Application of Electrical and 

Radioactive Well Logging to 

Ground-Water Hydrology

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-D

Prepared in cooperation with the 

Pennsylvania Geological Survey 

Department of Internal Affairs 

Commonwealth of Pennsylvania

Application of Electrical and 

Radioactive Well Logging to 

Ground-Water Hydrology

By EUGENE P. PATTEN, JR., and GORDON D. BENNETT

GENERAL GROUND-WATER TECHNIQUES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-D

Prepared in cooperation with the 

Pennsylvania Geological Survey 

Department of Internal Affairs 

Commonwealth of Pennsylvania

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

First printing 1963 

Second printing 1967

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 25 cents (paper cover)
CONTENTS

	Page 

Abstract___ __________-____-______-..--__-_-_-________--_____,___ D-1

Introduction..,.________ ___-___-_-_--_----___-_-___-_______-___ 1

Resistivity logging________ -__----_____---__-____--__-_--_-_ 2

Instrumentation and theory__________________________________ 2

Calibration and zones of investigation______________________ 6

Borehole effect__________________________________________._ 7

Mechanism of electrical conduction in earth materials._____________ 9

General lithologic interpretation...........______________________ 10

Interpretation based upon the relative magnitudes of the normal

curves.. _ _______________________________________ 11

Interpretative practices in the oil industry.___________________ 11

Conditions in a mud-filled borehole...-...-----..--.-------.. 13

Conditions in a water-filled borehole......-..---------------- 14

Summary of interpretation of the relative magnitude of normal

curves______________.___-_____-___.____-_____-_-_--_ 18

Relation of porosity to formation factor_______-_______-._ __.. 18

Recognition of secondary porosity in limestone and crystalline rocks. _ 20

Secondary porosity in sandstone-shale sections-________--____-__-- 24

Spontaneous-potential logging.______________________________________ 26

Instrumentation ___ _________________-_-___---_-_-_--__---_-. 26

History...__________________________________________ 27

Analysis of quantitative interpretation______._________--___--_-__ 27

The general liquid-junction equation-__-____--___-_-_-_--_--- 29

Equation for direct junction between two sodium chloride

solutions._____._.________-_-_____-_____-__------------_ 30

Junction of sodium chloride solutions through an ion-selective

membrane....______._________--_-___-___---_-____-__ 30

Role of shale as an ion-selective membrane ___________________ 31

Liquid-junction potentials in an oil well______________________ 32

Relation of the spontaneous-potential measurement to the theoretical electromotive force_-__-__-------_--------_-------- 34

Objections to quantitative interpretation for water wells__________ 36

Interaquifer flow_______._______________-______-_----_------_-_ 37

Streaming potentials..________._______-_____-__---___-.-_-.- 38

Zones containing highly mineralized water.______--___--_-_-_---__ 38

Artificially induced spontaneous-potential deflections-__----_-_----_ 39

Abnormal spontaneous-potential deflections.______________________ 39

Summary of spontaneous-potential logging______________________ 39

Fluid-conductivity logging______________-_________-___----_.-_ 40

Factors controlling conductivity......_________________________ 40

Interpretation of fluid-conductivity logging in a single-aquifer well 40

Interpretation of fluid-conductivity logging in a multiaquifer well... 41

in
IV CONTENTS

Page 

Gamma-ray logging,_______________________________________________ D-15

General discussion of radiation and gamma-ray-logging instrumentation_____________________________________________________ 45

Sources of radiation in common sediments________________________ 47

Shale and clay____________-___-__..___-__-__--_____________ 47

Sandstone.________-_______--___---_______--___________.__ 49

Carbonate rocks____._____--___-_--_--_-_---__-_.__-_____ 50

Evaporite rocks and coal_____-_-_----_----_-------_----____ 50

General lithologicinterpretation_____________-____---_--___-_____ 51

Gamma-ray interpretation as a supplement to resistivity data.______ 51

Assumptions underlying the method-________________________ 52

Interrelation of gamma radiation, formation factor and porosity

under the assumed conditions________--__--____---__-_____ 53

Graphical method of interpretation__-_--___---___-__________ 54

Conclusion_____________________________________________________ 57

References__----___--__-____-____--___--___-____-_______________ 57

Index__________________________________________________________ 58

ILLUSTKATIONS

Page

FIGURE 1. Equipment and current patterns, logging in a homogeneous

medium. ____________________________ ____ ______ D-3

2. Diagram showing division of medium into spherical shells

which act as resistances in series__---_-_----_--_-_--____ 4

3. Zones of investigation of the resistivity devices in a homogeneous medium__________ ___. 8

4. Internal flow in a multiaquifer well___ __ 15

5. Resistivity curves opposite a zone of thin alternating beds of

sand and shale_________ 17

6. Current pattern, logging in a limestone or crystalline section.. 22

7. Resistivity curves for a water well in limestone____ ____ 25

8. Resistivity curves for a water well in crystalline rocks___-_-_ 26

9. Spontaneous-potential current and electromotive-force pattern at a sand-shale contact -- ________ 33

10. Fluid-conductivity log in a multiaquifer well in which ionic

diffusion is negligible--..--.------------------- -- - 42

11. Graph showing interrelation of radiation, formation factor,

and porosity in an ideal sedimentary section ______ _ 54
GENERAL GROUND-WATER TECHNIQUES

APPLICATION OF ELECTRICAL AND RADIOACTIVE WELL 

LOGGING TO GROUND-WATER HYDROLOGY

By EUGENE P. PATTEN, JR., and GORDON D. BENNETT

ABSTRACT

This report discusses in detail several problems pertaining to the interpretation of electrical and radioactive well logs in ground-water hydrology. Emphasis 

has been placed upon situations in which interpretation departs from the 

practices common in petroleum engineering. Certain interpretive methods 

of the oil industry are demonstrated to be unsatisfactory for hydrologic purposes, and certain other methods which have not been significant in the oil 

industry are recommended for use in ground-water hydrology. For all methods, 

an effort has been made to analyze the interpretive methods in terms of underlying theory, as an understanding of theory is superior to any memorized set 

of rules or principles in analyzing the data of well logging.

INTRODUCTION

Electrical and radioactive well logging has come into widespread 

use in ground-water hydrology during recent years, and many articles 

have been published dealing with its application in this field. Most 

of these articles are general and do not treat particular interpretive 

probems in detail.

This report is one of several resulting from an investigation of 

subsurface geophysical methods made by the U.S. Geological Survey in cooperation with the Pennsylvania Geological Survey.

The report is not intended as a comprehensive manual of log interpretation but, rather, as a discussion of selected problems of interest 

to the ground-water hydrologist. Special attention has been given to 

differences in interpretative practice between oil-reservoir and 

ground-water investigations. Such differences may arise when the 

assumptions underlying the interpretive techniques of the oil industry cannot be extended to hydrologic work, or when the objectives 

of interpretation differ between the two situations.

D-l
D-2 GENERAL GROUND-WATER TECHNIQUES

Many aspects of lithologic interpretation are basically the same in 

ground-water and oil-reservoir studies; most of these are not treated 

in detail in this report, as they are described adequately in the literature of the oil industry and are well known to ground-water 

hydrologists.

RESISTIVITY LOGGING

The following discussion of resistivity logging is confined to the 

single-point resistance and normal arrangement, multiple-electrode 

resistivity methods. Although these have been supplemented by advanced electric-logging techniques in the oil industry, they remain the 

most popular methods of logging in hydrologic work. It is doubtful 

that the application of advanced electric-logging techniques to 

ground-water problems would yield information of equivalent or 

greater value, at the present time. Most of the new techniques were 

developed to deal with reservoir or borehole conditions that are not 

common in ground-water studies. It seems preferable that advances in 

instrumentation in the ground-water field follow a somewhat different 

line, according to the specialized problems of the field.

Although this report is not comprehensive, it includes a section on 

the general theory of resistivity logging to prepare the reader for 

the discussion of interpretive problems. An understanding of interpretive methods in logging is impossible without a general knowledge 

of the underlying electrical theory. The theory presented here 

follows that given by Guyod (1952) for single-point and normalresistivity devices.

INSTRUMENTATION AND THEORY

A typical logging apparatus might be arranged according to the 

diagram of figure 1. A constant current is maintained between the 

two spherical terminals G and Z>, and a recording galvanometer may 

be set to read the voltage between G and either <7, $, or L. The distance OS is approximately 16 inches, and OL is approximately 64 

inches. The distances CD and CG are large relative to OS and OL. 

If the galvanometer is set to read the potential difference between 0 

and £r, the apparatus is termed a single-point device; if it is set to 

read the potential between S and G, the apparatus is called a shortnormal device; and if it is set between L and 6f, the apparatus is a 

long-normal device.

If the earth and well bore are considered to be an infinite, homogeneous, and isotropic electrical medium, a simplified mathematical 

treatment is possible. To begin this treatment, an expression will be 

derived for the resistance of a spherical shell in such a medium to a
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-3

Galvanometer Generator

FIGCEH 1. Equipment and current patterns, logging In a homogeneous medium.

three-dimensional radial current, as from a point source embedded 

in the medium. The shell is considered to be divided into a series 

of thin concentric elements, as shown in figure 2. The resistance of

each element to a radial current is given by the expression ^R=

where p is resistivity of the medium, AT- the radial thickness of the 

element, and r the mean radius of the element from the center of the
D-4 GENERAL GROUND-WATER TECHNIQUES

FIGURE 2. Diagram showing division of medium into spherical shells which act as

resistances in series.

current pattern. This will be recognized as a special case of the more 

general formula for resistance,

*->z

in which L is the length of the current path and A the cross-sectional 

area of flow.

The spherical elements of figure 2 obviously constitute resistances 

in series to the radial current, and the total resistance of the shell is 

determined by summing these resistances between the inner and outer 

bounding surfaces of the shell that is,

pAr

r2 4

The analysis leading to equation 1 indicates that the greatest part 

of the resistance of the shell occurs near the inner surface, where 

the cross-sectional area of flow is smallest. As r increases, this flow 

area expands rapidly, causing the resistance of the successive elements 

to decrease sharply. This result can be extended qualitatively to most 

nonhomogeneous electrical systems, where p may vary with r and the 

other spherical coordinates. The resistance of earth material to a
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-5

radial current is controlled largely by the resistivity of the material 

nearest the current source. This is the general condition in resistivity 

well logging.

If a single spherical conductor is embedded in an infinite, homogeneous, and isotropic medium, and its potential is made positive with 

respect to that of the medium, a radial current pattern is established. 

Equipotential surfaces are spherical and concentric with the current 

source; the potential difference between any two such surfaces may 

be calculated by Ohm's law, in which the expression from equation 1 

is used for the total resistance of the spherical shell between the surface; that is,

The potential difference between any two points in the medium is 

the difference between the potential spheres through those points and 

is, thus, dependent only upon the coordinate r. The total current / 

is the same across any equipotential surface in the medium, although 

current density decreases as the cross-sectional area of the flow 

increases.

The potential difference between a point at a distance TI from the 

center of the current source and a remote point (effectively an infinite distance from the source) is given by

A trial calculation with equation 2 shows that nine-tenths of the 

voltage drop that might be recorded between ^ and infinity takes 

place between rt and 10/v This follows directly from the fact that 

the resistance is concentrated chiefly in a zone near the inner surface 

of the shell.

If the analysis given here is applied to the system shown in figure 1, 

it can be seen that a potential measurement made between G and either 

Z, $, or the surface of terminal O is effectively the potential difference between infinity and an equipotential of relatively small radius. 

This can be demonstrated by substituting re (the radius of electrode 

G) and the distance CG- into equation 2, and similarly by substituting 

OS and CG, and GL and CG, noting that in each substitution the

term -^ is negligibly small. The equations then take the form of

Otr

equation 3, with rc, C8, or GL used in place of r.

An immediate objection that may be raised to the application of 

equations 2 or 3 to the system illustrated in figure 1 is that the flow is
D-6 GENERAL GROUND-WATER TECHNIQUES

between the two current terminals rather than being truly radial to 

an infinite distance. In order to be entirely rigorous, the effect of the 

current sink, or negative electrode Z>, must be considered. This can 

be done by deriving an expression for the potential difference between 

any two points because of a radial flow toward the sink, assuming it 

to be alone in the system. An expression of the form of equation 2 

is obtained, the only difference being the use of a negative current and 

of distances measured from D rather than from G. The potential difference between any two points in the two-terminal system of figure 1 

can then be calculated by scalar addition of the potential difference 

resulting from the operation of terminal G alone and that resulting 

from the operation of terminal D alone. The distances DG, LD, $Z>, 

and GD are all large with respect to rc, OS, and GL. Accordingly, 

the effect of terminal Z> on the potential difference between G and tf,

$, or Z, is negligible. Mathematically, the terms -f7f)> "OTJ» fj)» an(i 

i drop out, and the equation reverts to the form of equation 3;

physically, D is sufficiently remote from #, $, and L that it does not 

appreciably change their potential or alter the radial distribution of 

current in their vicinity. Thus, the analysis leading to equation 3 

accurately describes the conditions in the vicinity of terminals #, $, 

and L of figure 1, if the earth and well bore constitute an isotropic 

and homogeneous electrical system. The effects of the inevitable deviations from these conditions which occur in a practical situation 

are discussed in later sections.

CALIBRATION AND ZONES OF INVESTIGATION

When logging is done by the single point resistance method, the 

galvanometer is connected between G and G. The potential measurement made by this device, under a known current held constant by a 

servo-mechanism, indicates the resistance of a segment of borehole 

and earth extending to a radius of approximately Wrc . As has been 

pointed out, the potential drop beyond !Qr0 is negligible. The galvanometer may be calibrated to read resistivity according to the 

formula

P=j4irrc (4)

obtained by solving the appropriate equation of the form of 3 for />. 

A similar analysis can be made for the short-normal arrangement, 

leading to the calibration equation
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-7

(5)

and for the long normal arrangement, leading to the equation

t-j**(OL) (6)

The short normal measures effectively the resistivity of a shell of 

borehole and earth material extending from a radius of OS to a radius 

approximately 1QC/S, and the long normal measures the resistivity of 

a shell extending from GL to 100L. Thus, each of the devices has 

a zone of investigation that is, a region within which a change in 

resistivity will produce an appreciable change in the response of the 

device. In practice, the zones of investigation commonly are considered to be even further restricted ; for example, they may be considered to extend from rc to 27*c , from OS to 2CS, and from GL to 2CL.

Zones of investigation of the point-resistance, short-normal, and 

long-normal devices are shown in figure 3, constructed assuming 

the borehole and earth to be a homogeneous electrical system. 

Figure 3 shows that much of the zone of investigation of the pointresistance device lies within the open borehole. The zone of investigation of the short normal includes a greater proportion of the surrounding formation, and that of the long normal includes an even 

greater proportion.

Equations 4, 5, and 6 show that the logging instruments are calibrated on the assumption that the earth and borehole constitute a 

homogeneous medium. If this condition were met, the resistivity 

reading by each device obviously would be the same. If electrical 

heterogeneity prevails within the zone of investigation of one of the 

devices, the resistivity measured by that device is a composite value, 

its magnitude depending upon the resistivities of the component parts 

and the amounts and disposition of those parts within the zone of investigation. The zone of investigation is no longer a spherical shell, 

as the radial current pattern is disrupted by the electrical heterogeneity; thus the calibration equation is geometrically and physically 

inapplicable. Electrical heterogeneity within the zone of investigation of one device may cause a measurable change in the response 

of the other devices, owing to disruption of the radial symmetry.

BOREHOLE EFFECT

In the simplest situation encountered in practice, the earth surrounding the bore may be assumed to be perfectly homogeneous, the 

only heterogeneity being due to the borehole. The zone of investigation of the point-resistance device, where the percentage of open
D-8 GENERAL GROUND-WATER TECHNIQUES

PO NT 

RES STANCE

"- SHORT :: 

: ; NORMAL!

LONG 

NORMAL

FIGURE 3. Zones of investigation of the resistivity devices tn a homogeneous medium.

borehole is greatest, is subject to the most severe heterogeneity, and 

the zone of investigation of the long-normal device, where open borehole constitutes a relatively small part of the total volume, is subject 

to the least. The resistivity reading of the long-normal device, thus, 

is closer to the true resistivity of the earth than that of the shortnormal device and much closer than that of the single-point device.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-9

When PBH represents borehole resistivity (that is, the resistivity of 

the fluids in the borehole) and pt the true resistivity of the surrounding

formation, the ratio may be used as an index for the borehole

pt 

effect in the response of a device calibrated according to equation 4,

5, or 6. If the ratio ^- is equal to unity, the system will be electrically

homogeneous, current will be radial, and the apparent resistivities 

will equal pt. If the ratio is less than one, the apparent resistivities

will be less than pt. As ^^ increases toward unity, the apparent

pt

resistivities increase toward p t. If ^ is greater than one, the appt

parent resistivities will exceed pt and as decreases toward unity,

pt

the apparent resistivities decrease toward pt.

MECHANISM OP ELECTRICAL CONDUCTION IN EARTH MATERIALS

The conductivity of the solid materials in a rock is in general small; 

electrical current through a rock consists largely of the movement 

of ions in the water saturating the pore spaces of the rock. The conductivity of a rock thus depends upon the relative amount of interconnected fluid in the rock and the conductivity of this fluid. The effective or interconnected porosity of the rock determines the relative 

volume that can be occupied by conducting fluid. The concentrations, 

charges, and mobilities of the various ionic species in the interstitial 

fluid determine the conductivity of the fluid at a given temperature. 

The resistivity of a rock thus is generally inversely proportional to 

its porosity and to the ionic concentration of its interstitial fluid. The 

origin of the porosity is immaterial; either primary or secondary 

porosity, as long as it is interconnected, will serve to lower rock 

resistivity.

Empirical relations between rock resistivity, interstitial fluid resistivity, texture, and porosity have been in use for many years and are 

discussed in a later section of this paper. These parameters determine the "formation-resistivity factor" of a rock. The formationresistivity factor is defined as the constant ratio of true rock resistivity 

to the resistivity of the water saturating the rock; that is,

F-&. (7)

pw

A modified definition is sometimes given in oil-reservoir work, where 

several fluid phases may be saturating the rock. In a single-phase-
D-10 GENERAL GROUND-WATER TECHNIQUES

fluid system, however, equation 7 is a sufficient definition. Large 

amounts of clay minerals in a sand may cause the ratio to vary,

PW

invalidating equation 7.

The effects of clay minerals upon rock resistivity are caused by an 

ionic double layer that forms along the surfaces of the clay particles 

as a result of the tendency of the clay minerals to adsorb negative 

charge. An abnormally high concentration of mobile positive ions in 

this double layer causes an increased conductivity through the 

saturated porous medium (Winsauer and McCardell, 1953).

The relative effect of clay minerals in decreasing the resistivity 

of a rock becomes more severe as the ionic concentration (and electrical conductivity) of the water saturating the rock decreases. In 

problems of ground-water hydrology, the saturating fluid is normally 

fresh or slightly salty water, and the effect of clay minerals is 

relatively great. This is in contrast to most oil-reservoir conditions, 

where the saturating fluid is generally brine and the relative effect 

of the clay minerals is small. The presence of clay minerals can lead 

to many mistaken interpretations of electrical logs, both lithologic 

and hydrologic, in ground-water studies.

GENERAL LITHOLOGIC INTERPRETATION

The preceding section describes how the electrical properties of 

earth materials depend upon certain other physical properties and 

indicates that electrical properties can be expected to change wherever 

lithology changes significantly. This is, of course, the basis of conventional lithologic interpretation, whether in the oil industry or in 

ground water.

As the logging assembly is lowered through a thick, homogeneous, 

and isotropic formation, the apparent resistivity recorded by each 

device reflects the resistivity of the formation and the relative effect 

of the borehole within the zone of investigation of the device.

The large zone of investigation of the long normal serves to minimize the borehole effect so that the response of this device is generally 

close to pt in a thick homogeneous formation. At the same time, however, this large zone of investigation makes it impossible for this 

device to indicate lithologic detail in zones of thin, alternating beds. 

The single-point device, on the other hand, because of its relatively 

small zone of investigation, defines thin beds in detail and identifies 

geologic contacts with greater accuracy, but it generally gives a 

rather poor approximation of pt.

Simple interpretation of lithology from the electric logs follows 

the same lines in hydrologic work as in oil-reservoir work. In the
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-ll

following sections special methods of interpretation that differ between the two fields are emphasized.

INTERPRETATION BASED UPON THE RELATIVE MAGNITUDES OF 

THE NORMAL CURVES

There are certain interpretive practices, formerly common in oilreservoir work, in which unusual differences between the normal 

resistivity curves are attributed to electrochemical differences between 

the fluid in the borehole and that in the formation. In an oil well this 

difference is usually that between drilling mud and a highly concentrated brine. In a water well it may be the difference between drilling mud and fresh water, or that between two fresh waters. In some 

water wells there may be no difference whatsoever. Some typical 

electrolytic characteristics of brine, drilling mud, and fresh water are 

summarized below.

Electrolytic characteristics of typical well fluids

Prine Drilling mvA Freth water

Typical ionic concentration_______ppm._ 150,000 500 200

Typical resistivity_________ohmmeters.- . 03-. 05 5-10 30-40

INTERPRETIVE PRACTICES IN THE OIL INDUSTRY

During the logging of an oil well, the borehole is usually filled with 

drilling mud, and the PBH is of the order of 5 ohmmeters. The formation, on the other hand, may contain brine having a resistivity 

of 0.05 ohmmeter. If a formation factor of 20 is assumed, pt becomes 

1 ohmmeter. The resistivity of the borehole will, thus be roughly 

five times that of the formation.

If the drilling mud has invaded the formation to a certain radius 

and if contamination of the drilling mud by ionic diffusion is negligible, the borehole will be surrounded by a region of high resistivity. The resistivity in this invaded zone, again given by the product of the formation factor and the resistivity of the saturating fluid, 

is 100 ohmmeters.

This situation is certain to cause a characteristic reaction on the 

three resistivity curves. The zone of investigation of the long normal 

device contains a relatively small percentage of boreholes and invaded 

zone, and the long normal will show a resistivity close to p*, or roughly 

1 ohmmeter. The zone of investigation of the short normal device 

probably includes all three regions of resistivity, but the short normal 

is affected strongly by the highly resistant invaded zone and will 

usually show the highest apparent resistivity of the three curves. 

The single-point device will generally show a composite resistivity of 

the borehole and the invaded zone. Its resistivity measurement will,
D-12 GENERAL GROUND-WATER TECHNIQUES

thus, be higher than the long-normal reading, but because of the 

strong effect of the borehole it will be less than the short-normal 

reading.

If the bed is not invaded by drilling fluid, the difference between 

the apparent resistivities shown by the long- and short-normal curves 

is smaller and is due only to the greater effect of the borehole in 

the zone of investigation of the short normal. Also, because the 

borehole is the more resistive of the two regions, the apparent resistivity of the single-point device will exceed that of the short normal.

The conditions outlined above have been used, in the oil industry, 

for the identification of permeable zones, on the assumption that 

only permeable zones will be invaded. Thus, zones for which pSN 

(short-normal resistivity) is observed to be much greater than pLN 

(long-normal resistivity) are considered to be permeable, and zones 

for which the two apparent resistivities are closer together, and PPR 

(single-point resistivity) is greater than psy, are considered to be 

relatively impervious.

In addition to this qualitative interpretation, the relation

PJW £m (8) 

PLN pw

has been used in the oil industry as a more quantitative form of interpretation based upon the relative magnitudes of the curves. In this 

equation pm is the resistivity of the drilling fluid. The relation is 

used to calculate pw, the resistivity of the formation water, from the 

electric-log data. It has now been largely abandoned in the oil industry, but it merits discussion, inasmuch as it seems to have been 

adopted by many workers in hydrology.

The assumptions upon which this equation is based are that drilling 

mud (1) completely saturates the zone of measurement of the short 

normal, (2) is uncontaminated by diffusion from the brine, and (3) 

lias not entered the zone of investigation of the long normal. The 

effect of the borehole is assumed to be negligible in both apparent 

resistivities. The relations

are then divided to give equation 8.

The validity of the assumptions underlying equation 8 is obviously 

questionable. The assumptions are most nearly realized in an oil 

well, but even then the equation is no more than an approximation. 

The problem of concern here, however, is whether equation 8, or the 

less quantitative forms of this method of interpretation, can be applied to a water well.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-13

During the logging of a water well, the fluid within the well bore 

opposite a given formation generally will be one of the following 

three: (1) Drilling mud, in rotary-drilled holes; (2) water that is 

chemically identical with that of the formation; (3) water that is 

chemically different from the water in the formation. The similarity 

between oil-well and water-well logging is greatest in (1), but even in 

mud-filled holes, certain basic differences are present.

CONDITIONS IN A MUD-FILXED BOREHOLE

As indicated in the tabulation on page D-ll, formation water usually 

is 3 to 5 times as resistive as the drilling mud in a water well. The 

contrast may be less than this, and occasionally the mud may be 

more resistant than the formation water. The resistivity contrast 

between mud and formation water in a water well, however, will be 

much smaller than that in the average oil well and most frequently 

will be in the opposite direction.

If pm exceeds pw, it is unlikely that it ever will exceed Fpw, the 

true formation resistivity; the borehole, thus, will be the region of 

lowest resistivity and will act to decrease the various apparent resistivities, according to its influence in each zone of investigation. If a zone 

is invaded by drilling fluid, it is unlikely that the resistivity of the 

zone, Fpm, ever will exceed Fpw by a significant factor that is, a factor 

sufficient to overcome the strong effect of the borehole in decreasing 

the apparent resistivity of the short normal.

The apparent resistivities of fresh-water aquifers, then, usually 

are in the order PLN>PSN>PPR, regardless of the effect of invasion. 

If pm is less than pw, as it usually is, the short-normal resistivity may 

be somewhat less for an invaded zone than for a zone of the same 

pt that is not invaded, but many other phenomena can cause a short 

normal of low resistivity for example, an increase in borehole size. 

The resistivity differences involved will be relatively small in any case. 

Obviously, under these conditions, a low short normal resistivity is 

not a reliable indication of invasion of the formation.

If pm exceeds pw the short-normal resistivity may be slightly higher 

opposite an invaded zone than opposite a zone of the same pt that 

is not invaded, but it rarely will exceed the long-normal resistivity. 

Under these circumstances, also, the interpretation is subject to too 

much doubt to be of appreciable use.

If the qualitative identification of permeable zones is subject to a 

high degree of uncertainty, the application of equation 8 must be 

regarded as even less reliable. The objections to the use of this relation in an oil well are serious; they become even more so in a water well
D-14 GENERAL GROUND-WATER TECHNIQUES

where the resistivity contrast of the fluids is much smaller and differences in the apparent resistivities are, accordingly, affected more by 

other factors. In summary, this lack of a strong resistivity contrast 

between the invaded zone and the uncontaminated formation may be 

considered to be the basic weakness of any interpretation based upon 

relative resistivities in a mud-filled water well.

CONDITIONS IX A WATER-PILLED BOREHOLE

Two examples of water as borehole fluid were mentioned earlier : 

(1) the water in the borehole, opposite a given formation, may be 

chemically identical to the water in the formation, or (2) it may differ 

chemically from the formation water. The first example is the 

simpler. It may occur in wells penetrating a single aquifer or in 

wells penetrating several aquifers having chemically identical waters. 

It may occur also in wells penetrating several aquifers having waters 

of different chemical character, if interaquif er flow and ionic diffusion 

through the well bore are negligible. Finally, if interaquifer flow 

prevails, water in the bore opposite a zone from which water is entering the well may be chemically identical with water in that zone.

If formation water and borehole fluid are chemically identical, the 

ratio of the resistivity of the borehole to the resistivity of the formation will be the inverse of the formation factor, as

PBH__ 1

pt Fpw F

There will be no invaded zone, and the effect of the borehole will be 

to lower the apparent resistivity, according to the relative influence 

of open borehole in the zone of investigation of the device. Thus the 

apparent resistivities will be in the order

and, because pLn f^pt for a thick bed, the formation factor may be determined by

& PLS F is=t'- 

PW

where pw may be obtained from a logging device measuring the resistivity of borehole fluid.

Where the water in the bore is known to be identical with that in 

the surrounding formation, there is no need for equation 8, and the 

designation of a permeable zone by a difference in the apparent resistivities is inapplicable. Where the waters are identical but the 

fact is not known to the interpreter, the use of either method will 

obviously lead to erroneous results.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-15

The water in the borehole and that in the surrounding formation 

often differ chemically in multiaquifer wells. Where a well intercepts two or more aquifers whose hydrostatic heads are different, an 

internal discharge will be established from the aquifers of high to 

those of low head (Bennett and Patten, 1960). The effect of this 

internal discharge is illustrated in figure 4. Water flows from the 

upper aquifer to the lower when the well is not in use. The waters 

of the two aquifers differ chemically. Opposite the upper aquifer, 

the water in the borehole is the same as that in the formation. This

Piezometric

surface" 

First aquifer Observed water level in well

Piezometric

surface 

Second aquifer

Land surface

First aquifer

Second aquifer

FIGURE 4. Internal flow in a multiaquifer well.
D-16 GENERAL GROUND-WATER TECHNIQUES

water invades the lower formation apparently in a manner analogous 

to the invasion of a formation by drilling mud. Thus, the question 

may arise: Can internal flow of this sort be recognized by differences 

in the normal resistivity curves opposite the lower aquifer? The 

answer to this question is indicated by the fact that the resistivity 

contrast almost always will be small and its direction unknown to the 

interpreter. Thus, the arguments against the use of these interpretive 

methods for a well filled with drilling mud and penetrating freshwater formations, apply to a well filled with water. The two problems have certain differences, however, which make the uncertainty 

of interpretation for a water-filled hole even greater than that for a 

mud-filled hole. These differences are described briefly in the following pages.

The invasion of a formation by drilling mud may be treated, to a 

first approximation at least, as a problem in immiscible-fluid displacement. In contrast, the two formation waters in figure 4 are 

entirely miscible. Two processes can, therefore, be expected to combine to produce some sort of radial variation in the ionic content of 

the water in the lower aquifer: (1) ionic transport due to fluid velocity 

with associated lateral dispersion and (2) simple ionic diffusion. 

The rate of ionic transfer due to fluid velocity is a function of the 

flow velocity, and except for very low velocities, ionic diffusion is 

neglible by comparison. In the lower aquifer of figure 4, velocity 

varies inversely with radial distance away from the well; the process 

of velocity transport must, therefore, decrease in relative importance 

as the radial distance from the well increases, until a radius is attained at which diffusion is of equal significance. The nature of the 

final ionic distribution will, therefore, depend upon a great number of 

factors such as the original ionic content of the formation waters, the 

magnitude of the internal discharge, and the thickness, porosity, and 

dispersion constants of the lower aquifer. The radial variation in 

fluid resistivity that results from this ionic distribution is, accordingly, 

difficult to determine and can be expected to differ widely from one 

well or aquifer to another. In general, therefore, the assumption 

that internal discharge of the sort shown in figure 4 will produce a 

sharp contrast in fluid resistivity between the zones of measurement 

of the long-normal and short-normal devices is not justified in theory.

The interpretive methods discussed in this section, however, are 

based upon this assumption. For this reason, as well as for those 

reasons indicated earlier in the discussion, these methods generally 

cannot be relied upon to indicate internal flow or to identify permeable 

thieving zones.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-17

Certain lithologic conditions can bring about unusual differences 

between the normal resistivity curves. The authors believe that such 

conditions often have been mistaken for differences in fluid resistivity in hydrologic work.

The effective porosity within the zone of measurement of the short 

normal commonly is increased and the resistivity is lowered by fracturing and shattering of the rock surrounding the hole as the well 

is drilled. An isolated pocket of material having low or high resistivity within the zone of measurement of either device also will affect 

the resistivity reading of that device; for example, a pocket of shaly 

sand, within the zone of measurement of the long normal, in a sandstone bed. Also, in a zone of thin alternating beds of sand and shale, 

where the bed thickness is approximately the same as the penetration 

of the short normal, the short normal will oscillate, according to the 

lithologic changes; the long normal, however, will indicate an average resistivity of the zone (fig. 5). An increase in borehole size can

RESISTIVITY, OHM-METERS

Resistant sand beds 

/Thickness betweerA 

V 16 and 64 inches /

-Short normol

 Long normal

FIGURE 5. Resistivity curves opposite a zone of thin alternating beds of sand and shale.

decrease the apparent resistivity logged by the short normal device if 

pm<Fpw Similarly, a contraction in borehole size can increase the 

reading of the short normal.
D-18 GENERAL GROUND-WATER TECHNIQUES

SUMMARY OF INTERPRETATION OF THE REIjATIVE MAGNITUDE OF

NORMAL CURVES

Any interpretation based on the relative magnitudes of the normal 

curves is hazardous in hydrologic work, because the resistivity contrasts are generally small. Even in oil-reservoir work, where strong 

resistivity contrasts prevail, the use of the normal curves in this type 

of interpretation is open to question. It may be noted that advances 

in instrumentation have provided more reliable ways of employing 

these interpretive methods in the oil industry. For example, the difference in apparent resistivity between a microlog and a laterolog 

can provide a reliable indication of mud invasion, if a strong resistivity 

contrast is present. However, these interpretive methods cannot be 

improved appreciably in ground-water work by the use of such instrumentation, as the strong resistivity contrast is generally lacking.

RELATION OF POROSITY TO FORMATION FACTOR

Empirical relations between porosity and formation factor have 

been used extensively in the oil industry, and have also been applied 

frequently to hydrologic problems. A brief discussion of the applicability of these relations in hydrology will be given in this section.

Archie (1942) first recognized a relation between porosity and 

formation factor, as a result of experiments on various sands from 

the Gulf Coast region. Archie restricted the validity of his equation 

to sandstones ranging from 10 to 40 percent in porosity, and saturated 

with brine containing from 20,000 to 100,000 milligrams per liter of 

sodium chloride. A great deal of further experimentation followed 

Archie's work, and the relation commonly used today is a slight modification of the equation he proposed. The modified equation has the 

form

F=C$- (9)

where <f> is the porosity, and G and m are constants for the formation. 

Equation 9 is basically empirical in nature; although various theoretical derivations of the equation have appeared in the literature, all 

of these are open to question on one ground or another. In these 

derivations, for example, it is assumed that the effect of the porous 

medium is purely geometrical that it acts only to decrease the cross 

sectional area available to the ionic current and to extend the effective 

length of current path. This assumption is not applicable to rocks 

containing an appreciable fraction of clay minerals, because these 

minerals tend to modify the mechanism of conduction, as described in 

an earlier section. Even if it can be assumed that the rock is free of 

clay minerals, the theoretical derivations of equation 9 remain open
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-19

to some question. Equation 9 should, therefore, be treated as an 

empirical relation. For example, the equation should not be applied 

to a formation until experimental control has established (1) the 

validity of the equation in the formation and (2) the values of the 

constants C and m for the formation.

In the oil industry this experimental control is normally established 

by core analysis. Formation factor and porosity are measured in the 

laboratory for a number of cores from the formation in question. A 

plot of log F versus log <£ is then constructed. If the plot is a straight 

line, the equation is known to apply, and the constants C and m can 

be obtained from the intercept and slope of the line. A great deal has 

been published concerning the correction of formation-factor data 

for the effect of clay minerals, and such corrections are sometimes attempted in the core analysis procedure if the formation is known to 

be shaly. This generally involves an increase in the amount of core 

data which must be analyzed.

Under the conditions prevailing in the oil industry, equation 9 

can be a very useful relation. Core analyses from a small group of 

wells in an oil field can frequently establish the porosity-formationfactor relations for the various strata, and porosity determinations in 

the remainder of the wells can then be made on the basis of electric 

logging data alone. It is seldom necessary to apply the relations at 

any great distance from the region represented in the laboratory control, as most oil fields are limited in areal extent.

These conditions, however, are rarely duplicated in hydrologic 

work. Aquifers are normally much greater than oil fields in areal 

extent. The amount of laboratory control necessary for the application of equation 9 throughout an aquifer is, therefore, usually greater 

than that necessary in an oil field operation. The opportunities to 

obtain core data, however, are normally far fewer in a hydrologic study 

than in an oil reservoir investigation. In unconsolidated aquifers 

it is virtually impossible to obtain undisturbed samples for laboratory 

analysis, and even in consolidated aquifers it is seldom possible to 

obtain enough cores for adequate control.

Because of the difficulty in obtaining adequate control, there has 

been a tendency among hyclrologists to make use of equation 9 without 

such control, using arbitrarily chosen values for G and m. There 

are three basic assumptions involved whenever this is done: (1) the 

equation applies to the aquifer, (2) the term G has the particular 

value chosen, and (3) the term m has the particular value chosen. 

Each of these assumptions is open to question owing to the empirical 

nature of equation 9. Used without control, therefore, the equation 

is at best a method of rough approximation. Results obtained
D-20 GENERAL GROUND-WATER TECHNIQUES

through its use in this manner should be labelled and qualified accordingly.

A reliable method of porosity determination in the field, without 

extensive laboratory control, would obviously be of great importance 

in hydrology. Such a method may eventually be provided by the 

neutron-neutron or acoustic-velocity techniques now in use or under 

development in the oil industry.

RECOGNITION OF SECONDARY POROSITY IN LIMESTONE AND 

CRYSTALLINE ROCKS

Electric logging in igneous and metamorphic rocks has been studied much less intensively than that in sedimentary rocks, because 

crystalline rocks are rarely penetrated in oil wells. Crystalline rocks 

constitute some important aquifers, however, and the question naturally arises as to whether any useful information can be gained from 

electric logs in such material.

Crystalline rock is similar to dense limestone both hydrologically 

and electrically, and the principles of log interpretation are essentially 

the same for aquifers of either type. These principles of interpretation are similar to those used in the study of limestone petroleum reservoirs, but the complex instrumentation commonly used in the oil 

industry for logging in limestone is seldom used in hydrologic work.

Crystalline rocks are highly impervious hydrologically and highly 

resistant electrically. Water and ionic charges can move only through 

fractures in the rock and through the shattered or weathered zones 

associated with fractures. In other words, the familiar features of 

secondary porosity in crystalline rocks fractures, joint planes, shattered fault zones, and associated features are the water-bearing zones 

of the rocks and are characterized by a relatively low electrical 

resistivity.

The same principles hold true regarding dense limestone, except 

that in limestones the origin of the secondary porosity is usually solution along fracture zones or bedding planes. These principles can be 

applied also to a section of dense limestone containing porous sand 

beds. The sand beds are zones of primary porosity but are hydrologically and electrically similar to solution zones in that they are usually 

permeable and permit ionic conduction. Dense limestone, like crystalline rock, is relatively impervious and highly resistant.

The success or failure of a particular well in crystalline rock or 

in limestone depends upon the number of permeable zones intercepted 

by the well and the capacity of each to yield water to the well. In 

the development of a well field, it is desirable to know the thickness 

and depths of these zones, as the location of the zones in a few wells
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-21

may aid in the selection of new drilling sites. Similarly, in a study 

of regional hydrology, the location of permeable zones in several wells 

may help to outline a regional pattern of occurrence. In a well that 

penetrates both sedimentary and crystalline material, it may be necessary to know which is the principal aquifer. Fractures in the crystalline rock indicate that the crystalline rock may be the aquifer; the 

absence of fractures, on the other hand, definitely establishes the sedimentary rock as the aquifer.

It has been mentioned that there are many similarities between logging in limestone or crystalline aquifers and logging in limestone oil 

reservoirs. In the logging of oil wells in limestone, the conventional 

normal device fails to locate accurately the boundaries of porous zones. 

These failures are due to the poor conducting qualities of the limestone 

relative to those of the drilling mud. The logging current tends to concentrate in a linear pattern within the well bore, as shown in figure 6. 

The extreme deviation from the radial current pattern assumed in the 

calibration equations prevents determination of true limestone resistivity. The response of the logging device indicates the potential drop 

between the measuring electrode and a reference electrode at some remote point, however, and a brief analysis of the nature of this potential 

drop explains some of the difficulties of logging in highly resistive 

formations. For a more complete treatment of this subject the reader 

is referred to Schlumberger Well Surveying Corp. (1950).

The current from C follows the borehole until a porous, conductive 

zone is reached. It then spreads radially through this porous zone; as 

it does so, the surface area of dense limestone exposed to current penetration expands rapidly. The logging current thus enters the impervious limestone over a wide cross-sectional area, at a low current density, 

and returns to the ground terminal through the limestone. The logging circuit, therefore, includes a segment of borehole, the porous zone, 

a large volume of impervious limestone, and the logging cables. The 

large cross-sectional area of the limestone causes the total resistance of 

that segment of the circuit to be effectively zero, in spite of the high 

resistivity of the material. The flow area begins to expand as soon as 

the current enters the porous zone, and except for a small region immediately surrounding the borehole, the resistance of the porous zone 

also is effectively zero. Thus the voltage drop between a measuring 

electrode at L and a ground electrode will be controlled more heavily 

by the resistance of the borehole fluid between L and the porous zone 

than by the resistance of any material outside the bore.

In practice, the constant logging current leaving the source normally will divide into two current paths one up the borehole and the
D-22 GENERAL GROUND-WATER TECHNIQUES

n

^»* N

"^~ - ^ ^S ,

v

^'

<~""' '

'

s 

4? /

\ /

\" 'll

"'ll l|l'

iJi/. i\'('I'' 1

!|l M

'(JlS (JBi I

 'T' 

^*

iii ii ' i Ml 1 1 1

in i 1 1 1 ' i

Hi'iii 

' i 1 1 1 ' i ' 1 1

iii H 

n

i ii 

> u

1 ii' /' *\

f \

/

X

/

s

1

--)

\

S

\

X

\

.r POROUS

.'* ZONE

^-^

\

7

IGNEOUS ROCK

(... OR 

LIMESTONE

7 -2

t

-± POROUS

XA ZONE

FIGURE 6. Current pattern, logging in a limestone or crystalline section.

other down as porous zones usually are located both above and below 

the logging assembly. Because the voltage drops outside the borehole 

are small relative to those within the mud column, the potential opposite each porous zone will be approximately at ground, or approximately equal to the potential at G. The two current paths through the
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-23

borehole, thus, may be considered parallel resistances between the 

current source and ground, and the two currents will be in the ratio

I\ __ RZ __ pBaZzfA _ ^2

/2 RI

where /t is the current toward the upper porous zone, /2 the current 

toward the lower porous zone, Zt and Z2 the corresponding distances, 

and A the borehole area. Thus, the two factors governing the potential 

drop between L and G the current /i and the resistance of the segment 

of borehole between L and the upper porous zone both vary with the 

position of the logging assembly between the two zones.

If the logging assembly is of the design shown in figures 1 and 6, it 

can be demonstrated that the voltage difference (or the apparent resistivity) follows a parabolic curve, having a maximum at the midpoint of the limestone interval and minima opposite the porous zones. 

On many normal-resistivity devices, however, one or both of the terminals D and G (fig. 1) are mounted on the logging cable at some distance far enough above L to be considered at infinity in formations 

of moderate resistivity. In limestone sections, the symmetry of the 

resistivity parabola will be disrupted if either of these terminals lies 

between L and the upper porous zone, although the minima opposite 

the porous zones still will be present.

Whether the terminals D and G are on the cable or at the surface, 

the porous zone is located approximately by the minimum in the apparent resistivity; however, its boundaries may not be marked by 

the relatively sharp resistivity breaks characteristic of a sandstoneshale section. In the oil industry, accurate location of the boundaries 

of a porous zone is generally necessary, particularly when a well is 

to be cemented and perforated. This has led to the development of 

such devices as the "limestone sonde," which are capable of outlining 

the boundaries of a porous zone with relatively high accuracy.

Devices of this sort would be useful in solving ground-water problems in limestone or crystalline rock, but satisfactory logs generally 

can be obtained with the conventional normal device. This is due 

partly to the fact that an approximate delineation of the porous 

zones is satisfactory in solving many ground-water problems and 

partly to the fact that the borehole often contains fresh water that 

is more resistive than the drilling mud used in oil wells.

In the above analysis of apparent resistivity in zones of high formation resistivity, the current was assumed to remain entirely within 

the borehole, in a linear pattern. This is, of course, an idealization, 

which can be attained only when the resistivity of the formation is

infinite or, in other words, when the ratio ^^ is zero. Similarly, the

pt
D-24 GENERAL GROUND-WATER TECHNIQUES

radial flow assumed in the calibration equations also is an idealization, which, can be attained only when the above ratio is unity. In 

ground-water work, the current pattern usually lies somewhere between these two extremes, according to the value of the resistivity 

ratio. Although the ratio always will be low in a water well in limestone or crystalline rock, it often will be several times greater than 

in an oil well in limestone, since the resistivity of the borehole fluid 

in the water well often will be greater. A greater proportion of the 

logging current will, therefore, penetrate the formation directly. This 

helps to explain the relatively good quality of the normal curves for 

many water wells penetrating material of high resistivity, when the 

borehole fluid is fresh water.

Figure 7 shows the resistivity curves for a water well in limestone, 

and figure 8 shows the same curves for a well in crystalline rock. The 

interpretation of the curves in figures 7 and 8 is somewhat the opposite of that in a sandstone-shale section. In a sandstone-shale section, the water-bearing zones are usually the beds of sandstone, which 

have a high resistivity relative to the shale owing to the effect of clay 

minerals in decreasing the shale resistivity. In limestone or crystalline rock, the water-bearing zones are the intervals of low resistivity.

SECONDARY POROSITY IN SANDSTONE-SHALE SECTIONS

In the conventional description of ground-water hydrology in a 

sandstone-shale section, the sandstone beds are assumed to be the principal aquifers and to have uniform primary porosity and permeability, and the shale beds are assumed to be aquicludes. The principal 

water-bearing zones may be fractures, joints, or other features of 

secondary porosity, however, and bear little or no relation to the 

stratigraphy. Features of secondary porosity can be indicated by 

resistivity logging in dense limestone and crystalline rocks; in a sandstone-shale sequence, however, resistivity logging is of little help in 

identifying zones of this type.

The effect of clay minerals in decreasing the resistivity of shale 

generally overshadows any resistivity variation due to changes in 

porosity. Thus the difference in resistivity between a fracture zone 

in a shale interval and the unf ractured shale itself is usually too small 

to be indicated by resistivity logging.

If the secondary porosity is in a sandstone bed, the situation is 

somewhat improved but still presents difficulties. The increase in 

porosity generally can be recognized by the accompanying decrease 

in resistivity but rarely can be identified as secondary in origin. Thus, 

flow through secondary fractures might easily be mistaken for percolation through a unif orm-textured porous medium.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-25

Depth,

in feet RESISTIVITY, OHI^METERS

60

100

200-

::v::-V.-V:. 300

Long normal

[::'/..'.':'."v Porous zone 

FIGURE 7. Resistivity curves for a water well in limestone.
D-26 GENERAL GROUND-WATER TECHNIQUES

Depth, 

in feet

RESISTIVITY, OHM-METERS

Triassic 

arkose

_ _ _ _ _ _j'_ _Contact

100

Short normal

Cambrian 

quartzite

FIGURE 8. Resistivity curves for a water well In crystalline rocks.

These situations illustrate the inadequacy of resistivity logging to 

supply complete information, even qualitative information, regarding 

the hydrology of a well. Thus, before the interpretation of resistivity data is attempted, all available evidence from other sources, including other types of well logs, should be studied.

SPONTANEOUS-POTENTIAL LOGGING

The spontaneous-potential curve is of great importance to the petroleum engineer, and it is natural that it should have been adopted in 

hydrology, especially because spontaneous potentials are related to 

the movement and chemical quality of the formation water. This 

method probably exceeds all others, however, in the number and gravity of the errors that have characterized its application to ground 

water.

INSTRUMENTATION

The spontaneous-potential logging device is certainly the simplest 

logging device in use. It consists only of a recording galvanometer
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-27

connected between a ground terminal at the surface and a moving 

electrode on an insulated conductor in the borehole. The galvanometer measures the potential difference between the earth at the surface 

and the point in the mud- or water-filled borehole occupied by the 

moving electrode, and it records this potential difference as a function 

of depth. The result is a log in which the deflections indicate potential differences between points along the axis of the well.

HISTORY

The spontaneous-potential log came into common use shortly after 

1927, when potential differences in the borehole between points opposite sandstone beds and points opposite adjacent shales were recognized. Deflections on the spontaneous-potential log thus were associated with sandstone-shale contracts, and an excellent method of 

lithologic correlation was obtained. A further use for the spontaneous-potential log became evident when a theoretical analysis was made 

relating the magnitude and direction of the spontaneous-potential 

deflection to the difference in sodium chloride concentration between 

the fluids of the bore and the formation. This theoretical analysis 

led to the relation given by Wyllie (1949)

A/S7>=-70.51og10 (10)

in which ASP is the spontaneous-potential deflection, aw is the mean 

ionic activity, or effective concentration, of sodium chloride in the 

formation water, and asn is the mean ionic activity of sodium chloride 

in the borehole fluid.

By use of this equation, aw can be calculated from the measured 

spontaneous-potential deflection from shale base and the known activity of the drilling mud, if the temperature also is known. The 

sodium chloride concentration of the formation water then can be 

obtained from graphs of activity versus concentration. Equation 10 

has become popular with hydrologists and has been used to determine 

the concentration of formation waters in both mud-filled and waterfilled boreholes. The question of the applicability of the equation 

to ground- water problems is, therefore, of considerable importance; 

it can be analyzed by a review of spontaneous-potential theory and 

by a consideration of some of the assumptions implicit in the derivation of equation 10.

ANALYSIS OF QUANTITATIVE INTERPRETATION

If two solutions having different concentrations of the same monovalent salt are brought into contact, ions will be diffused toward the
D-28 GENERAL GROUND-WATER TECHNIQUES

solution of lower activity. It is assumed that the fluids are static 

and that ions move only as a result of diffusion. Each ion carries 

a charge, either positive or negative, which is equal in magnitude to 

the charge of an electron. If equal numbers of positive and negative 

ions diffuse across a given boundary in a unit time, there will be no 

net transport of charge across the boundary. In general, however, 

the positive and negative ions will not diffuse at equal rates, and there 

will be a net flow of charge across the boundary. The tendency of 

the anions and cations to diffuse at different rates thus establishes 

a potential, or electromotive force, in a direction that depends upon 

the sign of the excess ionic charge crossing the boundary.

The difference in the rates of diffusion arises from a difference in 

the mobilities of the two ionic species and tends, in the absence of a 

complete circuit, to produce a separation of positive and negative 

charge. The resultant electrostatic forces eventually oppose any further net movement of charge and, thus, eliminate any current. If, 

however, a circuit is completed between the high- and low-activity 

solutions through a conducting path external to the liquid junction, 

a current will be established, because the excess charge diffusing into 

the low-activity region will be balanced by an inflow of opposite charge 

through the external branch of the circuit.

The components of a liquid junction need not be pure solutions of 

the same monovalent salt, as in the example discussed above. More 

generally, the potential represents the net effect of the diffusion of 

several ionic species, each in the direction of decrease in its own 

activity.

In a liquid junction between two pure solutions of sodium chloride, 

the number of chloride ions diffusing across an area in a unit time 

exceeds the number of sodium ions approximately in the ratio of six to 

four, owing to the greater mobility of the chloride ion. Thus, the 

net transfer of charge in the direction of the low-activity solution is 

negative, which corresponds to a current and emf (electromotive 

force) directed toward the high activity solution.

The transport number of an ion in a liquid-junction problem is 

defined as the ratio of the quantity of charge carried by this type of 

ion across a given plane in a unit time to the total charge moved across 

the plane in both directions in a unit time. The transport number 

of an ion depends upon the concentration, mobility, and valence of 

that ion, and the concentrations, mobilities, and valences of all other 

ions present. The sum of the transport numbers of all the ions in any 

diffusion problem is unity. In a liquid-junction involving several 

ionic species, the transport number of any given species is extremely 

difficult to determine and must, in general, be treated as an unknown
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-29

function. This makes a mathematical analysis of such a liquid junction difficult, if not impossible.

The determination of transport numbers in liquid junction between 

two pure sodium chloride solutions, however, is straightforward. Each 

solution contains the same number of cations as anions, and each ion 

carries a single positive or negative charge. Neglecting transport by 

the solvent, all charge that is not carried by the anion must be carried 

by the cation. The transport numbers, thus, become functions only of 

the mobilities of the two species. The transport number of the chloride ion is approximately 0.6, and that of the sodium ion is 0.4. Although these transport numbers vary slightly with the total sodium 

chloride concentrations, this variation can be neglected without introducing serious errors, as far as electrical well logging is concerned.

THE GENERAL, LIQUID-JUNCTION EQUATION

The general equation derived by Glasstone (1951) for a liquidjunction potential between two solutions is

p'T'___ 1 f*II

F i Zijj

in which Zn is the valence, ti the transport number, and at the activity 

of the ith ionic species; R is the universal gas constant, T is the absolute temperature, and F is the Faraday. Each term in the summation 

represents the contribution made to the net emf by the diffusion of a 

single ionic species, and the summation is taken over all the species 

in the problem. Thus, if only a single species of ion were diffused, 

the equation would simplify to

'//

(12)

where Z^ £15 and a^. now refer to the species of ion present.

The integration in equation 12 and each integration in equation 11 

are carried out over the range of activity of a particular ionic species. 

The limits / and // refer to the log of the activity of the species at the 

two endpoints of the problem, between which the measurement of emf 

is made. An infinitesimal difference in the activity of a particular 

ionic species produces a difference of potential according to the relation

ac.=-f^\ /JfT\ 1

( \ tid In «!

Integration sums these changes over the entire range present to obtain 

the total emf that is due to diffusion of the species 1.
D-30 GENERAL GROUND-WATER TECHNIQUES

The sign of the emf of equation 12, or of the individual terms in the 

summation of equation 11, is controlled by the sign of the valence, in 

accordance with the principle that positive and negative ions diffusing 

in the same direction produce emf 's of opposite sign. The direction 

of diffusion of each species also controls the sign ; this is expressed in 

the equations by the relative magnitudes of the limits / and //.

The denominator, FZ^ on the right side of the equations is the charge 

carried by 1 mole of the diffusing species ; the potential change is a 

measure of the energy expended per unit charge in the diffusion 

process.

EQUATION FOB DIRECT JUNCTION BETWEEN TWO SODIUM CHLORIDE

SOLUTIONS

The integrals in equation 11 usually are difficult to evaluate, as the 

transport numbers of the various species are usually unknown functions. Equation 11 assumes a greatly simplified form, however, when 

applied to a liquid junction between two pure sodium chloride solutions. The summation includes only two ions, and because the transport numbers are effectively constant, they may be taken outside the 

integrals, giving

n 06

= FLTT, <"B <*"+(±I

or

RT TO 4 C E= FLTTJ,

[~

L

=~- 0.4 In

Na-/

Each of the individual activities of the sodium and chloride ions, 

<zNa and flci, may be replaced by the mean ionic activity of the sodium 

chloride, am. After making these substitutions and carrying out the 

integrations, equation 13 simplifies to

=-r (-0.2) log ^=+11.5 log %=& (14) 

r dm -i a>m-i

at 25 °C, when E is expressed in millivolts and common logarithms are 

used in place of the natural logarithms.

JUNCTION OF SODIUM CHLORIDE SOLUTIONS THROUGH AN 

ION-SELECTIVE MEMBRANE

If the two sodium chloride solutions, rather than being brought into 

direct contact, are brought into contact through a porous membrane 

through which only positive ions can pass, the situation is considerably 

altered. The anions are prevented from crossing the membrane, and, 

in the absence of an external circuit branch between the two solutions, 

electrostatic attraction will prevent any sustained transfer of charge
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-31

through the membrane by the diffusion of cations. Just as in a direct 

liquid junction, however, a flow of charge will begin as soon as a complete circuit is available that is, as soon as some means is available 

to balance the excess positive charge appearing on one side of the 

membrane and the excess negative charge remaining on the other. 

The flow of charge through the membrane will consist entirely of the 

movement of positive ions and can be expected to have a different value 

than that of a flow maintained by a difference in the normal rates of 

diffusion of the positive and negative ions. The sodium ion may be 

assigned a transport number of 1, and the chloride ion a transport 

number of 0, in accordance with the definition of transport number. 

The potential, or emf , maintained in the separation of the two solutions by the membrane then can be calculated by applying equation 11 ; 

that is,

7?T

RTT 1 C" 1 Cn ~\ = Y I q-^ I (l)cnnaNa+ I (0)dlnaCi\

Again using mean ionic activity in place of aNa, equation 15 may be 

written as

= 

j

j=r In F

which becomes

at 25°C, using common logs and the units employed in equation 14. 

Thus the emf is several times larger than that of a direct liquid junction and is oppositely directed.

HOLE OF SHALE AS AN ION-SELECTIVE MEMBRANE

Many investigations have been made into the role of clay and shale 

in controlling the spontaneous-potential log. Various physical and 

mathematical models have been used to describe the processes by which 

clay minerals control the diffusion of ions. The reader is referred 

to the work of McCardell, Winsauer, and Williams (1953), Wyllie 

(1955), and DeWitte (1955) for detailed analyses of the interaction 

of ions with clay particles. The overall effect of shale is to block
D-32 GENERAL GROUND-WATER TECHNIQUES

the diffusion of negative ions in the manner of an ion-selective membrane. The action of the shale as an ion-selective membrane follows 

from the same basic clay properties that cause the low resistivity of 

shale.

If two sodium chloride solutions are brought into contact through a 

segment of shale, transfer of negative ions through the shale will not 

be possible, and a potential measurement between the solutions will 

show the result predicted by equation 16. This holds true even if the 

shale is saturated with a solution of different activity from either of 

the two solutions that it separates. The net potential between the 

end solutions is the algebraic sum of the two potentials (each of which 

follows the form of equation 16) between the solution within the shale 

and each end solution. Thus, if the activity of the cation in the solution within the shale is a Na-s, the potential between the end solutions 

would be

= 

"3- lm ^Na-// | / RT\ j =- In - H w } In

* %Ta-S \ $ /

R T

, QNa-77 

"'*

am-JI

The concentration of the solution within the shale does not affect 

the potential between the solutions separated by the shale; in calculating the spontaneous-potential, the shale may be treated simply as 

an ion-selective membrane.

LIQUID-JUNCTION POTENTIALS IN AN OIL WELL

In the drilling of an oil well, liquid- junction potentials arise from 

chemical differences between borehole and formation fluids. Figure 

9 illustrates the electrochemical reactions at the contact of a bed of 

sand and beds of shale in the borehole. Both the borehole fluid and 

the formation water in the sand bed are assumed to be pure sodium 

chloride solutions of different activities. A direct liquid junction 

will exist at the borehole wall opposite the sand bed. The formation 

water generally will have the higher activity, and the net charge 

moving into the borehole will be negative, owing to the fact that 

the chloride ion is more mobile than the sodium ion.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-33

Spontaneous 

potential log

Shale

Shale

FIGUHE 9. Spontaneous-potential current and electromotive-force pattern at a sand-shale

contact.

The borehole and formation fluids also are in contact across a segment of shale that is, along the path A-B of figure 9. Cations are 

free to move from the high-activity formation water to the low-activity 

borehole fluid along this path, but anions are not; the result is a 

potential of the type described by equation 16.

The electrochemical phenomena in the vicinity of the sand-shale 

contact may be summarized as follows:

(1) An emf directed into the borehole occurs along the path A-B; 

this emf is independent of the activity of the solution within the shale 

and is described by the equation:

where 

and

aw=activity of the formation water 

activity of the borehole fluid. (17)
D-34 GENERAL GROUND-WATER TECHNIQUES

(2) An emf directed away from the borehole occurs opposite the 

sand at G. This emf is described by the equation :

#=11.5 log 2*- (18)

(3) A complete circuit is established: the path A-B forms the external conducting branch for the liquid junction at 0 '; the sandstone 

and borehole form the external conducting branch for the "membrane" emf between A and B.

(4) As a complete circuit is present, a movement of charge occurs. 

Positive ions diffuse into the borehole through the shale, and both 

positive and negative ions diffuse into the bore through the sand, with 

the negative ions here diffusing at a higher rate. The resultant separation of charge sets up a field that causes positive ions to move 

through the borehole from B to O and negative ions to move from C 

to Z?. Thus, the diffusion of ions into the borehole produces a current, 

or circulation of positive charge, in the direction of the arrows in 

figure 9.

(5) This circulation of charge occurs at both contacts of the sandstone bed and is such that the movement of positive charge in the 

borehole is from shale to sand, when the water in the sand is the highactivity solution.

Equations 17 and 18 are derived from electrochemical principles, 

and the signs in these equations, therefore, follow electrochemical 

conventions. The opposite signs of emf indicate that one is directed 

from the high-activity to the low-activity solution, and the other is 

directed from the low-activity to the high-activity solution. In order 

to deal with a circuit such as that formed by the spontaneous potential 

current loop in figure 9, however, a new sign convention must be chosen 

in which emf is taken as positive or negative, according to its direction 

around the current loop. Each emf is in the same direction in the 

spontaneous-potential current loop ; they are, therefore, both given the 

same sign, taken as negative, in the logging equations. Where the 

borehole fluid is higher in activity than the formation fluid, the direction of each emf will be reversed, as will the direction of the spontaneous-potential current.

RELATION OF THE SPONTANEOUS-POTENTIAL MEASUREMENT TO 

THE THEORETICAL ELECTROMOTIVE FORCE

The three-dimensional circuit at the sandstone-shale contact in figure 

9 may be analyzed using the loop rule of Kirchoff, which states that 

the algebraic sum of the emf's around a circuit loop is equal to the
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-35

algebraic sum of the IR drops around the loop. In the circuit of 

figure 9, the algebraic sum of the emf ' s is

#=-59 log -^-11.5 log -2s 70.5 log

Q>BH

Assuming that the relations

& = k

Pu,

and

PBH

holds true, in which pw and PBH are the resistivities of the two fluids 

and k is a constant, the sum of the emf 's may be expressed as

#=-70.5 log

Pio

The circuit loop may be divided into three sections, considered as 

resistances in series. The total logging current remains constant 

through each segment, and the voltage drop across any segment is 

given by the product of this current and the total resistance of that 

segment. Denoting the effective resistance of the sand to the spontaneous-potential current as TJsg, that of the shale as RSa, and that of 

the borehole as Ran, Kirchoff's law may be written for the problem as

E= -70.5 log =I8PRss+ISPRSIt+ISPRBH (19)

Pm

Geometrically, the spontaneous-potential current could assume 

many patterns of flow through the formations and borehole. The 

current always will distribute itself, however, in the pattern for which 

the total resistance of the circuit is a minimum. If the true formation resistivities are not high relative to the resistivity of the borehole 

fluid, the resistance of the borehole, RBH^ will constitute the major 

part of the total resistance in this current pattern. This follows 

from the fact that the current is free to spread over a considerable 

area within the formations, whereas it is constrained to a small area 

as it passes through the borehole. The indefinite geometry involved 

makes calculation of the relative values of Rn^ -#ss, and Ran extremely difficult.

Equation 10 is based upon the assumption that the term RBn constitutes the major part of the spontaneous-potential circuit resistance, 

so that the terms IspRsH and IspRss can be dropped from equation 19.
D-36 GENERAL GROUND-WATER TECHNIQUES

The spontaneous-potential device actually measures the potential difference between points along the well axis. According to Ohm's law, 

the potential difference between two points is equal to the IB drop 

between the points. Thus, the spontaneous-potential deflection actually measures the quantity ISP^BH of equation 19. Equation 10 is 

obtained from equation 19 by neglecting the terms IspRss, and lapRsH, 

and substituting A/S73 for ISP^BHOBJECTIONS TO QUANTITATIVE INTERPRETATION FOR WATER

WELLS

The theoretical analysis by which equation 10 is established as the 

basis of quantitative spontaneous-potential interpretation involves 

several assumptions, which are summarized and discussed briefly here.

It was assumed, in the first place, that both the formation water and 

the borehole fluid were pure sodium chloride solutions. Formation 

waters penetrated by oil wells frequently contain sodium chloride in 

far greater concentration than any other salt. This is not generally 

true, however, in water wells. The concentrations of all ions are usually low, both in the formation and in the borehole, and sodium 

chloride is seldom in strong predominance. Frequently such ions as 

calcium, potassium, sulf ate, or carbonate are of equal or greater concentration. Further, the ionic contents of the formation water and 

the borehole fluid sometimes differ in a complex manner, so that certain ions predominate in the borehole and others predominate in the 

formation. Obviously the application of equation 10 to such situations will lead to erroneous results. The appropriate relation is 

equation 11, but the number of unknown functions and variables makes 

quantitative analysis by this equation impossible.

Another assumption in the analysis is that the shale behaves as an 

ideal ion-selective membrane and that the sand has no ion-sieving 

properties whatsoever. This assumption is apparently acceptable if 

the shale is free of sand and the sand is free of clay minerals. Otherwise, the result will be an emf different from that predicted by equation 19.

The effects of ions other than sodium and chloride, as well as the 

effects of nonideality of the sand or shale, have received considerable 

attention in the literature of the oil industry. Such corrections as 

have been devised for these effects, however, generally require a degree 

of laboratory control that is not available to the hyolrologist.

Finally, it was assumed that the resistance of the borehole (Rao} in 

the spontaneous-potential circuit was much greater than the combined 

effective resistance of sandstone and shale (Bsa+Rao}' This assumption is generally valid if the true formation resistivities are not
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-37

high relative to the resistivity of the borehole fluid. In the oil industry, where the sandstones are saturated with a low-resistivity brine, 

this condition is usually met ; in hydrologic work, the true resistivity of 

the sand (pt) is normally many times that of the borehole fluid, and 

the assumption that

is, therefore, open to considerable doubt, in spite of the restricted area 

of the borehole.

Thus, there are several points upon which the conditions in a typical 

water well can be expected to deviate from the conditions assumed in 

the derivation of equation 10, and the hydrologist will not generally 

have any means of controlling or correcting for these deviations. 

Equation 10, therefore, generally cannot be expected to give valid 

results. Its use in a hydrologic investigation is certain to produce a 

great deal of erroneous data, regardless of whether the wells involved 

contain drilling mud or water as their borehole fluid.

INTERAQUIFER FLOW

The invasion of one aquifer by water from another may establish 

a difference between borehole fluid and formation fluid, resulting in 

a spontaneous-potential reading. This invasion also presumably will 

establish some sort of radial concentration distribution in the thieving 

aquifer, which, in turn, will have an effect upon the spontaneouspotential deflection opposite that aquifer. This effect would be difficult to evaluate even if the form of the concentration function were 

known, but because the form of this function is generally not known, 

the effect becomes virtually impossible to evaluate. If the concentration remains nearly that of the invading water for a considerable 

radius into the thieving aquifer, the effect may simply be to remove 

the diffusion process from the vicinity of the borehole, thus eliminating any spontaneous-potential current in the borehole. The possibility of this sort of interaquifer flow further complicates the question 

of quantitative spontaneous-potential interpretation in ground-water 

studies. On the other hand, the spontaneous-potential deflections can 

serve as a preliminary indication of the existence of internal circulation. This applies not only to the electrochemical potentials described 

above, but also to the streaming potentials that may accompany the 

internal flow, and which are discussed more fully in the following 

section. Whenever a large spontaneous potential is recorded in a 

water-filled borehole, therefore, it is advisable to log the well by flowmeter or to employ some flow-tracing technique.
D-38 GENERAL GROUND-WATER TECHNIQUES 

STREAMING POTENTIALS

Small potentials, generally termed streaming potentials, are set up 

when an electrolyte flows through a porous solid. Such potentials 

have received some attention in the oil industry, on the theory that 

they may result from the invasion of a formation by drilling mud 

and may, thus, contribute to the spontaneous-potential reading. It 

is possible that they occur in some water wells.

On the basis of theory, streaming potentials should be proportional 

to the pressure differential causing the flow and inversely proportional to the conductivity and viscosity of the electrolyte. Kozary 

(1948) indicates, however, that streaming potentials in wells cannot 

be predicted by equations derived from theory. The common practice in oil reservoir work is to assume that streaming potentials are 

negligible in comparison to the electrochemical potential. This assumption appears to be acceptable in view of the agreement between 

the observed spontaneous potential and the calculated electrochemical 

potential in oil wells for wliich an independent method of determining 

aw is available.

A comparison of streaming potential between oil wells and water 

wells is difficult to make. If, in a water well, the borehole fluid is 

water and the flow is actually an interaquifer circulation, the pressure 

differentials will generally be smaller than in a deep oil well. However, the conductivity and viscosity of the water will usually also be 

smaller than those of drilling mud, and the net effect on the streaming 

potential will be difficult to predict, even on a theoretical basis. If 

the borehole fluid is drilling mud, the pressure differentials should 

generally be smaller than in deep oil wells, and this should tend theoretically to make the streaming potentials smaller. Whether the borehole contains water or mud, however, the electrochemical potentials 

in most water wells are smaller than those in oil wells. This tends 

to make the streaming potential relatively more significant, and further contributes to the uncertainty of quantitative spontaneous-potential interpretation.

ZONES CONTAINING HIGHLY MINERALIZED WATER

The qualitative recognition of zones containing highly mineralized 

water is an important aspect of interpretation of spontaneous potential. The spontaneous-potential device is particularly valuable in this 

respect in mud-filled boreholes. In water-filled boreholes, recognition of the highly mineralized zones is possible as long as the borehole 

contains water that is chemically different from that in the zone in 

question.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-39 

AETIFICIALLY INDUCED SPONTANEOUS-POTENTIAL DEFLECTIONS

A flat and featureless spontaneous-potential log generally indicates 

that the ion content between the water of the several formations 

penetrated by the borehole and the borehole fluid opposite the formations is only slightly different. In these circumstances, a spontaneouspotential log suitable for lithologic interpretation can be obtained by 

increasing the salinity of borehole fluid. The borehole fluid, thus, 

becomes a solution of higher activity than the formation waters, and 

positive spontaneous-potential deflections should result opposite each 

sandstone. The potentials observed will be due largely to the diffusion 

of sodium chloride and should obey equation 19. The term Run, however, will be decreased, because the resistivity of the borehole fluid is 

lowered by the addition of the sodium chloride. Therefore, the assumption that Ras and Ran are negligible, compared to RSH becomes 

less tenable than ever, and the use of equation 10 is still unreliable.

ABNOEMAL SPONTANEOUS-POTENTIAL DEFLECTIONS

Occasionally, the spontaneous-potential log may exhibit characteristics which do not lend themselves to any explanation in terms of 

liquid junction or streaming potentials. A spontaneous-potential deflection always measures an IR drop in the borehole indicating that 

ions are moving through the borehole in such a way as to cause a net 

transfer of positive charge in the direction of more negative potential. 

No set rules of interpretation for abnormal spontaneous-potential data 

can be based upon this fact; however, it may sometimes be possible to 

assign some reason for the ionic movements indicated by an abnormal 

spontaneous-potential log, and, thus to increase understanding of the 

hydrology or geology of the well. In any interpretation of this sort, 

full advantage should be taken of evidence from other logs and other 

sources of information concerning the well.

Large electrical installations in the immediate vicinity of a well may 

often cause a spurious response on the spontaneous-potential log.

SUMMARY OF SPONTANEOUS-POTENTIAL LOGGING

The spontaneous-potential log is a valuable qualitative method in 

ground-water studies. It has great value as a means of lithologic correlation, and can sometimes aid in the identification of internal flow, 

or in the location of zones of highly mineralized water. The assumptions involved in quantitative interpretation of spontaneous potential, 

however, are seldom satisfied in ground-water work. The use of the 

method as a quantitative tool is, therefore, likely to produce erroneous 

results.
D-40 GENERAL GROUND-WATER TECHNIQUES 

FLUID-CONDUCTIVITY LOGGING

The fluid-conductivity log is generally of somewhat greater importance to the hydrologist than it is to the petroleum engineer. Its role in 

the oil industry has been chiefly to serve as a check on the drilling mud, 

where the mud conductivity is required in the quantitative interpretation of other logs. In hydrology, on the other hand, the fluidconductivity log of a water-filled borehole often can give a general 

indication of water quality and can sometimes provide information on 

the hydraulics of a well.

Some instruments presently available record the conductivity of the 

borehole fluid, and other record its resistivity. The discussion presented here will be worded in terms of fluid conductivity.

FACTORS CONTROLLING CONDUCTIVITY

The conductivity of the water in the well at a given depth depends 

upon the concentrations, mobilities, and valences of the ions in the 

water at that depth. It is, therefore, controlled partly by the processes of ionic diffusion and dispersion and ion transport by moving 

fluids. These processes are frequently at work both within the well 

bore and in the formations surrounding the hole. They will generally 

proceed at different rates and in different manners in these two regions. The ionic content at a given point in the water-filled borehole, 

under equilibrium conditions, represents a balance of the various 

processes in effect at that point.

INTERPRETATION OF FLUID-CONDUCTIVITY LOGGING IN A 

SINGLE-AQUIFER WELL

With reference to fluid-conductivity logging, water wells can be 

divided into two groups those that penetrate, wholly or partly, a single 

aquifer, and those that penetrate several aquifers separated by reasonably effective aquicludes. In a well penetrating a single aquifer, the 

conductivity of the water in the borehole generally will be the same as 

that of the water in the aquifer, assuming that this conductivity is uniform throughout the aquifer. If ionic content and, therefore, conductivity differ at various depths in the aquifer, the effect will be shown 

on the conductivity log. However, this variation on the log may have 

a different form from that in the formation, because vertical ionic 

diffusion may be proceeding at a different rate in the borehole than in 

the aquifer.

The interpretation of fluid-conductivity data for wells penetrating 

a single aquifer is controlled by the following principles: If the log 

shows no gradient, the conductivity of the water in the aquifer is
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-41

probably the same from top to bottom and is equal to the conductivity 

shown on the log; if the log displays a gradient, the conductivity of 

the water in the aquifier differs from top to bottom, although perhaps 

not in exactly the same way as does the water in the borehole. Nevertheless, the conductivity range observed in the borehole usually gives 

an approximate idea of the range in the aquifer.

Conductivity, in itself, is of secondary interest to the hydrologist; in 

a single-aquifier well it is valuable principally because it provides 

some idea of the chemical quality of the water. There is no general 

theoretical method by which the types and concentrations of ions in a 

solution can be determined from conductivity data alone. Nevertheless, experience in a particular area or with a particular acquifier 

will often enable the log interpreter to estimate water quality from 

the conductivity log, and to decide whether a laboratory analysis is 

necessary.

INTEBPBETATION OP FLUID-CONDUCTIVITY LOGGING IN A 

MULTIAQUIFEE WELL

The fluid-conductivity log in a multiaquifer well is controlled 

largely by ionic transport by moving fluid. The interstitial waters 

of the various aquifers usually differ in conductivity, and the aquifers 

usually have different hydrostatic heads, so that internal flow prevails in the well. Some of the characteristics of internal flow have 

been discussed in previous sections; in this section, the effects of internal flow on the fluid-conductivity log are considered.

Figure 10 shows a three-aquifier well in which the lower and middle 

aquifiers are yielding while the upper aquifier is thieving. The fluidconductivity log of the well is also shown. The conductivity of the 

water in the lower aquifer will be denoted CL, that of the water in the 

middle aquifer CM, and that of the water native to the uppermost 

aquifer GU. It will be assumed that CL>CM>CU> It also will be 

assumed that the velocity within the well bore, at all points between 

the bottom of the lower aquifer and the top of the upper aquifer, is 

great enough so that the effect of ionic diffusion is negligible by 

comparison.

The interval between the bottom of the lower aquifer and the bottom 

of the middle aquifer is occupied by the water of the lower-most 

aquifer, which has a constant conductivity, CL. In the interval opposite the middle aquifer, the conductivity changes gradually from 

GL to a value between CL and CM as the flow in the bore is gradually 

increased by the discharge from the middle aquifer. The final conductivity of the mixture depends to a certain extent upon the relative 

proportions of the discharge from each aquifer. It is difficult to de-
D-42 GENERAL GROUND-WATER TECHNIQUES

Conductivity

Possible zone of 

radial mixing

FIGURE 10. Fluid-conductivity log in a multiaquifler well in which ionic diffusion is

negligible.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-43

termine the exact nature of this dependence, however, because the 

effects of interionic forces may be different in the mixture than in 

either component solution. In any event, a conductivity gradient will 

exist opposite the middle aquifer. If mixing occurs instantaneously 

as the water of this aquifer enters the borehole (so that conductivity is 

nearly constant radially across the well at any given depth), the conductivity log will show a constant reading in the interval between the 

middle and uppermost aquifers.

If mixing is not instantaneous, a zone of mixing will extend above 

the upper contact of the middle aquifer and will be characterized by 

variation in ionic content both radially, across the borehole, and vertically. The process of radial diffusion within the well bore will 

cause conductivity along the well axis to vary with depth within this 

zone of mixing. The situation will be further complicated if velocity 

as well as ionic content varies radially across the borehole. It is practically useless to attempt to analyze the net effect of these processes 

upon the fluid-conductivity log because the logging instrument does 

not normally measure the conductivity along the well axis. Most 

instruments are designed to measure an average conductivity involving as much of the hole cross section as possible; it is usually impossible, moreover, to know whether the instrument is centered or hanging against the wall at a given depth. About all that can be said 

is that if mixing is not instantaneous opposite the middle aquifer, 

some form of conductivity gradient or perhaps some slightly erratic 

conductivity variation may be observed on the log for a short distance 

above the aquifer.

A constant conductivity should be observed on the log once the zone 

of mixing has been passed. This conductivity will prevail at least 

to the top of the uppermost aquifer, and it probably will hold in the 

zone above this level, because diffusion from the stagnant water of 

this zone would tend to remove any chemical differences.

It is the authors' belief, as outlined in the discussion of resistivity 

logging, that the decreasing radial-flow velocity within the thieving 

formation causes ion transport by moving fluid to decline in importance relative to ionic diffusion. The balance of these two processes 

tinder equilibrium conditions should, therefore, create a radial concentration distribution within the thieving aquifer, by which conductivity ranges from that of the mixture in the well bore to that of 

the water native to the upper aquifer. The important consideration 

in fluid-conductivity interpretation is that within the well bore opposite the thieving zone velocity is high, diffusion is negligible, and the 

concentration is that of the mixture from the lower aquifers.
D-44 GENERAL GROUND-WATER TECHNIQUES

The reader may verify, by an analysis similar to that given for the 

situation assumed above, that the conductivity log would have a similar form if the flow were downward that is, if the lowermost aquifer 

were the thieving zone. The only difference in form that might occur 

would be that the mixing zone, if present at all, would extend downward from the lower contact of the middle aquifer.

The difficulties of stating a definite set of interpretive principles 

under these conditions are obvious. The interpreter can be relatively 

certain that there is measurable internal flow because there are no 

concentration gradients except in the vicinity of one of the aquifers. 

This, however, is about as far as reliable interpretation can go, on 

the basis of the conventional conductivity log alone.

Information on the direction and the magnitude of the internal 

flow can be obtained by releasing a small amount of brine in the well 

and tracing its movements with the conductivity device. The brine 

may be released at any desired depth by breaking a suspended container or by siphoning through a hose from a container at the surface. 

Velocity measurements can be made by timing the traverse of the 

brine between two points in the well. If flowmeter equipment is available, such tracing experiments are unnecessary.

When the direction of the internal flow is established, the conductivity log may be evaluated properly. In the example given in this section, once the flow direction is known, the conductivity in the region 

between the lower and middle aquifers is established as that of the 

water native to the lower aquifer. A rough idea of the quality of this 

water is, thus, obtained. It is established also that the water of the 

middle aquifer is less conductive and, therefore, probably of better 

quality than that of the lowermost aquifer. If the discharge of each 

aquifer to the well has been measured, a better idea of the order of 

magnitude of On is possible, because the conductivity of the mixture is 

governed by the proportions as well as the conductivities of the component solutions. Here again, however, no calculation is proposed, 

because the effects of interionic forces in the mixture may be different 

than that in either component.

Finally, the flow-tracing data established that the conductivity log 

gives no information about the water native to the uppermost aquifer. 

The only way in which information on this water can be obtained is by 

logging during pumping and only after pumping has been in progress 

long enough to produce a drawdown sufficient to cause the thieving 

zone to yield water. Even here, the only information provided is that 

the water of this aquifer is less conductive and, therefore, probably 

fresher than the mixture from the lower two aquifers. Effects of this 

sort are of interest in many problems not involving well logging; for
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-45

example, the quality of the water discharge by a well often changes 

during the course of pumping. This may be caused by the reversal of 

a thieving process, as outlined here.

Given a set of circumstances, a fluid-conductivity log is easy to interpret ; it is difficult, however, to phrase a set of interpretive principles 

general enough to cover all of the possible situations in a problem involving internal flow. However, if the log shows extensive intervals 

of constant conductivity and conductivity gradients only in the vicinity of certain aquifers, measurable internal flow usually is indicated, 

and brine-tracing or flowmetering experiments should be run to establish the direction and magnitude of the flow. The conductivity log 

then can be analyzed in the light of this new information in the manner 

indicated in the example.

GAMMA-RAY LOGGING

Interpretive procedures for utilizing gamma-ray logs have, for the 

most part, been restricted to qualitative identification of lithology and 

formational contacts. In this capacity the gamma-ray log is a valuable supplemental tool to resistivity methods, as it is normally unaffected by adverse borehole conditions such as those caused by oil-base 

or highly mineralized drilling fluids. It should be noted, however, that 

drilling fluids containing radioactive minerals can have a serious effect 

on the gamma-ray log.

Various attempts have taen made to develop more quantitative techniques for using gamma-ray log information. Many of these have been 

attempts to relate the gamma intensity of a particular formation to its 

clay content or sand-shale ratio.

GENERAL DISCUSSION OF RADIATION AND GAMMA-RAY-LOGGING

INSTRUMENTATION

Gamma radiation originates in the spontaneous disintegration of 

atomic nuclei of various radioactive elements. Other forms of radiation, alpha and beta rays and neutron emission, are of no direct interest in gamma logging, as their effects are not detected by gammasensitive instruments.

Eadiation intensity at any particular point in a well depends on 

several factors, the most obvious of which is the concentration and 

activity of radioactive elements disseminated in the rocks around the 

borehole. Of the many radioactive isotopes in nature, only a few 

are concentrated to the extent that their radiation may be measured 

by ordinary means. Gamma radiation from uranium, thorium, and 

their daughter products, and an isotope of potassium (atomic weight 

40) constitutes virtually all the radiation usually measured in the
D-46 GENERAL GROUND-WATER TECHNIQUES

borehole, although some other elements have radioactive isotopes that 

occur naturally. The relative abundance of the radioactive isotopes 

of the three above-named elements in sedimentary rocks is small; 

for example, the abundance of K40 in potassium is 0.011 percent, and 

only 10 percent of the disintegrating atoms of this isotope emit gamma 

radiation (Faul, 1954). The radiation from uranium and thorium 

also originates largely from particular isotopes, but in this discussion 

the element will be referred to rather than the specific radioactive 

isotope.

The radioisotopes of uranium, thorium, and potassium are not uniformly radioactive, as they decay at different rates. The rate at 

which these isotopes decay, or the number of atomic disintegrations 

per second, is defined as the activity of the isotope. The standard 

unit of activity is the curie, which is equal to 3.7 XlO10 radioactive 

disintegrations per second. The amount of Ea226 necessary to have 

an activity of 1 curie is 1 gram, but the less active isotope U238 requires 

a mass of 3 million grams to have an equal activity (Faul, 1954). 

The activities of uranium, thorium, and potassium in sediments are 

small and, therefore, difficult to compute, although their relative concentrations have been obtained using gamma-ray spectroscopy (Brannon and Osaba, 1955).

Apparatus used in gamma-ray logging measures the borehole radiation intensity in terms of dosage, or the number of rays incident 

on the detecting device per unit time. The unit of radiation flux is 

roentgens per hour, but in gamma-ray logging it is more convenient 

to use either microroentgens or milliroentgens per hour. The National Bureau of Standards reference for radiation flux is a point 

source of 50 microcuries of radium which, at a distance of 108 inches, 

will have a flux of 5 microroentgens above the background.

The gamma-ray flux is principally a function of the concentration 

and activity of each of the individual radioisotopes disseminated in 

the rock around the borehole, but it is also a function of the density of 

the rocks in which it originates. As the density of a rock increases, 

fewer gamma rays will be able to penetrate to the open borehole, and 

the flux will be decreased. Where borehole diameter is constant, all 

radiation measured by the probe probably originates within a radial 

distance of about 1 foot of the well, depending on the density of the 

rock and the energy of the gamma rays.

At the time this report was written the most efficient device used to 

detect gamma radiation was the scintillometer. This instrument 

usually consists of a thallium-activated sodium iodide crystal that 

emits a small flash of light when it absorbs a gamma ray. An electronic photomultiplier tube optically coupled to the crystal converts
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-47

the light energy to an electrical pulse, which then is amplified by appropriate circuits. As the scintillometer is lowered down a borehole, 

the amplified pulses may be recorded on a continuous graph plotted 

against depth. In use, however, it is seldom practical to record the 

individual pulses resulting from gamma rays striking the photo 

crystal, because where small time intervals and low concentrations are 

concerned, the number of pulses from the scintillometer may vary 

widely over short periods. To overcome such statistical fluctuations, 

an integrating circuit, which averages the radiation pulses over a 

known time interval, is usually placed ahead of the recorder. The 

resultant signal is a measure of radiation flux. An adequate summary of radiation theory and instrumentation is presented by Jones 

and Skibitzke (1956).

SOURCES OF RADIATION IN COMMON SEDIMENTS

Gamma-ray logging is based on the observation that changes in 

radiation are commonly associated with changes in lithology. From 

the preceding discussion, it is apparent that only a minute fraction of 

a rock unit contributes to its radiation. In light of this fact, it is 

invalid to assign a radiation value to any particular lithology or to 

assume that the radiation from that lithology will be constant over a 

wide areal extent, as minute compositional changes can produce large 

changes in radiation.

In the "normal" or usual sedimentary series, shale is indicated on 

the gamma log by the highest radiation and dirty sand, sandstone, 

limestone, and evaporite rocks following in order of decreasing radiation. The change in radiation between shale and sand is usually large 

and unmistakable, but between sand, limestone, and evaporite rocks 

the change commonly is small, and it is difficult to differentiate these 

sediments on the basis of the gamma-ray log alone.

Before any meaningful discussion can be made of gamma-ray log 

interpretation, it is necessary to determine the source of radiation from 

the various rock types and to establish relationships between their 

radiation intensity and other rock parameters. The following section 

discusses, in qualitative terms, the occurrence of radioactive material in 

common sediments.

SHAIKH AND CLAY

The amount of radiation in beds of shale deposited under different 

circumstances and chemical environments differs widely, although 

almost without exception shale is more radioactive than other common 

sediments.
D-48 GENERAL GROUND-WATER TECHNIQUES

Shale generally is composed of different proportions of clay minerals, fine silica, and other clay-size rock materials, and usually is 

saturated with an electrolyte. Some shale may contain organic and 

carbonaceous matter, iron compounds, and various salts.

In any discussion of shale or clay two opposing concepts are likely 

to complicate the use of the term "clay." One use refers to texture or 

particle size and the other to mineralogic composition. In this report, 

the term "clay" refers to one of the three general classes of clay 

minerals: kaolin, montmorillonite, and the illite or hydrous mica 

groups. The term "clay size" will refer to very fine, nonclay material.

Radioactive elements are concentrated in shale by several means, 

and the ultimate radiation of a particular shale is a function of its 

depositional environment, subsequent enrichment by circulating 

waters, and compaction by overlying beds. A minor part of the radiation from shale originates from fine clastic fragments of heavy minerals, such as zircon and tourmaline. Shale deposited in a highly 

reducing environment with an abundance of organic material is probably the most radioactive of the common sediments. The chemical 

reactions by which uranium is precipitated from sea water are not 

completely understood, but a reducing environment and the absence 

of the carbonate ion are important. Carbonaceous material and 

layered clay minerals can adsorb significant amounts of uranium, and 

this may be an important factor in concentrating uranium in organic 

shales.

All clay minerals in shale have the ability to concentrate potassium 

ions by cation exchange and adsorption, and the degree of this exchange is probably an important factor in determining the amount of 

radiation from a shale. Although the specific radioactivity of potassium is considerably less than that of either uranium or thorium, 

Senftle (1948) indicates that the greater concentration of potassium 

in many sedimentary rocks makes it the most significant radioactive 

element (Johnson, 1954).

The degree to which K+ ions (and also organic ions with incorporated uranium) are concentrated in clay minerals depends on several 

factors, one of the most important of which is the type of clay mineral 

predominant in the shale. Of the three clay mineral groups mentioned above, the illite or hydrous mica group has the greatest ability 

to preferetially adsorb and "fix" potassium ions; montmorillonite is 

next, and the kaolinite group has the least ability. Other factors 

influencing the degree of cation exchange are: type and concentration 

of ions in the saturating solution, saturation of the clay minerals or 

the number of vacant exchange positions available, and the degree of 

hydration of the clay minerals.
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-49

The relative abundance of illite in most shale has been reported by 

several authorities (Grim, 1953; Eankama and Sahama, 1950), and 

it would appear that the high radioactivity of shale in relation to 

other sediments is due, at least in part, to the preferential adsorption 

of potassium by this mineral. Eadium and thorium also are important (though subordinate) sources of radiation in normal shale. In 

black marine shale, the content of radium and thorium apparently 

increases in rough proportion to the organic carbon content of the 

shale until these elements become the predominant sources of radioactivity (Whitehead, 1954).

The effect of compaction of clay material to shale has not been 

definitely established, but it is logical to assume that radiation would 

increase as the density of radioactive material increases.

SANDSTONE

A clean orthoquartzite composed exclusively of clastic rock fragments has only a slight radiation, which is due largely to the fraction 

of heavy minerals contained in the rock. These minerals, such as 

zircon, tourmaline, sphene, monazite, and apatite, are sometimes rich 

in radioactive elements owing to the isomorphic substitution of thorium and uranium for zirconium and calcium in the crystal structures 

(Rankama and others, 1950). The quartz grains themselves may have 

a slight radiation, as Larsen and Phair (1954) have measured uranium 

concentrations that averaged 2.3 ppm (parts per million) in quartz 

derived from several granitic rocks.

Both the concentration and radiation intensity of the heavy-mineral 

suite can range over wide limits in sediments of different origins and, 

to some degree, within a particular sediment.

Arkose and f eldspathic sand tend to be more radioactive than quartzite but less so than shale. The abundance of potassium in some feldspar results in a higher radiation; of course, if the predominant feldspar is plagioclase, the radiation due to K40 will not be increased. 

However, according to Larsen (1954), plagioclase may have a somewhat larger concentration of uranium than potash feldspars; so, it 

might be expected that both plagioclase and potash feldspars would 

tend to increase the radiation of arkose and f eldspathic sand.

Although the radiation from quartzite, arkose, and sandstone is 

finite and has a wide range, a large part of the radiation measured 

from beds of these rocks may be due to included shale or clay minerals. Such "dirty sand" is more the rule than the exception. The 

amount of shale in "dirty sand" ranges from a fraction of 1 percent 

to several percent of the bulk volume of the rock, even in some good 

aquifers. It should be expected that the radiation from a "dirty
D-50 GENERAL GROUND-WATER TECHNIQUES

sandstone" would be a function of the amount and specific radiation 

of the included sale, plus the radiation of the sand. This assumption 

is valid where the distribution of the shale in the sandstone is uniform but not where the shale is concentrated in zones.

CARBONATE ROCKS

Limestone and dolomite are among the least radioactive of sedimentary rocks. The carbonate ion inhibits the precipitation of uranium; therefore, little of the radiation from carbonate rocks can be> 

attributed to uranium. Potassium also is seldom incorporated in carbonate sediments, except as contained in included clay minerals; the 

net radiation from potassium is, therefore, also small. Most radiation 

from carbonate rocks probably is due to included shale or clay minerals. Probably only a small part of the clay minerals responsible for 

the radiation in carbonate rocks is deposited syngenetically; most of 

the clay is of secondary origin and occurs as fill in pore space and solution channels and as coating on the walls of such cavities.

EVAPORITE ROCKS AND COAIi

Although evaporite rocks and coal are not genetically related, they 

are the least radioactive of common sediments.

Bell (1954) gives the following explanation for the absence of uranium in evaporite sediments:

Bodies of water undergoing desiccation are usually rather shallow, and subject 

to considerable turbulence, and therefore tend to be aerated and form oxidizing 

environments. These conditions are not favorable for the precipitation of uranium compounds or the adsorption of uranium on sediments. Because of their 

low initial concentration and high solubilities, uranium salts tend to be concentrated in the lost residual mother-liquors during the desiccation of lakes and 

seas. The last-deposited sediments are rarely preserved, being blown away by 

winds or carried into the overlying clastic sediments by capillary action and 

subsequently leached.

It is to be expected, however, that salt beds rich in potassium would 

have a higher radiation than other evaporites.

According to Eussell (1941), coal is one of the least radioactive sediments known, but some coals have been considerably enriched with 

uranium. Eankama and others (1950) state that coal in the alum 

shales of Sweden has been enriched to more than 1 percent uranium. 

In the author's experience, coals of Pennsylvanian age are indicated by 

distinct lows on gamma-ray logs, indicating that they contain no 

great concentration of radioactive elements.

This outline of the occurrence of radioactive elements in sediments 

is wholly qualitative, and no quantitative significance is placed on the 

differences in radiation between the various sediments. The unusual
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-51

or normal modes of occurrence have been described. It is possible for 

exceptions to arise, but in general the occurrences will be as described 

above, and the conventional methods of lithologic interpretation will 

apply.

GENERAL LITHOLOGIC INTERPRETATION

The most frequent use of the gamma-ray log, in both the petroleum 

industry and in ground-water work, is to provide information on the 

sequence of rocks in the borehole. In normal practice, the beds of 

highest radioactivity are interpreted as shale and the formations of 

lower radiation as sand, sandstone, limestone, or evaporite rocks. To 

obtain lithology and formational contacts directly from gamma-ray 

log data, it is usually necessary to know at least the general sequence of 

rocks in the area.

In other nonquantitative applications, the gamma-ray log is used 

extensively for the exploration of mineral deposits that exhibit a 

characteristic deflection on the log. Thus beds of coal, salt, and lignite may be recognized in a normal sedimentary series by their anomalously low radiation.

Quantitative interpretation of the gamma-ray log is restricted to 

the relatively few places where radioassays may be made of known 

ore deposits. Faul (1954) used the gamma-ray log is assaying oregrade uranium deposits in the Colorado Plateau and described a similar method for the uranium-rich phosphate sediments of Florida. The 

gamma-ray log also is used as a supplementary tool in some forms of 

neutron logging used by the oil industry.

GAMMA-RAY INTERPRETATION AS A SUPPLEMENT TO 

RESISTIVITY DATA

The transmissibility and storage coefficients of a formation, as defined by Theis (1938), determine the performance of the formation 

as an aquifer. Although no completely satisfactory theoretical relation between these quantities and porosity has been established to 

date, a rough correspondence is generally recognized for sandstone 

aquifers. For example, sandstones having a high effective porosity 

tend to have high transmissibility and storage coefficients. Identification of the zones of highest porosity, therefore, constitutes an important aspect of log interpretation.

Quantitative methods of determining porosity from formation factor are not widely applicable in hydrology, because of the lack of 

sufficient laboratory control. In this section, a method is suggested 

for the qualitative comparison of the formations penetrated by a well, 

in order to estimate relative porosity. The method is based upon a
D-52 GENERAL GROUND-WATER TECHNIQUES

combination of gamma-ray and resistivity data. It is intended primarily for the evaluation of sandstone aquifers where logging and 

flowmetering of the well are not possible, but local geology indicates 

that the assumptions underlying the method can be accepted. However, the method can also yield useful information in situations where 

little is known about the local geology, if pumping and flowmetering 

are possible.

ASSUMPTIONS UNDERLYING THE METHOD

A simple qualitative correlation between the effective porosity, 

gamma radiation, and formation factor of a sandstone can be made 

if a number of conditions are satisfied. These conditions ma $ be summarized briefly as follows:

1. The well penetrates a section that consists largely of alternating 

sandstones and shales; the permeability of the shales is relatively 

low; and the sandstones constitute the important aquifers.

2. The shales of the section are similar to one another in composition that is, they each contain approximately the same proportions 

of the various clay minerals and other clay-size material.

3. The sandstones of the section each contain a "shale fraction" 

made up of clay minerals and clay-size particles, similar in composition to the shales of the section. However, the total percentage of the 

rock represented by the shale fraction may differ from one sandstone 

to another. In each sandstone the shaly material is largely disseminated throughout the rock, rather than concentrated in streaks or 

pockets.

4. The sandstones are virtually free of radioactive minerals other 

than those associated with the shale fraction, and the gamma-ray 

intensity recorded opposite each sandstone is, therefore a function 

primarily of the percentage of shaly material in the sandstone.

5. Porosity is primary throughout the section; fractures and other 

features of secondary porosity are of minor significance.

The conditions outlined above are somewhat restrictive but are, 

nevertheless, approximated in many geologic sections. Alternating 

sandstones and shales can originate from a variety of depositional 

processes, and many of these processes can produce sections that satisfy 

the required conditions, provided the sediment source remains the 

same throughout the depositional sequence. For example, in a situation in which sand is deposited near a shoreline and clay and silt are 

deposited farther seaward, a fraction of the fine material will normally 

settle out along with the sand. Local transgression of the sea may then 

cause silt and clay to be deposited over the sand. If the sediment 

source has remained unchanged, the resultant overlying shale should 

be essentially similar in composition to the seaward shale and, there-
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-53

fore, to the fraction of fine material in the sand. Kepetition of this 

depositional sequence will result in a section meeting the required 

conditions.

In many instances, geologic reconnaissance of an area will indicate 

whether the required conditions can be assumed. Further evidence 

can sometimes be obtained from the spontaneous-potential and gammaray logs of a well. If these logs return to the same baseline opposite 

each shale penetrated by a well, the shales are probably similar in 

composition because both of these logs are affected by the quantities of 

the various clay minerals contained in the shale. Conversely, if these 

logs do not show a constant shale base the shales probably differ in 

composition, and the required conditions are not satisfied. The probability of finding the required conditions is good because they must 

apply only through a relatively narrow section, as most water shells 

are shallow.

INTERRELATION OF GAMMA RADIATION, FORMATION FACTOR AND 

POROSITY UNDER THE ASSUMED CONDITIONS

In a section that meets the required conditions, the sandstones having 

relatively high shale content will show correspondingly high gammaray readings and relatively low formation factors, because the included clay minerals tend to lower resistivity. These sandstones 

should be low in porosity also, because of their poor sorting. Each of 

these effects increase in gamma radiation, decrease in formation factor, and lowering of porosity depends greatly upon the percentage of 

shaly material in the sandstone.

The porosities of the sandstones are of course affected by many factors other than particle sorting. In general, decreases in porosity due 

to causes other than increase in shale content will be indicated by increases in formation factor. This applies, for example, to decreases in 

porosity due to increased cementation or compaction.

The sandstones of highest porosity in a section meeting the required 

conditions will, therefore, be indicated by relatively low formation 

factors and low radiation intensities. Sandstones that are lower in 

porosity because of high clay content will be indicated by low formation factors and high radiation intensities. Sandstones that are lower 

in porosity because of other causes will be indicated by high formation 

factors and low radiation intensities. Thus, it should be possible to 

estimate the relative effectiveness of the sandstones as aquifers by 

comparing their formation-factor and gamma-ray data. The graphical technique described in the following section provides an effective 

means of making this comparison.
D-54 GENERAL GROUND-WATER TECHNIQUES

GRAPHICAL METHOD OF INTERPRETATION

When it is determined that the formations penetrated by a well 

meet the required conditions, the logging data for each sandstone may 

be plotted as a point on the set of coordinates shown in figure 11. The

Curves of equal porosity

^ X 

' \ \ \

* V \ 

\ \ X

z

i

5*-

<

\ \ \

I \ \ \

I \ \ \

\ \ \ \ 

\ \ \ \

\ \ X N

\ \ \ V

\ » \ > \x Afe0. \V \ \ ^° \ X 

\ v*° N x

\ 

\ \

\ \

F * 

FORMATION FACTOR

FIGURE 11. Graph showing interrelation of radiation, formation factor, and porosity in 

an ideal sedimentary section.

ratio of formation radiation to shale-base radiation is plotted on the 

ordinate, and formation factor is plotted on the abscissa. A family 

of equal-porosity curves has been sketched on the sheet in order to 

facilitate comparison of data. The points representing the best aquifers will obviously fall in the lower left sector of this graph. Beds 

of shaly sandstone will tend to have high ordinate values, and wellcemented sandstones will have high abscissa values.

To lend precision to the discussion of the interrelation of effective 

porosity and the logging parameters of figure 11, effective porosity 

can be considered to be a function of these parameters and can be represented on the graph by the equal-porosity curves. Emphasizing 

again that the discussion pertains only to sections meeting the prescribed conditions, it is possible to demonstrate that these curves of 

equal porosity have the form shown by the dashed lines on figure 11. 

For reasons that will be discussed later in this section, the curves are
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-55

shown only for the region of sandstone and shaly sandstone; they 

are not extended into the region of shale.

The condition that no change in porosity occurs along the curves 

may be expressed by stating that the directional derivative of porosity 

along the curves is everywhere zero. Because porosity is here considered as a function of the two variables, 7 and F, this leads to the 

condition.

or

-

d^ds OT'.OS

where s denotes distance along an equal porosity curve, y is the value 

of the radioactivity ratio, and F is the formation factor.

O# The derivative >~ is negative, because increases in formation factor at a constant clay content correspond to decreases in porosity. The

O# derivative ^- is likewise negative, within the region of interest, by

virtue of the assumption that the increase in clay content results in 

poorer sorting and, therefore, lower porosity. Because these derivatives have the same sign, the condition of equation 21 can be satisfied

only if j and °^ are opposite in sign, which in turn is true

only if the curves of equal porosity have negative slopes, as shown in 

figure 11.

The behavior of the equal-porosity curves as the radiation ratio, or 

clay content, increases, can be discussed on the basis of logging experience with shaly formation. Experience has shown that as clay content 

increases toward the level of a true shale, the change in formation 

factor produced by a change in porosity decreases rapidly. Because

^ 77* 2\A

 is decreasing, - must increase rapidly as the radiation ratio of

figure 11 increases, and the equal-porosity curves must converge with 

respect to the variable F. Referring to equation 21, moreover, it can

be seen that because neither nor can be expected to increase

07 ds ~*.jfi

rapidly as the clay content increases,- must decrease toward zero in

OS

o# order to balance the increase in -. The slope of the equal-porosity

or

curves must, therefore, aproach the vertical as the radiation ratio increases, as indicated in figure 11.
D-56 GENERAL GROUND-WATER TECHNIQUES

The behavior of the curves at high values of radiation is in agreement with general experience in the logging of the fresh-water formations. The resistivity of sandstone is observed to vary widely, whereas 

the resistivity of shale, regardless of location or stratigraphic position, 

is generally confined to a relatively narrow range of very low values. 

Shale must, moreover, include a fairly wide range of porosities, and 

this general tendency of shale to show low resistivity agrees with the 

convergence of the equal porosity curves of figure 11.

To establish fully the form of the equal-porosity curves, the manner 

in which they intercept the abscissa must be considered. As shown in 

figure 11, the intercepts occur at gradually widening intervals as F 

increases. This behavior is based upon experience with clean sandstone formations, and the low radiation ratio of the horizontal axis 

corresponds to a shale-free formation (clean sandstone). In a clean 

sandstone, increases in formation factor correspond to decreases in 

porosity and to decreases in the rate of porosity variation as well. 

This has been described quantitatively by relations of the form of 

equation 9; as already indicated, there are serious objections to the

50

use of this equation in hydrology. The fact that ^-= must decrease of

as F increases, however, indicates that the equal-porosity curves must 

intercept the abscissa in the manner shown in figure 11.

In the preceding paragraphs, the form of the equal-porosity curves 

has been established by considering the slope of these curves, their 

behavior with increase of shale, and their manner of intercepting the 

abscissa. No attempt at quantitative analysis has been made. The 

curves have not been assigned values of porosity, nor have their intercepts on the abscissa been assigned values of formation factor. This is 

in keeping with the basic purpose of figure 11, which is the comparison 

of sands in a section to determine relative porosity values, rather than 

absolute porosity values.

The use of figure 11 in interpretation is straightforward. The radiation-formation factor points representing the various sandstones are 

plotted on the graph or on a transparent overlay. The relative positions of these points in the system of equal porosity curves then indicate which sandstones are highest in porosity.

The assumptions upon which these interpretive methods are based 

are valid only for sandstone and shaly sandstone, not for true shales. 

For example, an increase in clay-mineral content need not mean poorer 

sorting in shale (as it does in shaly sandstone); thus, an increase in 

clay-mineral content need not indicate lower porosity in shales. Furthermore, the poor aquifer characteristics of a true shale may be due 

to causes other than low porosity, whereas in sandstones and shaly
ELECTRICAL AND RADIOACTIVE WELL LOGGING D-57

sandstones porosity normally has an important influence on hydraulic 

properties. For these reasons, it is considered pointless to extend the 

equal-porosity lines of figure 11 into the region of true shale.

In employing the method outlined here, the interpreter should always first establish whether or not the well penetrates a sequence of 

beds meeting the necessary requirements. If figure 11 is used to compare sandstones which do not meet these conditions, the results may be 

misleading. Where it is uncertain whether or not the geology meets 

the required conditions, the methods of this section may be used in a 

reverse sense, in combination with flowmeter work, to provide some 

information on the nature of the aquifers. If flow measurement shows 

that the sandstones that plot most favorably on figure 11 are actually 

the zones of highest yield, the original assumptions are probably satisfied to some extent. For example, porosity and permeability can be 

considered to be primary, and the best aquifers are the sandstones exhibiting the highest relative porosities. It may be possible also to 

assign some reason for the performance of certain of the zones. For 

example, it may be possible to tell whether a zone has a low yield because it is shaly or because it is a relatively "tight" clean sandstone.

The procedures discussed in this section are designed to help the 

interpreter evaluate aquifers by using radioactivity logs in conjunction with other logging data. The restrictions of these methods have 

been outlined, and it is hoped that those using the methods will do so 

with these restrictions in mind.

CONCLUSION

Although the several types of logs are, for the most part, discussed 

separately in this paper; they should never be interpreted separately. 

A given feature on a log of one type usually can be attributed to any 

of several possible causes; commonly an examination of the other 

types of logs for the well will serve to eliminate all except one of these 

causes. Where possible, logs and flow-tracing experiments should be 

run as the well is pumped, for comparison with those made under 

static conditions. Finally, the interpreter should consider all available 

data from other sources before attempting interpretation. Each interpretation should be based upon an understanding of logging theory 

and well hydraulics, rather than upon any memorized set of interpretive principles.

REFERENCES

Archie, G. B., 1942, The electrical resistivity log as an aid in determining some 

reservoir characteristics: Am. Inst. Mining Metall. Engineers Trans., v. 146, 

p. 54-62.

Bell, K. G., 1954, Uranium and thorium in sedimentary rocks, in Nuclear geology a symposium: New York, John Wiley & Sons, p. 98-114.
D-58 GENERAL GROUND-WATER TECHNIQUES

Bennett, G. D., and Patten, E. P., Jr., 1960, Borehole geophysical methods for 

analyzing specific capacity of multiaquifer wells: U.S. Geol. Survey WaterSupply Paper 1536-A, 25 p.

Brannon, H. B., Jr., and Osaba, J. S., 1956, Spectral gamma-ray logging: Am. 

Inst. Mining Metall. Engineers Tech. Kept. 4208.

DeWitte, Leendert, 1955, A study of electric log interpretation methods in shaly 

formations: Am. Inst. Mining Metall. Engineers, Petroleum Trans., v. 204, 

p. 103-110.

Faul, Henry, 1954, Nuclear logging of drill holes for mineral exploration and 

soil studies, in Nuclear geology a symposium: New York, John Wiley & 

Sons, Inc., p. 250-255.

Glasstone, S., 1951, An introduction to electrochemistry: New York, D. Van 

Nostrand Co.

Grim, R. E., 1953, Clay mineralogy: New York, McGraw-Hill Book Co., 384 p.

Guyod, Hubert, 1952, Electrical well logging fundamentals: Houston, Tex., 

164 p.

Johnson, D. H., 1954, Radiometric prospecting and assaying, in Nuclear geology a symposium: New York, John Wiley & Sons, p. 219-241.

Jones, P. H., and Skibitzke, H. E., 1956, Subsurface geophysical methods in 

ground-water hydrology, in Advances in Geophysics: New York, Academic 

Press, v. 3, p. 241-300.

Kozary, M. T., 1948, Streaming potentials in electrical well logging: Pennsylvania State Coll. Bull., v. 43, no. 8, p. 76-96.

Larsen, E. S., Jr., and Phair, George, 1954, Distribution of uranium and thorium 

in igneous rocks, in Nuclear geology a symposium: New York, John Wiley 

& Sons, p. 75-89.

McCardell, W. M., and others, 1953, Origin of the electric potential observed 

in wells: Am. Inst. Mining Metall. Engineers, Petroleum Trans., v. 198, p. 

41-50.

Rankama, Kalervo, and Sahama, J. G., 1950, Geochemistry: Chicago, 111., Univ. 

Chicago Press, 911 p.

Russell, W. L., 1941, Well logging by radioactivity: Am. Assoc. Petroleum 

Geologists Bull., v. 25, no. 9, p. 1768-1788.

Schlumberger Well Surveying Corp., 1950, Interpretation handbook for resistivity logs (Schlumberger Doc. No. 4) : Houston, Tex., Schlumberger Well Surveying Corp., July 1950.

Senftle, F. E., 1948, The effect of potassium in prospecting for radioactive 

ores: Canadian Mining Jour. 69, no. 11, p. 55-57.

Theis, C. V., 1938, The significance and nature of the cone of depression in ground 

water bodies: Economic Geology, v. 33, no. 8, p. 889-902.

Whitehead, W. L., 1954, Hydrocarbons formed by the effects of radioactivity 

and their role in the origin of petroleum, in Nuclear geology a symposium: 

New York, John Wiley & Sons, p. 195-218.

Winsauer, W. O., and McCardell, W. M., 1953, Ionic double layer conductivity 

in reservoir rock: Am. Inst. Mining Metall. Engineers, Petroleum Trans., 

v. 198, p. 129-134.

Wyllie, M. R. J., 1949, A quantitative analysis of the electrochemical component 

of the S.P. curve: Am. Inst. Mining Metall. Engineers Trans., v. 186, p. 

17-26.

 1955, Role of clay in well-log interpretation: California Div. Mines Bull. 

169, p. 282-305.
INDEX

Page 

Apatite... -. .. D49

Apparent resistivities of aquifers ... 13 

Arkose_ ..__ 49

Clay minerals, effects of, on rock resistivity... 10, 24

Coal, uranium-enriched..._ . 50

Conclusion . 57

Conduction in earth materials.___.-_... 9-10

Conductivity, factors controlling.. .. ... 40

Core analysis____._.__.. _ 19

Curie, unit of radioactivity__ . 46

Current patterns.__ ___-----_ 3,22

Direct-junction equation.

Effective porosity.... __ 54 

Electrochemical phenomena. .. 33-34 

Electrolytic characteristics of well fluids. 11 

Equal-porosity curves....__.. ... 55-56

Fluid-conductivity logging, interpretation, in

multiaquiferwell. ____-___- 41-45

interpretation in single-aquifer well__ 40-41

Formation-resistivity factor.... _ 9

Gamma-ray logging, assumptions underlying

interpretation..___.. .._ 52-53 

general lithologic interpretation 61 

graphical interpretation.... ___ 54-57 

instrumentation_____________. 45-47 

interpretation as supplement to resistivity

data... .. . 51-62

Illite___....__.._...... . .. 48,49

Interaquifer flow 37 

Introduction . 1-2 

Ionic diffusion.____ ........ .... .. 28

Ionic transport___________.__ 16 

Isomorphic substitution.._ 49

Junction of NaCl solutions through ionselective membrane___. ___ 30-31

EaoUn............ - - 48

Kirchoff'sloop rule. . .. 34

Limestone sonde..... .... .. 23

Liquid-junction equation__........___.. 29-30

Liquid-junction potentials in an oil well. 32-34 

Liquid-junction problem. 28 

Long-normal device. _~ 2,7,8,11

Page 

Mica, hydrous groups.._------_------ D48

Monazite____________________ 49 

Montmorillonite________________ 48 

Mud-filled borehole, conditions in____... 13-14 

Multiaquifer well, internal flow in_ ____ 15

Ohm's law... ________________.. 5,36

Permeable zones, identification of____ . 12 

Photomultiplier tube_____________ 46 

Plagioclase______.____._____.. 49 

Point-resistance device.__________... 7,8 

Porosity, relation to formation factor. ____ 18-20 

Potassium______.____________ 46,48

Quartz. 49

Radiation, general discussion of._ __ .. 45-46

sources of, carbonate rocks.. _______ 50

common sediments__________ 47

evaporite rocks and coal._______ 50-51

sandstone...._____________ 49

shale and clay__ _____... 47-49 

Radioisotopes.. ___.._._.___._.. 45-46 

Kadium.-. .. _ 49 

References___________________ 57-58 

Resistance, formula for. ___________ 4 

Resistivity curves..... . ....... 17,24,25,26

Resistivity logging, borehole effect______ 7-9 

calibration and zones of investigation.. _ 6-7 

instrumentation and theory..___..... 2-9

interpretation based on normal curves.... 11-19

interpretive practices in oil industry.._ 11-13

introduction_._.___._..___.. 2

lithologic interpretation--. ________ 10

Roentgens, units of radiation flux_... _. _ 46

Scintillometer..._._._..............__ 46

Secondary porosity, in limestone and crystalline rocks.____.____.__ 20-24

in sandstone-shale sections________ 24 

Shale as an ion-selective membrane.... . 31-32 

Short-normal device___ _.. 2,7,8,11 

Single-point device.___________. 6,11 

Sphene__________________..... 49 

Spontaneous-potential current loop. 34 

Spontaneous-potential deflections, abnormal. 39

artificially induced- ____._.._.... 39 

Spontaneous-potential log.... .... 31,33

D59
D60 INDEX

Page 

Spontaneous-potential logging, analysis of

quantitative interpretation. _ D-27-29 

history.___________________ 27 

Instrumentation____________.. 26-27 

objections to quantitative interpretation

for water wells_.________ 36-37 

recognizing mineralized-water zones..._ 38 

summary. . ...__.________ 39 

Spontaneous-potential measurement related

to emf... _______.___ 34-36 

Storage coefficient___ _________ 51

Page 

Streaming potentials.... ....__.____ D-38

Thorium___._....._....-_____.__ 46,49 

Tourmaline____________________ 48,49 

Transmissibility coefficient___ ______ 51

Uranium. 46

Water-filled borehole, conditions in. 14-17 

Well fluids, electrolytic characteristics__. _ 11

Zircon__________ __.._ __ 48,49

U. S. GOVERNMENT PRINTING OFFICE : 1967 O - 249-459