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Reactor Theory (Nuclear Parameters)
DOE-HDBK-1019/2-93
NEUTRON LIFE CYCLE
An equation can be developed for the thermal utilization factor in terms of reaction rates as
follows.
f
rate of absorption of thermal neutrons by the fuel
rate of absorption of thermal neutrons by all reactor materials
f
S
U
a
fUVU
S
U
a
fUVU S
m
a
fmVm S
p
a
fpVp
The superscripts U, m, and p refer to uranium, moderator, and poison, respectively. In a
heterogeneous reactor, the flux will be different in the fuel region than in the moderator region
due to the high absorption rate by the fuel. Also, the volumes of fuel, moderator, and poisons
will be different. Although not shown in the above equation, other non-fuel materials, such as
core construction materials, may absorb neutrons in a heterogeneous reactor. These other
materials are often lumped together with the superscript designation OS, for "other stuff." To
be completely accurate, the above equation for the thermal utilization factor should include all
neutron-absorbing reactor materials when dealing with heterogeneous reactors. However, for the
purposes of this text, the above equation is satisfactory.
In a homogeneous reactor the neutron flux seen by the fuel, moderator, and poisons will be the
same. Also, since they are spread throughout the reactor, they all occupy the same volume. This
allows the previous equation to be rewritten as shown below.
(3-1)
f
S
U
a
S
U
a
S
m
a
S
p
a
Equation (3-1) gives an approximation for a heterogeneous reactor if the fuel and moderator are
composed of small elements distributed uniformly throughout the reactor.
Since absorption cross sections vary with temperature, it would appear that the thermal
utilization factor would vary with a temperature change. But, substitution of the temperature
correction formulas (see Module 2) in the above equation will reveal that all terms change by
the same amount, and the ratio remains the same. In heterogeneous water-moderated reactors,
there is another important factor. When the temperature rises, the water moderator expands, and
a significant amount of it will be forced out of the reactor core. This means that Nm, the number
of moderator atoms per cm3, will be reduced, making it less likely for a neutron to be absorbed
by a moderator atom. This reduction in Nm results in an increase in thermal utilization as
moderator temperature increases because a neutron now has a better chance of hitting a fuel atom.
Because of this effect, the temperature coefficient for the thermal utilization factor is positive.
The amount of enrichment of uranium-235 and the poison concentration will affect the thermal
utilization factor in a similar manner as can be seen from the equation above.
Rev. 0
NP-03
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