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'''''Processing.''''' The results of directional surveying usually take the form of inclination, ''α'', and azimuth, ''β'', of a borehole at a sequence of survey stations. The only other information available is the difference in measured depths for two adjacent stations, but this does not describe the shape of the well path. Starting with the coordinates of the surface reference point, the actual distance between adjacent survey stations needs to be calculated so that the coordinates of any station can be found by addition and those of any intermediate point can be found by interpolation. There are several ways of doing this interpolation. The following account is based on Inglis’ work.<ref name="r4">Inglis, T. 1987. Directional Drilling. London: Graham & Trotman.
'''''Processing.''''' The results of directional surveying usually take the form of inclination, ''α'', and azimuth, ''β'', of a borehole at a sequence of survey stations. The only other information available is the difference in measured depths for two adjacent stations, but this does not describe the shape of the well path. Starting with the coordinates of the surface reference point, the actual distance between adjacent survey stations needs to be calculated so that the coordinates of any station can be found by addition and those of any intermediate point can be found by interpolation. There are several ways of doing this interpolation. The following account is based on Inglis’ work.<ref name="r4">Inglis, T. 1987. Directional Drilling. London: Graham & Trotman.fckLR</ref><br/><br/>The balanced tangential method assumes that the actual wellpath between two adjacent measurement stations can be approximated by two straight lines of equal length, ''L''/2, shown as AX and BX in '''Fig. 3G.4'''. This leads to the following expressions for the incremental distances between adjacent survey stations in the vertical direction (Δ''V''), in the direction of the northing (Δ''N''), and in the direction of the easting (Δ''E''):<br/><br/>[[File:Vol5 page 0381 eq 001.png|RTENOTITLE]]....................(3G.1)<br/><br/>[[File:Vol5 page 0381 eq 002.png|RTENOTITLE]]....................(3G.2)<br/><br/>and [[File:Vol5 page 0384 eq 001.png|RTENOTITLE]]....................(3G.3)<br/><br/>where the subscripts 1 and 2 denote the upper and lower survey stations, respectively.<br/><br/><gallery widths="300px" heights="200px">
</ref><br/><br/>The balanced tangential method assumes that the actual wellpath between two adjacent measurement stations can be approximated by two straight lines of equal length, ''L''/2, shown as AX and BX in '''Fig. 3G.4'''. This leads to the following expressions for the incremental distances between adjacent survey stations in the vertical direction (Δ''V''), in the direction of the northing (Δ''N''), and in the direction of the easting (Δ''E''):<br/><br/>[[File:Vol5 page 0381 eq 001.png|RTENOTITLE]]....................(3G.1)<br/><br/>[[File:Vol5 page 0381 eq 002.png|RTENOTITLE]]....................(3G.2)<br/><br/>and [[File:Vol5 page 0384 eq 001.png|RTENOTITLE]]....................(3G.3)<br/><br/>where the subscripts 1 and 2 denote the upper and lower survey stations, respectively.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0384 Image 0001.png|'''Fig. 3G.4 – Principles of the balanced tangential method for modeling the well path between directional survey stations A and B.<ref name="r4" />'''
File:vol5 Page 0384 Image 0001.png|'''Fig. 3G.4 – Principles of the balanced tangential method for modeling the well path between directional survey stations A and B.<ref name="r4" />'''
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An improvement on the balanced tangential method is the minimum curvature method, which replaces the two straight lines by an arc. The position of the arc is based on the amount of bending in the wellpath between the two survey stations. The amount of bending is described by a ratio factor, ''F''<sub>''r''</sub>, and quantified by a dogleg angle, ''ψ'' ('''Fig. 3G.5'''), so that:<br/><br/>[[File:Vol5 page 0384 eq 002.png|RTENOTITLE]]....................(3G.4)<br/><br/>where<br/><br/>[[File:Vol5 page 0384 eq 003.png|RTENOTITLE]]....................(3G.5)<br/><br/>The ratio factor is applied to each of the quantities Δ''V'', Δ''N'', and Δ''E'' as calculated by the balanced tangential method ('''Eqs. 3G.1''' through '''3G.3'''). Thus, for example, '''Eq. 3G.1''' becomes<br/><br/>[[File:Vol5 page 0385 eq 001.png|RTENOTITLE]]....................(3G.6)<br/><br/>The minimum curvature method is the most widely used for computing the coordinate deliverables of directional surveys. Inglis<ref name="r4">Inglis, T. 1987. Directional Drilling. London: Graham & Trotman.
An improvement on the balanced tangential method is the minimum curvature method, which replaces the two straight lines by an arc. The position of the arc is based on the amount of bending in the wellpath between the two survey stations. The amount of bending is described by a ratio factor, ''F''<sub>''r''</sub>, and quantified by a dogleg angle, ''ψ'' ('''Fig. 3G.5'''), so that:<br/><br/>[[File:Vol5 page 0384 eq 002.png|RTENOTITLE]]....................(3G.4)<br/><br/>where<br/><br/>[[File:Vol5 page 0384 eq 003.png|RTENOTITLE]]....................(3G.5)<br/><br/>The ratio factor is applied to each of the quantities Δ''V'', Δ''N'', and Δ''E'' as calculated by the balanced tangential method ('''Eqs. 3G.1''' through '''3G.3'''). Thus, for example, '''Eq. 3G.1''' becomes<br/><br/>[[File:Vol5 page 0385 eq 001.png|RTENOTITLE]]....................(3G.6)<br/><br/>The minimum curvature method is the most widely used for computing the coordinate deliverables of directional surveys. Inglis<ref name="r4">Inglis, T. 1987. Directional Drilling. London: Graham & Trotman.fckLR</ref> provided a detailed description of the calculations.<br/><br/><gallery widths="300px" heights="200px">
</ref> provided a detailed description of the calculations.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0385 Image 0001.png|'''Fig. 3G.5 – Principles of the minimum curvature method for modeling the well path between directional survey stations A and B, drawn in the plane of the wellbore. '''
File:vol5 Page 0385 Image 0001.png|'''Fig. 3G.5 – Principles of the minimum curvature method for modeling the well path between directional survey stations A and B, drawn in the plane of the wellbore. '''
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=== Downhole Magnetics ===
=== Downhole Magnetics ===


Downhole magnetic surveys have been most commonly applied in highly magnetized igneous rocks, which have usually been studied within pure geoscience, especially beneath the ocean floor. These rocks preserve the direction of the Earth’s field at the time of their formation (i.e., the prevailing magnetic field is "frozen" in the rocks as they solidify, giving them a strong natural remnant magnetization). A primary application has been to identify points in time at which the Earth’s magnetic field has undergone a polarity reversal. These reversals have been dated globally (e.g., isotopically in the case of volcanic series or by correlation with biostratigraphy in the case of volcaniclastics) and have given rise to a geomagnetic polarity time scale (GPTS) that is based on laboratory measurements. This, in turn, has allowed dates to be assigned to a given magnetozone that is bounded by reversal phenomena. It has been possible to recognize these reversals through downhole measurements and, therefore, to date the rocks accordingly.<br/><br/>Sedimentary rocks have much weaker remnant magnetizations than igneous sequences, and it has been much more difficult to investigate their magnetic character. However, recent advances in instrumentation have led to progress in downhole magnetic measurements of sedimentary strata.<ref name="r40">Pages, G., Barthies, V., Boutemy, Y. et al. 1994. Wireline Magnetostratigraphy Principles and Field Results. Presented at the SPWLA 35th Annual Logging Symposium, 1994. SPWLA-1994-XX.</ref><br/><br/>'''''Theory.''''' The following magnetic theory is extracted from Lalanne ''et al.''<ref name="r41">Lalanne, B., Bouisset, P., Pages, G. et al. 1991. Magnetic Logging: Borehole Magnetostratigraphy and Absolute Datation in Sedimentary Rocks. Presented at the Middle East Oil Show, Bahrain, 16-19 November 1991. SPE-21437-MS. http://dx.doi.org/10.2118/21437-MS
Downhole magnetic surveys have been most commonly applied in highly magnetized igneous rocks, which have usually been studied within pure geoscience, especially beneath the ocean floor. These rocks preserve the direction of the Earth’s field at the time of their formation (i.e., the prevailing magnetic field is "frozen" in the rocks as they solidify, giving them a strong natural remnant magnetization). A primary application has been to identify points in time at which the Earth’s magnetic field has undergone a polarity reversal. These reversals have been dated globally (e.g., isotopically in the case of volcanic series or by correlation with biostratigraphy in the case of volcaniclastics) and have given rise to a geomagnetic polarity time scale (GPTS) that is based on laboratory measurements. This, in turn, has allowed dates to be assigned to a given magnetozone that is bounded by reversal phenomena. It has been possible to recognize these reversals through downhole measurements and, therefore, to date the rocks accordingly.<br/><br/>Sedimentary rocks have much weaker remnant magnetizations than igneous sequences, and it has been much more difficult to investigate their magnetic character. However, recent advances in instrumentation have led to progress in downhole magnetic measurements of sedimentary strata.<ref name="r40">Pages, G., Barthies, V., Boutemy, Y. et al. 1994. Wireline Magnetostratigraphy Principles and Field Results. Presented at the SPWLA 35th Annual Logging Symposium, 1994. SPWLA-1994-XX.</ref><br/><br/>'''''Theory.''''' The following magnetic theory is extracted from Lalanne ''et al.''<ref name="r41">Lalanne, B., Bouisset, P., Pages, G. et al. 1991. Magnetic Logging: Borehole Magnetostratigraphy and Absolute Datation in Sedimentary Rocks. Presented at the Middle East Oil Show, Bahrain, 16-19 November 1991. SPE-21437-MS. http://dx.doi.org/10.2118/21437-MSfckLR</ref> The magnetic field measured downhole has three parts: the Earth’s magnetic field of the present day; the field that is induced in the rocks by the prevailing Earth’s field; and the remnant magnetic field, which is the preservation in the rocks of a paleomagnetic field. The effect of the Earth’s magnetic field can be accommodated during logging by extrapolating downhole the measurements made by a surface magnetometer that records diurnal variations in the Earth’s field and allows the downhole data to be corrected for these variations where they are significant. The induced field is proportional to the magnetic susceptibility of the rock, which is governed by (ferro-magnetic) mineralogy and fluid composition. The remnant magnetic field adopts the direction of the Earth’s field at the time that the rock was forming. For sediments, it is most pronounced in clays.
</ref> The magnetic field measured downhole has three parts: the Earth’s magnetic field of the present day; the field that is induced in the rocks by the prevailing Earth’s field; and the remnant magnetic field, which is the preservation in the rocks of a paleomagnetic field. The effect of the Earth’s magnetic field can be accommodated during logging by extrapolating downhole the measurements made by a surface magnetometer that records diurnal variations in the Earth’s field and allows the downhole data to be corrected for these variations where they are significant. The induced field is proportional to the magnetic susceptibility of the rock, which is governed by (ferro-magnetic) mineralogy and fluid composition. The remnant magnetic field adopts the direction of the Earth’s field at the time that the rock was forming. For sediments, it is most pronounced in clays.


A measurement of magnetic induction or field strength, ''B''<sub>''T''</sub>, can be written as<br/><br/>[[File:Vol5 page 0413 eq 001.png|RTENOTITLE]]....................(3G.21)<br/><br/>where ''B''<sub>''o''</sub> is the magnetic induction associated with the present Earth’s field, ''B''<sub>''i''</sub> is the magnetic induction caused by the field induced in the rock, and ''B''<sub>''r''</sub> is the magnetic induction caused by the remnant field. Magnetic induction is measured in units of nanoTesla (nT). It is a measure of field strength expressed in terms of the field’s ability to induce magnetization. Typically, ''B''<sub>''i''</sub> and ''B''<sub>''r''</sub> are no more than a few tens of nanoTesla, and they have to be measured against a prevailing Earth’s field that is a thousand times greater. Therefore, the exercise becomes very much one of analyzing residuals. For this reason, the prevailing Earth’s field, ''B''<sub>''o''</sub>, is removed from the value of ''B''<sub>''T''</sub>, which then becomes a "net" field ''B''<sub>''t''</sub>.<br/><br/>[[File:Vol5 page 0413 eq 002.png|RTENOTITLE]]....................(3G.22)<br/><br/>The induced magnetic field, ''B''<sub>''i''</sub> (nT), is proportional to the magnetic susceptibility, ''χ'' (units SI), of the rock:<br/><br/>[[File:Vol5 page 0413 eq 003.png|RTENOTITLE]]....................(3G.23)<br/><br/>where ''μ''<sub>''o''</sub> is the magnetic permeability of the void (4''π'' × 10<sup>–1</sup> μH/m), and ''H''<sub>''T''</sub> is the Earth’s magnetic field (A/mm). Therefore, ''B''<sub>''i''</sub> can be evaluated if susceptibility can be measured.<br/><br/>If ''B''<sub>''t''</sub> and ''B''<sub>''i''</sub> can be determined, ''B''<sub>''r''</sub> can be quantified,<br/><br/>[[File:Vol5 page 0413 eq 004.png|RTENOTITLE]]....................(3G.24)<br/><br/>If ''B''<sub>''r''</sub> is positive, the remnant magnetization and, therefore, the paleomagnetic field that caused it are aligned as per the present-day Earth’s field, and ''B''<sub>''r''</sub> is described as "normal." Otherwise, its polarity is "reversed." The polarity of remnant magnetization is evaluated through a numerical comparison of ''B''<sub>''t''</sub> and ''B''<sub>''i''</sub>.<br/><br/>'''''Measurement.''''' A magnetic logging sonde developed for sedimentary rocks is Schlumberger’s Geological High-Resolution Magnetic Tool (GHMT™). It actually comprises two tools: one to measure the total magnetic field and one to measure magnetic susceptibility. The tool housings are nonmagnetic and electrically insulating with a diameter of 4 in. [100 mm].<br/><br/>Because sedimentary rocks have a very low magnetization, a very high precision magnetometer is required. This requirement is satisfied by Schlumberger’s Nuclear Magnetic Resonance Tool (NMRT™), which uses the principles of nuclear magnetic resonance whereby the frequency of precession of relaxing protons is proportional to ''B''<sub>''T''</sub> (see Chap. 3E in this section of the ''Handbook''). The problem, therefore, reduces to a very precise measurement of frequency. The NMRT measurement has a sensitivity of 10<sup>–2</sup> nT. Data are recorded at a logging speed of 1970 ft/hr [600 m/hr] with a sampling interval of 4 in. [100 mm].<br/><br/>A second tool measures the magnetic susceptibility of the rock, which is proportional to ''B''<sub>''i''</sub> ('''Eq. 3G.23'''). This tool, Schlumberger’s Susceptibility Measurement Tool (SUMT™), uses the principles of electromagnetic induction. The voltage induced in the receiver coil increases with susceptibility, which is determined from the complex character of the induced signal. Susceptibility is dimensionless. The downhole measurement of susceptibility has a sensitivity of approximately 10<sup>–6</sup> units SI. Data measured in sedimentary rocks are typically in the range 10<sup>–5</sup> to 10<sup>–4</sup> units SI. Data can be recorded at a logging speed of up to 3940 ft/hr [1200 m/hr] with a sampling interval of 6 in. [150 mm]. The tools are rated to a temperature of 257°F [125°C] and a pressure of 15,000 psi [103 MPa].<br/><br/>The key measurement deliverable from the combined use of these two integral tools is a depth record of the polarity of remnant magnetization based on the sign of ''B''<sub>''r''</sub> in '''Eq. 3G.24'''. This display is called the well magnetic stratigraphy (WMS).<br/><br/>'''''Application.''''' '''Fig. 3G.24''' illustrates the application of the measured data. It shows how a magnetostratigraphic sequence was established for a well in the Paris basin using GHMT log data.<ref name="r40">Pages, G., Barthies, V., Boutemy, Y. et al. 1994. Wireline Magnetostratigraphy Principles and Field Results. Presented at the SPWLA 35th Annual Logging Symposium, 1994. SPWLA-1994-XX.</ref> For dating purposes, this sequence has to be tied to the GPTS.<br/><br/><gallery widths="300px" heights="200px">
A measurement of magnetic induction or field strength, ''B''<sub>''T''</sub>, can be written as<br/><br/>[[File:Vol5 page 0413 eq 001.png|RTENOTITLE]]....................(3G.21)<br/><br/>where ''B''<sub>''o''</sub> is the magnetic induction associated with the present Earth’s field, ''B''<sub>''i''</sub> is the magnetic induction caused by the field induced in the rock, and ''B''<sub>''r''</sub> is the magnetic induction caused by the remnant field. Magnetic induction is measured in units of nanoTesla (nT). It is a measure of field strength expressed in terms of the field’s ability to induce magnetization. Typically, ''B''<sub>''i''</sub> and ''B''<sub>''r''</sub> are no more than a few tens of nanoTesla, and they have to be measured against a prevailing Earth’s field that is a thousand times greater. Therefore, the exercise becomes very much one of analyzing residuals. For this reason, the prevailing Earth’s field, ''B''<sub>''o''</sub>, is removed from the value of ''B''<sub>''T''</sub>, which then becomes a "net" field ''B''<sub>''t''</sub>.<br/><br/>[[File:Vol5 page 0413 eq 002.png|RTENOTITLE]]....................(3G.22)<br/><br/>The induced magnetic field, ''B''<sub>''i''</sub> (nT), is proportional to the magnetic susceptibility, ''χ'' (units SI), of the rock:<br/><br/>[[File:Vol5 page 0413 eq 003.png|RTENOTITLE]]....................(3G.23)<br/><br/>where ''μ''<sub>''o''</sub> is the magnetic permeability of the void (4''π'' × 10<sup>–1</sup> μH/m), and ''H''<sub>''T''</sub> is the Earth’s magnetic field (A/mm). Therefore, ''B''<sub>''i''</sub> can be evaluated if susceptibility can be measured.<br/><br/>If ''B''<sub>''t''</sub> and ''B''<sub>''i''</sub> can be determined, ''B''<sub>''r''</sub> can be quantified,<br/><br/>[[File:Vol5 page 0413 eq 004.png|RTENOTITLE]]....................(3G.24)<br/><br/>If ''B''<sub>''r''</sub> is positive, the remnant magnetization and, therefore, the paleomagnetic field that caused it are aligned as per the present-day Earth’s field, and ''B''<sub>''r''</sub> is described as "normal." Otherwise, its polarity is "reversed." The polarity of remnant magnetization is evaluated through a numerical comparison of ''B''<sub>''t''</sub> and ''B''<sub>''i''</sub>.<br/><br/>'''''Measurement.''''' A magnetic logging sonde developed for sedimentary rocks is Schlumberger’s Geological High-Resolution Magnetic Tool (GHMT™). It actually comprises two tools: one to measure the total magnetic field and one to measure magnetic susceptibility. The tool housings are nonmagnetic and electrically insulating with a diameter of 4 in. [100 mm].<br/><br/>Because sedimentary rocks have a very low magnetization, a very high precision magnetometer is required. This requirement is satisfied by Schlumberger’s Nuclear Magnetic Resonance Tool (NMRT™), which uses the principles of nuclear magnetic resonance whereby the frequency of precession of relaxing protons is proportional to ''B''<sub>''T''</sub> (see Chap. 3E in this section of the ''Handbook''). The problem, therefore, reduces to a very precise measurement of frequency. The NMRT measurement has a sensitivity of 10<sup>–2</sup> nT. Data are recorded at a logging speed of 1970 ft/hr [600 m/hr] with a sampling interval of 4 in. [100 mm].<br/><br/>A second tool measures the magnetic susceptibility of the rock, which is proportional to ''B''<sub>''i''</sub> ('''Eq. 3G.23'''). This tool, Schlumberger’s Susceptibility Measurement Tool (SUMT™), uses the principles of electromagnetic induction. The voltage induced in the receiver coil increases with susceptibility, which is determined from the complex character of the induced signal. Susceptibility is dimensionless. The downhole measurement of susceptibility has a sensitivity of approximately 10<sup>–6</sup> units SI. Data measured in sedimentary rocks are typically in the range 10<sup>–5</sup> to 10<sup>–4</sup> units SI. Data can be recorded at a logging speed of up to 3940 ft/hr [1200 m/hr] with a sampling interval of 6 in. [150 mm]. The tools are rated to a temperature of 257°F [125°C] and a pressure of 15,000 psi [103 MPa].<br/><br/>The key measurement deliverable from the combined use of these two integral tools is a depth record of the polarity of remnant magnetization based on the sign of ''B''<sub>''r''</sub> in '''Eq. 3G.24'''. This display is called the well magnetic stratigraphy (WMS).<br/><br/>'''''Application.''''' '''Fig. 3G.24''' illustrates the application of the measured data. It shows how a magnetostratigraphic sequence was established for a well in the Paris basin using GHMT log data.<ref name="r40">Pages, G., Barthies, V., Boutemy, Y. et al. 1994. Wireline Magnetostratigraphy Principles and Field Results. Presented at the SPWLA 35th Annual Logging Symposium, 1994. SPWLA-1994-XX.</ref> For dating purposes, this sequence has to be tied to the GPTS.<br/><br/><gallery widths="300px" heights="200px">
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<nowiki>*</nowiki>
<nowiki>*</nowiki>
Conversion factor is exact.</div></div>[[Category:PEH]] [[Category:5.6.1 Open hole or cased hole log analysis]]
Conversion factor is exact.</div></div>[[Category:PEH]]  [[Category:Volume V – Reservoir Engineering and Petrophysics]] [[Category:5.6.1 Open hole or cased hole log analysis]]

Latest revision as of 16:57, 26 April 2017

Publication Information

Vol5REPCover.png

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 3G – Specialized Well-Logging Topics

Paul F. Worthington, Gaffney, Cline, and Assocs.

Pgs. 379-420

ISBN 978-1-55563-120-8
Get permission for reuse


This chapter describes three categories of specialized well logging: downhole measurements that are concerned with the geometry and integrity of the wellbore; acoustic and electrical imaging of the geological architecture and fabric of the rock system penetrated by the well; and downhole measurements that use the Earth’s gravitational and magnetic fields to infer large-scale changes through density and magnetization, respectively. Although some of these technologies are applied beyond the petroleum industry (e.g., geotechnical studies and hydrogeology), this overview concentrates on their hydrocarbon applications. Each topic has a brief introduction, a description of the principles of each method, a discussion of its practical application, and, in selected cases, an illustrative case history. Fig. 3G.1 summarizes how these specialized logging methods relate to reservoir characteristics and the techniques for measuring them, as presented in Chaps. 3B through 3F and Chap. 4 in this section and Chap. 15 in the Drilling Engineering section of this Handbook.



Geometry and Integrity of the Wellbore

Directional Surveys

Principles. With the growth in drilling deviated, extended-reach, and horizontal wells, the location of the wellbore is increasingly a 3D problem. It is encountered in one of two situations: to direct and define the trajectory of the well during the drilling process (geosteering) or to characterize the well path after drilling. The former has contributed to huge increases in well productivity. The latter is a vital element of integrated reservoir studies in which the aim is to generate a 3D model of the reservoir based on correct well locations. This discussion is set within the context of the latter. Geosteering is a benefit of logging-while-drilling technology (see Chap. 15 in the Drilling Engineering section of this Handbook).

In directional-survey terminology, the azimuth is the orientation of the wellbore to "north," which has been variously defined as magnetic north, geographic north (latitude and longitude), or grid north [e.g., the Universal Transverse Mercator (UTM) geographic coordinate system]. Azimuth is typically measured clockwise from north. The inclination is the deviation of the wellbore from the vertical. The azimuth and inclination define the coordinates of the wellbore along its length, usually relative to the location of the wellhead. Tool face quantifies the direction in which the tool is pointing. It is the angle between a reference direction on a downhole tool and a fixed reference in space. For near-vertical wells, the fixed reference is magnetic north and the (magnetic) tool face is the angle between magnetic north and the projection of the tool’s reference direction onto a horizontal plane. For more deviated wells, the fixed reference is the top of the hole and the (gravity or high side) tool face is the tool orientation with respect to the top of the hole. Directional surveys allow azimuth and inclination to be determined so that the coordinates of well location can be computed at each survey station.

Measurement. There are two types of directional surveys: magnetic and gyroscope surveys. Traditionally, each of these has been run using either single- or multishot tools. The tools are self-contained and can be powered from the surface or with downhole batteries. For a detailed description, see Bourgoyne et al.[1]

Magnetic surveys can be run on the drillstring while tripping or on a wireline (conducting cable) after drilling. They are openhole measurements. In the simplest form, a magnetic-survey tool comprises a downhole inclinometer and a compass unit. More advanced tools comprise arrays of three-axis accelerometers (inclinometers) and magnetometers. A three-axis accelerometer measures three orthogonal components of gravity, which combine vectorially to give the direction of the Earth’s gravitational field relative to the axis of the tool and a reference position on its circumference. A three-axis magnetometer measures the direction of the Earth’s magnetic field relative to the tool axis. As Fig. 3G.2 illustrates, by combining the accelerometer and magnetometer data, it is possible to calculate the inclination, I, and azimuth, A, of the tool. Through the tool face, it is then possible to calculate the inclination, α, and azimuth, β, of the wellbore itself. The magnetic measurements are impacted by short-term variations in the Earth’s magnetic field and by proximity to magnetic materials such as drillpipe and casing or to magnetic minerals such as pyrite and/or hematite, the latter also occurring as a mud additive. These problems can be mitigated through the use of nonmagnetic drill collars and repeat measurements with different alignments of the tool in the wellbore. It should be noted that even where magnetic-survey tools are run in long lengths of nonmagnetic drill collars, there can still be a significant effect from steel drillstring tools.[2]

One of the problems with gyroscope surveys is that the instrumentation is very sensitive and cannot withstand downhole vibrations and stresses. For this reason, gyroscope surveys have to be run on wireline, usually while entering the hole with a few additional checkshots on coming out. They interrupt the drilling process, and this adds to cost. However, they can be run in cased hole. In the simplest form, a gyro tool comprises a downhole inclinometer and gyroscope unit. Gyroscope surveys are usually mechanically driven, but other methods, which use a rotating beam of light, have been developed on the basis of fiber optics and laser technology. Mechanical gyroscopes are grouped in terms of their freedom of movement and the number of flywheels (between one and three). Three-axis systems (i.e., three orthogonal accelerometers and gyroscopes mounted on an inertial platform) have proved superior, especially in highly deviated and horizontal wells, where, for example, the axial component of the Earth’s gravity field is small. Here, the tool position is calculated from the accelerometer and gyroscope data through the tool’s inertial navigation system.

Fig. 3G.3 shows the reporting format of a typical directional survey. A synopsis of the errors associated with these measurements and their application has been provided by Theys.[3]

Processing. The results of directional surveying usually take the form of inclination, α, and azimuth, β, of a borehole at a sequence of survey stations. The only other information available is the difference in measured depths for two adjacent stations, but this does not describe the shape of the well path. Starting with the coordinates of the surface reference point, the actual distance between adjacent survey stations needs to be calculated so that the coordinates of any station can be found by addition and those of any intermediate point can be found by interpolation. There are several ways of doing this interpolation. The following account is based on Inglis’ work.[4]

The balanced tangential method assumes that the actual wellpath between two adjacent measurement stations can be approximated by two straight lines of equal length, L/2, shown as AX and BX in Fig. 3G.4. This leads to the following expressions for the incremental distances between adjacent survey stations in the vertical direction (ΔV), in the direction of the northing (ΔN), and in the direction of the easting (ΔE):

RTENOTITLE....................(3G.1)

RTENOTITLE....................(3G.2)

and RTENOTITLE....................(3G.3)

where the subscripts 1 and 2 denote the upper and lower survey stations, respectively.

An improvement on the balanced tangential method is the minimum curvature method, which replaces the two straight lines by an arc. The position of the arc is based on the amount of bending in the wellpath between the two survey stations. The amount of bending is described by a ratio factor, Fr, and quantified by a dogleg angle, ψ (Fig. 3G.5), so that:

RTENOTITLE....................(3G.4)

where

RTENOTITLE....................(3G.5)

The ratio factor is applied to each of the quantities ΔV, ΔN, and ΔE as calculated by the balanced tangential method (Eqs. 3G.1 through 3G.3). Thus, for example, Eq. 3G.1 becomes

RTENOTITLE....................(3G.6)

The minimum curvature method is the most widely used for computing the coordinate deliverables of directional surveys. Inglis[4] provided a detailed description of the calculations.

Applications. The uses of directional surveys include monitoring the actual wellpath to ensure that the drilling target has been reached, defining the X–Y coordinates of points in the wellbore, and determining the true vertical depth (TVD) for geological mapping. Other important operational objectives are to ensure that well paths do not collide (a noteworthy risk given that several production wells are drilled from the same platform) and that there are no changes in angularity (e.g., doglegs) that might impede tool deployment or production efficiency.

An important exercise for integrated reservoir studies is to use the TVD to evaluate the true stratigraphic thickness, hts, and the true vertical thickness, htv, of constituent reservoir beds. Fig. 3G.6a shows a well with inclination or deviation, α, penetrating a bed with dip, φ, over a measured bed thickness, hm, for the particular case in which the azimuths of the well and the dip are the same. Here, the values of hts and htv can be calculated as

RTENOTITLE....................(3G.7)

and RTENOTITLE....................(3G.8)

In the more general case, for which the azimuth of the well, β, is not the same as the azimuth of the dip, βd (Fig. 3G.6b), the equations are more complex:

RTENOTITLE....................(3G.9)

and RTENOTITLE....................(3G.10)

As an illustration of the derivation of these expressions, Eq. 3G.10 can be derived from Eq. 3G.8 by projecting the true angle of dip, φ, onto the vertical plane that contains the wellbore azimuth within the layer of interest (Fig. 3G.6b). This introduces an apparent dip, φa, which is related to the true dip by the relationship:

RTENOTITLE....................(3G.11)

If the apparent dip is used instead of the true dip in Eq. 3G.8, we have

RTENOTITLE....................(3G.12)

Eq. 3G.12 will give the correct answer. If we now use Eq. 3G.11 to substitute for φa in Eq. 3G.12, we obtain Eq. 3G.10. Other derivations of Eq. 3G.10 are available (e.g., those that rotate the dip or deviation to zero to simplify the equations). Eqs. 3G.9 and 3G.10 can also be written in terms of wellbore coordinates.[5]


Openhole Caliper Logs

Openhole calipers comprise up to six arms attached to the body of a sonde and held against the borehole wall by spring action. They provide a continuous measurement of borehole diameter. In general, one- and two-arm calipers measure only the maximum diameter where a hole is not circular. Four- and six-arm tools define the hole size and shape, and this is especially important in deviated wells and elliptically shaped wellbores. However, the size and pressure of the contacting arms also affect the measured data. This means that a caliper run with the density-log tool string (Chap. 3D in this section of the Handbook) might show a larger hole diameter than one run with the induction log (Chap. 3B in this section of the Handbook). This is because the density tool is a pad device, and the pad cuts through the mudcake to sense a larger diameter, whereas the induction tool is a mandrel device (i.e., it is essentially contained within a cylindrical housing). For these reasons, different openhole caliper logs should not be expected to show precise repeatability.

The movement of the caliper arms must be converted to something that is measurable at the surface. Most modern calipers use a potentiometer circuit connected to the caliper arms using transducers. The circuitry can use direct current or pulses. In the former case, the displacement of the arms translates directly to a voltage within the measuring circuit. Pulsed caliper tools use the potentiometer to deliver a variable voltage to a voltage-frequency circuit. The frequency of the pulse train is proportional to the extension of the caliper arm. A basic problem with armed calipers is that the extension of an arm is not directly proportional to the displacement of the transducer. This gives rise to a nonlinear response, which is linearized through data processing based on detailed calibration data. A caliper tool is designed to operate over a specified range of hole diameter. The design sets out to minimize nonlinearity of tool response over this range.

Openhole caliper data are used to estimate the volumes of gravel and cement needed for well-completion planning. Other openhole uses include providing information on the buildup of mudcake over permeable intervals and locating seats for packers (hydraulic seals used to isolate sections of the wellbore for flow-test purposes). They also indicate where boreholes are washed out or penetrate swelling clays as a result of rock/filtrate interaction. Yet again, calipers can be used to center or eccenter logging-tool strings. However, in a logging context, the greatest application of caliper data is in environmental corrections to other logs such as natural gamma ray, density, and neutron logs (Chap. 3D in this section of the Handbook). It is this application that makes the calibration and depth matching of caliper data especially important. Calibration is carried out using rings or sleeves of known diameter. Depth matching is usually done by applying to caliper data those same depth shifts that were generated by comparing the gamma log on the same tool string with the depth-reference gamma log where this has been measured on a different logging run.

Casing-Collar Locators

The casing-collar locator (CCL) is an important tool because it is used for depth control. When combined with a gamma ray log, it allows depth correlation of a cased-hole logging run with the openhole logs and, therefore, reservoir units or zones. This is essential for subsequent downhole operations such as perforating. Because it constitutes the primary depth control, the CCL is run on almost every cased-hole tool string. The tool comprises a coil-and-magnet arrangement with a downhole amplifier. The most sensitive of these arrangements is two like-facing magnetic poles positioned on either side of a central coil. The magnetic lines of flux are distorted when the tool passes a location at which the metallic casing is enlarged by a collar. This distortion gives rise to a classical change in the magnetic field around the conducting coil, within which current is induced. The signal is amplified and recorded at the surface in the form of a voltage spike known as a collar "kick."

CCLs can be run in standard wireline logging mode or on a slickline (i.e., a nonconducting line).[6] Pure-memory slickline CCLs record their data simultaneously with, for example, a full production logging suite, but these CCL data are not available until the memory section has been retrieved and downloaded at the surface. Real-time slickline tools convert the voltage spike to a tension spike by using spring-loaded electromagnets that increase the apparent drag through the greater attraction between the electromagnets and the casing at collar locations. The tension spike can be detected at the surface. CCLs have had to be modified for coiled-tubing applications. The primary difference arose because the heaviness of a coiled-tubing string did not allow relatively small tension spikes to be detected with confidence. For this reason, a solenoid/piston/valve arrangement is used to transmit pressure spikes through the fluid within the coiled tubing to the surface, where they can readily be detected. These tools have recently been improved for high-pressure/high-temperature applications.[7] Some types of downhole tractor that are used to deploy tool strings in deviated wells also have the ability to produce a CCL during the tractor operation and thereby provide the same depth control.

Casing Inspection Logs

There are four commonly used techniques for the inspection of casing: cased-hole calipers, flux-leakage tools, electromagnetic phase-shift tools, and ultrasonic tools.

Cased-Hole Calipers. Multifinger calipers are used to identify changes in casing diameter as indicators of wear and corrosion. They are also used to monitor casing deformation.[8] They can have up to 80 spring-loaded feelers or fingers, depending on the nominal casing diameter (Fig. 3G.7). Different multifinger caliper tools can log casing sizes from 4 to 20 in. [100 to 500 mm]. Smaller tools are available for tubing inspection. Each hardened finger can measure the internal casing diameter with a radial resolution of a few thousandths of an inch and a vertical resolution of a few hundredths of an inch at a typical logging speed of 1800 ft/hr [550 m/h]. Measurements are taken many times per second for each finger, giving a typical spatial-sampling interval of approximately 0.15 in. [4 mm] as the tool travels up the borehole. A finger extends where it encounters a pit or hole and retracts where there is scale present or there has been partial collapse. A potential disadvantage is that the fingers can damage the casing, although modern electronic tools have a very low finger pressure to avoid this. The tool also indicates which finger is the one on the highest side of the well. Moreover, fingers can be grouped azimuthally. All these data can be combined with the measurements of diameter to produce a 3D picture of the casing, including cross-sectional distortions and changes in the trajectory of the well axis as small as 0.01°. The data can be either transmitted to the surface where the tool is run on a wireline or stored downhole where the tool is deployed on a slickline.

There are two types of multifinger calipers, mechanical and electronic, although the distinction is misleading because all such calipers are mechanical in their deployment. The difference is in the way in which data are recorded. Older calipers were truly mechanical in that they were operated on a slickline and used a scribe chart for downhole data recording. These mechanical calipers have high temperature ratings because they are not limited by the ratings of downhole electronics [e.g., 600°F (315°C) for the Kinley caliper offered by the Expro Group]. Modern tools convert the mechanical data into electronic information for downhole memory storage or for transmittal uphole for real-time data display. Operating temperatures for these electronic tools are typically up to 350°F [177°C].

Multifinger tools contain an inclinometer so that tool deviation and orientation can be recorded. If these brmeters are known, the high-quality output from modern multifinger calipers allows several image-based products to be generated. Deliverables include digital "maps" of the ovality of the casing and its internal diameter. The logs can be run and displayed in time-lapse mode to quantify the rates of corrosion or scale buildup. A digital image of variations in the inner diameter of the casing is the principal tool for identifying corrosion. In its basic form, this is an electronic version of what one might see using a downhole video camera; however, the electronic image can be rotated and inspected from any angle. Artificial colors are used to bring out anomalies.

Another processed product is the 3D shape of downhole tubulars to map the trajectory of the wellbore and to quantify casing deformation. An interesting example of the use of multifinger-caliper data to evaluate casing deformation in primary heavy-oil production in northeastern Alberta has been described by Wagg et al.[9] (Fig. 3G.8). Several postulates for formation movement were modeled and compared with the observed casing deformations. In the end, it was concluded that sand production from an elongated disturbed zone caused reservoir shortening to an extent that could account for the wellbore observations. The use of casing-deformation logs as a tool in reservoir geomechanics leads to an improved knowledge base for well design.

Although they are intended for cased-hole application, it is possible to use multifingered calipers in open hole. The results are much more detailed than with a standard openhole caliper, and the output can be displayed as images similar to those obtainable with ultrasonic imaging tools (see the "Ultrasonic Tools" section below).

Flux-Leakage Tools. Flux leakage is a semiquantitative method that uses a strong magnetic field to identify and, to a certain extent, quantify localized corrosion on both the inner and the outer surfaces of the casing. A downhole electromagnet that fits snugly within the casing creates a low-frequency or a direct-current magnetic field. This can be a permanent magnet so it is possible to use this tool on a memory string for which battery power is at a premium. Magnetic flux is concentrated within the casing, which is close to magnetic saturation. The tool contains spring-loaded, coil-type, pad-mounted sensors that are pushed close to the casing during logging. Where casing corrosion is encountered, the lines of flux "bulge out" from the casing as though they were leaking from it. The primary sensors pass through this excluded flux and measure the induced voltage. The amplitude and spatial extent of the sensor response is related to the volume and shape of the corrosion metal loss, thereby allowing an estimate of the size of the defect. Because the primary measurement cannot distinguish between internal and external casing defects, many tools use an additional higher-frequency eddy-current measurement. This is a shallower measurement that responds only to casing flaws on the inner wall. It uses a separate transmitter coil. The flux-leakage and eddy-current signals are distinguished using frequency filters.

The major advantage of flux-leakage tools is that they can identify localized casing defects such as corrosion patches, pits, and holes as small as 0.2 in. [5 mm] on both the inside and the outside of the pipe. A disadvantage is that the tool does not detect large areas of corrosion. It does not see nonmagnetic scale, which can degrade the sensor response. The tool is affected by changes in the electromagnetic properties of the casing. It is of limited accuracy, coverage, and resolution. The coil-sensor response is sensitive to logging speed, and this sensitivity makes quantitative interpretation more difficult.

Electromagnetic Phase-Shift Tools. The electromagnetic phase-shift technique provides an estimate of casing thickness across approximately 1 ft [300 mm] of casing length, so its spatial resolution is weaker than that of the first two methods. Electromagnetic phase-shift tools make measurements that are averages around the circumference of the pipe. They lack the localized investigative capability of flux-leakage tools and are best used to investigate larger-scale corrosion. Essentially, a transmitter coil generates a low-frequency alternating magnetic field, which couples to a receiver coil. It also induces eddy currents in the surrounding casing and formation. These eddy currents generate their own magnetic field, which is phase-shifted by the presence of casing. The phase-shifted field is superimposed on the transmitted field. This total field is detected by a receiver coil. The phase shift between the transmitted and received signals is related to the thickness, electrical conductivity, and magnetic permeability of the casing. If the last two are known, the casing thickness can be determined. Higher phase shifts indicate a higher casing thickness, all other things being equal. In practice, the electromagnetic properties of the casing can vary with composition, aging, and stress. To overcome this problem, modern tools comprise multiple sensor coils, which allow variations in the electromagnetic properties of the casing to be factored into the computation of casing thickness. Advantages are that the method is sensitive to large areas of corrosion and to gradual thinning of the casing. The sensors do not need to be in close proximity to the casing, so a single tool can examine a range of casing sizes. Disadvantages are the low spatial resolution and the lack of response to nonmagnetic scale. Moreover, the alternating-current magnet requires a relatively high power, which makes the tool difficult to deploy in memory mode.

Ultrasonic Tools. The ultrasonic method provides a full quantitative record of casing radius and thickness. The first ultrasonic casing-inspection tools were the borehole televiewers, but these only "saw" the inner casing surface and their use is now mainly in open hole (see Sec. 3G.3.2). Later tools had fixed ultrasonic transducers, but these were principally directed at cement evaluation, and they provided an incomplete coverage of casing-thickness measurements. This problem was overcome by a rotating ultrasonic transducer that was initially directed at cement evaluation (see Sec. 3G.2.5).

More recently, tools have been designed for a better spatial resolution.[10] Schlumberger’s Ultrasonic Corrosion Imager (UCI™) was designed with a short-pulse 2-MHz transducer, 0.5 in. [12.5 mm] in diameter, focused at a distance of 2 in. [50 mm] from its front face. The higher-frequency measurement sharpened the spatial resolution so that internal pits of diameter 0.16 in. [4 mm] could be defined quantitatively. The velocity of sound in the borehole fluid is measured using a built-in reflector at a known offset while running into the hole. The wellsite computer calculates the internal radius from internal echo time and the measured fluid velocity. Downhole processing extracts the time difference between the internal and external echoes for an improved determination of casing thickness using the velocity of sound in steel. This information allows external casing defects to be identified. Azimuthal sampling interval is 2°. Vertical sampling interval in high-resolution mode is 0.2 in. [5 mm] at a logging speed of 425 ft/hr [130 m/hr]. The signal is attenuated by the borehole fluid. Best results are achieved with brine, oil, or very light drilling muds. Fig. 3G.9 shows UCI images of 2D percentage metal loss and 3D views of casing integrity in a 5.5-in. [140-mm] saltwater-injection casing in Canada.[10]

Frisch and Mandal[11] described a "new generation of ultrasonic tools" for use in large-diameter casings. Their (Halliburton) tool uses two ultrasonic transducers, one of which rotates while the other is fixed for real-time measurements of borehole-fluid velocity. The tool operates in image mode or cased-hole mode. In image mode, the tool can be operated in open hole or in cased hole, where it examines only the inner casing surface. In cased-hole mode, it determines the inner radius and the casing thickness, so that defects on the outer casing can be discerned. Waveform processing allows the evaluation of cement bonding from the same logging run.

Cement-Evaluation Logs

Conventional cement-bond logs (CBLs) comprise a pulsed transmitter and several receivers of acoustic energy positioned as a vertical array of transducers. The acoustic signal travels through borehole fluid, casing, cement, and the formation itself. The signal is received, processed, and displayed as a microseismogram. The recorded waveforms are presented together with the travel time and a casing-amplitude curve, which displays the amplitude of the acoustic signal that has traveled through the casing but not through the cement and formation. The waveform and amplitude data allow two bonds to be investigated. These are the bond between casing and cement and, to a lesser extent, that between cement and formation. A "straight" waveform display is traditionally interpreted to mean no cement bonding. Variations in the acoustic display are interpreted as indicating the presence of bonded cement.[12] These displays have been enhanced by the application of statistical variance processing to ultrasonic data.[13] CBLs clearly indicate the top of cement, where there is unbonded pipe, and they indicate where the pipe is well cemented (Fig. 3G.10). However, they are not reliable as indicators of hydraulic sealing by the cement, because they cannot detect small channels therein. Part of the problem is that conventional CBL transducer arrays are vertical, whereas bonding problems need to be investigated circumferentially.

Baker Atlas’ Segmented Bond Tool (SBT™) uses six pads, on each of which there is a transducer arrangement of receivers and transmitters of acoustic energy.[14] The pads are in contact with the casing. Energy is transmitted at one pad and is received at an adjacent pad. The pad spacing is such that the first arrival is the wave that has passed through the casing. The rate of attenuation can be computed across each 60° segment of the casing circumference. A high rate of attenuation is indicative of a good cement bonding to the casing and an absence of channels within the cement. The method allows localized zones of good hydraulic seal to be identified in a way that is independent of borehole-fluid type. The bonding between cement and formation is investigated through a CBL-type receiver array for wave-train presentation (Fig. 3G.11).

Ultrasonic tools are superior to the acoustic CBLs, although they remain adversely affected by highly attenuating muds. They are often grouped as "cement evaluation tools." One of the earlier ultrasonic tools was actually called the Cement Evaluation Tool (CET™). This Schlumberger tool comprised an array of eight ultrasonic transducers that allowed a limited radial inspection of the casing and its annulus. The most recent tools have a single rotating transducer that incorporates both the source and receiver of ultrasonic energy. The tool has to be centered. The data for circumferential inspection of the casing, as described above, and for the evaluation of cement bonding are obtained on the same logging pass. Acoustic energy is reflected at interfaces that correspond to changes in acoustic impedance (the product of acoustic velocity and density). The first reflection is at the casing itself. The second reflection may be at the outside of the casing. If cement is bonded to the casing, there will be a strong reflection. If there is unset cement or water behind the casing, there will be a weak reflection. The received waveform is the sum of the reflected waveform from the original burst and the exponentially decaying waveform from the resonant energy that is trapped between the inner and outer edges of the casing. By analyzing the entire waveform, an acoustic-impedance map of the cement can be constructed. This map can indicate the presence of channels and their orientations.

Schlumberger’s Ultrasonic Imager (USI™) is one such tool.[15] It operates from 200 to 700 Hz and provides a full high-resolution coverage of the casing and cement integrity. Channels as narrow as 1.2 in. [30 mm] can be detected. It is used with a conventional CBL tool. An interesting example of the complementary nature of these data has been presented by De Souza Padilha and Da Silva Araujo.[16] It deals with the problem of gas-contaminated cement, which has been a longstanding interpretation problem in the industry. Essentially, the CBL reads low-amplitude values in gas-contaminated cements. The USI cannot distinguish between gas-filled cement and fluids, but it can quantify the acoustic impedance of the cement. Therefore, the presence of gas-contaminated cement is indicated where the CBL reads low and the USI indicates fluids. If there is only gas behind the casing, the CBL reads high and the USI shows gas. The CBL and USI were used conjunctively to distinguish these cases. The application of statistical variance processing to the conjunctive use of CBL and ultrasonic impedance data has led to an improved cement evaluation.[17] The CBL is also discussed in the chapter on Acoustic Logging in this volume of the Handbook.

Simultaneous Casing Inspection and Cement Evaluation

As indicated above, the ultrasonic tools can be operated to address two objectives concurrently: casing integrity and cement evaluation. A further example is Halliburton’s Circumferential Acoustic Scanning Tool—Visualization version (CAST-V™), which allows separate or simultaneous casing inspection and cement evaluation.[18] The tool can operate in two modes: an image mode, whereby the scanner evaluates only the inner surface of the casing, or a cased-hole mode, whereby circumferential maps of casing thickness and acoustic impedance are used to assure casing integrity and to distinguish between fluids and cement in the annulus. Figs. 3G.12 and 3G.13 show examples of CAST-V data displays. This tool can also operate in open hole as a formation imager (see Sec. 3G.3).

Borehole Imaging


As introduced here, the term "borehole imaging" refers to those logging and data-processing methods that are used to produce centimeter-scale images of the borehole wall and the rocks that make it up. The context is, therefore, that of open hole, but some of the tools are closely related to their cased-hole equivalents. Borehole imaging has been one of the most rapidly advancing technologies in wireline well logging. The applications range from detailed reservoir description through reservoir performance to enhanced hydrocarbon recovery. Specific applications are fracture identification, analysis of small-scale sedimentological features, evaluation of net pay in thinly bedded formations, and the identification of breakouts (irregularities in the borehole wall that are aligned with the minimum horizontal stress and appear where stresses around the wellbore exceed the compressive strength of the rock).

The subject area can be classified into four parts: optical imaging, acoustic imaging, electrical imaging, and methods that draw on both acoustic and electrical imaging techniques using the same logging tool. Prensky[19] has provided an excellent review of this important subject.

Optical Imaging

Downhole cameras were the first borehole-imaging devices. Today they furnish a true high-resolution color image of the wellbore. The principal drawback is that they require a transparent fluid in liquid-filled holes. Unless transparent fluid can be injected ahead of the lens, the method fails. This requirement has limited the application of downhole cameras. The other major historic limitation, the need to wait until the camera is recovered before the images can be seen, has fallen away with the introduction of digital systems.

The principal application of downhole video has been in air-filled holes in which acoustic and contact electrical images cannot be obtained. Most applications described in the literature are directed at fracture identification or casing inspection.

Acoustic Imaging

Acoustic borehole-imaging devices are known as "borehole televiewers." They are mandrel tools and provide 100% coverage of the borehole wall. The first borehole televiewer, operating at a relatively high ultrasonic frequency of 1.35 MHz, was developed by Mobil Corp. in the late 1960s.[20][21] Since then, a succession of improvements have been made, principally through advances in digital instrumentation and computer-image enhancement. Modern tools contain a magnetometer to provide azimuthal information.

The borehole televiewer operates with pulsed acoustic energy so that it can image the borehole wall in the presence of opaque drilling muds. Short bursts of acoustic energy are emitted by a rotating transducer in pulse-echo mode. These travel through the drilling mud and undergo partial reflection at the borehole wall. Reflected pulses are received by the transducer. The amplitudes of the reflected pulses form the basis of the acoustic image of the borehole wall. These amplitudes are governed by several factors. The first is the shape of the borehole wall itself: irregularities cause the reflected energy to scatter so that a weaker reflected signal is received by the transducer. Examples of these irregularities are fractures, vugs, and breakouts. Moreover, the reflected signal is degraded in elliptical and oval wellbores because of non-normal incidence. The second factor is the contrast in acoustic impedance between the drilling mud and the material that makes up the borehole wall. Acoustic impedance provides an acoustic measure of the relative firmness of the formations penetrated by the wellbore material and, thus, it has the capability of discriminating between different lithologies, with high acoustic impedance giving rise to high reflected amplitudes. Borehole televiewers work best where the borehole walls are smooth and the contrast in acoustic impedance is high. The third factor is the scattering or absorption of acoustic energy by particles in the drilling mud. This problem is more serious in heavily weighted muds, which are the most opaque acoustically, and it gives rise to a loss of image resolution.

The borehole televiewer can provide a 360° image in open or cased holes. It can operate in all downhole environments other than gas-filled holes. The travel time for the acoustic pulse depends on the distance between the transducer and the borehole wall, as well as the mud velocity. Modern televiewers allow some independent method of measuring the mud velocity. Thus, the borehole televiewer also operates as an acoustic caliper log. For best results, the tool should be centered, although correction algorithms have been developed for eccentered surveys.

An example of a modern ultrasonic imaging tool is Schlumberger’s Ultrasonic Borehole Imager (UBI™), which is based on the cased-hole USI (see Sec. 3G.2.5) with two hardware modifications: a focused transducer was fitted for improved resolution, and an openhole centralizer was added.[22] The tool incorporates a rotating transducer within a subassembly. The size of the subassembly is selected on the basis of the diameter of the hole that is to be logged. The direction of rotation of the subassembly governs the orientation of the transducer. There are two positional modes: the standard measurement mode with the transducer facing the borehole wall (Fig. 3G.14) and the fluid-property mode with the transducer facing a target within the tool. In standard mode, the tool measures both amplitude and transit time at one of two frequencies, 250 or 500 kHz, with recommended logging speeds of 800 ft/hr [244 m/hr] and 400 ft/hr [122 m/hr], respectively, where logging speed is primarily determined by vertical sampling density and the rate of transducer rotation. The higher frequency allows a sharper image resolution of 0.2 in. [5 mm], but it is less effective in highly dispersive muds where the lower frequency should be used. The tool can also be used for investigating the geometry of the inner surface of casing where it is not desired to measure resonant ringing as an indicator of cement integrity.

Baker Atlas’ Circumferential Borehole Imaging Log (CBIL™) has a similar range of capability but is rated to 20,000 psi [138 MPa] and 400°F [204°C]. Halliburton’s Circumferential Acoustic Scanning Tool (CAST™) additionally offers simultaneous casing inspection and cement evaluation. It is rated to 20,000 psi [138 MPa] and 350°F [177°C], as is Schlumberger’s UBI. Both of these tools predated the UBI.[23][24]

Data are usually presented as depth plots of enhanced images of amplitude and borehole radius. Applications include fracture detection, analysis of borehole stability, and identification of breakouts.

Fig. 3G.15 shows an example of breakout identification using an ultrasonic borehole televiewer.[25] The data presented are from the Cajon Pass scientific borehole in southeastern California. The aim was to investigate the orientation and magnitudes of in-situ stresses using borehole-image data. The televiewer has superseded multiarm dipmeter calipers for these applications. Although the caliper can reveal the orientation of breakouts, the tool provides little information about their size and, more generally, about the overall shape of the borehole wall. The ultrasonic televiewer can detect much smaller features than the multiarm caliper and can distinguish between features that are stress induced and those that are drilling artifacts.


Electrical Imaging

Microresistivity imaging devices were developed as an advancement on dipmeter technology, which they have mostly superseded. Traditionally, they have required a conductive borehole fluid, but it will be seen later that this requirement has been obviated by oil-based-mud imaging tools. Originally, in the mid-1980s, they comprised two high-resolution pads with 27 button electrodes distributed azimuthally on each. This arrangement provided a coverage of 20% of an 8.5-in. [216-mm] wellbore in a single pass.[26] This coverage was doubled by the development of a four-pad microresistivity imaging tool, each with 16 button electrodes arranged azimuthally in two rows of eight. The number of electrodes was limited by tool-transmission electronics.[27] Coverage was increased still further through the use of pads with flaps that opened to give a borehole-wall coverage of 80% in an 8-in. [203-mm] hole.[28] In another approach, the six-arm dipmeter evolved into a six-pad microresistivity imager,[29] Halliburton’s Electrical Micro-Imaging tool (EMI™). Each pad contained 25 button electrodes also arranged azimuthally in two rows. With this arrangement, a 60% coverage was achieved in an 8-in. [203-mm] hole.

The measurement principle of the microresistivity imaging devices is straightforward. The pads and flaps contain an array of button electrodes at constant potential (Fig. 3G.16). An applied voltage causes an alternating current to flow from each electrode into the formation and then to be received at a return electrode on the upper part of the tool. The microelectrodes respond to current density, which is related to localized formation resistivity. The tool, therefore, has a high-resolution capability in measuring variations from button to button. The resistivity of the interval between the button-electrode array and the return electrode gives rise to a low-resolution capability in the form of a background signal. The tool does not provide an absolute measurement of formation resistivity but rather a record of changes in resistivity. The resolution of electrical microimaging tools is governed by the size of the buttons, usually a fraction of an inch. In theory, any feature that is as large as the buttons will be resolved. If it is smaller, it might still be detected. The tools can be run as dipmeters.

Data are presented as orientated, juxtaposed pad outputs whereby the cylindrical surface of the borehole wall is flattened out. This has the effect of distorting quasiplanar features such as dipping layers or fractures, which appear as sinusoidal in the data display. Fig. 3G.17 shows a typical data display and identifies some of the key features.

Electrical microimaging tools have proved superior to the ultrasonic televiewers in the identification of sedimentary characteristics and some structural features such as natural fractures in sedimentary rocks. They are especially useful for net-sand definition in thinly laminated fluvial and turbidite depositional environments.

There are several microimaging tools available, each with similar capability. For example, Schlumberger’s fullbore FMI™ has two horizontally offset rows of 24 button electrodes on each pad and each flap, making a total of 192 electrodes (Fig. 3G.18). The buttons have a diameter of 0.2 in. [5 mm], which determines the intrinsic spatial resolution of the tool. However, features as small as 50-μ fluid-filled fractures can be detected (but not fully resolved). Current is focused into the formation, where a depth of investigation of several tens of centimeters is claimed. However, the image probably relates to a depth of investigation of no more than 0.8 in. [20 mm]. The high-resolution image is normalized with respect to the low-resolution part of the signal or to another resistivity logging tool.

The conventional microresistivity imaging devices require a conductive mud in which to function. However, drilling with oil-based or synthetic muds has increased because of the improved drilling efficiency and greater borehole stability relative to water-based muds. Rather than have to change out the mud specifically for a microresistivity imaging survey, two other approaches have been pursued. The first has been to develop a new synthetic mud that retains all the stabilizing characteristics of conventional synthetic muds but is sufficiently conductive to permit microresistivity imaging measurements.[30] The second has been to develop an electrical imaging device that operates in oil-based muds. This problem was addressed by the so-called oil-based mud dipmeters. These are conventional four-arm dipmeters for which the four microelectrodes are replaced by microinduction sensors.[31] More recently, contact resistivity methods have been applied in oil-based or synthetic muds.[32] Schlumberger’s Oil-Base MicroImager (OBMI™) uses four pads positioned at 90° to one another to achieve a 32% coverage of an 8-in. [203-mm] wellbore. Each pad contains two current electrodes and a set of five pairs of closely spaced potential electrodes positioned centrally between the current electrodes (Fig. 3G.19). The arrangement is reminiscent of the Schlumberger electrode array that is still used for surface resistivity sounding in geoelectrical prospecting. However, in this downhole case, the aperture of the sensor gives an intrinsic spatial resolution of 0.4 in. [10 mm] with a nominal depth of investigation of 3.5 in. [90 mm]. Although the OBMI tool is sensitive to borehole rugosity, it has performed well in oil-based and synthetic muds for which water content lies between 1 and 30%. Examples of microresistivity image displays are shown in Figs. 3G.20 and 3G.21.


Conjunctive Acoustic and Electrical Imaging

To some extent, the ultrasonic and electrical images are complementary because the ultrasonic measurements are influenced more by rock properties, whereas the electrical measurements respond primarily to fluid properties. Another difference is that the ultrasonic image covers 360°, whereas the electrical image is somewhat less than 80% of the surface of an 8-in. [203-mm] wellbore. Ultrasonic measurements can be made using the same tool in all types of drilling mud, and this can facilitate interwell comparisons. On the other hand, most microresistivity imaging devices require a water-based mud; otherwise, an alternative tool, such as the OBMI, has to be used.

These differences can be accommodated through the combined use of electrical and acoustic imaging. As an example, Baker Atlas’ Simultaneous Acoustic and Resistivity Imager (STAR™) uses a combination of a CBIL and a six-pad resistivity imager with 12 electrodes per pad. The tool delivers a more complete data set than is achievable using either of the components separately. The combined tool is 86 ft [26.2 m] in length with a diameter of 5.70 in. [145 mm]. It is rated to 20,000 psi [138 MPa] and 350°F [177°C].

Natural Field Methods

Borehole Gravimetry

Borehole gravity was pioneered by Smith[33] and then applied to problems of reservoir evaluation by McCulloh et al.[34] The borehole gravity meter or gravimeter responds to variations in density. Modern instruments sense a rock volume that is approximately the same as that investigated by deep resistivity tools. Unlike the shallower-sensing density log, the borehole gravimeter is insensitive to wellbore conditions such as rugosity and the presence of casing. Its principal applications are (through-casing) time-lapse monitoring of saturations/fluid contacts in gas reservoirs and downhole calibration of surface geophysical mapping of geological structures.

Theory. Any two masses, mi and mj, separated by a distance, r, experience a gravitational force of attraction, f, which is expressed as

RTENOTITLE....................(3G.13)

where G is the universal gravitational constant (6.6726 × 10 –8 cgs units). More specifically, a mass, m, on the surface of the Earth would experience a gravitational force given by

RTENOTITLE....................(3G.14)

where M is the mass of the Earth, R is its radius, and an acceleration due to gravity, g, is given by

RTENOTITLE....................(3G.15)

Because the Earth is a rotating oblate spheroid, the quantity g at mean sea level varies with latitude, and it must be corrected for tidal effects. The unit of g is the Gal [1 cm/s2]. Surface gravity surveys use the milliGal as the preferred unit. Borehole gravity surveys often use the microGal. The acceleration due to gravity, or just "gravity," is measured with a gravimeter.

Measurement. A borehole gravimeter follows the same principles of operation as a surface gravity meter. It is essentially a very sensitive spring balance. The weight of a horizontal hinged beam with a small mass attached to its free end is balanced by a combination of the tension in a compensating spring and an electrostatic force (Fig. 3G.22). When the acceleration due to gravity increases, the weight of the beam increases, and there is a greater tension in the spring. The spring tension is directly related to the acceleration due to gravity. It is controlled by an adjusting screw for which the number of turns is calibrated in gravitational units. The electrostatic force brings the beam to a horizontal position for reading purposes. It, too, is calibrated in gravitational units. The gravity reading is the difference between the spring tension and the electrostatic force: a tidal gravity correction has to be applied. In this way, differences in gravity can be measured between two places (e.g., between two depth locations in a borehole). Downhole measurements are made by occupying selected gravity stations. They are not continuous measurements with depth.

It can be shown[35] that the difference in gravity, Δg (mGal), between two locations at the top and bottom of an infinite horizontal reservoir layer penetrated by a vertical well is related to the density, ρ (g/cm3), and thickness, hm (m), of that layer by the expression:

RTENOTITLE....................(3G.16)

where F is the vertical gradient of gravity (mGal/m), and G is in cgs units. Eq. 3G.16 can be solved for the layer density so that

RTENOTITLE....................(3G.17)

The gradient, F (mGal/m), is a function of latitude, λ (degrees), and elevation, h (m), as per the Intl. Gravity Formula of 1967, as follows:

RTENOTITLE....................(3G.18)

By substituting for F in Eq. 3G.17, we have

RTENOTITLE....................(3G.19)

where RTENOTITLE is the mean elevation of the layer (m), and Δg/hm is in mGal/m. Eq. 3G.19 is that most commonly used for deriving density from borehole gravity measurements. If the borehole is deviated at an angle, α, the measured depth interval has to be converted to a true stratigraphic thickness using a specific form of Eq. 3G.7 for zero dip. Corrections are needed where the model of an infinite layer breaks down because of the presence of structural discontinuities away from the wellbore. Modern borehole gravimeters can detect gravity differences of a few microGals.

The borehole gravity meter delivers an interval density. It is the only tool that can furnish through-casing density. Where the layer is heterogeneous, the computed density is an average or apparent density. The error in density is a function of the layer thickness. With a LaCoste-Romberg borehole gravimeter, a single measurement of gravity above and below a layer of thickness 6.6 ft [2 m] should result in an error in apparent density of approximately ± 0.025 g/cm3. This expected error can be reduced through repeat measurements and by selecting a larger depth interval. Turning this around, the spatial resolution of a borehole gravimeter is governed by the accuracy to which density is required. For example, an accuracy of ±0.01 g/cm3 would be achieved through three measurements of gravity at the top and at the base of the target layer, provided that the latter is at least 9 ft [2.7 m] thick.

Borehole gravity tools have different sizes for different hole conditions. For example, the EDCON tools range in diameter from 3.875 in. [98 mm] for low-temperature (110°C), low-pressure (8,000 psi) applications to 5.25 in. [133 mm] for high-temperature (204°C), high-pressure (20,000 psi) applications. The temperature range can be extended to 260°C with special ring seals. Because of the tool size, there are limits on the deviation of boreholes in which it can be deployed. The measurement stations are located relative to other logging runs by using the gamma log and the CCL (see Sec. 3G.2.3). The depth of investigation within a homogeneous layer is governed by the contrast between the mud filtrate and formation fluids. It is typically more than 23 ft [7 m]. A larger station spacing, hm, will not increase this range. It will merely reduce the ability of the tool to see near-well density anomalies. Like surface gravity meters, the tool suffers from drift (of the spring tension), which makes accurate calibration difficult.

Application. Key thrusts in reservoir evaluation have been the sensing of vuggy, fractured, and heterogeneous reservoirs, in which a deep-sensing porosity measurement is needed to complement the volumetric-sensing capability of deep resistivity logs.[36][37] More recent applications have been directed at through-casing monitoring of gas saturations.[38][39] In this respect, it is noteworthy that the larger volumes sensed by the borehole gravity meter, relative to conventional density logs, are more closely associated with the simulator grid scale. Moreover, time-lapse gravity measurements are not degraded by structural anomalies.

As an example, time-lapse borehole gravimetry has been used to determine the residual oil saturation to gas within the oil rim of the onshore Rabi field in Gabon.[35] The reservoir comprises clean, coarse-grained sands with high-salinity formation water. The required accuracy for residual oil saturation was ± 10 saturation units. A baseline gravity survey was run over an undepleted oil-bearing interval near the gas/oil contact (GOC) (Run 1). As the reservoir is depleted, the GOC moves down and the oil saturation decreases toward its residual value. A second gravity survey (Run 2) allowed the change in gas saturation, ΔSg, to be calculated from the change in measured density, Δρb, porosity, ϕ, and the densities of oil, ρo, and gas, ρg.

RTENOTITLE....................(3G.20)

Once ΔSg was known, the oil saturation could be calculated, assuming no change in connate-water saturation.

Three surveys were undertaken twelve months apart (Fig. 3G.23). All measurements were made in a data-dedicated borehole. Gravity was measured four to six times at each station, with station intervals as low as 3.3 ft [1 m]. Stations were reoccupied with a shuttle-based system for enhanced depth control. The overall accuracy of the density difference in Eq. 3G.20 was 0.015 g/cm3. This accuracy corresponds to an accuracy of 0.7 μGal on the station-specific readings and an accuracy of 1.0 μGal on the gravity difference. The residual oil saturation was determined as 15±10 saturation units. Of this uncertainty, eight saturation units could be ascribed to the borehole-gravity measurements and two saturation units to uncertainties in porosity and connate-water saturation. This study set new objectives and standards for borehole gravimetry.

Downhole Magnetics

Downhole magnetic surveys have been most commonly applied in highly magnetized igneous rocks, which have usually been studied within pure geoscience, especially beneath the ocean floor. These rocks preserve the direction of the Earth’s field at the time of their formation (i.e., the prevailing magnetic field is "frozen" in the rocks as they solidify, giving them a strong natural remnant magnetization). A primary application has been to identify points in time at which the Earth’s magnetic field has undergone a polarity reversal. These reversals have been dated globally (e.g., isotopically in the case of volcanic series or by correlation with biostratigraphy in the case of volcaniclastics) and have given rise to a geomagnetic polarity time scale (GPTS) that is based on laboratory measurements. This, in turn, has allowed dates to be assigned to a given magnetozone that is bounded by reversal phenomena. It has been possible to recognize these reversals through downhole measurements and, therefore, to date the rocks accordingly.

Sedimentary rocks have much weaker remnant magnetizations than igneous sequences, and it has been much more difficult to investigate their magnetic character. However, recent advances in instrumentation have led to progress in downhole magnetic measurements of sedimentary strata.[40]

Theory. The following magnetic theory is extracted from Lalanne et al.[41] The magnetic field measured downhole has three parts: the Earth’s magnetic field of the present day; the field that is induced in the rocks by the prevailing Earth’s field; and the remnant magnetic field, which is the preservation in the rocks of a paleomagnetic field. The effect of the Earth’s magnetic field can be accommodated during logging by extrapolating downhole the measurements made by a surface magnetometer that records diurnal variations in the Earth’s field and allows the downhole data to be corrected for these variations where they are significant. The induced field is proportional to the magnetic susceptibility of the rock, which is governed by (ferro-magnetic) mineralogy and fluid composition. The remnant magnetic field adopts the direction of the Earth’s field at the time that the rock was forming. For sediments, it is most pronounced in clays.

A measurement of magnetic induction or field strength, BT, can be written as

RTENOTITLE....................(3G.21)

where Bo is the magnetic induction associated with the present Earth’s field, Bi is the magnetic induction caused by the field induced in the rock, and Br is the magnetic induction caused by the remnant field. Magnetic induction is measured in units of nanoTesla (nT). It is a measure of field strength expressed in terms of the field’s ability to induce magnetization. Typically, Bi and Br are no more than a few tens of nanoTesla, and they have to be measured against a prevailing Earth’s field that is a thousand times greater. Therefore, the exercise becomes very much one of analyzing residuals. For this reason, the prevailing Earth’s field, Bo, is removed from the value of BT, which then becomes a "net" field Bt.

RTENOTITLE....................(3G.22)

The induced magnetic field, Bi (nT), is proportional to the magnetic susceptibility, χ (units SI), of the rock:

RTENOTITLE....................(3G.23)

where μo is the magnetic permeability of the void (4π × 10–1 μH/m), and HT is the Earth’s magnetic field (A/mm). Therefore, Bi can be evaluated if susceptibility can be measured.

If Bt and Bi can be determined, Br can be quantified,

RTENOTITLE....................(3G.24)

If Br is positive, the remnant magnetization and, therefore, the paleomagnetic field that caused it are aligned as per the present-day Earth’s field, and Br is described as "normal." Otherwise, its polarity is "reversed." The polarity of remnant magnetization is evaluated through a numerical comparison of Bt and Bi.

Measurement. A magnetic logging sonde developed for sedimentary rocks is Schlumberger’s Geological High-Resolution Magnetic Tool (GHMT™). It actually comprises two tools: one to measure the total magnetic field and one to measure magnetic susceptibility. The tool housings are nonmagnetic and electrically insulating with a diameter of 4 in. [100 mm].

Because sedimentary rocks have a very low magnetization, a very high precision magnetometer is required. This requirement is satisfied by Schlumberger’s Nuclear Magnetic Resonance Tool (NMRT™), which uses the principles of nuclear magnetic resonance whereby the frequency of precession of relaxing protons is proportional to BT (see Chap. 3E in this section of the Handbook). The problem, therefore, reduces to a very precise measurement of frequency. The NMRT measurement has a sensitivity of 10–2 nT. Data are recorded at a logging speed of 1970 ft/hr [600 m/hr] with a sampling interval of 4 in. [100 mm].

A second tool measures the magnetic susceptibility of the rock, which is proportional to Bi (Eq. 3G.23). This tool, Schlumberger’s Susceptibility Measurement Tool (SUMT™), uses the principles of electromagnetic induction. The voltage induced in the receiver coil increases with susceptibility, which is determined from the complex character of the induced signal. Susceptibility is dimensionless. The downhole measurement of susceptibility has a sensitivity of approximately 10–6 units SI. Data measured in sedimentary rocks are typically in the range 10–5 to 10–4 units SI. Data can be recorded at a logging speed of up to 3940 ft/hr [1200 m/hr] with a sampling interval of 6 in. [150 mm]. The tools are rated to a temperature of 257°F [125°C] and a pressure of 15,000 psi [103 MPa].

The key measurement deliverable from the combined use of these two integral tools is a depth record of the polarity of remnant magnetization based on the sign of Br in Eq. 3G.24. This display is called the well magnetic stratigraphy (WMS).

Application. Fig. 3G.24 illustrates the application of the measured data. It shows how a magnetostratigraphic sequence was established for a well in the Paris basin using GHMT log data.[40] For dating purposes, this sequence has to be tied to the GPTS.

Fig. 3G.25 illustrates another example, this time from the Ocean Drilling Program (ODP). This example reveals some geomagnetic features that are not yet part of the global standard. Notwithstanding these disparities, this chronal benchmarking allows the absolute dating of much of the sedimentary succession.

Future applications will examine the direction of remnant magnetization to investigate the movement of fault blocks and enhancing the fieldwide correlation of the sedimentary column.

Discussion


There are two principal drivers for the further advancement of the technologies that have been described here.

The first is the need for improved reservoir characterization to help us deal with problematic reservoirs that have low-permeability characteristics, thin beds, laminations, low-resistivity-contrast pay, and fracture networks. Fracture networks lead us to the question of carbonates and their petrophysical differences from clastic rocks. One might ask why it is that with so much technology available, the industry still perceives a shortfall in its interpretative capability. The reason is that recent attention has been directed at data acquisition and management rather than methods of interpreting the data themselves. Thus, for example, we have not yet succeeded in reconciling petrophysical data measured at different scales. The gap between our ability to measure and our ability to interpret the measurements widened still further during the 1990s, the decade of the horizontal well. This drove the analysis of downhole measurements further into three dimensions and emphasized the need for us to get more out of our data if our reservoir models are to deliver the greatest benefit.

The second technology driver is the cost-effectiveness of multiwell platforms from which deviated, extended-reach, horizontal, and multilateral wells can be drilled to target hydrocarbon accumulations that have been identified in a reservoir model. This heralds a further thrust in the need to drill more difficult subsurface environments in a way that allows full control of the wellbore trajectory. This, in turn, will require a full casing- and cement-evaluation service, especially with regard to the monitoring of casing deformation. Only in this way can one be assured of an absence of flow constrictions or impediments to tool deployment.

Both reservoir characterization and the cost-effectiveness of multiwell platforms will continue to benefit from further developments in data recording, transmittal, processing, and visualization, which have underpinned the technical progress made to date.

Summary


This chapter has addressed several specialized logging tools and the information they can provide in assessing borehole trajectory, wellbore conditions, and reservoir characteristics. Directional, caliper, and cement-bond surveys can be used to determine well location, the quality and condition of the open hole, the condition of the tubing, the presence of cement, the quality of the bond between tubing and cement, and, to a lesser extent, the degree of bonding between cement and formation. Borehole imaging can be used in open hole to picture the different strata encountered, and it is of particular use in detailing thinly bedded (sand/shale) intervals and identifying both natural and induced fractures. Finally, borehole gravimetry and downhole magnetics can be used to measure formation properties at a larger scale. Each of these specialized tools is experiencing a stronger application base as better sensor technology delivers the information needed for improved reservoir characterization and reservoir management.

Acknowledgements


The author is obliged to those oilfield service companies and petroleum technical societies who have granted permission for subject matter to be included here. Special mention is made of Baker Atlas, EDCON, Halliburton Energy Services, Schlumberger, and Sondex. This material has been included to give a balanced overview of the state of technology in this important subject area rather than to endorse any particular commercial service. In this rapidly changing world, the material is current as of June 2003.

Nomenclature


A = tool azimuth relative to magnetic north, –, degrees
Bo = magnetic induction associated with the present Earth’s field, m/qt, nT
Bi = magnetic induction due to the field induced in the rock, m/qt, nT
Br = magnetic induction due to the remnant field, m/qt, nT
Bt = "net" field, m/qt, nT
c = gravimeter design constant, L, m
d = gravimeter design constant, L, m
f = gravitational force of attraction, mL/t2, N
Fr = ratio factor for the minimum curvature method
F = vertical gradient of gravity, 1/t2, mGal/m
g = acceleration due to gravity, L/t2, mGal
G = universal gravitational constant, L3/mt2, dyne cm2/g2
h = elevation, L, m
hm = measured bed thickness, L, m
hts = true stratigraphic thickness, L, m
htv = true vertical thickness, L, m
HT = Earth’s magnetic field, q/tL, A/mm
i = current, q/t, A
I = tool inclination relative to gravitational vector, –, degrees
L = length of equal straight lines representing dogleg in wellbore, L, m
mi, mj = any two gravitationally attracting masses, m, kg
m = mass, m, kg
M = mass of the Earth, m, kg
r = distance between two gravitationally attracting masses, L, m
R = Earth’s radius, L, km
Rxo = apparent formation resistivity, mL3/tq2, Ωm
T = tension, mL/t2, N
RTENOTITLE = mean elevation of layer, L, m
α = inclination or deviation of wellbore, –, degrees
φ = dip, –, degrees
φa = apparent dip, –, degrees
β = azimuth of wellbore, –, degrees
βd = azimuth of dip, –, degrees
δV = potential difference, mL2/qt2, V
ΔE = incremental distances between adjacent survey stations in the direction of the easting, L, m
Δg = difference in gravity between two locations at the top and bottom of an infinite horizontal reservoir layer penetrated by a vertical well, L/t2, Gal
ΔN = incremental distances between adjacent survey stations in the direction of the northing, L, m
ΔSg = time-lapse change in gas saturation
ΔV = incremental distances between adjacent survey stations in the vertical direction, L, m
Δρb = change in measured density, m/L3, g/cm3
λ = latitude, –, degrees
μo = magnetic permeability of the void, mL/q2, μH/m
ρ = density, m/L3, g/cm3
ρg = gas density, m/L3, g/cm3
ρo = oil density, m/L3, g/cm3
ψ = dogleg angle, –, degrees
ϕ = porosity
χ = magnetic susceptibility of the rock, –


Subscripts


1 = upper directional survey station
2 = lower directional survey station


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SI Metric Conversion Factors


degree × 1.745329 E − 02 = rad
dyne × 1.0* E − 05 = N
ft × 3.048* E − 01 = m
°F (°F − 32)/1.8 = °C
Gal × 1.0* E − 02 = m/s2
in. × 2.54* E + 00 = cm
psi × 6.894 757 E + 00 = kPa


*

Conversion factor is exact.