Nuclear logging-while-drilling (LWD) measurements acquired in high-angle and horizontal (HA/HZ) wells are influenced by tool, geometrical, and petrophysical effects. Reliable interpretation of petrophysical and geometrical properties from LWD measurements acquired in thinly-bedded formations requires that gamma ray, density, photoelectric (PEF), and neutron measurements be quantitatively integrated with explicit consideration of their effective volume of investigation (EVOI). One of the effects of different tool EVOIs is false gas density-neutron crossovers across thinly-bedded formations. Also, in the presence of tool eccentricity, azimuthally-varying standoff gives rise to an azimuthally-varying effective depth of investigation (EDOI), which introduces errors in the inference of formation dip. Conventional Monte Carlo simulations of nuclear measurements are computationally expensive in reproducing multi-sector LWD responses in HA/HZ wells. Using linear iterative refinement of pre-calculated flux sensitivity functions (FSFs), we introduce a fast method for numerical simulation of LWD nuclear images in the presence of tool eccentricity along any well trajectory. Our investigation of measurement responses from FSFs motivates techniques to explicitly consider the EVOI of LWD nuclear measurements. Simple radial DOI and standoff corrections suffice for interpretation of gamma-gamma images but are inadequate for neutron responses due to larger EVOI and azimuthal aperture. We introduce a new azimuthal deconvolution method of neutron images to improve bed-boundary detection. Neutron DOI varies significantly with porosity, whereby we correct neutron images for penetration length due to changes of porosity along the well trajectory. In addition, we implement a new method of separate linear iterative refinement on neutron thermal group responses to improve the resolution of neutron images across heterogeneous and thinly-bedded formations. The method reduces shoulder-bed effects and false neutron-density gas crossovers. We corroborate these techniques with rigorous Monte Carlo simulations in vertical and deviated wells. A field example of application conclusively indicates that numerical simulation of LWD nuclear measurements is necessary for reliable estimation of petrophysical properties. / text

Undulating well trajectories are often drilled to improve length exposure to rock formations, target desirable hydrocarbon-saturated zones, and enhance resolution of borehole measurements. Despite these merits, undulating wells can introduce adverse conditions to the interpretation of borehole measurements which are seldom observed in vertical wells penetrating horizontal layers. Common examples are polarization horns observed across formation bed boundaries in borehole resistivity measurements acquired in highly-deviated wells. Consequently, conventional interpretation practices developed for vertical wells can yield inaccurate results in HA/HZ wells. A reliable approach to account for well trajectory and bed-boundary effects in the petrophysical interpretation of well logs is the application of forward and inverse modeling techniques because of their explicit use of measurement response functions. The main objective of this dissertation is to develop inversion-based petrophysical interpretation methods that quantitatively integrate logging-while-drilling (LWD) multi-sector nuclear (i.e., density, neutron porosity, photoelectric factor, natural gamma ray) and multi-array propagation resistivity measurements. Under the assumption of a multi-layer formation model, the inversion approach estimates formation properties specific to a given measurement domain by numerically reproducing the available measurements. Subsequently, compositional multi-mineral analysis of inverted layer-by-layer properties is implemented for volumetric estimation of rock and fluid constituents. The most important prerequisite for efficient petrophysical inversion is fast and accurate forward models that incorporate specific measurement response functions for numerical simulation of LWD measurements. In the nuclear measurement domain, first-order perturbation theory and flux sensitivity functions (FSFs) are reliable and accurate for rapid numerical simulation. Albeit efficient, these first-order approximations can be inaccurate when modeling neutron porosity logs, especially in the presence of borehole environmental effects (tool standoff or/and invasion) and across highly contrasting beds and complex formation geometries. Accordingly, a secondary thrust of this dissertation is the introduction of two new methods for improving the accuracy of rapid numerical simulation of LWD neutron porosity measurements. The two methods include: (1) a neutron-density petrophysical parameterization approach for describing formation macroscopic cross section, and (2) a one-group neutron diffusion flux-difference method for estimating perturbed spatial neutron porosity fluxes. Both methods are validated with full Monte Carlo (MC) calculations of spatial neutron detector FSFs and subsequent simulations of neutron porosity logs in the presence of LWD azimuthal standoff, invasion, and highly dipping beds. Analysis of field and synthetic verification examples with the combined resistivity-nuclear inversion method confirms that inversion-based estimation of hydrocarbon pore volume in HA/HZ wells is more accurate than conventional well-log analysis. Estimated hydrocarbon pore volume from conventional analysis can give rise to errors as high as 15% in undulating HA/HZ intervals. / text

This thesis provides a feasibility study on the determination of formation anisotropy parameters from logging-while-drilling (LWD) borehole acoustic measurements. For this reason, the wave propagation in fluid-filled boreholes surrounded by transverse isotropic (TI) formations is investigated in great detail using the finite-difference method. While the focus is put on quadrupole waves, the sensitivities of monopole and flexural waves are evaluated as well. All three wave types are considered with/without the presence of an LWD tool. Moreover, anisotropy-induced mode contaminants are discussed for various TI configurations. In addition, the well-known plane wave Alford rotation has been generalized to cylindrical borehole waves of any order, except for the monopole. This formulation has been extended to allow for non-orthogonal multipole firings, and associated inversion methods have been developed to compute formation shear principal velocities and accompanying polarization directions, utilizing various LWD (cross-) quadrupole measurements.:1 Introduction 1.1 Borehole acoustic configurations 1.2 Wave propagation in a fluid-filled borehole in the absence of a logging tool 1.3 Wave propagation in a fluid-filled borehole in the presence of a logging tool 1.4 Anisotropy 2 Theory 2.1 Stiffness and compliance tensor 2.1.1 Triclinic symmetry 2.1.2 Monoclinic symmetry 2.1.3 Orthotropic symmetry 2.1.4 Transverse isotropic (TI) symmetry 2.1.5 Isotropy 2.2 Reference frames 2.3 Seismic wave equations for a linear elastic, anisotropic medium 2.3.1 Basic equations 2.3.2 Integral transforms 2.3.3 Christoffel equation 2.3.4 Phase slowness surfaces 2.3.5 Group velocity 2.4 Solution in cylindrical coordinates for the borehole geometry 2.4.1 Special case: vertical transverse isotropy (VTI) 2.4.2 General case: triclinic symmetry 3 Finite-difference modeling of wave propagation in anisotropic media 3.1 Finite-difference method 3.2 Spatial finite-difference grids 3.2.1 Standard staggered grid 3.2.2 Lebedev grid 3.3 Heterogeneous media 3.4 Finite-difference properties and grid dispersion 3.5 Initial conditions 3.6 Boundary conditions 3.7 Parallelization 3.8 Finite-difference parameters 4 Wave propagation in fluid-filled boreholes surrounded by TI media 4.1 Vertical transverse isotropy (VTI) 4.1.1 Monopole excitation 4.1.2 Dipole excitation 4.1.3 Quadrupole excitation 4.1.4 Summary 4.2 Horizontal transverse isotropy (HTI) 4.2.1 Monopole excitation 4.2.2 Theory of cross-multipole shear wave splitting 4.2.3 Dipole excitation 4.2.4 Quadrupole excitation 4.2.5 Hexapole waves 4.2.6 Summary 4.3 Tilted transverse isotropy (TTI) 4.3.1 Monopole excitation 4.3.2 Dipole excitation 4.3.3 Quadrupole excitation 4.3.4 Summary 4.4 Anisotropy-induced mode contaminants 4.4.1 Vertical transverse isotropy (VTI) 4.4.2 Horizontal transverse isotropy (HTI) 4.4.3 Tilted transverse isotropy (TTI) 4.4.4 Summary 5 Inversion methods 5.1 Vertical transverse isotropy (VTI) 5.2 Horizontal transverse isotropy (HTI) 5.2.1 Inverse generalized Alford rotation 5.2.2 Inversion method based on dipole excitations 5.2.3 Inversion method based on quadrupole excitations 5.3 Tilted transverse isotropy (TTI) 5.4 Challenges in real measurements 5.4.1 Signal-to-noise ratio (SNR) 5.4.2 Tool eccentricity 6 Conclusions References List of Abbreviations and Symbols List of Figures List of Tables A Integral transforms A.1 Laplace transform A.2 Spatial Fourier transform A.3 Azimuthal Fourier transform A.4 Meijer transform B Stiffness and compliance tensor B.1 Rotation between reference frames B.2 Cylindrical coordinates C Christoffel equation C.1 Cartesian coordinates C.2 Cylindrical coordinates D Processing of borehole acoustic waveform array data D.1 Time-domain methods D.2 Frequency-domain methods D.2.1 Weighted spectral semblance method D.2.2 Modified matrix pencil method