Examination of some approximations for heterogeneous reactors

The approximation inherent in using cell-averaged homogenized cross sections in computations for heterogeneous reactors is investigated for slab reactors by discrete integral transport (DIT) theory. Small, but significant, differences in reactivity and anisotropies in migration area are found. The DIT technique is extended to include an exact asymptotic reactor boundary condition and a separable transverse flux. Approximate solutions are investigated in which a reactor is subdivided into a number of zones with the coupling between zones expressed in terms of the directional currents at the interfaces. The sticking probabilities for these currents are derived from Taylor expansions of the source through linear terms. Generally good results are obtained when the zones correspond with the cells in a reactor.