ISTC Project # 1763p
Issues of Generation of Neptunium
and Americium Isotopes in Nuclear
Reactors by Thermal Neutrons and
Nonproliferation
(Technical report for phases C-1 and C-2)
Project Manager
Yuri A. Yudin.
2
Abstract
This report contains the results obtained from the first research phase within the
project “Control of Alternative Nuclear Materials and Non-Proliferation” under ISTC project
#1763p “Support of the Analytical Center for Non-Proliferation and Efforts of RFNC-VNIIEF
Specialists to Strengthen Non-Proliferation and to Reduce the Nuclear Threat”.
3
Table of Contents
Introduction ...........................................................................................................................5
1. The Generation Process of Np-237, Am-241 and Am-243 Isotopes in UraniumUranium Fuel....................................................................................................................5
2. General Physical Properties of Neptunium and Americium..................................................6
3. Radioactive Properties of Neptunium and Americium Isotopes ...........................................7
3.1. Neptunium ..................................................................................................................7
3.2. Americium...................................................................................................................9
3.2.1. Am-241 Isotope....................................................................................................9
3.2.2. Am-243 Isotope..................................................................................................10
3.2.3. Am-242m Isotope...............................................................................................11
4. Radiation and Environment Characteristics of Neptunium and Americium Isotopes ..........11
5. Critical Mass of Neptunium and Americium Isotopes........................................................12
5.1. Neutron Multiplication in Infinite Medium .................................................................12
5.2.Critical Masses of Np-237, Am-241, Am-243 Spheres ................................................13
5.2.1 Np-237 Isotope....................................................................................................15
5.2.2. Am-241 Isotope..................................................................................................17
5.2.3. Am-243 Isotope..................................................................................................19
5.2.4. Americium from Spent Nuclear Fuel ...................................................................22
6. Single Group Approximation for the Generation of Np-237, Am-241 and Am-243
Isotopes .........................................................................................................................23
6.1. Problem Formulation .................................................................................................23
6.2. VVER-440 Reactor...................................................................................................26
6.3. VVER-1000 Reactor.................................................................................................33
6.4. RBMK-1000 Reactor ................................................................................................40
6.5. Natural Uranium Reactor...........................................................................................47
7. Generation of Np-237, Am-241 and Am-243 Isotopes in Reactors by Thermal
Neutrons ........................................................................................................................54
7.1. Physical Basis and Implementation Scheme of the Method.........................................54
7.2. Method Testing .........................................................................................................56
7.2.1. The Computational Results for the Effective Neutron Multiplication Coefficient in
Critical Uranium and Plutonium Assemblies with Water Moderator.....................57
7.2.2. The Description Results for the IAEA Computational Experiment.......................58
7.3. Characteristics of Isotope Generation in Thermal Reactors ........................................61
4
7.3.1 VVER-1000 Reactor ...........................................................................................61
7.3.2. RBMK-1000 Reactor..........................................................................................63
7.3.3. CANDU Reactor ................................................................................................64
Conclusions..........................................................................................................................65
References ...........................................................................................................................66
5
Introduction
In the second half of the 20-th century the nuclear power industry progressed
dramatically using mainly thermal reactors. These reactors use nuclear fuel in the form of
natural uranium or low enriched uranium over U-235 isotope. Spent nuclear fuel contains
significant amounts of fissile isotopes, primarily plutonium isotopes that compose the material
known as reactor-grade plutonium. A part of reactor-grade plutonium was obtained in some
countries from radiochemical processing of spent fuel and the major portion of reactor-grade
plutonium resides in non-processed fuel elements in various storage facility types. The threats
to nonproliferation regimes resulting from the generation of reactor-grade plutonium are well
known to responsible national institutions and scientific community.
Spent fuel also contains fissile isotopes of neptunium and americium, though in
amounts lower than that of reactor-grade plutonium. Though the major portion of
nonproliferation problem relating to the progress of nuclear energy is determined by reactorgrade plutonium the handling issues for neptunium and americium isotopes are also of
particular interest.
This study has the objective to obtain a realistic estimate of the potential threat to
nonproliferation regime resulting from possible use of neptunium and americium isotopes. He
study consists of two parts.
The first part develops and applies some physical and computer models to estimate the
generation of neptunium and americium isotopes in various reactor types. The critical mass
parameter estimates are presented obtained from world wide libraries of neutron constants; the
radiation and radiological characteristics of neptunium and americium isotopes are also given
The results of the first part serve the base required for the implementation of the
second part after which the appropriate conclusions will be made.
1. The Generation Process of Np-237, Am-241 and Am-243 Isotopes
in Uranium-Uranium Fuel
In standard uranium-uranium reactor fuel (235Ux, 238U1-x) Np-237 isotope is generated
from U-235 isotope while Am-241 and Am-243 isotopes are generated from U-238 isotope in
the following isotopic sequences /1/:
6
235
236
U
237
U
-
β
n,γ
237
U
238
Np
6.75 days
n,f
β
n,γ
238
β
n,γ
n,γ
239
U
U
23.5 minutes
238
Np
Pu
2.12 days
β
239
-
-
n,γ
239
Np
2.36 days
n,γ
240
Pu
241
Pu
Pu
n,f
n,γ
241
242m
Am
14.4 years β
Am
-
n,γ
241
Pu
β
n,γ
242
243
Pu
-
Pu
4.96 hours
n,f
β
n,γ
243
244
Am
Am
244
Ñm
10.1 hours
This is accompanied by the fission of start U-235 isotope and generated isotopes of
Pu-239 and Pu-241 ensuring the energy release and chain reaction sustenance.
2. General Physical Properties of Neptunium and Americium
This section presents the basic physical characteristics of neptunium and americium
metals as well as those of their oxides, NpO2 and AmO2 /1/.
Table 2.1
Density,
3
g/cm
Melting point,
°C
Heat capacity,
J/g⋅⋅ deg
Melting heat,
kJ/g
Neptunium metal
20.25
637
0.124
0.22
Americium metal
13.65
1180
0.107
0.06
NpO2
11.1
2560
0.246
0.235
AmO2
11.7
7
3. Radioactive Properties of Neptunium and Americium Isotopes
3.1. Neptunium
Long lived neptunium isotopes generated in significant amounts in thermal reactors
include Np-237 isotope with the half life of = 2.14⋅106 years The scheme of its decay to the
nearest long lived neighbor nucleus is as follows:
Np-237 (T = 2.14⋅106 years; α) → Pa-233 (T = 27 days; β) → U-233 (T = 1.59⋅105 years; α)
The amount of Ðà-233 resulting from the decay of Np-237 is:
m ( Pa - 233) = m ( Np - 237 )
≈ m ( Np - 237 )
τ( Pa - 233)
(1 − exp −t / τ( Pa -233) ) ≈
τ(Np - 237)
τ( Pa - 233)
τ(Np - 237)
t >> τ ( Pa − 233 )
where τ ≡ T / ln 2 is the isotope life time.
Clearly, if t >> τ the activity of the daughter an parent isotope is the same, so that
C ( Np - 237 ) =
m ( Np - 237 )
τ( Np - 237 )
= C ( Pa - 233) =
m ( Pa - 233 )
τ( Pa - 233)
.
Since the life time of Ðà-233 is relatively low as compared to the typical life time of a
material containing neptunium for the application in question (several years or decades) we
must assume Np-237 and Ðà-233 to be in radiation equilibrium and their activities to be equal.
Instead, for U-233, t << τ and its amount resulting from the decay of Np-237 is:
m ( U - 233) = m ( Np - 237 )
t >> τ ( Pa -233 )
t
τ(Np - 237)
t << τ ( U -233 )
and correspondingly,
C ( U - 233) = C ( Np - 237 )
t
τ( U - 233)
<< C ( Np - 237 ) .
Therefore we shall not consider the contribution of U-233 and subsequent products of
its decay to the total activity of the material containing Np-237.
8
Thus the radioactive characteristics of the material containing neptunium are
determined by two radionuclides, Np-237 and Ðà-233. The radioactive characteristics of these
nuclides are given in Table3.1.
Table 3.1
C0
Decay type
Eα
Eβ
Eγ
nc
Np-237
0.7
α
4.77
0
0.09
0.11
Pa-233
0.7
β
0
0.064
0.34
0
Isotope
where C 0 –specific material activity per 1 kg of Np-237 (Ci/kg);
E α - energy of α particles (MeV);
E β - average energy of β particles (MeV);
E γ - total energy of γ quanta (MeV);
nc - intensity of spontaneous fission neutron formation (n/sec kg).
It is seen from Table 3.1 that the energy release and neutron radiation of the material is
determined by Np-237 and γ-radiation of the material is determined by Ðà-233. Diagram 3.1
shows the structure of dominant γ transitions in β decay of Ðà-233 determining γ background
of the material containing Np-237.
The major portion of γ radiation can be efficiently characterized by the number of hard
γ quanta, 0.95 quantum per decay with Eγ = 0.34 MeV. The maximum energy release in the
material is determined by the absorption energy of α and β particles and γ quanta that is
2.18⋅10-2 W/kg.
Level energy,
MeV
Level population
probability
27%
0.415
0.44
0.17
0.17
0.22
15%
0.4
0.41
0.59
36%
0.34
0.4
0.6
17%
0.31
0.98
0.02
0.04
0
Diagram 3.1. Structure of basic γ transitions in β decay of Pa-233
9
3.2. Americium
Long lived americium isotopes generated in significant amounts in thermal reactors
include those of Àm-241 and Am-243. The isotope of Àm-242m is generated in much lower
amounts; however its concentration in americium obtained from spent fuel may significantly
affect the characteristics of material neuron radiation.
3.2.1. Am-241 Isotope
The scheme of Am-241 decay to the nearest neighbor long lived nucleus is as follows
/1, 2, 3/:
Am-241 (T = 432 years; α) → Np-237 (T = 2.14⋅106 years; α)
Since this scheme does not contain intermediate short lived nuclei the radiation
characteristics of the process are determined by the decay parameters of Àm-241 which are
presented in Table 3.2.
Table 3.2
C0
Isotope
3.44⋅⋅ 10
3
Am-241
Decay type
Eα
Eγ
nc
α
5.48
0.068
1.25⋅⋅ 10
3
Diagram 3.2 shows the structure of basic γ transitions for α decay of Am-241.
Level population
probability
Level energy,
MeV
12.8%
0.103
0.25
0.03
0.72
36%
0.06
0.94
0.06
0.033
0
Diagram 3.2. Structure of basic γ transitions for α decay of Am-241
The main portion of hard γ radiation of Am-241 can be characterized by the intensity
of 1 quantum per decay with Eγ = 0.06 MeV. The energy release in Am-241 is 113 W/kg.
10
3.2.2. Am-243 Isotope
The scheme of Am-243 decay to the nearest neighbor long lived nucleus is as follows
/1, 2, 3/:
Am-243 (T = 7380 years; α) → Np-239 (T = 2.35 days; β-) → Pu-239(T = 2.42⋅104 years; α)
Thus the radiation characteristics of the material containing Àm-243 are determined by
the radioactivity of this material and Np-239 isotope that is in the equilibrium state relative to
the material.
The energy release and neutron radiation of the material are determined by the
radioactivity of Am-243 γ radiation is determined by the decay of Np-239 nuclei. Diagram 3.3
shows the structure of basic γ transitions for β decay of Np-239.
Table 3.3
C0
Decay type
Eα
Eβ
Eγ
nc
Am-243
200
α
5.27
0
0.08
3.9⋅⋅ 10
Np-239
200
β
0
0.118
0.31
0
Isotope
Level population
probability
3
Level energy,
MeV
36%
0.39
0.36
0.28
0.18
0.18
7%
0.33
0.26
0.34
0.37
45%
0.285
0.03
0.98
0.37
0.11
0.075
0.057
7%
0.008
0
Diagram 3.3. Structure of basic γ transitions for β decay of Np-239
The main portion of γ radiation can be efficiently characterized by the number of hard γ
quantum in 0.85 quantum per decay with Eγ = 0.28 MeV. The maximum energy release in the
material determined by the absorption of α, β particles and γ quanta is 6.85 W/kg.
11
3.2.3. Am-242m Isotope
Long lived americium isotopes generated in small amounts in thermal reactors include
Am-242m isomer having the following decay scheme /1, 2, 3/:
Am-242m (T = 1.52⋅102 years; γ) → Am-242 (T = 16 hours; 82% β-; 18% EC*)) →
→ Pu-242 (T = 3.76⋅105years; α)
→ Cm-242 (T = 1.63⋅102days; α) → Pu-238 (T = 88 years; α)
The contribution to the radioactivity of the material containing Am-242m is made by
the following radionuclides: Am-242m, Am-242, Cm-242.
Table 3.4
C0
Decay type
Eα
Eβ
Eγ
nc
Am-242m
9.75⋅⋅ 103
γ
0
0
0.049
1.5⋅⋅ 105
Am-242
1.75⋅⋅ 103
8⋅⋅ 103
EC
0
0.16
0.045
0.042
0
β
0
0
Cm-242
8⋅⋅ 10
α
6.1
0
0.011
5.2⋅⋅ 107
Isotope
3
he energy release and neutron background of the material containing Am-242m are
determined by the decay of the daughter Ñm-242 nucleus. Gamma radiation can be
characterized by the output of about 1.8 quanta per decay with Eγ ≅ 0.045 MeV. The energy
release is approximately 300 W/kg. Note a high neutron background resulting from
spontaneous decay of Ñm-242 that is in equilibrium with Àm-242m in the material.
Note that for americium and plutonium dioxides a contribution to the neutron radiation
will be made by (α,n) reaction occurring on oxygen isotopes Î-17 and Î-18 that exist in small
amounts in natural oxygen.
(α,n) reaction may be also of some importance for americium and neptunium metals if
they contain significant quantities of light element impurities.
4. Radiation and Environment Characteristics of Neptunium and
Americium Isotopes
The basic radiation and environment characteristics of neptunium and americium
isotopes are defined by the collection of parameters regulated by the radiation safety
requirements. These are as follows:
*)
Electron capture
12
dose ratio determining inhaled radioactivity dose (Zv/Bq);
dose ratio determining the radioactivity dose absorbed by the organism with
food and water (Zv/Bq);
maximum allowed concentration of the radionuclide in air (Bq/l);
maximum allowed concentration of the radionuclide in water (Bq/l);
maximum allowed income of the radionuclide through breathing (Bq/year);
maximum allowed income of the radionuclide with food and water
(Bq/year);.
DAIR
DWAT
LAIR
LWAT
LIAIR
LIWAT
L and LI parameters correspond to irradiation dose limits for people not greater than
1 mZv/year
Isotope
DAIR
DWAT
L AIR
9.2⋅⋅ 10
-7
L WAT
LIWAT
1.2⋅⋅ 10
8.9
1.4
1.1⋅⋅ 103
-6
1.4⋅⋅ 10
10
1.6
1.3⋅⋅ 103
1.1⋅⋅ 10
Am-241
0.95⋅⋅ 10
7.8⋅⋅ 10
Am-243
0.96⋅⋅ 10-4
7.9⋅⋅ 10-7
1.4⋅⋅ 10-6
10
1.6
1.3⋅⋅ 103
Am-242m
0.99⋅⋅ 10-4
8.1⋅⋅ 10-7
1.4⋅⋅ 10-6
10
1.5
1.2⋅⋅ 103
-4
-7
LIAIR
Np-237
-4
-6
Liquid material relates to the category of radioactive waste whose handling is
regulated by appropriate rules if the specific concentration of radionuclide exceeds LWAT.
Similarly, solid material relates to the category of radioactive waste whose handling is
regulated by appropriate rules if the specific concentration of radionuclide types of interest
exceeds 3.7⋅102 Bq/kg.
5. Critical Mass of Neptunium and Americium Isotopes
5.1. Neutron Multiplication in Infinite Medium
The existence of critical isotope mass is determined by the potential neutron
multiplication from this isotope in an infinite medium. This implies that
(
)
K e f f = νσ f / σ f + σ c , where σ f and σ c are effective cross-sections for nuclei fission and
neutron capture by nuclei and ν is the number of secondary neutrons resulting from nuclear
fission.
Table 5.1 shows the values of K eff for infinite medium composed of neptunium and
americium metals and their oxides when ENDF-B5 constants are used.
He neuron multiplication rate, α ∞ , in infinite medium is defined by
[
]
dn
dt
= α ∞ n , so that
α ∞ = ( ν − 1) σ f − σ c ⋅ V , where V is the effective neutron velocity. The values of α ∞ in
13
1/µsec are also given in Table 5.1. The same table shows the neutron life time with respect to
ν−1 1
nuclear fission τ f (µsec). Here α ∞ =
− , where τ c is the neutron life time as
τf
τc
compared to capture by nuclei.
Table 5.1 also contains the effective values of the number of secondary neutrons ν and
neutron life time τ c as compared to neutron capture. Clearly, the relation
(1 − 1 / K eff ) ν = α ∞ τ f is met.
Table 5.1
ρ0
K eff
α∞
τf
τc
Np-237
20.25
1.609
131.4
9.4⋅⋅ 10
Np237O2
11.1
1.32
43.2
1.13⋅⋅ 10-2
Am-241
13.65
1.661
135.6
1.01⋅⋅ 10-2
241
Am
O2
Am-243
243
Am
O2
-3
11.7
1.405
75.4
8.85⋅⋅ 10
13.65
1.563
110.9
1⋅⋅ 10-2
11.7
1.307
54
9.1⋅⋅ 10-3
9.2⋅⋅ 10
-3
9.4⋅⋅ 10-3
-3
1.03⋅⋅ 10-2
5.2.Critical Masses of Np-237, Am-241, Am-243 Spheres
For Np-237, Am-241, Am-243 isotopes critical masses are numerically calculated for
spheres composed of these isotopes and their compounds. The critical mass is one of basic
characteristics determining the potential threat to nonproliferation regime that can be related
with a fissile material. the calculations used the Monte Carlo “Polina” code /6/ with neutron
constants from worldwide known ENDL-82, ENDF-B5 and JENDL-32 libraries.
The values of the critical sphere radius and critical mass were determined from the
requirement for the calculation of effective neutron multiplication coefficient
νR fis
K eff =
= 1 within the discrepancy not greater than the double statistical
R fis + R a b s + R l e a k
computational uncertainty (2σ). Here R is the intensities of nuclear fission, neutron absorption
by nuclei and neutron leakage from the system, respectively. For each isotope of interest, the
following systems were calculated:
• bare sphere”;
• sphere with U-238 shell 7 cm thick;
• bare dioxide sphere;
• dioxide sphere with U-238 shell 7 cm thick
Standard densities were used for these elements and their compounds.
The computational results are presented in Table 5.2.
It is seen from Table 5.2 that the resulting critical core radii and critical masses
strongly depend on the neutron constants used.
14
Table 5.2
Bare spheres and reflecting spheres. Critical mass and radius. Monte Carlo “Polina”
computations with ENDL-82, ENDF-B5, JENDL-32 constants
Element or
compound
Shell
(thickness)
density
Density of
element or
compound,
3
g/cm
Core
radius,
cm
K eff
Error
1σ
σ%
Mass, kg
Library
Np-237
no
20.25
9.60
9.35
9.60
1.0008
1.0036
1.0009
0.10
0.09
0.10
75.04
69.24
75.04
ENDL-82
ENDF-B5
JENDL-32
Np-237
U-238 (7 cm)
3
19 g/cm
20.25
8.30
8.08
8.30
1.0035
1.0042
0.9968
0.10
0.08
0.11
48.50
44.74
48.50
ENDL-82
ENDF-B5
JENDL-32
Np237O2
no
11.1
20.60
20.20
20.04
0.9984
0.9978
1.0012
0.12
0.08
0.13
406.45
383.23
374.19
ENDL-82
ENDF-B5
JENDL-32
Np 237O2
U-238 (7 cm)
3
19 g/cm
11.1
18.66
18.05
17.92
1.0007
1.0000
1.0005
0.11
0.08
0.11
302.09
273.42
267.56
ENDL-82
ENDF-B5
JENDL-32
Am-241
no
13.65
9.86
12.30
10.79
0.9998
1.0007
0.9995
0.11
0.08
0.11
54.89
106.40
71.82
ENDL-82
ENDF-B5
JENDL-32
Am-241
U-238 (7 cm)
3
19 g/cm
13.65
8.42
10.48
9.45
0.9989
0.9982
0.9963
0.12
0.09
0.12
34.13
65.90
48.25
ENDL-82
ENDF-B5
JENDL-32
Am241O2
no
11.7
12.77
16.82
14.46
1.0001
1.0031
1.0071
0.11
0.08
0.11
102.06
233.42
148.17
ENDL-82
ENDF-B5
JENDL-32
Am241O2
U-238 (7 cm)
3
19 g/cm
11.7
11.34
15.15
13.05
1.0002
1.0031
1.0005
0.12
0.08
0.12
71.47
170.41
108.92
ENDL-82
ENDF-B5
JENDL-32
Am-243
no
13.65
13.67
13.65
21.25
13.96
16.93
1.0005
0.9991
0.9997
0.11
0.07
0.12
548.64
155.71
277.45
ENDL-82
ENDF-B5
JENDL-32
Am-243
U-238 (7 cm)
3
19 g/cm
13.65
18.38
12.27
15.30
0.9989
0.9980
1.0011
0.12
0.08
0.12
355.02
105.62
204.78
ENDL-82
ENDF-B5
JENDL-32
Am243O2
no
11.7
33
20.7
26.95
1.0016
1.0016
0.9994
0.12
0.08
0.12
1761.19
434.69
959.27
ENDL-82
ENDF-B5
JENDL-32
Am243O2
U-238 (7 cm)
3
19 g/cm
11.7
29.7
18.76
25.25
0.9983
0.9948
1.0013
0.09
0.08
0.12
1283.91
323.57
788.95
ENDL-82
ENDF-B5
JENDL-32
15
5.2.1 Np-237 Isotope
The use of neutron data from ENDF-B5 library for Np-237 in the calculations gives
the critical mass of Np-237 sphere equal to Mcr ≈ 69 kg. ENDL-82 and JENDL-32 neutron
data yield the same critical mass of Mcr ≈ 75 kg which seems to result from the fact that data
for Np-237 were taken from ENDL-82 to be included in JENDL-32. The difference in the
estimated critical masses of 8% indicates the accuracy level of estimated neutron constants
determined by the incomplete constant measurements and measurement uncertainty.
The use of U-238 shell decreases the neptunium mass needed to ensure the critical
state of the entire system by about a factor of 1.5. As shown by the high level of studies for U238 neutron constants, these constants are similar in all three libraries. Therefore the
discrepancy in the amount of neptunium required to reach the critical state remained like that
for bare spheres.
The use of NpO2 instead of neptunium metal resulted in a dramatic growth of critical
mass and sphere radius (by about a factor of 5) which is due to two factors:
• decrease of material density by a factor of 2;
• softening of the equilibrium neutron spectrum by oxygen which is of particular
importance for this class of isotopes with the threshold dependence of the fission
cross section on energy.
The use of U-238 reflector 7 cm thick decreases twice the mass of neptunium dioxide
required to reach the critical state of the entire system.
Tables 5.3-5.6 show the neutron density and fluence spectrum distributions normed to
unity in average over the total mass of fissile material for four critical assemblies using Np-237
based materials (ENDF-B5 constants).
Table 5.3
Np-237, R = 9.35 cm, ρ = 20.25 g/cm3; no reflector
Energy, MeV
Neutron flux
Number of neutrons
7
Neutron velocity, 10 cm/sec
0
0.01
1.39E-03
1.16E-02
10.74
0.0465
2.32E-02
9.06E-02
23.03
0.1
4.9E-02
1.19E-01
37.04
0.2
1.02E-01
1.73E-01
52.80
0.4
1.74E-01
2.12E-01
73.92
0.8
1.98E-01
1.72E-01
103.48
1.4
1.6E-01
1.01E-01
141.96
2.5
1.52E-01
7.28E-02
187.48
4.0
8.73E-02
3.23E-02
243.21
6.5
4.37E-02
1.29E-02
305.08
10.5
1.01E-02
2.32E-03
381.99
The average neutron velocity is 90⋅107 cm/señ.
16
Table 5.4
Np-237, R = 8.08 cm, ρ = 20.25 g/cm3; U-238 reflector (7 cm, ρ = 19 g/cm3)
7
Neutron flux
Number of neutrons
Neutron velocity, 10 cm/sec
0.01
1.87E-03
1.42E-02
10.68
0.0465
3.14E-02
1.11E-01
23.08
0.1
6.56E-02
1.45E-01
36.90
0.2
1.22E-01
1.88E-01
52.71
0.4
1.93E-01
2.13E-01
73.70
0.8
1.98E-01
1.56E-01
103.16
1.4
1.42E-01
8.15E-02
141.61
2.5
1.28E-01
5.55E-02
187.43
Energy, MeV
0
4
7.27E-02
2.43E-02
243.10
6.5
3.62E-02
9.65E-03
305.15
10.5
8.42E-03
1.79E-03
381.76
The average neutron velocity is 81.3⋅107 cm/sec.
Table 5.5
Np237O2, R = 20.2 cm, ρ = 11.1 g/cm3; no reflector
Energy, MeV
Neutron flux
Number of neutrons
7
Neutron velocity, 10 cm/sec
0
0.01
5.29E-03
3.35E-02
10.87
0.0465
6.18E-02
1.91E-01
22.32
0.1
9.41E-02
1.77E-01
36.72
0.2
1.48E-01
1.95E-01
52.37
0.4
1.71E-01
1.62E-01
72.58
0.8
1.74E-01
1.13E-01
105.92
1.4
1.18E-01
5.76E-02
140.99
2.5
1.17E-01
4.28E-02
188.29
4
7.11E-02
2.03E-02
240.92
6.5
3.29E-02
7.43E-03
305.00
10.5
7.03E-03
1.27E-03
381.12
The average neutron velocity is 68.9⋅107 cm/sec.
17
Table 5.6
237
Np
O2, R = 18.05 cm, ρ = 11.1 g/cm ; U-238 reflector (7 cm, ρ = 19 g/cm )
3
3
Neutron flux
Number of neutrons
Neutron velocity, 107 cm/sec
0.01
6.49E-03
3.79E-02
10.93
0.0465
7.62E-02
2.18E-01
22.27
0.1
1.08E-01
1.88E-01
36.59
0.2
1.58E-01
1.92E-01
52.28
0.4
1.75E-01
1.54E-01
72.48
0.8
1.69E-01
1.02E-01
105.64
1.4
1.07E-01
4.86E-02
140.86
2.5
1.04E-01
3.52E-02
188.17
Energy, MeV
0
4
6.2E-02
1.64E-02
240.97
6.5
2.86E-02
5.99E-03
304.88
10.5
6.07E-03
1.02E-03
381.01
The average neutron velocity is 63.7⋅107 cm/sec.
To estimate the relative role of critical mass characteristics for the isotopes of interest
as compared to traditional weapon grade materials, U-235 and Pu-239, we shall use the
following critical mass values for the latter: 50 kg for U-235 /7/ and 10 kg for Pu-239 /8/.
The critical mass risk characteristic for uranium meal proliferation is assumed to be
Pcr = 1. In this case the similar risk characteristic for plutonium metal is Pcr = 5.
Accordingly, the critical mass risk characteristics for neptunium metal and NpO2
proliferation are:
• Pcr(Np) – 0.725-0.67;
• Pcr(NpO2) – 0.133-0.123.
5.2.2. Am-241 Isotope
The calculated critical mass of Am-241 sphere varies from 55 to 106 kg depending on
the neutron constants used. To reduce this uncertainty of the critical mass estimate, more
precise evaluation of neutron constants is required.
Like for Np-237, the use of uranium reflector, reduces the amount of Am-241, needed
to obtain the critical state of the assembly. The use of Am241O2 dioxide increases the critical
mass of spheres by a factor of 2. Lower impact on the critical mass for metal-dioxide transition
as compared to Np-237 is primarily determined by a different variation scale of the active
material density. The transition from neptunium metal to NpO2 results in decrease of density
by a factor of 2, while the transition from americium metal to AmO2 reduces the density by
1.17 times.
Tables 5.7-5.10 show the neutron density and fluence spectrum distributions normed
to unity in average over the total mass of fissile material for four critical assemblies using Am241 based materials (ENDF-B5 constants).
18
Table 5.7
Am-241, R = 12.3 cm, ρ = 13.65 g/cm ; no reflector
3
Neutron flux
Number of neutrons
Neutron velocity, 107 cm/sec
0.01
6.81-04
6.34E-03
10.58
0.0465
1.31E-02
5.49E-02
23.46
0.1
3.82E-02
1.01E-01
37.29
0.2
9.23E-02
1.72E-01
52.92
0.4
1.63E-01
2.17E-01
74.05
0.8
2.08E-01
1.98E-01
103.60
1.4
1.5E-01
1.05E-01
141.52
2.5
1.55E-01
8.11E-02
188.59
Energy, MeV
0
4
1.08E-01
4.35E-02
243.77
6.5
5.78E-02
1.87E-02
304.98
10.5
1.21E-02
3.13E-03
381.06
The average neutron velocity is 98.5⋅107 cm/sec.
Table 5.8
Am-241, R = 10.48 cm, ρ = 13.65 g/cm ; U-238 reflector (7 cm, ρ = 19 g/cm )
3
Energy, MeV
3
Neutron flux
Number of neutrons
Neutron velocity, 107 cm/sec
0
0.01
8.3E-04
6.74E-03
10.64
0.0465
1.96E-02
7.12E-02
23.75
0.1
5.81E-02
1.35E-01
37.14
0.2
1.21E-01
1.98E-01
52.76
0.4
1.93E-01
2.26E-01
73.87
0.8
2.17E-01
1.82E-01
103.08
1.4
1.31E-01
8.02E-02
141.11
2.5
1.23E-01
5.66E-02
188.38
4
8.27E-02
2.93E-02
243.69
6.5
4.4E-02
1.25E-02
304.95
10.5
9.14E-03
2.07E-03
381.28
The average neutron velocity is 86.5⋅107 cm/sec.
Table 5.9
241
Am
Energy, MeV
O2, R = 16.82 cm, ρ = 11.7 g/cm ; no reflector
Neutron flux
3
Number of neutrons
Neutron velocity, 107 cm/sec
19
0
0.01
1.82E-03
1.3E-02
10.96
0.0465
3.7E-02
1.25E-01
23.17
0.1
8.02E-02
1.76E-01
36.90
0.2
1.39E-01
2.08E-01
52.46
0.4
1.76E-01
1.89E-01
72.79
0.8
1.87E-01
1.38E-01
105.69
1.4
1.15E-01
6.41E-02
140.75
2.5
1.24E-01
5.12E-02
189.29
4
8.81E-02
2.85E-02
241.56
6.5
4.32E-02
1.11E-02
304.80
10.5
8.44E-03
1.74E-03
380.53
The average neutron velocity is 78.3⋅107 cm/sec.
Table 5.10
Am241O2, R = 15.15 cm, ρ = 11.7 g/cm3; U-238 reflector (7 cm, ρ = 19 g/cm3)
Energy, MeV
7
Neutron flux
Number of neutrons
Neutron velocity, 10 cm/sec
0.01
2.33E-03
1.51E-02
11.01
0.0465
5.03E-02
1.55E-01
23.13
0.1
9.84E-02
1.91E-01
36.76
0.2
1.54E-01
2.09E-01
52.36
0.4
1.84E-01
1.8E-01
72.73
0.8
1.83E-01
1.24E-01
105.32
1.4
1.04E-01
5.27E-02
140.55
2.5
1.07E-01
4.02E-02
189.01
4
7.43E-02
2.2E-02
241.62
6.5
3.63E-02
8.5E-03
304.97
10.5
7.05E-03
1.32E-03
380.40
0
The average neutron velocity is 71.4⋅107 cm/sec.
The critical mass characteristics of proliferation risk for Am-241 based materials are:
•
•
—cr(Am-241) – 0.91-0.47;
—cr(Am241O2) – 0.49-0.215.
5.2.3. Am-243 Isotope
The calculated critical masses for Am-243 bare spheres differ by about 3.5 times
depending on the constants used.
20
His high uncertainty is due to that of neutron constants. JENDL-32 constants may
have been obtained from the compromise between two US estimates and are not more
accurate. Therefore more accurate estimates for the critical mass of Am-243 requires more
accurate neutron constants. However the increase of the critical mass of Am-243 sphere as
compared to that of Am-241 is indeed reasonable.
The use of U-238 reflector reduces the critical mass of Am-243 by 1.5 times. The
transition from americium metal to AmO2 for 243Am isotope results in a much higher growth
of the critical mass as compared to Am-241 isotope (the increase by 3-3.5 times) which is due
to the behavior of the cross section.
Tables 5.11-5.14 show neutron density and fluence spectrum distributions normed to
unity in average over the total mass of fissile material for four critical assemblies using Am243 based materials (ENDF-B5 constants).
Table 5.11
Am-243, R = 13.96 cm, ρ = 13.65 g/cm3; no reflector
Energy, MeV
Neutron flux
Number of neutrons
7
Neutron velocity, 10 cm/sec
0
0.01
1.79E-03
1.38E-02
10.59
0.0465
2.98E-02
1.04E-01
23.37
0.1
7.27E-02
1.6E-01
37.02
0.2
1.31E-01
2.04E-01
52.50
0.4
1.84E-01
2.04E-01
73.57
0.8
1.79E-01
1.42E-01
103.00
1.4
1.25E-01
7.21E-02
141.50
2.5
1.25E-01
5.43E-02
188.67
4
9.09E-02
3.04E-02
243.96
6.5
4.95E-02
1.32E-02
304.73
10.5
1.02E-02
2.18E-03
381.41
The average neutron velocity is 81.6⋅107 cm/sec.
Table 5.12
Am-243, R = 12.27 cm, ρ = 13.65 g/cm 3; U-238 reflector(7 cm, ρ = 19 g/cm3)
Energy, MeV
7
Neutron flux
Number of neutrons
Neutron velocity, 10 cm/sec
2.44E-03
1.65E-02
10.67
0
0.01
0.0465
4.2E-02
1.3E-01
23.45
0.1
9.73E-02
1.91E-01
36.84
0.2
1.55E-01
2.15E-01
52.36
0.4
2E-01
1.97E-01
73.37
21
0.8
1.76E-01
1.24E-01
102.62
1.4
1.08E-01
5.55E-02
141.12
2.5
1.01E-01
3.89E-02
188.49
4
7.1E-02
2.11E-02
243.89
6.5
3.83E-02
9.11E-03
304.68
10.5
7.85E-03
1.49E-03
380.86
The average neutron velocity is 72.4⋅107 cm/sec.
Table 5.13
Am243O2, R = 20.7 cm, ρ = 11.7 g/cm3; no reflector
Energy, MeV
Neutron flux
Number of neutrons
7
Neutron velocity, 10 cm/sec
0
0.01
6.75E-03
3.85E-02
10.87
0.0465
8.24E-02
2.27E-01
22.57
0.1
1.24E-01
2.1E-01
36.52
0.2
1.62E-01
1.94E-01
52.10
0.4
1.66E-01
1.42E-01
72.41
0.8
1.48E-01
8.74E-02
105.42
1.4
9.19E-02
4.05E-02
140.75
2.5
9.99E-02
3.27E-02
189.58
4
7.44E-02
1.91E-02
241.41
6.5
3.65E-02
7.45E-03
304.58
10.5
6.96E-03
1.14E-03
380.41
The average neutron velocity s 62.1⋅107 cm/sec.
Table 5.14
Am243O2, R = 18.76 cm, ρ = 11.7 g/cm3; U-238 reflector (7 cm, ρ = 19 g/cm3)
Energy, MeV
Neutron flux
Number of neutrons
7
Neutron velocity, 10 cm/sec
0
0.01
7.87E-03
4.21E-02
10.90
0.0465
9.63E-02
2.49E-01
22.52
0.1
1.37E-01
2.18E-01
36.45
0.2
1.69E-01
1.9E-01
52.05
0.4
1.69E-01
1.36E-01
72.43
0.8
1.45E-01
8.04E-02
105.16
1.4
8.47E-02
3.51E-02
140.65
2.5
8.87E-02
2.73E-02
189.42
4
6.47E-02
1.56E-02
241.46
22
6.5
3.16E-02
6.04E-03
304.70
10.5
5.99E-03
9.18E-04
380.38
The average neutron velocity is 58.2⋅107 cm/sec.
The critical mass characteristics of proliferation risk for Am-243 based materials are:
• —cr(Am-243) – 0.32-0.091;
• —cr(Am243O2) – 0.115-0.028.
5.2.4. Americium from Spent Nuclear Fuel
Americium contained in spent nuclear fuel can be recovered in two ways.
The first way is to process spent fuel radiochemically to separate reactor-grade
plutonium that includes Pu-241 isotope. This isotope with the half life of = 14.4 years
transforms to Am-241 during β decay to be accumulated with time in reactor-grade
plutonium. When reactor-grade plutonium is cleared americium can be chemically separated in
which case the resulting material will contain pure Am-241 isotope.
The other way allows to separate also power americium in addition to reactor-grade
plutonium from the primary processing of spent fuel; americium will be composed of Am-241
and Am-243 with a low concentration of Am-242m isotope. The relation between the amounts
of Am-241 and Am-243 depends on the cooling time of spent fuel till the radiochemical
processing as well as on the energy yield of spent fuel and reactor type. His relation can vary
within a significant range.
If the fraction of Am-241 in the material is α and that of Am-243 is 1-α the critical
radius
of
the
system
is
determined
by
the
approximate
relation
1
α
1−α
=
+
.
R
R c r ( A m - 241)
R c r ( A m - 243)
Because of low concentration Am-242m isotope does not actually affect the critical
mass characteristics of power americium material.
One of typical compositions of power americium is defined by the values α = 0.8;
1-α = 0.2. The critical radii and critical masses for such material as given by the above
relations are as follows:
Table 5.15
ENDL-82
ENDF-B5
JENDL-32
11.05
12.61
11.64
M(Am)
77.2
114.7
90.2
R(AmO2)
14.56
17.45
15.95
M(AmO2)
151.3
260.5
198.9
R(Am)
The critical characteristics of the proliferation risk for spent fuel americium based
materials are:
23
• —cr(americium of SNF; α = 0.8) – 0.32-0.091;
• —cr(AmO2) – 0.115-0.028.
Note, that in comparison with —cr characteristics for Am-241 these values decreased
together with the variation range.
6. Single Group Approximation for the Generation of Np-237, Am-241
and Am-243 Isotopes
6.1. Problem Formulation
The generation characteristics of isotopes are defined by cross-sections for fission and
neutron capturing on isotopes included in reactor fuel and resulting from the burning process.
To evaluate effective cross-sections, we used the neutron spectrum model for thermal reactors
where the main(thermal) portion of the neutron spectrum has Maxwell distribution with the
effective temperature T and the superthermal portion is distributed according to n ∼ 1 / ε 3 / 2 .
For this approximation, the neutron transmutation time, τ i , for any nucleus in a reactor is
determined by:
1
τi
[
]
= n 0 υ M ασ iT + (1 − α) I pi f i ,
Where n 0 is neutron density;
υ M is the average neutron velocity as given by Maxwell distribution;
σ iT is the process cross-section averaged over the fluence with Maxwell distribution at
temperature T;
i
I p is the resonance process integral;
α is the parameter determining the fraction of neutrons in the thermal part of spectrum;
f i is the parameter determining the potential reduction of resonance contribution to
the process due to nuclei self-shielding effect related with a weaker neutron spectrum in
resonance domain as compared to n ∼ 1 / ε 3 / 2 .
Table 6.1 shows the cross-sections a thermal point σ 0 (¯ n = 0.025 ýÂ), σ T (averaging
over the fluence with Maxwell distribution of neutron densities at temperature = 0.07 eV)
for neutron fission and capturing; I f and I c - resonance integrals for neutron fission and
capturing and the number of secondary neutrons ν resulting from the fission of basic isotopes
/1/.
24
Table 6.1
σ 0f
σ c0
σ Tf
σ cT
If
Ic
ν
U-235
583
98
283
51
275
144
2.42
U-236
0
5.2
0
2.8
0
365
U-238
0
2.71
0
1.43
2
278
Np-237
0.02
169
~0
108
7
660
Pu-238
16.5
547
6.6
228
23
162
Pu-239
742
269
1105
467
310
190
Pu-240
0.05
287
~0
186
0
8260
Isotope
Pu-241
1011
358
830
292
570
162
Pu-242
< 0.2
18.5
~0
10.6
5
1280
Am-241
3.1
835
1.6
444
22
1410
→ Am-242g
752
400
1190
→ Am-242m
83
44
220
Am-242m
6900
1100
3660
580
1900
230
Am-243
0.2
79
~0
67
10
2050
Cm-242
<5
20
2.6
10.6
0
150
Cm-244
1
13.5
0.5
7.1
19
625
2.87
2.96
If in the vicinity of the thermal point ε0 = 0.025 eV the cross-section depends on
neutron energy as σ ∼ 1 / ε then the result of averaging over the fluence n υ with the
neutron density determined by Maxwell distribution with temperature T yields:
σT =
π
2
ε0
T
, and at
= 0.07 eV σ T ≅ 0.53 σ 0 .
Table 6.1 shows that this relation meets for many isotopes; however significant
difference is observed for some of them. This is particularly true for Pu-239 for which
σ T > σ 0 which is due to the fact that this isotope has the resonance in the thermal part of the
neutron spectrum.
The isotope generation in the approximation of interest is determined by the system of
equations:
dn ( i )
dt
=
n ( i − 1)
τ c (i − 1)
−
n( i )
τ(i )
,
where n(i) is the concentration of i-isotope in fuel for example, in W/kg).
τ c ( i − 1) is the life time of the predecessor nucleus where the i-isotope is generated in
reactor as compared to neutron capture;
τ( i ) is the life time of the i-isotope in reactor determined by fission processes, neutron
capture forming the (i-1) isotope and natural decay.
25
The energy yield in fuel is defined by:
dn ( f )
dt
=∑
n( i )
τ f (i )
,
where n ( f ) is the total number of fission acts;
τ f (i ) is the life time of i-isotope as compared to the fission process.
The energy yield per fission is assumed to be the same and approximately constitutes
200 MeV.
Usually, each reactor type demonstrates a relation between the initial and final amount
of U-235 in reactor fuel, energy yield in reactor fuel and campaign duration, TC . Accordingly,
we defined the total life time of U-235 nuclei in reactor as
τ( U - 235) = TC / ln
m0
mF
( U - 235) ,
where m 0 and m F are the initial and final amount of U-235 in spent fuel. Then all remaining
life times of nuclei relative to fission and capture processes in the model of interest are defined
by:
τ
τ( U - 235)
=
σ t ( U - 235)
,
σ
where σ = ασ T + (1 − α) I pf .
Here, the quantity σ t ( U - 235 ) = ασ T ( U - 235 ) + (1 − α) I p ( U - 235) . For U-235, f = 1.
The effective average neutron flux in reactor is q = n 0 υ M and defines the effective average
neutron density n 0 at the known temperature T.
For this model, all concentrations of generated isotopes can be represented as
functions of the energy yield in spent fuel, W, that more preferably should be given in kg/t.
Various reactor types in this model differ by the initial amount of U-235 in reactor fuel,
α parameter determining the neutron spectrum type and f parameter that is significant for two
isotopes, U-238 and Pu-240.
The relative variation of the supercriticality of nuclear fuel is characterized by the
change of χ determining the multiplication properties of the infinite reactor medium in
homogeneous approximation.:
dn
dt
=
n
τ
= ( n υ) 0 .6 ρ T ∑
i
[( ν − 1) σ
A
αi
i
i
i
f
]
− σ ic ≅ ( n υ)
0 .6
A
ρ T ∑ α i χ i ≡ ( n υ)
i
0 .6
A
ρ T χ ≡ αn ,
26
where the summation is accomplished only over the heavy isotopes of the reactor fuel and
fission fragments;
n is the neutron density in the system;
υ is the average neutron velocity;
αi is the fraction of i-isotope in the reactor fuel;
Ai is the mass number ( A is the average mass number of heavy isotopes in reactor
fuel);
ρ T is the reactor fuel density;
ν is the number of fission-produced secondary neutrons;
σ f , σ c are the effective cross-sections for fission and capture on the i-isotope (barn).
For A = 238, ρ T = 10 g/cm3, T = 0.07 eV, the neutron multiplication rate is
α = 1.05⋅104⋅χ 1/sec.
he quantity χ is related with K e∞f f for the infinite medium through the obvious relation
∞
K eff = 1 + χ /
∑ α (σ
i
i
f
)
+ σ ic , where σ f and σ c are the effective cross-sections of neutron
i
fission and capture.
T should be noted that in this model we neglected the life time of short lived isotopes
of U-237 ( = 6.75 days), Np-238 ( = 2.12 days), U-239 ( = 23.5 minutes), Np-239
( = 2.35 days), Pu-243 ( = 4.95 hours), Am-244 ( = 10.1 hours) and a potential burn-out
of these isotopes resulting from neutron-driven irradiation in reactor. This approximation is
motivated by that the life times of all these isotopes as compared to neutron transmutation is
much higher than the life times relative to natural decay.
6.2. VVER-440 Reactor
VVER-440 reactors constituted one of the bases of the Soviet nuclear power industry.
They are operated in the Russian Federation, Ukraine and in some countries of Eastern and
Northern Europe.
The basic features of VVER-440 are as follows:
The reactor use nuclear fuel in the form of uranium dioxide with low enrichment by
uranium isotope U-235. Water is used as the neutron moderator.
• Thermal power —T = 1375 MW.
• Electric power —el = 440 MW.
• Uranium load U = 42 tons.
• Campaign time TC = 3 years.
• Fuel energy yield W = 31.9 kg/t (30 GW⋅day/t).
• Initial U-235 enrichment - 36 kg/t.
The generation of isotopes in spent fuel of VVER-440 reactor is described here for the
following parameter values:
f(U-238) = 0.12;
f(Pu-240) = 0.4.
α = 0.8;
τ t (U-235) = 2.88 years;
27
Table 6.2 shows the values obtained under the above assumptions for the basic
constants included in the equations governing the generation of isotopes.
Table 6.2
σf
σc
σ0
τ0
τf
τc
281.40
69.60
351.00
2.88
3.59
14.52
U-236
75.24
75.24
13.44
13.44
U-238
7.82
7.82
129.33
129.33
U-235
Np-237
1.40
218.40
219.80
4.63
Pu-238
9.88
214.80
224.68
4.50
102.32
4.71
Pu-239
946.00
411.60
1357.60
0.74
1.07
2.46
809.60
809.60
1.25
Pu-241
778.00
266.00
1044.00
0.93
1.30
3.80
Pu-242
1.00
264.48
265.48
3.82
3.82
Am-241
5.68
637.20
642.88
1.59
1.59
→ Am-242g
558.00
558.00
1.81
1.81
→ Am-242m
79.20
79.20
12.76
12.76
3308.00
510.00
3818.00
0.26
Am-243
2.00
463.60
465.60
2.18
2.18
Cm-242
2.08
38.48
40.56
0.62
26.27
Cm-243
570.00
98.20
668.20
1.51
Cm-244
4.20
130.68
134.88
5.97
Cm-245
1014.00
168.80
1182.80
0.85
Pu-240
Am-242m
τp
4.63
1.25
0.31
1.77
1.98
0.64
10.29
7.74
1.00
20.8
26.1
5.99
Table 6.3 compares the isotopic composition of spent fuel obtained with this model
and reference data /9/ for the energy yield of W = 30 GW⋅day/t.
Table 6.3
Isotope
U-235
U-236
Pu-239
Pu-240
Pu-241
Pu-242
Am-241
Am-243
Model
12.5
4.08
5.36
2.25
1.26
0.33
0.047
0.057
Reference
12.7
4.28
5.49
1.98
1.28
0.37
0.035
0.069
The table shows that the model of interest for the generation of isotopes in VVER-440
is relatively well calibrated to the reference data.
This model can give some basic values for the generation of isotopes as a function of
the fuel energy yield. These include:
• the amount of basic plutonium isotopes in spent fuel (Pu-239, Pu-240 and
Pu-241);
• percentage of Pu-239 spent fuel plutonium;
• generation of Np-237, Am-241 and Am-243 isotopes;
• the amount of Am-242m isotope in spent fuel americium;
• variation of the amount of spent fuel americium as a function of the cooling time.
28
Figures 6.1-6.11 present the basic dependencies for VVER-440 obtained with this
model.
6
Pu-239 and Pu-240, kg per ton
5
4
Pu239
Pu240
3
2
1
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.1. The amount of Pu-239 and Pu-240 isotopes in VVER-440 spent fuel
1.6
1.4
Pu-241, kg per ton
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
Spent fuel burnout, kg per ton
Fig. 6.2. The amount of Pu-241 isotope in VVER-440 spent fuel
40
29
Pu-239 fraction in spent fuel plutonium, %
100
90
80
70
60
50
40
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.3. Fraction of Pu-239 in VVER-440 spent fuel plutonium
0.7
0.6
Np-237, kg per ton
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.4. The amount of Np-237 in VVER-440 spent fuel
35
40
30
0.6
Np-237 mass, kg per ton
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Plutonium mass, kg per ton
Fig. 6.5. The amount of Np-237as a function of plutonium mass in VVER-440 spent fuel
0.2
0.18
Americium, kg per ton
0.16
0.14
0.12
Am241
Am243
SNF americium
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.6. The amount of Am-241 and Am-243 isotopes in VVER-440 spent fuel
31
1.4
Am-242m mass, gramm
1.2
1
0.8
0.6
0.4
0.2
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Mass of spent fuel americium, kg per ton
Fig. 6.7. The amount of Am-242 isotope in VVER-440 spent fuel americium
1.2
Americium mass, kg per ton
1
0.8
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.8. The amount of americium in VVER-440 spent fuel as a function of cooling time
32
100
Am-241 fraction, %
95
90
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
85
80
75
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.9. Fraction of Am-241 isotope in VVER-440 spent fuel americium as a function of
cooling time
Characteristic of medium multiplication properties χ
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.10. Characteristic of the medium multiplication properties χ for VVER-440
33
Effective neutron multiplication coefficient
1.3
1.25
1.2
1.15
1.1
1.05
1
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.11. Effective neutron multiplication coefficient, K e f f in VVER-440
6.3. VVER-1000 Reactor
VVER-1000 reactors are a part of the Russian nuclear power complex and serve the
base of the Ukrainian nuclear power industry.
The basic features of VVER-1000 are as follows:
The reactor use nuclear fuel in the form of uranium dioxide with low enrichment by
uranium isotope U-235. Water is used as the neutron moderator.
• Thermal power —T = 3200 MW.
• Electric power —el = 1000 MW.
• Uranium load U = 70 tons.
• Campaign time TC = 3 years.
• Fuel energy yield W = 43.1 kg/t (40.5 GW⋅day/t).
• Initial U-235 enrichment - 44 kg/t.
The generation of isotopes in spent fuel of VVER-1000 reactor is described here for
the following parameter values:
τ t (U-235) = 2.35 years;
α = 0.75;
f(U-238) = 0.11;
f(Pu-240) = 0.33.
Table 6.4 shows the values obtained under the above assumptions for the basic
constants included in the equations governing the generation of isotopes.
34
Table 6.4
σf
σc
σ0
τ0
τf
τc
281.00
74.25
355.25
2.35
2.97
11.24
U-236
93.35
93.35
8.94
8.94
U-238
8.72
8.72
95.77
95.77
U-235
Np-237
1.75
246.00
247.75
3.39
Pu-238
10.70
211.50
222.20
3.76
78.02
3.95
Pu-239
906.25
397.75
1304.00
0.64
0.92
2.10
820.95
820.95
1.02
Pu-240
3.39
1.02
Pu-241
765.00
259.50
1024.50
0.78
Pu-242
1.25
327.95
329.20
2.55
2.55
Am-241
6.70
685.50
692.20
1.22
1.22
→ Am-242g
597.50
597.50
1.40
1.40
→ Am-242m
88.00
88.00
9.49
9.49
Am-242m
τp
1.09
0.26
3.22
3220.00
492.50
3712.50
0.22
Am-243
2.50
562.75
565.25
1.48
1.48
Cm-242
1.95
45.45
47.40
0.62
18.37
Cm-243
631.25
105.50
736.75
1.13
Cm-244
5.13
161.58
166.70
4.31
Cm-245
1000.00
164.75
1164.75
0.72
1.32
1.70
0.64
7.91
5.17
0.83
20.8
26.1
5.07
Table 6.5 compares the isotopic composition of spent fuel obtained with this model
and reference data /9/ for the energy yield of W = 40.5 GW⋅day/t.
Table 6.5
U-235
U-236
Pu-239
Pu-240
Pu-241
Pu-242
Am-241
Am-243
Model
Isotope
12.4
5.43
6.18
2.65
1.67
0.5
0.058
0.12
Reference
12.3
5.73
5.53
2.42
1.5
0.58
0.037
0.12
The table shows that the model of interest for the generation of isotopes in VVER1000 is relatively well calibrated to the reference data.
This model can give some basic values for the generation of isotopes as a function of
the fuel energy yield. These include:
• the amount of basic plutonium isotopes in spent fuel (Pu-239, Pu-240 and
Pu-241);
• percentage of Pu-239 spent fuel plutonium;
• generation of Np-237, Am-241 and Am-243 isotopes;
• the amount of Am-242m isotope in spent fuel americium;
• variation of the amount of spent fuel americium as a function of the cooling time.
Figures 6.12-6.22 present the basic dependencies for VVER-1000 obtained with this
model.
35
7
Pu-239 and Pu-240, kg per ton
6
5
4
Pu239
Pu240
3
2
1
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.12. The amount of Pu-239 and Pu-240 isotopes in VVER-1000 spent fuel
1.6
1.4
Pu-241, kg per ton
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
Spent fuel burnout, kg per ton
Fig. 6.13. The amount of Pu-241 isotope in VVER-1000 spent fuel
40
36
Pu-239 fraction in spent fuel plutonium, %
100
90
80
70
60
50
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.14. Fraction of Pu-239 in spent fuel plutonium of VVER-1000
0.8
0.7
Np-237, kg per ton
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.15. The amount of Np-237 in VVER-1000 spent fuel
35
40
37
0.8
0.7
Np-237 mass, kg per ton
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
Plutonium mass, kg per ton
Fig. 6.16. The amount of Np-237as a function of plutonium mass in VVER-1000 spent fuel
0.14
0.12
Americium, kg per ton
0.1
0.08
Am241
Am243
SNF americium
0.06
0.04
0.02
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.17. The amount of m-241 and Am-243 isotopes in VVER-1000 spent fuel
38
1
0.9
0.8
Am-242m mass, gramm
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Mass of spent fuel americium, kg per ton
Fig. 6.18. The amount of Am-242m isotope in VVER-1000 spent fuel americium
1.2
Americium mass, kg per ton
1
0.8
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.19. The amount of americium in VVER-1000 spent fuel as a function of cooling time
39
100
Am-241 fraction, %
95
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
90
85
80
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.20. Fraction of Am-421 isotope in VVER-1000 spent fuel americium as a function of
cooling time
Characteristic of medium multiplication properties χ
8
7
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.21. Characteristic of the medium multiplication properties χ for VVER-1000
40
Effective neutron multiplication coefficient
1.3
1.25
1.2
1.15
1.1
1.05
1
0
5
10
15
20
25
30
35
40
Spent fuel burnout, kg per ton
Fig. 6.22. Effective neutron multiplication coefficient K e f f for VVER-1000
6.4. RBMK-1000 Reactor
RBMK-1000 reactors are a part of the Russian nuclear power industry and currently
serve its base.
The basic features of RBMK-1000 are as follows:
The reactor use nuclear fuel in the form of uranium dioxide with low enrichment by
uranium isotope U-235. Graphite is used as the moderator.
• Thermal power —T = 3200 MW.
• Electric power —el = 1000 MW.
• Uranium load U = 192 tons.
• Campaign time TC = 3 years.
• Fuel energy yield W = 26.5 kg/t (24.9 GW⋅day/t).
• Initial U-235 enrichment - 20 kg/t.
The generation of isotopes in spent fuel of RBMK-1000 reactor is described here for
the following parameter values:
τ t (U-235) = 1.57 years;
α = 0.85;
f(U-238) = 0.06;
f(Pu-240) = 0.3.
Table 6.6 shows the values obtained under the above assumptions for the basic
constants included in the equations governing the generation of isotopes.
41
Table 6.6
σf
σc
σ0
τ0
τf
τc
281.80
64.95
346.75
1.57
1.93
8.38
U-236
57.13
57.13
9.53
9.53
U-238
3.72
3.72
146.44
146.44
U-235
Np-237
1.05
190.80
191.85
2.85
Pu-238
9.06
218.10
227.16
2.40
60.09
2.50
Pu-239
985.75
425.45
1411.20
0.39
0.55
1.28
529.80
529.80
1.03
Pu-240
2.85
1.03
Pu-241
791.00
272.50
1063.50
0.50
Pu-242
0.75
201.01
201.76
2.71
2.71
Am-241
4.66
588.90
593.56
0.92
0.92
→ Am-242g
518.50
518.50
1.05
1.05
→ Am-242m
70.40
70.40
7.73
7.73
Am-242m
τp
0.69
0.16
2.00
3396.00
527.50
3923.50
0.14
Am-243
1.50
364.45
365.95
1.49
1.49
Cm-242
2.21
31.51
33.72
0.62
17.28
Cm-243
508.75
90.90
599.65
0.91
Cm-244
3.28
99.79
103.06
4.51
Cm-245
1028.00
172.85
1200.85
0.45
1.07
1.03
0.64
5.99
5.46
0.53
20.8
26.1
3.15
Table 6.7 compares the isotopic composition of spent fuel obtained with this model
and reference data /9/ for the energy yield of W = 24.9 GW⋅day/t.
Table 6.7
U-235
U-236
Pu-239
Pu-240
Pu-241
Pu-242
Am-241
Am-243
Model
Isotope
3.3
2.59
2.54
1.84
0.81
0.42
0.026
0.096
Reference
2.94
2.61
2.63
2.19
0.73
0.51
0.019
0.074
The table shows that the model of interest for the generation of isotopes in RBMK1000 is relatively well calibrated to the reference data.
This model can give some basic values for the generation of isotopes as a function of
the fuel energy yield. These include:
• the amount of basic plutonium isotopes in spent fuel (Pu-239, Pu-240 and
Pu-241);
• percentage of Pu-239 spent fuel plutonium;
• generation of Np-237, Am-241 and Am-243 isotopes;
• the amount of Am-242m isotope in spent fuel americium;
• variation of the amount of spent fuel americium as a function of the cooling time.
Figures 6.23-6.33 present the basic dependencies for RBMK-1000 obtained with this
model.
42
3
Pu-239 and Pu-240, kg per ton
2.5
2
Pu239
Pu240
1.5
1
0.5
0
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.23. The amount of Pu-239 and Pu-240 isotopes in RBMK-1000 spent fuel
0.9
0.8
Pu-241, kg per ton
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
Spent fuel burnout, kg per ton
Fig. 6.24. The amount of Pu-241 isotope in RBMK-1000 spent fuel
30
43
Pu-239 fraction in spent fuel plutonium, %
100
90
80
70
60
50
40
30
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.25 Fraction of Pu-239 in RBMK-1000 spent fuel plutonium
0.4
0.35
Np-237, kg per ton
0.3
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
25
Spent fuel burnout, kg per ton
Fig. 6.26. The amount of Np-237 in RBMK-1000 spent fuel
30
44
0.4
0.35
Np-237 mass, kg per ton
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
Plutonium mass, kg per ton
Fig. 6.27. The amount of Np-237 as a function of plutonium mass in RBMK-1000 spent fuel
0.14
0.12
Americium, kg per ton
0.1
0.08
Am241
Am243
SNF americium
0.06
0.04
0.02
0
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.28. The amount of Am-241 and Am-243 isotopes in RBMK-1000 spent fuel
45
0.45
0.4
Am-242m mass, gramm
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Mass of spent fuel americium, kg per ton
Fig. 6.29. The amount of Am-242m isotope in RBMK-1000 spent fuel americium
0.7
Americium mass, kg per ton
0.6
0.5
0.4
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
0.3
0.2
0.1
0
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.30. The amount of americium in RBMK-1000 spent fuel as a function of cooling time
46
100
95
Am-241 fraction, %
90
85
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
80
75
70
65
60
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.31. Fraction of Am-241 isotope in RBMK-1000 spent fuel americium as a function of
cooling time
Characteristic of medium multiplication properties χ
4
3.5
3
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
Spent fuel burnout, kg per ton
Fig. 6.21. Characteristic of the medium multiplication properties χ for RBMK-1000
47
Effective neutron multiplication coefficient
1.4
1.3
1.2
1.1
1
0.9
0
5
10
15
20
25
30
Spent fuel burnout, kg per ton
Fig. 6.33. Effective neutron multiplication coefficient K e f f for RBMK-1000
6.5. Natural Uranium Reactor
Reactors that use natural uranium as nuclear fuel and heavy water as the neutron
moderator are widely presented in the world nuclear power industry. The Canadian CANDU
reactor is a typical representative of such reactors.
The basic reactor features are as follows:
• Thermal power —T = 2830 MW.
• Electric power —el = 915 MW.
• Uranium load U = 120 tons.
• Campaign time TC = 0.55 years.
• Fuel energy yield W = 7.45 kg/t (7 GW⋅day/t).
• Initial U-235 enrichment - 7.1 kg/t.
The generation of isotopes in spent fuel of CANDU reactor is described here for the
following parameter values:
τ t (U-235) = 0.5 year; α = 0.96;
f(U-238) = 0.06;
f(Pu-240) = 0.25.
Table 6.8 shows the values obtained under the above assumptions for the basic
constants included in the equations governing the generation of isotopes.
48
Table 6.8
σf
σc
σ0
τ0
τf
τc
282.68
54.72
337.40
0.50
0.60
3.08
U-236
17.29
17.29
9.76
9.76
U-238
2.04
2.04
82.70
82.70
U-235
Np-237
0.28
130.08
130.36
1.30
Pu-238
7.26
225.36
232.62
0.73
23.25
Pu-239
1073.20
455.92
1529.12
0.11
0.16
261.16
261.16
0.65
Pu-240
1.30
0.75
0.37
0.65
Pu-241
819.60
286.80
1106.40
0.15
Pu-242
0.20
61.38
61.58
2.75
2.75
Am-241
2.42
482.64
485.06
0.35
0.35
→ Am-242g
431.60
431.60
0.39
0.39
→ Am-242m
51.04
51.04
3.31
3.31
Am-242m
τp
0.21
0.05
0.59
3589.60
566.00
4155.60
0.04
Am-243
0.40
146.32
146.72
1.15
1.15
Cm-242
2.50
16.18
18.67
0.60
10.43
Cm-243
374.00
74.84
448.84
0.38
Cm-244
1.24
31.82
33.06
4.41
Cm-245
1058.80
181.76
1240.56
0.14
0.45
0.30
0.64
2.25
5.30
0.16
20.8
26.1
0.93
This model can give some basic values for the generation of isotopes as a function of
the fuel energy yield. These include:
• the amount of basic plutonium isotopes in spent fuel (Pu-239, Pu-240 and
Pu-241);
• percentage of Pu-239 spent fuel plutonium;
• generation of Np-237, Am-241 and Am-243 isotopes;
• the amount of Am-242m isotope in spent fuel americium;
• variation of the amount of spent fuel americium as a function of the cooling time.
Figures 6.34-6.44 present the basic dependencies for CANDU reactor obtained with
this model.
The computational results for the generation of isotopes in various reactor types
obtained with the single group mode described here agree relatively well with direct
computations with the codes using elementary constants and Monte Carlo method (see
Section 7).
49
1.4
Pu-239 and Pu-240, kg per ton
1.2
1
0.8
Pu239
Pu240
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.34. The amount of Pu-239 and Pu-240 isotopes in CANDU spent fuel
0.2
0.18
0.16
Pu-241, kg per ton
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
Spent fuel burnout, kg per ton
Fig. 6.35. The amount of Pu-241 isotope in CANDU spent fuel
8
50
Pu-239 fraction in spent fuel plutonium, %
100
90
80
70
60
50
40
0
1
2
3
4
5
6
7
8
7
8
Spent fuel burnout, kg per ton
Fig. 6.36. Fraction of Pu-239 in CANDU spent fuel plutonium
0.025
Np-237, kg per ton
0.02
0.015
0.01
0.005
0
0
1
2
3
4
5
6
Spent fuel burnout, kg per ton
Fig. 6.37. The amount of Np-237 in CANDU spent fuel
51
0.025
Np-237 mass, kg per ton
0.02
0.015
0.01
0.005
0
0
0.5
1
1.5
2
2.5
3
Plutonium mass, kg per ton
Fig. 6.38. The amount of Np-237 as a function of plutonium mass in CANDU spent fuel
0.0045
0.004
Americium, kg per ton
0.0035
0.003
0.0025
Am241
Am243
SNF americium
0.002
0.0015
0.001
0.0005
0
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.39. The amount of Am-241 and Am-243 isotopes in CANDU spent fuel
52
0.014
Am-242m mass, gramm
0.012
0.01
0.008
0.006
0.004
0.002
0
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
Mass of spent fuel americium, kg per ton
Fig. 6.40. The amount of Am-242m isotope in CANDU spent fuel americium
0.12
Americium mass, kg per ton
0.1
0.08
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.41. The amount of americium in CANDU spent fuel as a function of cooling time
53
100
99
Am-241 fraction, %
98
97
Americium at tc=5 years
Americium at tc=10 years
Americium at tc=20 years
96
95
94
93
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.42. Fraction of Am-241 isotope in CANDU spent fuel americium as a function of cooling
time
Characteristic of medium multiplication properties χ
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.43. Characteristic of the medium multiplication properties χ for CANDU reactor
54
Effective neutron multiplication coefficient
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0
1
2
3
4
5
6
7
8
Spent fuel burnout, kg per ton
Fig. 6.44. Effective neutron multiplication coefficient K e f f for CANDU reactor
7. Generation of Np-237, Am-241 and Am-243 Isotopes in Reactors
by Thermal Neutrons
7.1. Physical Basis and Implementation Scheme of the Method
Since the up-to-date thermal reactors generate fission spectrum neutrons and the
reactor fuel absorbs basically thermal and epithermal neutrons an accurate description is
required for the neutron moderation and kinetics in a broad energy range. The use of group
methods in this case can result in approximations and uncertainties considerably exceeding the
uncertainties of estimated neutron constants. Therefore the direct use of Monte Carlo method
in neutron physics of multizone heterogeneous systems seems to be more promising.
This section considers the following subjects:
• formulation of the computer model allowing a reliable description of neutron
kinetics and isotopic transformation in reactors;
• introduction of core feeding by fissile material to the kinetics;
• direct use of Monte Carlo method in neutron physics calculations;
• illustration of the computational capability and accuracy of the method on test
systems
This computational method includes the calculation of the following problems:
• eigenvalue problem determining the neutron equilibrium spectrum for some
statistical reference states of a multizone cell;
55
•
processing of computational results to provide input data for the isotopic kinetics
code;
• calculation of isotopic kinetics during the campaign period and upon the reactor
shut-down.
The general scheme of the computational method for the calculation of the neutron
physics parameters and the isotopic composition of the thermal reactor core cell is given n
Diagram 7.1. The initial data used are the start parameters of the core ( N k0 i , the concentration
of i isotopes in the cell over k zones, geometry parameters, fuel and moderator temperatures,
T f and Tm ) and the library of elementary neutron constants in ENDF format. These initial data
are introduced to C-90 code /6/. The C-90 computational results for the group cross-sections
and flux densities are transferred to the isotopic kinetics code as input data through the
processing unit. The computational results for the concentrations of isotopes calculated by the
isotopic kinetics code for energy yield reference points are transferred to C-90. This cycle is
closed thus allowing the calculation of the amount of start and generated isotopes in reactor
fuel for any energy yield value.
The calculation of the first problem uses Monte Carlo method implemented in C-90
code /6/. The code has actually no restrictions in the description of the system geometry, the
composition of the fuel rods and moderator, considers the moderator and fuel temperatures. It
reflects in the most straightforward way the heterogeneity of the cell and fuel temperature in
the calculations of reaction rate resonance blocking effects.
C-90 calculates the following using selected geometry, cell temperature characteristics
and isotopic concentration of zones with the library of elementary neutron constants:
• neutron flux density distribution over the energy groups and zones;
• neutron reaction numbers for isotopes, energy groups and zones;
• neutron multiplication coefficient in the cell.
The isotopic kinetics code calculates the concentration of all isotopes including the
fission products at any irradiation time given the energy yield rate and introduced neutron
energy distributions and group neutron constants for start and generated isotopes.
The computational data processing unit receives the group neutron constants in
reference cutsets, then forms and transfers the group neutron flux densities to the isotopic
kinetics code. It functions only as a support unit ensuring the linking between two codes.
The isotopic kinetics code does not allow to calculate the variations of neutron
spectrum in zones and neutron reaction cross-sections as a function of the changes in the
isotopic composition. Therefore the implementation of the computational scheme uses the
assumption about the potential interpolation of zone values of fuel isotope group neutron
cross-sections and neutron flux density energy distributions between their values in the
reference calculations.
56
Library of elementary neutron
constants
0i
Initial parameters of the core:
N k , T f , Tm
0i
N k , T f , Tm
C-90
, geometry
i
0i
Nk
Nk
Isotopic kinetics
σ ikp , Φ
Processing module
Diagram 7.1. Computational method scheme for the calculation of neutron physics
parameters and isotopic composition of the thermal reactor core cell
7.2. Method Testing
The accuracy and reliability of the computational results obtained with the method
under development are determined by those of its basic codes that is C-90 and isotopic
kinetics code.
C-90 in reference cutsets with fixed isotopic content solves the eigenvalue problem
using the neutron constants, geometry, composition, temperature and other values of the
macroscopic system parameters as initial data. It determines all of the neutron physics
characteristics of the system multiplying the neutrons. To illustrate its capabilities and testing,
we can use the description of experiments with reference critical assemblies imitating the
reactor core.
The isotopic kinetics code calculates in group approximation the isotopic
transformation in the neutron flux given the isotopic neutron constants. As was mentioned
above, group fluxes and neutron constants are linearly interpolated between the reference
cutsets. The performance of this code and that of the data processing unit for C-90
computational results are analyzed with a test proposed by IAEA /1/.
57
7.2.1. The Computational Results for the Effective Neutron Multiplication
Coefficient in Critical Uranium and Plutonium Assemblies with Water
Moderator
The description of assembly parameters is taken from the compilation of critical
reference systems performed by the international working group for the estimation of crosssections /12/. The assemblies cover a relatively wide range of uranium and plutonium dilution
by hydrogen and demonstrate various geometries and heterogeneity. He collection of
assemblies is sufficiently complete to test whether it is possible to describe the neutron kinetics
laws and features in thermal water-water reactors.
Table 7.1 shows the calculated values of K eff for these assemblies obtained with C-90
using Monte Carlo method and ENDF-B6 neutron constants. The parentheses contain the
relative uncertainty, (1σ), for the computations.
For comparison, the same table presents the computational results obtained by other
authors with the well known code MCNP /13, 14, 15/ using, the constants from ENDF-B5
and ENDF-B6.
The resulting values of the effective multiplication coefficient for the majority of
critical assemblies agree with the experimental and theoretical data by other authors within less
than 2σ. This allows to suggest the agreement between Ñ-90 and MCNP data, good accuracy
level of ENDF constants and consequently the reliability of neutron physics calculations for
reactor systems.
Table 7.1
Computational results for K e f f of critical assemblies obtained with C-90 and their comparison
with MCNP data
N
Assembly
/12/
Ñ-90
ENDF-B6
MCNP
ENDF-B5
MCNP
ENDF-B6
1
ORNL1
0.9959
(0.0031)
1.0007 /13/
0.9965 /13/
2
ORNL2
0.994
(0.0024)
1.0005 /13/
0.9964 /13/
3
ORNL3
0.999
(0.003)
0.9975 /13/
0.9935 /13/
4
ORNL4
0.9963
(0.003)
0.9989 /13/
0.9950 /13/
5
ORNL10
1.0005
(0.0036)
0.9993 /13/
0.9961 /13/
6
TRX-1 ∗
)
0.9993
(0.002)
1.0003 /14/
(0.0013)
7
TRX-2 ∗
)
0.9981
(0.003)
0.997 /14/
(0.0013)
58
8
TRX-1
0.991
(0.0025)
9
TRX-2
0.997
(0.003)
10
PNL-1
1.0065
(0.003)
1.0157 /14/
(0.0015)
1.0089 /13/
11
PNL-2
1.00967
(0.0024)
1.0115 /14/
(0.0017)
1.0037 /15/
12
PNL-3
0.9927
(0.0021)
0.9978 /15/
0.9904 /15/
13
PNL-4
0.997
(0.002)
1.0049 /15/
0.9971 /15/
14
PNL-5
1.0004
(0.00175)
15
PNL-6A
1.0066
(0.00139)
16
PNL-6B
1.0075
(0.00138)
1.0025 /13/
17
PNL-7A
1.0032
(0.0032)
1.0052 /13/
18
PNL-7B
1.0032
(0.0031)
19
PNL-8A
1.0084
(0.0021)
20
PNL-8B
1.0071
(0.0021)
21
PNL-9
0.9998
(0.0022)
22
PNL-10
0.9966
(0.0027)
23
PNL-11
1.010
(0.003)
24
PNL-12A
1.0087
(0.0032)
25
PNL-12B
1.00867
(0.0032)
1.0066 /13/
1.0066 /13/
∗) infinite lattices
7.2.2. The Description Results for the IAEA Computational Experiment
IAEA created the coordination research program to investigate the potential use of
thorium fuel cycle to reduce the accumulation of plutonium and to minimize the radioactivity
from the long-lived waste of nuclear energy industry. On the program authors initiative, it was
proposed to the leading world laboratories to run the neutron physics calculations for a
specific cell in PWR with Pu-Th fuel. The computational results were integrated in the report
59
/11/. The comparison of our computational results with those of the leading world laboratories
is undoubtfully of methodical interest.
The cell geometry is characterized by the following parameters: outer fuel radius
R f = 0.47 cm; outer fuel shell radius R shell = 0.54 cm; outer water radius R m = 0.85 cm. The
fuel represents a mixture of Pu and Th dioxides. The values of partial density of isotopes and
elements in the cell in atoms/cm3 for the fuel shell zones and moderator are given in Table 7.2.
The average fuel temperature T f = 1023°K, the average water temperature Tm = 583°K. The
specific power in the cell s P = 211 W/cm.
Table 7.2
Original density of isotopes (atoms/cm 3)
Isotope
Cell-averaged
Fuel
Th-232
6.45E+21
2.11E+22
Pu-238
2.97E +18
9.72E+18
Pu-239
1.83E +20
5.99E+20
Pu-240
7.10E +19
2.32E+20
Pu-241
2.35E+19
7.69E+19
Pu-242
1.46E+19
4.78E+19
Cr
1.99E+20
Mn
1.26E+19
Fe
5.20E+20
Ni
2.24E+20
Zr
4.27E+21
C
1.60E+18
H
2.86E+22
O
2.78E+22
Shell
Moderator
8.14E+19
3.20E+20
2.11E+19
1.60E+20
8.46E+20
3.76E+20
4.37E+22
2.68E+18
4.80E+22
4.41E+22
2.40E+22
Tables 7.3-7.4 present the following cell characteristics calculated in our laboratory
and by foreign laboratories as a function of the energy yield
• neutron multiplication coefficient in infinite medium;
• total neutron flux density;
• ratio between plutonium and the start amount;
• ratio between the amount of Pu-239, Pu-241 isotopes and the total amount of
plutonium;
• ratio between generated minor actinides (americium and curium) and original
amount of plutonium;
60
Table 7.3
Total neutron flux densities Φ [neutron/cm ⋅ sec] in reactor fuel and K ∞ as a function of the
2
energy yield  [MW⋅⋅ day/kg]
Φ ⋅ 10
-14
Â
K∞
Our
calculations
Results of other
laboratories
Our
calculations
Results of other
laboratories
0.0
2.844
2.86 ÷ 2.99
1.122
1.110 ÷ 1.133
30.0
3.393
3.49 ÷ 3.87
0.942
0.889 ÷ 0.975
40.0
3.586
3.63 ÷ 4.02
0.894
0.796 ÷ 0.941
60.0
3.832
3.79 ÷ 4.45
0.861
0.724 ÷ 0.91
The energy yield dependence of the following ratios:
• current amount of all plutonium isotopes N(Pu, B) to the start amount N(Pu);
• current amount of fissile plutonium isotopes N(Pu-239, Pu-241, B) to the current
amount of all plutonium isotopes N(Pu, B);
• current amount of americium and curium isotopes N(Am, Cm, B) to the start
amount of plutonium N(Pu);
• current amount of thorium-generated isotopes of U-233 and Pa-233 N(U-233, Pa233, B) to the start amount of fissile plutonium isotopes N(Pu-239, Pu-241).
Table 7.4
Basic characteristics of isotope generation as a function of energy yield
 [MW⋅⋅ day/kg]
B
N(Pu, B)/N(Pu)
N(Pu-239, Pu-241, B)/
N(Pu, B)
N(Am, Cm, B)/N(Pu)
Our
calculation
s
Results of
other
laboratories
Our
calculation
s
Results of
other
laboratories
Our
calculation
s
Results of
other
laboratories
0.0
1.0
1.0
0.7
0.7
0.
0.
30.0
0.425
0.40 ÷ 0.43
0.409
0.39 ÷ 0.42
0.035
0.0315 ÷ 0.046
40.0
0.300
0.28 ÷ 0.31
0.336
0.29 ÷ 0.34
0.0462
0.0428 ÷
0.0612
60.0
0.142
0.12 ÷ 0.16
0.211
0.12 ÷ 0.23
0.0677
0.06 ÷ 0.087
Comparing the data obtained we can say that:
• the resulting values are within the range of values from other laboratories;
• the entire collection of numerical data corresponds to water-water pressure
reactors.
61
Thus we can conclude that the method developed for the calculation of the neutron
physics parameters of the cell and isotopic transformation allows to obtain reliable and
relatively accurate results.
7.3. Characteristics of Isotope Generation in Thermal Reactors
he generation of Np-237, Am-241, and Am-243 isotopes depends on the start
composition of uranium fuel, energy distribution of the neutron flux density, campaign
scenario and other reactor features.
Accordingly, this work contains the estimates of isotope generation for three thermal
reactor types:
• Water-Water Power Reactor with the electric power of 1000 MW (VVER-1000);
• High Power Channel Reactor (1000 MW) (RBMK-1000);
• Canadian Deuterium Uranium Reactor, CANDU.
All of them are characterized by the same collection of basic parameters that must be
reasonably related with the parameters of the system of chained equations. The difference in
parameters of specific reactors will result in different generation level of isotopes.
The time the fuel resides inside the reactor is characterized by the campaign time TC
[days]. A part of this time is spent for fuel reloading, repair operations and unscheduled shutdowns. Therefore the usage coefficient of selected power, ϕ, is introduced to characterize the
normal reactor operation. The chained system is solved just within the time interval ϕ⋅ TC . The
normal reactor operation is characterized by thermal power, WT [MW]. Given the power WT
and uranium mass MU [t] we determine the energy intensity of the reactor, I = WT/M [MW/t].
The most important characteristic of spent fuel is the reactor energy yield, ´ , which
W ⋅T
is B = T C [GW⋅day/t]. It just defines the irradiation intensity and time of reactor fuel.
M
Obviously, B is related with the fuel burnout resulting from the fission reaction α [kg/t] by
ratio α = k ⋅ B . The coefficient k characterizes the number of fission-burnt nuclei in kilograms
to ensure the energy yield of 1 GW⋅day and is k ≈ 1.064 kg/1 GW⋅day. We assume the
effective energy yield per fission reaction to be 200 MeV. The fuel irradiation regime is
defined by uranium enrichment by U-235 isotope.
7.3.1 VVER-1000 Reactor
This reactor uses water as moderator and coolant at the same time. The neutron
physics calculations were run for VVER-1000 core characterized by the following basic
parameters:
• thermal power WT = 3200 MW;
• uranium load = 70 tons;
• campaign time TC =1100 days;
•
designed power utilization coefficient ϕ = 0.8;
62
• uranium enrichment ı = 4.4 %.
The remaining parameters correspond to those from /9/.
The computational results for the specific amount of start Ni [kg/t] and generated
isotopes including Np-237, Am-241, Am-243, depending on the energy yield in this reactor
are given in Table 7.5.
The energy yield of 13.4 GW⋅day/t corresponds to one year long irradiation , 26.94
GW⋅day/t corresponds to two years of irradiation, 40.48 GW⋅day/t - three-year irradiation and
53.9 GW⋅day/t - four-year irradiation. It should be noted that the calculations were run with
the fixed reactor power during the irradiation time which, of course, was followed by the
increase in neutron flux density as active isotopes were burning out.
The data from Table 7.5 demonstrate the burnout dynamics of start isotopes U-235
and U-238 the generation of basic isotopes.
The main irradiation mode is defined by the campaign time, TC = 3 years with yearly
replacement of about of 30% of spent fuel and is characterized by the average energy yield of
´ = 40.48 GW⋅day/t. And one ton of yearly unloaded fuel will contain 0.6 kg of Np-237
isotope, 0.041 kg of Am-241 isotope and 0.086 kg of Am-243 isotope.
Table 7.5
Specific amount of start Ni [kg/t] and generated isotopes as a function of the energy yield
 [GW⋅⋅ day/t] in VVER-1000 reactor
Isotopes
Energy yield
0
13.42
26.94
40.48
53.9
Am-243
0
0.00094
0.019
0.086
0.22
Pu-242
0
0.018
0.17
0.5
0.94
Pu-241
0
0.25
0.99
1.61
1.99
Am-241
0
0.0024
0.018
0.041
0.058
Pu-240
0
0.74
1.7
2.44
2.92
Pu-239
0
4.32
5.95
6.38
6.37
U-238
956
948
939
928
917
Pu-238
0
0.0093
0.06
0.17
0.35
Np-237
0
0.11
0.33
0.6
0.84
U-236
0
2.61
4.24
5.25
5.74
U-235
44
30
19.8
12.4
7.22
Note that basically it is possible to choose the campaign time TC = 4 years with yearly
replacement of about 25% of fuel. This implies the yearly unloading of spent fuel with the
average energy yield ´ = 53.9 GW⋅day/t. In this case one ton of yearly unloaded fuel will
contain 0.84 kg of Np-237 isotope, 0.058 kg of Am-241 isotope and 0.22 kg of Am-243
isotope.
For the evaluation of Am-241 isotope generation, keep in mind a relatively low Pu-241
half life in Am-241 which is 1/2 = 14.4 years and a relatively high specific concentration of
63
Pu-241 in spent fuel. The spent fuel after three years of irradiation and the energy yield
´ = 40.48 GW⋅day/t contains 1.61 kg/t of Am-241. The cooling period of t years results in the
generation of Am-241 as given by the following expression:


 0.693 t  
  kg/t.
 14 .4  
N A m −241 ( t ) = 1.61  1 − exp  −
That is within the period t = 14.4 years Pu-241 forms 0.8 kg/t of Am-241 which
exceeds significantly the amount of Am-241 produced during the irradiation period in the same
reactor fuel.
7.3.2. RBMK-1000 Reactor
Unlike the above described water-water reactor, RBMK-1000 uses graphite as
moderator, water as coolant and functions in the mode of continuous fuel assembly reloading.
The neutron physics calculations were run for the reactor core with the following parameters:
• thermal power WT = 3200 MW;
• uranium load = 192 tons;
• campaign time TC =1187 days;
• uranium enrichment ı = 2%.
The remaining parameters correspond to those from /9/.
The continuous reloading mode ensures the fixed density of thermal neutron flux that
was taken to be Φ T = 0.5⋅1014 [neutrons/(cm2⋅sec)] for the campaign time. Accordingly, the
energy yield rate in each fuel assembly decreased as active isotopes were burning out.
The computational results for the specific amount of start Ni [kg/t] and generated
isotopes including Np-237, Am-241, Am-243, depending on the irradiation time and
corresponding the energy yield are given in Table 7.6.
The basic irradiation mode can be taken to be the irradiation of the fuel assembly
during the period TC = 1187 days and the energy yield ´ = 23.5 GW⋅day/t. For this fuel, one
ton spent fuel will contain 0.16 kg of Np-237 isotope, 0.021⋅ kg of Am-241 isotope and 0.047
kg of Am-243 isotope.
Note that the amount of Pu-241 isotope in spent fuel is 0.61 kg/t. In t [years] of
cooling, this fuel will accumulate Am-241 as given by


 0.693 t  
  kg/t.
 14 .4  
N A m −241 ( t ) = 0 .61  1 − exp  −
64
Table 7.6
Specific amount of start Ni [kg/t] and generated isotopes as a function of the energy yield Â
[GW⋅⋅ day/t] or irradiation time TC [days] in RBMK -1000 reactor
Isotopes
Â; TC
0; 0
4.96; 182.5
9.53; 365
17.2; 868
23.5; 1187
28.9; 1486
Am-243
0
0.00005
0.0011
0.014
0.048
0.1
Pu-242
0
0.0027
0.028
0.17
0.4
0.66
Pu-241
0
0.04
0.17
0.44
0.61
0.72
Am-241
0
0.00024
0.0022
0.011
0.021
0.029
Pu-240
0
0.26
0.7
1.49
2.04
2.4
Pu-239
0
1.67
2.38
2.78
2.82
2.81
U-238
980
977.3
974.5
969
963.7
958.4
Pu-238
0
0.00063
0.0036
0.018
0.039
0.062
Np-237
0
0.013
0.039
0.1
0.16
0.21
U-236
0
0.87
1.49
2.23
2.58
2.72
U-235
20
14.6
10.7
5.65
3
1.58
7.3.3. CANDU Reactor
The Canadian Deuterium Uranium reactor uses heavy water as the moderator and
coolant and it is a channel reactor like RBMK-1000 functioning in continuous reload mode.
Similarly to RBMK-1000, the fuel is irradiated by a fixed density thermal neutron flux,
Φ T = 1.33⋅1014 [neutrons/(cm2⋅sec)]. Because the active isotopes burn out the specific
assembly power drops during the irradiation while the average reactor power remains constant
due to continuous reloading.
The computational results for the specific amount of start and generated isotopes are
given in Table 7.7. Because of high level of neutron saving, the reactor uses natural uranium.
A low stored reactivity and relatively poor breeding of plutonium K B < 1 ensure a low energy
yield.
In normal mode the fuel is unloaded when the energy yield of ´ ≈ 7 GW⋅day/t is
achieved. One ton of unloaded spent fuel will contain 0.0274 kg of Np-237 isotope, 0.014 kg
of Am-241 isotope, 0.0022 kg of Am-243 isotope and 0.2 kg of Pu-241 isotope.
According to Pu-241 decay the accumulation of Am-241 in irradiated fuel during the
cooling period of t years is determined by the expression:


 0.693 t  
  kg/t.
 14 .4  
N A m −241 ( t ) = 0 .2  1 − exp  −
65
Table7.7
Specific amount of start Ni [kg/t] and generated isotopes as a function of the energy yield
 [GW⋅⋅ day/t] or irradiation time TC [days] in CANDU reactor
Isotopes
Â; TC
0; 0
0.99; 30
1.7; 50
3.46; 100
7.0; 200
Am-243
0
0
0
0.00011
0.0022
Pu-242
0
0.00007
0.00051
0.0062
0.052
Pu-241
0
0.0024
0.01
0.055
0.2
Am-241
0
0
0.00002
0.00018
0.0014
Pu-240
0
0.042
0.11
0.36
0.95
Pu-239
0
0.73
1.15
1.86
2.51
U-238
993
992
991.2
989.5
985.8
Pu-238
0
0.00003
0.00012
0.00067
0.0033
Np-237
0
0.0018
0.0039
0.01
0.027
U-236
0
0.16
0.26
0.45
0.71
U-235
7
6
5.35
4.06
2.33
Conclusions
This report contains the results for the first research phase within the project “Control
of Alternative Nuclear Materials and Non-Proliferation” under ISTC project #1763p “Support
of the Analytical Center for Non-Proliferation and Efforts of RFNC-VNIIEF Specialists to
Strengthen Non-Proliferation and to Reduce the Nuclear Threat”.
These results serve the base for the second research phase implementation after which
the appropriate conclusions will be presented.
66
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