Nuclear Fission • Recoverable energy release ≈ 200 MeV per 235U fission. • Fission rate = 2.7x10 2 7x1021 P fissions per day day. P in MW MW. • 3.12x1016 fissions per second per MW, or 1.2x10-5 gram of 235U per second per MW (thermal). • Burnup B rate t : 1.05 1 05 P g/day. /d P in i MW MW. • The fissioning of 1.05 g of 235U yields 1 MWd of energy. • Specific Burnup = 1 MWd / 1.05 g ≈ 950000 MWd/t (pure 235U !!!!!!!!!). • Fractional Burnup = ??? Actually much less (all heavy material). • Thermal reactor loaded with 98 metric tons of UO2, 3% enriched, operates at 3300 MWt for 750 days. y • ≈ 86.4 t U. Specific burnup ≈ 28650 MWd/t. • Fast fission of 238U. • 238U converted to plutonium ⇒ more fission. fission Not all fissions from 235U.
Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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Nuclear Fission σ γ ((E ) • Capture-to-fission C t t fi i ratio: ti α (E) = σ f (E) • Consumption rate: 1.05(1+α) 1 05(1 ) P g/day. /d
• Read all relevant material in Lamarsh Ch 4. We will come back to this later Ch. later. •Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor reactor. Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
4.8x1012 m-2s-1
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Nuclear Fission • 3.1x1010 fissions per second per W. • In I thermal th l reactor, t majority j it off fissions fi i occur iin thermal energy region, φ and Σ are maximum. • Total T t l fission fi i rate t in i a th thermall reactor t off volume l V
V Σ fφ • Thermal reactor power (quick calculation)
Pth =
V Σ fφ 10
3.1x10
st Semester, Nuclear Reactors, Reactor Theory, BAU, 1BAU, Second2007-2008 Semester, 2011-2012 (Saed(Saed Dababneh). Dababneh).
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Controlled Fission Fast second generation neutrons g
• 235U + n Î X + Y + ν n • Moderation of second generation neutrons X Chain reaction. • Water, D2O or graphite moderator. • Ratio R ti off number b off ““neutrons” t ” (fissions) (fi i ) iin one generation ti tto the preceding ≡ k∞ (neutron reproduction or multiplication factor). factor) Infinite medium (ignoring leakage at the surface).
• k ≥ 1 X Chain reaction. • k < 1 X subcritical. • k = 1 X critical system. • k > 1 X supercritical. iti l For steady release of energy (steadystate operation) we need k =1. =1 Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
Chain reacting pile
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Controlled Fission • • • • •
•
Average number of all neutrons released per fission Æ ν (for thermal neutrons neutrons, 0.0253 0 0253 eV). eV) 233U : 2.492 235U : 2.418 239Pu : 2.871 241Pu : 2.927
Reactor is critical (keff = 1): rate of neutrons produced by fission = rate of neutrons absorbed + leaked.
Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
Size and composition of the reactor.
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Controlled Fission 235U
tthermal e a ccross oss sect sections o s
σfission ≈ 584 b. Check σscattering ≈ 9 b. numbers! σradiative capture ≈ 97 b.
Probability for a thermal neutron to cause fission fi i on 235U is i
σf
1 ≈ = σ f + σγ 1+ α
If each fission produces an average of ν neutrons, then the mean number of fast fission neutrons produced per thermal neutron = η
σf σf ν η =ν =ν = σa σ f + σγ 1+ α Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
η 1.3). (Light water?). water?) • In this case η is further from 1 and allowing for more neutrons to be lost while maintaining criticality. Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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Moderation (to compare x-section) (n,n)
2H
(n,n)
(n,γ)
1H
(n,γ)
• Resonances? • 3H production. Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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Controlled Fission HW 11 • Verifyy
1 η= Σa
∑ν (i)Σ
f
(i )
i
• Comment on the calculation for thermal neutrons and a mixture of fissile and non-fissile materials,, giving an example. • Comment for fast neutrons and a mixture of fissionable materials, giving an example. Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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Conversion and Breeding Converters: Convert non non-thermally-fissionable thermally fissionable material to a thermally-fissionable material. _
U + n → 239 U ⎯23 ⎯min ⎯→ 239 Np + β − + ν
238
.3 d ⎯2⎯ ⎯ →
239
_
Pu + β − + ν
σf,th = 742 b
232
_
Th + n → 233Th ⎯22 ⎯min ⎯→ 233 Pa + β − + ν India
⎯27 ⎯→ ⎯d
Nuclear Nuclear Reactor Reactors, Theory, BAU,BAU, 1st Semester, Second Semester, 2007-20082011-2012 (Saed (Saed Dababneh). Dababneh).
_
U + β − +ν
233
σf,th = 530 b
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Conversion and Breeding
• If η = 2 X Conversion C i and d fifission i possible. ibl • If η > 2 X Breeder reactor. • 239Pu: Thermal neutrons (η ~ 2.1) 2 1) X hard for breeding. breeding Fast neutrons (η ~ 3) X breeding X fast breeder reactors. • After sufficient time of breeding, fissile material can be easily (chemically) separated from fertile material material. Compare to separating 235U from 238U. • Reprocessing. p g Nuclear NuclearReactor Reactors, Theory, BAU,BAU, 1st Semester, Second Semester, 2007-20082011-2012 (Saed (Saed Dababneh). Dababneh).
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Controlled Fission • Note that η is greater than 2 att thermal th l energies i and d almost 3 at high energies. • These Th ““extra” t ” neutrons t are Used to convert fertile into fi il ffuel. fissile l • Plutonium economy. • India I di and d th thorium. i • Efficiency of this process is d t determined i db by neutron t energy spectrum. Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
Variations in η
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Controlled Fission • Conversion ratio CR is defined as the average rate of fissile atom production to the average rate of fissile atom consumption. • For LWR's CR ≅ 0.6. • CR is called BR for values > 1 (fast breeder). • They are called “fast” because primary fissions inducing neutrons are fast not thermal, thus η > 2.5 but σf is only a few barns. • Moderator??
Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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Controlled Fission • N thermal neutrons in one generation have produced so far ηN fast neutrons. neutrons • Some of these fast neutrons can cause 238U fission X more fast neutrons X fast fission factor = ε ((= 1.03 for natural uranium). • Now we have εη εηN N fast neutrons. • We need to moderate these fast neutrons X use graphite as an example X for 2 MeV neutrons we need ??? collisions. How many for 1 MeV neutrons? • The neutron will pass through the 10 - 100 eV region during the moderation process. This energy region has many strong 238U capture captu e resonances eso a ces (up to ????? b) X Ca Can not ot mix u uranium a u a and d moderator. • In graphite, an average distance of 19 cm is needed for thermalization X the resonance escape probability p (≈ 0.9). Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
Reactor design.
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Controlled Fission • Now we have pεη εηN N thermal neutrons. • Moderator must not be too large to capture thermal neutrons; when thermalized, neutrons should have reached the fuel. • Graphite thermal cross section = 0.0034 b, but there is a lot of it present. • Capture can also occur in the material encapsulating the fuel elements l t (clad). ( l d) • The thermal utilization factor f (≈ 0.9) gives the fraction of thermal neutrons that are actually available for the fuel fuel. • Now we have fpεη εηN N thermal neutrons neutrons, could be > or < N thus determining the criticality of the reactor. The four four--factor formula. ∞
k = fpεη f k = keffff = fpεη(1 (1-lfast )(1-lthermal f )(1 h l)
Nuclear Reactor Theory, BAU, Second Semester, 20112012 (Saed Dababneh).
Fractions lost at surface
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Controlled Fission k∞ = fpεη,
keff = fρεηPnon −leak
1 ν (i )Σ f (i ) as defined in HW 11. • Fast from thermal, η = ∑ Σ a i • Fast from fast, fast ε. ε • Thermal from fast, p. ∑ f = • Thermal available for fuel ∑ +∑ +∑ +∑ +∑ +.. f l fuel a
l d clad a
fuel a modd erator t a
rods d a
poison i a
Thinking QUIZ • For each thermal neutron absorbed, how many fast neutrons are produced? Will need this when discuss two two-group group diffusion. diffusion Nuclear Reactor Theory, BAU, Second Semester, 2011-2012 (Saed Dababneh).
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