# Physics and rapid forward modeling of logging-while-drilling Neutron-Gamma density measurements

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Although radioactive chemical sources have long been used in borehole nuclear tools for in-situ porosity estimation, they pose non-negligible health, safety, and environmental risks. Pulsed neutron generators were successfully introduced as replacements for americium-beryllium (AmBe) sources in neutron-based measurements. However, bulk density is still generally measured using Gamma-Gamma density tools operating with cesium-137 sources. Neutron-activated gamma-ray measurements (Neutron-Gamma) are a safer alternative to Gamma-Gamma density measurements because cesium-137 is replaced with a pulsed neutron generator. Thereafter, bulk density is estimated from neutron-induced non-capture gamma-ray counts corrected for neutron transport. Field studies with commercial Neutron-Gamma density tools revealed several practical limitations, including sensitivity to borehole conditions and decreased accuracy in high-density formations, shales, and shaly formations. The main purpose of this dissertation is to develop new measurement and interpretation procedures to mitigate such limitations. With the objective of accurately capturing the measurement physics, I designed a new theoretical, albeit realistic logging-while-drilling (LWD) Neutron-Gamma density tool. This new tool combines inputs from two gamma-ray detectors and two fast neutron detectors to deliver density accuracies that favorably compare to those obtained with traditional Gamma-Gamma density measurements, i.e., 0.013 g/cm³ in shale-free formations, and 0.019 g/cm³ in shale and shaly formations. Similar to other nuclear measurements, Neutron-Gamma density is affected by bed-boundary and layer-thickness effects that can mask the true formation bulk density when implementing conventional interpretation methods. Borehole environmental effects are additionally mitigated using empirical corrections because “spine-and-rib” compensation is impractical. However, for standoff values greater than 0.63 cm (0.25 in), such empirical corrections should be avoided as they no longer remain independent of formation properties. Three-dimensional geometrical and borehole effects can be mitigated using fast numerical simulations coupled with inversion-based interpretation. To simulate borehole LWD Neutron-Gamma density measurements, I developed a fast-forward modeling algorithm based on first-order approximations and flux sensitivity functions. The algorithm is over 500,000 times faster than industry-standard Monte Carlo methods and achieves root-mean-square errors of less than 1% (0.023 g/cm³) in formations with spatially complex geometry, including high-angle wells, thinly-bedded formations, and invaded beds. However, fast numerical simulations based on first-order approximations have limited accuracy when modeling borehole environmental effects. The Neutron-Gamma density fast-forward algorithm can improve the interpretation of measurements when standoff is less than 1.27 cm (0.5 in). Conversely, for larger values of standoff, spatial flux perturbations give rise to higher-order measurement responses that are not captured with first-order approximations, yielding density errors of up to 0.04 g/cm³ for 2.54 cm (1 in) standoff. The second part of this dissertation introduces new methods to improve borehole environmental corrections of nuclear measurements based on single-particle transport. They rely on higher-order rapid forward simulations wherein sensitivity flux perturbations are quantified using approximations to the Boltzmann transport equation. For neutron measurements, the diffusion flux-difference method is enhanced with a two-step algorithm that minimizes the size of the perturbation and yields average errors of 1 porosity unit (p.u.) in boreholes with up to 2.5-cm (1-in) standoff. For Gamma-Gamma density measurements, the gamma flux-difference (GFD) method is introduced to quantify gamma-ray flux perturbations using exponential point kernels and a Rytov approximation. This latter procedure yields maximum density errors of 0.02 g/cm³ in boreholes with up to 4.44 cm (1.75 in) standoff. The methods developed in this dissertation represent the first step toward future improvements in fast modeling of borehole environmental effects for nuclear measurements based on coupled neutron and gamma-ray transport, such as Neutron-Gamma density