Borehole nuclear measurements are fundamental for the geosciences in general, and the petroleum industry in particular. They provide a variety of well logs from which petrophysicists estimate in-situ porosity, mineral/ fluid composition, water saturation, and shale/clay content, among other properties. Nuclear modeling is commonly used to design borehole logging tools, calibrate the measurements to nuclear properties, relate nuclear properties and rock properties, perform sensitivity analysis, and improve the petrophysical interpretation of measurements acquired under complex geological, petrophysical, and geometrical conditions.

There are two main approaches to numerically simulate borehole nuclear measurements. The first and most common approach uses Monte Carlo methods to reproduce the transport of millions of individual particles and infer their average behavior. Algorithms, such as the Monte- Carlo N-Particle code (MCNP), are essential for designing and calibrating borehole nuclear instruments because they simulate nuclear tool responses with a high degree of accuracy for a wide range of material properties and measurement conditions. Such algorithms are, however, computationally expensive and therefore impractical for routine petrophysical analysis. The second approach employs quasilinear perturbation approximations to rapidly and accurately simulate nuclear tool responses using the concept of spatial flux sensitivity functions (FSFs). Fast- forward models based on FSF perturbations have been used successfully in inversion-based interpretation workflows to mitigate environmental, layer-thickness, and mud-filtrate invasion effects on nuclear measurements. This paper is intended as a practical, open, and reproducible guide to implement the above two methods for modeling borehole nuclear measurements.

We first provide practical guidelines for modeling borehole nuclear measurements with MCNP. After describing important requirements for defining both source and detectors, a method is introduced to accurately model gamma-ray spectra acquired with borehole logging tools. The method couples MCNP with the gamma detector response and analysis software – detector response function (GADRAS-DRF) to compute the response of gamma-ray and neutron detectors when they are exposed to radiation sources. Instructions are also given for processing MCNP tally results and simulating tool rotation and tool movement along the borehole.

Next, we review best practices for developing rapid numerical simulations of borehole nuclear measurements using FSFs. By superimposing mesh tallies upon the forward-adjoint generator embedded in MCNP, a new procedure is introduced to compute FSFs without modifications to the MCNP source code. This updated method yields improved approximations of the FSFs because it makes use of track-length estimates when calculating particle flux within the formation. Calculated FSFs are also independent of grid-size variations, a notable improvement upon previous implementations.

The accompanying downloadable documents are central components of this paper: they include input decks for a set of generic wireline (WL) and logging-while- drilling (LWD) nuclear tools, referred to as the Longhorn nuclear well-logging tools, as well as useful algorithms to process MCNP tally results efficiently and to generate FSFs for the purpose of performing fast and accurate numerical simulations of borehole nuclear measurements.