## Resistivity Logs

**Definitions of Resistivity and Dielectric Constant **

The first logging device ever designed measured formation resistivity. It was a modification of a method previously used to detect underground resistivity anomalies associated with either geologic features or concentrations of metallic ores. Figure 1 illustrates this old surface surveying method.

A voltage source sent a current through the ground between two widely spaced electrodes. The voltage drop between two other more closely spaced electrodes was used as a measure of the ground resistivity. By moving the whole electrode array across the countryside, it was possible to "map" underground features, as shown in** **Figure 2 . By rotating the whole setup through a 90 angle and lowering it into a borehole, the electric log was born.

**Conventional Resistivity Measurements**

The measured voltages provided the resistivity determinations for each device, as follows: In Figure 3 , a current I flows between electrode A and electrode N in a homogeneous, isotropic medium. The corresponding equipotential surfaces surrounding the current emitting electrode A would be spheres. The voltage on electrode N situated on one of these spheres is proportional to the resistivity of the formation, and the measured voltage can be scaled in resistivity units.

Although the original electric logging principles were sound, their practical embodiments left much to be desired. Efforts to improve the measurement of formation resistivity have been busily pursued for over 60 years. As a result, three main branches of resistivity logging have evolved. They *are focused electric logs, induction logs, and microwave devices*.

*Focused Electric Logs* The responses of conventional electrical logging systems can be greatly affected by the borehole and adjacent formations. These influences are minimized by a family of resistivity tools that use focusing currents to control the path taken by the measure current. These currents are emitted from special electrodes on the sondes.

The focusing electrode tools include the laterolog and spherically focused devices (SFL). These tools are much superior to the conventional electrical logs (ES) because they eliminate many of the detrimental borehole effects. They are also better for resolution of thin beds. Focusing electrode systems are available with deep, medium, and shallow depths of investigation.

*Induction Logs* The induction logging tool was originally developed to measure formation resistivity in boreholes containing oil-base muds and in airdrilled boreholes. Electrode devices did not work in nonconductive muds.

Experience soon demonstrated that the induction log had many advantages over the conventional ES log when used for logging wells drilled with water-base muds. Designed for deep investigation, induction logs can be focused in order to minimize the influences of the borehole, the surrounding formations, and the invaded zone.

*Microwave Devices* Recently, microwave devices (also called electromagnetic propagation logging) have been designed to measure the dielectric constant and the conductivity of the formation. Strictly speaking, they do not measure formation resistivity. However, they are sometimes classified as resistivity devices since the end use of their measurement is the same as for resistivity tools, i.e., determination of formation-fluid saturation.

*Unfocused Electric Logs* The original conventional electrical logs are still used occasionally for special applications.

*Spontaneous Potential* Very early in the development of electric logging, the spontaneous potential (SP) was discovered and put to good use.

**Tool Response**

**Philosophy of Measuring Formation Resistivity **

Whatever device is used to measure formation resistivity, there are common factors that conspire to confound these efforts. Although modern resistivity-measuring devices represent a considerable improvement over the original unfocused electric log (commonly called the old E-log), there is still plenty of room for improvement. In addition to measuring the resistivity of the undisturbed zone, R_{t}, the tool, by its design, is influenced by the resistivities of the mud in the borehole, the adjacent beds, and the invaded zone ( Figure 1 ). Thus, we cannot assume that the reading from a resistivity log represents R_{t}. Depending on the device used, the particular circumstances of the well, and the formations logged, the actual reading nay be greater or less than R_{t}.

We discuss below how to recognize those cases where resistivity measurements depart radically from R_{t}. For now, use this rule: a big contrast between the resistivity of the bed of interest and the resistivity of either the mud column or the adjacent bed is a danger signal that calls for the use of correction charts. In this context, "big" means a factor of 10 or more. Of particular note are conditions where the bed of interest is thin (say, 15 ft or less) and/or invasion is deep ( d_{i} greater than 40 in).

To summarize, assume that a deep-resistivity device measures R_{t} unless

- R
_{t}/R_{m}is greater than 10

R_{t}/R_{s} is greater than 10

hole size is greater than 12 in.

the bed is thinner than 15 ft

invasion is greater than 40 in.

If any of these adverse conditions exists, refer to the appropriate correction chart. As will become apparent, induction logs and focused electric logs (laterologs) behave differently when faced with these problems; in many cases, what may adversely affect an induction tool can be an advantage to a laterolog, and vice versa.

**Philosophy of Measuring Formation Resistivity**

Whatever device is used to measure the resistivity of the undisturbed zone (R_{t}), three elements, individually or collectively, make measurement more difficult. They are the borehole itself, the adjacent beds, and mud filtrate invasion.

Although modern resistivity-measuring devices represent a considerable improvement over the original unfocused electric log, there is still plenty of room for improvement. When using a resistivity log, the analyst must remember that the device is not perfect, and the measurement displayed is a composite of the four items in Figure 2 .

Note that in addition to R_{t}, the resistivity of the undisturbed zone (which is what we are trying to measure), the tool, by its design, is influenced by the resistivity of the mud in the borehole, the adjacent beds, and the invaded zone, if present.

It is unwise to assume that the reading from a resistivity log represents R_{t}. Depending on the device used, the particular circumstances of the well, and the formations logged, the actual reading may be greater or less than R_{t}. In the sections that follow, we shall learn how to recognize those cases where resistivity measurements depart radically from R_{t}. As a rule of thumb, a large contrast between the resistivity of the bed of interest and that of the mud column or the adjacent bed is a danger signal that calls for the use of correction charts. In this context a "large" contrast could be classified as a factor of 10 or more. Of particular note are conditions where the bed of interest is thin (say, 15 ft or less) and/or invasion is deep (di is greater than 40 in.).

By way of summary, assume that a deep resistivity device measures R_{t} unless:

- R
_{t}/R_{m}is greater than 10

R_{t}/R_{s} is greater than 10

hole size is greater than 12 in.

the bed is thinner than 15 ft

invasion is greater than 40 in.

If any of these adverse conditions exists, then the appropriate correction chart is called for. As will become apparent later, induction logs and focused electric logs (laterologs) behave differently when faced with these problems. What is poison to an induction tool is often an advantage to a laterolog, and vice versa.

**Tool Spacing**

UNDER CONSTRUCTION … !

**Conventional Electric Logs**

**Introduction**

The basic electric logging system consists of two current electrodes A and B (the ground return) and two voltage measuring electrodes M and N. These can be arranged in a variety of configurations and spacings to suit particular requirements, such as bed resolution or deep investigation. Some of these arrangements became industry standards, such as the normal and the lateral electrode spacings.

**Normal Devices**

Figure 1 illustrates a normal device. Constant current is passed between electrodes A and B. The measure voltage appears between electrodes N and N. The distance AN is called the spacing. Thus, the 16-in. short-normal device has electrode A separated from electrode M by 16 in.

**Lateral Devices**

Figure 2 illustrates a lateral device. A constant current is sent between the A and B electrodes and the measure voltage appears between the M and N electrodes.

**Shortcomings of conventional Devices**

All of these old electric devices, though used for many years, were plagued with inherent shortcomings related to borehole and adjacent bed effects. Their idiosyncrasies are numerous. Students requiring further details to complete a study of old electric logs are directed to the References section at the back of the manual.

The only survivors from the early electric log are the microlog and a device known as the ULSEL, the ultra-long spacing electric log, which is a normal device with AM spacings from 100 to 1000 ft. It is used for remote sensing of one borehole from another (blowout control) or for remote sensing of resistive anomalies such as salt domes.

**Laterolog: General Description**

**Introduction **

In the 1920s, Conrad Schlumberger put forward the idea of a "guarded electrode" in an attempt to improve on the electrical logs of the time that had undesirable borehole effects. His idea was not put into practice until H. G. Doll designed a working guard electrode system. From this starting point, laterologs evolved in a number of ways. The laterolog 7, which used small guard electrodes, operated on the same principle of a constant survey current (io) being "forced" into the information by bucking currents from the guard electrodes. By monitoring the voltage required to maintain the fixed current io, the formation resistivity was measured. later the laterolog 3, which used long guard electrodes, was placed in service. It was known as the conductivity laterolog, and maintained a constant voltage on the measure electrode so that current variations monitored the formation conductivity.

Today, the laterolog tool most commonly used is the simultaneous dual laterolog. It is neither a conductivity nor a resistivity laterolog, but rather a hybrid using a constant product of current and voltage (constant power). The design of this tool solved many problems associated with earlier laterologs and it is now the standard basic resistivity log for salt mud environments.

**When to Use a Laterolog**

laterologs should be used when the following conditions exist:

- There is seawater or brine mud in the hole.

The R_{mf}/R_{w} ratio is less than 3.

Hole size is less than 16 in.

Furthermore, the laterolog is superior to the induction log when Rt exceeds 150 Wm2/m. It also gives a better estimate of R_{t} than the induction log when bed thickness is less than 10 ft. Figure 1 provides specifics about when to run a laterolog. This figure shows a plot of the R_{mf} /R_{w} ratio versus porosity (f). The laterolog is preferred for use when the crossplot of R_{mf} /R_{w} versus f falls on the left side of the chart.

**Laterolog: Dual Laterolog Tool**

**The Dual Laterolog Tool **

The dual laterolog tool makes two resistivity measurements: the laterolog deep (LLd) and the laterolog shallow (LLs). A microspherically focused log (MSFL) may be run in conjunction with the laterolog measurements. In addition to these resistivity measurements, auxiliary curves, such as caliper, gamma ray, and spontaneous potential curves, may be recorded. The resistivity curves are presented on a standard four-decade logarithmic scale ( Figure 1 ).

Figure 2 shows one version of the tool with its associated measure electrodes.

The mechanics of measuring both a deep and shallow laterolog from a single set of electrodes are handled by circuitry inside the tool. Figure 3 shows the respective current paths for the lid and LLs devices. The lid uses long-focusing electrodes and a distant return electrode, while the shallow laterolog uses short focusing electrodes and a near return electrode.

Figure 4 shows the current paths for the MSFL, which has five rectangular electrodes mounted on a pad carried on one of the caliper arms.

Under the normal conditions found when using a dual laterolog, the radial profile of resistivities is as shown in Figure 5 ; i.e., R_{t} > R_{xo} > R_{m}. Between the invaded zone and the undisturbed formation is a transition zone with a resistivity value between R_{t} and R_{xo}.

If a horizontal slice were made through the tool and its surrounding formation and examined in plan view, the image in Figure 6 would be seen. Here the current is flowing radially outward from the tool and has to pass through the mud, the invaded zone, and the undisturbed formation before arriving at the return electrode. The current, if held constant, thus develops a series of voltage drops across each zone encountered. The relationship between these voltages may be simplistically expressed as

V_{total} = V_{mud} + V_{invaded} + V_{undisturbed}

Each voltage drop is proportional to the product of the current, the resistivity of the zone, and some geometrical constant, depending on the size of the zone.

**Dual Laterolog "Fingerprints"**

The characteristic behavior of the DLL tool in zones with movable hydrocarbons makes quick-look interpretation very simple. The golden rule is that the pattern in which R_{LLD} > R_{LLS} > R_{MSFL}

is a good indication that hydrocarbons are present, and conversely, the pattern in which R_{MSFL} > R_{LLS} > R_{LLD} is a good indication that the zone is wet ( Figure 7 )

Any relative ordering of the curves other than the two cases above suggests little or no invasion and indicates that the zone is impermeable ( Figure 8 ).

**Log Quality Control**

Deep and shallow laterolog curves should read the same in impermeable formations (shales and evaporites). In porous and permeable zones, some separation between the two laterolog curves is to be expected, depending on the invasion diameter and the ratio of R_{xo} to R_{t}

.

**Laterolog Corrections**

**Borehole and Invasion Corrections **

Borehole corrections to the raw data may be necessary. Charts are available from wireline service companies to make such corrections.

The MSFL, a pad contact device, is sensitive to mudcake thickness (hmc) and mudcake resistivity (Rmc).

In the range of normal interest, when laterolog readings lie in the range of 10 < (R_{LL}/Rm) < 100, all corrections are within ±10%. where hole diameters are large, however, the LLs correction can become intolerably large.

Once raw log readings have been corrected for borehole effects, they may be corrected for invasion effects, using what is commonly known as a "butterfly chart" ( Figure 1 ). This chart plots the ratio of R_{LLD}/R_{LLS} against the ratio of R_{LLD}/R_{xo}. There are three families of lines on the chart. They are constant values of R_{t}/R_{LLD} constant values of R_{t}/R_{xo}, and constant values of d_{i}.

In order to use the chart, it is first assumed that (R_{MSFL})_{cor} is equal to R_{xo}. A point is then located on the chart at the coordinates RLLD/RLLS and RLLD/R_{MSFL}. This point uniquely defines the three unknowns: R_{t}, R_{xo}, and d_{i}.

The lower left portion of the chart corresponds to the invasion pattern R_{MSFL} > RLLS > RLLD , which usually occurs in water-saturated zones where R_{mf}

> R_{w}.

**Laterologs Anomalies**

**Anomalous Laterolog Behavior **

The early laterologs were prone to various types of anomalous behavior, which are chronicled here to give some insight into the few anomalies that can still occur, even with the dual laterolog.

**The Delaware Effect**

In the early 1950s in the Permian basin, logging engineers found that laterologs behaved anomalously when approaching a thick resistive bed, such as the massive anhydrite and salt that overlies the Delaware sand. *The effect manifested itself by a gradual increase in apparent resistivity, starting when the bridle entered the highly resistive bed.* Apparent resistivities would climb to as much as 10 times the value of R_{t} before the sonde itself entered the highly resistive bed. The solution for the laterolog 7 was to place the B return electrode at the surface. For the conductivity laterolog, the solution was not so easy, since these devices were using a 280 Hz survey current generated in the cartridge. Having the return at the surface did not solve the problem, since skin effect restricted the return current to a sheath around the borehole, thus resulting in the effective return electrode as the lower part of the cable ( Figure 1 ).

Compensation for this effect with the Laterolog 3 involved a messy setup, with two sondes, one on each side of a cartridge, and a B return electrode on the bottom for Delaware situations. However, for all practical purposes, the laterolog 3 remains susceptible to the Delaware effect.

**The Anti-Delaware Effect**

In an attempt to improve on the situation and provide a dual spacing laterolog, a tool was introduced with both deep and shallow devices. However, this device also behaved anomalously beneath highly resistive beds. *The deep laterolog showed a gradient of decreasing resistivity, the exact opposite of the Delaware effect.* With the B electrode at surface (effectively at zero potential), the N electrode acted as the takeoff point of a potential divider formed by the borehole below and above N; thus the approaching sonde, at some positive potential, would cause N to raise its potential. The anti-Delaware effect would at worst cause a 50% reduction in the deep laterolog and would only be noticeable within 35 ft of the resistive bed. In fact, the effect had been present on the earlier B electrode at surface, Delaware-free laterologs, but it had not been noticed since there was no shallow laterolog with which to compare the deep laterolog.

The dual laterologs in use today have incorporated features that assure virtual freedom from Delaware and anti-Delaware effects. However, a new effect has been observed on the dual laterolog, again associated with highly resistive beds.

**The Groningen Effect**

The Groningen effect, first observed in the course of logging gas wells in Holland, manifests itself as the lid reading too high when the N electrode enters a highly resistive bed. From *a distance of AN below the bed boundary (about 102 ft), the LLd will rise over a short distance to an anomalously high value, which it will then maintain until the bed is entered.* Experiments have indicated that the effect depends on the operating frequency, and is only trouble-some in low-resistivity formations immediately below a massive salt or anhydrite bed. Modern laterolog devices can detect and correct for the Groningen effect.

The Groningen effect appears (if at all) within 102 ft (31 m) of a resistive bed and will be of interpretive importance only where R_{t} in the underlying bed is less than 10 m2/m. It can appear even if casing is set to the bottom of the resistive bed.

**Dual Laterolog "Normal" Anomalies**

Dual laterologs experience environmental effects, even if resistive bed effects do not occur. A tool has not yet been designed that is entirely free of the disturbing effects of the borehole and adjacent beds, although progress has been made in reducing these effects. For interpretive work, these environmental effects must be taken into account. The hole size and invasion effects have already been covered in the previous discussions, and another set of corrections is worth noting.

**Shoulder Bed Corrections--Squeeze and Antisqueeze**

When the sonde is in front of a bed with a resistive shoulder on either side, current tends to concentrate in the least resistive path; in other words, it is "squeezed" between the resistive shoulders into the formation of interest. Charts are available to correct for this effect. The correction factor to be applied to the borehole corrected log reading is a function of bed thickness and the contrast between the apparent reading and the shoulder resistivity R_{a}

/R_{s}. where this factor is less than one, a squeeze situation exists and the apparent log reading is too high. where R_{a}

/R_{s} is greater than one, the bed is surrounded by a *conductive* shoulder and the current tends to fan out into the path of least resistance--the conductive shoulders. Since this is the reverse of "squeezed," it is called "antisqueeze." The apparent log readings are too low in this situation.

The LLd is much more affected by squeeze and antisqueeze than is the LLs even in what might be considered thick beds (50 ft or more). When making detailed interpretations, one should use the Shoulder Bed Correction Charts for lid after borehole correction and before any other step.

Invasion corrections may then be made. A word of caution is in order. In general, an *ideal* laterolog has a depth of investigation response that behaves logarithmically with respect to invasion diameter, but it is also a function of the contrast between R_{xo} and R_{t}

.

Furthermore, the effect of a hole larger than 8 in. (20.32 cm) is to replace part of the R_{xo} zone by mud, thus changing the effective position of the origin on the invasion correction chart.

**Induction Tools: Introduction**

**Introduction**

Logging systems used before the introduction of induction logging depended on the presence of an electrically conductive fluid in the borehole to transmit electric current to the formation. In most rotary drilled wells, the drilling fluid is a water-base mud that conducts electricity. However, some wells are drilled with nonconductive fluids, such as oil-base muds, air, and gas. Under such conditions, it is impossible to obtain a satisfactory electrical log using conventional electric logging tools.

Induction logging does not depend upon physical contact between the walls of the wellbore and the logging tool. The induction logging tool acts like a transformer: the transmitter coil is energized with alternating current, which induces in the formation a secondary current that is proportional to the electrical conductivity of the formation and to the cross-sectional area affected by the energizing coil. The higher the conductivity of the formation, the lower the resistivity, and the larger the formation current will be. This current in turn induces a signal into a receiver coil, the intensity of which is proportional to the formation current and conductivity. The signal detected by the receiver coil is amplified and recorded at the surface.

The direct measurement is therefore one of conductivity. Both the conductivity and reciprocated conductivity (resistivity) curves are shown on the log. The deflections of these curves are proportional to formation conductivity. Formations having resistivities of 10, 100, or 1000 ohm-m would have conductivities of 100, 10, and 1 mmho/m, respectively.

Induction logging equipment provides a record of the formation conductivity over a wide range. The accuracy is excellent for conductivity values higher than 20 mmho/m (resistivity values less than 50 ohm-m) and is acceptable in lower conductivity ranges (down to 5 mmho/m). Beyond this limit, the induction log continues to respond to formation conductivity variations, but with diminished accuracy. There is a small uncertainty of about ±1 mmho/m on the zero of the present equipment.

**When to Use an Induction Log**

Induction logs are recommended for use when:

the hole to be logged is filled with fresh water or oil-base mud

the hole to be logged was air drilled

the Rmf/Rw ratio is greater than 3

the Rt is less than 150 ½m2/m

The induction log is the only resistivity device that works in oil-base mud (where oil is the continuous phase) or air-filled holes. The laterolog measurement is preferred when Rmf/Rw falls to the left of the vertical dashed line and to the left of the solid line for the appropriate value of Rw ( Figure 1 ). The induction log is preferred above the appropriate Rw line. To the right of the dashed line and below the appropriate Rw curve, either or both logs may be required for an accurate interpretation.

**Tool Types**

Two commonly used induction tools are the single- and dual-induction devices. Each of these tools can be combined with the other sensors, thereby allowing both porosity and resistivity logs to be recorded simultaneously. Figure 2 shows a typical tool string.

**Presentations and Scales**

Induction logs and combination induction logs are recorded on a variety of scales and presentations. The primary measurements of conductivity are always recorded on a linear scale when presented. In contrast, resistivity can be plotted on a linear or logarithmic scale. when porosity data are presented, a split grid is usually employed. Figure 3 , Figure 4 , and Figure 5 illustrate the various possibilities.

**Induction Tools: Operating Principles**

**Theory of Induction Devices**

Today's induction tools have many transmitter and receiver coils. The principle can be understood clearly by considering a sonde with only one transmitter coil and one receiver coil ( Figure 1 ).

A high-frequency alternating current of constant intensity is sent through a transmitter coil. The alternating magnetic field created induces currents into the formation surrounding the borehole. These currents flow in circular ground loops coaxial with the transmitter coil and create, in turn, a magnetic field that induces a voltage in the receiver coil.

Because the alternating current in the transmitter coil is of constant frequency and amplitude, the ground loop currents are directly proportional to the formation conductivity. The voltage induced in the receiver coil is proportional to the ground loop currents and, therefore, to the conductivity of the formation.

The induction tool works best when the borehole fluid is an insulator, such as air or gas. The tool also works well when the borehole contains conductive mud, unless the mud is too salty, the formation too resistive (above 150 ohm-m), or the borehole diameter too large.

Calibration of the system is a two-step process. First, the tool is suspended high off the ground away from any conductive materials. Since the tool is in a zero-conductivity environment, it is adjusted to read zero conductivity (infinite resistivity). Second, a circular loop or ring of a known conductivity (known resistivity of either 1 or 2 ohm-m) is placed on the tool. The tool response is now adjusted to measure this "calibration" value.

Now, with the two end points defined and measured (the high end simulated by the tool in air and the low end simulated by the test loop), the tool is capable of measuring most normally encountered oilfield resistivity or conductivity values.

Of course, when the tool is at the bottom of a l0,000-ft well, there is no way a test loop can be placed around the sonde, so an internal calibrator is included in the tool. The calibrator will have a nominal value of 1 or 2 ohm-m; its precise value is determined monthly by reference to the test loop. These internal calibrators shift with age but behave reasonably well under normal use. A check of the zero conductivity point when the tool is in the hole is accomplished by simply opening the receiving coil. Any extraneous signal is canceled out by a zero adjustment.

**Skin Effect**

Linkage of each ground loop with its own magnetic field (a ground loop has self-inductance), and with the magnetic fields of the other nearby ground loops creates a cross-coupled system and the resultant eddy currents will not be quite as predictable on the basis of the theory already discussed. That is, it cannot be assumed that the individual ground loops are independent of one another. It can be predicted that, with increasing distance from the source (i.e., transmitter coil), there will be attenuation in the amount of transmitted power because

1. The dissipation of energy by the flow of eddy currents in the region near the source decreases the energy available for transmission to regions farther out.

2. Regions far from the source are shielded from the magnetic field of the transmitter coil by the annulling effect of magnetic fields of opposite sign from the eddy currents in the conductive medium closer to the transmitter. In a sense, the "shielding" of the outer regions is equivalent to a reflection of the energy back toward the source.

As a consequence of these interactions, there is a reduction in the receiver-coil signal; i.e., a reduction in high conductivity. This reduction is commonly called a "skin effect."

Thus, if g is the conductivity reading observable in a given configuration of media without skin effect and a is the conductivity actually observed, then the difference, s, is the "skin effect."

s = g - a

An amount s is added to the observed reading by means of a skin effect compensating network. It is nonlinear and can best be illustrated by Figure 2 . In practical terms, the tool reads a resistivity that is too high unless the skin effect compensation is working properly.

**Environmental Effects**

In addition to the transmitting and receiving coils of the simple two-coil device ( Figure 1 ), a practical field tool also includes additional focusing coils ( Figure 3 ). These focusing coils make the current ground loop flow as far away from the borehole as possible to eliminate borehole and drilling-mud-filtrate invasion effects.

**Bed Thickness Corrections**

Unfortunately, a tradeoff has to be made when designing an induction tool. Good bed resolution can only be obtained with closely spaced transmitter-receiver coil arrangements, but this close spacing results in a relatively shallow radial depth of investigation. Conventional induction devices, designed for deep investigation, have poor vertical bed resolution. Effectively, the signal received is a mixture of signals from points both above and below the horizon being measured.

The surface control equipment offsets the poor bed resolution characteristic by emphasizing the zone of interest and playing down the measurement made on either side of the horizon ( Figure 4 ).

The electronic circuitry used in this tool can manipulate three measurements in such a way that the reading recorded on the log is equal to a "weight" value A times the value of the interval being measured plus B times the values at points 78 inches above and below the point being measured. The values for A and B should be chosen so that A - 2B = 1. This is logical: in a homogeneous formation where all three measurements are the same, the net effect is similar to the gross effect. This scheme assists in correcting the log for the effects of adjacent beds.

The more modern phaser processing of the induction tool signals allows for enhanced bed thickness response.

**Induction Current Paths**

Current loops flow around the borehole in a horizontal plane. The measured signal includes signals from the mud, the filtrate invaded zone, and the undisturbed zone. The tool "sees" three resistances in parallel ( Figure 5 ).

**Hole Size Corrections**

The borehole effects due to the current loop in the mud can be corrected by using a special chart. The size of the correction is insignificant in fresh, resistive muds, but quite significant in salty, conductive muds.

If an SFL

(spherically focused log) is run in conjunction

with an induction

log, a hole size correction is also needed. Figure 6 is provided for this purpose. The R_{SFL}/R_{m} ratio is plotted against the ratio of (R_{SFL})cor to R_{SFL}. The lines on the chart are for different hole sizes.

_{Invasion Affects}

The radial response of the induction tool is described by the "integrated radial geometric factor," or "G." The G factor reveals which fraction of the measured signal comes from which radial distance from the tool. Mathematically, it can be described by the equation

If d_{i} (the diameter of invasion) is small, then G is small and all the signal comes from the undisturbed zone; in this case, R_{ID }is equal to R_{t}. If d_{i} is large, then G also is large and a large pert of the total signal comes from the filtrate invaded zone. In this case, R_{ID} reads somewhere between R_{t} and R_{xo}.

Figure 7 shows G as a function of di for the deep induction tool. This plot can be used to solve the following case. Suppose di is 80 in., R_{xo} = 20, and Rt = 10. what will the induction tool read? From Figure 7 , G for a di of 80 in. is 0.4.

Therefore, the equation given above can be written as:

RID = 1/0.08 = 12.5

Thus, R_{ID} reads greater than R_{t}.

Figure 8 illustrates a typical invasion pattern with high filtrate saturation in the invaded zone and low connate water saturation in the undisturbed zone.

We should realized that this treatment of the invasion problem is the reverse of what is encountered in the field; i.e., in practice R_{xo}, R_{t}, and di are not known in advance. The objective is to find R_{xo}, Rt, and d_{i} from the measured log values. In fact, if only the value of RID is known, there is no solution to the problem. If three unknowns exist, then three known quantities are needed to solve the problem. The solution is to use the dual induction _{SFL} combination logging tool. Since the geometric factor for the medium induction log (G') is different from the geometric factor for the deep induction log (G) at the same d_{i}, the following three equations can be solved simultaneously:

R_{SFL} = f (R_{xo})

**Tool Calibration**

Induction tool calibration can be performed on land at any time. The sonde is placed in a zero conductivity environment. This is normally done by raising the sonde up in the air well away from metallic objects. This defines a zero point. A calibration loop is then placed around the sonde to give a known conductivity signal, usually 500 mmhos. This calibration is performed monthly. It is almost impossible to perform on an offshore rig because of the surrounding metal structure. In cases where it is not possible to set the zero point under controlled conditions at the surface, it is permissible to set it with the tool in the hole opposite a thick, very highly resistive zone (salt, anhydrite, dense low-porosity carbonate, etc.) if one exists. The sonde and its associated electronic cartridge form a matched set and should always be used together.

**The High-Resolution Induction**

Because of the design limitations of conventional induction tools the resulting measurements of formation resistivity are distorted by the adjacent beds, by the invaded zone, and to some extent by the borehole. Recent (mid 1980s) advances in signal processing have led to improved output from the standard dual induction hardware. These "new". induction tools are referred to as the high-resolution induction (HRI) and the phasor induction. These improvements stem from the use of both the conventional (indirect) EMF's induced in the receiver coil and the directly coupled, out of phase, ones known as the "X signals."

The result of the additional data is a measurement of formation resistivity, which is less affected by adjacent beds and allows far better precision in correcting for invasion effects. Modern software routines allow real-time deconvolution in the logging truck and hence output of R_{t}, R_{xo} and di directly on the log.

Figure 9 shows the same formation logged with (a) a conventional dual induction and (b) an HRI log. Note the improvement in bed resolution between (a) and (b).

**Microresistivity Tools**

**Introduction**

Microresistivity tools make measurements that have a variety of applications in well-to-well correlation, and are used to determine the following:

- flushed zone saturation, S
_{xo}

S_{xo}

- residual oil saturation, (ROS)

- hydrocarbon movability

- hydrocarbon density,

hy

- invasion diameter, di

- invasion corrections to deep resistivity devices

**Microresistivity Tools**

A variety of tools, old and new, are available. Each tool has its own special characteristics. The following list covers the majority of the microresistivity devices that are now, or have been, used extensively. These tools can be divided into two main groups: the mandrel tools and the pad contact tools.

Mandrel Tools:

16-in. SN Short Normal

LL8 Laterolog 8

SFL Spherically Focused Log

Pad Contact Tools:

MLL Microlaterolog

PL Proximity Log

MSFL Microspherically Focused Log

ML Microlog

The mandrel tools have electrodes placed on a cylindrical mandrel. Such tools do not require physical contact with the formation. In contrast, the pad contact tools have their electrodes embedded in an insulating pad carried on a caliper arm that is forced against the borehole wall.

The microlog is worthy of special mention as an underrated device that should be run more frequently than it is. It was one of the first microresistivity devices on the market and has had a spectacular career. Originally, it was used as a pseudo-porosity device. When that function was improved with modern porosity devices, the microlog was relegated to the pile of has-beens by many people in the logging industry. It is still a valuable tool because it offers a superb visual identification of porous and permeable zones. Figure 1 shows a microlog and proximity log presentation. The presence of permeability is indicated wherever the microinverse curve reads higher than the microinverse curve, and the microinverse curve reads close to R_{mc}.

The microlog records two resistivity curves with shallow depths of investigation. The microlog looks for a resistivity contrast between the mudcake and the flushed zone. If no porosity or permeability are present in the formation, there is no filtrate invasion, and thus no mudcake buildup. Hence, there is no positive separation between the two resistivity curves.

**Depth of Investigation**

Each microresistivity tool has its characteristic depth of investigation. It is important to know these values for each of the tools in order to select the one with the right characteristics for the job. A tool with a shallow depth of investigation is needed if invasion is shallow and the tool is to read R_{xo} without undue influence from Rt. Conversely, in situations where deep invasion exists, a deep investigation tool will ensure a reading of R_{xo} free from any effects of R_{mc}.

As with other tools, no single value for the depth of investigation can be used. Rather, a pseudogeometric factor must be used. This factor indicates how much of the total tool signal is received from an annular formation volume represented by distances (expressed in inches) from the borehole wall ( Figure 2 ).

**Bed Resolution**

Just as each of the microresistivity tools has its characteristic depth of investigation, so too does each tool have its own characteristic bed resolution; i.e., some tools are better than others at distinguishing thin beds. Tools with coarse bed resolution values are "blind" to thin shale and/or sandstone layers. For example, 3-in. shale streaks will not be "seen" by a short normal log but may easily be delineated by a microlog. By way of contrast, a shallow-focused log, depending on its electrode spacing, may be able to resolve beds 1 or 2 ft thick at best.

**Environmental Corrections**

Microresistivity devices of the mandrel type are subject to aberrations caused by the size of the wellbore. These effects can be quite severe. The pad contact tools, however, are only affected by excessive mudcake buildup, hole rugosity, and fractures.

The mudcake corrections can be made by using appropriate charts, available from the wireline service companies, that relate a correction factor to the mudcake thickness and resistivity.

The mudcake thickness is calculated as half the difference between the bit size and the measured caliper reading when the caliper reads less than bit size.

The mandrel-type tool corrections can be made by use of service company charts that relate the log reading, the mud resistivity (Rm), and the hole size.

**S _{xo} and Hydrocarbon Movability**

The water (filtrate) saturation in the flushed zone (S_{xo}) may be estimated by using Archie's equation

(S_{xo})n = F R_{mf}/R_{xo }

where ;

F = a/ m

To solve this equation, the values of a, m, n, , R_{mf}, and R_{xo} must be known. R_{mf} should be corrected for formation temperature.

The value of S_{xo} may not reveal much about the amount of oil in place, but it will reveal a great deal about whether the oil that is in place is likely to flow or not. The invasion process acts like a miniature waterflood. Invading filtrate displaces not only connate water, but also any movable hydrocarbons. In the undisturbed state at initial reservoir conditions, the fractional pore volume occupied by oil is (1 - S_{w}). After filtrate invasion has taken place, the fractional pore volume occupied by oil is (l - S_{xo}). The difference between these two values is the fractional pore volume that contained movable oil. Figure 3 shows this process.

The pore volume fraction of movable oil is determined by the relationship (S_{xo} - Sw). The fraction of the original oil in place that has moved is determined by

(S_{xo} - S_{w}) / (1 - S_{w})

This index can then be used as a measure of the quality of the pay. In formations where the relative permeability to oil is low, S_{xo} is likely to be close to S_{w} and the index will be low. This same formation will not be as productive as another with the same value of S_{w} but better relative permeability to oil and hence a higher value of S_{xo}

**Hydrocarbon Density**

The computation of the hydrocarbon density in a pay zone can be critical when there is doubt about the type of hydrocarbon present; i.e., does the formation contain oil, light oil, condensate, or gas? Since the porosity tools make their measurements in the flushed zone, they "see" a bulk volume of hydrocarbon equal to (1 - S_{xo}). This leads to the interesting paradox that where hydrocarbons are movable they will have been flushed away from the zone where they can be seen. Thus large hydrocarbon effects on porosity tools may be misleading and really only indicate large volumes of residual hydrocarbons. lack of pronounced hydrocarbon effects could mean either that movable hydrocarbons are present or the formation is wet. Either way, a good value of S_{xo} is essential for correct prediction of hydrocarbon density and hence the type of hydrocarbon present in the formation.

**Quality Control**

Quality control for these devices can be summarized by the following maxims:

- Beware of washed-out holes because (a) pad contact tools lose contact with the formation and "float" in the mud column and (b) mandrel tools give severely inaccurate readings.

- Beware of thick mudcakes because pad contact tools require large corrections.

- If hole conditions are bad, forget about trying to measure R
_{xo}, because either the tool will stick or the pad will tear up. Either way, no usable log reading will be obtained.

It should also be noted that pad contact resistivity devices do not measure accurately in oil-base

**Exercise 1.**

a. Convert 5 ohm-m (ohm-m2/m) to millimhos.

b. Convert 2000 millimhos to ohm-m.

Solution 1:

To convert from ohm-m to millimhos, divide 1000 by the resistivity value you wish to convert. For example,

1000/5 ohm-m = 200 millimhos

To convert from millimhos to ohm-m, divide 1000 by the millimhos value you wish to convert. For example,

1000/2000 milimhos = 0.5 ohm-m

The solutions are

a. 200 millimhos/m

b. 0.5 ohm-m

**Exercise 2.**

If

R_{LLD} = 33 ohm-n

R_{LLS }= 11 ohm-n

R_{MSFL} = 3 ohm-n

a. What is R_{t}?

b. What is d_{i}?

Solution 2:

R_{LLD} = 33 ohm-m

R_{LLS} = 11 ohm-m

RM_{SFL} = 3 ohm-m

Using Figure 1 and RM_{SFL} = R_{xo},

Crossplot 3 and 11 to find

R_{t}/R_{xo} = 15

d_{i} = 40 in.

R_{t}/R_{LLD} = 1.4

Therefore,

R_{t}/R_{LLD} = 1.4

R_{t} = 1.4 R_{LLD}

R_{t} = 1.4 (33) = 46.2 ohm-m

The solutions are

a. R_{t} = 46.2 ohm-m

b. d_{i} = 40 in.

**Exercise 3.**

If

R_{ID} (log reading) = 20 ohm-m

R_{m} = 0.1 ohm-m

S_{O} (Standoff) = 1.5 in.

hole diameter (caliper) = 12 1/4 in.

Find (R_{ID})_{cor}.

Solution 3:

Using Figure 1 , crossplot hole diameter versus the 1.5 standoff and find borehole geometrical factor at 0.0004, since R_{m} = 0.1 ohm-m (10,000 millimhos). (R_{a} = apparent resistivity.)

10,000 0.0004 = 4 millimhos = hole signal

R_{a} = 20 ohm-m = 50 millimhos

50 millimhos - 4 millimhos = 46 millimhos

46 millimhos = 21.7 ohm-m

The solution is (RID)cor = 21.7 ohm-m.

The hole-signal effect reduces the actual reading from 21.7 ohm-m to 20 ohm-m on the log.

**Exercise 4.**

If

R_{SFL} = 20 ohm-m

R_{m} = 0.2 ohm-m

hole size = 14 in.

What is (R_{SFL})_{cor}?

Solution 4:

Using Figure 1 :

Plot R_{SFL}/R_{m} = 20 versus hole size of 14 to find (RSLL) cor/RSFL at 1.17.

R_{SFL} cor

= 1.17 R_{SFL}

= 1.17 (20)

= 23.4 ohm-m

The solution is 23.4 ohm-m.

**Exercise 5.**

Use Figure 1 to solve the following case:

RID = 10.0 ohm-m

RIM = 13.8 ohm-n

R_{SFL} = 65.0 ohm-m

Find the values for R_{t}, R_{xo}, and d_{i}.

Solution 5:

Using Figure 1 ,

We plot 1.38 versus 6.5 and find that

d_{i} = 50

R_{xo}/R_{t} = 10

R_{t}/RID = 0.9

Therefore,

R_{t}

= 0.9 (RID)

= 0.9 (10)

=9

R_{t} = 9 ohm-m

Further,

R_{xo}/R_{t} = 10

Therefore,

R_{xo}/9 = 10

R_{xo} = (9) (10)

R_{xo} = 90

The solutions are:

R_{t} = 9 ohm-m

R_{xo} = 90 ohm-m

d_{i} = 50 in.

**Exercise 6.**

Apply Archie's equation to the following case to find S_{xo}:

R_{mf} = 0.5 ohm-m @ 75 F

T_{Form} = 175 F

R_{xo} = 10 ohm-m

F = 25

Find S_{xo} in %, assuming that n = 2.

Solution 6:

Archie's basic formula is

Step 1: Correct R_{mf} for formation temperature, using the Arps formula.

(Where: T_{1} = 75, T_{2}_{ }= 175, and R_{1} = 0.5 ohm-m)

R_{mf} = 0.20

Solving the Archie formula,

Sxo = 0.71

The solution is S_{xo} = 71%.

**Exercise 7.**

If S_{w} = 30% and S_{xo} = 65%, what percentage of the original oil in place (OOIP) has been moved?

Solution 7:

If S_{w} = 30%, then S_{hydrocarbon} = 70% (that is, 1 - S_{w}).

If S_{xo} = 65%, then S_{hydrocarbon}_{ }= 35% (that is, 1 - S_{xo}).

S_{hydrocarbon}_{ }has changed from 70% to 35% because of mud filtrate invasion, hence 50% of the original oil in place

has been flushed by the invasion of the drilling fluids.

The solution is % OOIP moved = 50%.

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