Principles of Induction Logging (eBook)

Yu.A. Dashevsky, Avital Kaufman (Herausgeber)

eBook Download: PDF

2003 | 1. Auflage
656 Seiten
Elsevier Science (Verlag)
978-0-08-053962-1 (ISBN)

Infos

The monograph introduces the reader to the world of inductive well logging - an established method for surveying the electrical conductivity of rocks surrounding a borehole. The emphasis is on developing a theory of inductive logging and on understanding logging tools basic physics, since this theory and understanding furnish valuable insights for inventing practical induction logging techniques.

The first chapter of the book presents the basic laws of electromagnetism from a point of view that will facilitate the application of the theory to problems in electromagnetic logging. Many topics that play an important role in the design and interpretation of tools readings are covered. The vertical resolution and radial depth of investigation of different induction tools is systematically considered. Special attention is paid to principles of induction logging with transversal induction coils, to transient method of induction logging in media with cylindrical and horizontal interfaces and to the influence of anisotropy on the electromagnetic field measured in a conducting medium. Multi-coil differential induction probes and induction logging based on measuring the inphase component of the secondary field or the quadrature component difference are also described in detail. The last chapter is devoted to mathematical modeling of the response of induction logging tools in 3D geometries. The theory of inductive logging presented in this volume can be applied to logging after drilling as well as logging while drilling.

Inhalt

Cover 1
Contents 6
Acknowledgments 10
List of Symbols 12
Introduction 14
Chapter 1. Basic electromagnetic laws and Maxwell's equations 18
1.1. Coulomb's law 18
1.2. Biot–Savart law 47
1.3. The postulate of conservation of charge and the distribution of charges in conducting media 65
1.4. Faraday's law and the first Maxwell equation 80
1.5. Electromagnetic field equations 105
1.6. Relationships between various responses of the electromagnetic field 120
Chapter 2. Electromagnetic field of the magnetic dipole in a uniform conducting medium 132
Chapter 3. Methods for the solution of direct problems of induction logging 156
3.1. The method of separation of variables 157
3.2. The method of shells 159
3.3. The method of integral equations 172
3.4. Approximate methods of field calculation in induction logging 183
Chapter 4. Electromagnetic field of a vertical magnetic dipole on the axis of a borehole 200
4.1. Formulation of the boundary problem 200
4.2. Derivation of the formula for the vertical component of the magnetic field 202
4.3. The quadrature component of the magnetic field at the range of very small model parameters 215
4.4. Radial characteristics of a two-coil induction probe at the range of small parameters 226
4.5. Influence of the skin effect in the formation on the radial characteristics of a two-coil induction probe 235
4.6. Asymptotic behavior of the magnetic field in the borehole in the range of small parameters 242
4.7. Behavior of the field on the borehole axis in the near and far zones 249
4.8. Frequency responses of the magnetic field of the vertical magnetic dipole on the borehole axis 258
4.9. Influence of finite dimensions of induction probe coils 262
4.10. Electrical field of a current ring in a medium with cylindrical interfaces 282
4.11. Radial responses of two-coil induction probes displaced with respect to the borehole axis 303
4.12. The influence of magnetic permeability and dielectric constant in induction logging 312
Chapter 5. Quasistationary magnetic field of a vertical magnetic dipole in a formation with a finite thickness 324
5.1. Derivation of formulae for the vertical component of the magnetic field of a vertical magnetic dipole 324
5.2. The vertical responses of the two-coil induction probe in the range of small parameters 332
5.3. The theory of the two-coil induction probe in beds with a finite thickness 344
5.4. Curves of profiling with a two-coil induction probe in a medium with two horizontal interfaces 365
Chapter 6. The two-coil induction probe on the borehole axis, when the bed has a finite thickness 378
6.1. Doll's theory of the two-coil induction probe located on the borehole axis when a formation has a finite thickness 379
6.2. The theory of a two-coil induction probe, taking into account the skin effect in an external medium 384
6.3. Influence of the finite thickness of the formation on the magnetic field behavior 389
Chapter 7. Multi-coil differential induction probes 398
7.1. Methods of determination of probe parameters 399
7.2. Physical principles of multi-coil differential probes 408
7.3. Radial and vertical responses of the differential probe l.L–1.2 410
7.4. Radial and Vertical Responses of Probes 6F1M, 4F1 and 4F1.1 428
7.5. The influence of finite height of the invasion zone on radial responses of probes 6F1M, 4F1 and 4F1.1 450
7.6. Three-coil differential probe 454
7.7. The influence of eccentricity on focusing features of multi-coil induction probes 466
7.8. Choice of a frequency for differential probes 469
7.9. Determination of the coefficient of differential probes 470
Chapter 8. Induction logging based on measuring the inphase component of the secondary field or the quadrature component difference of type Q Hz(.1) – .1/.2 Q Hz(.2) 476
Chapter 9: Transient induction logging 490
9.1. The transient field of the magnetic dipole in a uniform medium 491
9.2. Transient field of the vertical magnetic dipole on the borehole axis at the late stage 509
9.3. Apparent resistivity curves of the transient method in a medium with cylindrical interfaces 515
9.4. The transient responses of a vertical magnetic dipole in a formation with a finite thickness 521
9.5. About a nonstationary field of the electric dipole 541
Chapter 10. Principles of induction logging with transversal induction coils 546
10.1. Electromagnetic field of the magnetic dipole in a uniform isotropic medium 546
10.2. Boundary problem for the horizontal magnetic dipole on the borehole axis 548
10.3. Magnetic field on the borehole axis in the near zone 563
10.4. The magnetic field on the borehole axis in the far zone 571
10.5. The magnetic field in a medium with two cylindrical interfaces 579
10.6. Cylindrical surface with transversal resistance T 584
10.7. The magnetic field in a medium with one horizontal interface 588
10.8. The magnetic field of the horizontal dipole in the formation with finite thickness 593
10.9. Curves of profiling with a two-coil induction probe in a medium with horizontal interfaces 611
Chapter 11. The influence of anisotropy on the field of the magnetic dipole in a conducting medium 618
11.1. Anisotropy of a layered medium 618
11.2. Electromagnetic field of the magnetic dipole in a uniform anisotropic medium 621
11.3. Magnetic field in an anisotropic medium with two horizontal interfaces 630
Chapter 12. Mathematical modeling of the response of induction logging tools in 3D geometries 640
References 652
Subject Index 654

Textauszug

Introduction

A.A. Kaufman    Department of Geophysics Colorado School of Mines Golden, CO 80401, U.S.A.

Yu.A. Dashevsky    Institute of Geophysics Siberian Branch Russian Academy of Sciences, Novosibirsk, Russia

Induction well logging is an established method for surveying the electrical conductivity of rocks surrounding a borehole and proceeded from the early efforts of H. G. Doll (1949, 1952). In its simplest form, an induction well-logging device consists of two coils; one is a transmitter and the other is a receiver. The transmitter coil is energized with an alternating current at frequencies of twenty kilohertz and much higher, while the electromotive force, caused by a change of the magnetic field, is detected at the receiver coil. In almost all cases with some important exceptions, the axes of the coils are coincident with the axis of the borehole. The separation between the transmitter and receiver coils is termed the probe length, and this parameter is commonly used to control the depth of investigation of the logging device away from the borehole axis. The electromotive force, which is detected at the receiver coil, is linearly dependent on the amount of the current provided to the transmitter coil, as well as strengths of currents that are induced in the surrounding medium. The actual distribution of these additional currents depends on the electrical structure of the medium, and in particular, on the conductivity. For this reason, by measuring the electromotive force in the receiver coil one can, in principle, determine the conductivity of the formation opposite which the induction device is located.

In those cases, when the borehole axis is perpendicular to the boundaries between formations, the current flow path in the medium forms a circle, located in a horizontal plane and centered on the borehole axis. Correspondingly, induction logging is very sensitive to thin conductive layers, but it has difficulty in detecting relatively thin and resistive beds.

H. Doll also introduced the differential multi-coil probes, which became very efficient logging tools and defined the path of development and application of induction logging over almost forty years. The use of these differential measurements in induction logging provides a result in which the effect of the borehole fluid, and in many cases also the invasion zone, on measurements is greatly reduced. Such devices are described in detail in this monograph.

H. Doll did not only invent induction probes, but also suggested a very useful though approximate theory for the method, which helped immensely to develop principles of an interpretation and to aid in the design parameters of focusing probes. For simplification of the mathematical problem Doll has considered that the induction coils on the logging tool are essentially magnetic dipoles, and for sufficiently low frequencies or a highly resistive medium the skin effect can be neglected. In other words, an interaction between the various induced currents is not strong enough to affect their magnitude appreciably. Respectively, the currents everywhere in the medium are in phase with one another, this phase being ninety degrees shifted with respect to the current in the transmitter coil.

With these approximations the magnitude of the current, induced in the formation at any point, can be calculated by using quite simple formulae. This also allows the definition of a straightforward geometrical factor, which characterizes the relationship between the magnetic fields and the conductivity at an arbitrary point of a medium. According to this approximate theory, the magnetic field, contributed by the induction currents, has only the quadrature (out-of-phase) component, with the in-phase component of the magnetic field being zero.

The concept of the geometric factor for an assembly of elementary rings with centers located on the axis of the borehole plays an essential role in Doll’s theoretical approach. By using such geometrical factors Doll was able to calculate the electromotive force, arising in the receiver and caused by various parts of a medium, and to investigate the vertical and radial responses of different induction probes.

The approach, developed by Doll, is so satisfactory that it remains virtually unchanged in developing procedures of interpretation, if the so-called induction parameter is sufficiently small. Of course, this theory is valid when the electric field is tangential to boundaries and, correspondingly, surface charges are absent.

In almost sixty years, since the first development by H. Doll, research on various aspects of induction well-logging has been carried out around the world, and there have been some rather significant advances in theory, interpretation, probe design and equipment. Moreover, completely new modifications of induction logging have been developed and their principles are described in our monograph. As a result of the efforts of scientists and engineers in the United States, former Soviet Union and other countries, induction well- logging has become the most powerful tool for a determination of formation conductivity in uncased wells.

Because much of the development of induction logging was done in proprietary research by logging services and oil companies, the technical articles that appeared in journals do not properly reflect the real volume of research that has been done on the method. For this reason, it is probably impossible to attribute the proper respect to everyone who has contributed in the development of induction well-logging in the western community. Among those who carried through the work started by H. Doll, are J. H. Moran, K. S. Kunetz, W. C. Duesterhoeff, J. L. Dumanoir, M. P. Tixier, M. Martin, A. J. deWitte, and D. A. Lowitz. Later their activity was continued by S. Gianzero, J. Tabanou, B. Anderson, T. Barber, G. Minerbo, B. Clark, S. Chang, V. Druskin, T. Habashy, and many others.

In the USSR, parallel development of theory, interpretation and equipment of induction logging, based on Doll’s concepts of the geometric factor and focusing probe, was started at almost the same time. Also, during this research, new modifications of induction logging were introduced and some of them became conventional and are now used over the world.

Theoretical investigations performed by L. Alpin, S. Akselrod, A. Kaufman, Y. Ku- dravchev, and V. Nikitina allowed us to understand the behavior of the quasistationary electromagnetic fields, caused by the magnetic dipole in a medium with cylindrical as well as horizontal interfaces. These studies helped to design equipment and focusing probes with optimal radial and vertical characteristics (S. Akselrod, M. Plusnin).

Almost from the beginning, the frequency of the transmitter current was chosen much higher than in the west, and it was done in order to improve the vertical responses of probes (Kaufman, 1962). At the same time, it was demonstrated that the quadrature and in-phase components of the secondary magnetic fields deliver a different depth of investigation (Kaufman, 1959). For this reason, it is natural that the conventional equipment of induction logging is able to measure both these components.

As was pointed out, the remarkable simplicity of Doll’s theory is related to the fact that interaction of induced currents is neglected. In order to take into account this effect and improve the quality of an interpretation of logging data, a new approach, also an approximate one. was suggested (Kaufman, 1962). This method allows us relatively quickly to evaluate the field, subjected to an influence of the skin effect in a formation, when there are both cylindrical and horizontal interfaces. Much later, this rather complicated problem was solved by V. Dimitriev, L. Tabarovsky, V. Zakharov using the method of integral equations.

At the beginning of the 1960’s there was the first attempt to develop induction logging without the use of multi-coil focusing probes. By analogy with the lateral logging soundings with lateral probes, widely used in the former Soviet Union, the induction lateral soundings were suggested (Kaufman, 1962). The patent was applied, several papers were published that described principles of an interpretation of the apparent conductivity curves with two- and three-coil probes of a different length. Additionally, an influence of the in-phase component of the magnetic field on the radial responses was studied, as well as the use of different frequencies for probes of different lengths.

At that time, the logging industry was not ready to accept this approach and rejected it. However, with time, attitude to multi-array systems was completely changed, and during the last twenty years this type of induction logging has been widely used as the conventional method. To a great extent its progress is related to the development of the dielectric logging. At the beginning, borehole measurements of the dielectric constant of formations were performed with a tool that is similar to the capacitor. Then, it was suggested to measure this parameter inductively, that is, using the induction probe (Kaufman, 1963). This approach was successfully developed by D. Daev, who introduced a new approach, namely, measuring the ratio of amplitudes of the magnetic field and the difference of phases with the three-coil probe. It turned out that measurements of these parameters in induction logging also provide excellent radial and vertical responses, if frequencies are properly chosen. For this reason, they are either measured or calculated in the multi-array tool, as well as in the logging while drilling.

At the end of the 1960’s...

Produkt-Details

• Erscheint lt. Verlag: 23.5.2003
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
• Themenwelt: Technik
• ISBN-10: 0-08-053962-9 / 0080539629
• ISBN-13: 978-0-08-053962-1 / 9780080539621