Plutonium Production
Back of the Envelope Calculations
Moritz Kütt
[email protected]
Friederike Fassnacht, Matthias Englert
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 1
Organized by
Gewerkschaft Erziehung und Wissenschaft
(GEW)
The union calls for:
●
Raise wages by 6.5%
●
Limitation of fixed-term contracts
●
●
Back to old vacation regulations (Employers
canceled vacation clause, 30 → 26 days for
new employees)
negotiation result should be valid for
Beamtinnen und Beamte
Outline
What is the task?
Complex Solution
Simplify!
Results & Example
Conclusion
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 4
Outline
What is the task?
Complex Solution
Simplify!
Results & Example
Conclusion
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 5
Proliferation Risk
How much plutonium can be
produced?
●
Annually/design burnup,
total/per fuel element
What is the isotopic vector of
the produced plutonium?
Reactor-grade Plutonium
(> 19% Pu-240)
Weapon-Grade Plutonium
(< 7% Pu-240)
●
●
different reactor types
–
Pu-production reactor
–
PWR / VVER
–
BWR
–
CANDU
–
New models/Prototypes:
SMR, ADS, FBR, Fusion
different reactor fuels
different reactor operation
procedures
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 6
Outline
What is the task?
Complex Solution
Simplify!
Results & Example
Conclusion
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 7
Knowledge about reactors
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 8
Reactor Geometries
PWR
VVER
CANDU
Magnox (Calder Hall)
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 9
Knowledge about reactions
●
Cross section pictures
●
Fission yield pictures
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 10
Bateman Equation
[ (
]
)
∞
d i
i
i
i
N (t )= − ∫ dE σ f ( E ,t )+ ∑ σ R ( E , t ) ϕ( E , t ) N (t )
dt
R ∈AR
0
+∑
j≠i
+
[
∞
]
∫ dE f ij ( E)σ fj ( E , t ) ϕ( E ,t ) N j (t )
0
R∈ AR
[
i
i
∞
∑ ∫ dE σ
]
R
→i
R
R
→i
( E , t ) ϕ( E ,t ) N (t )
0
ij
j
j
−λ N (t )+ ∑ l λ N (t )
j≠i
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 11
✔
Code System MCMATH
Iterative Solution:
Mathematica: Initial
Composition and
progress control
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 12
✔
Code System MCMATH
Iterative Solution:
Calculation of eff. Cross-Sections (MCNPX)
●
●
Mathematica: Initial
Composition and
progress control
Evaluated nuclide data
For specific problem geometry
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 13
✔
Code System MCMATH
Iterative Solution:
Calculation of eff. Cross-Sections (MCNPX)
●
●
Mathematica: Initial
Composition and
progress control
Evaluated nuclide data
For specific problem geometry
Solve Differential Equations (Mathematica)
●
●
First for actinides
Fission product chains
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 14
Code System MCMATH
History
Year
Author
Description
1998
Alexander Glaser/
Christoph Pistner
Basic development during diploma thesis
19982000
Christoph Pistner
Center calculations
20002005
Christoph Pistner
Isomers, burnable neutron poisons
2007
Moritz Kütt
Automatization, distributed calculations
2009
Matthias Englert
Fusion reactors, multi cell calculations
20102011
Moritz Kütt
Fast reactors, extended multi cell capabilities
2013
???
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 15
Results
4 different enrichments
VVER (2.6)
PWR (3.4)
PWR (4.0)
PWR (5.0)
4 different reactors
PWR (4.0)
VVER (3.28)
CANDU
MAGNOX
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 16
Outline
What is the task?
Complex Solution
Simplify!
Results & Example
Conclusion
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 17
Cubic Burnup Fit
VVER (3.28%)
Pu(B)=(0.130+0.518⋅B−0.00642⋅B 2 +0.0000368⋅B 3 ) kg/tU
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 18
Double Linear Fit
CANDU
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 20
Double Linear Fit
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 21
Even Simpler?
●
●
Rule of Thumb: 1% Pu in spent fuel
True for most of the currently calculated
reactors
But:
●
Unloading of fuel before design burnup
●
Isotopic vector?
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 22
Outline
What is the task?
Complex Solution
Simplify!
Results & Example
Conclusion
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 23
Results
Pu mass (kg/tU)
Enr. (wt%)
Other
VVER
PWR
2,6
3
3,4
3,8
4
4,2
4,6
5
Enr. (wt%)
2,6
3,28
4,6
Type
Candu
MAGNOX
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 0,522
0,373
20,0 4,547 0,167
50,0
0 0,462
0,368
20,0 4,328 0,172
50,0
0 0,405
0,364
20,0 4,109 0,177
50,0
0 0,362
0,360
20,0 3,911 0,182
50,0
0 0,353
0,357
20,0 3,807 0,185
50,0
0 0,328
0,354
20,0 3,697 0,187
50,0
0 0,374
0,340
22,5 3,762 0,186
50,0
0 0,344
0,337
22,5 3,578 0,191
50,0
Lower B
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 0,803
0,413
21,0 5,602 0,176
60,0
0 0,458
0,401
21,0 5,016 0,190
60,0
0 0,611
0,354
30,0 7,065 0,144
60,0
Lower B
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 0,074
0,616
3,4 0,931 0,354
8,0
0 0,055
0,656
3,0 0,981 0,358
9,1
Lower B
Pu239 content (wt%)
Enr. (wt%)
2,6
3
3,4
3,8
4
4,2
4,6
5
Enr. (wt%)
1,6
3,28
4,6
Type
CANDU
MAGNOX
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 95,53 -1,663
20,0 74,19 -0,605
50,0
0 96,37 -1,574
20,0 77,51 -0,645
50,0
0 96,47 -1,426
22,5 78,91 -0,637
50,0
0 96,98 -1,355
22,5 81,33 -0,655
50,0
0 97,24 -1,326
22,5 82,43 -0,661
50,0
0 97,44 -1,293
22,5 83,44 -0,667
50,0
0 97,79 -1,233
22,5 85,11 -0,668
50,0
0 98,05 -1,175
22,5 86,65 -0,667
50,0
Lower B
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 90,63 -1,647
21,0 62,79 -0,326
60,0
0 95,51 -1,305
24,0 76,16 -0,503
60,0
0 97,60 -1,170
21,0 87,25 -0,664
60,0
Lower B
Lower Function
Upper Function
Mid B
Upper B
b
m
b
m
0 98,29 -6,191
4,0 89,49 -3,990
8,0
0 95,28 -5,500
4,5 85,68 -3,408
9,1
Lower B
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 24
PWR Grafenrheinfeld
Enrichment 4% - Fuel: 103t - Power: 3765 MW
1/3 refuelled 150 days ago
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 25
PWR Grafenrheinfeld
Enrichment 4% - Fuel: 103t - Power: 3765 MW
1/3 refuelled 150 days ago
B=
3765 MW⋅150 d
103 t
=5.5
GW d
t
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 26
PWR Grafenrheinfeld
Enrichment 4% - Fuel: 103t - Power: 3765 MW
1/3 refuelled 150 days ago
B=
3765 MW⋅150 d
103 t
Pu ( B )=( m B + b )
kg
tU
=5.5
GW d
t
Pu (5.5
MW d
tU
)=(0.357 B+ 0.353)
kg
tU
=2.3
kg
tU
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 27
PWR Grafenrheinfeld
Enrichment 4% - Fuel: 103t - Power: 3765 MW
1/3 refuelled 150 days ago
B=
3765 MW⋅150 d
103 t
Pu ( B )=( m B + b )
=5.5
kg
tU
Pu239 ( B )=( m B + b ) wtp
GW d
t
Pu (5.5
MW d
tU
)=(0.357 B+ 0.353)
Pu239 (5.5
MW d
tU
kg
tU
=2.3
kg
tU
)=(−1.326 B +97.24) wtp =89.9 wtp
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 28
PWR Grafenrheinfeld
Enrichment 4% - Fuel: 103t - Power: 3765 MW
1/3 refuelled 150 days ago
B=
3765 MW⋅150 d
103 t
Pu ( B )=( m B + b )
=5.5
kg
tU
Pu239 ( B )=( m B + b ) wtp
30 tU∗2.3
kg
tU
=69 kg
GW d
t
Pu (5.5
MW d
tU
)=(0.357 B+ 0.353)
Pu239 (5.5
MW d
tU
kg
tU
=2.3
kg
tU
)=(−1.326 B +97.24) wtp =89.9 wtp
→ fuel for ~10 nukes...
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 29
Conclusion
●
Estimate of plutonium production not necessarily complicated
●
Preparation of input variables necessary
●
With more reactor types tables could become suitable tool for different
tasks
(BWR, AGR, FBR, Fusion, ADS...)
ToDo (?):
●
Produce “Pu-Production Refernce Card”?
●
Error estimate
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 30
Conclusion
●
Estimate of plutonium production not necessarily complicated
●
Preparation of input variables necessary
●
With more reactor types tables could become suitable tool for different
tasks
(BWR, AGR, FBR, Fusion, ADS...)
ToDo (?):
●
Produce “Pu-Production Refernce Card”?
●
Error estimate
Thank you for
your attention!
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 31
End
DPG Spring Meeting | Dresden | 06.03.2013 | Plutonium Production – Back of the Envelope Calculations | 32