-
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.
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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
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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
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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
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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
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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
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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
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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
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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.
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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,
-
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--"---- COEFlcrENr--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
1J4. 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~fJ~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