http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Modeling of resistivity and acoustic borehole logging measurements using finite element methods
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.
Front Cover -- Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods -- Copyright -- Contents -- Preface -- 1 Introduction -- 1.1 Borehole resistivity measurements -- 1.1.1 Borehole resistivity instruments -- 1.1.2 Main simulation challenges -- 1.1.3 Simulation methods -- 1.2 Borehole acoustic measurements -- 1.2.1 Types of borehole acoustic waves -- Monopole source -- Dipole source -- Quadrupole source -- Other types of modes -- 1.2.2 Acoustic logging instruments -- Wireline tools -- LWD tools -- 1.2.3 Main simulation challenges -- 1.2.4 Simulation methods -- 1.3 The finite element method (FEM) -- 1.3.1 Abstract variational formulation -- 1.3.2 Discretization parameters: h, p, r, and k -- 1.3.3 Convergence analysis and computational cost -- Main convergence results -- Error estimates for resistivity logging simulations -- Error estimates for acoustic logging simulations -- Computational cost estimates -- Cost estimates for integration -- Cost estimates for the FE solver -- Summary -- Part 1 Electromagnetics -- 2 Maxwell's equations and variational formulations -- 2.1 Time-harmonic Maxwell's equations -- 2.2 Boundary conditions (BCs) -- 2.2.1 Perfect electric conductor (PEC) -- 2.2.2 Truncation of the spatial domain -- 2.2.3 Modeling sources as BCs -- 2.3 3D variational formulation in Cartesian coordinates -- 2.3.1 Alternating current (AC) -- E-formulation -- H-formulation -- Stabilized formulations -- Vector potential formulations -- 2.3.2 Direct current (DC) -- 2.4 3D variational formulation in an arbitrary system of coordinates -- 2.4.1 Alternating current (AC) -- 2.4.2 Direct current (DC) -- 2.4.3 Cylindrical coordinates -- 2.5 2.5D variational formulation in 2D Cartesian geometries -- 2.5.1 Alternating current (AC) -- 2.5.2 Direct current (DC).
2.6 2.5D variational formulation in axisymmetric geometries -- 2.6.1 Alternating current (AC) -- 2.6.2 Direct current (DC) -- 2.7 2D variational formulation in Cartesian coordinates -- 2.7.1 Alternating current (AC) -- 2.7.2 Direct current (DC) -- 2.8 2D axisymmetric variational formulation -- 2.8.1 Alternating current (AC) -- 2.8.2 Direct current (DC) -- 2.9 1.5D variational formulations -- 2.10 Summary -- 3 Modeling of resistivity geophysical measurements -- 3.1 Through-casing resistivity measurements -- 3.1.1 Main principles -- 3.1.2 Vertical wells -- 3.1.3 Deviated wells -- 3.1.4 Characterization of hydrofractures -- 3.1.5 Other applications -- 3.2 Dual-laterolog (DLL) instruments -- 3.2.1 Description and operating modes -- Monitoring conditions -- 3.2.2 Deviated wells -- Variational formulation -- Quantity of interest: apparent resistivity -- Synthetic focusing method -- Embedded post-processing method (EPPM) -- Dip effects -- Invasion effects in deviated wells -- Anisotropy effects in deviated wells -- 3.2.3 Groningen and Delaware effects -- Numerical simulations of Delaware effects -- Numerical simulations of Groningen effects -- 3.3 Tri-axial induction instruments -- 3.3.1 Description, operating modes, and governing equations -- Governing equations and variational formulations -- Quantity of interest: apparent resistivities -- 3.3.2 Wireline -- 3.3.3 Logging-while-drilling (LWD) -- 3.3.4 Deep and extra-deep azimuthal -- Part 2 Acoustics -- 4 Linear acoustics in fluids and solids and variational formulations -- 4.1 Time-harmonic equations of acoustics -- 4.1.1 Acoustic waves in fluids -- 4.1.2 Acoustic waves in elastic solids -- Isotropic solid -- Vertically transversely isotropic (VTI) solid -- 4.1.3 Acoustic waves in poroelastic solids -- Equations of motion -- Constitutive equations -- Isotropic poroelastic solid.
Vertically transversely isotropic poroelastic solid -- 4.2 Coupling and boundary conditions -- 4.2.1 Coupling between two poroelastic materials -- 4.2.2 Coupling between elastic solid and acoustic fluid -- 4.2.3 Coupling between poroelastic solid and acoustic fluid -- 4.2.4 Coupling between poroelastic and elastic materials -- 4.2.5 Acoustic excitation -- 4.2.6 Domain truncation -- 4.3 Acoustic source modeling -- 4.3.1 Acoustic pulses in time and frequency domains -- Gaussian pulse family -- The Berlage pulse family -- Sine burst -- Gaussian-modulated cosine pulse -- 4.3.2 Radiation patterns in acoustic logging -- 4.4 3D variational formulation in an arbitrary system of coordinates -- 4.4.1 Weak form for an acoustic medium -- 4.4.2 Weak form for an elastic medium -- 4.4.3 Weak form for a poroelastic medium -- 4.4.4 Weak form for the coupled problem -- 4.5 2D axisymmetric variational formulation -- 4.6 2.5D axisymmetric variational formulation -- 4.6.1 Change of coordinates -- Variational formulation in the new system of coordinates -- 4.6.2 Fourier series expansion -- Acoustics -- Elasticity and poroelasticity -- Solution procedure -- 5 Numerical modeling of borehole acoustic measurements -- 5.1 VTI elastic formation -- 5.2 Heterogeneous poroelastic formation -- 5.3 Isotropic elastic fast formation with slow layer -- 5.4 LWD logging in a cased well -- 5.4.1 Monopole, fast formation -- 5.4.2 Monopole, slow formation -- 5.4.3 Quadrupole, fast formation -- 5.4.4 Quadrupole, slow formation -- 5.5 Modeling of the internal structure of an LWD tool -- 5.6 Fast formation with a fluid-filled fracture -- 5.7 Logging in thinly bedded slow formations -- 5.7.1 Open borehole -- 5.7.2 Cased well -- 5.8 Eccentered logging device -- 5.8.1 Wireline logging -- Monopole, fast formation -- Dipole, fast formation -- Monopole, slow formation -- Dipole, slow formation.
5.8.2 Logging-while-drilling (LWD) -- 5.8.3 Summary -- Part 3 Advanced modeling topics -- 6 Attenuation modeling in anelastic materials -- 6.1 Simple model problem -- 6.2 Aki-Richards attenuation model -- 7 Absorbing boundary conditions -- 7.1 Introduction -- 7.2 Perfectly matched layer -- 7.3 The idea of the PML -- 7.3.1 Model problem -- 7.3.2 Construction of the PML -- 7.3.3 How PML works / PML stretching function -- 7.4 Energy spaces, exact sequence, parametric elements, and Piola transforms -- 7.5 PML in Cartesian coordinate system -- 7.6 PML in curvilinear coordinate system -- 7.6.1 Problem solved in curvilinear coordinates -- 7.6.2 Problem solved in Cartesian coordinates -- 7.7 PML in cylindrical coordinates -- 7.8 PML in spherical coordinates -- 7.9 Instability in the PML -- 8 Linear solvers -- 8.1 Direct solvers -- 8.2 Iterative solvers -- 8.3 Preconditioning techniques -- 9 Parallel implementation -- 9.1 Types of parallel architectures -- 9.2 Parallelization in geophysical problems -- 9.3 Parallel solvers and preconditioners -- 9.4 Future trends -- 10 Inverse problems -- 10.1 Formulation -- 10.1.1 Notation -- 10.1.2 Cost functional -- 10.1.3 Discretization -- 10.2 Solution method -- 10.2.1 Step size -- 10.2.2 Nonlinear constraints -- 10.2.3 Jacobian and Hessian matrices -- 10.2.4 Regularization parameter -- 10.2.5 Stopping criteria and uncertainty quantification -- 10.3 Numerical simulations -- Bibliography -- Index -- Back Cover.