Three-dimensional neutron diffusion theory within a borehole environment

The flux distribution which arises from an eccentered neutron source within a borehole is an important problem in well logging. Conventional numerical codes are often inadequate to describe this because of statistics (Monte Carlo) or because they are two-dimensional (discrete ordinates transport). In this paper we present an analytical solution for the neutron flux produced by an eccentered source within the borehole environment. We derive expressions for the neutron flux using diffusion theory for three energy groups within three physical regions. We then use this solution to investigate the effects of eccentricity for an idealized neutron logging tool. (author)