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Introduction.. 1Nuclear Power Plants
Laboratory for Reactor Physics and Systems Behaviour
Introduction,Nuclear Physics Basics, Fission
R. Chawla
Power Plants and Heat Pumps:Nuclear Power Plants
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Introduction.. 2
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Power Plants and Heat Pumps
! Prof. Favrat 7 x 2 hrs (lectures), 14 x 1 hr (exercises)
Energy, economics and environment (general)
Thermal power plant cycles and equipment
Heat pumping technologies
!
Prof. Chawla 7 x 2 hrs (lectures, with exercises integrated therein)
Nuclear power plants
March 1, 8, 15, 29
April 12, 26
May 3
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Nuclear Power Plants
Nuclear Power Plants (NPPs)
! Weeks 1 & 2:Introduction, nuclear physics basics, fission, nuclear reactors
Critical size, nuclear fuel cycles, NPPs (CROCUS visit?)
! Week 3:Neutronics, reactor physics design
!
Week 4:Reactor heat transfer (thermalhydraulics), technological constraints
!
Week 5:Reactor (reactivity) control
!
Week 6:Principal types of nuclear power plants
! Week 7:Environmental aspects, nuclear safety, advanced systems (NPP visit?)
Course Material:
Elements of Nuclear Engineering, J. Ligou, Chs. 1, 3, (4), 5, (6) Effectively, English translation of Introduction au gnie nuclaire (PPUR, 1997)
Pdfs of book chapters, as also of ppt-slides (incl. solved exercises), available at:
https://documents.epfl.ch/groups/l/lr/lrs-unit/www/NPPs.2010/
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Nuclear Power Plants
Introduction
! Nuclear (fission) energyCommercially established since 1956
Calder Hall, gas-cooled Magnox NPP at Sellafield (UK), 50 MW (later 200 MW)
Today: ~16% of worlds electricity generation (18% hydro, 66% fossil)
Switzerland: ~40% (nearly all the rest: hydro)
!
General situation
Evergrowing, worldwide energy demand (population, standard of living,..)
Acknowledged hazards of continued dependence on fossil fuels (climate change,..)
New renewables important, but not sufficiently established for medium-term
Nuclear needs to contribute to growthFusion in long-term (when?)
Fission (increase possible, but further developments needed.. safety, wastes, etc.)
Various factors importantEconomics, environmental aspects, socio-political considerations,..
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Introduction.. 5
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Nuclear Power Plants
Nuclear Physics Basics (Historical Overview)
! Structure of the atom (Rutherfords model)Mass concentrated in the nucleus (mH/me ~ 1837)
Nuclear charge: +Ze (Z: atomic number, e ~ 1.6.10-19 coulomb)
Quantum mechanical basis for atomic, nuclear structure
Classical dimensions: nucleus ~ 10-13 cm, atom ~ 10-8 cm
! Energy units (1eV ~ 1.6.10-19 J)Binding energy of outermost electrons ~ order of eV
Energy involved in chemical reactions ~ same order
Binding energy of nucleons (constituents of nucleus) ~ order of MeV !Energy in nuclear reactions ~ x 106times greater than in chemical..
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Introduction.. 6
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Nuclear Power Plants
Constituents of the Nucleus
!
Atomic mass A A gm contain NAatoms (Avogadros Number.. 6.023.1023)
1 a.m.u. (atomic mass unit) = 1/12 m (C12) = 1.66.10-24gm
The nucleus has A nucleons Z of these are protons (1H
1!p) What is the rest, (A-Z) ?
!
Discovery of the neutron (Chadwick, 1932): 2He4+ 4Be9"6C12+ 0n1, or Be9(#,n)C12 Neutral (uncharged) radiation
Interaction with hydrogenous materials results in emission of protonsElastic scattering of the neutral particles mn~ mp~ 1 a.m.u. (n: 1.0087, p: 1.0073)
! Nucleus:ZXA Z protons, (A-Z) neutrons
Isotopes: same Z, different A e.g. 1H1(99.985%), 1H
2(0.015%)
..
92U234(0.006%), 92U
235(0.72%), 92U238(99.27%)
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Introduction.. 7
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Chart of the Nuclides
! Stability of nucleus depends on N/Z For light stable atoms, N~Z
For Z>20, N>Z: strongly attractive forcebetween nucleons compensates repulsive
coulombian force between protons
!
Unstable nuclei, radioactive (natural, artificial) ZX
A!Z-2YA-4+ 2He
4 (!-decay) .. heavy ZX
A!Z+1YA+ e-+ "o (#
--decay) .. n-rich ZX
A*! ZXA+$ ($-decay) .. excited
-------
Also #+, EC
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Radioactivity Calculations-1
! Spontaneous disintegration (decay) of a nucleus radioisotope, radionuclide
! Often encountered in nuclear engineering
Nuclear fuel, activation of materials, fission products, wastes
! Fundamental law: (!: decay constant)
! Units of (radio)activity:
Historical.. 1 curie (Ci) = 3.7 x 1010dis/s (activity of 1 gm of Ra226)
Actual.. 1 becquerel (Bq) = 1 dis/s
For example: 1 mCi = 10-3Ci = 3.7 x 107Bq = 37 MBq
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Introduction.. 9
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Radioactivity Calculations-2
! By integration of
! Half-Life : time for N(t) or A(t) to become half initial value
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Introduction.. 10
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Nuclear Reactions-1
! Radioactivity, particular example of a nuclear reaction
Single reactant (cf. chemical dissociation)
! In general, X1 + X2 ! X3 + X4
Number of nucleons remains constant
Electric charge remains the same
! One sees this in the example of 2He4+ 4Be
9"6C12+ 0n
1
! Reaction used for laboratory sources of neutrons, e.g. Ra-Be, Pu-Be,
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Introduction.. 11
Laboratory for Reactor Physics and Systems Behaviour
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Nuclear Reactions-2
! Energy balance of reaction depends on binding energy of the nucleons
on mass defects ("m) of the individual nuclei
!
Mass of nucleus (bound nucleons) < Sum of masses of isolated nucleons
Mass defect: "m (X) = Z.mp + (A-Z).mn - mX
! Binding energy: Eb = "m.c2 (Einstein)
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Introduction.. 12
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Atomic Mass, Mass Defect, Binding Energy
! Eb/A, measure of force between nucleons
!
Sharp increase at low A value, broad
maximum at ~ A=50
! Reactions which result in a shift towards
the broad maximum Eb , #m increase (products more stable) Energy released (reaction: exoenergetic)
! Two possibilities:
Fusionof light nuclei, e.g.
1H2+ 1H
2! 1H
3+ 1H1
Fissionof a heavy nucleus, e.g.
92U235+ 0n
1! 2 F.P. + (2 to 3) 0n
1
Binding energy / nucleon
!fission
"
fusion
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Introduction.. 13
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Reaction Energy-1
! For fission (from the figure):
Eb/A $ 7.5 MeV/nucleon for 92U235
$ 8.4 MeV/nucleon for the FPs
Increase in Eb/A $ 0.9 MeV/nucleon
Release energy $ 0.9 x 235 ! 210 MeV
! In general, for a reaction X1 + X2 ! X3 + X4
Energy of reaction : Q = (Eb)3 + (Eb)4 - (Eb)1 - (Eb)2
= (#m.c2)3 + (#m.c2)4 - (#m.c
2)1 - (#m.c2)2
= (m1 + m2 - m3 - m4).c2
!fission
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Introduction.. 14
Laboratory for Reactor Physics and Systems Behaviour
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Reaction Energy-2
! Energy / mass equivalence : 1 amu $1.66.10-24g x (3.1010cm/s)2
= 1.492.10-3erg = 931 MeV
!Q = (m1 + m2 - m3 - m4).c
2
= 931. (m1 + m2 - m3- m4) MeV
! Example : 1H2+ 1H
2! 1H
3+ 1H1 ... (d,d) fusion reaction..
Q = 931. (2.0141 + 2.0141 3.0166 1.0073) MeV
$ 4.0 MeV
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Introduction.. 15
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Ex. 1
What is the mass of U235fissionedper day in a nuclear reactor operating at a power of
1000 MWth?
(Take energy liberated per fission, Ef"210 MeV)
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Ex. 1... Solution
Energy liberated per day = (1000.106 J/s) . (24 . 3600 s) = 8.64.1013J
Energy per fission of a U235nucleus = 210 MeV = 210.106 . 1.6.10-19J = 3.36. 0-11J
No. of nuclei fissioned per day = (8.64.1013) (3.36.10-11) = 2.57.1024
Mass of U235fissioned per day = (2.57.1024) . (235 g NA)
= (6.04.1026) (6.023.1023) $1 kg
NB: The quantity of oil needed would be"
2000 t !
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Introduction.. 17
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Nuclear Power Plants
Flux of Particles, Interaction Rate
! Fission, fusion are exoenergetic What is their probability of occurrence?
! Monoenergetic particle beam & a target Density of particles in beam = n (cm-3)
Intensity (flux, cm-2 s-1),I = n v
(v : velocity, cm s-1)
! Total interaction rate with nuclei in target
R %I N V = &I N V (V : volume of target, cm3)
! &: cross-section, probability of interaction Depends on type, particle energy Pro target nucleus, r = &I (&: microscopic c-s)
!
Pro cm3 of target, R = &NI = 'I
(': macroscopic cross-section)
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Introduction.. 18
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Cross-sections: Dimensions, Units
!&: dimensions of an area (cm2)
r (per nucleus, s-1) = &(cm2) . I (cm-2 s-1)
Effective area offered by the nucleus for the interaction-type involved
Unit : 1 barn (b) = 10-24 cm2
!
Values vary $from hundreds of barns to a few millibarns (mb)
! For ' (&N), dimensions: cm-1
R (cm-3 s-1) = '(cm-1) . I (cm-2 s-1)
!
': effectively the probability of interaction as particle traverses 1 cm of target
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Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Types of Interactions
! Scattering
The particle is deviated
The target nucleus:
Does not change (elastic scattering))
Is excited (inelastic scattering)
!
Absorption
The particle is absorbed by the nucleus, the products are new, e.g.
Radiative capture: ZXA+ 0n
1"ZXA+1+ (
Fission, a special case:
92U235+
0n1
!
2 F.P. + (2 to 3)
0n1
Other types (less important):
(n,2n), (n,3n), (n,#),
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Laboratory for Reactor Physics and Systems Behaviour
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Cross-section Notations
!
Scattering: &s
!Absorption: &a &a = &f+ &c (fission, capture)
! Total cross-section: &t &t = &s + &a = &s+ &f+ &c
! Macroscopic cross-sections : 't= N&t , 'a= N&a , 'f= N&f , etc.
! For a mixture of nuclei: 't= , etc.Nj "t( ) j[ ]j
#
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Ex. 2
!A beam of 1 MeV neutrons, with an intensity of 5108ncm-2s!1strikes a
carbon target ( "100% C12, density "1.6 g/ cm3). The surface area of the target
is 0.5 cm2and its thickness is 0.05 cm. The beam has a cross-sectional area of
0.1 cm2. For 1 MeV neutrons, the total cross-section of C12is 2.6 b.
(a) Calculate #t for the target
(a) What is the macroscopic interaction rate of the neutrons with the target?
(b) What is the number of interactions per second in the target?
(b) What is the probability that a neutron will suffer a collision while traversing thetarget?
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Introduction.. 22
Laboratory for Reactor Physics and Systems Behaviour
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Ex. 2 Solution
(a) %t = &t N = (2.610-24 )
[1.6(6.0231023)/ 12]
= 2.610-24[8.031022] = 0.209 cm-1
(b) Rt = %t'= 0.2095108= 1.04108 cm-3s-1
(c) No. of interactions = RtVolume
=1.04108[0.10.05] = 5.2105 s-1
(d)Probability of interaction = (5.2105 s-1) / (No. of neutrons incident per s)
= (5.2105) / [(5108)0.1] = 1.0410-2 (only $1%)
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Introduction.. 23
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, Functions of Energie, e.g.
! &(U235) )as neutron energy *
No resistance from electrostatic field
of the nucleus
!
Neutrons slowed down in a reactor(use of a moderator)
! Lowest energy possible: ns in thermal
equilibrium with moderator atoms:
Eth$0.0235 eV at 20C
+ &f$600 b!
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Introduction.. 24
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Fission, Fusion Differences
! For fusion reactionse.g. (d,t): 1H
2+ 1H3"2He
4+ 0n1 (d,d): 1H
2+ 1H2"1H
3+ 1H1
&= 0 for E Eth)
! Scattering, a big help in fission (slowing down), great disadvantage in fusion
! Solution: have a thermal equilibrium with Eth >Es ($10 keV "108 K !)
The ionised medium needs to be heated tremendously (plasma)
"Thermonuclear fusion still a great technological challenge!
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Introduction.. 25
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Fission: History - 1
! Following the discovery of the neutron
Fermi studied the activation of the elements (neutron capture)
ZXA + 0n
1!ZXA+1!(,--decay)! Z+1Y
A+1 + ( artificial radioactivity
each time, one observed a transmutation
occurred more easily if the neutron was first slowed down
! With U (Z = 92), one expected to create transuranics (Z = 93, 94,)
Instead, one (initially) found nuclei of intermediate mass (e.g. Ba, Z = 56)
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Introduction.. 26
Laboratory for Reactor Physics and Systems Behaviour
Nuclear Power Plants
Fission: History - 2
! Otto Hahn and Fritz Strassmann provided the explanation (1939)
The U235 nucleus can be split into 2 fragments (discovery of fission)
92U235 + 0n
1!2 FPs + . 0n1+ 207 MeV
The emission of , i.e. $2.5, neutrons
gave the possibility of a chain reaction
Neutron excess "related to shape of
the Z-vs.-N curve of the nuclide chart !
"
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Introduction.. 27
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Nuclear Power Plants
Fission Products - 1
!
Asymmetric splitting, more probable
! Considering FPs from 100 fissions
Yield y(A), with Sum [y(Ai)]= 200
y(A) vs. A: double-hump curve
Most probable, FPs with Ai$94, 140
e.g. 92U235
+ 0n1!
38Sr94
+ 54Xe140
+ 2 0n1
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Introduction.. 28
Laboratory for Reactor Physics and Systems Behaviour
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Fission Products - 2
! The FPs are unstable (excess of ns)
,--radioactivity (increases Z/N), e.g.
54Xe140!(16s) 55Cs
140!(66s) 56Ba140!(12.8d) 57La
140!(40h) 58Ce140 (stable)
! Radioactivity of FPs problematic
Radiation protection (irradiated fuel)
Residual heat after reactor shutdown
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Introduction.. 29
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Fission Neutrons-1
! neutrons created per fission (number varies between $0 and 5, per event)
Average value $ 2.4 to 2.9
! Energy of the fission neutrons varies Spectrum -(E)
"
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Introduction.. 30
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Fission Neutrons-2
! E for -max $0.75 MeV
! Eaverage:
!
Slowing down factor in a thermal reactor > 107
! ($2 MeV to 0.0253 eV)
Moderators needed (light nuclei: H2O, graphite,)
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Introduction.. 31
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Chain Reaction
! If each absorption were useful
+Reaction strongly divergent
! In practice, certain neutrons are lost
+Captures, Leakage! For a self-sustaining reaction (static neutron flux)
Productions = Losses = Absorptions + Leakage
(criticality condition)
! For a supercritical system, the neutron flux increases exponentially
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Introduction.. 32
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Nuclear Power Plants
Control of the Chain Reaction Delayed Neutrons
!
Small fraction of the neutrons, not prompt (~ 0.6% for U235)
Produced by disintegration of FPs, e.g.
! Many different precursors
~ 6 groups (of precursors, i.e. of delayed neutrons), Ti: 0.2 56 s
! Population of delayed neutrons, rather limited (~ 0.6%), bit indispensable for control
of the chain reaction
+ Response of a reactor which becomes slightly supercritical, much slower
created (
with delay
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Fission Energy
! Most, absorbed in the fuel
~ 180 to 190 MeV (FPs, ,-s, part of (s ), in
form of heat (recovered by coolant)
!
Following reactor shutdown
Component FP-radioactivity remains
~ 7% immediately after shutdown
Slow decrease
~ 1% after 1 day
(Very important factor for nuclear safety)
Components Energy
(MeV)
FPs 168
ns 5
(s 7
FP-radioactivity (,-, () 15
Neutrinos (non-interacting) 12
TOTAL ~ 207
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Nuclear Power Plants
Summary, Week 1
! Nucleus: protons + neutrons (atomic number Z, atomic mass A)
! Radioactivity, specific type of nuclear reaction (spontaneous disintegration)
!
Energy in a nuclear reaction: linked to binding energies (mass defects) of reactants
- Fission, fusion: movement towards the large maximum of the BE-curve
! Different types of reactions: absorption (fission, capture,), scattering
!
Reaction rate = Flux x Cross-section (microscopic, macroscopic)
!
Fission discovered relatively soon after discovery of neutron
!
On average, (2 to 3) ns emitted per fission chain reaction rendered possible
!
Small fraction of neutrons delayed: crucial for reactor control
!
Most of fission energy deposited in fuel (as heat)
"