Electrical Properties of 

Sandstones of the 

Morrison Formation

GEOLOGICAL SURVEY BULLETIN 1052-J

This report concerns work done on behalf 

of the U.S. -Atomic Energy Commission 

and is published with the permission of 

the Commission

Electrical Properties of 

Sandstones of the 

Morrison Formation

By GEORGE V. KELLER

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

GEOLOGICAL SURVEY BULLETIN 1052-J

This report concerns work done on behalf 

of the U.S. Atomic Energy Commission 

and is published with the permission of 

the Commission

"JNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON j 1959
UNITED STATES DEPARTMENT OF THE INTERIOR 

FRED A. SEATON, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

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

Washington 25, D.C. - Price 55 cents (paper coyer)
CONTENTS

	Page 

Abstract__________________________________ 307

Introduction _____________________________________ 307

Electric logging._______________________________________ 308

Equipment and techniques___________________________________ 310

Results_____________________________________ 311

Laboratory measurements.____________________________________ 315

Nature of rock resistivity.________________________________ 315

Resistivity measurements on cores_________________________ 318

Spontaneous-potential measurements_______________________ 328

Correlation of laboratory and field data______________________________ 335

Quantitative interpretation of logs_________________________________ 340

Use of electric logging in exploration_._______________________________ 341

References cited_______________________________..__________________ 343

ILLUSTRATIONS

[All plates to pocket]

PLATE 12. Electric, radioactivity, and core logs.

13. Correlation of laboratory measurements.

Page

FIGUHE 95. Index map of Colorado Plateau__________________________ 309

96. Cumulative frequency curve of resistivity_______________ 312

97. Map of Spud Patch area.__________________.___ 314

98. Idealized diagram of a single pore structure______________ 316

99. Device used in measuring resistivity._____________________ 319

100. Formation factor as function of porosity_________________ 322

101. Resistivity index as function of water saturation.__________ 325

102. Variations of formation factor__________________________ 327

103. Device used in measuring diffusion potentials._____________ 331

104. Ion concentration in double layer_______________________ 332

105. Sources of potential variations_____-__-___-______--______ 333

106. Calculated relationship between spontaneous potential and

connate-water salinity__________________ __________ 334

107. Inch-to inch variation of porosity._____________________ 338

108. Empirical relationship between porosity, resistivity, and

spontaneous potential_______________________________ 339

TABLES

Page

TABLE 1. Quality of logging water__________________________________ 310

2. Apparent salinities associated with clay conductance.-..______ 328

3. Results of the quantitative interpretations of electric logs. _ _ __ 341

m

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

ELECTRICAL PROPERTIES OF SANDSTONES OF THE 

MORRISON FORMATION

By GEORGE V. KELLER

ABSTRACT

The electrical properties of the Morrison formation in the Uravan mineral belt 

of the Colorado Plateau have been studied to determine whether there are 

anomalous variations in these properties in and near zones of uranium-vanadium 

minerals which might serve as a target for geophysical prospecting. Measurements of electrical properties of the Morrison formation in place were obtained by 

the electric logging of 147 drill holes, and measurements were made of the resistivity and porosity of 440 drill cores in the laboratory to aid in the interpretation 

of the electric logs. The resistivity of the sandstone members of the Morrison 

formation is highest in areas that are the most favorable for the occurrence of ore. 

This increase in resistivity is probably due to a lower water saturation or a lower 

salinity of the water in the favorable areas.

INTRODUCTION

Uranium- and vanadium-bearing sandstones are widely distributed 

in the Colorado Plateau province, which covers parts of Colorado, 

Utah, New Mexico, and Arizona. Deposits have been found in many 

formations in the area; many of the important deposits are in the 

Morrison formation, particularly in an area of west-central and southwest Colorado called the Uravan mineral belt. The deposits are 

usually small in extent, ranging from a few tons to some thousands of 

tons of ore. The ore bodies form irregularly tabular masses that tend 

to be parallel to the bedding, but they do not follow the beds in detail 

(Fischer, 1942).

In southwestern Colorado the Morrison formation comprises two 

recognized members; the Brushy Basin and the Salt Wash. The 

Brushy Basin member consists predominantly of mudstones which 

may be gray, red, green, purple, and brown. The Brushy Basin also 

contains several thin sandstones and limestones. Locally, there are 

thick lenses of conglomerate.

The lower member, the Salt Wash, consists of massive lenses of 

medium- to coarse-grained sandstones interbedded with red and blue307
308 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

gray mudstones. Much of the ore is in sandstones hi the upper part 

of the Salt Wash member but commonly it is found in the lower parts 

of the individual sandstone lenses. The Salt Wash is not sharply 

separated from the Brushy Basin, particularly where there are sandstone lenses in the lower part of the Brushy Basin.

In general, the localization of the ore seems to be related to certain 

geologic features that can serve as guides to the presence of ore. 

Such guides are the tendency of the ore to occur in the thicker central 

parts of sandstone lenses, the association of ore with medium-grained 

pale-yellow to light-brown sandstone, the association of ore with the 

thicker parts of mudstone that have been altered from red to gray or 

gray green, and the association of ore with an abundance of carbonaceous material.

In hopes of delineating favorable areas and locating ore more rapidly 

and at less expense, various geophysical exploration methods were 

tested on the Colorado Plateau, beginning in 1949. Electricalresistivity surveys were tried in several areas, and in several known 

ore deposits, higher resistivities were noted over the ore zones. However, the exact interpretation of these surveys proved difficult, 

particularly when the ore-bearing member was at a depth of several 

hundred feet.

In order to determine the possibilities and limitations of surface 

resistivity surveys, a program of measurements of the electrical properties of the Morrison formation was undertaken. The program consisted of two parts: the measurement of the resistivity of the Morrison 

formation in place and the measurement of resistivity and associated 

properties of drill cores with restored water saturations.

Both field and laboratory studies described in this report were made 

as part of a program carried on by the Geological Survey on behalf of 

the Division of Raw Materials of the Atomic Energy Commission.

ELECTRIC LOGGING

Measurements in place, consisting of electrical well logs, were made 

in 147 drill holes (fig. 95) in four areas where surface resistivity surveys 

had been made previously to determine whether there are any pronounced differences in the electrical properties of the Morrison formation in these areas. In the Spud Patch area of San Miguel County, 

Colo., 103 measurements were made, so that it was possible to determine the areal variation of electrical properties. A smaller number of 

drill holes, 23 in all, were logged in the Gramlich group of claims at 

La Sal Creek, Montrose County, Colo. A few holes were also logged 

at Long Park in Montrose County, Colo., and at Yellow Cat, Grand 

County, Utah.
ELECTRICAL PROPERTIES OF SANDSTONES 309

Monticello 

EXPLANATION

Areas In which electric logt were liken 

in 1952

r

20 UIL£S

FIGURE 95. Index map of the Colorado Plateau showing areas discussed in this report.

The electric logs taken on the Colorado Plateau were of three 

types: natural-potential measurements, resistivity measurements with 

a normal electrode arrangement, and resistance measurements with a 

single-point electrode arrangement. Natural-potential logs are made 

by recording the voltage between a moving electrode in the drill hole 

and a reference electrode, usually placed on the ground surface near 

the drill hole. In the work reported here, resistivity logs with
310 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

radii of investigation of 4, 8, and 24 inches were taken in each drill 

hole; single-point resistance logs were made to provide sufficient 

data to determine rock resistivity. By comparing the apparent 

resistivities measured with these several electrode arrangements, it 

is possible to estimate the true resistivity more accurately than can 

be done with a single measurement.

EQUIPMENT AND TECHNIQUES

The electric logging unit used for this work consisted of a threeconductor cable and an electric hoist to raise the electrode sonde 

through the drill hole. The current to the electrodes was provided 

by dry batteries, regulated with a servomechanical regulator, and 

commutated at a frequency of 21 cycles per second. The voltage 

between pick-up electrodes was rectified with a set of commutator 

rings coupled mechanically to the current commutator, as in the 

Gish-Rooney system. This rectified current was recorded on one 

channel of a modified servomechanical recorder, calibrated in ohmmeters.

The spontaneous potential, present as a d-c voltage between the 

pickup electrodes, was separated from the 21-cycle resistivity-logging 

current by means of a blocking condenser and recorded simultaneously 

on the other channel of the recorder, which was calibrated in millivolts.

The chart drive of the recorder was controlled by a selsyn motor 

coupled to a selsyn generator on a calibrated sheave over the drill 

hole. The logging cable passed over this sheave as it was lowered 

or raised in the drill hole, so that the paper in the recorder was driven 

forwards or backwards through the recorder. Paper drive ratios 

of 1 inch to 20, 50, and 100 feet of electrode movement were used.

Because most of the drill holes on the Colorado Plateau are dry, 

it was necessary to haul water to fill the drill holes in order that 

contact could be made between the in-hole electrodes and the rock. 

Obtaining water for logging proved to be one of the biggest handicaps 

to logging on the Colorado Plateau. In all the areas logged, surface 

drainage either from springs or from reservoirs was used to fill the 

drill holes. The water sources and then- qualities are listed hi table 1.

TABLE 1. Quality of logging water

Logging area Water source

Resistivity 

at5°C. 

(ohm-cms)

6,500

1,780

3,230

4,200

Equivalent 

salinity 

(ppm 

NaCl)

130

430

240

185
ELECTRICAL PROPERTIES OF SANDSTONES 311

RESULTS

Analysis of the electric logs showed that the resistivity of the 

several members of the Morrison formation in the drill holes that were 

logged ranged from a low of 8 ohm-meters to a maximum of 2,000 

ohm-meters. The resistivity of the mudstone members ranged from 

8 ohm-meters to 35 ohm-meters, and the average resistivity did not 

change greatly from drill hole to drill hole.

The average resistivity of the sandstone members of the Morrison 

formation within any one drill hole showed a greater variation, ranging from 130 ohm-meters to 430 ohm-meters. Moreover, the resistivity of the sandstone within any one drill hole showed wide variations about the average.

An apparent correlation was noted between resistivity of the sandstone and favorability for occurrence of ore as determined by geologic 

guides. This apparent correlation was studied in more detail by a 

statistical analysis of the resistivity logs of 35 drill holes in which the 

complete section of the ore-bearing member had been logged. Of these 

35 drill holes, 20 had been classed as favorable with respect to geologic 

guides, and 15 were considered to be semifavorable or unfavorable. 

The logs were studied by taking resistivity intervals of progressively 

larger size; 56 to 80 ohm-meters, 80 to 115 ohm-meters, and so on up 

to the interval 1,400 to 2,000 ohm-meters. The number of feet of 

sandstone in each of these classes in each group of drill holes was then 

measured. These data are presented on a cumulative frequency 

graph in figure 96. The shape of the curves indicates that the number 

of feet of sandstone of a given resistivity is a statistically normal variable when the resistivity is considered logarithmically. The curve for 

favorable sandstones is significantly different from the curve for semifavorable and unfavorable sandstones; the median of the curve of 

resistivity in favorable sandstones is 50 percent higher than that in 

the less favorable sandstones.

In addition to the generally higher resistivities found in the drill 

holes in more favorable ground, especially high resistivities were found 

in drill holes through mineralized ground at approximately the depth 

of mineralized area. Plate 12 shows the electric logs, the core logs, and 

the radioactivity logs of seven typical drill holes through mineralized 

ground.

With one exception, a thin layer of high resistivity is found near the 

depth of the radioactivity anomaly. This exception is drill hole SP 

210 (pi. 12.4), in which there is a small increase in resistivity at the 

depth of the mineralized ground. In other holes, (pi. 12(7, F), the 

high-resistivity layer is the most striking feature of the log. In the 

remaining examples the resistivity of the ore zone is one of the highest 

recorded on the log but is not so large as to be outstanding.

496731* 59 2
312 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

08 9TT see oet sss

SM313W-WHO Nl 'A1IAI1SIS3H 3N01SQNVS

086 OOlrl 2
ELECTRICAL PROPERTIES OF SANDSTONES 313

The resistivity anomaly occurs in the upper part of the radioactivity anomaly or is offset up the hole by 1 or 2 feet. This offset 

indicates that the anomaly is not directly associated with mineralized 

ground but may be caused by some other factor. The combination 

of high resistivity and high natural-potential deflection shown by the 

logs in plate 9 indicates that the anomalous layer has a low saturation 

of water of high salinity. This relation in turn implies that the layer 

has been subject to an extreme amount of evaporation, as if it had 

high permeability. The mineralized layer seems to be covered by a 

desaturated caprock that gives rise to a resistivity anomaly.

One of the geologic guides to ore is the association of ore with the 

thicker Salt Wash sandstone. Because of this association and the 

observation that the resistivity of the sandstones in drill holes through 

mineralized ground is generally higher than the resistivity in drill 

holes in unfavorable ground, it was reasoned that a combined measure 

of sandstone thickness and resistivity would be a sensitive index to the 

favorability of a drill hole. To check this, the area under the 8-inch 

normal-resistivity logs was planimetered for the drill holes in which 

logs were obtained for 60 percent or more of the ore-bearing sandstone. 

None of the sandstones in the overlying Brushy Basin were included 

in these measurements. When a log did not cover the entire thickness 

of ore-bearing sandstones, it was assumed that the average resistivity 

in the unlogged section was the same as in the logged section, and the 

resistivity integral was extrapolated to include the unlogged section 

of the sandstone.

The 8-inch normal curve was used in these studies, as no correction 

is necessary for the influence of mud resistivity and hole diameter. In 

all holes the mud resistivity was 65 ohm-meters, within an accuracy 

of 20 percent. The diameter of each hole was 3 inches. Corrections 

for these conditions are less than 10 percent for all resistivities less 

than 2,500 ohm-meters and for beds thicker than 3 feet according to 

Schlumberger departure curves. Corrections may be made for 

thinner beds, but such corrections usually are no more accurate than 

the original data.

These measurements were made for 58 drill holes of the Spud 

Patch area; the resulting integral ranged from 3,800 to 29,600 ohmmeter-feet. A contour map (fig. 97) of these data shows six pronounced features, three highs and three lows. The highs include all 

but one of the drill holes through mineralized ground and many of the 

drill holes through favorable ground. One drill hole through mineralized ground occurs in a low, but this drill hole was classed as unfavorable according to geologic guides. The low areas include all 

the drill holes in unfavorable ground and a majority of the drill holes 

in semifavorable ground.
Drill hole

Drill hole classed as semifavorable

o 

Drill hole classed as unfavorable

a at jr

Drill holes which show high 

values on radiation log

z=topOf sand v»z=

Contour of/ />(z)dz 

J z=z(= bottom of sand 

Contour interval 2.5 ohm- Kilometer-feet

FIGURE 97. I
ELECTRICAL PROPERTIES OF SANDSTONES 315 

LABORATORY MEASUREMENTS

To interpret the logs quantitatively in terms of texture and composition it is necessary to have detailed information on the properties of 

the rock, such as can be obtained by the physical analysis of cores. 

Usually this additional information is obtained from resistivity 

measurements on cores taken from a typical drill hole. These 

measurements are designed to determine how rock resistivity depends 

upon the rock texture and the composition of the contained water. 

The results are then extrapolated to drill holes from which no cores 

have been studied.

NATURE OF ROCK RESISTIVITY

The electrical conductivity of sedimentary rocks such as those 

which comprise the Morrison formation is readily shown to be a 

consequence of the presence of small amounts of water in the rock. 

If a sedimentary rock is dried completely, it is an insulator. However, 

if even a small amount of water is present, a rock exhibits an appreciable capacity to conduct electric currents. Because the conduction is ionic, rather than electronic as in metals, the nature of the 

conductivity of the rock and water combination is more complex 

than if the conduction were metallic.

Current conduction in sedimentary rocks can be understood by 

considering what happens in a small portion of the pore structure. 

Clastic detrital rocks, such as the sandstones and mudstones which 

constitute the Morrison formation, consist of a network of void 

spaces separating the solid grains. These void spaces, or porosity, 

can be classified into two general types of pores. Most of the void 

spaces are relatively large, for the most part equidimensional pores 

that make up the storage capacity of the rock. The remainder are 

small elongated channels that connect the larger voids. These 

channels are only a small part of the total porosity, but they are the 

primary factor in controlling current conduction because of their 

small cross-sectional area. To aid in visualizing this, the concept of 

the ideal porelet (fig. 98) is useful. The porelet consists of a spherical 

body, or storage chamber, with small tabular extensions that connect 

with other porelets. Clay particles are shown lining this porelet, 

particularly in the small connecting pores, where the clays tend to 

occur. A porous isotropic rock can be thought of as consisting of a 

large number of these porelets, randomly oriented and connected to 

each other in a geometrically complicated manner.

If such a rock were fully saturated with a brine solution, the resistance presented to an electrical current would depend on the length of 

the connecting pores, their cross-sectional area, the average angle that
316 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Water Exchange positions

e

Anions Clay particles

FIOUKE 98. Idealized diagram of a single pore structure, or porelet, showing the features which control the

resistivity of a rock.

the porelets make with the overall direction of current flow, and the 

total number of porelets per unit area.

In the study of the resistivity of porous materials, it has become 

customary to use a quantity designated by the term "formation 

factor," which is the resistivity of the bulk material, such as the 

rock, divided by the resistivity of the conductive material in it, such 

as the brine. In simple ohmic conduction, the formation factor 

would be a constant for a given rock, and would represent the geometric distribution of the porelets as described above. The formation factor would decrease as the volume of conductive material, or 

number of porelets, increased. Similarly, as the degree of consolidation of the rock increased and the size of the connecting tubes was 

reduced by the deposition of cement, the formation factor should 

increase. The relationship between electrical resistivity and porosity 

has been determined empirically as:

F=c<t>" (1) 

where

F is the formation factor as defined above, 

<f> is the porosity,

and

c and * are constants determined by the various dimensions of the porelets.

This equation implies that the resistivity of the brine within the 

pores is known or can be measured. Generally it is assumed that the 

conductivity of the brine in the pores is due solely to the presence 

of ionized salts and is the same as the conductivity of a similar brine 

outside the rock. This is not always true. If a rock contains any 

surface-active material, such as clay, there may be a reaction between 

the water and the rock that tends to increase the conductivity of the 

rock. This effect is known as double-layer conductivity, because it is
ELECTRICAL PROPERTIES OF SANDSTONES 317

related to the presence of a Helmholtz double layer of charge on the 

surfaces of the clay particles (Winsauer, and McCardell, 1952).

Many different phenomena can occur when water comes in contact 

with these clays in the rock. Many clays, such as montmorillonite 

and illite, are colloidal electrolytes. These clays have a number 

of cations in their crystal structure that are free to leave the clay 

particle and go into a state resembling ionic solution. The number 

of these cations and the ease with which they may leave the clay 

particle depend on the type of clay, the type of ion that is in the 

exchange position, and the nature of the brine in contact with the 

clay. The exchangeable cations that leave the clay add to the 

capacity of the water to conduct current, but the mobility of these 

ions may not be the same as in true ionization because of the presence 

of the charged clay particle or micelle.

More complex reactions may occur also. Over certain ranges in 

salinity of the external solution, the plates of the clay particle become 

separated as water molecules are attracted between them by the 

unsatisfied electrical charges of the exchange positions. Under these 

conditions the clay will swell to many tunes its original size, the 

viscosity of the clay-water mixture will be increased, and the cross 

section available for current conduction will be reduced.

As the salinity of the water in the pores is increased, the relative 

effect of the ions added by cation exchange becomes small. As a 

result, resistivity measurements made with a high-salinity brine 

saturating the rock generally approach the constant formation factor 

expectable if the clay were not present.

In nature the pore space in most rocks is only partly filled with 

water. As a result, the rock has a higher resistivity than if it were 

completely saturated. In studying the effect of saturation on resistivity, it is common practice to use a quantity called designated 

by the term "resistivity index." This index is the resistivity of a 

rock partly saturated by water divided by the resistivity of the same 

rock fully saturated with a brine of the same composition.

As the water saturation of a rock is reduced, water is first removed 

from the centers of large voids (fig. 98), because the water is held in 

the smaller pores by capillary tension. The removal of water from 

these larger pores increases the distance that the current has to flow 

through the pore and decreases the cross-sectional area available for 

current conduction. Ideally the process continues until all the water 

is removed from the pores with the exception of a uniform coating 

over the pore walls. If there is further reduction hi water content, 

the water film in a pore becomes discontinuous; and the remaining 

water in that pore is unavailable for current conduction. The result 

is a rapid increase in resistivity as the water content is reduced beneath
318 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

the critical saturation. It has been found (Keller, 1953) that the 

relationship between resistivity and saturation generally takes the 

form:

where

7 is the resistivity index defined above,

Sw is the water saturation, expressed as a fraction of the total pore space,

n\ is the saturation exponent at high-water saturation,

n2 is the saturation exponent at low-water saturations,

S*>e is a critical water saturation separating high- and low-water saturations,

and

a is a constant that enters the equation at low-water saturations.

As this discussion indicates, in order to specify the resistivity of a 

rock from measurable quantities, it is necessary to know the influence 

of the water saturation, porosity, and clay content individually on 

resistivity. To determine this influence, a series of measurements was 

made on cores from six Spud Patch drill holes. Three groups of 

resistivity data and one group of natural-potential data were obtained.

RESISTIVITY MEASUREMENTS ON CORES

To study the relation between resistivity and porosity, a group of 

346 cores was selected. These cores were taken at intervals of 1 to 2 

feet through the sandstone members penetrated in the 6 drill holes. 

The cores as they came from the coring bit were l%e inches in diameter 

and a few inches to several feet long. The cores at the selected depths 

were faced with a diamond cut-off wheel to a length of 1 inch. The 

flat faces of these cores were then coated with a conductive silver 

paint such as is used in printed electronic circuits.

The cores were saturated with tap water and permitted to soak in 

tap water for 2 weeks; the water was changed daily to remove any 

salt remaining from the original water saturation. At the end of the 

soaking period the electrical resistance between the silver-coated 

faces of the cores was measured by placing the core in a clamp consisting of two lead-plated brass plates in contact with the ends of a 

core (fig. 99). The resistance between these brass plates and through 

the core was measured with a Wheatstone bridge circuit. A 20-cycleper-second current was caused to flow through the bridge and regulated 

so that a constant 5 milliamperes of current flowed through the core. 

The null position of the Wheatstone bridge was detected with an 

oscilloscope.

After the resistances had been measured, the cores were dried for 

6 hours at 105° C. The dried cores were then weighed and placed in 

a vacuum dessicator. The pressure was reduced to a few millimeters 

of mercury for a period of 2 to 4 hours.
ELECTRICAL PROPERTIES OF SANDSTONES 319

Screw clamp

Swivel joint

Brass plate, lead*

coated

Sandstone core 

with silver-coated faces

Brass plate,- 

lead-coated

Core clamp

Oscilloscope

Milliammeter 

B

FIOUBE 99. Device used in measuring resistivity of cores.

When the air had been removed from the cores, a deaerated salt 

solution containing a known amount of sodium chloride in solution 

was introduced into the dessicator. The cores were covered with this 

salt solution and subjected to atmospheric pressure, forcing the salt 

solution into the pore spaces of the cores. The cores were reweighed, 

and the resistance between silvered faces was measured as before. 

The volumes of the cores were determined by weighing them while 

they were suspended in a salt solution of the same composition as the 

one with which they were saturated.

4967*1-
320 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

The resistivity of the salt solution, which contained 30,000 ppm? 

sodium chloride, was determined from tables and checked with a 

calibrated dip cell.

The volume of the salt solution in the cores was calculated_from the

following equation:

, W2 -W1

 W2 -W3 

where

(3)

0W is the fraction of tiie total volume of the core occupied by brine, 

Wi is the weight of the dry core,

Wz is the weight of the core saturated with salt solution, and 

Wz is the weight of the core suspended in salt solution.

The quantity <£ is the effective porosity to water, which would beonly slightly smaller than the total porosity because of the method 

by which the cores were saturated.

The resistivity of the cores was readily determined from:

where

r is the radius of the core,

I is the length of a core,

RI is the resistance of a core saturated with tap water, and

Ra is the resistance of a core saturated with salt solution.

Resistivity at very high brine salinities should be approximated 

by this formula because the conductivity of the core saturated with 

tap water is considered to be in parallel with the conductivity of the 

brine when the core is saturated with salt solution, and the error caused 

by the action of clay and the presence of an unknown amount of salt 

from the original connate water is approximately corrected. Inasmuch as this correction does not exceed 10 percent, the assumption 

that the two conductances are parallel is accurate within 1 percent.

The formation factor was determined for each core by dividing 

resistivity of the rock by the resistivity of the salt solution used tosaturate the cores.

Because of the large number of measurements, it was possible todetermine an empirical relation between formation factor and porosity 

by a statistical method. The data were grouped into 11 classes or 

ranges of porosity: 14.01 percent to 15.00 percent, 15.01 percent to 

16.00 percent, and so on. Then it was assumed that the logarithms 

of the formation factors in each group were normally distributed 

about some mean. This mean of the logarithm of formation factor
ELECTRICAL PROPERTIES OF SANDSTONES 321

was calculated for each of the 11 intervals, and a standard deviation 

was calculated for each group by the formula:

S(logF-logF)2

N

where

VP is the standard deviation of log F,

N is the number of cores in any one porosity class,

tiand

» log F is the average value of log F.

The standard deviation of the mean value of the logarithm of theformation factor was also computed from the equation:

where o^ is the standard deviation of the average value of log F. 

In figure 100 the mean values of the formation factor have been 

plotted as a function of the mean values of the porosities in each, 

class. The table from which this graph was plotted is given below. 

The 95-percent confidence limits of the means are indicated by the 

length of the bar through each point, and the 95-percent confidence 

limits of the individual datum points are indicated by the dashed 

lines.

Number of cores

44...-.-.... .. 

29-. 

39... ........... . .......

44- 

37..... .................

34.........................

Average 

porosity 

(percent)

21.7

19.5

18.4

17.5

16.5

15.5

Average 

formation 

factor

16.8

20.7

00 (S

26.1

29 9

31.6

Number of cores

16 

34 

25

oo

oo

Average 

porosity 

(percent)

14.3

13.1

11.0

7.2

2.6

Average 

formation 

factor

39.8

40.8

60.1

101.0

296.0

The equation of the form of equation 1 that best fits these data 

between porosities of 14 percent and 23 percent is:

The data for lower porosities are probably unreliable because of the 

difficulty of obtaining uniform saturation in cores with low porosity 

and poor permeability.

A smaller group of cores, 45 in all, was selected for study of resistivity 

as a function of water saturation. These cores were prepared in thesame manner as those used in the study of formation factor. The 

cores were leached in tap water, weighed, dried, and saturated with a 

salt solution containing 7,500 ppm sodium chloride. The porosity-
322 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

§8S

/

i p o o c i P * ift 9

'

| t

 a

«* 

c (

o! 

j

1

:

x

P 8 8 2«

of limits confidence 95-percent of 'factors formation means 

+ 

limits of95-percent confidence individual offormation values

factor

/

/

/

<,f

/^

;

X

r

/

» eo r- <o «

l>

f

f

J

/i

I/

/

< 

g 8 8 g 8 ' 8 § 8 8 g » « r- «

/

/

X

* 1* 0

/

/

/

s

r 

/

/

s'

 '

X

^

700 50 2080 1025

'FORMATION FACTOR*

factor FIOXTBE 100, Formation function ofporosity. as 

0 IO * 10 CM

Nl 01 3AllD3dd3
ELECTRICAL PROPERTIES OF SANDSTONES 323

and formation factor of these fully saturated cores were determined 

as before.

In order to reduce the water content of the cores to partial saturations, groups of these cores were permitted to dry slowly in air. As 

evaporation progressed, the weights and resistances of the cores were 

measured at intervals of approximately 30 iniriutes. The resistivity 

was then calculated as in the previous expedients. The instantaneous 

water saturation of a core was determined from the equation:

where

8W is the water saturation expressed as a fraction of its maximum value, 

Wi is the instantaneous weight of a core during evaporation, 

s is the weight of sodium chloride in a core,

and

Wi and Wt are the weights of the dry core and core saturated with salt 

solution.

The amount of salt in a core is constant, so that as the water evaporates from the core, the salinity of the remaining water increases. 

Thus, the resistivity of the water decreases as the saturation decreases. 

In order to calculate the resistivity index, it is necessary to determine 

the instantaneous resistivity of the saturating water from tables. 

Then the resistivity index can be computed from the equation:

7=^--^ (9)

Pwi PlOO

where

pi is the instantaneous value of the core resistivity at the water saturation Sn, 

pwi is the instantaneous value of water resistivity at the saturation 8W, 

pw is the water resistivity before evaporation,

and

PIOO is the resistivity of the core at 100-percent water saturation.

A total of 387 measurements of / and Sw were made on 45 cores. 

The results of these measurements are summarized graphically in the 

table below and in figure 101. These data were treated statistically 

in the same manner as the data on formation factors. The data 

were divided into groups according to class intervals of water saturation. It was then assumed that in each class the values of the logarithm of resistivity index are distributed normally about some mean 

value. The mean values were calculated and are shown in figure 101.
324 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

The standard deviation and confidence limits of the data were also 

computed; but, because the data showed only negligible scatter, these 

computations are not shown on the graph.

Number of measurements

25 

39 

44 . ._ 

50 

38 

Average 

water 

saturation

H ii.<n

18.5

25.9

3d. 9

45.0

Average 

resistivity 

index

Ifc 117.0

30.7

13.2

7 4ft

4.36

Number of measurements

39 

46 

57 

49 

Average 

water 

saturation

54.4

65.8

79.4

91.4

Average 

resistivity 

index

3.33

2.31

1.67

1.26

The data fit equation 2 with the following constants:

/=

(10)

This equation agrees well with the results that have been obtained 

from measurements on a number of water-wetted oil-reservoir sandstones.

The influence of clay on resistivity was studied in a third group of 

45 cores by measuring formation factors at several different water 

salinities. Because some of these salinities were quite low, it was 

deemed necessary to remove the salt remaining in the cores from their 

original connate-water content more completely than was possible by 

the diffusion method. The cores were electrodialyzed to remove then* 

ion content.

In electrodialysis the cores are saturated with distilled water and 

placed in a tray containing distilled water. A direct current is then 

passed through the cores for a long period of time, in this experiment 

96 hours. This current causes ions in the cores to migrate to the oppositely charged electrode. The electrodes were carbon rods so that 

they themselves could not supply ions for current conduction. The 

electrodes were placed in porous alundum cups so that the water 

around the electrodes could be charged frequently and so that the 

migrating ions could be prevented from reaching an equilibrium stage 

in which the potential due to their concentration gradient would stop 

further migration.

Resistivity measurements on these cores after electrodialysis indicated that their ion concentrations had been reduced to the range of 

100 to 500 ppm equivalent sodium chloride salinity. This concentration probably was the lowest that could be obtained, as any clay 

present in the cores would account for that much conduction.

These cores were then saturated with a deaerated salt solution containing 1,875 ppm sodium chloride, using the same procedure. The 

volume of water taken by the cores and their resistances were meas-
ELECTRICAL PROPERTIES OF SANDSTONES 325

7

if

> 3

3; a

NI 'NOi'ivanivs
326 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

ured. Following this, the cores were dried and saturated a second 

time with a salt solution of 1,875 ppm sodium chloride. The cores 

were saturated for only a short period, about 30 minutes, so that the 

salt remaining in a core from the first saturation would not have a 

chance to diffuse into the external salt solution. In this way, the 

second salt solution when it entered the cores would take up the salt 

from the first saturation into solution, and result in a solution containing 3,750 ppm sodium chloride. This process was repeated to obtain 

saturations of 7,500, 15,000, 30,000, 60,000 and 120,000 ppm sodium 

chloride. Each time the cores were weighed both dry and saturated^ 

and the resistances measured.

Eesistivities were calculated from the resistance measurements, and 

these were used to determine apparent values of the formation factor 

corresponding to each water salinity. It was found that as the salinity 

of the saturating water increased, the formation factor increased to a 

maximum and then decreased slightly at very high salinities.

The data were treated statistically as before by dividing the cores 

into two groups: those with high porosities and those with low. The 

percentages that the formation factor at a given salinity deviated from 

the formation factor of the same core at the highest salinity was. 

calculated by the formula:

Percent deviation: (11)

where F0 is the formation factor of a core saturated with a brine of 

120,000 ppm sodium chloride, and F is the formation factor at any 

other salinity. It was then assumed that these deviations were 

normally distributed about some average value for each water salinity 

and for each porosity group. The average values were computed, 

as well as the 92-percent confidence limits of these averages; the 

results of the measurements and computations are shown in the table 

below and in figure 102. The deviations for the low-porosity cores 

are higher than those for the high-porosity cores, as expected. The 

negative deviations shown in figure 102 are unexpected, but they 

possibly arise from an increase in the viscosity of the brine-clay mixture 

in the cores over that range of salinity, or possibility from progressive 

errors in the water salinities during the repeated saturations.

Brine 

resistivity 

(ohm-cm)

6.7 _ ......

11.4 -. ......

20.0 ..

38.0 .-

Mean 

(l-£o )of!2 

cores in group 1

0.000

-.006

-.044

-.050

Mean 

(l-£)of33 

cores in group 2

0.000

-.018

-.030

Brine 

resistivity 

(ohm-cm)

ftn n

158.0 _

285.0

Mean («-*)«»

cores in group 1

-0. 193

-.321

.545

Mean 04,) °f33

cores in group 2

-0.065

-.024

.424
ELECTRICAL PROPERTIES OF SANDSTONES 327

^ Nl 

\

./

<o /

8.5 ?s2 * 

xl

<N it O ^i-L

« o

gl

2-S

**" Itt

U o S *

per mea

o 5

(j-l)OOl
328 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

It is evident that the data do not precisely fit the concept of the clay 

(or double-layer) conductivity electrically in parallel with the brine 

conductivity. The apparent salinity added to the brine in the core 

was calculated for several salinities and the results are given in table 2.

TABLE 2. Apparent salinities associated with clay conductance

Salinity of the saturating brine (ppm)

1,875... 

3,750.. 

7,600.. ...

15,000.. 

30,000...-..-

Equivalent salinity of 

clay (ppm)

Group 1 (low 

porosity)

3,700 

2,800 

2,500 

2,000 

-1,000

Group 2 (high 

porosity)

1,900 

1,300 

500 

-300 -200

SPONTANEOUS-POTENTIAL MEASUREMENTS

The measurement of the natural potentials existing in a fluid-filled 

drill hole was first described by the Schlumbergers and Doll (1934). 

They attributed the differences in potential that could be measured 

between adjacent sand and shale beds in a drill hole to a combination 

of diffusion and electrokinetic potentials. The diffusion potential 

was said to arise from a difference in ion concentrations between the 

fluid in the drill hole and the fluid in the rock and to obey Nernst's 

equation:

emf=Klog (12) 

where

K is a constant dependent on ion mobilities,

pm is the resistivity of the water in the drill hole, and

pw is the resistivity of the water contained in the rock around the drill hole.

The electrokinetic potential was attributed to the flow of the 

electrolyte from the drill hole past the solid surfaces of the sand 

grains as water is forced from the drill hole into the rock around it. 

This flow would give rise to an electrokinetic potential given by the 

equation (Wyllie, 1951):

emf=fcP» (13)

where P is the pressure differential between the drill hole and the 

rock, and k and y are constants dependent on the nature of the 

moving fluid and the properties of the solid surface along which the 

fluid is moving.

Unfortunately, even when this streaming potential can be taken 

into account, the remaining potential is usually too large to be 

explained by the Nernst equation. Only recently has a satisfactory 

explanation been given for the mechanism involved in the generation
ELECTRICAL PROPERTIES OF SANDSTONES 329

of the diffusion potential in clay-bearing rocks. McCardell, Winsauer, 

and Williams (1953) have studied the diffusion potential arising when 

there is a concentration gradient in the presence of a distributed 

surface charge, or when there is a gradient in the distributed charge 

itself.

In an idealized pore the clay particles lining the pore have a negative 

charge represented by the small circles in figure 98 in the clay 

lattice positions vacated by cations during dissociation. This negative charge on the clay particle attracts an equal number of positive 

ions in the surrounding solution. As a result, when there is an 

equilibrium distribution of charge, there are more cations than anions 

in solution in the vicinity of the clay. If there is a large amount of 

clay, then the brine throughout the pore will be richer in cations 

than in anions by a number equal to the charge of the clay.

Where such a clay-bearing rock is in contact with an external 

solution, there is a difference of cation concentration between the 

brine in the rock and the external brine. This gives rise to a phaseboundary potential, the magnitude of which is given by the equation 

(McCardell, Winsauer, and Williams, 1953):

where

k is Boltzman's constant, T is the absolute temperature,

E is the ionic charge (one for sodium chloride),

no is the ion concentration in equilibrium with the clay charge, and

n is the ion concentration in the free solution at some distance from the clay*

In addition to this phase-boundary potential that exists when the 

anion concentration is the same in the internal and external solutions, 

there is a diffusion potential when there is an actual difference in 

salinity of the internal and external solutions. This potential is 

given by an equation similar- to that of Nernst (McCardell, Winsauer, 

and Williams, 1953):

kT ui 1*9,

 =- 

c W -TM2 Ml »A (15)

where

jui is the cation mobility,

jua is the anion mobility,

nB is the concentration of the concentrated electrolyte, and

nA is the concentration of the dilute electrolyte.

In practice, the quantity no will be large for shales or muds tones, in 

which all the pores are clay lined, and small for sandstones with little 

or no clay. As a result, the phase and diffusion potentials will differ
330 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

between sandstones and mudstones. This difference in potential will 

cause current to flow along the drill hole, and the ohmic drop in 

potential due to this current flow is recorded as a deflection on the 

spontaneous potential log as the inhole electrode passes a sandstonemudstone contact.

Under ideal logging conditions the spontaneous-potential deflection 

between sandstones and mudstones should be a function of only three 

variables: the salinity of the water in the drill hole, the salinity of the 

connate water, and the equivalent salinity immobilized by the clay. 

The salinity of the water hi the drill hole is a readily measurable 

quantity; so the spontaneous-potential log can be used to calculate 

the connate water salinity when n0 is known or can be estimated.

With this possibility in mind, the potentials across cores in contact 

with brines of two different salinities were measured. The cores used 

in these measurements were prepared in the same manner as those 

used in the resistivity experiments, and the porosities and formation 

factors were determined. The cores were then saturated with a solution contaning 60,000 ppm sodium chloride.

These cores were coated with paraffin to prevent evaporation of 

their water content during the experiments. Two small holes in the 

coating on opposite sides of the cores permitted access of the external 

brine solutions. To make a measurement, a core was placed hi the 

clamp (fig. 103), from which tubes extended to two brine reservoirs 

containing lead-lead chloride electrodes so that the brines could be 

brought in contact with opposite sides of the core. A solution with a 

salinity of 60,000 ppm was placed in one reservoir, and a solution 

with a salinity of 600 ppm was placed in the other. The potential 

between the two lead-lead chloride electrodes was amplified with a 

d-c amplifier that had an input resistance of 10 megohms. The output of this amplifier was registered on a d-c voltmeter, and the recording system was calibrated at frequent intervals with a known 

voltage.

The potential developed in the cell was observed for a period of 30 

minutes to 2 hours so that an equilibrium value might be determined. 

It was observed that the potential had a nonzero value as the brines 

were first brought in contact with a core, and that within a few seconds 

the potential reached a maximum; the saline solution was negative 

with respect to the dilute solution. Following this, the potential 

changed sign and approached a positive value asymptotically over a 

period of approximately 1 hour. For very porous cores the potential 

approached a positive maximum and then decreased, probably 

because of a change hi the salinity of the brines in the reservoirs by 

rapid diffusion.
ELECTRICAL PROPERTIES OF SANDSTONES 331

Tank containing 600 ppm sodium ctilotiJe

Binding post

Uod electrode ceatej 

with lead cfllorife

Drain plug

FIGURE 103. Measurement of diffusion potentials of cores. A, Device used in measuring. B, Circuit

components.

In order to eliminate the effects of electrode polarization at the two 

lead electrodes, the potential across an alundum membrane was 

measured. The difference between this potential and the theoretical 

potential for the experimental conditions was subtracted from each of 

the other measurements.

The asymptotic value of potential was then used to calculate apparent values of the immobilized double-layer concentration according 

to equations 14 and 15. The results of these measurements and computations are presented in figure 104 in which UQ has been plotted as a 

function of porosity.

These data show that n^ varies from 40 to 56,000 ppm for the cores 

studied, all sandstone specimens. There is no pronounced relation 

between HQ and porosity, except at low porosities. At porosities 

greater than 10 percent an average value for nQ is 1,500 ppm. These 

values of n^ were then used to determine the relation between the 

deflection recorded on the spontaneous-potential logs taken in the 

Spud Patch area and the connate-water salinity.

In spontaneous-potential logging, a single electrode is raised through 

the drill hole, and its potential is measured with respect to a reference
7 10

_ 

01 O

ro <j\

H

2

o20 

tr. , UJ I Q- r

POROS O

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

100 1000 10.000______100,000

30

25

20

15

10

10 100 1000 10,000 IOO,OOO 

/70=ION CONCENTRATION IMMOBILIZED IN DOUBLE-LAYER, 

IN PARTS PER MILLION

FIGURE 104. Ion concentration immobilized in double layer as a function of porosity.

electrode at the surface. In interpretation, the deflection of this 

curve between a sandstone at depth A and a mudstone at depth B is 

measured. This deflection is equivalent to the voltage that would be 

measured between a pair of electrodes at A and B, The voltage is 

caused by the current flowing through the three media: the water in 

the drill hole, the sandstone, and the mudstone. The current arises 

from three phase-boundary potentials and two diffusion potentials 

if it is assumed that there is no diffusion between the sandstone and 

^the mudstone. A current tube, idealized to a considerable extent, 

is shown in figure 105 to indicate where each of five potentials exists. 

The sum of the five is given by:

SP= (16)

where Ed and Ep are the diffusion and phase potentials respectively 

between the pairs of media represented by the numerical prescripts. 

In terms of ion concentrations, these potentials would be:
ELECTKICAL PROPERTIES OP SANDSTONES 333

A*2 M2 0«2

(17)

where

ni is the concentration of the anions in the internal electrolyte of the sandstone and mudstone,

ona is the mobilized-ion concentration in the mudstone, 

o»2 is the immobilized ion concentration in the sandstone, and 

HZ is the ion concentration in the external solution filling the drill hole.

:=-=? Shale or mudstone

Total voltage in circuit«SP= ,/p + l

FIQUSE 105. Schematic representation of the sources of potential variations measured in electric logging.
334 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

I_L

O §

o s

O 

00

8 !

(S> a

-s!

O ^ £ 

Q ^ |

^ 1

o _Jg

O < i

Z § g o 3

(~\ UJ « "3

o^^ X % "

C£) y g

oo o o

OQ O O

Q.Q. Q. Q.

o ° o o

3:8 ^ «

Q. Q.

o o

cvj 

IO o

<M

o

S o

o *

IV NOmiW B3d SlHVd Nl 

<lN31VAin03 IQDN 'A1INHVS d31VM-31VNNOO
ELECTRICAL PROPERTIES OF SANDSTONES 335

This equation was evaluated for the two extreme ranges of conditions to be expected for the logging conditions at Spud Patch:

1. Salinity of the water in the drill hole, n\, was assumed to be approximately 150 ppm, close to the salinity determined by resistivity 

measurements on a sample of water from Bell Canyon Reservoir.

2. The immobilized concentration in the sandstone, On2, was assumed 

to be between the limits zero and 1,500 ppm.

3. The immobilized concentration in the mudstone, On3 , was assumed 

to be between the limits 150,000 and 75,000 ppm.

4. A range in connate-water salinity from 1,000 to 240,000 ppm was

considered.

The spontaneous-potential deflections that would be recorded for 

this range in conditions are included as the shaded area in figure 106. 

On the basis of present information, the best estimate of the relation 

between spontaneous potential and connate-water salinity may be 

that given by the dashed line on this graph. This line was drawn on 

the assumption that the largest recorded spontaneous potentials would 

probably be associated with the most porous sandstones, which had 

undergone the most evaporation and in which the salinity of the connate water would be high and the amount of clay low.

CORRELATION OF LABORATORY AND FIELD DATA

The measurements on the cores were made to provide a basis for 

the quantitative interpretation of electric logs in terms of porosity 

and water content. If we assume that the constants in the empirical 

equations obtained in these experiments are generally valid and that 

the effect of clay on resistivity and spontaneous potential can be 

ignored or estimated, then there remain three unknown variable 

quantities: porosity, water saturation, and water salinity. Only two 

measurements are available hi the field data for the determination of 

these three factors, so that the problem would seem to be indeterminate.

One hope of determining these quantities from the field data lies 

in the possibility of finding a natural relationship between them 

that is, to find that they are not independent variables. It is possible 

that the sandstone members of the Morrison formation were at one 

time saturated with a connate water of uniform salinity. It is likely 

that the Morrison formation has been dehydrated to some extent in 

the areas in which these studies were carried out, because it is close 

to the surface and frequently crops out on mesa runs. The present 

values of water saturation, resistivity, and natural potential of the 

sandstone should be interrelated.
336 EXPEKIMENTAL AND THEORETICAL GEOPHYSICS

The resistivity of the sandstone around a drill hole at the time of 

electric logging is:

pr=0.62pu, r^2 -10<Sfw-1 -92 (18) 

where

pW)> is the resistivity of the connate water at the time of logging, 

Sw is the water saturation, and

<t> is the porosity, restricted to the limits 14 percent to 25 percent and with 

Sw greater than 25 percent.

If the present connate water is a remnant of an original connate 

water of resistivity pwt that has evaporated without the removal or 

addition of salt, then the present water resistivity is a function of the 

present water saturation and the original water resistivity:

(19)

This relationship is valid for a temperature of 20°C and is accurate 

within 5 percent over the range from 100 to 100,000 ppm.

By using this relationship, one unknown quantity can be eliminated 

from equation 18, and

This can be written as:

In addition, the resistivity of the connate water is related to the 

spontaneous potential by equation 17, which can be expressed simply

(22)

Pv> r/

where pm is the resistivity of the water in the drill hole and K varies 

from 35 for low porosities to 70 for high porosities and salinities and 

represents the influence of the various factors involved in equation 17. 

By combining equation 21 with equation 22, the following is obtained:

log constant-log pr<^-'°=1.02 +log P« (23)

Thus, the equation for the resistivity of the sandstone members of 

the Morrison formation has been reduced to a form in which there are 

only two quantities not measurable in normal logging routine: the 

porosity and the spontaneous-potential coefficient K. However, 

the coefficient K can be predicted within reasonable limits, as indi-
ELECTRICAL PROPERTIES OF SANDSTONES 337

cated by figure 106. This means that porosity is determinable from 

electric-log data if the initial assumptions of a constant water salinity 

and consequent evaporation are correct.

To test this hypothesis, the quantity pr<f>2, determined from the 

resistivity log and core analysis, was plotted as a function of the 

spontaneous-potential deflection for each of the six drill holes from 

which cores were studied (pi. 10). For all six holes, there is a trend 

recognizable in the data that indicates that there is at least some 

truth in the original assumptions.

The considerable scatter apparent in these data is probably not 

all caused by the shortcomings of the original hypothesis. There 

are other sources of error that almost certainly contribute considerable 

deviations. Among these is the error involved in matching the core 

depths with depths on the electric log, so that the correct values of 

resistivity and spontaneous potential can be read.

Another major source of error is the inability of determining 

accurately the resistivity of thin layers by a logging arrangement. 

The apparent resistivity recorded on the log may be larger or smaller 

than the true resistivity, depending on the resistivities of the adjoining 

strata. The single-point log was the most sensitive device used, but 

it was also the most subject to errors from variations in the resistivity 

of the water in the drill hole. Single-point logs of adequate quality 

for use in these correlations were available for only two of the six 

wells under consideration: SP-131 and SP-284. For the other four 

drill holes, the 8-inch normal-spacing resistivity log was used because 

it was a compromise of the large disturbing effects of the water in 

the drill hole on the log with 4-inch spacing and the large disturbing 

effect of bed thickness on the log with 24-inch spacing.

There may also be errors because the properties measured on the 

individual core are not representative of the material around the 

drill hole that controls the response of the electric logs. The laboratory 

measurements were made on a specimen of core of approximately 

1 cubic inch in, but the resistivity measured in the electric logs is the 

average resistivity of a minimum of 1 cubic foot of material around a 

drill hole. The degree to which this difference is the source of the 

scatter in the correlation diagrams of plate 10 is a measure of the 

inch-to-inch variation of the physical properties of sandstone.

In a number of drill holes, four samples had been cut from cores over 

a 6-inch depth interval. Measurements of porosity and formation 

factor had been made on all these cores, and the data were used to 

compute the variance of the averages for each group. The variance 

for any one group is given by the equation:

4 4

(24)

1 1
338 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

where 0 is the variance or square of the standard deviation. The 

value computed from this equation is not the variance of the actual 

data, but a best estimate of the variance of the population from 

which the data are a subsample. Forty-one values of this best 

estimate of variance were computed; the highest values were those 

for the groups of cores of low average porosity. The results of these 

computations are shown in figure 107 in which the standard deviation

2 roil

20 30

STANDARD DEVIATION -v 1M 

AVERAGE POROSITY

FIGXJBE 107. Summary of data on the inch-to-inch variations of porosity in sandstone cores.

is expressed as a percentage of the average porosity. This graph 

shows for a given porosity how closely a single value of porosity 

measured on a core represents the average porosity of the bed from 

which it came. It is obvious that the limits of error are quite wide. 

Because of the magnitude of these different sources of error, it is 

likely that the correlations indicated in plate 10 are considerably 

better than the scatter of the data would lead one to believe. In 

order to find the relationship indicated by these correlations, it is
ELECTRICAL PROPERTIES OP SANDSTONES 339

necessary to use the same statistical approach used earlier on the 

core data.

The absolute range of the variables plotted in plate 10 varies 

considerably from dill hole to drill hole, so that the data from the 

several drill holes cannot be compared directly. In order to normalize 

the data from all the drill holes to the same scale, the variables SP 

and p<j>2 were expressed as percentages of their maximum values in 

each drill hole.

The data were grouped in classes according to the value of the 

quantity (p<£2/maxp<£2), and it was assumed that for each class the 

values of SP/Maximum SP are normally distributed about a mean. 

The average was computed, and the standard deviation of the values 

of SP/Maximum SP for each class of p02/maxp<£2 determined. The 

65 percent confidence limits were calculated for both individual values 

of the data and for the mean values of SP/Maximum SP. The results 

are shown in figure 108 in which the horizontal scale is logarithmic 

and the vertical scale is doubly iterated logarithmically.

The data are also presented in tabular form on figure 108, and the 

standard deviation of the average porosity corresponding to each 

plotted mean is listed. This standard deviation indicates the minimum part of the scatter of the data that can be attributed to nonrepresentative values of porosity.

Average values of the spontoneousypotentiol (unction 

with 65;percent confidence limits

65-percent confidence limits on Individual 

values of spontaneousTpotenf ial {unction.

FIQTJEE 108. Empirical relationship between porosity, electric-log resistivity and spontaneous-potential

deflection.
340 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

The conclusion is that there is a significant correlation between the 

electric-log data and the core data, and this correlation supports the 

hypothesis that sandstones of the Morrison formation were originally 

fully saturated with a water of uniform salinity and that the present 

salinity of the connate water is a result of the evaporation of this 

original water without removal of salt by circulating ground waters.

m QUANTITATIVE INTERPRETATION OF LOGS

The correlation of the core data with the electric-log data indicates 

that porosity can be determined directly from electric-log data. Once 

porosity is determined and the salinity of the water is found from the 

spontaneous-potential log, it is possible to calculate the water saturation from the resistivity log.

Such an interpretation was attempted on logs of the Salt Wash 

member of the Morrison formation in 44 drill holes in the Spud Patch 

area. The procedure was as follows:

1. The maximum values of resistivity and spontaneous potential were 

read directly from the logs.

2. The average values of resistivity and spontaneous potential were 

determined by planimetering the areas between the respective 

logs and their baselines. These areas were divided by the thickness of the logged section to give average values.

3. The average porosity was determined by forming the ratio SP/ 

maximum SP and determining the corresponding value of P<£2/ 

max. P<£2 from figure 108. The average porosity was determined 

by assuming a maximum porosity of 22 percent, corresponding 

to the maximum resistivity.

4. The average connate-water salinity was determined from the average spontaneous potential, by using figure 106.

5. The average water saturation was determined by dividing the average resistivity from the electric log by the resistivity of connate 

water determined above. This average salinity was corrected 

for the influence of clay by using the data in figure 102. The 

water saturation was then computed from equation 18.

6. The apparent salinity of the original brine saturating the sandstone 

was estimated by calculating the dilution of the average water 

salinity necessary to fill the pore space completely. 

The results of these interpretations are presented in table 3 as 

average values for the several classes of favorability to which the drill 

holes belonged.

Table 3 gives an idea of the physical properties associated with 

favorability that result in the apparent correlation of resistivity with 

occurrence of ore. There is no correlation between spontaneous
ELECTRICAL PROPERTIES OF SANDSTONES 341

potential and favorability for ore occurrence. Large- and smallamplitude spontaneous potential curves are obtained in drill holes in 

both favorable and unfavorable ground, and the spontaneous-potential 

measurements are the same for favorable and unfavorable holes, as 

shown in table 3.

The salinities that were calculated from these spontaneous-potential 

measurements are in terms of sodium chloride as the ionized salt. 

It is likely that the salinity is due to some other salt, such as calcium 

bicarbonate. If this is so, the equivalent sodium chloride salinity is 

not the same as the actual salinity in a different salt. If that salt is 

calcium bicarbonate, then the equivalent sodium chloride salinity is 

about one-half the actual salinity.

TABLE 3. Results of the quantitative interpretion of electric logs

Favorability class

Maximum SP average for drill holes of each class _____ mv._

Average SP (mv) average for drill holes of each class... .mv 

Corresponding water salinity (ppm) ____ . __ __ ppm 

Maximum resistivity (ohm-m), average for drill holes for each class 

ohm-m 

Average resistivity (ohm-m), average for drill holes of eaeh class 

ohm-m _

Average water saturation (percent) _____________ percentMinimum water-saturation average for drill holes of each class 

percentOriginal water salinity before evaporation.. _________ ppm.. 

Product of sandstone thickness and average resistivity ohm-m-ft 

Favorable

24

66.4 

6400

38.9 

3050

423

230 

19.1

43

21 

1310 

16400

Semifavorable

12

28.6 

2100

16.7 

1300

385

203

18.2

57

32 

740 

13300

Unfavorable

8

64.4 

6100

36.2 

2730

338

180 

18.1

53

32 

1450 

7710

The calculated average porosities seem to vary with favorability, 

as evidenced by the decrease in prosity for the less favorable drill 

holes. The saturations, however, show a more pronounced variation 

from drill holes in favorable ground to those in unfavorable ground. 

Saturation seems to be the property which causes the correlation of 

resistivity with favorability: that is, the saturation seems to be 

reduced most in the drill holes that are most favorable for the 

occurrence of ore.

When the salinities are calculated on the assumption that the 

connate water is diluted to 100 percent of the pore space in all but 

three of the drill holes, they fall in the range 650 to 1,800 ppm equivalent sodium chloride. The three exceptions, which fall far out of 

this range, are between 3,500 and 6,500 ppm.

USE OF ELECTRIC LOGGING IN EXPLORATION t

Studies of the magnitude and extent of electrical anomalies that 

may be associated with occurrence of ore on the Colorado Plateau 

have shown that there is an increase in the average sandstone resis-
342 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

tivity and a large increase in the product of resistivity and sandstone 

thickness in the areas that are most favorable for ore occurrence. 

Anomalously high resistivities are apparent in many drill holes in 

mineralized ground, but in general these anomalies are too small in 

extent to be detectable by surface-resistivity measurements.

A contour map of the product of resistivity and sandstone thickness has indicated that the dimensions of favorable areas are of the 

order of one to several thousand feet, at least in the area studied. 

If this is so generally, it would be expected that, even with ideal 

conditions in the overlying beds, the variations in resistivity of the 

ore-bearing member at depths of 500 feet, would not be detectable 

by surface-resistivity measurements, as Wenner electrode spacings of 

1,000 feet and more would be required; and with these large spacings 

no single resistivity sounding could be made with the electrode 

arrangment entirely within the favorable area.

Electric logs, however, are capable of giving much of the information that is obtained by visual examination of cores. The electric 

log is particularly suited to the differentiation of sandstone from 

mudstone and should give a more reliable distinction between the 

two than is possible from core inspection.

Mudstone exhibits a minunum on the resistivity log and a maximum (deflection to the right) on the spontaneous-potential log. 

These minimum and maximum deflections are referred to by the 

term "shale baseline" by convention.

Because the Morrison formation is composed of mudstones and 

sandstones, any deflection to the right of the resistivity baseline 

accompanied by a deflection to the left of the spontaneous-potential 

baseline can be attributed to the presence of a sandstone at that 

depth. Small deflections correspond to shaly sandstone and large 

deflections correspond to relatively pure sandstone. Deflections of 

only one curve from its base line are usually caused by changes in the 

salinity of the water in the drill hole rather than by lithologic changes.

The identification of mudstone and sandstone from the electric log 

is usually the same as that from visual examination of the core. However, there may be some disagreement where there is a gradational 

contact between sandstone and mudstone which makes it difficult to 

separate the two visually. Under these conditions the electric log 

may be superior to the actual examination of the core, as it provides 

a physical basis for the division between the two strata.

On the other hand, the electric log cannot give information on 

color and the presence of vanadium minerals or of certain accessory 

minerals that are factors used by the geologist in determining favorability. However, the electric log may be able to provide an index
ELECTRICAL PROPERTIES OF SANDSTONES 343

of favorability which is comparable in reliability determined by 

geologic guides to ore.

The advantage of electric logging is that when combined with 

radioactivity logging it will give most of the information necessary 

in the exploration for ore at a lower cost than coring and examination 

of cores. In addition to reduced drilling costs, the time required to 

interpret a group of electric logs in the office would be much less than 

the time required to examine core at a group of drill holes, with 

resulting economy.

The utility of the electric log is not limited to the determination 

of information now obtained from cores; it is also capable of giving 

additional information, such as porosity and water saturation, which 

may be of value in the future. If production from the deeper Morrison deposits should become practical, it would be necessary to know 

porosities and water saturation for proper production practice. It 

has been found in oil-field practice that the determination of such 

properties from the electric log is more reliable than core analysis, as 

electric-log data give an average value representative of the rock in 

place. Core analysis is subject to the errors caused by the inch-toinch variation in physical properties described in this report.

In the petroleum industry the electric log has become an indispensible tool for the determination of the textural properties of the 

rock in place in a drill hole. There is reason to believe that the electric log may be valuable in the evaluation of the strata penetrated by 

exploratory drilling here also.

The electric logs can be used not only to identify different lithologic units but to correlate such units between neighboring drill holes. 

Correlation of very small sandstone units is possible where drill holes 

are on a 50-foot spacing. Correlation between more widely spaced 

drill holes must necessarily be less detailed.

REFERENCES CITED

Fischer, R. P., 1942, Vanadium deposits of Colorado and Utah, a preliminary

report: U.S. Geol. Survey Bull. 936-P, p. 363-394. 

Keller, G. V., 1953, The role of wettability in the electrical resistivity of sands:

Oil and Gas Jour., v. 51, no. 35, p. 62-65.

McCardell, W. M., Winsauer, W. O., and Williams, M., 1953, Origin of the electric potential observed in wells: Am. Inst. Min. Met. Eng. Trans., v. 198,

p. 41-51. 

Schlumberger, C., Schlumberger, M., and Doll, H. G., 1934, A new contribution

to subsurface studies by means of electrical measurements in drill holes:

Am. Inst. Min. Met. Eng. Trans., v. 110, p. 273-289. 

Wen-, D. B., 1952, Geologic guides to prospecting for carnotite deposits on the

Colorado Plateau: U.S. Geol. Survey Bull. 988-B, p. 15-27.
344 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Winsauer, W. O., and McCardell, W. M., Ionic double layer conductivity in 

reservoir rock: Am. Inst. Min. Met. Eng.; paper presented at the Los Angeles 

meeting, Petr. Branch, October 1952.

Winsauer, W. O., Shearin, H. M., Masson, P. H., and Williams, M., 1952, Resistivity of brine saturated sands in relation to pore geometry: Am. Assoc. 

Petroleum Geologists Bull., v. 36, p. 253-277,

Wyllie, M. R. J., 1951, An investigation of the electrokinetic component of the 

self potential curve: Am. Inst. Min. Met. Eng. Trans., v. 192, p. 1-18.

O
Experimental and Theoretical 

Geophysics

GEOLOGICAL SURVEY BULLETIN 1052

This volume was printed as 

separate chapters A-J

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON \ 1959
UNITED STATES DEPARTMENT OF THE INTERIOR 

FRED A. SEATON, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director
CONTENTS

[Letters In parentheses designate the separately published chapters]

Paw

(A) Scattered gamma rays from thick uranium sources, by A. Y; Sakakura. 1

(B) Three-dimensional heat conduction in permafrost beneath heated

buildings, by Arthur H. Lachenbruch.____ _ _____ 51

(C) Infrared luminescence of minerals, by David F. Barnes___ 71

(D) Magnetic-doublet theory in the analysis of total-intensity anomalies,

by Roland G. Henderson and Isidore Zietz _ __ 159

(E) Physical behavior and geologic control of radon in mountain streams,

by Alien S. Rogers..________________________ 187

(F) Scintillation counters for geologic use, by W. W. Vaughn, V. C.

Rhoden, E. E. Wilson, and Henry Faul_______________. 213

(G) A comparison among caliper-log, gamma-ray log, and other diamonddrill-hole data, by C. M. Bunker and H. C. Hamontre__ ______ 241

(H) Dielectric constant and electrical resistivity of natural-state cores,

by G. V. Keller and P. H. Licastro_______________-_._ 257

(I) Equation of continuity in geology with application to the transport 

of radioactive gas, by A. Y. Sakakura, Carolyn Lindberg, and 

Henry Faul_________________________ 287

(J) Electrical properties of sandstones of the Morrison formation, by

George V. Keller____________---_-----_ __--_ -- . 307

(HI)