Theory of Electromagnetic Well Logging

Chapter 1. Introduction to Well Logging

• Abstract
• 1.1 Oil and Gas Exploration
• 1.2 Well Logging Methods
• 1.3 Nuclear Logging
• 1.4 Sonic Logging
• 1.5 Nuclear Magnetic Resonance Logging
• 1.6 Dielectric Logging
• 1.7 Wireline Logging and Logging While Drilling
• 1.8 Geosteering
• 1.9 Summary of Electromagnetic Logging Tools
• References

Chapter 2. Fundamentals of Electromagnetic Fields and Induction Logging Tools

• Abstract
• 2.1 Maxwell’s Equations
• 2.2 Complex Permittivity
• 2.3 Sources Js¯,Ps¯ and Ms¯
• 2.4 Hertz Potential Π¯m
• 2.5 Electromagnetic Fields Due to a Magnetic Dipole in a Homogeneous Medium
• 2.6 Induced Electromotive Force (EMF) in the Receiving Coil and the Use of Bucking Coil
• 2.7 Quasistatic Approximations and Skin Depth
• 2.8 Apparent Conductivity
• 2.9 Tool Constant and Skin-Effect Correction
• 2.10 Direct Inversion of Induction Logging Data
• 2.11 Spectrum Domain Solutions and Two-Coil Induction Tools in Layered Media
• 2.12 Induction Arrays
• References

Chapter 3. Electrical Properties of Sediment Rocks: Mixing Laws and Measurement Methods

• Abstract
• 3.1 Resistivity and Dielectric Constant of Rocks
• 3.2 Archie’s Law
• 3.3 Mixing Laws
• 3.4 Frequency Dispersion of the Dielectric Constant
• 3.5 Frequency Dispersion of the Conductivity
• 3.6 Measurement Methods of Electrical Properties of Rocks
• 3.7 TM₀₁₀ Resonant Cavity Technique
• References
• Appendix A E Field Analysis of the Circuit Model of the Parallel-Disk Sample Holder
• Appendix B Equipment Calibration Synopsis

Chapter 4. Triaxial Induction and Logging-While-Drilling Resistivity Tool Response in Homogeneous Anisotropic Formations

• Abstract
• 4.1 Magnetic Dipole in Homogeneous Lossy Media
• 4.2 Finite Coil in Homogeneous Formation
• 4.3 LWD Tool Response in Homogeneous Formation
• 4.4 Triaxial Induction Logging Tool Response in Biaxial Anisotropic Homogeneous Formation
• References
• Appendix A Derivation of Parameters a and b in Eqs. (4.53)–(4.55)

Chapter 5. Triaxial Induction Tool and Logging-While-Drilling Tool Response in a Transverse Isotropic-Layered Formation

• Abstract
• 5.1 Introduction
• 5.2 Summary of a Magnetic Dipole Source in a Transverse Isotropic Homogeneous Formation
• 5.3 Magnetic Dipole in a Layered Formation
• 5.4 Convergence Algorithm
• 5.5 Simulation Results and Analysis
• 5.6 Analysis of Anisotropy Impact to the Resistivity LWD Tool
• References
• Appendix A Derivation of Hertz Vector Potential in Multiple Layer Formation

Chapter 6. Triaxial Induction and Logging-While-Drilling Logging Tool Response in a Biaxial Anisotropic-Layered Formation

• Abstract
• 6.1 Spectral-Domain Solution to Maxwell’s Equations in a Homogeneous Biaxial Anisotropic Medium
• 6.2 Propagation in Unbounded Medium
• 6.3 Propagation in Layered Medium
• 6.4 Computation of the Double Integrals
• 6.5 Numerical Examples
• References
• Appendix A Derivation of Matrix A

Chapter 7. Induction and LWD Tool Response in a Cylindrically Layered Isotropic Formation

• Abstract
• 7.1 Introduction
• 7.2 Induction and LWD Tool Response in a Four-Layer Cylindrical Medium
• 7.3 Response of Induction and LWD Tools in Arbitrary Cylindrically Layered Media
• 7.4 Conclusions
• References
• Appendix A Derivation for the Magnetic Fields in Spectral Domain
• Appendix B Derivation for the Expression of Electrical Field for the Homogeneous Formation in Spectral Domain
• Appendix C Derivation for the Expression of Electrical Field for Arbitrary Cylindrical Layered Formations in Spectral Domain

Chapter 8. Induction and Logging-While-Drilling Resistivity Tool Response in a Two-Dimensional Isotropic Formation

• Abstract
• 8.1 Introduction
• 8.2 Formulations
• 8.3 Numerical Consideration
• 8.4 Verifications
• 8.5 Array Induction Logs
• 8.6 Measurement-While-Drilling Logs
• 8.7 Simulation of Effects of Mandrel Grooves on MWD Conductivity Logs
• 8.8 Summary
• References

Chapter 9. Theory of Inversion for Triaxial Induction and Logging-While-Drilling Logging Data in One- and Two-Dimensional Formations

• Abstract
• 9.1 Introduction
• 9.2 Gauss–Newton Algorithm
• 9.3 Cholesky Factorization
• 9.4 Line Search
• 9.5 Jacobian Matrix
• 9.6 Constraints
• 9.7 Initial Values
• 9.8 Inversion Results and Analysis
• 9.9 Inversion of Induction Logs in a Two-Dimensional Formation
• 9.10 Summary
• References

Chapter 10. The Application of Image Theory in Geosteering

• Abstract
• 10.1 Introduction
• 10.2 Theory of Forward Modeling Using Image Theory
• 10.3 Simulation Results and Discussions
• 10.4 Boundary Distance Inversion
• 10.5 Conclusion
• References

Chapter 11. Ahead-of-the-Bit Tools and Far Detection Electromagnetic Tools

• Abstract
• 11.1 Introduction
• 11.2 Ahead-of-the-Bit Field Distribution of LWD Tools
• 11.3 Toroidal Transmitter
• 11.4 Boundary Detection Using Orthogonal Antennas
• 11.5 Deep-Looking Directional Resistivity Tool
• 11.6 Distance Inversion Based on the Gauss–Newton Algorithm
• 11.7 Conclusions
• References

Chapter 12. Principle of Dielectric Logging Tools

• Abstract
• 12.1 Introduction
• 12.2 History of Dielectric Tool Study
• 12.3 Frequency Selection of a Dielectric Tool
• 12.4 Antenna Spacing
• 12.5 Sensitivity Analysis
• 12.6 Sensitivity Analysis in Anisotropic Formation
• 12.7 Dielectric Logging Tool Design and Modeling Using Three-Dimensional Numerical Modeling Software Package
• 12.8 Cavity-Backed Slot Antenna
• 12.9 Effects of the Pad
• 12.10 Borehole Mud Influence
• 12.11 Vertical Resolution
• 12.12 Mud Cake and Invasion
• 12.13 Depth of Investigation
• 12.14 Applications of Dielectric Tools
• 12.15 Summary
• References
• Appendix

Chapter 13. Finite Element Method for Solving Electrical Logging Problems in Axially Symmetrical Formations

• Abstract
• 13.1 Overview of the Numerical Simulation Methods for Well Logging Problems
• 13.2 Finite Element Method Based on Magnetic Field
• 13.3 Analysis of Transverse Electric Mode and Transverse Magnetic Mode
• 13.4 Vector Matrix Equation of Magnetic Field and Impedance Matrix
• 13.5 The Basis Functions
• 13.6 Evaluation of Impedance Element Matrix for Rectangular Element Based on H_ϕ
• 13.7 Evaluation of Impedance Element Matrix for Rectangular Element Based on ρH_ϕ
• 13.8 Evaluation of Impedance Element Matrix for Triangular Element Based on H_ϕ
• 13.9 FEM Based on Electric Field
• 13.10 Evaluation of Triangular Element Matrix Based on E_ϕ (TE Mode)
• 13.11 FEM Model of Sources
• References
• Appendix A Vector Analysis in Cylindrical Coordinates
• Appendix B Computation Method for Matrix Assembling Rule
• Appendix C Computation Method of Element Matrix for Rectangular Element Based on H_ϕ (Section 13.6)
• Appendix D Computation Method of Element Matrix for Rectangular Element Based on ρH_ϕ (Section 13.7)
• Appendix E Term 4 (Section 13.8.3.9)
• Appendix F Computation Method of Element Matrix for Triangular Element Based on H_ϕ (Section 2.7.4)
• Appendix G Computation Method of Element Matrix for Triangular Element Based on E_ϕ (Section 3.3)

Chapter 14. Resistivity Imaging Tools

• Abstract
• 14.1 Introduction
• 14.2 Water-Based Mud Resistivity Imaging Tool
• 14.3 The Oil-Based Mud Resistivity Imager
• 14.4 Conclusions
• References

Chapter 15. Laterolog Tools and Array Laterolog Tools

• Abstract
• 15.1 Introduction
• 15.2 Basics of Electrode Type of Logging Tools
• 15.3 The Laterolog Focusing Principle and the Model of Dual Laterolog Tool
• 15.4 Application of Finite Element Method on Alternating Current Dual Laterolog Tool
• 15.5 Validation of the Computational Method
• 15.6 Simulation Result
• 15.7 Array Laterolog Tool
• References
• Appendix A Computation Method of Source Model for Alternating Current Dual Laterolog Tool

Chapter 16. Theory of the Through-Casing Resistivity Logging Tool

• Abstract
• 16.1 Introduction
• 16.2 Through-Casing Resistivity Measurement Procedure
• 16.3 Circuit Model of the Through-Casing Resistivity Tool
• 16.4 Finite Element Method Simulation of the Through-Casing Resistivity Logging Tool
• 16.5 Through casing logs from a Toroidal Antenna
• References

Chapter 17. Electromagnetic Telemetry System and Electromagnetic Short Hop Telemetry in a Logging-While-Drilling/Measuring-While-Drilling Tool

• Abstract
• 17.1 Introduction to Logging-While-Drilling/Measuring-While-Drilling Uplink and Downlink Technologies
• 17.2 The Numerical Model of Electromagnetic Telemetry System
• 17.3 Application of Finite Element Method on Electromagnetic Telemetry Systems
• 17.4 Validation of the Computation Algorithm in a Cased Borehole
• 17.5 Simulation Result Without Casing
• 17.6 Short Hop Electromagnetic Telemetry Used in a Near Bit Logging-While-Drilling Sensor
• 17.7 Conclusions
• References
• Appendix A Computation Method of Source Model for EM Telemetry System (Section 17.3.2)

Appendix A. LogSimulator User Manual: Theory of Electromagnetic Well Logging

• A.1 Introduction
• A.2 Use of the Program
• A.3 Run Simulation