This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Neutronic Evaluation of GCFR Core Diluents and Reflectors
Signature of Author Kun Yu Department of Nuclear Engineering June 10, 2003 Certified by Michael J. Driscoll Professor Emeritus of Nuclear Engineering Thesis Supervisor Certified by Pavel Hejzlar Program Director, Center for Advanced Nuclear Energy Systems Thesis Reader Accepted by Jeffrey Coderre Associate Professor of Nuclear Engineering Chairman, Department Committee on Graduate Students
i
Neutronic Evaluation of GCFR Core Diluents and Reflectors
By
Kun Yu
Submitted to the Department of Nulcear Engineering
on June 11, 2003 in Partial Fullfillment of the Requirements for the Degree of Master of Science in
Nuclear Engineering
ABSTRACT
Materials are evaluated for use as in-core diluents and as peripheral reflectors for Gas-Cooled Fast Reactor (GFR) service, using coupled Monte Carlo (MCNP) and isotopics (ORIGEN) codes. The principal performance indices compared were effects on beginning of irradiation multiplication factor, reactivity-lineated burnup, and coolant (here CO2) void reactivity.
While low values of the macroscopic absorption cross section, Σa, and slowing down power, ξΣs, are qualitatively useful predictors of good performance, it was found that only full scope calculations were valid for quantitative assessment. For example, several materials (Ni, Nb) having poor performance as in-core diluents proved to be good reflectors. Many materials which reduced coolant void reactivity also proved detrimental to reactivity lifetime. Others, mostly the strong moderators, increased initial reactivity, but decreased reactivity lifetime. Cores fueled with plutonium exhibited a much larger void reactivity than those started up using U-235 as the fissile material.
While there are no ideal candidates that are superior in all respects, considering only neutronic performance, the following appear worthy of further investgation: Metallic fuel diluents or matrices (eg. CERMET or METMET): Zr, Ti, V, Ba2Pb; High temperature fuel diluents or matrices (eg, CERMET, CERCER): SiC, BaS Cladding: Fe alloys with Cr, Al (eg ODS) Reflector: Zr3Si2, Pb, Ba2Pb, ZrS2, MoSi2 plus a variety of sulfides and silicides
Thesis Supervisor: Michael J. Driscoll
Title: Professor Emeritus of Nuclear Engineering
ii
ACKNOWLEDGMENTS
The help, patient guidance and generous support of Professor Michael J. Driscoll
and Dr Pavel Hejzlar, my thesis supervisors, are greatly appreciated.
I am also grateful to two members of the Physics and Materials group of the Gas
Cooled Fast Reactor Project at MIT: Pete Yarsky for his discovery of the possible cross
section library deficiency of Potassium, and Mike Pope for beneficial discussions on the
coolant void coefficient.
This work has been funded by the Idaho National Engineering & Environmental
Laboratory (INEEL) under their LDRD program.
iii
TABLE OF CONTENTS
ABSTRACT......................................................................................................................... i ACKNOWLEDGMENTS .................................................................................................. ii TABLE OF CONTENTS ................................................................................................ iii LIST OF TABLES ............................................................................................................ v LIST OF FIGURES ......................................................................................................... vi Chapter 1 Introduction ........................................................................................................ 1
1.1 Foreword ................................................................................................................... 1 1.2 Background............................................................................................................... 1 1.3 Organization of this report ........................................................................................ 8
2.4 Whole Core Model for matrix and reflector configuration..................................... 16 2.5 Summary ................................................................................................................. 26
Chapter 3 Review of core diluent material candidates ..................................................... 27 3.1 Introduction............................................................................................................. 27 3.2 Review of element properties ................................................................................. 27 3.3 Review of material candidates for matrix core ....................................................... 28
3.3.1 Neutronic Evaluation parameters..................................................................... 28 3.3.2 Results for matrix study ................................................................................... 30 3.3.3 Fissile and fertile properties in the energy range of interest ............................ 32 3.3.4 Promising materials ......................................................................................... 34
3.4 Applicability of superposition................................................................................. 42 3.4.1 Non-linearity of neutronic effects as a function of matrix concentration........ 42 3.4.2 Neutronic effects for a compound and its constituents.................................... 43 3.4.3 Relation of reactivity to enrichment ................................................................ 45
3.5 Conclusions............................................................................................................. 47 Chapter 4 Review of reflector material candidates........................................................... 48
4.1 Introduction............................................................................................................. 48 4.2 Review of material candidates for reflector............................................................ 48
5.1 Summary and Conclusions ..................................................................................... 62 5.2 General Evaluation Results..................................................................................... 62 5.3 Recommendations for future work ......................................................................... 65
References......................................................................................................................... 67 Appendix A Estimate of Gas Produced By Sulfur........................................................... 69 Appendix B Relation of reactivity ρ to enrichment x...................................................... 70 Appendix C Sample input files for matrix material study............................................... 72
v
LIST OF TABLES
Table 1-1 Periodic table of the chemical elements showing excluded candidates....... 2
Table 1-2 Footnotes to Table 1–1..................................................................................... 3
────────────────────────────────────────────────── Total 109
3
Table 1-2 Footnotes to Table 1–1
(a) Some elements have more than one reason for exclusion. We assign only one, based on its most serious shortcoming. (b) Some elements could only be used in compounds, such as N, O, F, Cl, Br, I. (c) Metal prices were obtained from ref. [1].
(d) Li-7 and Be are light moderators. But FLiBe molten salt is used as coolant in some
recent concepts (see ref [2]). Beryllium also has a relatively large (n, 2n) cross section,
which improves the neutron economy, so we re-instate these two materials as candidates.
(e) The one group spectrum averaged neutron absorption cross sections of 90 elements
were obtained using the Pb matrix core model discussed in Chapter 2. The results are
shown in Table 1.3. The results are generally consistent with the central worth
measurements in fast critical assemblies compiled in ref [3].
(f) Some strong absorbers could not be used as matrix material but could be used as a reflector. Thus there are 45 potentially usable reflector elements, 13 more than as matrix candidates (Li, B, As, Se, Br, Ag, Cd, In, Sb, I, Cs, Ta, W).
We now have in all 33 matrix candidate elements and 45 reflector candidate elements
remaining.(including Li-7) Based on their distinctive properties, we can classify them
under 4 main categories; see Table 1.4.
8
Table 1-4 Roster of Potential Diluent Candidates
Possible Form of Use Elements
In Ceramics (6)
(including CERCER, CERMET) C, N, O, P, S, Si
As metals and alloys (19)
(including CERMET, METMET)
Mg, Ca, Sr, Ba, Ti, V, Cr, Mn, Fe, Co, Ni,
Cu, Zn, Al, Sn, Zr, Nb, Mo
As liquid metal (5)
(coolants, pools) Na, K, Pb, Bi, Hg
In molten salts (3 + 1)**
(coolants, pools)
F, Cl, Be*
(also the separated isotope Li-7) [2]
*Be could also be used in metallic form and as BeO ceramic.
** see ref [2]
1.3 Organization of this report
Chapter 2 describes the computer codes employed and the whole-core model used to
evaluate important neutronic parameters such as multiplication factor, its rate of change
with burnup, initial conversion ratio and spectrum-averaged cross sections. This degree
of sophistication is necessary because a priori judgments are unreliable for hard spectrum
fast reactors in view of the influence of less familiar phenomena such as (n,p) (n,α) and
(n,2n) reactions, the effect of scattering resonances on leakage and inelastic scattering on
moderation.
In chapter 3 results for matrix studies are shown and analyzed. Issues such as the non-
linearity of neutronic effects vs. diluent concentration and the failure of the superposition
principle in predicting the effect of compounds based on their individual components are
discussed.
Chapter 4 reports a detailed study for reflector material candidates. The candidate
material range is broadened and more compounds are included. Materials good as in-core
9
matrix diluents are not necessarily good as reflectors. The different demands for different
functions are discussed.
Chapter 5 presents a summary, principal overall conclusions, and recommendations
for follow-on work.
An appendix is included discussing the potential problem due to helium production
via (n, α) reactions in sulfur.
10
Chapter 2 Computer Codes and Models
2.1 Introduction
In this chapter descriptions are presented of the computer codes employed in the
evaluation of core diluents in whole core models. Sufficient descriptive information and
data are provided that others could reproduce or extend the results to be presented later in
chapters 3 and 4. Appendices to this report provide sample copies of code input and
output in further fulfillment of this goal.
2.2 MCODE Description
2.2.1 Introduction MCODE (MCNP-ORIGEN Depletion program)[4] is a linkage program (~3000
lines of ANSI C), which uses MCNP and ORIGEN to do burnup calculations for
arbitrarily-defined MCNP regions[5]. MCNP is used to calculate neutron flux and from it
determine the effective one-group cross sections for materials in different MCNP-defined
regions. ORIGEN, in turn, can carry out depletion calculations for each region and output
time-dependent isotopic composition. MCODE serves as a console program to control the
data flow between MCNP and ORIGEN as well as the alternate running of these two
codes.
MCNP-4c, the latest MCNP version, was used, which is a general purpose,
generalized geometry, continuous energy, time-dependent, Monte Carlo transport code
for neutrons/photons/electrons developed at the Los Alamos National Laboratory
(LANL)[5]. The Monte Carlo method is employed in MCNP, which sets up a virtual
world analog to reality to solve neutron transport problems. It follows each of many
particles from a source to their death in some terminal category (absorption, escape, etc.).
Probability distributions are randomly sampled to determine the outcome at each step. In
MCODE burnup calculations, three kinds of data are needed from MCNP:
1. criticality or eigenvalue, keff,
2. effective one-group cross sections,
11
3. one-group neutron flux data.
Specifically, the effective one-group cross sections of fission products and actinides are
needed. For fission products, only neutron capture cross sections are calculated. For
actinides, four types of cross sections are considered including capture, fission, (n, 2n),
and (n, 3n) reactions. Although not all nuclides and all reactions are calculated, the
representation of fission products and actinides is quite complete for burnup calculations
(i.e. altogether the chosen isotopes account for more than 99% of neutron absorption). In
addition to the effective one-group cross sections, the one-group flux value in each
MCNP depletion cell is needed.
ORIGEN (version 2.1) is a one-group depletion and radioactive decay computer
code developed at the Oak Ridge National Laboratory (ORNL)[6]. Given appropriate
one-group cross sections and decay constants, ORIGEN 2.1 uses a matrix exponential
method to solve a large system of coupled, linear, first-order ordinary differential
equations with constant coefficients. Both nuclear reactions and isotope decay are
considered. Several generic reaction specific cross section and fission product yield data
libraries are available with ORIGEN 2.1. For cross sections not provided from MCNP,
ORIGEN uses library values, which are fairly representative of a given type of reactor.
The cross section data used in our work is from the fast flux test facility core library
(FFTFC.LIB).
2.2.2 Normalization
Since there are two modes of depletion in ORIGEN, constant power or constant
flux, there are two corresponding ways to do depletions. In burnup calculations, the total
power of the reactor is usually assumed to be known and maintained constant. However,
the power fractions among different zones vary. Therefore, the two options should not
affect final results if small time steps are used. MCODE provides the user with both of
the above options to run depletion calculations. The flux values from MCNP are in units
of number of neutrons per fission source neutron per cm2, which must be multiplied by an
appropriate factor to convert into n/cm2 per second if an actual flux value is wanted.
12
For power normalization, the power of each cell is determined and fixed in each
time step. It is not necessary to normalize relative flux values from MCNP because the
power fractions for each cell can be obtained using only these relative values:
( ) ( ){ }( ) ( ){ }∑∑ ∫
∑ ∫
= =
=
⋅⋅
⋅⋅= n
k
m
j
jkkk
jfk
jk
m
j
jiii
jfi
ji
i i
i
RVdEEEN
RVdEEENf
1 1,
1,
φσ
φσ, (2-1)
where fi is the power fraction of cell i,
jiN is the number density of isotope j in cell i,
Vi is the volume of cell i,
jiR is the recoverable energy of isotope j in cell i,
( )Ejfi,σ is the fission cross section at energy E for isotope j in cell i,
( )Eiφ is the neutron flux at energy E,
The j summation is over all actinides,
and the k summation is over all depletion cells.
Then, the power of each cell can be determined by multiplying the fraction factor fi by the
given total power.
For flux normalization, the absolute flux value for each depletion cell is needed.
Therefore, the relative flux values from MCNP are multiplied by a constant factor. This
flux multiplication factor (FMF) in units of fission neutrons per second can be calculated
by either of the following two ways:
eff
FMFkQ
P⋅⋅
=ν , (2-2)
where P is the total power of the modeled system (watts),
ν is the average number of neutrons per fission,
Q is the average recoverable energy per fission (Joules/fission),
keff is the eigenvalue of the system;
( ) ( ){ }∑∑ ∫= =
⋅⋅= n
i
m
j
jiii
jfi
ji
i
RVdEEEN
P
1 1,
FMFφσ
. (2-3)
13
Equation (2-2) has a simpler form but with some ambiguities in its quantities. For
instance, the average recoverable energy per fission needs to be computed carefully. One
can imagine that for different kinds of fuel Q can be very different. For a relevant
discussion see Ref. [16]. Equation (2-3) appears complicated, but has a very clear
meaning and no ambiguities with regard to its quantities. However, both Eq. (2-2) and
Eq. (2-3) give an instantaneous flux multiplying factor only. For the real situation in each
depletion cell, the flux level changes continuously with burnup. The time step average
flux should be used instead of beginning-of-time-step instantaneous flux. This might be
done by the internal “predictor-corrector”, namely after the first trial ORIGEN depletion
gives an average flux to satisfy given energy production, the second ORIGEN depletion
uses the average flux (corrector).
In the ideal case, the two ways of normalization produce identical results. But
when the time step is long, power normalization assumes constant power in each cell,
which is incorrect; flux normalization assumes constant flux in each cell, which is also
incorrect. Hence the specified time step length must be sufficiently short such that the
two approaches give comparable results.
2.2.3 Predictor-Corrector Algorithm The coupling of MCNP and ORIGEN requires careful attention to detail. Because
the cross sections, flux and power fraction in each depletion cell are varying during
reactor operation, it is not valid to use beginning-of-time-step values to represent the
entire time step. A better estimate of time step average value is required.
The predictor-corrector algorithm is the standard algorithm to solve depletion
problems. For each burnup step the depletion is calculated twice, first using the spectra at
the start of the step and then, after a new spectrum calculation, using the spectra at the
end of the step. Average number densities from these two calculations are used as start
values for the next burnup step. This algorithm has proven to be efficient and useful to
solve depletion problems, especially in poisoned assemblies [4]. It has been implemented
in MCODE, which distinguishes MCODE from other MCNP-ORIGEN linkage codes,
such as MOCUP, MONTEBURNs, etc.
14
2.2.4 Running MCODE
One of the best features of MCODE is its user-friendly interface. Users need a
minimal amount of time to learn and initiate MCODE runs. Only three input files are
needed:
• initial MCNP input,
• MCODE input file,
• MCNP source file (optional).
Users have many options to run the code, such as the predictor-corrector option,
normalization option, etc. The flow chart is shown in Figure: 1.
The default and recommended settings are to employ the predictor-corrector, plus
flux normalization. Power normalization is usually used to check the result. When time is
limiting, the predictor-corrector can be turned off: this reduces overall time per step by
approximately a factor of two.
15
Parse MCODE input and initialize variables
Initial run?
Preprocess initial mcnp input and run MCNP
Extract beginning-of-timestep cross-sections and flux values
Loop through all timesteps
Run ORIGEN depletions for all active cells
Update MCNP input based on ORIGEN outputmaterial composition (predictor), and run MCNP
Predictor-Corrector?
Finish all timesteps?
Extract end-of-timestep cross-sections and flux values
Re-run ORIGEN depletions for all active cells
Average the predictor and corrector material,update MCNP input, and re-run MCNP
NO (restart)
YES
YES
YES
NO
NO
END Figure 2-1 Flow diagram for MCODE
16
2.4 Whole Core Model for matrix and reflector configuration
A simplified matrix core model was developed from the homogenization of the
hexagonal cell core developed in ref[9]. See Figure: 2.3. Axial leakage is assumed to be
zero. The extruded coolant tubes and the cladding of the assembly are made of the same
material as the matrix. These two parts are included in the calculated matrix volume
fraction. The core parameters for matrix tests are given in tables 2.5 and 2.6. Similarly,
the parameters for reflector tests are given in tables 2.7 and 2.8.
Figure 2-2 Original fuel assembly and core layout of the MFGR-GT [6]
2)
matrix metal serves as clad
extruded sheath matrix metal
CERMET or METMET fuel in matrix
active core
reflector
36 cm
Gas coolant (CO2) D = 1.2cm, 106holes/cell
17
Figure 2-3 Final homogenized cylindrical core layout
For matrix tests, the reflector is always Nickel and the core diameter 300cm; for reflector
tests, the matrix is always Lead and the core diameter 180cm. The reflector thickness is
always 90cm.
Table 2-1 Matrix test core model parameters
Parameters Values Parameters Values
Fuel* UC, UPuC Coolant CO2 Fuel temperature (ºK) 773.15 reflector thickness (cm) 90.00 Fuel percent of theoretical density 100.00 volume percent of fuel (%) 26.92 Fuel enrichment (%) 13.00 volume percent of coolant (%) 10.28 core diameter (cm) 300.00 volume percent of matrix (%)** 62.80 core height (m) 1.00 Power density (kW/l) 10.61 * We are mainly using UC fuel. The UPuC fuel with matrix study is limited.
** volume fraction of matrix material is kept the same for performance comparisons.
18
Table 2-2 Initial region–homogenized compositions in matrix test core model
Nuclide Weight percent
Number density
(w/o) (#/barn.cm) Fuel U238 - 7.685943E-03
(UC+matrix+CO2) U235 - 1.163166E-03 Cell1* C - 9.041788E-03
O - 3.853585E-04 Fuel U238 - 7.685943E-03
(US+matrix+CO2) U235 - 1.163166E-03 Cell1* C - 1.926790E-04
Cell1* Pu239 - 7.342604E-04 Pu240 - 3.365826E-04 Pu241 - 1.155801E-05 Pu242 - 6.906098E-05 C - 9.041788E-03 O - 3.853585E-04
Reflector Ni 9.995943E+01 8.898912E-02 (Ni+CO2) C 1.107238E-02 4.816981E-05
Cell2 O 2.949893E-02 9.633962E-05
* Since UC/US/UPuC and CO2 keep their same volume percentages when matrix
material changes, the homogenized atom number densities of uranium carbide and
carbon dioxide in the core cell are always the same. The parameters for the reflector
cell are fixed. The weight percent of UC/US/UPuC and CO2 depend on the density
and formula weight of the specified matrix.
Table 2-3 Reflector test core model parameters
Parameters Values Parameters Values
Fuel UC Coolant CO2 Fuel temperature (ºK) 773.15 reflector thickness (cm) 90.00 Fuel percent of theoretical density 100.00 volume percent of fuel (%) 26.92 Fuel enrichment (%) 13.00 volume percent of coolant (%) 10.28 core diameter (cm) 180.00 volume percent of matrix (%)* 62.80 core height (m) 1.00 Power density (kW/l) 10.61 * Volume fraction of reflector material is kept the same for performance
comparisons.
19
In the matrix model, the core diameter is set to 300.0cm, which makes the core’s leakage
negligible. When assessing radial reflector performance, we need larger leakage to get
accurate performance comparisons. The 180cm(d) × 100cm(h) cylinder bare(unreflected)
core has keff = 1.02368. Thus keff – 1.02368 can be considered as mainly gains
attributable to the reflector.
Table 2-4 Initial region homogenized compositions in reflector test core model
Nuclide Weight percent Number density
(w/o) (#/barn.cm) Fuel U238 28.10 7.685943E-03 (UC+Pb+CO2) U235 4.20 1.163166E-03 Cell1 C 1.67 9.041788E-03 O 0.09 3.853585E-04 Pb 65.94 2.071776E-02
reflector C - 4.816981E-05 (reflector+CO2) O - 9.633962E-05 Cell2
Since CO2 keeps the same volume percentage when reflector material changes, the
homogenized atom number densities of carbon dioxide in the reflector cell are always the
same. The parameters for the matrix/fuel cell are fixed.
Table 2-5 Matrix material cell 1 homogenized composition for whole core model
matrix component weight percent numberdensity ( % ) (#/barn.cm) Al Al 100.00 3.783206E-02 Al4C3 Al 74.97 2.480135E-02 C 25.03 1.860101E-02 Ba Ba130 0.10 1.024670E-05 Ba132 0.10 9.763390E-06 Ba134 2.36 2.336450E-04 Ba135 6.48 6.372300E-04 Ba136 7.77 7.592240E-04 Ba137 11.20 1.085766E-03 Ba138 72.00 6.930846E-03 BaO Ba130 0.09 1.495680E-05 Ba132 0.09 1.425130E-05 Ba134 2.18 3.410430E-04 Ba135 6.00 9.301440E-04
20
matrix component weight percent numberdensity ( % ) (#/barn.cm) Ba136 7.20 1.108214E-03 Ba137 7.26 1.108214E-03 Ba138 66.73 1.011672E-02 O 10.43 1.363355E-02 BaS Ba130 0.08 1.055130E-05 Ba132 0.08 1.005360E-05 Ba134 1.91 2.405890E-04 Ba135 5.25 6.561700E-04 Ba136 6.30 7.817900E-04 Ba137 9.08 1.118037E-03 Ba138 58.37 7.136843E-03 S 18.93 9.954034E-03 BeO Be 36.03 4.536367E-02 O 63.97 4.536367E-02 Bi Bi 100.00 1.769952E-02 C C 100.00 8.344854E-02 Ca Ca 100.00 1.462735E-02 CaC2 Ca 62.52 1.311143E-02 C 37.48 2.622286E-02 CeO2 Ce 81.41 1.566749E-02 O 18.59 3.133498E-02 Co Co 100.00 7.539229E-02 Cr Cr 100.00 5.193445E-02 Cu Cu 100.00 5.325470E-02 Fe Fe 100.00 5.282486E-02 Fe3C Fe 93.31 4.862416E-02 C 6.69 1.620805E-02 HT9 Fe 84.7 4.474266E-02 Ni 0.5 2.513063E-04 Cr 12 6.808213E-03 Mo 1 3.074843E-04 Si 0.2 2.100731E-04 V 0.3 1.737289E-04 W 0.5 8.023293E-05 C 0.2 4.912298E-04 Mn 0.6 3.221816E-04 K K 100 8.280259E-03 Mg Mg 100.00 2.704544E-02 Mn Mn 100.00 5.142513E-02 Mo Mo 100.00 4.052822E-02 Na Na 100.00 1.592461E-02 Nb Nb 100.00 3.488987E-02 Ni Ni 100.00 5.740094E-02 P P 100.00 2.225978E-02 Pb Pb 100.00 2.071776E-02 PbO Pb 92.83 1.633518E-02
21
matrix component weight percent numberdensity ( % ) (#/barn.cm) O 7.17 1.633518E-02 PbS Pb 86.60 1.201358E-02 S 13.40 1.201358E-02 Ba2Pb Ba130 0.06 8.172440E-06 Ba132 0.06 7.786950E-06 Ba134 1.34 1.863470E-04 Ba135 3.69 5.082330E-04 Ba136 4.43 6.055320E-04 Ba137 6.38 8.659700E-04 Ba138 41.04 5.527809E-03 Pb 43.00 3.854926E-03 S S 100.00 2.311814E-02 Si Si 100.00 3.137716E-02 SiC Si 70.05 3.034421E-02 C 29.95 3.034421E-02 Sn Sn 100.00 2.328939E-02 Sr Sr84 0.54 6.35777E-05 Sr86 9.67 0.001119422 Sr87 6.94 0.000794721 Sr88 82.85 0.00937544 SrO Sr84 0.45 9.61E-05 Sr86 8.18 0.001691917 Sr87 5.87 0.001201158 Sr88 70.06 0.014170237 O 15.44 1.72E-02 SrS Sr84 0.39 6.55E-05 Sr86 7.08 0.001152786 Sr87 5.08 0.000818408 Sr88 60.65 0.009654873 S 26.79 0.011691539 Sr2Pb Sr84 0.11 4.90E-05 Sr86 1.95 0.000862324 Sr87 1.40 0.000612197 Sr88 16.68 0.007222178 Pb 79.86 1.47E-02 Ti Ti 100.00 3.56E-02 TiC Ti 79.94 3.118990E-02 C 20.06 3.118990E-02 TiN Ti 77.36 3.184884E-02 N 22.64 3.184884E-02 TiN15 Ti 77.36 3.184884E-02 N15 22.64 3.184884E-02 U238 U238 100.00 3.027119E-02 V V 100.00 4.536256E-02 VC V 80.92 3.466758E-02 C 19.08 3.466758E-02
22
matrix component weight percent numberdensity ( % ) (#/barn.cm) W W 100.00 3.960215E-02 Zn Zn 100.00 4.129666E-02 ZnC Zn 84.48 3.288503E-02 C 15.52 3.288503E-02 Zr Zr 100.00 2.696982E-02 ZrO2 Zr 74.03 1.743353E-02 O 25.97 3.486706E-02 ZrC Zr 88.37 2.465768E-02 C 11.63 2.465768E-02 Void - - -
A total of 39 actinides and 100 fission products (including some excited states as
different nuclides) have been tracked in MCODE burnup runs. 34 elements are used
singly or in combination as matrix material. See tables 2.10, 2.11 and 2.12.
extrapolated reactivity-limited burnup potential, and for reflector candidates, their albedo.
5.2 General Evaluation Results
Materials cause spectrum changes and absorb neutrons to an extent which differs
when they are used for different functions, e.g. diluent, cladding, coolant, and reflector.
Based on our results, the best of the candidate materials can be grouped into several
categories:
63
Table 5-1 General Evaluation Results
Element Possible
Use Usable Forms
Al REF SNG, ALY Ba DIL REF SNG, COM Bi COO REF ALY C DIL REF SNG, COM Ca DIL REF SNG Co REF SNG, ALY Cr REF CLA SNG ALY Si REF DIL SNG COM Cu REF SNG ALY Fe REF CLA ALY K COO DIL ALY SNG
Mn REF CLA ALY SNG
Mo REF CLA ALY SNG COM
Na COO DIL SNG ALY
Element Possible
Use Usable Forms
Ni REF CLA SNG ALY P DIL COM
Pb COO REF
DIL SNG ALY
COM S REF DIL SNG COM Sn REF SNG ALY
Ti REF CLA
DIL SNG ALY
COM U REF COM ALY
V REF CLA
DIL SNG ALY
Zn REF SNG ALY
COM
Zr REF CLA
DIL ALY COM
SNG
KEY: CLA = cladding,
REF = reflector,
COO = coolant,
DIL = diluent, cermet or metmet matrix,
ALY = alloy,
SNG = single element, principal constituent of alloy
COM = chemical compound, eg. sulfide, silicide, etc.
Criteria leading to the classification in table 5.1 are as follows:
[3] ANL-5800, Reactor Physics Constants, U.S. Atomic Energy Commission, Division
of Technical Information , Washington, (1963).
[4] Zhiwen Xu, Pavel Hejzlar, Michael J. Driscoll, and Mujid S. Kazimi, An Improved MCNP-ORIGEN Depletion Program (MCODE) and Its Verification For High-Burnup Applications, PHYSOR, Seoul, Korea, (2002).
[5] Judith F. Briesmeister, MCNP TM — A General Monte Carlo N-Particle Transport Code, Version 4C, LA-13709-M, Los Alamos National Laboratory, (2000). [6] Allen G. Croff, A User’s Manual for the ORIGEN2 Computer Code, ORNL/TM-7175, Oak Ridge National Laboratory, (1980). [7] Xianfeng Zhao, Pavel Hejzlar, M.J. Driscoll, Comparison of Code Results for PWR Thorium/Uranium Pin Cell Burnup, MIT-NFC-TR-027, Center for Advanced Nuclear Energy Systems, MIT (2000). [8] C.M. Kang, R.O. Mosteller, Incorporation of a Predictor-Corrector Depletion Capability into the CELL-2 Code, Trans. Am. Nucl. Soc., (1983), vol. 45, pp. 729-731. [9] Hejzlar P., Driscoll M.J., and Todreas N.E., A Modular, Gas Turbine Fast Reactor Concept (MFGR-GT), Trans. Am. Nucl. Soc.Vol. 84, Milwaukee, June 17-21, p. 242, (2001). [10] John A. Dean, Lange’s Handbook of Chemistry, McGRAW-HILL, New York, (1999) [11] Corrosion Survey Database (COR·SUR), NACE and NIST, Gaithersburg, MD, (2002) [12] Eugene A. Avallone, Theodore Baumeister III, Marks' Standard Handbook for Mechanical Engineers, 10th ed., McGRAW-HILL, New York, (1996), pp. 6-82 [13] Charles A. Harper, Handbook of Materials for Product Design, McGRAW-HILL, New York, (2001), ch7, pp 7.41-7.42
68
[14] Richard P. Pohanish, Sittig's Handbook of Toxic and Hazardous Chemicals and Carcinogens, 4th ed. Noyes Publications, Norwich, NY, (2002) [15] L. Biondi, Research and Development Proposal for a Fuel Element Made up with Uranium Oxide Grains and a Lead Mixture Contained in a SAP Tube in Fuel Element Fabrication with Specific Emphasis on Cladding Materials(Proceedings of IAEA Symposium, Vienna May 10-13, 1960), Academic Press, (1961), vol. 2 [16] M. K. Sheaffer, M. J. Driscoll, I. Kaplan, A one-group method for fast reactor calculations Nucl. Sci. Eng. 48, P459(1972) [17] National Research Council of USA, International Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st ed., Knovel, Norwich, NY, (2003), vol. 5, pp. 92 [18] Michael de Podesta, Understanding the properties of matter, Taylor & Francis, Washington, DC (1996), pp.178 [19] M. J. Driscoll, T.J. Downar, E.E.Pilat, The linear reactivity model for nuclear fuel management, American Nuclear Society, La Grange Park, IL (1990)
69
Appendix A Estimate of Gas Produced By Sulfur
I Sulfur in the fuel For a 13wt% enriched US fuel, the gas produced by sulfur is estimated as following:
S-32 (n, α) gas production in US relative to fission
25 28 25
( , )( )(1 )
s
U f
N nR yN g
σ αχ δ σ
=⋅ ⋅ +
(B-1)
where y = abundance of S-32 in S = 0.95 g = gas atom yield per fission (Kr + Xe) = 0.30 δ28 = ratio of U-238 to U-235 fissions = 0.41 σf25 = U-235 fission cross section = 1525mb σ(n,α) = S-32 (n, α) cross section = 12.5mb χ25 = enrichment = 0.13 (Ns/Nu) = atom ratio of sulfur to uranium = 1.0 for US Thus R(n,α) = 0.14 which is significant. We also have production by (n,p) of H2: 0.5 molecules per reaction, thus:
1 ( , )( , ) ( , )2 ( , )
n pR n p R nn
σ ασ α
= •
(B-2)
where σ(n,p) of S-32 = 5.2mb Thus R(n,p) = 0.030, and Rgas(total) = 0.17. This is probably tolerable, but if we also use a sulfur compound for the matrix, the added gas would be quite significant. II Sulfur in the matrix For a pure natural sulfur matrix and 13wt% enriched UC fuel, the gas produced by sulfur can still be calculated by equation (B-1), but the parameters change to: y = abundance of S-32 in S = 0.95 g = gas atom yield per fission (Kr + Xe) = 0.30 δ28 = ratio of U-238 to U-235 fissions = 0.174 σf25 = U-235 fission cross section = 1685mb σ(n,α) = S-32 (n, α) cross section = 13.6mb χ25 = enrichment = 0.13 (Ns/Nu) = atom ratio of sulfur to uranium = 2.61 for S matrix, UC fuel Thus R(n,α) = 0.36 which is more than twice that of the US fuel case. Taking the H2 generation into consideration, R(n,p) = 0.089, one obtains Rgas(total) = 0.45. This is a quite large number, and would be even larger (~0.55) if US fuel is employed.
70
Appendix B Relation of reactivity ρ to enrichment x
25 28
25 28
025 028
025 028
028
025 025
02825
025
1
1
(1 )1(1 )
(1 )1
(1 )
f a
f
a
f
a a ad
f f
a a ad
f f
a ad
a a
f
a
x xx x
x x
x x
νρ
ν
ρν
ρν ν
ρν ν
ρ νη
Σ − Σ=
Σ
Σ= −
Σ
Σ + Σ + Σ= −
Σ + Σ
Σ + − Σ + Σ= −
Σ + − Σ
Σ Σ+ − +
Σ Σ= −
Σ+ −
Σ
Let
28
25
025
a
a
ad
a
σλσ
γ
=
Σ=
Σ
Then
25 28
25 28
25 28
25 28
25 28
(1 )1(1 )
(1 ) (1 )(1 )
( 1) (1 )( 1)(1 )
x xx x
x x x xx x
x xx x
λ γρη η λ
η η λ λ γρη η λ
η η λ γρη η λ
+ − += −
+ −+ − − − − −
=+ −
− + − − −=
+ −
η28 ≈ 0.46, for x → 0, 28
28
1 1.17ηρη
−= ≈ −
In a fission spectrum, η25 = 2.46. Omit the γ term, then
[ ][ ]
1.46 (1 ) ( 0.54)2.46 (1 ) (0.46)
1.46 0.37(1 )2.46 0.19(1 )
x xx xx xx x
λρλ
λρ
λ
+ − −≅
+ −
− −≅
+ −
Furthermore, 28
25
0.21 0.131.57
a
a
σλσ
= ≈ = for a very hard spectrum
71
If so, 0.64 0.0290.025
xx
ρ −=
+
The least square curve fit to MCNP calculation gives 0.60 0.0320.017
xx
ρ −=
+. Comparing
each term in the two equations, we can see that the theoretical deduction gives a fairly good explanation and estimation.
72
Appendix C Sample input files for matrix material study