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Submit a ProposalElectromagnetic Well Logging
 | Models for MWD/LWD Interpretation and Tool Design By Wilson C. Chin Copyright: 2014 | Status: Published ISBN: 9781118831038 | Hardcover | 630 pages Price: $195 USD  |
One Line Description
Mathematically rigorous, computationally fast, and easy to use, this new approach to electromagnetic well logging does not bear the limitations of existing methods and gives the reservoir engineer a new dimension to MWD/LWD interpretation and tool design.
Audience
Petrophysicists, reservoir engineers, petroleum engieners, professionals working in MWD and LWD, oil service company hardware tool designers, and geosteering engineers. The book will also appeal to students of physics and mathematics, and to numerically oriented practitioners, outside of the petroleum industry.
Petrophysicists, reservoir engineers, petroleum engieners, professionals working in MWD and LWD, oil service company hardware tool designers, and geosteering engineers. The book will also appeal to students of physics and mathematics, and to numerically oriented practitioners, outside of the petroleum industry.
Description
Almost all publications on borehole electromagnetics deal with idealizations that are not acceptable physically, and unfortunately, even these models are company proprietary. On the other hand, “exact models” are only available through detailed finite element or finite difference analysis, and more often than not, simply describe case studies for special applications. In either case, the models are not available for general use and the value of the publications is questionable.
This new approach provides a rigorous, fully three-dimensional solution to the general problem, developed over almost two decades by a researcher familiar with practical applications and mathematical modeling. Completely validated against exact solutions and physics-based checks through over a hundred documented examples, the self-contained model (with special built-in matrix solvers and iteration algorithms) with a “plain English graphical user interface” has been optimized to run extremely fast – seconds per run as opposed to minutes and hours – and then automatically presents all electric and magnetic field results through integrated three-dimensional color graphics.
In addition to state-of-the-art algorithms, basic “utility programs” are also developed, such as simple dipole methods, Biot-Savart large diameter models, nonlinear phase and amplitude interpolation algorithms, and so on. Incredibly useful to oilfield practitioners, this volume is a must-have for serious professionals in the field, and all the algorithms have undergone a laborious validation process with real use in the field.
Back to Top
Almost all publications on borehole electromagnetics deal with idealizations that are not acceptable physically, and unfortunately, even these models are company proprietary. On the other hand, “exact models” are only available through detailed finite element or finite difference analysis, and more often than not, simply describe case studies for special applications. In either case, the models are not available for general use and the value of the publications is questionable.
This new approach provides a rigorous, fully three-dimensional solution to the general problem, developed over almost two decades by a researcher familiar with practical applications and mathematical modeling. Completely validated against exact solutions and physics-based checks through over a hundred documented examples, the self-contained model (with special built-in matrix solvers and iteration algorithms) with a “plain English graphical user interface” has been optimized to run extremely fast – seconds per run as opposed to minutes and hours – and then automatically presents all electric and magnetic field results through integrated three-dimensional color graphics.
In addition to state-of-the-art algorithms, basic “utility programs” are also developed, such as simple dipole methods, Biot-Savart large diameter models, nonlinear phase and amplitude interpolation algorithms, and so on. Incredibly useful to oilfield practitioners, this volume is a must-have for serious professionals in the field, and all the algorithms have undergone a laborious validation process with real use in the field.
Back to Top
Author / Editor Details
Wilson C. Chin, who earned his Ph.D. from M.I.T. and M.Sc. 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. Mr. Chin is the author of ten books, more than one hundred papers and over forty patents, and winner of five prestigious contract awards from the United States Department of Energy’s SBIR and RPSEA affiliates.
Wilson C. Chin, who earned his Ph.D. from M.I.T. and M.Sc. 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. Mr. Chin is the author of ten books, more than one hundred papers and over forty patents, and winner of five prestigious contract awards from the United States Department of Energy’s SBIR and RPSEA affiliates.
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Table of Contents
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
1.3.1 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 and
MWD logging 22
1.5.5 Example 5. Longitudinal magnetic fields 24
vi Contents
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, 45 ‚° dip, 20 KHz 84
2.6.5 Example 5. Tilted beds, 45 ‚° dip, 2 MHz 88
2.6.6 Example 6. Tilted beds, 60 ‚° dip, 2 MHz 92
2.6.7 Example 7. Tilted beds, 75 ‚° dip, 2 MHz 93
2.6.8 Example 8. Tilted beds, 90 ‚° dip, 2 MHz 95
2.6.9 Example 9. 90 ‚° 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 --‚¬ËœAnswer.Dat--‚¬„¢ files in rectangular coordinates 131
2.10.2 Output --‚¬ËœQuiklook.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 Benchmarks 142
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, 45 ‚° dip, 20 KHz 249
3.3.5 Example 5. Tilted beds, 45 ‚° dip, 2 MHz 253
3.3.6 Example 6. Tilted beds, 60 ‚° dip, 2 MHz 257
3.3.7 Example 7. Tilted beds, 75 ‚° dip, 2 MHz 258
3.3.8 Example 8. Tilted beds, 90 ‚° dip, 2 MHz 260
3.3.9 Example 9. 90 ‚° 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 intersections 273
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
4.2.1 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 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
5.2.1 Observations on variable mesh system 357
5.2.2 Review of results for 0 ‚° and 90 ‚° 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 Ž©m
formation runs next, model the borehole with
0.01 Ž©m if there is a hole, so we can see -- 0.02
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 45 ‚° 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 45 ‚° 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
Back to Top
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
1.3.1 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 and
MWD logging 22
1.5.5 Example 5. Longitudinal magnetic fields 24
vi Contents
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, 45 ‚° dip, 20 KHz 84
2.6.5 Example 5. Tilted beds, 45 ‚° dip, 2 MHz 88
2.6.6 Example 6. Tilted beds, 60 ‚° dip, 2 MHz 92
2.6.7 Example 7. Tilted beds, 75 ‚° dip, 2 MHz 93
2.6.8 Example 8. Tilted beds, 90 ‚° dip, 2 MHz 95
2.6.9 Example 9. 90 ‚° 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 --‚¬ËœAnswer.Dat--‚¬„¢ files in rectangular coordinates 131
2.10.2 Output --‚¬ËœQuiklook.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 Benchmarks 142
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, 45 ‚° dip, 20 KHz 249
3.3.5 Example 5. Tilted beds, 45 ‚° dip, 2 MHz 253
3.3.6 Example 6. Tilted beds, 60 ‚° dip, 2 MHz 257
3.3.7 Example 7. Tilted beds, 75 ‚° dip, 2 MHz 258
3.3.8 Example 8. Tilted beds, 90 ‚° dip, 2 MHz 260
3.3.9 Example 9. 90 ‚° 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 intersections 273
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
4.2.1 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 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
5.2.1 Observations on variable mesh system 357
5.2.2 Review of results for 0 ‚° and 90 ‚° 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 Ž©m
formation runs next, model the borehole with
0.01 Ž©m if there is a hole, so we can see -- 0.02
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 45 ‚° 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 45 ‚° 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
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BISAC SUBJECT HEADINGS
TEC031030: TECHNOLOGY & ENGINEERING / Power Resources / Fossil Fuels
SCI032000: SCIENCE / Physics / Geophysics
SCI024000: SCIENCE / Energy
BIC CODES
THF: Fossil fuel technologies
TQ: ENVIRONMENTAL SCIENCE, ENGINEERING & TECHNOLOGY
RBGK: Geochemistry
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