Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods provides a comprehensive review of different resistivity and sonic logging instruments used within the oil industry, along with precise and solid mathematical descriptions of the physical equations and corresponding FE formulations that govern these measurements. Additionally, the book emphasizes the main modeling considerations that one needs to incorporate into the simulations in order to obtain reliable and accurate results. Essentially, the formulations and methods described here can also be applied to simulate on-surface geophysical measurements such as seismic or marine controlled-source electromagnetic (CSEM) measurements. Simulation results obtained using FE methods are superior. FE methods employ a mathematical terminology based on FE spaces that facilitate the design of sophisticated formulations and implementations according to the specifics of each problem. This mathematical FE framework provides a highly accurate, robust, and flexible unified environment for the solution of multi-physics problems. Thus, readers will benefit from this resource by learning how to make a variety of logging simulations using a unified FE framework. Provides a complete and unified finite element approach to perform borehole sonic and electromagnetic simulations Includes the latest research in mathematical and implementation content on Finite Element simulations of borehole logging measurements Features a variety of unique simulations and numerical examples that allow the reader to easily learn the main features and limitations that appear when simulating borehole resistivity measurements

Borehole acoustic measurements are often affected by instrument noise, motion and eccentricity, environmental conditions, and spatial averaging that can compromise the accuracy of elastic properties of rock formations calculated with conventional interpretation methods. Forward and inverse modeling can be used to improve the interpretation of acoustic logs acquired in the presence of spatially complex rock formations and adverse borehole conditions. However, forward modeling of acoustic modes often requires time-consuming numerical algorithms. The main objective of this dissertation is to develop fast-forward modeling and inversion-based interpretation procedures of borehole acoustic logs for isotropic and vertical transversely isotropic (VTI) formations. Fast-forward modeling is achieved with spatial sensitivity functions which are calculated from frequency-domain linear perturbation theory of borehole acoustic modes. Spatial sensitivity functions quantify both the dependence of measured slowness on elastic properties and the spatial averaging introduced by acoustic tools. Fast-forward modeling using spatial sensitivity functions is applied to synthetic examples that include thin layers, anisotropy, and dipping layers, and is successfully validated with numerical simulations performed with finite-difference and finite-element methods. Two inversion-based interpretation methods are then developed: (1) a physics-based inversion method to reduce noise and spatial averaging effects on acoustic logs acquired in horizontally layered formations penetrated by vertical wells, and (2) a sequential inversion method to estimate stiffness coefficients of VTI formations from multi-frequency flexural/quadrupole, Stoneley, and compressional logs. The physics-based inversion method is applied to mitigate measurement noise and spatial averaging effects of acoustic logs acquired in two hydrocarbon reservoirs. Results confirm the accuracy and reliability of the estimated layer-by-layer elastic properties compared to conventional numerical filters and are obtained in less than 14 CPU seconds for a 100 ft-depth log. In VTI formations penetrated by vertical wells, sequential inversion is applied to estimate layer-by-layer stiffness coefficients of synthetic formations from borehole acoustic logs. Results indicate that mitigating spatial averaging of frequency-dependent slowness logs prior to inversion improves the layer-by-layer estimation of slownesses by a factor of 2, and that sequential inversion yields accurate and reliable estimates of rock stiffness coefficients. Finally, in high-angle wells fast-forward modeling yields flexural slownesses measured with orthogonal dipoles with 2% relative errors and in 3 CPU minutes for a log consisting of 50 measured-depth samples, compared to 15 CPU hours when using finite-difference simulation methods. Analysis of field and synthetic examples confirms that inversion-based interpretation methods yield more accurate estimations of elastic properties than conventional sonic-log interpretation procedures. Spatial sensitivity functions constitute a fast, reliable, and efficient alternative for interpreting acoustic logs acquired in isotropic and VTI formations.

This book covers the principles, historical development, and applications of many acoustic logging methods, including acoustic logging-while-drilling and cased-hole logging methods. Benefiting from the rapid development of information technology, the subsurface energy resource industry is moving toward data integration to increase the efficiency of decision making through the use of advanced big data and artificial intelligence technologies, such as machine/deep learning. However, wellbore failure may happen if evaluations of risk and infrastructure are made using data mining methods without a complete understanding of the physics of borehole measurements. Processed results from borehole acoustic logging will constitute part of the input data used for data integration. Therefore, to successfully employ modern techniques for data assimilation and analysis, one must fully understand the complexity of wave mode propagation, how such propagation is influenced by the well, and the materials placed within the well (i.e., the cement, casing, and drill strings), and ultimately how waves penetrate into and are influenced by geological formations. State-of-the-art simulation methods, such as the discrete wavenumber integration method (DWM) and the finite difference method (FDM), are introduced to tackle the numerical challenges associated with models containing large material contrasts, such as the contrasts between borehole fluids and steel casings. Waveforms and pressure snapshots are shown to help the reader understand the wavefields under various conditions. Advanced data processing methods, including velocity analyses within the time and frequency domains, are utilized to extract the velocities of different modes. Furthermore, the authors discuss how various formation parameters influence the waveforms recorded in the borehole and describe the principles of both existing and potential tool designs and data acquisition schemes. This book greatly benefits from the research and knowledge generated over four decades at the Earth Resources Laboratory (ERL) of the Massachusetts Institute of Technology (MIT) under its acoustic logging program. Given its scope, the book is of interest to geophysicists (including borehole geophysicists and seismologists), petrophysicists, and petroleum engineers who are interested in formation evaluation and cementation conditions. In addition, this book is of interest to researchers in the acoustic sciences and to 4th-year undergraduate and postgraduate students in the areas of geophysics and acoustical physics.