Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell-logging problems

Simulating radiation transport of neutral particles (neutrons and γ‐ray photons) within subsurface formations has been an area of research in the nuclear well‐logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase‐space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite‐difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross‐sectional libraries using a variety of group‐collapsing codes, whilst the nuclear well‐logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well‐logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well‐logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups. We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron–γ energy structure. Although we test our theoretical approaches on nuclear well‐logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and γ‐ray fluxes deterministically for the different group‐collapsing options. The best collapsing option is chosen as the one which minimizes the effect on the γ‐ray spectrum. During this methodology, parallel processing is implemented to reduce computational times. The second approach uses the uncollapsed output from neural network simulations in order to estimate the new, collapsed fluxes for the different collapsing cases. Subsequently, an inversion technique is used which calculates the properties of the subsurface, based on the collapsed fluxes. The best collapsing option is chosen as the one that predicts the subsurface properties with a minimal error. The fundamental difference between the two methodologies relates to their effect on the generated γ‐rays. The first methodology takes the generation of γ‐rays fully into account by solving the transport equation directly. The second methodology assumes that the reduction of the neutron groups has no effect on the γ‐ray fluxes. It does, however, utilize an inversion scheme to predict the subsurface properties reliably, and it looks at the effect of collapsing the neutron groups on these predictions. Although the second procedure is favoured because of (a) the speed with which a solution can be obtained and (b) the application of an inversion scheme, its results need to be validated against a physically more stringent methodology. A comparison of the two methodologies is therefore given.