Wilson C. Chin, who earned his PhD from MIT and MSc from Caltech, heads StrataMagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering, and managed pressure drilling. He is the author of ten books, more than 100 papers, and over forty patents.

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• Preface xv Acknowledgements xxi 1 Motivating Ideas – General Formulation and Results 1 1.1 Overview 1 1.2 Introduction 2 1.3 Physical Model and Numerical Formulation 4 1.4 Validation Methodology 13 1.5 Practical Applications 16 1.6 Closing Remarks 34 1.7 References 35 2 Detailed Theory and Numerical Analysis 37 2.1 Overview 37 2.2 Introduction 40 2.3 Preliminary Mathematical Considerations 47 2.4 Boundary Value Problem Formulation 58 2.5 Computational Issues and Strategies 66 2.6 Typical Simulation Results 80 2.7 Post-Processing and Applications 112 2.8 Restrictions with Fast Multi-frequency Methods 126 2.9 Receiver Design Philosophy 128 2.10 Description of Output Files 131 2.11 Apparent Resistivity Using Classic Dipole Solution 138 2.12 Coordinate Conventions for Mud and Invasion Modeling 139 2.13 Generalized Fourier Integral for Transient Sounding 140 2.14 References 141 3 Validations – Qualitative Benchmarks 142 3.1 Overview 142 3.2 Introductory Problems 148 3.3 Advanced Problems 245 3.4 Sign Conventions and Validation Methodology 277 3.5 References 279 4 Validations – Quantitative Benchmarks at 0° and 90° 280 4.1 Overview 280 4.2 Wireline Validations in Homogeneous Media 281 4.3 Wireline Validations in Two-Layer Inhomogeneous Media 304 4.4 Electric and Magnetic Field Sensitive Volume Analysis for Resistivity and NMR Applications 328 4.5 MWD “Steel Collar” and Wireline Computations in Homogeneous and Nonuniform Layered Dipping Media 340 4.6 Exact Drill Collar Validation Using Shen Analytical Solution 347 4.7 Dipole Interpolation Formula Validation in Farfield 349 4.8 Magnetic Dipole Validation in Two-Layer Formation 352 4.9 References 355 5 Quantitative Benchmarks at Deviated Angles 356 5.1 Overview 356 5.2 Limit 1. No Collar, No Mud 356 5.3 Limit 2. Collar Only, No Mud 363 5.4 Limit 3. Mud Only, No Collar 371 5.5 Limit 4. Collar and Mud 377 6 Validations – Quantitative Benchmarks at Deviated Angles with Borehole Mud and Eccentricity 382 6.1 Overview 382 6.2 Repeat Validations 382 6.3 References 439 7 Validations – Receiver Voltage Response and Apparent Resistivity 440 7.1 Overview 440 7.2 Focused Studies 440 7.3 General Transmitter Design Philosophy 485 7.4 General Receiver Design Philosophy 487 7.5 Apparent Resistivity Estimation from Classic Dipole Model 490 8 Simulator Overview and Feature Summary 491 8.1 Overview 491 8.2 Simulator Comparisons 493 8.3 Technical Specifications 496 8.4 Advanced Logging Applications 498 8.5 Formulation Features 499 8.6 Computational Technology 503 8.7 User Interface 504 8.8 Integrated Utility Programs 505 8.9 Detailed Output and Integrated Graphics 506 8.10 System Requirements 507 8.11 Validation Approach 508 8.12 Simulator Speed Analysis 510 8.13 Sample User Interface Screens 511 8.14 Transmitter and Receiver Design Interface 517 9 Simulator Tutorials and Validation Problems 519 9.1 Problem Set 1. Dipole and Biot-Savart Model Consistency – Validating Magnetic Fields 520 9.2 Problem Set 2. Validating Farfield Phase Predictions 528 9.3 Problem Set 3. Drill Collar Model Consistency – Exact Drill Collar Validation Using Shen Analytical Solution 532 9.4 Problem Set 4. Magnetic Dipole in Two-Layer Formation 534 9.5 Problem Set 5. Effects of Eccentricity and Invasion 538 9.6 Problem Set 6. A Complicated Horizontal Well Geology 542 9.7 Problem Set 7. Effects of Layering, Anisotropy and Dip 546 9.8 Problem Set 8. Transmitter and Receiver Design 554 9.9 Problem Set 9. Apparent Anisotropic Resistivities for Electromagnetic Logging Tools in Horizontal Wells 560 9.10 Problem Set 10. Apparent Anisotropic Resistivities for Borehole Effects – Invasion and Eccentricity 577 Cumulative References 583 Index 585 About the Author 591

Wilson C. Chin, who earned his PhD from MIT and MSc from Caltech, heads StrataMagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering, and managed pressure drilling. He is the author of ten books, more than 100 papers, and over forty patents.

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• Preface xv Acknowledgements xxi 1 Motivating Ideas – General Formulation and Results 1 1.1 Overview 1 1.2 Introduction 2 1.3 Physical Model and Numerical Formulation 4 1.4 Validation Methodology 13 1.5 Practical Applications 16 1.6 Closing Remarks 34 1.7 References 35 2 Detailed Theory and Numerical Analysis 37 2.1 Overview 37 2.2 Introduction 40 2.3 Preliminary Mathematical Considerations 47 2.4 Boundary Value Problem Formulation 58 2.5 Computational Issues and Strategies 66 2.6 Typical Simulation Results 80 2.7 Post-Processing and Applications 112 2.8 Restrictions with Fast Multi-frequency Methods 126 2.9 Receiver Design Philosophy 128 2.10 Description of Output Files 131 2.11 Apparent Resistivity Using Classic Dipole Solution 138 2.12 Coordinate Conventions for Mud and Invasion Modeling 139 2.13 Generalized Fourier Integral for Transient Sounding 140 2.14 References 141 3 Validations – Qualitative Benchmarks 142 3.1 Overview 142 3.2 Introductory Problems 148 3.3 Advanced Problems 245 3.4 Sign Conventions and Validation Methodology 277 3.5 References 279 4 Validations – Quantitative Benchmarks at 0° and 90° 280 4.1 Overview 280 4.2 Wireline Validations in Homogeneous Media 281 4.3 Wireline Validations in Two-Layer Inhomogeneous Media 304 4.4 Electric and Magnetic Field Sensitive Volume Analysis for Resistivity and NMR Applications 328 4.5 MWD “Steel Collar” and Wireline Computations in Homogeneous and Nonuniform Layered Dipping Media 340 4.6 Exact Drill Collar Validation Using Shen Analytical Solution 347 4.7 Dipole Interpolation Formula Validation in Farfield 349 4.8 Magnetic Dipole Validation in Two-Layer Formation 352 4.9 References 355 5 Quantitative Benchmarks at Deviated Angles 356 5.1 Overview 356 5.2 Limit 1. No Collar, No Mud 356 5.3 Limit 2. Collar Only, No Mud 363 5.4 Limit 3. Mud Only, No Collar 371 5.5 Limit 4. Collar and Mud 377 6 Validations – Quantitative Benchmarks at Deviated Angles with Borehole Mud and Eccentricity 382 6.1 Overview 382 6.2 Repeat Validations 382 6.3 References 439 7 Validations – Receiver Voltage Response and Apparent Resistivity 440 7.1 Overview 440 7.2 Focused Studies 440 7.3 General Transmitter Design Philosophy 485 7.4 General Receiver Design Philosophy 487 7.5 Apparent Resistivity Estimation from Classic Dipole Model 490 8 Simulator Overview and Feature Summary 491 8.1 Overview 491 8.2 Simulator Comparisons 493 8.3 Technical Specifications 496 8.4 Advanced Logging Applications 498 8.5 Formulation Features 499 8.6 Computational Technology 503 8.7 User Interface 504 8.8 Integrated Utility Programs 505 8.9 Detailed Output and Integrated Graphics 506 8.10 System Requirements 507 8.11 Validation Approach 508 8.12 Simulator Speed Analysis 510 8.13 Sample User Interface Screens 511 8.14 Transmitter and Receiver Design Interface 517 9 Simulator Tutorials and Validation Problems 519 9.1 Problem Set 1. Dipole and Biot-Savart Model Consistency – Validating Magnetic Fields 520 9.2 Problem Set 2. Validating Farfield Phase Predictions 528 9.3 Problem Set 3. Drill Collar Model Consistency – Exact Drill Collar Validation Using Shen Analytical Solution 532 9.4 Problem Set 4. Magnetic Dipole in Two-Layer Formation 534 9.5 Problem Set 5. Effects of Eccentricity and Invasion 538 9.6 Problem Set 6. A Complicated Horizontal Well Geology 542 9.7 Problem Set 7. Effects of Layering, Anisotropy and Dip 546 9.8 Problem Set 8. Transmitter and Receiver Design 554 9.9 Problem Set 9. Apparent Anisotropic Resistivities for Electromagnetic Logging Tools in Horizontal Wells 560 9.10 Problem Set 10. Apparent Anisotropic Resistivities for Borehole Effects – Invasion and Eccentricity 577 Cumulative References 583 Index 585 About the Author 591

Wilson C. Chin, who earned his PhD from MIT and MSc from Caltech, heads StrataMagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering, and managed pressure drilling. He is the author of ten books, more than 100 papers, and over forty patents.

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• Preface xv Acknowledgements xxi 1 Motivating Ideas – General Formulation and Results 1 1.1 Overview 1 1.2 Introduction 2 1.3 Physical Model and Numerical Formulation 4 1.4 Validation Methodology 13 1.5 Practical Applications 16 1.6 Closing Remarks 34 1.7 References 35 2 Detailed Theory and Numerical Analysis 37 2.1 Overview 37 2.2 Introduction 40 2.3 Preliminary Mathematical Considerations 47 2.4 Boundary Value Problem Formulation 58 2.5 Computational Issues and Strategies 66 2.6 Typical Simulation Results 80 2.7 Post-Processing and Applications 112 2.8 Restrictions with Fast Multi-frequency Methods 126 2.9 Receiver Design Philosophy 128 2.10 Description of Output Files 131 2.11 Apparent Resistivity Using Classic Dipole Solution 138 2.12 Coordinate Conventions for Mud and Invasion Modeling 139 2.13 Generalized Fourier Integral for Transient Sounding 140 2.14 References 141 3 Validations – Qualitative Benchmarks 142 3.1 Overview 142 3.2 Introductory Problems 148 3.3 Advanced Problems 245 3.4 Sign Conventions and Validation Methodology 277 3.5 References 279 4 Validations – Quantitative Benchmarks at 0° and 90° 280 4.1 Overview 280 4.2 Wireline Validations in Homogeneous Media 281 4.3 Wireline Validations in Two-Layer Inhomogeneous Media 304 4.4 Electric and Magnetic Field Sensitive Volume Analysis for Resistivity and NMR Applications 328 4.5 MWD “Steel Collar” and Wireline Computations in Homogeneous and Nonuniform Layered Dipping Media 340 4.6 Exact Drill Collar Validation Using Shen Analytical Solution 347 4.7 Dipole Interpolation Formula Validation in Farfield 349 4.8 Magnetic Dipole Validation in Two-Layer Formation 352 4.9 References 355 5 Quantitative Benchmarks at Deviated Angles 356 5.1 Overview 356 5.2 Limit 1. No Collar, No Mud 356 5.3 Limit 2. Collar Only, No Mud 363 5.4 Limit 3. Mud Only, No Collar 371 5.5 Limit 4. Collar and Mud 377 6 Validations – Quantitative Benchmarks at Deviated Angles with Borehole Mud and Eccentricity 382 6.1 Overview 382 6.2 Repeat Validations 382 6.3 References 439 7 Validations – Receiver Voltage Response and Apparent Resistivity 440 7.1 Overview 440 7.2 Focused Studies 440 7.3 General Transmitter Design Philosophy 485 7.4 General Receiver Design Philosophy 487 7.5 Apparent Resistivity Estimation from Classic Dipole Model 490 8 Simulator Overview and Feature Summary 491 8.1 Overview 491 8.2 Simulator Comparisons 493 8.3 Technical Specifications 496 8.4 Advanced Logging Applications 498 8.5 Formulation Features 499 8.6 Computational Technology 503 8.7 User Interface 504 8.8 Integrated Utility Programs 505 8.9 Detailed Output and Integrated Graphics 506 8.10 System Requirements 507 8.11 Validation Approach 508 8.12 Simulator Speed Analysis 510 8.13 Sample User Interface Screens 511 8.14 Transmitter and Receiver Design Interface 517 9 Simulator Tutorials and Validation Problems 519 9.1 Problem Set 1. Dipole and Biot-Savart Model Consistency – Validating Magnetic Fields 520 9.2 Problem Set 2. Validating Farfield Phase Predictions 528 9.3 Problem Set 3. Drill Collar Model Consistency – Exact Drill Collar Validation Using Shen Analytical Solution 532 9.4 Problem Set 4. Magnetic Dipole in Two-Layer Formation 534 9.5 Problem Set 5. Effects of Eccentricity and Invasion 538 9.6 Problem Set 6. A Complicated Horizontal Well Geology 542 9.7 Problem Set 7. Effects of Layering, Anisotropy and Dip 546 9.8 Problem Set 8. Transmitter and Receiver Design 554 9.9 Problem Set 9. Apparent Anisotropic Resistivities for Electromagnetic Logging Tools in Horizontal Wells 560 9.10 Problem Set 10. Apparent Anisotropic Resistivities for Borehole Effects – Invasion and Eccentricity 577 Cumulative References 583 Index 585 About the Author 591