Rapid numerical simulation and inversion of nuclear borehole measurements acquired in vertical and deviated wells
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The conventional approach for estimation of in-situ porosity is the combined use of neutron and density logs. These nuclear borehole measurements are influenced by fundamental petrophysical, fluid, and geometrical properties of the probed formation including saturating fluids, matrix composition, mud-filtrate invasion and shoulder beds. Advanced interpretation methods that include numerical modeling and inversion are necessary to reduce environmental effects and non-uniqueness in the estimation of porosity. The objective of this dissertation is two-fold: (1) to develop a numerical procedure to rapidly and accurately simulate nuclear borehole measurements, and (2) to simulate nuclear borehole measurements in conjunction with inversion techniques. Of special interest is the case of composite rock formations of sand-shale laminations penetrated by high-angle and horizontal (HA/HZ) wells. In order to quantify shoulder-bed effects on neutron and density borehole measurements, we perform Monte Carlo simulations across formations of various thicknesses and borehole deviation angles with the multiple-particle transport code MCNP. In so doing, we assume dual-detector tool configurations that are analogous to those of commercial neutron and density wireline measuring devices. Simulations indicate significant variations of vertical (axial) resolution of neutron and density measurements acquired in HA/HZ wells. In addition, combined azimuthal- and dip-angle effects can originate biases on porosity estimation and bed boundary detection, which are critical for the assessment of hydrocarbon reserves. To enable inversion and more quantitative integration with other borehole measurements, we develop and successfully test a linear iterative refinement approximation to rapidly simulate neutron, density, and passive gamma-ray borehole measurements. Linear iterative refinement accounts for spatial variations of Monte Carlo-derived flux sensitivity functions (FSFs) used to simulate nuclear measurements acquired in non-homogeneous formations. We use first-order Born approximations to simulate variations of a detector response due to spatial variations of formation energy-dependent cross-section. The method incorporates two- (2D) and three-dimensional (3D) capabilities of FSFs to simulate neutron and density measurements acquired in vertical and HA/HZ wells, respectively. We calculate FSFs for a wide range of formation cross-section variations and for borehole environmental effects to quantify the spatial sensitivity and resolution of neutron and density measurements. Results confirm that the spatial resolution limits of neutron measurements can be significantly influenced by the proximity of layers with large contrasts in porosity. Finally, we implement 2D sector-based inversion of azimuthal logging-while-drilling (LWD) density field measurements with the fast simulation technique. Results indicate that inversion improves the petrophysical interpretation of density measurements acquired in HA/HZ wells. Density images constructed with inversion yield improved porosity-feet estimations compared to standard and enhanced compensation techniques used commercially to post-process mono-sensor densities.