lecture 5-6 PGE 311

7/21/2019 lecture 5-6 PGE 311

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Resistivity Logging

7/21/2019 lecture 5-6 PGE 311


Apparent Resistivity

• The theory for resistivity measurements iscomplex.

– Accurate treatment calls for involved

electromagnetic theory.

•The true complex geometry of a boreholethat penetrates several formations also has

to be considered.

• The concept of apparent resistivity can be

introduced by using the simplified case of aDC, point-power electrode in a

homogeneous, isotropic, and infinitely

extended medium.

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• Consider a DC source located at Point Ain a homogeneous, isotropic mediumwith resistivity R (Fig. 5.6).

•The current return electrode is placedso far from the electrode at Point A thatits presence may be neglected duringconsideration of the current flowaround Point A.

• The medium is completely

homogeneous, the current densityaround the source depends only on thedistance, r, from Point A.

• All points equidistant from the powerelectrode are then at the samepotential. The prevailing flow system isspherical with equipotential spheresand radial lines of current flow.

• The resistance, dp, of the spherical shellbetween the radii r and r+dr is given by

7/21/2019 lecture 5-6 PGE 311


7/21/2019 lecture 5-6 PGE 311


• This concept of apparent resistivity uses the simplified case of

spherical flow of DC and electrode-type devices. – It holds true in more complex cases of focused current and induction devices.

In those cases, the signal recorded by the tool is used to calculate an apparent

resistivity, which is the resistivity of a simplified medium electromagnetically

equivalent to the true medium surrounding the tool.

• The simplified medium is usually one where – (1) all the media surrounding the measuring device are assumed to be

homogeneous and isotropic,

– (2) the fluid column filling the drillhole has the shape of a circular and

infinitely long cylinder, and

– (3) the electrical logging tool is located on the drillhole axis.

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Types of Device arrangement

• Normal Device

• Lateral Device

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Normal Device• This is the basic electrode

arrangement of the normal device.

• The current Electrode A and potentialElectrode M are mounted on thesonde and lowered into the borehole.

• Electrodes B and N are located at thesurface far from Electrodes A and M.

• In practice, Electrode B is also put inthe borehole. The generator induces alow-frequency, constant currentbetween Electrodes A and B.

• Because Electrode N is remote fromthe current electrodes, its potential ispractically negligible.

• The voltmeter measures the potential

of Electrode M. This potential can beexpressed with Eq. 5.4, where r1 isreplaced by AM and r2 is infinite,resulting in

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• GN is the geometric coefficient of the normal sonde and AM is the sonde spacing.

• The value of Ra is plotted at a depth that corresponds to the midpoint betweenElectrodes A and M. This point is usually called the inscription point.

7/21/2019 lecture 5-6 PGE 311


Types of Normal Device

• Most of the electric tools contained at least two

normal devices of two different spacings.

• The most commonly used normal spacings are

–

the 16-in. short normal and – the 64-in. long normal

– An intermediate 36-in. spacing was also available

• The long normal device, which has a radius of

investigation of about 10 ft, was used to overcome

borehole and invaded-zone effects and to provide

a representative value of true formation

resistivity, Rt .

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Lateral Device• Electrodes A, M, and N are mounted on the lateral sonde (Fig. 5.9).

• The current induced between Electrodes A and B creates a voltage difference, ΔV,

measured between Electrodes M and N.• This voltage and the apparent resistivity derived from it are expressed by Eqs. 5.4 and

5.7. The geometric coefficient GL of the lateral curve is expressed by Eq. 5.6 and can be

written as

•The calculated apparent resistivity is transcribed on the log at a depth correspondingto the midpoint, O, of Electrodes M and N. The distance AO is called the spacing of the

lateral device.

• In a homogeneous, infinite medium, the lateral log measures the resistivity of the

imaginary spherical shell between potential Electrodes M and N.

• The most common lateral spacings, AO and MN, are 18 ft, 8 in. and 32 in., respectively.

•The radius of investigation of this tool is about 19 ft, which exceeds the 10-ft radius ofinvestigation of the long normal.

• The lateral device largely overcomes the effect of the invaded zone and yields a good

Rt value.

• This is true, however, only for beds 40 ft or more thick. In thinner beds, the lateral

loses most of its vertical resolution.

R f th N l

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Response of the Normal

and Lateral Devices

• Insight into the shape of the apparent resistivity curves was gained

through both theoretical and experimental work.• The theory of electrical images and the principle of superposition yield a

relatively simple solution for the case of the half-space of Fig. 5.10.

• The half-space is made up of two homogeneous beds of resistivities R1 and

R2 where R1>R2.

• The logging device consists of point electrodes traveling vertically,perpendicular to the boundary that separates the two beds. For the

current Electrode A situated above the potential Electrode M where both

electrodes are situated in Medium 1, the apparent resistivity can be

calculated from Dakhnov (1962)

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Continue

7/21/2019 lecture 5-6 PGE 311


• Fig. 5.11 shows Ra vs.

depth of the Inscription

Point 0 for both the 16-

in. short normal and the

64-in. long normal.• The difference in the

response of the two

devices shows the

effect of tool spacing on

response.

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• Fig. 5.12 shows the response of the normal device for a bed that is more

resistive than the adjacent beds and where the spacing AM is less than the

formation thickness.

– This case corresponds, for example, to a thick oil sand surrounded by conductive shales.

• The curve is symmetrical with respect to the bed centerline.

• Moving upward, the apparent resistivity begins increasing at some point

above the formation's lower boundary, attaining a maximum where the

midpoint O of AM coincides with the center of the bed.

• The apparent resistivity decreases from this maximum value and ultimately

reaches the surrounding bed resistivity at a point located several times the

spacing AM above the top boundary.

• The two segments of the curves marking the transition from Rs to a maximumapparent resistivity value, (Ra )max , display two inflection points situated within

the bed boundaries.

• The vertical distance between these two inflection points is equal to the bed

thickness minus one spacing length.

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• The maximum value reached by the apparent resistivity depends on the

bed thickness, h. It approaches R, as h increases.

• When h exceeds four times the spacing AM, the apparent resistivity valueapproximates the true formation resistivity, Rt .

• The 64-in. long normal reads the true formation resistivity in beds 20 ft or

more thick. This is true, of course, only in the absence of invasion.

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• When AM> h, a slight hump in the curve shows above and below thebed boundaries, as illustrated in Fig. 5.13. The distance betweenthese humps, called reflection peaks, is equal to the bed

thickness plus one spacing length.• Opposite the resistive bed, the curve is depressed below the Rs value,

and it erroneously appears to be conductive. This response, called areversed signal, is a distortion caused by geometry.

– It appears on the 64-in. long normal curve opposite beds 5 ft or less thick.In this case, Rt is not reflected by Ra readings.

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For Lateral Device

• In general, lateral curves are asymetrical about the center of the bed. Bedboundaries are harder to recognize from these curves.

• Fig. 5.16 shows a resistive bed much thicker than the AO spacing. The slightdepression of Ra above the layer can be explained qualitatively.

• When Electrodes A, M, and N are situated above the resistive bed boundary, thecurrent is forced upward because this is the path of least resistance. The currentintensity at Point O is less than it would be in a homogeneous, infinite medium.

• The apparent resistivity calculated from Eq. 5.7 with the nominal current value isless than Rs.

• When Electrodes M and N are situated below the top boundary but Electrode A isstill in the upper conductive bed, most of the current is forced upward and lowapparent resistivity is calculated over an interval equal to AO, the "delay“interval.

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• When Electrodes A, M, and N are in the resistive bed, Ra increases rapidlyand reaches a plateau. The resistivity of the plateau approximates the true

resistivity. A bed thickness greater than 2.5 times the spacing AO isneeded for a plateau to develop.

– In this condition, the bed appears as infinite to the tool situated in its middle.

• When Electrode A is near the lower boundary, the current is forceddownward toward the lower conductive bed. The current intensity at PointO is much higher than it would be in a homogeneous, infinite medium.

The calculated apparent resistivity overshoots Rt • The "overshot" interval ends when Electrodes M and N cross the lower

boundary of the resistive bed. Reaching the resistivity Rs is delayed over aninterval equal to AO as the current electrode and Point O straddle theboundary.

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• Fig. 5.17 illustrates the case of a resistive bed of a thickness slightly higher than A0(A0≤ h≤

2½A0). The curve shows a depression above the top boundary, a delay below both the top andlower boundaries, and an overshot above the lower boundary.

• A plateau does not develop, making the determination of Rt more difficult.

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• When h <AO, the lateral tool response is characterized by a sharp peak with anapparent resistivity less than Rt (Fig. 5.18).

• Other characteristic features are a zone of low resistivity below the lowerboundary followed by a second peak. This peak, the "reflection peak, ' ' is locatedat a distance AO from the lower boundary. The presence of the peak can beexplained qualitatively by the higher current intensity at Electrodes M and Nwhere Electrode A is situated close to the resistive boundary, causing the currentto deflect downward.

• The zone of low resistivity, called the "blind zone," occurs as Electrodes A and Ostraddle the bed and Electrodes M and N are shielded from the current source,Electrode A, by the resistive bed. The blind zone distorts the lateral curve,especially in sequences of thin beds at short distances from one another. Ra readings by4

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Electric Log

• The electric log is used to record, simultaneously or alternately,two normal curves of different spacings and a lateral curve.

• Several apparent resistivity curves of different radii ofinvestigation are required for the evaluation of thin and thickbeds.

• Several readings are also required to detect invasion.

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• Fig. 5.21 shows an example array of four electrodes that can be used torecord short normal, long normal, and lateral curves.

• While a current is induced between Electrodes 1 and 4, potential ismeasured between Electrode 2 and a surface electrode to generate ashort normal and between Electrode 3 and the same surface electrode to

generate a long normal.• For the lateral curve, a current is induced between Electrodes 2 and 3, and

the potential is measured between Electrode 4 and the surface electrode.This lateral circuit, M-AB, is the reciprocal of A-MN in Fig. 5.9. Both circuitsgive exactly the same result according to the principle of reciprocity.

• The current is sent between Electrodes 2 and 3 instead of between

Electrode 4 and the surface electrode because Electrode 4 is used torecord the self-potential (SP) curve at the same time that the lateral isrecorded.

• The number of electrodes used depends on the number of conductors inthe logging cable. The array of Fig. 5.21 requires four conductor cables.Cables with more conductors permit the use of more electrodes.

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•

The electric log is recorded on the grid shown in Fig. 5.22.• The log is divided into three recording tracks. The depth of the inscription

point is printed at 100-ft intervals in the vertical blank column thatseparates Track 1 from Tracks 2 and 3.

• Logs used for quantitative evaluation are recorded on a detailed depthscale of 5 in. = 100 ft.

• In this case, the space between two horizontal lines represents 2 ft ofhole. Intermediate 10-ft-depth lines are heavier than the 2-ft lines. Also,much heavier lines are printed at 50-ft intervals to facilitate curve reading.

• Logs used for qualitative evaluation (e.g., geologic correlations) arerecorded on a scale of either 1 in. = 100 ft or 2 in. = 100 ft.

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•

Each of the three recording tracks is divided by vertical lines into 10divisions that are scaled linearly. The range of the scale is selected toaccommodate a certain range of the parameter recorded on the track.

• When the parameter exceeds the upper limit of the scale, its value isdivided by a constant, usually 2, 5, or 10, and recorded on a less detailedscale, usually referred to as an "off-scale" or a "backup scale."

•

If a more detailed recording is needed, the parameter is multiplied by aconstant, usually 2, 5, or 10, and recorded on a more detailed scale,usually referred to as the "amplified scale."

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• Fig. 5.23 is an example of an actual electric log. The SP curve is recorded on Track 1on the left side of the log. Tracks 2 and 3 show four apparent resistivity curves.

•

Each resistivity curve shows a sequence of responses similar to those illustrated byFigs. 5.12 through 5.20.

• A single lateral curve obtained with an 18-ft, 8-in. spacing device is recorded onTrack 3 on a 0- to 20-Ω-m scale. Track 2 shows three normal curves—two solidcurves and one dashed curve.

• By convention, when more than one curve is recorded on the same track, thedashed curve represents the response of the tool with the deeper radius of

investigation.• In this case, it represents the 64-in. normal, which is recorded on a 0- to 20- Ω -m

scale.

• The two solid curves represent the 16-in. short normal. One is recorded on a 0- to20- Ω- m scale and the second on an amplified 0- to 4- Ω- m scale.

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• Salient features of this log example include the following.

• 1. A reversed signal is indicated by the 64-in. long normal in thin resistive Beds B,D, E, and F of thicknesses less than the tool spacing. Rt cannot be determinedfrom this curve in these thin beds.

• 2. Thin resistive Beds B, D, E, and F are indicated on the lateral curve by a

distinctive peak. None of these peaks reach the true resistivity value because oflimited bed thickness.

• 3. Resistive thin Beds B, D, E, and F are also indicated by the short normal curve.The 16-in. normal readings are affected by invasion, making the determination ofRt impractical.

• 4. Resistive Bed C does not appear on the lateral curve because it is hidden by theblind zone created by Bed B. The reflection peak of Zone B appears about 19 ft

below the lower boundary of Bed B. The boundary of Bed B is determined fromthe 16-in. normal, which displays the shortest spacing.

• 5. The short normal and long normal curves indicate apparent resistivities of 19and 5 Ω- m, respectively, in Bed C. This clearly indicates that Bed C is invaded (i.e.,permeable).

• 6. The thickness of Bed C is about 12 ft, or about twice the long normal spacing. Rt of Bed C is greater than 5 Ω -m. An empirical relationship indicates that for this

thickness Rt=2Ra. Hence, Rt can be approximated to be 10 Ω -m. Thisdetermination of Rt , however, carries a degree of uncertainty.

• 7. Both short and long normals indicate the same Ra in Zone A. This signals a lackof invasion (i.e., an impermeable zone). Zone A is shale, as also indicated by theSP log.

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Microlog

• Clear delineation of the boundaries of the permeable beds is not possiblewith normal and lateral devices that have spac-ings of a few inches.

• To overcome the borehole effect, these devices are pressed against theside of the wall.

• The Microlog™ (ML) in Fig. 5.26 consists essentially of a rubber pad withthree electrodes (Electrodes A, M 1, and M2) mounted 1 in. apart in itsface.

• The pad is pressed against the side of the wall by a mechanical andhydraulic system. A current is induced between Electrode A and a distantElectrode B.

• A potential is measured between Electrode M2 and another potentialelectrode far from M2. This arrangement constitutes a 2-in. short normal

device called a Micro-normal.• The apparent resistivity calculated and recorded on the log is called the

R2 in.

– The radius of investigation of this tool is twice its spacing (i.e., 4 in.).

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• Also recorded is the potential between Electrodes M1 and M

2. This

arrangement corresponds to a lateral device of spacing AO= 1 ½ in.

• The apparent resistivity derived from this device's response is referred toas R1in x1in . This device, called the Micro-inverse, has a radius ofinvestigation of 1 ½ in.

• The mechanical design of the tool permits the recording of a caliper logthat represents the distance between the pad that carries the electrodesand a back pad (Fig. 5.26).

• The pressure applied to the pads is controlled from the surface. With thearms collapsed, the tool is lowered into the borehole.

• The curves recorded this way give a curve called mud log.

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• Fig. 5.27 shows an example of a

Microlog. The log is recorded on a

linear grid like that in Fig. 5.22.• The caliper is recorded on the first

track on a linear scale that ranges

from 5 to 15 in.; each division

represents 1 in.

•The Micro-inverse R1inx1in and Micro-normal R2in. are recorded on Tracks 2

and 3. The field of both tracks is used

and scaled from 0 to 10 Ω-m (i.e., 1

division=0.5Ω- m).

•

Because the Micro-normal has thedeeper radius of investigation, it is

traced in a dashed line. The Micro-

inverse is traced in a solid line.

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• Following are some of the salient features of this log.

• 1. The borehole is enlarged at Level A because of the lithology type (shale). Because shale is

impermeable, no invasion or mud-cake buildup occurs. The Micro-normal and Micro-inverseare pressed directly against the formation. Because of the relatively limited radius ofinvestigation of both tools, this relatively thick bed appears as infinite. Both tools record thesame apparent resistivity, which is close to the true resistivity.

• 2. Zone B is a permeable formation, as indicated by the caliper log's mudcake buildup. At thelevel of permeable formations, the tool pad is pressed against the mudcake buildup. Theapparent resistivity recorded by both logs is a weighted average of the mudcake resistivity,

Rmc and the invaded-zone resistivity, R xo. For extremely shallow invasion, the true resistivity,R„ is also included in the average.

• The Micro-inverse with a 1 ½-in. spacing is affected by Rmc more than the 2-in.-spacingMicro-normal is. Because R xo is several times greater than Rmc , the Micro-normal reading ishigher than that of the Micro-inverse, and the two curves separate as shown. – This separation where R2 in. and R1 in.x1 in. called the "positive separation. ' ' Positive separation is a strong

qualitative indication of porosity and permeability. As explained later, R xo can be determined from the R1

in.x1 in. and R2in. values.• 3. The vertical resolution of the Microlog is excellent. It can detect extremely thin beds, such

as Zones C and D. These beds could certainly remain undetected by tools with poorervertical resolution, such as the long normal, the lateral, and even the short normal.

• The Microlog can be extremely useful in detecting permeable zones.

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Laterolog-3.

• The Laterolog-3 (LL3) tool consists of a long cylinder divided into three isolated electrodes. A

middle electrode, Electrode Ao , usually is 1 ft long and is called the measuring electrode.

• Upper and lower long electrodes, known as guard electrodes, are designated Electrodes G1 and G2 in Fig. 5.28. Guard electrodes are usually 5 ft long.

• A constant current Io is induced between Electrode AO and a remote return electrode. An

automatically adjustable current is induced between the guard and remote electrodes.

Because the current emitted by electrode A0 is kept constant, its potential, V O , with reference

to a remote potential electrode varies with the resistance of the medium offered to the flow

of current. An apparent resistivity of the medium is calculated by an equation similar to Eq.5.7:

• Ra = GT V o /I0 (5.19)

– The parameter G is dependent on tool design. GT is called the calibration coefficient because it usually is determined

experimentally.

• The tool vertical resolution is controlled by focusing the current induced by Electrode A0. This

is done by maintaining Electrodes AO

, G1

, and G2

at the same potential by adjusting the

current emitted by the guard electrodes. The current of the middle electrodes is thus forced

to flow in a plane perpendicular to the axis of the logging tool. The thickness of the current

beam is approximately equal to the length of electrode A0. The LL3 then has an excellent

vertical resolution.

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Laterolog-7 • For LL3 is the considerable mass of metal in

the sonde. The mass will disturb the flow ofnaturally emitted currents into the

borehole.

• Such a disturbance affects the quality of the

SP log unless the electrode measuring the

SP is placed far from the LL3 sonde, usually

25 ft away.

• To overcome this inconvenience, the

Laterolog-7 (LL7) focuses the current by

using multiple small electrodes arranged as

shown in Fig. 5.29. The thickness of the

current beam emitted by this tool is the

distance 0102 in Fig. 5.29, usually 32 in. The

length A1A2 of the sonde is 80 in. Because ofthe reduced amount of metal in the sonde,

an SP curve may be recorded on depth

simultaneously with this laterolog.

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• The LL3, LL7, and similar devices, such as theDeep Laterolog (LLd) , overcome the two

aforementioned limitations of the conventionalelectrode-type devices.

• For example, Fig. 5.30 shows the responses ofthe LL7 and conventional logs to a thin beddrilled with saltwater-based mud.

• As a result of the thinness of the bed, the shortand long normal tool responses are distorted

and give the characteristic reversed signal.• The lateral tool shows the bed as more resistive

than the surrounding formations. However, thedisplayed maximum apparent resistivity of 13Ω-m is only a small fraction of the 100-Ω-mtrue resistivity.

• Despite the adverse conditions of the thin bed

and saltwater-based mud, the LL7 clearlyindicates the resistive bed and displays anaverage apparent resistivity of the same orderof magnitude as the true resistivity.

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Laterolog Devices of Intermediate

Depth of Investigation

• To define the resistivity distribution around

the wellbore, several apparent resistivityreadings of tools of different radii of

investigation are required.

– This need prompted the design of the shallow-

investigation Laterolog-8 (LL8) device. Subsequently,

the spherically focused log (SFL) was developed as an

improvement over the LL8.

• As Fig. 5.33 shows, in these devices, the

current-return electrode is located a relatively

short distance from Electrode A0. With this

configuration, the equipotential surfaces

assume a spherical shape.

• The tool reading is influenced most by the

invaded zone. The LL8 and the SFL are usually

recorded in conjunction with an LLd or a deep

induction log.

7/21/2019 lecture 5-6 PGE 311


7/21/2019 lecture 5-6 PGE 311


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lecture 5-6 PGE 311

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