Page 114 - Dynamics and Control of Nuclear Reactors

108 CHAPTER 9 Space-time kinetics

9.4 Calculation requirements
Planning and operating a nuclear power reactor requires a detailed knowledge of the
spatial neutron flux and reaction rates. Both steady-state and transient analyses are
required. Enumerating the conditions to be analyzed and the information needed for
performing the analyses illustrates the enormity of the problem.
A typical light water reactor contains as many as 40,000 or more individual fuel
rods. As the reactor operates, the composition of the rods changes significantly.
Operation depletes fissile material, produces new fissile material, produces fission
products, and produces actinides. The concentrations of all of these materials depend
on neutron flux at all positions during prior reactor operation. The flux depends on
the localized isotopic concentrations, history of power generation, and history of
control rod positions. The fuel rods typically stay in the reactor for four years in light
water reactors and are moved during refueling. It is necessary to calculate the local
isotope concentrations before a new neutron diffusion calculation of the new flux
distribution can begin. The nuclear cross sections of all of the isotopes must be
known because they influence the neutron population and must be addressed in a
detailed analysis. It is clear that the analyst must know the concentrations of hun-
dreds of isotopes at hundreds of positions.
Reactivity feedback must be addressed along with neutron diffusion in a power
reactor space-time analysis. Space-dependent feedbacks occur simultaneously with
space-dependent power changes and these feedbacks alter the power distribution.
Therefore, a comprehensive simulation would require modeling the feedback pro-
cesses simultaneously with the neutronics.

9.5 Computer software
Powerful software provides computational capability for reactor analysis using
Boltzmann transport theory or neutron diffusion theory. The elementary theory pre-
sented above serves to help understand the phenomena that occur in a reactor rather
than to provide a basis for practical computations. But users of the available software
must understand the underlying phenomena for proper interpretation of computed
results.

9.6 Models and computational methods
Space-time models usually rely on the multi-group neutron diffusion equations.
Independent variables include time, group energies, and one to three position coor-
dinates. Various methods have been developed to solve the equations. These
methods include the following: