Electromagnetic Well Logging:

Models for MWD/LWD Interpretation and Tool Design

Wilson C. Chin, Ph.D., M.I.T.

Stratamagnetic Software, LLC

Houston, Texas and Beijing, China

Table of Contents

Preface, xi

Acknowledgements, xv

1. Motivating Ideas – General Formulation and Results, 1

1.1 Overview, 1

1.2 Introduction , 2

1.3 Physical Model and Numerical Formulation , 4

1.3.1 Design philosophy, 4

1.3.2 New discretization approach, 4

1.3.3 Analytical formulation , 5

1.3.4 An alternative approach, 6

1.3.5 Solution philosophy, 10

1.3.6 Governing equations , 11

1.3.7 Finite difference methodology, 11

1.4 Validation Methodology, 13

1.4.1 Fundamental physics, 14

1.4.2 Biot-Savart finite coil validations, 14

1.4.3 Analytical dipole validations, 15

1.4.4 Fully three-dimensional solutions , 15

1.5 Practical Applications, 16

1.5.1 Example 1. Granularity transition to coil source, 16

1.5.2 Example 2. Magnetic field, coil alone, 19

1.5.3 Example 3. Steel mandrel at dip, 20

1.5.4 Example 4. Conductive mud effects in wireline andMWD logging, 22

1.5.5 Example 5. Longitudinal magnetic fields, 24

1.5.6 Example 6. Elliptical coils, 28

1.5.7 Example 7. Calculating electromotive force, 30

1.5.8 Example 8. Detailed incremental readings , 32

1.5.9 Example 9. Coil residing along bed interface, 33

1.6 Closing Remarks , 34

1.7 References , 35

2. Detailed Theory and Numerical Analysis, 37

2.1 Overview , 37

2.2 Introduction, 40

2.2.1 Physical and mathematical complications, 40

2.2.2 Numerical challenges, 41

2.2.3 Alternative approaches , 42

2.2.4 Project summary , 43

2.3 Preliminary Mathematical Considerations , 47

2.3.1 General governing differential equations, 48

2.3.2 Anisotropic model, 48

2.3.3 Equivalent vector and scalar potential formulation, 49

2.3.4 Recapitulation and mathematical observations , 51

2.3.5 Matching conditions at bed interfaces , 52

2.3.6 Exact surface charge modeling, 55

2.3.7 Constant frequency analysis , 57

2.4 Boundary Value Problem Formulation, 58

2.4.1 Model for weak charge buildup , 59

2.4.2 Distributed surface charge , 62

2.4.3 Predictor-corrector model for strong polarization , 63

2.4.4 Fully coupled model for strong polarization, 64

2.5 Computational Issues and Strategies, 66

2.5.1 Alternative computational approaches , 67

2.5.2 Difference model at field points within layers, 68

2.5.3 Discontinuous functions and normal derivatives , 69

2.5.4 Scalar potential solution, 71

2.5.5 No limiting assumptions, 72

2.5.6 Logging tool mandrels, 72

2.5.7 Matrix analysis , 73

2.5.8 Programming notes, 74

2.5.9 Validation procedures, 74

2.6 Typical Simulation Results , 80

2.6.1 Example 1. Vertical hole, 20 KHz, 80

2.6.2 Example 2. Vertical hole, 2 MHz , 80

2.6.3 Example 3. Vertical hole, 2 MHz, collar, 80

2.6.4 Example 4. Tilted beds, 45o dip, 20 KHz, 84

2.6.5 Example 5. Tilted beds, 45o dip, 2 MHz, 88

2.6.6 Example 6. Tilted beds, 60o dip, 2 MHz, 92

2.6.7 Example 7. Tilted beds, 75o dip, 2 MHz, 93

2.6.8 Example 8. Tilted beds, 90o dip, 2 MHz, 95

2.6.9 Example 9. 90o dip, 2 Hz, with collar, 98

2.6.10 Example 10. Anisotropic effects, 101

2.6.11 Example 11. More anisotropic effects, 103

2.6.12 Example 12. Transmitter placement, 105

2.6.13 Example 13. More, transmitter placement, 106

2.6.14 Example 14. Double bed intersections , 108

2.7 Post-Processing and Applications, 112

2.7.1 Amplitude and phase, 112

2.7.2 Effects of interfacial surface charge , 116

2.7.3 Cylindrical radial coordinates, 118

2.7.4 Coordinate system notes, 121

2.7.5 Magnetic field modeling, 124

2.8 Restrictions with Fast Multi-frequency Methods, 126

2.8.1 Method 1, 126

2.8.2 Method 2, 127

2.9 Receiver Design Philosophy, 128

2.10 Description of Output Files 131

2.10.1 Output ‘Answer.Dat’ files in rectangular coordinates, 131

2.10.2 Output ‘Quiklook.Dat’ files in rectangular coordinates, 135

2.10.3 Output functions in cylindrical coordinates, 135

2.10.4 Typical "Point Summary" output , 135

2.10.5 Additional simulation files, 137

2.10.6 Creating color plots in planes perpendicular to z coordinate surfaces, 137

2.11 Apparent Resistivity Using Classic Dipole Solution, 138

2.12 Coordinate Conventions for Mud and Invasion Modeling, 139

2.12.1 Modeling borehole mud and invaded zones , 139

2.13 Generalized Fourier Integral for Transient Sounding , 140

2.14 References 141

3. Validations – Qualitative Benchmarks142

3.1 Overview, 142

3.2 Introductory Problems, 148

3.2.1 Example 1. Horizontal "coil alone," vertical well in homogeneous un-layered medium, 148

3.2.1.1 Validation of results, 152

3.2.1.2 Understanding electric fields, 153

3.2.1.3 Understanding magnetic fields, 156

3.2.1.4 Understanding point summaries, 163

3.2.2 Example 2. Vertical "coil alone," horizontal well in homogeneous unlayered medium, 166

3.2.3 Example 3. 45 degree "coil alone" problem in homogeneous unlayered medium, 172

3.2.4 Example 4. Ninety degree dip, three-layer problem, "coil alone" , 181

3.2.4.1 Understanding interfacial surface charge, 193

3.2.5 Example 5. Ninety degree dip, three-layer problem, "steel mandrel" 196

3.2.6 Example 6. Forty-five degree dip, three-layer problem, "coil alone" , 199

3.2.7 Example 7. Fully 3D, anisotropic, three-layer problem, with non-dipolar transmitter coil residing across three thin beds, 222

3.3 Advanced Problems , 245

3.3.1 Example 1. Vertical hole, 20 KHz, 245

3.3.2 Example 2. Vertical hole, 2 MHz , 247

3.3.3 Example 3. Vertical hole, 2 MHz, collar , 248

3.3.4 Example 4. Titled beds, 45o dip, 20 KHz , 249

3.3.5 Example 5. Tilted beds, 45o dip, 2 MHz , 253

3.3.6 Example 6. Tilted beds, 60o dip, 2 MHz , 257

3.3.7 Example 7. Tilted beds, 75o dip, 2 MHz , 258

3.3.8 Example 8. Tilted beds, 90o dip, 2 MHz , 260

3.3.9 Example 9. 90o dip, 2 MHz, with collar , 263

3.3.10 Example 10. Anisotropic effects , 265

3.3.11 Example 11. More anisotropic effects , 267

3.3.12 Example 12. Transmitter placement , 269

3.3.13 Example 13. More, transmitter placement, 271

3.3.14 Example 14. Double bed intersection, s273

3.4 Sign Conventions and Validation Methodolog, y277

3.5 References, 279

4. Validations – Quantitative Benchmarks at 0o and 90o, 280

4.1 Overview, 280

4.2 Wireline Validations in Homogeneous Media, 281

4.2.1 Simplified analytical models and comparison objectives, 281

4.2.1.1 Classical dipole model, 281

4.2.1.2 Nonconductive Biot-Savart model , 283

4.2.1.3 Electromagnetic versus simulation parameters, 284

4.2.1.4 Reiteration of basic ideas , 286

4.2.2 Inverse dependence of magnetic field source strength on coil diameter, 287

4.2.3 Calculating transmitter magnetic field source strength, 291

4.2.4 Validating receiver Bimag/Breal ratio on a wide range of variable grids , 292

4.2.4.1 Stretching Simulation Set No. 1, 294

4.2.4.2 Stretching Simulation Set No. 2, 295

4.2.4.3 Stretching Simulation Set No. 3, 296

4.2.4.4 Stretching Simulation Set No. 4, 297

4.2.5 Simulations holding resistivity fixed, with frequency varying , 299

4.2.6 Simulations holding frequency fixed, with resistivity varying, 302

4.3 Wireline Validations in Two-Layer Inhomogeneous Media, 304

4.3.1 Remarks and observations, 304

4.3.1.1 Detailed simulation results, 306

4.3.1.2 Simulation differences explained, 306

4.3.2 One inch diameter transmitter, vertical well, 308

4.3.2.1 Run 22a highlights, 309

4.3.2.2 Run 22b highlights , 312

4.3.2.3 Run 22c highlights, 313

4.3.3 Six inch diameter transmitter, vertical well, 314

4.3.3.1 Run 23a highlights , 314

4.3.3.2 Run 23b highlights , 315

4.3.3.3 Run 23c highlights , 316

4.3.4 One inch diameter transmitter, horizontal well, 317

4.3.4.1 Run 25a highlights , 318

4.3.4.2 Run 25b highlights , 320

4.3.4.3 Run 25c highlights , 324

4.3.5 Six inch diameter transmitter, horizontal well, 325

4.3.5.1 Run 26a highlights , 325

4.3.5.2 Run 26b highlights , 326

4.3.5.3 Run 26c highlights , 327

4.4 Electric and Magnetic Field Sensitive Volume Analysis for Resistivity and NMR Applications, 328

4.4.1 Depth of electromagnetic investigation in layered media with dip, 328

4.4.2 Typical layered media simulations (Cases 1-5) , 329

4.5 MWD "Steel Collar" and Wireline Computations in Homogeneous and Nonuniform Layered Dipping Media, 340

4.5.1 Wireline vs MWD logging scenarios, 340

4.5.2 Wireline "coil alone" simulation in uniform media, 341

4.5.3 MWD "steel drill collar" simulation in uniform media, 342

4.5.4 Wireline "coil alone" simulation in layered media , 344

4.5.5 MWD "steel drill collar" simulation in layered media, 345

4.6 Exact Drill Collar Validation Using Shen Analytical Solution347

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

5.2.1 Observations on variable mesh system, 357

5.2.2 Review of results for 0o and 90o, 358

5.2.3 Validation for general dip angles , 359

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

6.2.1 Simulation Set 1. Objective, validate steel drill collar logic for 6 inch transmitter coil in homogeneous medium, with borehole radius of "0" meaning "no mud" first. Later on, add mud effects, 382

6.2.2 Simulation Set 2. Objective, borehole modeling at 0 deg dip, vertical well application. Here, 1 Wm formation runs next, model the borehole with 0.01 Wm if there is a hole, so we can "see" its attenuative effects quickly, 383

6.2.3 Simulation Set 3. Objective, repeat calculations immediately above, but for 90 deg dip, horizontal well application. Intention is to duplicate above results with differently oriented logic loop, 383

6.2.4 Simulation Set 4. Objective, repeat work just above, but for 45o dip deviated well. Intention to duplicate prior results with differently oriented logic loop, 383

6.2.5 Simulation Set 5. Objective, next test eccentering of borehole relative to coil center, using our vertical well logic, 384

6.2.6 Simulation Set 6. Objective, test a 45o deviated well run with color reporting, 419

6.2.7 Simulation Set 7. Objective, consider magnetic fields with color reporting and validation, i.e., depth of investigation in layered media with dip, 426

6.2.7.1 Advanced electromagnetic modeling, 426

6.2.7.2 Layered media simulations, 428

6.2.7.3 Discussion, 435

6.2.7.4 Concluding remarks, 437

6.3 References, 439

7. Validations – Receiver Voltage Response and Apparent Resistivity, 440

7.1 Overview , 440

7.2 Focused Studies, 440

7.2.1 Pitfalls in calculating receiver voltage response using classical formula, 440

7.2.2 Operating the "custom receiver design" interface, 450

7.2.3 Validating receiver voltage calculations at different dip angles, 453

7.2.4 Apparent resistivity predictions can be dangerous, 474

7.2.5 Receiver voltage response in deviated wells without collars, 476

7.2.6 Apparent resistivity calculations, classical dipole versus 3D finite difference method for small 1 inch diameter coil shows consistent agreement, 482

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

8.4.1 Constant frequency electromagnetic tool operation, 498

8.4.2 Nuclear magnetic imaging , 498

8.4.3 Pulsed resistivity logging , 499

8.4.4 Downhole hardware design , 499

8.5 Formulation Features , 499

8.5.1 Partial differential equations , 499

8.5.2 Transmitter coil modeling , 500

8.5.3 Boundary conditions , 501

8.5.4 Finite difference grid system , 501

8.5.5 Electromagnetic properties , 502

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

8.11.1 Fundamental physical validations, 508

8.11.2 Biot-Savart finite coil validations, 509

8.11.3 Analytical dipole validations, 509

8.11.4 More demanding validations , 510

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