DETERMINING POROSITY WITH NEUTRON LOGS

FROM HAWAIIAN BASALTIC AQUIFERS

by

Frank L. Peterson Man Mohan Sehgal

Technical Report No. 80

August 1974

Project Completion Report of

CALIBRATION TECHNIQUES FOR RADIATION WELL LOGGING IN HAWAII

OWRT Project No. A-034~HI, Grant Agreement No. 14-31-0001-3811 Principal Investigator: Frank L. Peterson

Project Period: July 1, 1972 to June 30, 1973

The programs and activities described herein were supported in part by funds provided by the United States Department of the Interior as authorized under the Water Resources Act of 1964, Public Law 88-379.

ABSTRACT

Neutron count data for calibration purposes ~ere collected

by neutron logging in 4 boreholes~ and porosity data ~ere deter­

mined from photo logs run on the same 4 boreholes. A neutron

count-porosity calibration curve was constructed and ~as found

to take the form of the logarithm of n~dtron count versus poros­

ity. The calibration cUPVe ~as calculated by linear regression

analysis~ utilising empirical field data. The calibration curve

is valid ~thin the expressed 95 percent confidence intervals

only for neutron logs from (1) basaltic formations~ (2) uncased

hole8~ and (3) borehole diameters from 20.32 to 30.48 em (8 to

12 in.).

iii

v

CONTENTS

I NTRODUCT I ON ............ III •••••••••••••••••••••••••••••••• III ••••••••••• III ••••••••• 1

Background of Study it III ... III ••• III III III • III III III III III III III • III • III III III III III III III III III III III • III III III III • III III III • III III • III •• III III •• 1

Object; ve III III • III • III III III •• III III .. III III III III • III • III III III • III III III • III III • III III III III III III III III III •• III III III III • III •• III III III III • III ••• III III III III 2 Conduct of Study III III III III .. III III ...... III e III .. III III III III III .. III III ... III III ; .. III .. III .... III • III ......... III ........... III III ....... III .. 2

DISCUSSION OF CALIBRATION METHODS .........••...•............•.•..........•. 2 Neutron Curve-Poros i ty Re 1 at ions ...•••..•••••..•.•..•••....•••..••....•. 2 Empiri cal Cal ibrati on Methods ........................................... 5 Laboratory Cal ibration Methods .......................................... 6

CALIBRATION CURVES FOR HAWAIIAN BASALTS .....•....•..........•.•......•..... 7 Selection of Calibration Methods ........................................ 7 Porosi ty Determi nati on from Photo logs ................................... B Neutron-Porosity Calibration Curves .................................... 10

LIMITATIONS AND RECOMMENDATIONS .......•.•..••.....••.•....••..•..•.•...•.. 24 Limitations ................................................................. 24 RecoRDTIendati ons .. III ....................... III III .................... III .......................... III .............. III III ........ 25

ACKNOWLEDGMENTS .... III III ••••••••••••••••••••••••••••••••••••••••••••••••••••••• 26

REFERENCES ...•...•....•.........••....•.••...••....•....•.......••..•..... 27

APPENDIX ....•.•••....•..................•...•.•..........•............••.. 29

FIGURES

1a Photograph of a dense zone with 5 percent porosity •.........•••...•••. 9 1b Photograph of a deeply caved zone with 100 percent porosity ..•.••..... 9 2 Neutron count-porosity data for 2-foot depth intervals from

Well SBE ...............................•...•.....•................... 11

3 Neutron count-porosity data for 2-foot depth intervals from Well T86 ........•.......•..•...•..••..••....•.......•..•.•.......••.• 12

4 Neutron count-porosity data for 2-foot depth intervals from We 11 7 A •••...•••....•....••....••.•..••....•••..•••.•.•••••.•••.•..•• 13

5 Neutron count-porosity data for 2-foot depth intervals from Well T 143 ............................................................ 14

6 Logarithm of neutron count-porosity regression curves •...••.•.......• 1B 7 Neutron count-porosity regression curves ...••.••.......•........••.•. 19

vi

8 Neutron count-logarithm porosity regression curves ................... 20 9 Logarithm of neutron count-logarithm porosity regression

curves ...................................................................... 21

10 Neutron count-porosity calibration curve with 95 percent confi dence be 1 t ............................................. ., ................. 23

TABLE

1 Summary of coefficients for logarithm of neutron count-porosity regress;on curves .................................................................................. 15

INTRODUCTION

Background of Study

The principal aquifers in the Hawaiian Islands are comprised of ex­

tremely permeable and porous basalts in which fresh groundwater bodies

occur as Ghyben-Herzberg lenses. The permeability and porosity of the

aquifers are subject to frequent local deviations and can be best described

as extremely anisotropic and nonhomogeneous. Consequently, it has long

been desirable to develop a method of obtaining reliable quantitative esti­

mates of porosity and potential water yield on a depth-integrated basis.

In 1966, in order to determine the applicability of conventional

electric and geophysical well logging methods for use under Hawaiian

groundwater conditions, the University of Hawaii Water Resources Research

Center initiated a comprehensive study of electric well logging and other

geophysical well logging techniques in Hawaii. The functions logged in the

geophysical well logging study included spontaneous potential, resistivity,

temperature, conductivity, and hole diameter.

1

The logging study indicated that the interpretation of spontaneous

potential and resistivity logs from the few wells in Hawaiian sedimentary

rocks is similar to interpretation of logs from continental sedimentary

aquifers. However, the interpretation of spontaneous potential and resis­

tivity well logs in Hawaiian basalts, which constitute most of the aquifers,

is unusual because of the relatively uniform chemical composition of the

basalts, the complex relation of porosity to resistivity in basaltic aqui­

fers, and because logging usually is performed in water-filled boreholes.

Consequently, accurate quantitative determinations of aquifer porosity and

water yield have not been possible from the results of electric well logging

(Lao, Peterson, and tox 1969, pp. 55-59).

Because various types of neutron logs are highly sensitive to hydro­

'gen, and under saturated conditions provide a measure of formation porosity,

it was decided to apply neutron borehole logging techniques to Hawaiian

aquifers. In 1970-71, with financial support from the Honolulu Board of

Water Supply and the Hawaii State Division of Water and Land Development,

investigation of neutron borehole logging in the Hawaiian environment was

initiated. In 1971-72, with continuing support from the above two local

agencies plus OWRT support (Project No. A-032-HI), the neutron logging

2

study was continued. Results of this investigation have been published in

the Water Resources Research Centerts Technical Report No. 75 (Peterson

1974).

Objective

The objective of this project is to prepare neutron count-porosity

calibration curves for borehole neutron logs collected from wells in Hawai­

ian basaltic aquifers.

Conduct of Study

The investigation on which this report is based occurred during 1972-

73, with financial support from OWRT and technical field support from the

Honolulu Board of Water Supply. During this time, work consisted of two

parts; (1) continued field data collection, and (2) construction of

porosity-neutron count calibration curves.

Field logging work by the Water Resources Research Center ceased during

the summer of 1973 after a total of 18 wells had been neutron logged, all

on the island of Oahu. It is planned that once the Honolulu Board of Water

Supply obtains an Atomic Energy Commission radioactive materials use li­

cense, the neutron logging equipment will be transferred to the Board of

Water Supply for routine logging operations and maintenance. The Water Re­

sources Research Center will retain title to the source and basic equipment

for future research use.

Porosity-neutron count caiibration curves were prepared by a

correlation-regression analysis technique utilizing neutron log data and

porosity data from 4 different wells. The porosity data were obtained from

photographic surveys conducted previously in the 4 wells by the Honolulu

Board of Water Supply.

DISCUSSION OF CALIBRATION METHODS

Neutron Curve-Porosity Relations

In the neutron logging method, the recorded neutron curve is the

response of a neutron counter to bombardment by high-energy neutrons of the

formations penetrated by a borehole. This neutron curve is highly sensi­

tive to the amount of hydrogen around the sonde and, thus, in saturated

3

fonnations, provides a means of detennining porosity. In neutron-porosity

logging, the parameters of primary interest are the various formation charac­

teristics which control the distribution of porosity in the formation.

However, there are a number of additional factors which complicate the

application of the neutron curve for the measurement of porosity. Peterson

(1974, p. 12) listed the following factors which complicate neutron logging

in Hawaiian wells: (1) borehole effects, including borehole diameter and

casing diameter and thickness; (2) reservoir rock and fluid effects, in­

cluding rock density and chemistry, formation thickness, formation porosity

distribution, and borehole fluid characteristics such as density, chemistry,

salinity, temperature and fluid level; and (3) instrumental and logging

effects, including probe dimensions, source strength, probe eccentricity

during logging, and logging speed and direction.

A factor of fundamental concern in all neutron logging investigations

is the so-called "radius of investigation." The depth of penetration of

neutrons from any given neutron source into a fonnation is governed by the

formation lithology, the porosity, and the hydrogenous nature of the sub­

stances in the pore spaces. According to Pirson (1963), in dry consolidated

rock of low porosity, each neutron undergoes several hundred collisions

before it is thermalized. In such rocks (quartzite, tight limestone or

dolomite) this may occur several feet away from the source, and the average

straight-line distance is about 60.96 cm (24 in.). However, in high poro­

sity rocks rich in hydrogen, thennalization can occur in, say, 25 colli­

sions, within less than a foot. from the source, and only 17.78 cm (7 in.)

on the average. Furthennore, experiments by Barsukov (1965) show that when

a neutron sonde is surrounded- in all directions by a layer of water greater

than 35 cm (13.8 in.), it is practically incapable of reacting to any change

in formation moisture and produces readings which correspond to 100 percent

moisture in the medium.

Consequently, a factor which may cause serious complications in neutron

curve-porosity detenninations is borehole diameter ..... Owing to the greater

moderating effect of water in larger boreholes, the neutron count should be

smaller. It is normal practice to represent neutron-porosity calibration

curves as a family of parallel curves on a semilogarithmic plot, with a

different curve representing each different hole diameter (for example, see

Brown and Bower 1958). However, as described by Peterson (1974) and as

4

illustrated in a later section of this report, the borehole diameter effect

appears to be small and somewhat inconsistent in Hawaiian wells. Peterson

(1974) has suggested that a possible explanation for the apparent lack of

borehole diameter effects in Hawaiian wells results from the relationship

between nominal and actual borehole diameter. Most Hawaiian wells are cased

only in the upper portions, and in the uncased portions, due to caving of

clinkers and other permeable zones, actual well diameters often vary signi­

ficantly from nominal well diameters.

In addition to borehOle diameter effects, another factor of significance

is the position of the logging sonde within the borehole. If the logging

sonde were always centered in the borehole during logging, the effects of

borehOle diameter changes would be accentuated. However, logging experiments

(Dewan 1956) have shown that the sonde almost always is lying along the wall,

except in cases of deep cavings.

The presence or absence of iron casing is also a complicating factor

which must be considered in neutron-porosity logging. Laboratory experiments

by both Barsukov et al. (1965) and Dewan (1956) indicate that the neutron

count should be reduced when iron casing is present, due to the moderating

effect of iron on neutrons. Peterson (1974) has observed this effect to occur

in Hawaiian wells, and, as described later in this report, this effect must

be compensated for in the neutron-porosity calibration curve.

Another factor which may be expected to affect neutron-porosity deter­

minations is borehole fluid salinity. Experimental work by Barsukov et al.

(1965) and Dewan (1956) shows ~n increase in neutron count if the borehole

fluid salinity is sufficiently great. However, unless salinity is in excess

of at least 20,000 ppm, the effects are negligible (Dewan 1956), and Peterson

(1974) reports that no borehOle fluid salinity effects have been observed in

neutron logs from Ha~aiian wells.

Other complicating factors which must be considered in neutron-porosity

logging are probe dimensions and characteristics, source strength, and log­

ging speed and direction. However, as the probe and source characteristics

remain constant for any individual logging instrument, and logging speed and

direction can be standardized. these factors can be readily incorporated

into the calibration procedure for any given logging instrument.

To adequately take into account all the above complicating factors, and

because the response of the neutron curve to changes in porosity is not

5

linear and often cannot be predicted adequately from theoretical solutions,

it is necessary to construct a field calibration curve, or in some instances

a family of calibration curves, for the area and formations in which logging

is practiced. Furthermore, to adequately take into account the instrumental

effects described above. field calibration curves should be constructed for

each neutron logging instrument.

Empirical Calibration Methods

In neutron logging practice, a number of different techniques are used

to achieve neutron log-porosity calibration. Probably the most widely used

and often the simplest of these are various empirical methods which utilize

correlation of field neutron curves and porosity data. To employ these

empirical methods it is necessary that formation porosity data be available

from an independent source such as borehole core analysis.

A common methoa of plotting calibration curves for neutron logs assumes

that the logarithm of the porosity is proportional to the neutron counting

rate. For this case, the calibration curve can be represented by the equa­

tion (Brown and Bower 1958. p. B30):

log cp = -mNd

+ K ( 1 )

where

cp = porosity

Nd = neutron count

m = slope of best-fit line

K = a constant

There is no theoretical justification for the log cp relationship, and al­

though it works satisfactorily in the medium porosity range, large devia­

tions from this relation exist at high and low porosities (Lynch 1962,

p. 253).

A second empirical method of plotting calibration curves for neutron

logs assumes that the logarithm of the neutron counting rate is proportional

to porosity. Work by Brown and Bowers (1958) clearly demonstrates the

applicability of this relationship for empirical field data. In addition,

Stick, Swift, and Hartline (1960) have shown theoretical justification for

the logarithm neutron-porosity relation. The logarithmic form of their

equation for the neutron counting rate derived strictly from theoretical

6

considerations is:

(2)

where

N = counting rate a Nt = part of neutron response reaching

detector through the tool body

S = source-detector spacing

uh • uf = transmission characteristics of hydrogen and the formation rock

K' = constant

<p = porosity

Using this equation, (Na - Nt) versus <p plots as a straight line on

semi logarithmic paper. The slope of the straight line depends only on the

transmission characteristics, uh and uf ' and the source-detector spacing,

S, and is independent of borehole size. The porosity curves for different

hole sizes plot as a series of parallel lines.

The calibration curve for the logarithm of neutron counting rate vs.

porosity can be represented by the simplified equation (Brown and Bowers

1958, p. B32):

log N = -m<p + ~' d

(3)

for which K" is a constant, and all other terms have been previously defined.

When neutron deflection is plotted on a logarithmic scale, it is necessary

that deflections be measured f~om a proper reference point. Brown and

Bowers (1958) suggest that the most suitable reference point for this pur­

pose is the neutron curve deflection opposite a porosity of 100 percent,

which is usually called the neutron curve zero point. This can be determined

by measuring the neutron curve response in a large tank of water, and is

approximated closely by the response of the logging sonde opposite a deeply

caved zone.

Laboratory Calibration Methods

An alternative method to the use of empirical field data for neutron

count-porosity calibration involves the use of various laboratory calibra­

tion units. These calibration units may take the form of calibration

sleeves which fit over the neutron sonde or, more frequently, calibration

pits and wells. The best known of all the laboratory calibration units is

7

the Standard Neutron Calibration Pit developed by the American Petroleum

Institute. In an attempt to provide some standardization for different

neutron logs, the American Petroleum Institute, in 1956, constructed its

Standard Neutron Calibration Pit at the Nuclear Logging Test Facility in

Houston, Texas. The calibration pit consists of a water-filled wellbore

constructed through 3 different calcium carbonate rock units of varying

porosities. The standard unit of measurement obtained from this calibration

pit is termed the "API Neutron Unit," where on API Neutron Unit is defined

as 1/1000 of the difference between instrument zero and the neutron curve

deflection opposite the 19 per~ent porosity Indiana limestone rock unit in

the calibration pit (for a more detailed description, see American Petroleum

Institute 1959).

Unfortunately, the API Neutron Unit does not fully define the response

of different neutron logging systems over their entire ranges of operating

conditions. Neutron curves recorded either by different companies or dif­

ferent logging systems within a company cannot be expected to exhibit iden­

tical curve amplitudes. This precludes the direct comparison of neutron

logs recorded by a variety of tool types even though each is correctly

scaled.

CALIBRATION CURVES fOR HAWAIIAN BASALTS

Selection of Calibration Methods

In approaching the task of constructing neutron countjporosity calibra­

tion curves for the neutron logs obtained from wells in the Hawaiian basal­

tic environment, both empirical field and calibration pit methods were

considered. After careful consideration the empirical field calibration

method was selected, primarily because of the following reasons: (1) the

great difficultly involved in obtaining rock samples small enough to use in

the calibration pit which contained a distribution of porosities truly

representative of Hawaiian basalts, (2) the considerable cost involved in

construction and the problem of obtaining a suitable site for a calibration

pit, and (3) porosity data were available, from borehole photologs, for 4

different wells on Oahu. Furthermore, the results of similar neutron curve

calibration work from volcanic rocks in eastern Washington, using both

calibration pit and empirical field calibration methods, showed that the

8

empirical methods were clearly superior. 1

Porosity Determination from Photologs

In the summer of 1968, the Honolulu Board of Water Supply, with the

help of Western Well Services of Hanford, California, photo logged several

wells on Oahu. The main objective of photo logging was to study the condi­

tion of the casing in the wells and to provide means for positive identifi­

cation of aquifer lithology.

For this purpose a Laval-type well camera, using a pair of matched

lenses for stereoscopic photography was used to photograph the wells. The

camera was a 12.38 cm (4 7/8-in.) diameter device, .9144 m (3 ft) long with

a light source extending 10.668 m (3 1/2 ft) beyond the camera lenses. It

was operated by the Water Resources Research Center logger, and exposures

were made every .6096 m (2 ft) to provide a slight photo overlap. The

images were recorded on 35-mm, black-and-white negative film which was

immediately processed in the field. In general, excellent photographs were

obtained and considerable detail could be discerned (Figs. la and lb).

As described earlier, calibration of the neutron logger requires de­

tailed formation porosity data. This can be obtained either from core anal­

ysis of the formation or by computing porosities from electrical resistivity

logs. However, both possibilities were ruled out as no cores are available

from existing water wells on Oahu, and previous work by Lao, Peterson, and

Cox (1969) has demonstrated that the calculation of porosity from electrical

resistivity logs from Hawaiian'wells is not feasible.

As photologs can be utilized to identify the formation and also to

give a good idea of the borehole geometry, it was decided to use photologs

for porosity computations. Porosity values were assigned to each 2-ft depth

interval, based on an area grid determination of porosity, and also utiliz­

ing various formation characteristics such as flow type, nature of voids

and Vesicles, and well geometry. By necessity all assigned porosities

apply only to the surface of the well bore. Porosities ranged from less

than 5 percent in dense flows up to 50 percent in some aa clinker zones,

especially if unweathered, and 100 percent opposite large cavities. It

should be mentioned at the onset, that it was not possible to assign a defi-

1. Crosby 1974: personal communication.

FIGURE 1a. PHOTOGRAPH OF A DENSE ZONE WITH

5 PERCENT POROSITY.

FIGURE lb. PHOTOGRAPH OF A DEEPLY CAVED

ZONE WITH 100 PERCENT POROSITY.

9

10

nite error to the estimates of porosity obtained by the above-described

method. However, it is the feeling of the authors that some of the esti­

mates of porosity may be in error by as much as 10 to 20 percent, and con­

sequently, that the porosity data introduce the greatest single source of

uncertainty in the calculation of the calibration curves. The Appendix

gives a compilation of neutron counts and porosities (as obtained from the . photologs) as a function of borehole depth for the 4 wells for which both

neutron curves and photologs are available; wells 88E, T86, 7A, and T143 can

be located on the map in Peterson's report (1974, p. 20).

Neutron-Porosity Calibration Curves

As described previously, theory predicts a semilogarithmic relationship

between porosity and neutron count, which can be expressed by Equation (3)

as follows:

Consequently. as a first step to obtain a neutron count-porosity calibration

curve. the values of observed porosity and logarithm of neutron count for

each two-foot depth interval were plotted on a semi logarithmic scale (see

Figs. 2-5). After observing these plots it was readily apparent that to

properly analyze the data it would be necessary to employ statistical meth­

ods. As the data consist of pairs of measurements where one measurement is

the observed porosity and the other is the corresponding neutron count, the

relationship between these two measurements can be examined by regression and

and correlation analysis techniques. Linear regression analysis, using the

least squares fitting technique determines the best straight-line fit to

the observations of the sample. The best-fit regression line takes the form

Y = a + bX (4)

where. for neutron count-porosity data,

Y = porosity (as determined from the photologs)

X = neutron count (taken from the neutron logs)

a = intercept coefficient

b = slope coefficient

The regression lines are plotted by determining the coefficients, a and b,

which are given by the following equations (after Yamane 1967, p. 383):

• - • -

• • •• • • • •

100 - • -• • - • •• -• .... •• • -• ~ •• -l- • -~ -

• - -Q Z 0 -U ILl (I)

0::: ILl Q. -(I)

t-z :::I 0 U

Z 0 0::: I- 10 r- -:::I ILl r- -z

I- -.... -- -r- -

r- -

-

I- -

I ~ ________ ~ __________ ~I __________ ~I __________ ~I~ ______ ~~

o 20 40 60 80 100

POROSITY (%0)

FIGURE 2. NEUTRON COUNT-POROSITY DATA FOR 2-FOOT DEPTH INTERVALS FROM WELL SSE (ALL NEUTRON COUNTS HAVE BEEN ADJUSTED BY -210 CPS).

I 1

12

0 z 0 0 w (1:1

a:: w Q.

(I) I-Z :J 0 0

z 0 a:: I-:J W z

• r-• • • • • • , ....

• • 100 - • I • • • -- I. • -- .. • -• - -.. • -• • • 1. -•

~ • -• • - I • -

• - • -

• • I- -

• • 10 r- -

r- -~ -I- -~ • -I- -r- -

-

- -

1 I I I

o 20 40 60 80 100

POROSITY (%0)

FIGURE 3. NEUTRON COUNT-POROSITY DATA FOR 2-FOOT DEPTH INTERVALS FROM WELL T8G (ALL NEUTRON COUNTS HAVE BEEN ADJUSTED BY -210 CPS).

0 z 0 frl fI)

IX: I.IJ Q.

fI) I-Z

5 (.)

Z 0 IX: I-;:) I.IJ z

• ,... -

, • • •• • 100 l- • -• • l- • -

i- • -• • i- • , -i- ••• -• • i- • I • -

• i- • • • -

• • • • • • • •

• • • • • • • -• • • •

4

10 I- -l- • -I- -!- -... -I- -!- -

-

-

I~--------~I~--------~I--------~~I--------~I~------~ o 20 40 60 80 100

POROSITY (%0)

FIGURE 4. NEUTRON COUNT-POROSITY DATA FOR 2-FOOT DEPTH INTERVALS FROM WELL 7A (ALL NEUTRON COUNTS HAVE BEEN ADJUSTED BY -210 CPS).

14

0 z 0 U ILl U)

a: ILl Il.

U) ... Z ::l 0 U

Z 0 a: ... ::l ILl Z

"- -• •• • •• 1 • • .... • • • •• • • • • I • • • • • : ..

100 l- I • -l- • • -l- • -l- • -• l- • -l- • -

l- • • --

I-

10 ~ -~ -l- -I- -I- -I- -I- -

-

-

I I I I

o 20 40 60 80 100

POROSITY (%0)

FIGURE 5. NEUTRON COUNT-POROSITY DATA FOR 2-FOOT DEPTH INTERVALS FRO'1 WELL T143 (ALL NEUTRON COUNTS HAVE BEEN ADJUSTED BY -210 CPS).

where

nL:XV - L:XL:V b =.;..;..;;;..;.;.;..-...;;;.;..;.;;..;.-

nL:X2 - (L:X)2

v = individual porosity values

X = individual neutron count values

n = number of data points in sample

15

(5)

(6)

Regression curve coefficients for each of the 4 wells used for calibration

are given in Table 1.

TABLE 1. SLlr+tt>.RY OF COEFFICIENTS FOR LOGARITI-t1 OF NEUTRON COUNT-POROSITY REGRESSION CURVES.

WELL a b r r2

S8E 76.844 -31.116 -0.839 0.704

T86 26.342 - 4.926 -0.242 0.058

7A 99.491 -43.455 -0.706 0.499

T143 86.912 -34.433 -0.940 0.883

COMPOSITE WITHOUT T86 89.568 -36.669 -0.797 0.636

When neutron deflection is plotted on a logarithmic scale, it is useful

if the deflections can be measured from a proper reference ,pOint. As men­

tioned earlier, Brown and Bowers (1958) have suggested that the most suita­

ble calibration point for this purpose is the neutron curve zero point.

which is the deflection for 100 percent porosity. This neutron count read­

ing may be determined either by measuring the neutron curve response in a

large tank of water, or by approximating closely the response of the sonde

opposite a deeply caved zone. For the present study the value of neutron

curve zero has been obtained as 210 neutron counts per second opposite a

deeply caved zone (this value was also confirmed in an open body of water).

Consequently, all neutron count data used in this study to obtain neutron

count-porosity calibration curves are of adjusted neutron count, where

N = N - 210 a m (7)

and where

16

N = adjusted neutron count a N = measured neutron count m

In order to determine the degree of correlation between the porosity

and neutron count data, the correlation coefficient was determined. The

sample correlation coefficient, r, is given by (modified after Yamane 1967,

pp. 401, 402, 803):

r, <X-X) (V-V) r =

Vr,(X-X) 2r,(V_V) 2

where X and V are as previously defined, and where

x = r,X/n

V = r,V/n

(8)

Correlation coefficients range in value from 0 (no correlation) to I (per­

fect correlation), and a negative sign indicates inverse correlation.

Table 1 lists the correlation coefficients from each well, and Figure 6

shows the logarithm of neutron count-porosity regression curves for each of

the different wells.

When determining regression lines, it is customary, along with corre­

lation coefficients, to calculate coefficients of determination. The

coefficient of determination, r2, is a measure of the closeness of fit of

the regression line to the sample points, and is given by the equation

(after Yamane 1967, p. 393):

r,(Vc-V) 2 r2 =------

r,(v-V) 2

where V and V are as ?reviously defined, and Vc = V's taken from the

regression curve. Coefficients of determination range in value from 0 (no

fit) to I (perfect fit). Table 1 lists the coefficients of determination

for the regression curves for each of the 4 wells. The correlation coeffi­

cient, r, and the coefficient of determination, r 2, should not be confused

with each other, as they mean entirely different things. The correlation

coefficient, r, is a measure of the relative correlation between X and V,

whereas the coefficient of determination, r2 , is a measure of how close the

regression line fits the V sample points.

17

Examination of the regression curve in Figure 6 for Well T86 indicates

that the neutron count-porosity relationship for this well is markedly dif­

ferent from that of the other 3 wells. The porosity obtained from this re­

gression curve opposite the neutron curve zero point, which should be approx­

imately 100 percent, is in fact only about 26 percent. Consequently, the

high porosity portion of the curve most certainly is in error. Furthermore,

examination of the coefficients of correlation (-0.242) and determination

(0.058), in Table 1 from Well T86 shows that both the correlation between

logarithm of neutron count and porosity and the closeness of fit of the re­

gression line to the sample data points are quite poor. This is not overly

surprising, however, as Well T86 is a test well with a diameter of only

15.24 cm (6 in.), whereas the other 3 wells have larger diameters of 20.32

and 30.48 cm (8 and 12 in.). Consequently, because of the obvious misfit of

porosity and logarithm of neutron count data from Well T86 with the sample

data from the other 3 wells, and because in the logging practice that the

neutron curve-porosity calibration curve is intended for, normally no wells

with diameters as small as 15.24 cm (6 in.) will be logged anyway, the deci­

sion was made not to use the data from Well T86 in the construction of the

final neutron curve-porosity calibration curve.

Although according to theoretical considerations, the relationship be­

tween neutron count and porosity should follow a logarithm of neutron count­

porosity function, other possible functions also were evaluated to insure

the selection of the simplest linear function providing the best regression

curves. In particular, the neutron count-porosity, neutron count-logarithm

porosity, and logarithm of neutron count-logarithm porosity functions were

tested in the same manner as the logarithm of neutron count-porosity func­

tion. Coefficients of regression, correlation, and determination are given

in the Appendix for each of these functions for each of the 4 wells. Re­

gression curves for each of these functions also are shown in Figures 7 to

~. It can readily be seen that the coefficients of correlation and deter­

mination for the straight arithmetic neutron count-porosity function are

markedly lower than for the other 3 functions, and this function can be

eliminated immediately on this basis. However, it also is readily apparent

that on the basis of these coefficients alone, it would be difficult to

select the logarithm of neutron count-porosity function as the most appro­

priate of the 3 remaining functions for a neutron curve-porosity calibration

18

• I • , • , • , • , . ,

100

a z 0 U LIJ ., G: IIJ Q.

U) l-Z ::;')

0 U

Z 0 G: l-::;') IIJ z 10

1 0

. I . , •

. , ~ ... , "

_._._.- Tae ce") ................ T 145 CIa'"

aaE (la")

------ 7A ca ")

\ \ " ,ea. , , ,e .. \:' • • , '\

\ • , \

" • .. ~ , '" ... \ •

I ... \ • \, I ", \ • ... , , ... , . ". , I

. \ '. 0 , . .

\ . , , , , .

• . \ , , . . , , . , , . . , . . , ,

POROSITY (0/00)

, \ , , ,

FIGURE 6. LOGARITHM OF NEUTRON COUNT-POROSITY REGRESSION CURVES,

300

250

Q Z 0 () I&J f/)

It: 200 I&J Il..

f/) I-Z ::::> 0 ()

z 150 0 It: I-::::> .... z

100

50

· · · . . . . . . . . . .

\ ~,

... \ : \ ... \ . \ ~ \ . \

20

\ \

40

_._._._0- TSS (S")

................ TI43 (12")

.... _------

60

SSE (12")

711. (S")

80

POROSITY (%0)

FIGURE 7. NEUTRON COUNT-POROSITY REGRESSION CURVES.

19

100

300

250

0 z 8 200 L&.I en c: L&.I Q.

en ... 150 z ::l

8 z 0 c: ... ::l 100 L&.I Z

50

, , , . \ . \ . \ , \ , . , \ , . , \ , . , \. , \ , .', , " , ., , ". '. , ... \ , . , , . \ , '. , ., , "'\

~ .. ~\ "~ ~ ~ \.~ .". , . ,

" , ''5. .. ,

_._._.- TB6 (6")

............. TI4S (12")

BBE (12")

------ 711. (B")

" , , , 01 ! ""t' I

10 100 POROSITY (%0)

FIGURE 8. I\EUTRON COUNT-LOGARITI-M POROSITY REGRESSICl'-J CURVES.

N o

o 100 z o o w en a: LIJ Q.

en ~ z ::J o o z o a: ~ 10 LIJ Z

10

. , . , . , . \ .

_._._.- T8S (S")

............... T 14~ (12")

1\ .\ ~ , , \\ \ '-\ \ ... ~ \ '.~ . '., \ "., " \, . -.. \ \ ".\ ... \ , \, , ".' . . ... , , . \ .

100

'." ". , ... ,

8eE (/2")

7A C8")

POROSITY (%0)

FIGURE 9. L(x;ARITrM OF NEUTRON COUNT -L(x;ARITI-M POROSITY REGRESSION CURVES.

21

22

curve. Examination of the regression curves in Figures 6, 8, and 9, for the

3 functions, however, provides a more appropriate basis for selecting the

logarithm of neutron count-porosity function. Disregarding the regression

curves for Well T86 for the reasons described previously, it can be seen that

the regression curves for the logarithm of neutron count-porosity function

show much less scatter over their entire range than for the other two func­

tions. The regression curve for both the neutron count-logarithm porosity

and the logarithm of neutron count-logarithm porosity functions show consid­

erable scatter for both high and low porosity values. The porosities for the

neutron curve zero point for the neutron count-logarithm porosity curves are

all much too low (approximately 15 to 40 percent) and for the logarithm of

neutron count-logarithm porosity curves are all much too high (approximately

180 to greater than 1000 percent). On this basis, then, plus the fact that

theory predicts a logarithm of neutron count-porosity regression curve, the

logarithm of neutron count-porosity function was selected for the neutron

curve-porosity calibration curve.

From Figure 6 it is seen that the regression curves for Wells 7A

(20.32-cm or 8-in. diameter), 88E (30.48-cm or 12-in. diameter), and Tl43

(30.48-cm or 12-in. diameter), appear to be unaffected by borehole diameter.

If the neutron curve response were affected by borehole diameter, the regres­

sion curves should have formed a set of parallel, or at least sub-parallel,

lines, one for each different hole diameter. Instead, the regression curves

intersect each other, and over much of its length the curve for the 20.32-cm

(8-in.) hole falls between the curves for the two 30.48-cm '(12-in.) holes.

Consequently, a single composite regression curve can be used to represent

the COllective data from all ~ wells. This composite regression curve will

serve as the calibration curve for the computation of porosity from neutron

logs obtained from wells in the Hawaiian basaltic environment. This com­

posite regression curve is shown in Figure la, and its coefficients of

regression, correlation, and determination are listed in Table 1.

Finally, in order to indicate the statistical reliability of the cali­

bration curve, confidence intervals have been computed. The 95 percent

confidence belt is shown in Figure 10, and is calculated as follows (modi­

fied after Yamane 1967, p. 423):

(10)

where YO.95 is the 95 percent confidence interval, to.025 is read from a

Q Z 0 U LI.I (I)

0: LI.I Q.

(I) t-Z ;.:) 0 u

z 0 0: t-m z

100

10

\ \ , \ \ \

\ \ \ \ , \ ,\ ,\

\ \ \\ \\ \'

" \' \ \

\ ' \ ' \ "

\ \ \ ,

\ , \ \ \ \

\ ' \ ' \ "

\ , \ , \ \ \ , \ , \ \ \ \ \ \ \ ,

\ , \ \ \ \ \ , \ ' \ ' \ '

I~------~------~~----~~------~--~~~ o 20 40 60 80 100

POROSITY [%0)

FIGURE 10. NEUTRON COUNT-POROSITY CALIBRATION CURVE (SOLID LINE) WITH 95% CONFIDENCE BELT (DASHED LINES).

23

24

t distribution table (Yamane 1967, p. 878), and where the estimate of the

variance of Ye• 02(Ye). is given by

(x-X) 2

n

where 02yX is the standard error of estimate, and is given by

02yX = E(y-ye)2

n-2 ( 12)

The 95 percent confidence belt is constructed by calculating 95 percent

confidence intervals, as described above, for several different values of

X, and drawing a curve through all the confidence intervals.

The meaning of the 9S percent confidence belt can be interpreted as

follows (Yamane 1967). If 100 neutron count-porosity samples, similar to the

sample used in this study, which consists of 141 neutron count-porosity

data points, are selected, and a confidence belt is calculated for each of

the samples, approximately 95 of the confidence belts can be expected to

contain the regression curve for the entire neutron count-porosity popula­

tion. The confidence belt calculated in this study is one of 100 such

confidence belts. Explained another way, there is a 95 percent probability

that the confidence belt calculated in this study contains the true regres­

sion curve for the entire neutron count-porosity population.

LIMITATIONS AND RECOMMENDATIONS

Limitations

In the process of constructing the neutron count-porosity calibration

curve shown in Figur~ 10, several limiting conditions were introduced. If

satisfactory results are to be obtained, the following limitations must be

well recognized and adhered to when using the calibration curve:

1. All data were obtained from wells in basaltic aquifers, hence the

calibration curve should be used only for neutron logs taken from basaltic

formations.

2. All data were obtained from wells with diameters from 20.32 to

30.48 cm (8 to 12 in.), hence the calibration curve can be used with full

confidence only for wells within this diameter range. Use of this calibra-

25

tion curve for 35.56-cm (14-in.) diameter wells possibly will yield accepta­

ble results. As many water wells in Hawaii have diameters greater than

30.48 cm (12 in.), the use of this calibration curve for interpretation of

data from the larger wells should be considered to be of a qualitative, or

at best, semiquantitative nature only.

3. As can be seen from the distribution of the 95 percent confidence

belt in Figure 10, and the spread of the 3 individual well regression curves

in Figure 6, the calibration curve is least reliable over the very low and

very high porosity ranges. Consequently, very high and very low porosity

values obtained from this calibration curve should be used with caution.

Fortunately, the calibration curve is most reliable over the approximate

range of porosities most commonly encountered in the Hawaiian basaltic

environment, namely about 5 to 40 percent porosity.

4. All of the sample data used to prepare the calibration curve were

Obtained from the uncased portion of wells. It is well-documented (Peterson

1974) that an increase in neutron count, averaging about 50 neutron counts

per second, is observed at the terminus of the well casing in most of the

wells logged. Therefore, the calibration curve shown in Figure 10 can be

used only for data from the uncased portion of wells. It is possible,

however, to obtain rough estimates of porosity from neutron curves taken

from the cased portion of wells by simply subtracting 50 neutron counts per

second from the calibration curve and reading the appropriate porosity

values.

Recommendations

In order to improve the overall reliability of the neutron count­

porosity calibration curve, especially over a range of well diameters, addi­

tional input should continually be used to upgrade the calibration curve(s).

The statistical methods described in this report can be used on additional

calibration data as they become available. In this regard, three specific

recommendations are as follows:

1. Independent porosity data from a range of borehole diameters,

especially for those greater than 30.48 cm (12 in.), need to be obtained.

This would allow calculation of calibration curves for large diameter bore­

holes, which undoubtedly would be different from the calibration curve cal­

culated in this report.

26

2. Possibly, a more reliable set of porosity data could be obtained

from the existing photologs for the 4 wells used in this study. To do

this, at least one or two persons, acting completely independently, should

reexamine the existing photologs and recompute the entire porosity sample~

3. Further study also should be made of the possible errors in the

neutron count data. In particular, a value for the random sampling error

involved in the collection of neutron count data needs to be determined.

ACKNOWLEDGMENTS

The authors wish to express their grateful appreciation to William M.

Adams for his many helpful suggestions and careful review of the manuscript,

and to the Honolulu Board of Water Supply, and in particular Chester Lao,

Mike Murata and Glenn Matsui, for technical and field support throughout

the entire project, and Dr. L. Stephen Lau, Director of the Water Resources

Research Center of the University of Hawaii, for his continuing support

and assistance.

REFERENCES

American Petroleum Institute. 1959. Recommended praotioe for standard oalibration and foP.m for nuolear logs. Amer. Petrol. Inst. Rep. 33.

27

Barsukov, O.A.; Blinova, N.M.; Vyornykh, S.F.; Gulin. Y.A.; Dakhnov, V.N.; Larionov, V.V.; and Kholin, A.I. 1965. Radioaotive investigations of oil and gas wells. New York: Macmillan.

Brown, A.A., and Bowers, B. 1958. Porosity determinations from neutron logs. The Petroleum Engineer 5:830-834.

Dewan, J.T. 1956. Neutron log correction charts for borehole conditions and bed thickness. Petroleum Trans., AIME 207:50-58.

Lao, C.; Peterson, F.L.; and Cox, D.C. 1969. Applioation of well logging and other well logging methods in Hawaii. Tech. Rep. No. 21, Water Resources Research Center, University of Hawaii.

Lynch, E.J. 1962. FOP.mation evaluation. New York: Harper & Row.

Peterson, F.L. 1974. Neutron well logging in Hawaii. Tech. Rep. No. 75, Water Resources Research Center, University of Hawaii.

Pirson. S.J. 1963. Handbook of well log analysis. Englewood Cliffs, N.J.: Prentice-Hall.

Stick, J.C.; Swift, G.; and Hartline, R. 1960. Present techniques in nuclear radiation logging. Formation Evaluation Symposium, AIME, Texas. Sec. II, p. 15.

Yamane, T. 1967. Statistios: An introduotory analysis. New York: Harper & Row.

APPENDIX. INPUT AND OUTPUT DATA FOR NEUTRON CALIBRATION CURVES

29

WELL 88E

REG~ESS'foNANf'-tbRRHA~fioN- AN'ALVsfS'---­Of

N~lLTJ~,QN COUNT V~RSU_S.J)~~~,~e!L~9~_9SJ ___ _

_______________________ ~o~ePTH (FT.)

NEUTRON COUNT PElf SECOND

I...OG.NEMl.RON __ PQftOSU' __ ... 'OG, PQ~'U_IT-=-'t _____________ . CDUH

477. 86. 1.93 15. 1.18 _________ 419. 96.. 1.98 12. 1.08

-481. 9-1. -1.96----------14.------ 1.15-·-------483. 81... 1 .. 91 25. 1.40

___ ---0485. 96. 1.98 22 1.34 4el. 61. ·-----1.19 '25. .40 ------489. 91. 1.96 10. 1.00 491. "6. 1.66 25. 1.40

---/iq3. 106~' 2.03 13. 1.il 49,!;' 61. 1. 79 25. 1.4Q

___________ --.:4;-.91. 1'1. 85 20. 1.30 ItQ9';'sl;- qr -'-17.-----1.23 501. 71. 1.85 18. 1.26

________________ ~5~03. 81. 1.91 15. 1.18 ________________ __ 505. -86. ".93 "15. 1.18 507. .16. 1.88 15. 1.18

. _____ . _________ 509. 14.. 2.15 11. 1.23 ______________________ _ 511. ---1sT. 2;;i 8 10. 1.00 513. 151. 2.18 8. CI.9Q

__ ~ ______ ~51S. 12 2.08 12. 1.08 Sil. IS • '-2.18------'------8. 0.90--519. 126. 2.10 5. 0.10

_____________ 521. 181 26 12. 1.08 52j~n 1. 12----··-----·"io.--------·-l.00 ------525. 91. 1.96 15. 1.18 'Z7. JOlt 2.30 5. 0.10 52ii-. --'--iTf. -2~3'-------"'- s. (f;t'i:f 531. 18 Ie Z.26 5. 0.10 533. 166. b-22 ________ .5. 0.10

COEFFICIENTS OF REGRESSION ll~E CORRELATION DETERMINATION .-------=-::=.:... ·'V-.A+BX--"---- COEF¢lcrENr--COEFFICIENY----

-~ ----------~ I! _ , ____ ,~~o _______ _

NEUTRON COUNT ~s POROSITY 26.468 -0.110 -0.198 0.6)8

tOG NEUTRONccfuNTVsPORosTT'i 16.845 -U.IU -0.839 0.70~

~-:-;:-;:::-::--_. __ -,N~E ... UuT.£F .... CJ1N ,..tnlJNT ~ S lOG...1lJ.RO.s ..... I.L.TY.L-__ :'1 ... ",:ltiJ ~"I'Jrel

1.555 ~.QO!L ________ -,=O~ . .•. 8.ll. __ _ ~O.L695..-.. _____ _

LOG NEUTRON COUNT VS LOC POROStT't 3.324 -1.104 -0.841 0.107

~

""'"

WELL '186

REGRESSION AND CO"RREIATICNA"NALVsTs OF

" ___________________ ---'N"'E"--'U'-'T-'.-'R=ON COUNT V ~~ S.YL9BSE~V~JL!'9RO S I,...!.i-'-V _____ .

DEPTH NEUTRON COUNT LOG NEUTFON POROSITY LOG POROSITY iF"T.) PER SECON.,-----taUN'f " "-"-~.!..!-------

-"---------_._-- ._---------..... _--lItlt. 66. 1.82 22. 1.34 H6. 61. 1.19 18 .26

.-----~-~~--,--life. 6i~ 1.79 --90. .95 150. 81. 1.91 16. 1.20 152. 91. 1.9 .30 Bit. fie i~e 5. .40-156. 141. 2.15 30. 1.48 158. 126. 2.10 15. 1.18 160. lsi. 2.26-- 8;-----· O.qO 162. 39. 1.59 20. 1.30 H4. 96. 1.0; 8 14. 1.15 -------"---n6. 1t 1. '2.05 12. 1.08 166. I. 0.00 20. 1.30 170. 21. 1.32 25. 1.40 Hz. 44. 1.64-- 15 ~ 1~18· 174. 1. CI.OO 10. 1.00 116. 11. 1.04 20. 1.30 11S. 1. O~OO 10; 1.00 "-180. 121. 2.08 13. 1.11 182. 141. 2.15 10. 1.00 18'4". st. 1;91 15. 1.18 186. 121. 2.08 14. 1.15 16e. 61. 1.79 20. 1.30 190. 61. t;79 16; 1 ~20 192. 131. 2.12 10. 1.00 194. 63. 1.BO 18. 1.26 196. 101. 2~OO- Is'; 1.18 198. 11. 1. Olt 30. 1.48 200. 31. 1.49 25. 1.40 20"2~ 31. 1.49'- 25~ 1.40 204. 31. 1.It" 2S. 1.40 2()6. 21. 1.32 lO. 1.48 ZQS. -1. -"e.oc 35; i.54 210. 56. 1.75 20. 1.30 212. Q.18 15. 1.18 zH-.---' 1 • I;B 1'7. "1.23 216. 166. 2.22 10. 1.00 218. 101. 2.00 lS. .18 220. "sl. 1. 91-··------20~ .30 222. 11. 1.85 15. 1.18 224. 121. 2.0e 10. 1.00

~"~ ;." .:] .1 •.. ,i,. ft! 2"26-. 121. z.(fe- 10-: 1.00 228. 101. 2.00 12. 1.08 230. 11 \. 2.05 15. 1.18

j---

tN N

2:12. 111. 2.05 15. 1.18 2l1t. 121. 2.08 12. 1.08 2'3b. n. 1.85 15. 1.18 238. 101. 2.00 20. 1.30 2 ~ O. 91. 1. q6 15. 1.18

_______________________ 2~2. 101. 2.00 15. 1.18 i~lt. ---81; 1.9115; -1.18 246. 96. 1.98 10. 1.00 _______________________ 2~8. 121. 2.08 12 .08 _______________________________ __ '250;--- IS i. 2.18 10. ~OO 252. 126. 2.10 10. 1.00

. ________________ 2 !)~. 151. 2. t 6 1.00 _____________ ~ __________ _ 256. 66; '-1.82 • 1.00 258. 216. 2.33 5. 0.70

__________________________ ~260. 51. 1.11 20. 1.30 ________________________________ _ 262. 5 j. I. • .., i 26. "1 ~30 261t. 46. 1.66 10. 1.00

___________________ ,266. 106. 2.03 15. 1.18 ------- 268. 1 i:l.04 --30. i.4~(

270. 11. 1. es 16. 1.Z0 ____________________ 212. 80. 1.93 15. 1.18

211.'; "61;' 1.79--------' 16~ - - 1.20 216. 41. 1.61 20. 1.30

____________________ ~278. 71. 1.85 15. 1.18 280; 9 i; 1.Ci6 ---------15;-----"1.18 -------------282. 111. 2.05 12. 1.08

_________________________ 284. 121. 2.08 12. 1.08 286~ 1"1. --"2.15-----------10;-'- -i.oo--~

288. 11. 1.85 18. 1.26 ______________________ 2QO. 86. 1.93 16. 1.20

-292-:' Itl. 1~6C 25. 1';40 29". 101. 2.00 20. 1.30

_______________________ ~296. 61. 1.19 15. 1.18 ______________________________ _ 298. H. 1.61 25; 1~40 30'0. 81. 1.91 20. 1.30 302. 101. 2.00 i2. 1.08 ________________________ __ 30ti. 61. 1'; 79 20; r;30 306. 16. 1.a8 20. 1.30 308. 36. 1.56 ~5. 1~~=0 _____________________________ __

_____________________ ---"C.."O'-"E'-'-f-'-f-"'IC~JE!!!.N.TS OF REGRESS ION L II\I:..:.;E=--___ . Y--·-r+BX -"

, CGRRELAlION DETERMINATION c'tEfF Ie ia.r- coej=-j=icfEN";-"----

NEUTRON COUNT VS POROSJ1Y 25.03b -0.092 -0.408 0.167

lOG NEUTRCN COU~T VS FO~OSITY 26.342 -4.926 -0.242'-------0:058----tH

~EUTRON COUNT VS LOG POROSITY 1.~_~.S._ -0.Q02 -0!,60l 0.361t tH

LOG NEUTRON COUNT VS LOG POROSITY 1.412 -0.116 -0.325 0.106 ------

----_ .. _-----_.

lore, ~

~ElL 7A

~~~~TRON

DEPTH NEU1Ra~ CO UN'" (FT. ) PER SECOND

;U ."u" "UUIH lOG NE.!L!RON PORQ_S lTV lOG POR(),...S..,I'--'T'-'Y'--______________ _ --- ----.. - COUNT -

- - ------------ --- -----

110. 41. 1.61 15. 1.18 n~· " I.

llit. " ,. "---____ ~~~----- 1.53 18. 1.26 1~5Y ------18~-- 1.26

116. 49. 1.69 15. 1.18 118. 21-120. 51.

--=----______ 1.32 25. 1.40 1:-j1 15. i~18

122. 61. 1.79 10. 1.00 121t. 59 126. 16.

_~ _____ ~1.77 15. 1.18 1.20 to. ----- -i. 78

128. 26. 1.41 50. 1.70 130. u. 13-2. i.

~ ______ 1.61 30. 1.48 _________________ _ 0~60 fC:o.-------~.oo

Uit. 21. 1.32 70. 1.85 136. ~ t _

n-8. ::JO.

:-=-_____ :;:7'"---_____ ~1.32 70. 1.85 ________ _ 1~ 75 ZO. - t.3()"

litO. 69. 1.84 15. 1.18 li2. 16. 11t4. 26.

~ ______ I. 20 ~5. 1.54 ______ _ f~4i --:!o. -i.lts

11t6. 29. 1."6 25. 1.40 148. 16-150-. 31.

~ ______ ~1.20 40. 1.60 _________________ __ 1~49-- 20. 1.30

152. 26. 1.41 35. 1.51t 154. 21, i56~ i1.

_:!-_____ ~1.32 50. 1.70 1~49 35. 1.SIf-

158. 13. 1.11 100. 2.00 160. 'll 1 _

162. ,0. ~ ____ ~~~~-----~1.49 100. 2.00 (~(i ~o~ 1.48

164. 41. 1.61 20. 1.30 166. 9-168: t"li.

--=----_____ -----70.95 20. 1.30 f;zo 25~ 1~4(f

110. 46. 1.66 15. 1.18 172. 51. 1"14. 61.

______ 1.11 12. 1.08 __________ _ 1.7'1 12; i.OB

176. 71. 1.85 10. 1.00 17f. 121. 180-. n f.

______ 2.08 8. 0.90 ___________ _ ~~3t J. 0.70

182. 106. 2.03 8. 0.90 184. 96. 186. 71:

1.98 10. 1.00 _____ _ i.e515. 1.U;

leB. 81. 1.91 13. 1.11 1'l0. 1 IIA L

192. ':J ••

&--.". 2.16 10. 1.00 _______________ _ 1:96 10. f~o-o

1«J4. 51. 1.71 25. 1.40 196. 3~_. 1.56 30. 1.1t8

C,,:I .j::o.

198. 56. 1.15 40. 1.60 200. 21. 1.32 ~O. 1.60 202. 16. 1.88 20. 1.30 204. 106. 2.01 10. 1.00 ZOE. 96. 1.98 lS. 1.18 208. 10 1. 2.0C 15. _____ .. 1.18 210;- 151. 2.18 . i5. 1.1e 212. 76. 1.S8 lO. 1.30 214. 141. 2.15 10. 1.00 216. 11 i. 2.05 -i5~ i .lif HS. 36. 1.56 35. 1.54 220. 31. 1.49 ------_. 70. _______ 1.85 22Z. iii; i.bl 30. 1.48 224. 76. 1.B8 30. 1.4&

COEFfICIENTS OF REGRESSION LI~E CORRELATION OETER"INATION . ________________________________ ~ ____________ ~V • A + ex C O~f£J~J ~~.T __ t.Q~.F.fl~Ijf.4,..!.T ______ _

A 8 R "SQ

NEUIRCN COUNT VS POROSITY ~5.863 -0.302 -o.S~3 0.317

LOG t.EU!RQN COUMT ys POP.OSJIY 99.'t9L -43.~!t5..5.. ___ _ -0 .. 106. _____ O.1t92. ____ ~_

NEUTRON COUNT VS LOG POROSITY 1.642 -0.005 -0.137 0.'lt3

----------------------LOG ~EUTRON COUNT VS LOG POROSITY 2.31t2 -0.609 -0.161 0.580

I.N V1

WEll Tl43

REGRESSION AND COPREUTIOH ANlllviis OF

_________________ ---'N=E"-'U~T"'_'P.=ON!.!_.:C=O=U=N'_'_T___=VE:_R~_\,I~ CBSEAV~D P9KQ~~I_"__TY"____ __

_________ ~D~E.PTH NEUTPON COUNT lOG NE!.l1RON PORO.sJT'l LOG PQRQSnv (FT. • PER SECOND COUNT

118. 61. 1.79 30. 1.48 1 • 82 20 • 1.30 -------i • • .06 10. 1.00 1'18. 66. 1-82 20. 1.30 200. 91. 1. 5. 1.18 204. 266. 2 8. 0.90 210. 91. 1.96 15. 1.18 220. 71· 1.85 22. 1.34 230. 228. 2.36 10~ i.oo 23t:. 41. 1.l: 1 30. 1.48 240. 2~c:.. 2.42 5. 0.70 -246; 51. 1.71 20.------ 1.30 266. 41. 1.61 25. 1.40

.t;6 • 1.18 -----06 • 1.18

294. 131. 2.12 10. 1.00 3e8. 161. ___ 2·?L J~. --------- 1.18 j20~---- j9i~ 2.59 5. 0.10 328. 116. 2.06 10. 1.00 340. 2l~ .33._ 5. 0.70 346. 81. • 91 20 • 1.30 354. 241. 2.3e 5. 0.70

1. __ .96 15. 1.18 • 1 • .00 15.--------··- i.18

360. 121. 2.08 12. 1.08 390. 231. 2.36 10. 1.00 .---lioo-~- 11tI; 2.15 20. 1.30 404. 101. 2.00 10. 1.00 4ZC! 91. t. '116 • 1.18

.-~ ------_. 450. 22 e. 2.36 8. 0.90 452. 153. 2.18 15. 1.18 454. 166. 2.22 1.00

-It 51!. --- i 18. --2.25 o. ----i.oo 466. 191. 2.28 5. 0.10 470. 141 2.15 15. 1.18 ------ -_. - .. ~--------.--.----

-4eo~ lSI. 2.26 10. 1.00 48S. 228. 2.36 8. C.90 500 2.42 5. C.70

---506. 2.11 • 1.11f 510. 241. 2.38 10. 1.00 514. 91. 1.9t 25. 1.40

"';:"5$ 518. 141. i;15 10. 1-;;00 5'4. 291. 2.46 5. 0.70 536. 21~. 2.33 8. «:.90

t.N Q\

,itO. 558. 510. 5H. sea. SE8. Sqi. 596. 604. -606 ~

llO3. a91. ll1S. 228. a66. \It 6 • i2i; 203.

2.01 2.28 2.25 2.36 2.22 2016 2.08 2.31

10. 10.

1.00 1.00

8. 0.90 6. 0.78

15. 1.18 _____ 20. 1.30

10. -~--- 1.00 10. 1.00

1--=--_____ o.00 __ _ 2~1l

100. 2.00 __________________ ___ ~o.-· ).30 12 B.

COEfFICI ENTSOFREGRESSiON LI"E--- - CORRELATION DETERMINATION V • A + ex COEffICIENT COEffICIENT

A B ·---·--R-

RSQ

ltE.UIRON COUN.Lfl POROSlTt . 30 .. 500.. -O .. lO~ ________ ~O.5.9Z. O.3!iO ____ -.

LOG NEUTRCN COUNT VS POROSITY 86.912 -34.433 -0.940 0.883 ---------.-.-------

NEUTRON COUNT VS LO~ POROSITY 1.490 -0.003 -0.824 0.678

_______ L~.E!LlRON COUNT VS LOG PQACSITY 2.Z.1~ ___ . __ ~O • .510_ _ ____ ___ ~.84l _________ Q ..• 108 _______ _

!.N '-l