ht2004: reactor physicsreactor kinetics1 reactor kinetics. what is reactor kinetics? reactor...
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HT2004: Reactor Physics Reactor Kinetics 1
REACTOR KINETICS.What is reactor kinetics?
Reactor reaction on reactivity changes (whatever are the reasons of changes)
2 1 ( , , )( , ) ( , , ) ( , ) ( , , ) ( , ) ( , , )a f
E tD E E t E E t E E t
v t
r
r r r r r r
2( , ) ( , ) ( , ) ( , ) ( , ) ( , ) 0 ?a fD E E E E E E r r r r r r
2( , )
( , ) ( , ) ( , ) ( , ) ( , ) 0fa
eff
ED E E E E E
k
rr r r r r
1 11; ; ;eff
effeff
k kk k
k k
Generally not possible
HT2004: Reactor Physics Reactor Kinetics 2
Principles of a Nuclear Reactor
1
2
N
Nk
n/
fissi
onN1
N2Leakage
Fast fission
Resonance abs.
Non-fuel abs.
Leakage
Non-fissile abs.
Fission
Slo
win
g d
ow
n
Ene
rgy
E
2 MeV
1 eV
200 MeV/fission
ν ≈ 2.5
HT2004: Reactor Physics Reactor Kinetics 3
0
1 11ad
av ac av aPureM av a MP
fft
v v v v
1aF aF aM
ac aF aM ac
ff
Fuel-moderator mixture is dilute1aPureM
ac f
2 21 ; for pure moderatoracc
ac
DL f L
35
0.11.18 10
0.000385 2.2 10dt s
510 ;s p p dt t l t
1For moderator ( ) ( ) ; 2200aPureM aPureM MP MP MP
mE v const E v v
v s
Graphite-moderated: lp = 10-3
Water-moderated: lp = 10-4
Fast reactors: lp = 10-7
HT2004: Reactor Physics Reactor Kinetics 4
a th
nD r r q r
t
2 ( ) ( ) ( , )
Ba a
n tD t t t k e
t
22 ( , )( , ) ( , ) ( , )
rr r r
a
p
kdn tv n t k n t
dt l
1( )( ) 1 ( )
Homogeneous infinite reactor
p
p
lk tn t n t n T
l T k
0 0
1( ) exp exp ;
1
k k T s s e 101 1.001; 0.001; 1 10 22000
peff p
lk k l l
B L 2 2Finite reactor ; (effective life time)
1
HT2004: Reactor Physics Reactor Kinetics 5
Group
Half-life
T1/2(s)
Mean lifemi (s)
Decay constant
i(s-1)
Fraction of total fission neutrons, i
1 55.7 80.2 .0124 .000215
2 22.7 32.7 .0305 .001424
3 6.2 8.9 .111 .001274
4 2.3 3.3 .301 .002568
5 .61 .88 1.14 .000748
6 .23 .33 3.01 .000273
ii
6
235
1
U 0.0065 m i mii
t t s
6
235
1
1U 12.5
p p m p m m p ml l l t l t t l t s 2351 U 0.08
k k T s 1 1.001; 0.001; 80
i i 1
HT2004: Reactor Physics Reactor Kinetics 6
Kinetic Equations
a th i i a thi
dn tk t C t t
dt
6
1
( )(1 ) ( ) ( ) ( )
i ii
ii a av i i
dn t kn t C t
dt ldC t
k v n t C tdt
6
1
( ) ( )( ) ( )
( )( ) ( )
a av
dn t kn t C t
dt ldC t
k v n t C tdt
( ) ( )( ) ( )
( )( ) ( )
HT2004: Reactor Physics Reactor Kinetics 7
t tn t Ae C t Be ( ) ; ( ) ;
Solution of Kinetic Equations
k l l 21 0
l l and l
l
2
1 2
2 2
;
A n A n
1 0 2 0;
HT2004: Reactor Physics Reactor Kinetics 8
Time
ρ0
0 0
0
00
0 0
( ) exp exppl
n t n t t
ρ0 > 0
ρ0 < 0
n(t)/n(0)
C(t)/C(0)
Delayed neutrons ignored
HT2004: Reactor Physics Reactor Kinetics 9
Inhour Equation
i ii
ii a av i i
dn t kn t C t
dt ldC t
k v n t C tdt
6
1
( ) ( )( ) ( )
( )( ) ( )
st stn t Ae C t Be ( ) ; ( ) ;
i
i i
ssls
sl sl s
6
01
1( )
1 1
Unit “inverse hour” = inhour
1 inhour = amount of reactivity needed to make the reactor period equal to one hour
1 pcm (per cent mille) = 10-5 of Δk/k
1$ is equal to ρ = β
j jj
n t n st
7
1
( ) exp
HT2004: Reactor Physics Reactor Kinetics 10
1
s
s
s
0 1
0 1
0 1 11
0 0 (critical)
1 (supercritical)
1(subcritical) T= 80sec
j jj
n t n st
7
1
( ) exp
0
1 2 3 4 5 6l 1 s1
s( )
s
HT2004: Reactor Physics Reactor Kinetics 11
Special Cases
p i ii
lT inhour pcm
s
6
510
1 0 0
1 0.0831 2.3 10 2.3
01
11
plTs k
0 Break point
0 : Reactor responseDelayed criric Precursor a -l decay
0 or promptPrompt cri supercritrical ical
HT2004: Reactor Physics Reactor Kinetics 12
pl 310
pl 410
pl 510
pl 610
pl 710
pl 810
HT2004: Reactor Physics Reactor Kinetics 13
0 0.3%; 60pl s
0 0.3%; 1pl ms
0 0.1%; 1pl ms
HT2004: Reactor Physics Reactor Kinetics 14
n(t)
/n(0
)
ρ0 = –0.5%
ρ0 = –5%
ρ0 = –10%
HT2004: Reactor Physics Reactor Kinetics 15
The END
HT2004: Reactor Physics Reactor Kinetics 16
1
s
s
s
0 1
0 1
0 1 11
0 0 (critical)
1 (supercritical)
1(subcritical) T= 80sec
j jj
n t n st
7
1
( ) exp
HT2004: Reactor Physics Reactor Kinetics 17
HT2004: Reactor Physics Reactor Kinetics 18