Semi-Analytical and Empirical Methods for Local Reactor Reactivity Estimation

Abstract

A computer code has been developed to solve by Chernick's quadrature method the one-dimensional, one-group, non-linear, neutron diffusion equation for a nuclear reactor in order to determine the axial distribution of neutron flux when the latter is assumed symmetrical with respect to the reactor centre-plane, with the reactivity expressible as a function of the neutron flux, with flux-dependent feedback and with significant fissile-fuel depletion. The algorithm of the code is simple and has no instability problems, and the code itself is easy to use, inexpensive to run, and is sufficiently comprehensive for investigating a variety of situations for which no analytical solution appears to exist. In general, the results compare favourably with those produced by a different route by another research group. The code has been used to provide "benchmark" data to test out a number of simplified and empirical procedures for fast treatment of selected potential design cases. One such empirical correlation which has been tested assumes the reactivity to be a quadratic function of the neutron flux. The relevant burnup parameters are assumed to be third-order functions of the basic reactor parameters. These empirical correlations are also easy to use and computer time and cost can be further reduced. The empirical correlations can with advantage be applied both to light-water reactors (LWRs) and to thorium reactors. Examples are given.