ¢S 1 + f-H

The product of the two quotients then becomes
D - @ +b"S +c¢c’*H + d’-S-H)

) (A.6)
(1 +e”sS +f“H + g’-S-H)

 

where a’,b’, ¢’, d’, e’, ', g’ are the resultant regression coefficients.

The multiple nonlinear regression of this relationship resulted in the following equation:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sio H Sio H,0
35.38 - 0.026- | 22| + 100.6- | S22 | - 0.1436- | 222 | 22
; DU _ o 23y o 23y 0 233y 0 23y
, B33y Si0, T Sio HO
1+ 0.2597- . 0491 | 222~ 0.000626- | 2202 L[ B2
o 23315 o 23315 o 23315 g 2331y
(A.7)
for
gS 0gH,O
2 <1480 @ 2
g U g 233U
gSi10 gH.0
2 <66 @ 19 < =2 < 22,
g 233y g 23317

Table A.3 provides the observed (i.e., SCALE calculated) and predicted values for the multiple

nonlinear regression.

Given that uranium enriched to >1 wt % >*U must also be diluted to no more than 1 wt % >*°U to

ensure subcriticality in an infinite, optimumly water-moderated, homogeneous media, Eq. (A.7) must have
A-14

an additional term to account for enriched uranium commingled with 2*U. The additional term is:

gbU _(E-1 AS)
g U(E) 0.8 ’ '

where U(E) is enriched uranium at E wt % **°U.

Table A.3. SCALE calculated vs regression predicted values

 

 

 

 

 

 

 

 

 

 

 

 

 

SCALE Input SCALE Input SCALE Calculation Regression
g Si0o, g H,0 g DU g DU
Table l;.l Result ¢ 23y ¢ 2y ¢ 2y ¢ 2y

0.

6 0.0000 21.1764 187.6792 190.0602
17 5.5701 21.6977 184.5288 184.9562
27 12.2720 21.2037 181.4818 181.5200
36 20.4700 20.5778 177.5714 177.1913
46 30.5131 19.6504 171.4138 171.5264
56 46.7019 20.5397 165.6667 165.4380
67 65.6746 19.2556 155.2500 155.2522
83 0.0000 0.0000 35.3640 35.3800
84 71.3500 0.0000 11.9870 11.7509
85 199.0000 0.0000 4.4600 4.8972
86 499.0000 0.0000 1.6596 1.605
87 999.0000 0.0000 0.4400 0.3491
88 1480.4800 0.0000 0.0000 -0.0789

 

The final equation for predicting the necessary mass of DU (0.2 wt % ***U) for homogeneous dilution

of Si0,, H,0, **U, and uranium enriched in the ***U isotope is then

 
A-15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sio H,0 Sio H,0
35.38 - 0.026 - gm 21 +100.6 - gzgi - 0.1436 - g233 2 g23§
r DU = g~V g~u gu gu) |, g 23
Sio H,0 Sio H,0
1+ 02597 - | 2222 4 04991 - | 222 - 0.000626 - | 2222 S0
g 33U g 233U g 233U g 233U

 

 

 

 

 

 

 

 

 

+ ( EO_S 1) - g of enriched uranium,

(A.9)

for

 

 

If the calculated quantity of g DU using Eq. (A.9) is negative, the uranium material already contains ***U
sufficient such as to ensure subcriticality and no additional DU is needed.

If the enriched uranium, DU, and ***U mixture can be ensured to remain as unmoderated [i.e., no other
scattering media (e.g., iron, water, silicon, etc.)] metal, the result No. 83 of Table A.1 can be used with the

knowledge of the limiting critical enrichment for **°U to develop the following relationship:

E - 5.1

DU = 36 - ¢ 25U +
s s ( 4.9

) - g of enriched uranium. (A.10)

If no controls are available on the range of Si0, or H,O content, then the optimization of Eq. (A.1)

with H,O moderation and no Si0, results in the following relationship that should be used:

E -1

DU = 188 - g*¥U +
: : ( 0.8

) - g of enriched uranium. (A.11)

This results in a mixture of uranium that contains <1 wt % >**U and <0.53 wt % >**U.
A-16

Further calculations were performed to provide ensurance that the nonfissile fissionable uranium
isotopes of ***U and **°U can be assumed to be ?**U in the dilution of ***U and ***U using the previous
relationships if the atom ratio of (***U + #°U)/*°U is <1.0. Results of these calculations are presented in
Table A.4.

The first column in Table A.4 demonstrates the effect of substituting »**U or **°U for ***U in
optimumly water-moderated systems. At 1 atom % ***U in **U, the k. of the mixture is 0.994. The
substitution of **U or U reduces the k. substantially. Likewise, the addition of ***U or **°U to 1 atom %
2¥U in a ***U optimumly water-moderated mixture reduces the k. through thermal neutron absorption.

The second column in Table A.4 demonstrates the effect of extreme oxygen moderation of

Table A.4. Influence of >**U and ***U on infinite systems of **U diluted with **U

 

 

 

Highly-moderated oxygen Poorly-moderated
Water-moderated uranium uranium metal system atom oxygen uranium metal
metal ratios system

system atom ratios atom ratios
(H:**U = 500,

0:>°U = 250) k. (0:**U = 100,000) k. (0O:°U = 100) k.
202U = 100 0.430 2U2PU0 = 100 0.102 202U = 100 1.400
U0 = 100 0.847 U0 = 100 0.804 PUAU=100 0.670
U0 = 100 0.994 28U2U = 100 1.030 PUAU =100 0.480
U0 = 100 0.895 20U = 100 0.92 YU =100  0.500

234U:235U =1 234U:235U =1 234U:235U =1
28U2U = 100 0.972 28U2U = 100 1.017 PUAU =100 0476

236U:235U =1 236U:235U =1 236U:235U =1

 

neutrons without the presence of hydrogen as a thermal neutron absorber. Clearly, a 1-atom % mixture of
23U in #*U is super-critical because of the lack of hydrogen neutron absorption. Again, the substitution of
24U or #°U reduces the k. substantially. However, the addition of 1 wt % ***U to a 1 wt % **°U in #*U
mixture 1s inadequate to ensure subcriticality. The third column demonstrates the effects of substituting or
adding ***U or #*°U in poorly oxygen-moderated systems. As can be observed, 2**U or **°U can be a
contributor to the “fast fission” process.

Because of the lack of experimental data to confirm the behavior of 2*U, #**U, ***U, and ***U in poorly
water-moderated systems, Eq. (A.3) (based upon highly thermalized neutrons) is recommended for use in

the dilution process for all systems.
A-17

A.6 DEVELOPMENT OF GENERAL DILUTION EQUATION (A4)

Equations (A.1) through (A.3) were derived for and are applicable only when using DU with 0.2 wt %
2¥U. A large proportion of the DU stored in the United States has approximately this same composition,
and there is enough of this material to isotopically dilute all of the excess ***U slated for disposal.
However, if it is decided that excess 2*U will be coprocessed with another waste stream before disposal,
the 2°U and ***U content of the other waste stream may vary considerably from that found in average DU.
Therefore, a more general isotopic dilution equation was derived from Eq. (A.3) that allows the use of
uranium material with up to 1 wt % ***U for isotopic dilution of **U.

This general equation must take into account that some of the Z*U in the DU must be used to dilute
the 2°U that is also present in the DU. As discussed concerning Eq. (A.8), the *’U in the mixture must be
maintained below 1 wt % in order to maintain subcriticality. Therefore, 99 parts of Z*U are needed to
dilute every part of >**U in the mixture. Mathematically, the grams of ***U needed to dilute the *’Uin 1 g
of DU with z wt % **°U is 99 x (z/100) or (992/100). To determine how many grams of ***U per gram DU
are available to isotopically dilute ***U, the mass of **’U and the mass of ***U required to dilute the *°U
must be subtracted. Mathematically, the grams of 2**U in 1 g of DU with z wt % **°U that are available to
dilute the ***U is

z 997

- L T2 o1y
100 100

Therefore, the quantity of DU with z wt % U, or DU(z), that is required to obtain 1 g of ***U for isotopic
dilution of **U is 1/(1 - z).

From Eq. (A.3), it takes 188 g of DU (0.2) to dilute 1 g of ***U to ensure subcriticality. This quantity
of DU contains 0.376 g >**U. To dilute this ***U content to 1 wt % requires 188 x (99 x 0.2/100) or 37.224
g of 2*U. Therefore, the quantity of ***U from the 188 g DU(z) that is remaining to dilute the **°U is 188 -
23U - U needed to dilute the **°U, or 188 - 0.376 - 37.224 = 150.4 g. This implies that 150.4 g of ***U
are required to dilute 1 g of ***U to ensure subcriticality and that, therefore, the 2*U must be diluted to
1/150.4 or 0.66 wt %.

Therefore, a more general equation when using DU with other enrichments is

DU() = ~ L (1504 g7+ 99 g7~ ¢2%) (A4)
where
DU(z) = g DU with *°U content of z wt %
g3 = g *”U in material to be isotopically diluted
g = g ™”U in material to be isotopically diluted
g?3® = g ”*U in material to be isotopically diluted

The resulting mixture will contain no more than 0.66 wt % ***U and no more than z wt % **U.

A.7 APPLICATION OF DILUTION EQUATION

The following is an application of the dilution equation from the preceding section.

ORNL has a large quantity of contaminated ***U in temporary storage. The material, which resulted
from the Consolidated Edison Uranium Solidification Program (CEUSP), is a solid, monolithic material
with uranium, gadolinium, and cadmium oxides. Information regarding the material is presented in Table

A.S.

Table A.5. Characteristics of CEUSP material

 

 

 

Weight
Material inventory % U % total kg
2y 0.01 <1.0
2y 9.69 101.0
21U 1.39 14.5
2351) 76.52 797.8
236() 5.60 58.4
2381) 6.80 70.9
uo, 64.1 1072.6
CdO 19.6 328.0
Gd, 0, 2.2 36.8
Other metal contaminants 14.1 2359
Total uranium 1042.6

Total CEUSP material 1673.3

 
A-19

Because one cannot ensure that the cadmium, gadolinium, or other neutron-absorbing elements will
remain intimately mixed with the uranium, no credit can be taken for their presence in the application of

the dilution equation. Only the mass of elemental uranium can be applied in the dilution equation.

The 101.0 kg of **U from Table A.5 is applied to the dilution equation separately from the remaining
mass of uranium. Converted to grams, the mass of **U is 101,000 g ***U. The remaining mass of uranium
is then 1042.6 - 101.0 kg =941.6 kg U or 941,600 g U. Therefore, the effective enrichment of the
remaining uranium is (100) x (797.8 kg *°U) / (941.6 kg U) = 84.73 wt %. Substituting into Eq. (A.10):

g DU = 188 ¢ U + (EO—_Sl) - g of enriched uranium
g DU = 188 - 101,000 + (%) - 941,600
g DU = 117,538,210.

This is to say that it will require a dilution of about 117 t DU (0.2 wt % ***U) to denature the CEUSP
material such that no geological condition of the material nor condition during processing can result in
criticality. This amounts to increasing the mass of CEUSP uranium by a factor of about 113. This
evaluated subcritical mixture is predicated upon the condition that the DU is of the same chemical
composition as the CEUSP uranium such that no chemical separation of the mixture can occur.

Using the same computer codes and cross sections, test calculations were performed with the previous
diluted mixture of CEUSP uranium oxides (omitting all other cadmium, gadolinium, and metal
contaminants) with various proportions of water combined in an infinite homogeneous media. The water-
volume fractions were chosen to demonstrate a subcritical, infinite-media, neutron multiplication factor,
k., at optimum moderation. The resulting k_ for various water proportions within the mixture are shown
in Table A.6.
A-20

Table A.6. k_ vs water volume fraction

 

 

Water-volume fraction k.,
0.65 0.9817
0.67 0.9867
0.70 0.9921
0.73 0.9943
0.74 0.9943
0.75 0.9937
0.76 0.9926
0.80 0.9817

 

The relatively large k. values result from the mixture being predominately U (subcritical acceptance
criterion for 1 wt % *°U having a calculated k_ ~1.00) as compared to systems that are predominately ***U

(k.. < 0.95 for a subcritical acceptance criterion for optimumly moderated ***U (Primm, 1993).

A.8 CONCLUSIONS

We believe that the developed DU dilution equation provided in Sect. 4.2 is a good first
approximation for diluting 2*U and enriched uranium—providing that the mixture is homogeneous and
consists of uranium compounds (excluding compounds of beryllium and deuterium) and water. The
presence of other fissionable materials or non-neutron-absorbing, highly neutron-moderating elements
(e.g., carbon, beryllium, or deuterium) has not been considered in this work. Though other scattering or
absorbing nuclides may be present in a mixture, their effects have not been accounted for in the required
DU mass for dilution of ***U and enriched uranium.

Because the dilution equation uses DU as the diluent to approximate an equivalent 1 wt % *°U-
uranium and water-moderated system, the potential for an autocatalytic criticality accident (Kastenberg, et
al., September 1996) is rendered impossible. It is judged that homogeneous systems of 1 wt % **°U or
~0.66 wt % ***U cannot be made critical as a mixture of U and H,O.

Though other elements found in waste management process systems and geological deposits may be
effective neutron scatterers (e.g., silicon, aluminum, oxygen) or somewhat effective neutron absorbers

(e.g., iron, sodium, calcium), no assurance can be provided that such elements will always remain with the
A-21

uranium during some types of waste processing operations or hydrogeochemical processes over geological
time spans. Isotopic dilution of ***U and ***U with DU in an identical compound and form provides the
only method to ensure that changes in chemistry or geometry cannot transform the **U and **°U into a

critical configuration.

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L. F. Blankner 48. C. V. Parks
H. E. Clark 49. B. D. Patton
E. D. Collins 50. L. M. Petrie
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K. R. Elam 55. D. E. Reichle
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M. J. Haire 60. J. O. Stiegler
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M. W. Kohring 62. N.R. Sweat
A. M. Krichinsky 63. O.F. Webb
M. A. Kuliasha 64. R.M. Westfall
A. J. Lucero 65. B. A. Worley
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M. McBride 71. Central Research Library
L. E. McNeese 72. Laboratory Records—RC
G. E. Michaels 73. Document Reference Section
J. F. Mincey
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Joe Arango, U.S. Department of Energy, S-3.1, Rm. 6H-025,
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