Page 40 - Dynamics and Control of Nuclear Reactors

3.9 Fluid-fuel reactors 31

of other concepts and interest in simulating them disappeared. Now, the molten
salt reactor, a fluid-fuel reactor, is under consideration for possible implementation
as a Generation IV reactor. Since fluid-fuelreactorsareafuturepossibility and
because they require a different form of reactor kinetics equations, they are
discussed here.
For dynamic characteristics, the important distinction between solid-fuel reactors
and fluid-fuel reactors is the treatment and consequence of delayed neutron behavior
[3, 4]. In a solid fuel reactor, the delayed neutron precursors stay in place until they
release a neutron. In fluid-fuel reactors, the fuel is dissolved in a solvent that carries
the fuel through the reactor core, then through an external loop where heat is
extracted before returning to the core. The delayed neutron precursors are created
in the core, but they emit neutrons while in the core and while in the external loop.
This reduces the delayed neutron contribution to the neutron population in the core.
Thus, transients depend more on fission neutrons than delayed neutrons compared to
a solid-fuel reactor.
Because of the circulation effect on delayed neutrons, the point kinetics equations
must be modified as follows:

6
dP tðÞ ð ρ βÞ X
¼ PtðÞ + λ i C Ci (3.39)
dt Λ
1
β C Ci t τ L Þe λ i τ L
dC Ci i C Ci ð
¼ PtðÞ λ i C Ci + (3.40)
dt Λ τ C τ C
where the new terms are

C Ci ¼the i-th precursor concentration in the core
τ c ¼fluid residence time in the core
τ L ¼fluid residence time in the external loop
Solving this set of equations requires special attention to the initial conditions. For
steady state, offset reactivity must be added to compensate for the effect of losing
delayed neutrons during out-of-core decays. The offset reactivity for steady state
is given by.
6
X β i
ρ ¼ β (3.41)
T
0
i¼1 1+ 1 1 e λ i τ L
λ i τ c
For example, a U-235 fueled fluid fuel reactor with a core residence time of 8.46s
and an external loop residence time of 16.73s has an offset reactivity of 0.00247.
This is the reactivity that must be added (as by withdrawal of control rods) to
maintain steady state when flow begins. Of course, this rather large reactivity is
introduced if flow stops.
Further discussion of molten-salt reactor dynamics is presented in Appendix K.