# Explaining the Point Reactor Kinetics Equations

October 13, 2014

The point reactor kinetics equations are used in neutronic transient analyses when a fast, simple estimate of transient behavior is needed. However, not all nuclear engineers will ever take nuclear reactor dynamics. To describe the meaning of “point” in the PRKE to a graduate student collaborator today, I gave the following explanation in words (no equations).

# PRKE (without the math)

The point reactor kinetics equations assume a nueutron flux shape through the reactor. In this way, the dimensionality of the problem is reduced to a “point”. However, that point is not “the middle of the fuel pebble.” It is not anywhere, geometrically. The point simply refers to the magnitude of that assumed flux shape, (and therefore the magnitude of the reactor power).

The many partial differential equations that result can most simply and loosely be solved in two blocks. There is the neutronics block, which assumes a point reactor, as I have just discussed. There is also the thermal hydraulics block which captures the effect of the power generation on the temperatures in the materials. The neutronics block determines the power based on the reactivity in the reactor.

The reactivity calculation, however, relies on the temperature of each component. So, the thermal hydraulics block must calculate the those temperatures based on the most recent calculation of the power. The thermal hydraulics calculation can be conducted to any detail that is desired, however, the power distribution is not specified, so the standard way is to do it with a 0-D model like the lumped capacitance model (in which each component is treated as a lump.) The neutronics block in the point reactor kinetics equations solves for the total reactor power, so, in the thermal model, that power should be evenly distributed everywhere there is fuel. That is, it should be treated as if it is in the “fuel” lump of the lumped capacitance model.