Applicability of Diffusion Theory
Nowadays the diffusion theory is widely used in core design of the current Pressurized Water Reactors (PWRs) or Boiling Water Reactors (BWRs). It provides a strictly valid mathematical description of the neutron flux, but it must be emphasized that the diffusion equation (in fact the Fick’s law) was derived under the following assumptions:
- Infinite medium
- No sources or sinks.
- Uniform medium.
- Isotropic scattering.
- Low absorbing medium.
- Time – independent flux.
To some extent, these limitations are valid in every practical reactor. Nevertheless the diffusion theory gives a reasonable approximation and makes accurate predictions. Nowadays reactor core analyses and design are often performed using nodal two-group diffusion methods. These methods are based on pre-computed assembly homogenized cross-sections, diffusion coefficients and assembly discontinuity factors (pin factors) obtained by single assembly calculation with reflective boundary conditions (infinite lattice). Highly absorbing control elements are represented by effective diffusion theory cross-sections which reproduce transport theory absorption rates. These pre-computed data (discontinuity factors, homogenized cross-sections, etc.) are calculated by neutron trasport codes which are based on a more accurate neutron transport theory. In short, neutron transport theory is used to make diffusion theory work.
Two methods exist for calculation of the pre-computed assembly cross-sections and pin factors.
- Deterministic methods that solve the Boltzmann transport equation.
- Stochastic methods that are known as Monte Carlo methods that model the problem almost exactly.
These methods are very efficient and accurate when applied to the current Pressurized Water Reactors (PWRs) or Boiling Water Reactors (BWRs).