Evolution of Lattice Properties

1
Evolution of Lattice Properties

• B. Rouben
• McMaster University
• Course EP 6D03 Nuclear Reactor Analysis
• (Reactor Physics)
• 2009 Jan.-Apr.

2
Contents

• We study the evolution of nuclear properties with
  irradiation or burnup in CANDU reactors .

3
Fuel Depletion

• When nuclear fuel is burned in a reactor,
  changes occur in the fuel. These changes go
  under the general name of fuel (isotopic)
  depletion.
• Here we shall look at the changes which happen in
  the standard CANDU lattice, and at the
  quantitative changes in the reactivity and other
  nuclear properties of the lattice.
• Although we are looking specifically at the
  standard CANDU, a similar analysis needs to be
  done for any reactor which needs to be studied.
• 
  
  

4
Changes in Fuel with Irradiation/Burnup

• The following changes occur cumulatively in
  CANDU nuclear fuel with time
• The U-235 depletes (i.e., its concentration,
  which starts at 0.72 atom for fresh natural
  uranium, decreases)
• Fission products accumulate most of these are
  radioactive, and many have a significant
  neutron-absorption cross section
• Pu-239 is produced via neutron absorption in
  U-238 and two beta decays
• 238U n ? 239U ? 239Np ?
• 239Np ? 239Pu ?

5
Changes in Fuel with Irradiation/Burnup (cont.)

• Pu-239 participates in the fission chain reaction
  ? while it keeps being created at about the same
  rate from U-238, its net rate of increase slows.
• Further neutron absorptions lead from Pu-239 to
  Pu-240 (non-fissile), then Pu-241 (fissile)
• Other higher actinides are also formed (e.g.,
  curium, americium)
• The total fissile fraction in the fuel
  (U-235Pu-239Pu-241) decreases monotonically.

6
Fuel Irradiation and Burnup

• Two new reactor-physics concepts, on which we
  have not really focused up to now, have to do
  with the evolution in time of the fuel.
• These 2 concepts are those of fuel irradiation
  and burnup, and are very important.
• These concepts are related because, in a way,
  they are both a measure of the age of the fuel
  in the reactor.

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Fuel Irradiation

• Fuel irradiation, usually denoted ?, is the
  product of flux and time or, more precisely, the
  integral of neutron flux with time
• Therefore fuel irradiation starts at 0 when fresh
  fuel enters the reactor, and cumulates with time,
  depending on the magnitude of the neutron flux.
• From Eq. (1), we can see that the units of
  irradiation are those of flux times time, e.g.,
  (n.cm-2.s-2)s ? n.cm-2 ? n/cm2.
• Because there can be many different fluxes (e.g.,
  thermal flux, fast-neutron flux, total flux,
  etc.), the concept of irradiation is not
  absolute, but depends on the definition of the
  flux.
• Irradiation is also called exposure or fluence.

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Fuel Burnup

• The concept of fuel burnup bears an inappropriate
  name, because it does not have to do directly
  with the burning up of the fuel.
• Fuel burnup is defined as the fission energy
  produced by the fuel since its entry into the
  reactor per unit mass of uranium in the
  (original) fuel (or of heavy element, if the
  original fuel contains other fissionable
  elements).
• Since the fuel keeps releasing fission energy
  with time, it is clear that fuel burnup is also a
  measure of the age of the fuel in the reactor.
  Just like irradiation, fuel burnup starts at 0
  and cumulates with time, depending on its power
  level.
• Fuel burnup is reported in units such as
  MW.d/Mg(U) or MW.h/kg(U).
• Because energy is an absolute quantity (as
  opposed to flux), fuel burnup does not depend on
  the definition of the neutron flux.

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Interactive Discussion/Exercise

• If the fuel burnup is 180 MW.h/kg(U), what is it
  in the units of MW.d/Mg(U)?
• What is it in kW.d/kg(U)?
• If you are confused in a computation, and use
  electric energy instead of fission energy in
  calculating fuel burnup, how far (by what factor)
  off will you be?

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Evolution of Isotopic Densities of Fuel Nuclides
Note The irradiation scale is that of the
POWDERPUFS-V Code
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Relationship Between Irradiation and Burnup

• Note Irradiation scale is that of POWDERPUFS-V

12
Infinite Lattice

• CANDU basic cell ?
• Lattice (or cell) codes also calculate the
  nuclear properties (including the reactivity) of
  the infinite lattice, which consists of an
  infinite array of identical cells in all
  directions.
• POWDERPUFS-V is a lattice code for CANDU.

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Reactivity ?? of Infinite Lattice
Note Irradiation scale is that of POWDERPUFS-V
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Reactivity ?? of Infinite Lattice

• The following should be noted from the graph of
  ?? versus irradiation
• The fresh-fuel infinite lattice (0 irradiation)
  has a very high reactivity (76 mk)
• The reactivity starts to decrease immediately, on
  account of U-235 depletion
• It then starts to increase for a while, on
  account of the production of Pu-239, which is
  slightly more effective than U-235. Note the
  slight delay, due to the Np-239 2-day half-life.
• However the rate of increase of reactivity slows
  (because the net rate of plutonium production
  decreases), and the reactivity comes to a maximum
  at an irradiation of 0.3 n/kb. This is called
  the plutonium peak (note its not a peak in Pu,
  but in reactivity!)
• Following the plutonium peak, the reactivity
  decreases monotonically, on account of the
  continuing depletion of U-235 and the continuing
  accumulation of fission products.
  contd

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Saturating Fission Products

• Note that some of the fission products are called
  saturating fission products (sfp).
• This label is used because the concentration of
  these fission products does not keep increasing,
  but instead comes (relatively) quickly to an
  equilibrium value as long as the power is
  constant i.e., the rate of production of the sfp
  is equal to its decay.
• Note however that the sfps concentration may
  vary very significantly following changes in
  power!
• The most important sfp is 135Xe, because it has a
  very high absorption cross section it
  contributes -28 mk in CANDU at full power.
  Other sfps (of secondary importance) are 149Sm,
  151Sm, and isotopes of Rh, Gd, and Eu.

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Neutron Balance in CANDU6 Equilibrium Core

•  It is instructive to quantify the various events
  in the neutron cycle taking place in the nuclear
  lattice.
• The figure in the next slide gives the
  approximate rates of production and absorption of
  neutrons via various pathways in the
  equilibrium, or time-average CANDU-6 reactor
  core (normalized to an arbitrary 1000 fission
  neutrons born).

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Production
56.5 Neutrons From U238 Fast Fission
491.9 Neutrons From U235 Thermal Fission
438.4 Neutrons From Pu239 Thermal Fission
13.2 Neutrons From Pu241 Thermal Fission
Total 1000 Neutrons
Fast Leakage
Fast Absorp. In Fuel
6.0 Neutrons
31.7 Neutrons
Resonance Absorp. in U238
Slowing Down
89.4 Neutrons
Thermal Leakage
Thermal Absorption
23.0 Neutrons
849.9 Neutrons
Thermal Absorp. In Fuel
Thermal Absorption In
Non Fuel Components
242.5 Neutrons In U235
14.4 Neutrons In Moderator
238.2 Neutrons In U238
0.3 Neutrons In Coolant
228.1 Neutrons In Pu239

19.0 Neutrons In PT
15.6 Neutrons In Pu240
8.5 Neutrons In CT
6.2 Neutrons In Pu241
6.2 Neutrons In Sheath
0.1 Neutrons In Pu242

15.0 Neutrons In Adjusters
0.6 Neutrons In Np
Zone Controllers and
7.7 Neutrons In Sm"
Parasitic Absorbers
25.2 Neutrons In Xe
2.6 Neutrons In Rh"
Total 63.4 Neutrons
Notes
19.9 Neutrons In PFP
Fast group denotes 10 MeV gt E gt 100 keV
Total 786.5 Neutrons
Resonance group denotes 100 keV gt E gt 10 eV
Thermal group denotes sum of

Thermal group E lt 0.625 eV and
Epithermal group 10 eV gt E gt 0.625 eV
Neutron Balance in the CANDU-6 Equilibrium Core
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Interactive Discussion/Exercise

• What fraction of neutrons suffer absorption in
  U-238 in the resonance region?
• What total fraction of neutrons is absorbed in
  U-238? How does the absorption in the
  heavy-water moderator compare to this?
• What fraction of fissions are induced by fast
  neutrons?
• What fraction of fission neutrons originate in
  plutonium fissions?
• What is the total leakage (in or mk)?

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Neutron-Cycle Statistics

• 8.5 of neutrons are absorbed in U-238
  resonances
• 35 of neutrons are absorbed in U-238 this is
  about 6 times as many as the absorptions in the
  heavy-water moderator. Most of the absorptions
  in U-238 lead to the production of Pu-239
• Only 5 of fissions are induced by fast neutrons
• 45 of fission neutrons originate in plutonium
  fissions (and therefore plutonium is the source
  of 45 of the energy released over the lifetime
  of the fuel)
• The total leakage of neutrons is 3 (i.e., -30
  mk).

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Back to Reactivity ?? of Infinite Lattice )

• On the reactivity curve several slides back,
  note also
• When all fuel is fresh, a significant amount of
  negative reactivity must be added to the lattice
  to suppress the initial supercriticality.
• The infinite lattice reaches zero reactivity at
  an irradiation of 1.6 n/kb, corresponding to a
  burnup of 6,700 MW.d/Mg(U).
• A homogeneous infinite lattice with fuel beyond
  that burnup would be subcritical.
• However, remember that the infinite lattice does
  not have leakage also, it does not account for
  neutron absorption in all the reactivity devices
  within the core.
• Consequently, a homogeneous reactor with all fuel
  at the same irradiation would reach zero
  reactivity at a much lower burnup.

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The Yield and Thermal Absorption Cross Sections

• The two cross sections which vary most with
  irradiation, and therefore give the reactivity
  curve its shape, are the yield cross section
  (??f2) and the thermal absorption cross section
  (?a2)

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Other Cross Sections (Almost Constant)

• The downscattering cross section and the fast
  absorption cross section are almost constant with
  irradiation (because the U-238 and D2O
  concentrations are almost unchanged). Therefore
  they do not contribute to the reactivity curves
  shape

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Reactivity ?eff of Homogeneous Finite Reactor

• In the CANDU-6 reactor
• Leakage is about -30 mk.
• The average reactivity-device load is -18 mk.
• Therefore we can get an estimate of the
  reactivity of a homogeneous CANDU-6 reactor by
  subtracting 48 mk from the reactivity of the
  infinite lattice.
• This subtraction gives the curve in the next
  slide.

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Reactivity ?eff of Homogeneous CANDU-6 Reactor
Note Irradiation scale is that of POWDERPUFS-V
25
Reactivity ?eff of Homogeneous CANDU-6 Reactor

• Note also
• When all fuel is fresh, we need to add a
  significant amount of negative reactivity to the
  reactor to suppress the initial supercriticality.
• It looks as if the homogeneous CANDU-6 would
  reach zero reactivity at an irradiation of 1.0
  n/kb, corresponding to a burnup of 4,000
  MW.d/Mg(U).
• A homogeneous CANDU-6 with fuel beyond that
  burnup would be subcritical.

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The Real CANDU-6 Reactor

• Note however
• Real reactors are not homogeneous, except at the
  very start of life because the neutron flux
  varies with position, and so the fuel at
  different positions in core cumulates burnup at
  different rates.
• In addition, CANDU reactors are refuelled
  on-line, so there is always (except near start of
  life) a mixture of fresh fuel and fuel with high
  irradiation.
• The fuel with high irradiation has negative
  local reactivity, but this is compensated by
  the positive local reactivity of young fuel.
• The proper mixture of fuel in this inhomogeneous
  reactor (i.e., the rate of refuelling) gives a
  critical reactor!
  contd

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Interactive Discussion/Exercise

• How would you estimate the maximum fuel burnup in
  a mixture of burnups that would give a critical
  reactor?
• Explain.

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The Real CANDU-6 Reactor (contd)

• The mixture of new and old fuel allows us to
  drive the discharge irradiation (and therefore,
  burnup) to a much higher value than might be
  guessed from the homogeneous reactivity curve
  of 3 slides back (i.e., much higher than 1.0
  n/kb)
• We can guess (or calculate) approximately how far
  we can drive the exit irradiation by determining
  what value of irradiation gives equal positive
  and negative areas under the irradiation
  curve this tells us where the average ?eff would
  be 0.

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The Real CANDU-6 Reactor (contd)
Mixture of fuel with on-line refuelling
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The Real CANDU-6 Reactor (contd)

• From the figure we see that positive and negative
  areas are equal when the fuel goes to an
  irradiation of 1.8 n/kb. This is then the
  average exit irradiation to which we can take the
  fuel because we are refuelling the reactor on an
  on-going basis. This corresponds to an average
  exit burnup of 7,500 MW.d/Mg(U).
• The average discharge irradiation and burnup are
  almost twice (!!) the values (1.0 n/kb and 4,000
  MW.d/Mg(U)) that we could expect if we
  batch-refuelled the reactor, i.e., if we put
  all the fuel in at once.

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The Reactivity Curve

• The reactivity curve which we plotted in the last
  few slides is a typical one for a standard CANDU
  lattice.
• But the actual values on the curve are affected
  by design and operational parameters these
  parameters can move the curve up or down with
  respect to the horizontal axis.
• If the curve is moved up, it will cross the
  horizontal axis further to the right, and the
  positive area under the curve will increase.
  Then we can take the fuel to a higher exit burnup
  (i.e., well have to go further to the right to
  get a negative area equal to the positive
  area).
• And the opposite if the curve is moved down.
  contd

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Interactive Discussion/Exercise

• Name as many factors which can drive the
  reactivity curve up or down as you can.
• Which of these must be decided upon when the
  reactor is designed, and which ones can be
  manipulated as the reactor is operated?

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What Can Move the Reactivity Curve ? or ??

• Some examples (design or operation)
• The purity of the heavy-water moderator
  (operation)
• The thickness of the pressure tubes (design)
• The number and strength (reactivity worth) of
  control rods (design)
• The concentration of moderator poison (operation)
• The size of the lattice pitch (design)
• The size of the reactor related to leakage
  (design)
• The presence of a reflector (design)
• The purity of the coolant (design)
• The exact design of the fuel, e.g., fuel
  enrichment (operation)

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• END