Fundamentals of Quantitative Log Interpretation

Copyright 2012 Southern Pacific Exploration Company, LLC 1

FUNDAMENTALS OF

QUANTITATIVE LOG INTERPRETATION

Suta Vijaya

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2 Southern Pacific Exploration Company, LLC Copyright 2012

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Copyright 2012 Southern Pacific Exploration Company, LLC i

Table of Contents

Reservoir Parameters to be Evaluated .............................................................................................................. 1

Resistivity ................................................................................................................................................ 2

Metallic Conduction ................................................................................................................................. 2

Shale Conduction ...................................................................................................................................... 2

Formation Factor and Porosity .................................................................................................................. 2

Water Saturation ....................................................................................................................................... 3

Invasion .................................................................................................................................................... 3

Vertical Saturation Gradients ........................................................................................................................... 4

Water Fluid Migration ..................................................................................................................................... 4

Porosity ........................................................................................................................................................... 5

Secondary Porosity ................................................................................................................................... 5

The Spontaneous-Potential (SP) Curve ............................................................................................................. 6

Focusing-Electrode Logs ................................................................................................................................. 6

Equipment ................................................................................................................................................ 6

The Microresistivity Devices ........................................................................................................................... 8

Microlaterolog .......................................................................................................................................... 8

Conclusions .............................................................................................................................................. 9

The Sonic Log ................................................................................................................................................. 9

The Borehole Compensated (BHC®) System ............................................................................................ 9

Evaluation of Porosity ................................................................................................................................... 10

Consolidated and Compacted Sandstones ................................................................................................ 10

Carbonates .............................................................................................................................................. 10

Uncompacted Sands ................................................................................................................................ 11

The Formation Density Log ........................................................................................................................... 11

Equipment .............................................................................................................................................. 11

Neutron Logs................................................................................................................................................. 12

Effect of Lithology ................................................................................................................................. 13

Determining Porosity from Neutron Logs ................................................................................................ 13

Summary of Neutron Log Applications ................................................................................................... 13

The Gamma Ray Log..................................................................................................................................... 14

Properties of Gamma Rays ...................................................................................................................... 14

Applications of the Gamma Ray Log....................................................................................................... 14

Table of Contents

ii Southern Pacific Exploration Company, LLC Copyright 2012

The Thermal Decay Time Log ....................................................................................................................... 15

Identification of Gas Zones ..................................................................................................................... 16

Conclusion ............................................................................................................................................. 16

Determination of Lithology and Porosity ........................................................................................................ 17

Determination of Rw ..................................................................................................................................... 17

Rw from Water Catalogs ......................................................................................................................... 17

Rw from Chemical Analysis ................................................................................................................... 17

Rw from the SP ...................................................................................................................................... 18

Resistivity Interpretation (Rt, Rxo/Rt, Rxo) ............................................................................................. 18

Qualitative Interpretations ....................................................................................................................... 19

Determination of RXO................................................................................................................................... 19

Shaly Formations ........................................................................................................................................... 20

Permeability, Definitions ........................................................................................................................ 21


Reservoir Parameters to be Evaluated

Almost all oil and gas produced today comes from accumulations in the pore spaces of reservoir rocks.

The amount of oil or gas contained in a unit volume of the reservoir is the product of its porosity by the

hydrocarbon saturation. Porosity is the pore volume per unit volume of formation. Hydrocarbon

saturation is the fraction (or percentage) of the pore volume filled with hydrocarbons.

In addition to the porosity and the hydrocarbons saturation, the volume of the formation containing

hydrocarbons is needed in order to determine if the accumulation can be considered commercial.

Knowledge of the thickness and area of the reservoir is needed for the computation of its volume.

To evaluate the producibility of a reservoir, it is useful to know how easily fluid can flow through the

pore system. This property of the formation, which depends on the manner in which the pores are

interconnected, is its permeability.

The main physical parameters needed to evaluate a reservoir, then, are its porosity, hydrocarbon

saturation, permeable bed thickness, and permeability. These parameters can be derived or inferred for

electrical, nuclear and acoustic logs.

This article is concerned mainly with the determination of porosity and water saturation. It also explains

how logs are used to obtain valuable information about permeability, lithology, and producibility, and to

distinguish between oil and gas.

Of the formation parameters obtained directly from logs, resistivity is of particular importance. It is

essential to saturation determinations. Resistivity measurements are used, singly and in combination, to

deduce formation resistivity in the uninvaded formation; i.e., beyond the zone contaminated by borehole

fluids. They are also used to determine the resistivity close to the borehole, where mud filtrate has largely

replaced the original fluids. Resistivity measurements, along with porosity and water resistivity, are used

to obtain values of water saturation. Saturation values from both shallow and deep resistivity

measurements are compared in order to evaluate the producibility of a formation.

Several different logs may be used to determine porosity: Sonic, Formation Density, and Neutron Logs

have responses that depend primarily on formation porosity. They are also affected by rock properties,

each in a different way, so combinations of two or three of these logs yield better knowledge of the

porosity, lithology, and pore geometry; also, they will frequently distinguish between oil and gas.

Permeability, at the present time, can only be estimated from empirical relationships. These estimates

should be considered as having only order-of-magnitude accuracy.

Reservoir Parameters to be Evaluated


Resistivity

The resistivity of a substance is its ability to impede the flow of electric current through that

substance. The resistivity unit used in electrical logging is the ohm-meter2/meter, usually written

ohm-m. The resistivity of a formation in ohm-meters is the resistance on ohms of a one-meter cube

when the current flows between opposite faces of the cube.

Electrical conductivity is the reciprocal of resistivity, expressed in mhos per meter. In electrical

logging practice, to avoid decimal fractions, conductivity is expressed in millimhos per meter

(mmho/m). A resistivity of one ohm-m corresponds to a conductivity of 1000 mmho/m; 100 ohm-m

corresponds to 10mmho/m, etc.

Formation resistivity usually falls in the range from 0.2 to 1000 ohm-m. Resistivity higher than 1000

ohm-m is uncommon in permeable formations.

Metallic Conduction

Logs are sometimes used to locate and evaluate ore bodies. Many ores, such as galena, chalcopyrite,

etc., have very high conductivities. Their depth and thickness may be readily determined from

resistivity logs run in test borings.

Most formations logged for oil and gas are made up of rocks which when dry, will not conduct

electrical current. Current flows through the interstitial water, make conductive by salts in solution.

These salts dissociate into positively-charged cations (Na+, Ca++…) and negatively charged anions

(CI-, SO4–…). Under the influence of an electrical field these ions move, carrying an electrical

current through the solution. Other things being equal, the greater the salt concentration, the lower the

resistivity of the formation water,* hence of the formation.

Shale Conduction

Shaliness also contributes to formation conductivity. Shale conduction differs from electrolytic

conduction described above in that the current is not carried by ions moving freely in a solution.

Rather, conduction is an ion-exchange process whereby (usually the positively charged) ions move

under the influence of the impressed electric field between exchange sites on the surface of the clay

particles.

Surface conductance at the shale-liquid interfaces is an important factor in the effect of shaliness on

conductivity, and its influence is often disproportionate to the quantity of shale. The net effect of

shaliness depends on the amount, type, and distribution of the shale, and on the nature and relative

amount of the formation water.

Formation Factor and Porosity

It has been established experimentally that the resistivity of a clean formation (i.e., one containing no

appreciable amount of clay) is proportional to the resistivity of the brine with which it is fully

saturated. The constant of proportionality is called formation resistivity factor, F. Thus, if Ro is the

resistivity of a non-shaly formation sample 100% saturated with brine of resistivity Rw.

Fundamentals of

Quantitative Log Interpretation


Water Saturation

In a formation containing oil or gas, both of which are electrical insulators, the resistivity is a function

not only of F and Rw, but also of the water saturation, Sw. Sw is the fraction of the pore volume

occupied by formation water (1 – Sw) is the fraction of the pore volume occupied by hydrocarbons.

Archie (3) determined experimentally that the water saturation of a clean formation can be expressed

in terms of its true resistivity, Rt, as: FRw

Snw (1-3) n, the saturation exponent, is generally taken equal to 2.

In Eq. 1-3, FRw is equal to Ro, the resistivity of the formation when 100% saturated with water of

resistivity Rw. The equation may then be written: Ro

Sw = (1-4) Rt

The earliest quantitative interpretation used this formula based on resistivity only. Its use assumed

that the permeable formation had the same formation factor in the water-bearing interval of the bed

(where Ro was determined) as in the hydrocarbon-bearing interval (where Rt was determined). The

ration Rt/Ro was called the “resistivity index.”

The above formulas are good approximations in clean formations having a fairly regular distribution

of the porosity (intergranular or intercrystalline porosity). In formations with fractures or vugs, the

formulas can still be used, but the accuracy is not as good.

Invasion

During the drilling operation, the mud in the borehole is usually conditioned so that the hydrostatic

pressure of the mud column is greater than the pressure of the formation. The differential pressure

forces mud filtrate into the permeable formations, and the solid particles of the mud are deposited on

the borehole wall where they form a mud cake. Mud cake usually has very low permeability and

considerably reduces the rate of infiltration.

Very close to the hole all the formation water and some of the hydrocarbons, if present, are flushed

away by the filtrate. The resistivity, Rxo, of this “flushed zone” is expressed by the Archie formula

(Eq. 1-3) as: FRmf

Rxo = (1-5)

Sxo2

where Rmt is the resistivity of the mud filtrate and Sxo is equal to (1 – Shr), Shr being the residual

hydrocarbon saturation in the flushed zone. Shr depends to some extent on the hydrocarbon viscosity,

generally increasing as the viscosity increases.

Farther out from the borehole the displacement of formation fluid is less and less complete, resulting

in a transition zone with a progressive change in resistivity from Rxo to the resistivity Rt of the

uninvaded formation. Sometimes, in oil- or gas-bearing formations, where the mobility of the

hydrocarbons is greater than that of the water due to relative permeability differences, the oil or gas

moves away faster than the interstitial water. In this case, there may be formed between the flushed

zone an annular zone with a high formation water saturation; if Rmf is greater than Rw, this annulus

Vertical Saturation Gradients


will have a resistivity lower than either Rxo or Rt. Annuli do not occur in all oil-bearing formations,

and when they do, they generally disappear with time.

In fractured formations the mud filtrate goes easily into the fissures, but penetrates very little into the

unfractured blocks of low-permeability matrix. Therefore only a small proportion of the original fluid

is displaced by the filtrate even very close to the borehole. Rxo then, does not differ much from Rt,

and the Archie relationship as expressed in Eq. 1-5 is not applicable.

Vertical Saturation Gradients

In a reservoir, which contains water in the bottom and oil in the top, the demarcation between oil and

water is not always sharp; there is a more or less gradual transition from 100% water to mostly oil. If the

oil-bearing interval is thick enough, water saturation at the top approaches a minimum value, the

irreducible water saturation, (Sw) irr. Because of capillary forces, some water clings to the grain of the

rock and cannot be displaced. A formation at irreducible water saturation will produce water-free

hydrocarbons. Within the transition interval some water will be produced with the oil, the amount

increasing as Sw increases. Below the transition interval, water saturation is 100%.

Water Fluid Migration

When an invaded zone possesses appreciable vertical permeability, the process of invasion may be

divided into two distinct phases. The first proceeds as described above until the mud cake seal becomes

effective, after which only insignificant further quantities of filtrate enter the formation. The zone then

contains two or three fluids of different physical characteristics, including densities. (filtrate, formation

water, and possibly oil.) There being nothing to prevent it, a process of gravity migration begins to change

the vertical profile of the invaded section. (It actually begins at the same time as radial invasion, but it is

believed that little vertical profile of the invaded section. (It actually begins at the same time as radial

invasion, but it is believed that little vertical movement occurs until the mud cake seal becomes effective.)

In water-bearing zones, only two liquids are present, filtrate and formation water. With relatively fresh

muds, the filtrate is less dense, and will move upward toward the boundary of the permeable bed. (6)

Extreme cases have been observed in which the invaded zone has disappeared in the lower part of the

bed.

When oil is present as the movable liquid, two general patterns are possible. One appears after the

development of an annulus of formation water. This water, being the most dense fluid present, will have

the greatest tendency to migrate downward. The quantity to filtrate in the system is effectively fixed, so

oil will replace this migrating formation water. The zone formerly occupied by the annulus will then be

near Swirr in the upper part of the bed, and will follow a transition gradient toward the bottom boundary,

Sw increasing with depth.

When no annulus is formed, the vertical migration pattern can be more seriously significant. In this case,

also oil will displace the migrating fluid, which now is filtrate. The upper section will approach (Sw)irr

near the borehole, but the irreducible water will consist mainly of filtrate. One consequence of this is the

persistent presence close to the hole of a cylindrical volume whose resistivity is greater than either Rxo or

Rt (7). This condition has been termed an “antiannulus.”

Fundamentals of



Porosity

Porosity values can be obtained from a Sonic Log, a Formation Density Log, or a Neutron Log. In

addition to porosity, these logs are affected by other parameters, such as lithology, nature of the pore

fluids, and shaliness. More accurate values of porosity, as well as information about the other parameters,

can be obtained from a combination of two or three porosity logs.

The readings of these tools are determined by the properties of the formation close to the borehole. The

Sonic Log has the shallowest investigation. Neutron and Density Logs are affected by a little deeper

region, depending somewhat on the porosity, but generally within the flushed zone.

Secondary Porosity

Vuggy Formations

In addition to the intergranular or intercrystalline voids, which comprise primary porosity, carbonates

may contain vugs.

Neutron and Density tools respond to total porosity, regardless of porosity type. However, a Sonic Log

tends to ignore the vugs because the sound energy is propagated through the surrounding matrix,

bypassing the vugs. Therefore the use of a Sonic Log plus the Density and/or Neutron Log can provide an

estimate of the secondary porosity as well as intergranular porosity of a formation of know lithology.

Dolomitization

In Dolomitization the atom-for-atom replacement of calcium by magnesium results in less matrix

volume, hence more pore volume (greater porosity).

Fissured or Fractured Formations

These formations may show extremely high permeabilities together with low porosities. The matrix

material between fissures is usually dense, but even a small fissure can have a very high permeability.

As with vuggy formations, the porosity determinations are more complicated.

Shaly Formations

In shaly formations the shales contribute to the conductivity of the formations, and the usual

resistivity relationships do not apply. SP deflections are smaller than in the case of clean formations.

Also, all the “porosity Logs” (Neutron, Sonic, Density) are affected by the shale. For these reasons,

the evaluation of shaly formations is more difficult than for clean formations, and different

approaches must be used.

Overpressured Formations

When the fluids are trapped in compressible strata during the burying process, some of the

overburden pressure is borne by the hydraulic system. The physical traits governing log responses

The Spontaneous-Potential (SP) Curve


differ from those of normally compacted strata. These differences have been used in several ways to

predict abnormal pressure gradients and other geophysical parameters.

The Spontaneous-Potential (SP) Curve

The Spontaneous-Potential (or SP) curve is a recording versus depth of the difference between the

potential of a movable electrode in the borehole and the fixed potential of a surface electrode.

The SP is useful to:

Detect the permeable beds.

Locate their boundaries and to permit correlation of such beds.

Determine values of formation-water resistivity, Rw.

Give qualitative indications of bed shaliness.

The SP is generally recorded in Track 1 (left-hand track) of the log, usually in conjunction with resistivity

surveys, but it may also be recorded along with other logs, such as the Sonic.

Opposite the shales, the readings of the SP curve are usually fairly constant and tend to follow a straight

line on the log, called the shale base line. Opposite the permeable formations, the SP curve shows

excursions from the shale base line; in thick enough beds they often tend to reach an essentially constant

deflection defining a sand line. The deflection may be either to the left (negative) or to the right (positive),

depending mostly on the relative salinities of the formation water and of the mud filtrate.

The position of the shale base line on the log recording has no useful meaning for interpretation purposes.

The SP sensitivity scale is chosen and the shale-base-line position is set by the engineer running the log

so that the SP curve deflections remain in the SP track.

The SP cannot be recorded in the holes filled with non-conductive muds because such muds do not

provide electrical continuity between SP electrode and formation. Furthermore, if the resistivities of the

mud filtrate and formation water are about equal, the SP deflections will be small and the curve will be

rather featureless.

Focusing-Electrode Logs

Chapter I-3 reveals that the responses of conventional electrical logging (ES) systems can be greatly

affected by the borehole and adjacent formations. These influences are minimized by a family of

resistivity tools, which use focusing currents to control the path taken by the measure current. (1) These

currents are supplied from special electrodes on the sondes.

Equipment

The focusing-electrode tools include Laterlogs® and Spherically Focused Logs (SFLtm). These tools

are much superior to the ES devices for large Rt/Rm values (salt muds and/or highly resistive

formations) and for large resistivity contrasts with adjacent beds (Rt/Rs or Rs/Rt). They are much

better for resolution of thin to moderately thick beds. Focusing-electrode systems are available with

deep, medium, and shallow depths of investigation.

Fundamentals of



Devices using this principle have as quantitative applications the determination of Rt and of Rxo. The

Rt tools are Laterolog 7, Laterolog 3, and LLd of the Dual Laterolog. The medium-to-shallow-reading

devices, all integral with combination tools, are Laterolog 8 of the Dual Induction-Laterolog, LLs of

the Dual Laterolog, and the Spherically-Focused log of the ISFtm/Sonic.

Dual Laterolog

Since the measure current of a Laterolog has to traverse mud and invaded zone to reach the

undisturbed formation, the measurement is necessarily a combination of effects. With only one

resistivity measurement is necessarily a combination of effects. With only one resistivity

measurement, the invasion profile and Rxo had to be known or estimated in order to calculate Rt. The

need for a second measurement at a different depth of investigation resulted in the Dual Laterolog-

Gamma Ray tools(2)

One version of the tool records the two Laterologs sequentially, while another does it simultaneously,

and has added shallow SFL for Rxo information. Both can record a Gamma Ray curve on depth,

simultaneously with the resistivity curves. An SP can also be run.

By using effectively longer bucking electrodes and a longer spacing, the LLd (deep Laterolog) has

been given a deeper investigation than either LL7 or LL3.

The LLs (shallow Laterolog) uses the same electrodes in a different manner to achieve a current beam

equal in thickness to that of the LLd, 24 inches, but having a much shallower penetration. The LLs

depth of investigation lies between those of LL7 and LL8.

Spherically-Focused Log

The SFL is part of the ISF/Sonic combination,(3) and was developed as an improvement over both

the 16-inch normal and the LL8 as a short-spacing companion to the deep Induction log.

Induction Logging

The Induction Log was developed to measure formation resistivity in boreholes containing oil-base

muds. (1) Electrode devices do not work in these non-conductive muds, and attempts to use wall-

scratcher electrodes proved unsatisfactory. Experience soon demonstrated that the Induction tools had

many advantages over the conventional ES for logging wells drilled with water-base muds.(2)

Induction Logging devices are focused in order to minimize the influence of the borehole and of the

surrounding formations. They are also designed for deep investigation and reduction of the influence

of the invaded zone.

Principle

Practical Induction sondes include a system of several transmitter and receiver coils. However, the

principle can be understood by considering a sonde with only one transmitter coil and one receiver

coil.

High frequency alternating current of constant intensity is sent through the transmitter coil. The

alternating magnetic field thus created induces secondary currents in the formations. These currents

flow in circular ground-loop paths coaxial with the transmitter coil. These ground-loop currents, in

turn, create magnetic fields, which induce signals in the receiver coil. The receiver signals are

The Microresistivity Devices


essentially proportional to the conductivity of the formations. Any signal produced by direct coupling

of transmitter and receiver coils is balanced out by the measuring circuits.

The Induction Log operates to advantage when the borehole fluid is an insulator – even air or gas. But

the tool will also work very well when the borehole contains conductive mud, provided that the mud

is not too salty, the formations not too resistive, and the borehole diameter is not too large.

The Microresistivity Devices

Microlaterolog

On Microlog Chart Rxo-1, for values of Rxo/Rmc greater than about 15, the curves for constant

values of Rxo/Rmc are crowded; as a result, the accuracy of the determination of Rxo from the

Microlog is poor in the region. With the Microlaterolog method, it is possible to determine Rxo

accurately for higher values of Rxo/Rmc, provided, however, that the mud-cake thickness does not

exceed 3/8 in.

Principle

The Microlaterolog pad is shown in Fig. 6-2.(3) A small electrode, Ao, and three concentric circular

electrodes are embedded in a rubber pad applied against the hole wall. A constant current, Io, is

emitted through electrode Ao, Through the outer electrode, A1 is sent a current automatically

adjusted so that the potential difference between the two monitoring electrodes is maintained

essentially equal to zero. The I0 current flowing past the M1, electrode cannot reach M2 and is forced

to flow in a beam into the formations. The current lines are shown on the figure. The Io current near

the pad forms a narrow beam, which opens up rapidly at a few inches from the face of the pad. The

Microlaterolog reading is influenced mostly by the formation within this narrow beam.

THE MICRO-SFL

This is a pad-mounted Spherically Focused Logging device. It embodies two distinct advantages over

other microresistivity devices.

The first is its combinability with other logging with other logging tools, specifically the

Compensated Formation Density and the Simultaneous Dual Laterolog at present. This eliminates the

need for a separate logging run to obtain Rxo information.

The second improvement is in the tool’s response to shallow Rxo zones in the presence of mud cake.

The MICRO-SFL gives good Rxo resolution in thick-mud-cake conditions, but does not require as

great an invasion depth as does the Proximity Log. This characteristic makes it useful in a wider

range of conditions than either the Proximity Log or the Microlaterolog.

Principle

Spherical Focusing is the shaping of the equipotential surfaces produced by a resistivity device to

approximately spherical form. The focusing is accomplished by auxiliary instead of being focused

into a narrow beam, the measure current is merely prevented from following the borehole mud or

Fundamentals of



mud-cake paths. A careful selection of electrode spacings achieves an optimum compromise between

too much and too little depth of investigation.

Conclusions

The Microlog permits a very accurate delineation of permeable beds in all types of formations. It can

also provide satisfactory Rxo and porosity determination under favorable conditions, which are in

brief:

Rxo/Rmc 15; hmc ½ in.; depth of invasion greater than about four inches.

The focused microresistivity tools can provide good Rxo values under a much wider range of

conditions. The Microlaterolog is limited chiefly by mud-cake thickness, but is well adapted to salt-

base muds. When hmc exceeds 3/8 in., the Proximity Log or the MSFL is preferable.

The Sonic Log

The Sonic Log is a recording, versus depth, of the time, Δt, required for a compressional sound wave to

traverse one foot of formation. Known as the interval transit time, Δt is the reciprocal of the velocity of

the compressional sound wave. The interval transit time for a given formation depends upon its lithology

and porosity. Its dependence upon porosity, when the lithology is known, makes the Sonic very useful as

a porosity log. Intergrated Sonic transit times are helpful in interpreting seismic records.

The Borehole Compensated (BHC®) System

Sonic tools in current use are of the BHC (borehole compensated) type. This type sonde substantially

reduces spurious effects at hole-size changes (1) as well as errors due to sonde tilt.

The BHC (2) system uses one transmitter above and one transmitter above and one transmitter below

two pairs of Sonic receivers. When one of the transmitters is pulsed, the sound wave generated enters

the formation; the time elapsed between detection of the first arrivals of compressional sound energy.

The speed of sound in the Sonic sonde and in the drilling mud is less than that in the formations.

Accordingly, the first arrival at the two corresponding receivers is measured. The ray paths indicate

the paths followed by the first arrivals of compressional sound energy.

The BHC transmitters are pulsed alternately, and Δt values are read on alternate pairs of receivers.

The Δt values from the two sets of receivers are averaged automatically by a computer at the surface.

The computer also integrates the transit-time readings to obtain total travel times.

Sometimes the first arrival, although strong enough to trigger the receiver nearer the transmitter, may

be too weak by the time it reaches the far receiver to trigger it. Instead, the far receiver may be

triggered by a different, later arrival in the sonic wave train, and the travel time measured on this

pulse cycle will then be too large. When this occurs, the Sonic curve shows a very abrupt and large

excursion toward higher Δt values; this is known as “cycle skipping”. Such skipping is more likely to

occur when the signal is strongly attenuated by unconsolidated formations fractures, gas saturation,

aerated muds, or rugose salt sections.

Evaluation of Porosity


Evaluation of Porosity

Consolidated and Compacted Sandstones

After numerous laboratory determinations, M. R. J. Wyllie (4) (5) concluded that in clean and

consolidated formations with uniformly distributed small pores there is a linear relationship between

porosity and transit time:

Δtlog = Δtfluid + (1 – ) Δtmatrix

Or

Δtlog – Δtma

= (7-1)

Δtf – Δtma

where

Δtlog = reading on the Sonic Log in μsec/ft

Δtma = transit time of the matrix material

Δtf = about 189 μsec/ft (corresponding to “fluid velocity” vt of about 5,300 ft/sec)

Generally, these consolidated and compacted sandstones have porosities which are in the range of

perhaps 18 to 25 percent. In such formations, the response of the Sonic Log seems to be independent

of the contents of the pores: water, oil, gas, or disseminated shale. In some regions, on the other hand,

the porosities may be very high, around 30 to 35 percent. Then, in reservoirs which have very low

saturation, high residual-hydrocarbon saturation, and shallow invasion, the Δt values may be

somewhat greater than those in the same formations which are water-saturated.

If any shale laminae exist within the sandstone, the apparent Sonic porosity values are increased by an

amount proportional to the bulk-volume fraction of such laminae. The Δt readings are increased

because Δtshale generally exceeds Δtma of the sandstone.

Carbonates

In carbonates having intergranular porosity, Wyllie’s formula still applies. But sometimes pore

structure and poresize distribution are quite different from what they are in sandstones. There is often

some secondary porosity, consisting of vugs and/or fractures with much larger dimensions than the

pores of the primary porosity.

In vuggy formations, according to Wyllie, the velocity of sound depends mostly on the primary

porosity, and the porosity derived from the Sonic reading through the time average formula will tend

to be low by an amount approaching the secondary porosity.

Nevertheless field experience indicates that in many cases a time-average formula

Fundamentals of



Δt=A + B (1 – ), is useful in carbonates to represent the relationship between Δt and . However,

the coefficients A and B no longer correspond to well defined physical parameters as they do in the

case of the Wyllie formula (Eq. 7-1). They have to be determined empirically for each problem (that

is, for a given formation, or interval, in a given field).

Uncompacted Sands

Direct applications of the Wyllie formula gives values of porosity which are too high in

unconsolidated and insufficiently compacted sands. Such uncompacted sands are most prevalent in

the geologically younger formations, particularly at shallow depths. However, even in deep

formations these younger sands are uncompacted when the overburden-to-formation-fluid pressure

differentials are less than about 4000 to 5000 psi. Such lack of compaction may be indicated when

adjacent shales exhibit Δt values greater than 100 μsec/ft.

The Formation Density Log

The Formation Density Log is useful as a porosity-logging tool. Other uses of density measurements

include identification of minerals in evaporate deposits, detection of gas, determination of hydrocarbon

density, evaluation of shaly sands and complex lithologies, and determinations of oil-shale yield.

Principle

A radioactive source, applied to the hole wall in a shielded sidewall skid,(1) emits medium energy

gamma rays into the formations. These gamma rays may be thought of as high-velocity particles

which collide with the electrons in the formation. At each collision a gamma ray loses some, but not

all, of its energy to the electron, and then continues with diminished energy. This type of interaction

is known as Compton scattering.(2) The Schlumberger source and detector are so designed that the

tool response is predominantly due to this phenomenon. The scattered gamma ray reaching the

detector, at a fixed distance from the source, are counted as an indication of formation density.

The number of Compton-scattering collisions is related directly to the number of electrons in the

formation. Consequently, the response of the Density tool is determined essentially by the electron

density (number of electrons per cubic centimeter) of the formation. Electron density is related to the

true bulk density, ρb, in gms/cc, which in turn depends on the density of the rock matrix material, the

formation porosity, and the density of the fluids filling the pores.

Equipment

In order to minimize the influence of the mud column, the source and the detector, mounted on a skid,

are shielded. The openings of the shields are applied against the wall of the borehole by means of an

eccentering arm. The force exerted is substantially greater than in the case of a microsonde, and the

skid has a plow-shaped leading edge. Therefore, it is able to cut through soft mud cakes usually

encountered at medium and shallow depths. Some mud cake may remain interposed between the skid

and the formation at greater depths, when mud cakes are hard. Any mud cake or mud remaining

between the tool and the formation is “seen” as part of the formation and must be accounted for.

Neutron Logs


A correction is needed when the contact between the skid and the formations is not perfect (due to

mud cake or roughness of the borehole walls). In favorable cases this correction can be fairly large. If

only one detector is used, the correction is not easy to determine, as it depends on the thickness, the

weight, and even the composition of the mud cake or mud interposed between the skid and the

formations.

In the FDC (Formation Density Compensated) tool,(3) two detectors are used. Points for a given

value of ρb and various mud cake conditions fall on or very close to an average curve. Using these

average curves it is possible to enter the chart with the two count rates and determine the corrected ρb

from the plot without any explicit measurement of mud-cake density or thickness.

The distance between the face of the skid and the extremity of the eccentering arm is recorded as a

caliper log, from which it is possible to assess the quality of contact between the skid and the

formation.

A combination FDC-Rxo tool is also available. It uses a MICROSFL resistivity measurement for Rxo

determination.

Neutron Logs

Neutron Logs are used principally for delineation of porous formations and determination of their

porosity. They respond primarily to the amount of hydrogen present in the formation. Thus, in clean

formations whose pores are filled with water or oil, the Neutron Log reflects the amount of liquid-filled

porosity.

Gas zones can often be identified by comparing the Neutron Log with another porosity log or a core

analysis. A combination of the Neutron with one or two other porosity logs yield even more accurate

porosity values and lithology identification, including evaluation of shale content.

Principle

Neutrons are electrically neutral particles, each having a mass almost identical to the mass of a

hydrogen atom.(1) High-energy (fast) neutrons are continuously emitted from a radioactive source

which is mounted in the sonde. These neutrons collide with nuclei of the formation materials in what

may be thought of as elastic “billard-ball” type collisions. With each collision a neutron loses some of

its energy.

The amount of energy lost per collision depends on the relative mass of the nucleus with which the

neutron collides. The greatest energy loss occurs when the neutron collides. The greatest energy loss

occurs when the neutron strikes a nucleus of practically equal mass, —i.e., a hydrogen nucleus.

Collisions with heavy nuclei do not slow the neutron down very much. Thus, the slowing-down of

neutrons depends largely on the amount of hydrogen in the formation.

Within a few microseconds the neutrons have been slowed down by successive collisions to thermal

velocities, corresponding to energies of around .025 electron volts. They then diffuse randomly,

without losing any more energy, until they are captured by the nuclei of atoms such as chlorine,

hydrogen, silicon, etc.

Fundamentals of



The capturing nucleus becomes intensely excited and emits a high-energy gamma ray of capture.

Depending on the type of Neutron Logging tool, either these capture gamma rays or neutrons

themselves are counted by a detector in the sonde.

When the hydrogen concentration of the material surrounding the neutron source is large, most of the

neutrons are slowed down and captured within a short distance of the source. On the contrary, if the

hydrogen concentration is small, the neutrons travel farther from the source before being captured.

Accordingly the counting rate at the detector (with the source-detector spacings commonly used)

increases for decreased hydrogen concentration, and vice versa.

Effect of Lithology

The readings of all Neutrons logs are affected to some extent by the lithology of the matrix rock.

GNT readings are converted from API units to porosity index assuming a limestone matrix; if the

lithology is known to be sandstone or dolomite, the limestone porosity values are the corrected using

a lithology correction chart. SNP logs are usually scaled assuming a limestone matrix. Porosities for

other lithologies are obtained from charts, or from scales printed on the log headings. These SNP

corrections apply only to logs run in liquid-filled holes. When the hole is gas-filled, the lithology

effect is reduced to a negligible level, and porosity may be read directly subject to limitations

discussed below.

Most interpretation charts are entered with porosities recorded assuming a limestone matrix. .

Determining Porosity from Neutron Logs

Subject to various assumptions and corrections, values of apparent porosity may be derived from the

readings of any type of Neutron Log. However certain effects, such as lithology, clay content, and

amount and type of hydrocarbons, can be recognized and corrected for only if additional porosity

information – Sonic and/or Density Logs – is available. Therefore, any interpretation of a Neutron

Log alone should be undertaken with a realization of the uncertainties involved.

The following paragraphs discuss the use of each type of Neutron Log for porosity determination.

Summary of Neutron Log Applications

Determination of porosity is one of the most important uses of Neutron Logs. Corrections for

lithology and borehole parameters are necessary for accurate porosity determinations.

The SNP is specifically designed for use in open holes, and provides porosity readings having

minimum borehole effect. It is the only effective Neutron tool for use in gas-filled holes.

The CNL is designed for use in combination with other open-hole or cased-hole tools. The

compensation feature greatly reduces the effects of borehole parameters.

The GNT is applicable in either open holes or cased holes. Recorded in combination with a

Gamma Ray Log it qualitatively delineates shales, tight formations and porous sections.

In combination with another porosity log (or other porosity data) or used in a resistivity crossplot,

the Neutron Log is useful to detect gas-bearing zones. For this application the Neutron-Density

The Gamma Ray Log


combination is best, since the responses to gas are in opposite directions. Neutron Logs should be

corrected for excavation effect in gas zones, for greater accuracy in determining porosity and gas

saturation.

The Neutron Log is used in combination with other porosity logs for lithology interpretation.

The Neutron Log is used in combination with other porosity logs for shaly-sand interpretation.

The Gamma Ray Log

The Gamma Ray Log is a measurement of the Natural radioactivity of the formations. The log is therefore

useful in detecting and evaluating deposits of radioactive minerals such as potash or uranium ore.

In sedimentary formations the Gamma Ray Log normally reflects the shale content of the formations.

This is because the radioactive elements tend to concentrate in clays and shales. Clean formations usually

have a very low level of radioactivity, unless radioactive contaminants such a volcanic ash or granite

wash are present, or when the formation water contain dissolved potassium salts.

The Gamma Ray Log can be recorded in cased wells, which makes it very useful in completion and

workover operations. It is frequently used as a substitute for the SP in cased holes where the SP is

unsatisfactory. In both cases it is useful for the locations of the non-shaly beds and for correlation.

Properties of Gamma Rays

Gamma rays are bursts of high-energy electromagnetic waves which are emitted spontaneously by

some radioactive elements. Nearly all of the gamma radiation encountered in the earth is emitted by

the radioactive potassium isotope of atomic weight 40 and the radioactive elements of the uranium

and thorium series.

Each of these elements emits gamma rays, the number and energies of which are distinctive of each

element. Potassium (K40) emits gamma rays of a single energy at 1.46 MeV, whereas the two

radioactive series emit many gamma rays of various energies.

In passing through matter, gamma rays experience successive Compton-scattering collisions with the

atoms of the formations, losing energy with each collision. Finally, after the gamma ray has lost

enough energy, it is absorbed via the photoelectric effect. (In the photoelectric effect, low energy

gamma rays are completely absorbed by atoms of the formation material, resulting in the ejection of

electrons from the absorbing atoms.)

Applications of the Gamma Ray Log

The Gamma Ray Log is particularly useful for defining shale beds when the SP curve is rounded

(in very resistive formations) or flat (Rmf ≈ Rw), or when the SP curve cannot be recorded (non-

conductive muds – empty holes – cased holes).

The Gamma Ray Log reflects the proportion of shale and, in some regions, can be used

quantitatively as an indicator of shale content.

The Gamma Ray Log is used for the detection and evaluation of radioactivity minerals, such as

potash or uranium ore. The radioactivity reading corrected for borehole effect (Chart Por-7 or

Fundamentals of



Por-8) is practically proportional to the K2O content, approximately 15 API units for 1% of K2O.

This proportionality is due to the fact that potassium 40 emits mono-energetic gamma rays of

1.46 MeV. The Gamma Ray may also be used to detect and to evaluate uranium deposits, but in

this case there is no simple proportionality between Gamma Ray deflections and the “richness” of

the deposits.

The Gamma Ray Log can also be used for the delineation of non-radioactive minerals including

coal beds.(3,4)

The Gamma Ray Log is used for correlation in cased holes. The simultaneous recording of the

Gamma Ray and of a Casing Collar Locator makes it possible to position perforating guns very

accurately. As compared with the corresponding open-hole log, the deflections on the cased-hole

log are somewhat attenuated due to absorption of the gamma rays in the steel casing and cement.

The Gamma Ray Log is sometimes used in connection with radioactive tracer operations.(5)

Another specialized application is sometimes made possible by a phenomenon peculiar to old

wells, which have produced for long periods. The radiation level of zones believed to have

experienced large-scale passage of formation waters has been observed to increase significantly,

giving useful workover information.

The Thermal Decay Time Log

The Thermal Decay Time (TDTtm) Log records, versus depth, a time value indicating the rate of decay of

thermal neutrons in the formation. Because chlorine is by far the strongest neutron absorber of the

common earth elements, the response of the TDT log is determined primarily by the chlorine present (as

sodium chloride) in the formation water. Since the effects of water salinity, porosity, and shaliness on the

TDT are similar to those on resistivity logs, the TDT resembles the usual open-hole resistivity logs and is

easily correlatable with them. But the TDT differs in that it can be run in cased hole. Also, it is relatively

unaffected by drilling and completion conditions for the usual borehole and casing sizes encountered over

pay zones. Consequently, when formation-water salinity permits, TDT logging provides the means to

recognize the presence of hydrocarbons in formations which have been cased, and to detect changes in

water saturation during the production life of the well. The TDT log is thus useful for the evaluation of

old wells, for diagnosing production problems, and for following reservoir performance.

While the accuracy of the TDT measurement depends of conditions, so it can be used for quantitative

analysis. As in the case of the resistivity log, the most important parameter values needed for quantitative

interpretation are porosity and water salinity. Information is also required on shaliness, lithology, and the

nature of the hydrocarbon. Modern openhole logging programs and crossplot techniques usually provide

such information.

Principle

A neutron generator in the TDT sonde repeatedly emits pulses of high-energy neutrons. Following

each burst the neutrons are rapidly slowed down in the hole and information to thermal velocities.

They are the captured b nuclei with corresponding emission of gamma ray.(1,2,3) Relative changes in

the thermal neutron population in the media are sampled by a gamma-ray detector placed at a short

distance from the source. During the period of measurement the thermal neutron population decreases

exponentially. The thermal decay time measurement “log” is the corresponding decay time constant.

This decrease is due to either neutron capture or neutron migration (diffusion). The capture process is

The Thermal Decay Time Log


by far the most important in producing thermal neutron decay. Hence log reflects essentially the

neutron capture properties in the formation.

Identification of Gas Zones

Gas bearing zones have smaller capture cross sections than oil-bearing zones of the same porosity and

saturation; consequently gas levels generally plot apart from and below the general trend of oil-

bearing levels. In formation of low irreducible water saturation, the apparent water saturations of gas

zones (using saturation lines computed for oil) are much too low. Typically a point falling on the Sw

= 0% oil line corresponds to 15-25% water saturation for a gas zone.

Conclusion

Method for computing water saturation from TDT logs have been presented and illustrated on field

examples. Quantitative analysis depends on many parameters, the most important of which are water

salinity, formation porosity, formation shaliness, and lithology.

Although interpretation can be achieved with the help of only Neutron-porosity and Gamma Ray logs

in favorable cases, a complete set of open-hole logs is normally required to insure sufficient control

on the interpretation parameters. Even so the computed saturation becomes questionable at low water

salinity (less than 100,000 ppm) and low porosity (less than 15%) and particularly in shaly

formations. The time lapse technique offers an alternate approach which removes the main

uncertainties and extends considerably the range of an application of TDT. In this respect the

production cannot be overemphasized.

One serious limitation is TDT analysis is related to the shallow investigation of nuclear techniques.

TDT logs run in open hole are usually affected by filtrate invasion in permeable beds and are of little

value for quantitative evaluation of reservoirs. Even in cased holes, invasion may prevail, especially

when the log is run too soon after completion. This condition may be recognized by some crossplot

techniques. Invasion by casing fluid also occurs when the well is killed 1 11/16-inch TDT tool most

of the uncertainty concerning invasion has been removed, since this tool can be run through the

tubing under producing conditions. Thus the TDT log represents effectively the water saturation of

the producing zones during production.

With the appropriate technique, the TDT can be used to monitor changes in fluid saturation during the

life of the well. This unique ability has been used with remarkable economics success in several

ways, among them the following:

1. To detect channeling behind casing.

2. To permit control of reservoirs by detecting changes in water tables and in gas-oil ratios.

3. To allow better evaluation of the efficiency of recovery by measuring residual oil saturation, and

by detecting by-passed production intervals.

Fundamentals of



Determination of Lithology and Porosity

The readings of the Neutron, Sonic, and Density logs depend not only on porosity, but also on formation

lithology and fluid content. As explained in earlier chapters, when the appropriate matrix-lithology

parameters (Δtma, ma, ma) are known, correct porosity values can be derived from these logs,

appropriately corrected, in clean, water-filled formations. Under these conditions a single log, either

neutron or Density, or, if there is no secondary porosity, the Sonic, should suffice to determination .

Accurate porosity determination becomes more difficult when the matrix lithology is unknown or consists

of two or more minerals in unknown proportions. The interpretation is further complicated when the

influence on the log response of the pore fluid, in the portion of the formation investigated by the tools,

differs appreciably from that of water. In many open-hole cases, however, the invaded zone is well

flushed or originally fully saturated with water.

Sonic, Density, and Neutron logs respond differently and independently to the different matrix

compositions, and to the presence of gas or light oils. Combinations of these logs can furnish more

information about the formation and its contents than can be obtained from a single log.(1)

Except as indicated, clean (non shaly), liquid saturated formations with only primary porosity will be

assumed in the discussion, which follows.

If a formation consists of only two known minerals a pair of porosity logs, one of which is a Neutron Log,

will suffice to determine the proportions of the minerals in the rock matrix and to determine a better value

of porosity. Furthermore, if it is known that the lithology is more complex, but consist of only quartz,

limestone, dolomite, and anhydrite, then a relatively accurate value of porosity can again be determined

with the same two porosity logs; however, the mineral fractions in the matrix cannot be determined unless

the lithology is known.

Determination of Rw

Formation water resistivity, Rw, is an important interpretation parameter, since it is necessary for

saturation determination from electrical logs.

Rw from Water Catalogs

Water catalogs usually list chemical analyses and, sometimes, resistivity data for formation waters

collected from different fields and different producing horizons. Such catalogs have been compiled by

many geological societies, oil companies, etc. When available, they should be consulted, to augment

and verify Rw values obtained from the SP or by resistivity methods.

Rw from Chemical Analysis

Although direct measurements of Rw is to be preferred, sometimes only a chemical analysis of the

formation water is available, even in catalog listings.

Determination of Rw


A method for deriving electrical resistivity of a solution from its chemical analysis is described on

Chart Book page Gen-8. This method, using weighting coefficients proportional of concentrations, is

a refinement over the original Dunlap method (1) in which the coefficients had fixed values.

The method of Gen-8 uses a chart which, for the more concentrated solutions, incorporates data of

Desai and Moore and others.

Rw from the SP

In many cases a good value of Rw can easily be found from the SP curve. In some cases, however,

(where salts other than NaCl are present, where there are shifting base lines, or where Rw is variable)

certain precautions are required.

There are conditions in which important electrokinetic potentials sometimes exist (e.g. very-low-

permeability formations, depleted-pressure formations, and very heavy muds). In these cases it may

be inadvisable to use a value of Rw derived from the SP. However experience indicates that the

elecrokinetic component of the SP may generally be considered negligible when the formations have

appreciable permeability, formation waters are saline, and muds are not too resistive. In these cases

the Static SP is considered to be equal to the electrochemical potential.

For NaCl solutions, K=71 at 77F (25C), and K varies in direct proportion to absolute temperature.

For pure NaCl solutions that are not too concentrated, resistivities are inversely proportional does not

hold exactly at high concentrations or for all types of water. Therefore we use “equivalent

resistivities”, Rwe and Rmfe, which, by definition, are inversely proportional to the activities. (Rwe =

.075/aw at 77F.)

Resistivity Interpretation (Rt, Rxo/Rt, Rxo)

Interpretation of resistivity logs provides the most general approach for the detection and quantitative

evaluation of hydrocarbon saturation.

The resistivity parameters of interest are:

Rt (the resistivity of the formation far enough from the borehole to be unaffected by invasion). Rt is

used for determination of Sw in the Archie Saturation Equation

Rxo (the resistivity of the flushed zone near the borehole). The value of Rxo helpful in invaded cases

to obtain a better value or Rt. Rxo may also be used to obtain Sxo (to indicate residual saturation or

hydrocarbon movability), and to get a value of F.

Rxo/Rt is used in the ratio formula to obtain Sw/Sxo (itself an indicator of hydrocarbon movability),

and, if Sxo is know or estimated, to find Sw.

When invasion is very deep an accurate value of Rt is sometimes difficult to measure, because the

reading of the deep-investigation log is also affected by Rxo. This effect will be greater for larger

values of Rmt/Rw, because then the contrast between Rxo and Rt will be greater. When invasion is

very shallow, the measurements of so-called Rxo logs may be affected by the Rt zone.

Fundamentals of



It may also become very difficult or impossible to make accurate corrections for invasion for beds

that have been invaded by filtrates of different kinds. If a mud change is anticipated, the resistivity

logs should preferably be run before the change.

Assuming a sharp transition between the Rxo zone interpretation problem involves three unknown

parameters: Rxo, di and Rt. To solve it, as many as three different logs may be required. These

preferably include one whose response is affected by Rt, another mostly by Rxo, and a third by

variations in di.

When the invasion profile cannot be regarded as a step contact between the Rxo, and Rt zones, as, for

example, in the case of an annulus, the problem acquires additional unknowns, and an additional log

may be required.

Qualitative Interpretations

Quite often good qualitative interpretations can be made by visual inspection of resistivity and

associated logs. Steps involved are:

1. Identification of the permeable formations. This is usually done: by means of the SP; from

indications of presence of mud cake (by readings of decreased diameter on the Microcaliper,

or by positive separation between shallow and deep investigation resistivity curves.

2. Determination, by deep-investigation resistivity devices, that Rt in the permeable formation is

appreciably larger than Ro, the resistivity the formation would have if water bearing

3. When the resistivity logs are recorded on logarithmic scale the separation between the curves

is equal to the logarithm of the ratio of the two resistivity readings. The value of this ratio can

be read by measuring off the separation between curves on the logarithmic scale under the

heading, starting at the unity graduation. The value of Rshallow/R deep so determined can be

used to obtain an approximation of Rxo/Rt.

Determination of RXO

Rxo is determined preferably from the Microlaterolog or MSFL as disscused in Chapter I-6. Rxo can

sometimes be derived from the Micrology or the Proximity Log. The Proximity Log can be used directly

as an Rxo tool if invasion is deep enough (di greater than about 40”), For shallower invasion, the

Proximity Log is affected by the Rt zone; however, the log reading can be used to enter appropriately

constructed charts.

If necessary, the value of Rxo may be estimated from the porosity using a formula such as

.62 Rmf

Rxo = (14-1)

2.15(1 – Sor)2

using from a porosity log and an assumed value of Sor. The error in the estimated Rxo can be fairly

large, due to the uncertainties in and Sor, and this error will affect the Rt determination somewhat.

Shaly Formations


Pad devices for Rxo determination are sensitive to mud cake effects and boreholes rugosity, but are

usually insensitive to bed thickness effects.

Shaly Formations

The responses of many well logs are affected by formations shaliness. As a result, interpretation for

shaly formations become somewhat more involved than for clean formations.

In this chapter we will usually be talking about shaly sands. This is because of the high frequency of

occurrence of shaly sands in sand-shale sequences.(1) However, many of the techniques will be

applicable to shaly carbonates as well.(2)

The way shaliness affects a log reading depends on the proportion of shale and its physical properties.

For several logging tools (Resistivity, Sonic, SP, and Nuclear Magnetic Resonance log) it also

depends on the way the shale is distributed in the formation. Responses of the radioactivity tools

(Gamma Rays, Neutron, Density, Thermal Neutron Decay Time) are not affected by the way the

shale is distributed.

Inspection of cores reveals that shaly material may be distributed in formation in three possible ways

(Fig. 16-1):

1. Shale may exist in the form of laminae between which are layers of sand. The laminar shale does

not affect the porosity or permeability of the sand streaks themselves. However, when the amount

of laminar shale is increased and the amount of porous medium is correspondingly decreased,

overall porosity is reduced in proportion.

2. Shale may exist as grains or nodules in the formation matrix. This matrix shale termed structural

shale, and is considered to have properties similar to those of laminar shale.

3. The shaly material may be dispersed throughout the sand, partially filling the intergranular

interstices. The dispersed shale may be in the form of accumulations adhering to or coating the

sand grains, or it may partially fill the smaller pore channels. Dispersed shale in the pores

markedly reduces the permeability of the formation. All these forms of shale may, of course,

occur simultaneously in the same formation.

Laminar and structural shales have been subjected to the same overburden pressure as the bedded

shales, thus are presumed to have the same water content. In practical interpretation, they are

considered to have the same average properties as the shales in the adjacent beds. Log esponses are

taken to be identical for these two types of shales.

Dispersed shale may be assumed to have the same mineral composition as the “average” shale in the

interval. However, being subjected to only hydrostatic rather than overburden pressure, it can be

expected to contain more bound water. In usual core analysis determinations of porosity much of this

loosely bound water is removed during the drying process.(3) This results in an increased porosity

indication by the core analysis results, it may be desirable in log analysis to include some of the

bound water of dispersed shales in the porosity.

Useful shaly-sand evaluations may be performed by assuming one or both of two simplified

distributions. In one of these models laminated shale is interbedded with clean sand streaks. In the

other, all shale is dispersed. Relations will therefore be shown for use of these two simplified shale

Fundamentals of



distribution models. Interpretation experience has shown that the final saturation values found with

the two assumptions are generally not too different when the shale fraction is small.

With the availability of computers, a more nearly complete interpretation model is used. This model

incorporates to be deposited. Shales contain, in various proportions, the clay minerals (illite,

montmorillonite, kaolinite, etc.), as well as silt, carbonate, and other non-clay materials. Silt is a very

fine grained material that is predominantly quartz, but may include feldspar, calcite, and other

minerals. In sandshale areas where the principal non-clay material is silt, the silt content of the shale

has been observed to vary, being maximum near the sand bodies and minimum in the shale far from

the sands. This is consistent with sedimentation principles; silt is more likely to be present in the

higher energy environment associated with sand deposition than in the low-energy environment

required for the deposition of fine clays. When the shale is composed of wet clay and silt, obviously,

in terms of bulk-volume fractions

Peremeability, (Sw) irr, Water Cut

This chapter will develop some working concepts about permeability and capillary pressure, and

prevent some empirical methods in which well log data have been successfully used to determine

permeability, producibility, and water cut.

Permeability, Definitions

Permeability is a measure of the case with which a formation permits a fluid of given viscosity to

flow through it. To be permeable, a rock must have interconnected porosity (pores, vugs, capillaries,

or fractures). Greater porosity usually corresponds to greater permeability, but porosity which is not

interconnected (as is sometimes true of vuggy porosity) does not constitute effective (producible)

porosity and does not contribute to formation permeability.

Some fine-grained sands can have large interconnected porosities, but, at the same time, the paths

available through the narrow pores for the movement of fluid are quite restricted and tortuous; the

permeabilities of very fine-grained formations may be quite low.

Other formations, such as limestone, may be composed of a dense rock broken by a few small fissures

of great extent. The porosity of the dense formation would surely be very low, but the “permeability”

of a fissure can be enormous. Fissured limestones may thus have very low porosities, but exceedingly

high permeability.

The permeability of a given sample of rock to the flow of any homogenous fluid is a constant,

provided the geometry of the rock is not altered by the way the core is prepared or by the permeability

test itself. Permeability determined for a homogeneous liquid is called absolute permeability (k).

Permeability measurements made using air or gas have to be corrected for “slippage” effects, to

equivalent liquid permeability, by use of the so-called Klinkenberg corrections.

The unit of permeability is the “darcy”. This is a very large unit, so in practice the thousandth part of

a darcy, the millidarcy (md), is commonly used.

The range of permeabilities of producing formations is extremely wide – from less than 0.1 md to

well over 13,000 md. The lower limit of permeability for a commercial well depends on several

factors: the thickness of the pay, whether oil or gas, hydrocarbon viscosity, formation pressure, water

saturation, the price of oil, etc.

Shaly Formations


When two or more immiscible fluids (e.g., oil and water) are present in the formation their flows

interfere. The effective permeabilities (ko, kw) in these cases are therefore less than the absolute

permeability (k). The effective permeability depend not only upon the rock itself, but also upon the

relative amounts of the different fluids present in the pores.

The relative permeabilities are the ratios of the effective permeabilities to the absolute (homogeneous-

fluid) permeability. Thus, for an oil-water system the relative permeability-to-water (krw) is equal to

kw/k; similarly the relative permeability for oil (kro) is equal to ko/k. It is apparent that relative

permeabilities must lie between zero and unity. Relative permeabilities are usually expressed in

percent.

The shapes of the relative permeability diagram will depend on the formation and pore characteristics,

and on which fluids are present (water, oil, gas).

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Fundamentals of Quantitative Log Interpretation