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Nuclear Reactors
Nuclear Reactors
• Multiplication Factor k
• k=
•
•
•
•
= 1 ⇒ > 1 ⇒ < 1 ⇒ "
To adjust the value of k, it is necessary to balance
the rate at which neutrons are produced with the
rate at which they disappear.
• Multiplication Factor k
• Neutron production is from fission
• Neutron losses
– Absorption
– Leakage
If 2.42 n are produced per fission, then for critical
operation 1 fission must result and 1.42 n must be
lost to leakage or absorption.
Nuclear Reactors
Nuclear Reactors
Nuclear Reactor Fuels
Recall :
• ν = yield = avg. # of neutrons produced per fission
= 2.418 for U-235.
#
• η = effective yield per absorption = #$ ν
%
avg. # of neutrons produced per absorption.
= 2.14 for U-235.
In order to produce a satisfactory operating reactor,
we require a fuel for which η > 1.
Nuclear Reactor Fuels
• All fissile nuclides have η > 1 at all incident n
energies.
• All fissionable (non-fissile) nuclides have η > 1 for
n above the fission threshold, however the
fraction of all neutrons absorbed with energies
above the threshold is always < 1.
• Thus reactors can NOT be made critical with nonfissile material alone.
• Fissile nuclide are therefore essential ingredients
in all reactor fuels.
Nuclear Reactors
Nuclear Reactor Fuels
• Only 1 fissile nuclide is found in nature! U-235
• Fortunately, it is possible to manufacture certain
fissile isotopes from abundant non-fissile material
in a process known as conversion.
Three basic types of Reactor Cores
• Burners: Reactors that consume fuel w/o
conversion or breeding.
• Converters: Reactors that convert fuel to fissile
isotopes which are consumed as fuel.
• Breeders: Reactors that convert fuel to fissile
isotopes in excess of that consumed as fuel.
Nuclear Reactors
Conversion / Breeding Process
• The two most important fissile isotopes are U-235
and Pu-239.
• U-235 is found in nature.
• Pu-239 is produced from U-238
+,-&
)
/0
/0
+ ( → +,.& +,.1 +,.2
The fertile isotope is U-238 must be irradiated in a
nuclear reactor.
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Nuclear Reactors
Conversion / Breeding Process
Most currently designed power reactors are fueled with U
that is mostly U 238 and only slightly enriched with U 235.
Therefore, the conversion of U-238 to Pu-239 takes place
as a matter of course during the normal operation of
these reactors.
After Pu-239 has been formed in a reactor it may
1. Fission or absorb a neutron and form Pu-240 (not
fissile)
2. Pu-240 can absorb another neutron to form Pu-241
(fissile)
3. Pu-241 can fission or transform to stable Pu-242
The resulting Pu {239, 240, 241 , 242 in decreasing
amounts} can be later extracted from the fuel or
reprocessed.
Nuclear Reactors
Breeders
When more than one fissile atom is produced for
every fissile atom consumed, the process is called
breeding.
Reactors that are designed to breed are called
breeder reactors or breeders.
In addition to producing power, breeders produce
more fissile material than they consume.
Breeders are designed to have η > 2. Therefore 1
neutron must cause a fission, and at least 1 neutron
must be absorbed in the fertile material to produce
the new fissile isotope.
Nuclear Reactors
Nuclear Fuel Performance
1. Burn –Up The total energy released in fission by a
given amount of nuclear fuel.
Measured in Mega Watt days (MWd)
2. Specific Burn- Up burn -up per unit mass.
This is measured in MWd/Kg or MWd/ton.
3. Recall that the fission of 1.05 g of U-235 yields 1
MWd, thus the specific burn-up of U-235 is
1@AB 10004
=
= 950@AB/D4
1.054
1D4
Nuclear Reactors
Ex… A reactor is fueled with natural U. If for every
neutron absorbed in U-235, 0.254 neutrons are
absorbed in resonances of U-238, and 0.640 neutrons
are absorbed by U-238 at thermal energies.
A. Assume no leakage of neutrons, what is the
conversion ratio for the reactor?
# of Pu-239 produced per U-235 =
= 0.254 + 0.640 = 0.894 = conversion ratio
B. How much Pu-239 is produced when 1 kg of U-235
is consumed?
10004&
56 8.-.:
;
+,./
?
x
= /
?
+,7
<
56
=
= (1000g)(0.894)(239/235) = 0.909 kg of Pu-239
Nuclear Reactors
Breeders
Of the three fissile isotopes U-233, U-235 and Pu-239,
only U-233 has η sufficiently large (~2.29) to breed in
a thermal neutron flux.
However, at higher neutron energies > 100KeV, η rises
sharply in all three isotopes, and therefore it is
possible to design Fast Neutron Breeder Reactors.
e.g. Fast Breeders
Nuclear Reactors
Nuclear Fuel Performance
4. Fractional burn-up measure of the number of
fissions that have occurred in a specified mass of fuel.
#
β = ?#
?
-------------------------------------------------------------Ex… A reactor has 98 tons of UO2 fuel and the U is
enriched to 3 w/o U-235. If the reactor operates at
3300MW for 750 days.
a. What is the burn-up?
Burn- up = 3300 x 750 = 2.48 x 10 6 MWd of energy
released.
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Nuclear Reactors
Nuclear Fuel Performance
b. What is the specific burn up?
1. M(U-238 3 w/o U235) ~= 238 g
2. Of the 98t of UO2, 98=
3. Specific burn-up =
+,+,-H+(JK)
+.:-OJ8P QRS
-K.:
= 86.4&
= 28,700 MWd/ton
c. What is the Fractional burn-up?
T = WXYZ
W.[\]
+-,V88QRS/
O
W[P ]
_.78,888Q`S/
^
= 3.02%
4. Why is β > 3.0 %, if 3 w/o is U-235?
Because some U-238, and Pu will also fission.
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