Scaled neutron point kinetics (SUNPK) equations for nuclear reactor dynamics: 2D approximation

The aim of this paper is the mathematical derivation of the scaled neutron point kinetics (SUNPK) equations for nuclear reactor dynamics. The SUNPK equations are an extended model respect to classic neutron point kinetics (CNPK). The SUNPK model was derived considering a scaled neutron diffusion equation, whose up-scaled derivation is based on the averaging method considering the nuclear reactor as a porous medium. The SUNPK involves two terms: (1) the neutron leakage interchange at the moderator-fuel interface, related with an integral term on the interfacial area; (2) leakage of the fuel. Definitions in the SUNPK model show that the leakage reactivity is inversely proportional to diffusion area, and it decreases with increasing the moderator volume fraction. The SUNPK model is simple and straightforward for applications in reactor dynamics.