Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 1 Fuel Depletion Time scale: Time scale: Days and months. Days and months. • More depletion change steady state flux by means of reducing absorbers. • For a given fuel isotope • For constant flux constant flux 0 the solution is • For time varying flux time varying flux 1 2 14 3 22 10 ~ , 10 ~ s cm cm N ) , ( ) , ( ) , ( t r t r N t t r N f a f f ) , ( ) ( ) 0 , ( ) 0 , ( ) , ( 0 t r f t r f f f a f a e r N e r N t r N Neutron fluenc ) , ( ) , ( ) 0 , ( ) 0 , ( ) , ( 0 \ \ t r f dt t r f f f a t f a e r N e r N t r N Solve numerically. Exponential burnup
Fuel Depletion
Dec 31, 2015
Fuel Depletion. Time scale: Days and months. More depletion change steady state flux by means of reducing absorbers. For a given fuel isotope For constant flux 0 the solution is For time varying flux. Exponential burnup. Neutron fluence. Solve numerically. Fuel Depletion. - PowerPoint PPT Presentation
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Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
1
Fuel DepletionTime scale:Time scale:
Days and months.Days and months.
• More depletion change steady state flux by means of reducing absorbers.• For a given fuel isotope • For constant flux constant flux 00 the solution is
• For time varying fluxtime varying flux
1214322 10~,10~ scmcmN
),(),(),(
trtrNt
trN faf
f
),()( )0,()0,(),( 0 trf
trff
fa
fa erNerNtrN
Neutron fluence
),(),(
)0,()0,(),( 0
\\
trf
dttr
ff
fa
tfa
erNerNtrN
Solve numerically.
Exponential burnup
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
2
Fuel Depletion• Constant power.Constant power.
• Power ~ flux only over short time periods during which Nf is constant.
• The solution is obviously
)()0,(),(),(),( 0 rPrPtrtrwNtrP fff
Energy released per
fission
Fission rate
w
rPtrtrN
t
trN faf
f )(),(),(
),(0
tw
rPrNtrN ff
)()0,(),( 0
Linear depletion!
)0,()0,(),(),(
)0,()0,(),(),(
rrtrtr
rrNtrtrN
ff
ff
fa
ff
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
3
Fuel Depletion
Do the calculations for different
flux and power levels.
HW 31HW 31
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
4
Poisoning and Fuel DepletionInfinite, critical homogeneous reactor.Infinite, critical homogeneous reactor.
)()()()(
)(mod tttt
tfk
controla
poisona
eratora
clada
fa
fa
thus
trrN
trrNrN
ttrtrNrN
tw
rPrNtrN
faf
faff
faff
ff
)0,(1)0,(
)0,()0,()0,(
),(),()0,(
)()0,(),( 0
trrtr fa
fa
fa )0,(1)0,(),(
Constant powerConstant power
tr
rr
trN
rNtr
faf
f
)0,(1
)0,()0,(
),(
)0,(),(
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
5
Poisoning and Fuel Depletion
)(
)1()(
)(
)(
0
0
)(
0
0
0
0
ttXeaIXe
fI
tXeaXe
fXeI
IXeaXe
XeaXe
ee
etXe
Xe
),(
)0,()0,()(),(),(
tr
rrtrXetr
Xea
Xe
fXeIXea
Xea
Constant
Constant
trrtr fSmSma
Sma )0,()0,(),(
tr
rtr
fa )0,(1
)0,(),(
• Other fission products (poisons) with less capture cross sections.
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
6
Poisoning and Fuel Depletion
)()()()(
)(mod tttt
tfk
controla
poisona
eratora
clada
fa
fa
• Now we know all macroscopic cross sections.
Until = 0.Solve for t to get
upper limit for “core loading
lifetime”.Damaged
fuel…!
• When there are no absorbers left to remove, we need to refuel.• Absorbers are not only control rods.• All fuel nuclei should be considered.• For each species, all sources and sinks should be taken into account.• Online loading environmental.• 3H.
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
7
Poisoning and Fuel Depletion
)(tFNNNNdt
dNC
CBBAAAA
A
Fuel loading
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
8
Poisoning and Fuel Depletion
• Fixed burnable poisons.B, Gd. More uniform distribution than rods, more intentionally localized than shim.• Soluble poisons (chemical shim) with caution.Boric acid (soluble boron, solbor) in coolant.Boration and dilution.Scram emergency shutdown (sodium polyborate or gadolinium nitrate).• Non-burnable poisons.Chain of absorbers or self shielding.
• Some poisons are intentionally introduced into Some poisons are intentionally introduced into the reactor.the reactor.
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
9
Delayed Precursors
),()(),()(),()(
),()(),()(),(1
11 \
\\
\
\\\
trrDtrrtrr
Strrtrrtrtv
gggsggag
extg
G
gggsg
G
ggfgggg
g
),()(),()(
),()(),(1
trrDtrr
Strrtrtv
a
extf
• For one-group
• What about delayed neutrons?
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
10
Delayed Precursors
One of 66 delayedneutron
precursors known so far.
Data for all precursors are not accurately
known.
Delayedneutron emitter
dp
Delayed neutron fraction d
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
11
Fissile nucleus Delayed neutron / 100 fissions233U235U
238U*
0.6671.6214.39
239Pu240Pu*241Pu
242Pu*
0.6280.951.522.21
Delayed Precursors
Data for thermal neutron induced fission, except for * fast neutron induced fission.
Increases with N.
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
12
Delayed Precursors
),()(),(),(
),()(),()(
),()()1(),(1 6
1
trrtrCt
trC
trrDtrr
SCtrrtrtv
fiiii
a
ext
iiif
(s)
< 0.7% = 0.016 / 235U
p
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
13
Delayed Precursors• The multi-group equation now becomes
),()(),()(),()(
),()(
),(),()()1(),(1
1
6
11
\
\\
\
\\\
trrDtrrtrr
Strr
trCtrrtrtv
gggsggag
extg
G
gggsg
iii
Cg
G
ggfgg
pgg
g
G
ggfggiii
i trrtrCt
trC
1\
\\\ ),()(),(),(
Different energy spectra
Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).
14
Delayed Precursors• In steady statesteady state
G
ggfggiii trrtrC
1\
\\\ ),()(),(
)()()()()()()()(
)()()()()1(0
1
11
\
\\
\
\\\
\
\\\
rrDrrrrSrr
rrrr
gggsggagextg
G
gggsg
G
ggfgg
Cg
G
ggfgg
pg
)()()()(
)()()()(
)()()(0
1
1
\
\\
\
\\\
rrDrr
rrSrr
rr
gggsg
gagextg
G
gggsg
G
ggfgg
pg
Cg
pg
Significance of ggg depends on whether
we have fine or course energy groups.
Cg
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