Lithology and

Porosity Determination

The measurements of the neutron, density, and sonic logs The combination of measurements depends upon the
depend not only on porosity (4) but also on the forma- situation. For example, if a formation consists of only
tion lithology, on the fluid in the pores, and, in some in- two known minerals in unknown proportions, the com-
stances, on the geometry of the pore structure. When the bination of density and neutron logs or the combination
lithology and, therefore, the matrix parameters (t,,, of bulk density (Q) and photoelectric cross section will
emm 4 mo) are known, correct porosity values can be define the proportions of the two minerals and a better
derived from these logs, appropriately corrected for en- value of porosity. If it is known that the lithology is more
vironmental effects, in clean water-filled formations. complex but consists of only quartz, limestone, dolomite,
Under these conditions, a single log, either the neutron and anbydrite, then a relatively accurate value of porosity
or the density or, if there is no secondary porosity, the can again be determined from the density-neutron com-
sonic, can be used to determine porosity. bination; however, the mineral fractions of the matrix
Accurate porosity determination is more difficult when cannot be precisely determined.
the matrix lithology is unknown or consists of two or Crossplots are a convenient way to demonstrate how
more minerals in unknown proportions. Determination various combinations of logs respond to lithology and
is further complicated when the response of the pore porosity. They also provide visual insight into the type
fluids in the portion of the formation investigated by the of mixtures that the combination is most useful in
tool differs appreciably from that of water. In particular, unraveling. Charts CP-1 through -21 present many of
light hydrocarbons (gas) can significantly influence the these combinations.
response of all three porosity logs. Fig. 6-l (Chart CP-le) is an example in which neutron
Even the nature or type of pore structure affects the and density porosities are crossplotted on linear scales.
tool response. The neutron and density logs respond to Points corresponding to particular water-saturated pure.
total porosity-that is, the sum of the primary (in- Mologies define curves (sandstone, limestone, dolomite,
tergranular or intercrystaJline) porosity and the secondary etc.) that can be graduated in porosity units, or a single
(vugs, fissures, fractures) porosity. The sonic logs, mineral point (e.g., salt point) may be defined. This chart
however, tend to respond only to evenly distributed is entered with porositiescomputed as if the matrix had
primary porosity. the same properties as water-saturatedlimestone; as a
To determine porosity when any of these complicating result, the limestoneline is the straight line of equal den-
situations exists requires more data than provided by a sity and neutron porosities.
single porosity log. Fortunately, neutron, density, and When the matrix lithology is a binary mixture (e.g.,
sonic logs respond differently to matrix minerals, to the sandstone-limeor lime-dolomite or sandstone-dolomite)
presence of gas or light oils, and to the geometry of pore the point plotted from the log readingswill fall between
structure. Combinations of these logs and the photoelec- the corresponding lithology lines.
tric cross section index, P,. measurement from the Litho-
Density* log and the thorium, uranium, and potassium NEUTRON-DENSITY CROSSPLOTS
measurement from the NGS* natural gamma ray spec- Charts CP-la and -lb are for SNP neutron versusdensi-
trometry log can be used to unravel complex matrix or ty data. Thesecharts were constructed for clean, liquid-
fluid mixtures and thereby provide a more accurate saturated formations and boreholes filled with water or
porosity determination. water-basemud. The charts should not be used for air-

*Mark of Schlumberger

6-1
 LITHOLOGY AND POROSITY DETERMINATION

or gas-filled boreholes; in these, the SNP matrix effect is dolomite. In all cases, the porosity would be in the 18%
changed. Charts CP-le and -If are simiiar plots for range. Thus, although the rock volumetric fractions
CNL* neutron versus density data. estimated from the neutron-density data could be con-
The separations between the quartz, limestone, and siderably in error, the porosity value will always be essen-
dolomite lines indicate good resolution for these litholo- tially correct if only sandstone, limestone, and/or
gies. Also, the most common evaporites (rock salt, anhy- dolomite are present. This feature of the neutron-density
drite) are easily identified. combination, coupled with its use as a gas-finder, has
In the example shown on Fig. 6-l; 4DI, = 15 and &,,I, made it a very poptil~ar log combination.
= 21. This defines Point P, lying between the limestone
and dolomite curves. Assuming a matrix of limestone and SONIC-DENSITY CROSSPLOT
dolomite and proportioning the distance between the two Crossplots of sonic t versus density eb or $D have poor
curves, the point corresponds to a volumetric proportion porosity and reservoir rock (sandstone, limestone,
of about 30% dolomite and 70% limestone; porosity is dolomite) resolution, but they are quiteuseful for deter-
18%. mining some evaporite minerals. As can be seen from Fig.
6-2 (Chart CP-7), an error in the choice of the lithology
pair from the sandstone-limestone-dolomite group can
result in an appreciable error in porosity. Likewise, a
small error in the measurement of either transit time or
bulk density can result in an appreciable error in porosi-
ty and lithology analysis. The good resolution given by
the chart for salt, gypsum, and anhydrite is shown by the
wide separation of the corresponding mineral points on
the figure. Several log-data points are shown ihilt cor-
respond to various mixtures of anhydrite and salt and,
perhaps, dolomite.

-1o’ 0 IO 20 30 40
$~NL (Limestone)

Fig. B-l-Porosity and lithology determination from Litho-

Density and CNL neutron logs in water-filled holes.

An error in choosing the matrix pair does not result in

large error in the porosity value found, as long as the
choice is restricted to quartz (sandstone or chert), lime-
stone, dolomite, and anhydrite; shaliness and gypsum are
excluded. For instance, in the above example, if the
lithology were sandstone and dolomite instead of lime-
stone and dolomite, the porosity found would be 18.3%;
the mineral proportions would, however, be about 40%
sandstone and 60% dolomite.
In fact, the plotted Point P of Fig. 6-1 could cor- Fig. 6-Z-Porosity and lithology determination from FDC den-
respond to various mixtures of sandstone, limestone, and sity and sonic logs.

6-2
 LOG INTERPRETATION PRINCIPLEWAPPLICA TIONS

SONIC-NEUTRON CROSSPLOTS simple lithologies (one-mineral matrix). P, is little af-

Chart CP-2a is a plot of sonic tversus porosity from an fected by the fluid in the pores.
SNP log. As with the density-neutron plots, resolution The bulk density versus photoelectric cross section in-
between sandstone, limestone, and dolomite lithologies dex crossplot (Charts CP-16 and -17, Fig. 6-4) can be us-
is good, and errors in choosing the lithology pair will have ed to determine porosity and to identify the mineral in
only a small effect on the porosity value found. However, a single-mineral matrix; the charts can also be used to
resolution is lost if evaporites are present. Chart CP-2b determine porosity and the mineral fractions in a two-
is a similar plot of sonic t versus porosity from the CNL mineral matrix where the minerals are known. To use
log. these charts the two minerals known or assumed to be
The sonic crossplots (Charts CP-2 and -7) are con- in the matrix must be selected. A rib is then drawn
structed for both the weighted-average (Wyllie) and the through the log point to equal porosity points on the
observed (Raymer, Hunt, and Gardner) sonic transit time- spines of the assumed minerals. These spines correspond
to-porosity transforms. Chart CP-Zc is shown in Fig. 6-3. to pure mineral matrices. The ribs are constant porosity
For mineral identification and porosity determination, use approximates for any matria mixture of the two minerals
the transform previous experience has shown most ap- assumed. The distances from the log point to the pure
propriate for the area. mineral spines approximate the relative proportions of
the minerals in the matrix.
If the porosity value from Chart CP-16 or -17 is equal
to that of Chart CP-1, the choice of minerals is correct
and the porosity is liquid filled. If the two values are dif-
ferent, choosing another pair of minerals may reconcile
the difference.

z
1 2.6
I I I I J
0 10 20 30 40 ,” 2.7
~cNL~,,~. Neutron Porosity Index (pu)
(Apparent Limestone Porosity) 2.3

2.9 19
Fig. &S-Porosity and lithology determination from sonic log 5
and CNL* compensated neutron log; tf = 189 &t.
3 e
0 1 2 3 4 5 6
DENSITY-PHOTOELECTRIC
CROSS SECTION CROSSPLOTS P,, Photoelectric Cross Section (Barns/Electron)
The photoelectric cross section index, P,, curve is, by
itself, a good matrix indicator. It is slightly influenced
by formation porosity; however, the effect is not enough Fig. 6-4-Porosity and lithology determination from Litho-
to hinder a correct matrix identification when dealing with Density* log; fresh water, liquid-filled holes, et = 1.0.

6-3
 LITHOLOGY AND POROSITY DETERMINATION

If one knows which pair of minerals is present in the

matrix and the e,g porosity is less than the Q,-Pe
porosity, the presence of gas may be suspected. The loca-
tion of the log point on the porosity rib of the Qb-Pe plot
permits the computation of the matrix density (mixture
of two minerals in known proportions). If emon (from
the e,+,plot) is less than emoo (from the eb - P, plot),
the presence of gas is confirmed.

NGS CROSSPLOTS
Because some minerals have characteristic concentrations
of thorium, uranium, and potassium, the NGS log can
be used to identify minerals or mineral type. Chart CP-19
compares potassium content with thorium content for
several minerals; it can be used for mineral identification
by taking values directly from the recorded NGS curves. Fig. 6.6-Mineral identification from Litho-Density log and
Usually, the result is ambiguous and other data are need- natural gamma ray spectrometry log.
ed. In particular, P, is used with the ratios of the radioac-
tive families: Th/K, U/K, and Th/U. Use care when usually indicates organic matter, phosphates, and
working with these ratios because they are not the ratios stylolites. The thorium and potassium levels are represen-
of the elements within the formation but rather the ratios tative of clay content. In sandstones, the thorium level
of the values recorded on the NGS log, ignoring the units is determined by heavy minerals and clay content, and
of measurement. Charts have been constructed that allow the potassium is usually contained in micas and feldspars.
P, to be compared with either the potassium content, In shales, the potassium content indicates clay type and
Fig. 6-S (Chart CP-18 top), or the ratio of potassium to mica, and the thorium level depends on the amount of
thorium, Fig. 6-6 (Chart CP-18 bottom). detrital material or the degree of shaliness.
High uranium concentrations in a shale suggest that
the shale is a source rock. In igneous rocks the relative
proportions of the three radioactive families are a guide
to the type of rock, and the ratios Th/K and Th/U are
particularly significant.
The radioactive minerals found in a formation are, to
some extent, dependent on the mode of sedimentation.
The mode of transportation and degree of reworking and
alteration are also factors. As an example, because
thorium has a very low solubility, it has limited mobility
and tends to accumulate with the heavy minerals. On the
other hand, uranium has a greater solubility and mobili-
ty, and so high uranium concentrations are found in fault
planes, fractures, and formations where water flow has
occurred. Similarly, high concentrations can build up in
the permeable beds and on the tubing and casing of pro-
Fig. &B-Mineral identification from Litho-Density log and ducing oil wells. Chemical marine deposits are
natural gamma ray spectrometry log. characterized by their extremely low radioactive content,
with none of the three families making any significant
The major occurrences of the three radioactive families contribution. Weathered zones are often indicated by pro-
are as follows:
nounced changes in the thorium and potassium content
. Potassium - micas, feldspars, micaceous clays (illite), of the formation but a more or less constant Th/K ratio.
radioactive evaporites
. Thorium - shales, heavy minerals EFFECT OF SHALINESS ON CROSSPLOTS
l Uranium - phosphates, organic matter Shaliness produces a shift of the crossplot point in the
The significance of the type of radiation depends on the direction of a so-called shale point on the chart. The shale
formation in which it is found. In carbonates, uranium point is found by crossplotting the measured values (Q,,

6-4
LOG INTERPRETATION PRINCIPLES/APPLICATIONS

$Nsh, &) observed in the neighboring shale beds. General- where A&,,=is excavation effect (discussed in Chapter 5).
ly, the shale point is in the southeast quadrant of neutron-
For oil-bearing formations
density and sonic-density crossplots, to the northeast on
the neutron-sonic crossplot, and in the lower center of the A = (1.19 - 0.16 Pmf) Q,,
density-photoelectric cross section crossplot. These shale - 1.19 Qh - 0.032 @q. 6-4)
values, however, may only approximate the parameters of
the shaly material within the permeable beds. and
eh + 0.30
EFFECT OF SECONDARY . (Eq. 6-5)
B = ’ - e,(l - Pm,)
POROSITY ON CROSSPLOTS
Sonic logs respond differently to secondary porosity than For gas-bearing formations
the neutron and density logs. They largely ignore vuggy A = (1.19 - 0.16 P,f) em, - 1.33 eh (Eq. 6-6)
porosity and fractures and respond primarily to in-
tergranular porosity; neutron and density tools respond and
to the total porosity. 2.2 eh
Thus, on crossplots involving the sonic log, secondary B=l- 6%. ‘j-7)
emf (1 - Pmh’
porosity displaces the points from the correct lithology line
and indicates something less than the total porosity; the where
neutron-density crossplots yield the total porosity. shr = residual hydrocarbon saturation,
THE SECONDARY POROSITY INDEX LOG eh = hydrocarbon density in grams per cubic
centimeter,
In clean, liquid-filled carbonate formations with known
matrix parameters, a secondary porosity index (&,) can e mf = mud filtrate density in grams per cubic
be computed as the difference between total porosity, as centimeter,
determined from neutron and/or density logs, and porosi-
and
ty from the sonic log
P mf = filtrate salinity in parts per million NaCl.
42=4-Qsv. 0%. 6-l)

A relative secondary porosity index is sometimes com-

puted as the ratio of the absolute index, defined above,
to total porosity.

EFFECT OF HYDROCARBONS ON CROSSPLOTS

2.3
Gas or light hydrocarbons cause the apparent porosity
from the density log to increase (bulk density to decrease) eb
and porosity from the neutrdn log to decrease. On a
neutron-density crossplot this results in a shift (from the I 2.5
liquid-filled point of the same porosity) upward and to the
left, almost parallel to the isoporosity lines. If a gas cor-
rection is not made, the porosity read directly from the
crossplot chart may be slightly too low. However, the 2.7
lithology indication from the chart can be quite erroneous.
Arrow B-A on Fig. 6-7 illustrates the correction for this
hydrocarbon shift. Log Point B is for a clean limestone
containing gas of density 0.1 g/cm3. Corrected Point A 2.9
0 10 20 30
falls near the limestone line, and porosity can be read
$N---
directly.
The hydrocarbon shift (AQ,) hand (A$N) h are given by
Fig. SicEffect of hydrocarbon. Arrow B-A represents cor-
(AQh = - A&S,, (Eq. 6-3 rection of log Point B for hydrocarbon effect for a gas case.
and The arrows at lower right represent approximate hydrocar-
bon shifts for various values of Q, for 4 Shr = 0.15, P,f =
(A@,@ = - BWhr - MN,, cm. 6-3) 0, and e,,,t = 1.

6-5
 LITHOLOGY AND POROSITY DETERMINATION

The arrows at the lower right of Fig. 6-7 show, for in most cases as representing a mixture of limestone,
various hydrocarbon densities, the approximate dolomite, and quartz. However, it could also be a
magnitudes and directions of the hydrocarbon shifts as limestone-quartz-anhydrite mixture or, less likely, a
computed from the above relations for 4 S,, = 15%. dolomite-quartz-gypsum mixture; since the point is also
(Fresh mud filtrate was assumed and excavation effect contained in those triangles. The combination selected
was neglected.) This value of 4 S,,, could occur in a gas would depend on the geological probability of its occur-
sand (e.g., 4 = 20%, S,, = 75%). rence in the formation.
Gas will also shift the points on a sonic-neutron plot
as a result of the decrease in +,,,. Similarly, gas will shift Table 6-1
points on a sonic-density plot as a result of the increase Matrix and fluid coefficients of several minerals and types
m bD because of the presence of gas. In uncompacted of porosity (liquid-filled boreholes).
formations, the sonic t reading may also be increased
by the effect of the gas.
Hydrocarbon shifts in oil-bearing formations are usual-
ly negligible; for clean formations, porosities can be read Sandstone 1 55.5 2.65 -0.035' -0.05'
directly from the porosity graduations on the chart.

M-N PLOT
In more complex mineral mixtures, lithology interpreta-
tion is facilitated by use of the M-N plot. These plots
combine the data of all three porosity logs to provide
the lithology-dependent quantities M and N. M and N
are simply the slopes of the individual lithology lines on
D&m&t& to 1 43.5 1 2.85 1 0.035* / 0.085’
the sonic-density and density-neutron crossplot charts,
respectively. Thus, M and N are essentially independent
of porosity, and a crossplot provides lithology
identification. Dolomite 2 43.5 2.85 0:02* 0.065.
M and N are defined as: ($=1.5% to
5.5% & >
30%)
M = + - ’ x 0.01 (Eq. 6-8)
eb - ef Dolomite 3 43.5 2.85 0.005' 0.04*
$Nf - +N
N= (Eq. 6-9)
eb - ef
For fresh muds, fr ; t89, ef = 1, and 4Nr = 1. 1 Anhvdrite I 50.0 I 2.98 I -0.005 I -0.002
Neutron porosity 1s m hmestone porosity units. The Gypsum 52.0 2.35 0.49**
multiplier 0.01 is used to make the M values compatible
for easy scaling. Salt 67.0 2.03 0.04 - 0.01
If the matrix parameters (t,,, ema,$Nma) for a given
mineral are used in Eqs. 6-8 and 6-9 in place of the log
values, the M and N values for that mineral are defined.
For water-bearing formations, these will plot at definitive
points on the M-N plot. Based on the matrix and fluid
parameters listed in Table 6-1, M and N values are shown
EGyjyq
(Liquid-Filled): Fr;;+;;d

in Table 6-2 for several minerals in both fresh mud- and

salt mud-filled holes. (N is computed for the CNL log.)
Fig. 6-8 is an M-N plot showing the points for several
single-mineral formations. This plot is a simplified ver-
sion of Chart CP-8.
Points for a mixture of three minerals will plot within
the triangle formed by connecting the three respective
single-mineral points. For example, suppose a rock mix- (In Sandstone): pr.;hM;d
ture exhibits N = 039 and M = 0.81; in Fig. 6-8 this I 55.5 I ::t I ’ I
point falls within a triangle defined by the limestone- *Average values. 1551.86
dolomite-quartz points. It would therefore be interpreted “Based on hydrogen-index computation.

6-6
LOG INTERPRETATION PRINCIPLES/APPLICATIONS

Table 6-2
Values of M and N for common minerals.

l-r
Fresh Mud
h=l)
Mineral
M N’

Sandstone 1 0.810 0.636

v,, = 18,000

Sandstone 2 0.835 0.636

Yma= 19,500 I I
1 Limestone 1 0.827 1 0.585

Dolomite 1 0.778 0.489

$ = 5.5-30% I I

$
k
0.5
0.4 0.5 0.6 0.7
N
‘Values of N are computed for CNL neutron log.

Secondary porosity, shaliness, and gas-fiied porosity will Fig. 6-8-M-N plot showing points for several minerals (N is
shift the position of the points with respect to their true calculated using SNP neutron log). Arrows show direction of
shifts caused by shale, gas, and secondary porosity.
lithology, and they can even cause the M-N points to plot
outside the triangular area defined by the primary mineral Next, an apparent matrix transit time, J’,,, and an ap-
constituents. The arrows on Pig. 6-8 indicate the direc- parent grain density, emoa, arc calculated:
tion a point is shifted by the presence of each. In the case
of shale, the arrow is illustrative only since the position eb - 60 ef
of the shale point will vary with area and formation. emoo= (Eq. 6-10)
1 - hl
In combination with the crossplots using other pairs
of porosity logs and lithology-sensitive measurements, the t- Q,, f
M-N plot aids in the choice of the probable lithology. t moo = 1 _ 9 time-average relationship (Eq. 6-lla)
ta
This information is needed in the final solution for porosi-
ty and Ethology fractions. t mom = t- ‘$ field-observed relationship (Eq. 6-llb)
MID PLOT
where
Indications of lithology, gas, and secondary porosity can
also be obtained using the matrix identification (MID) eb is bulk density from density log,
plot. t is interval transit time from sonic log,
To use the MID plot, three data are required. Fist, es is pore fluid density,
apparent total porosity, &, must be determined using
if is pore fluid transit time,
the appropriate neutron-density and empirical (red
curves) neutron-sonic crossplots (Charts CP-1 and -2). Or0 is apparent total porosity,
For data plotting above the sandstone curve on these and
charts, the apparent total porosity is defined by a ver-
tical projection to the sandstone curve. c is a constant (c = 0.68).

6-l
 LmHOLOGY AND POROSITY DETERMINATION

The apparent total porosity is not necessarily the same

in the equations. For use in the t,, equations (Eq.
6-ll), it is the value obtained from the neutron-sonic
crossplot (Chart CP-2). For use in the emaaequation (Eq.
6-lo), it is the value obtained from the neutron-density
crossplot (Chart CP-1).
2.3
Chart CP-14 (Fig. 6-9) can be used to solve graphical-
ly for emna (Eq. 6-10) and for tmuu using the empirical 2.4
field-observed transit time-to-porosity relationship (Eq. n^
5 2.6
6-llb). The northeast half (upper right) of the chart solves
z
for the apparent matrix interval transit time, t,,,. The 2 2.6
southwest half (lower left of the same chart) solves for
QF 2.7
the apparent matrix grain density, emao

3
f
3.1 J

100 120 140 160 180 200 220 240

Fig. 6-lo-Matrix identification (MID) plot

Sulfur plots off the chart to the northeast at tmoa =

122 and emoo= 2.02. Thus, the direction to the sulfur
point from the quartz, calcite, dolomite, anhydrite group
is approximately the same as the direction of the gas-
effect shift. Gypsum plots to the southwest.
The concept of the MID plot is similar to that of the
M-N plot. However, instead of having to compute values
of M and N, values of em,,aand t,,,, are obtained from
charts (Chart CP-14). For most accurate results, log
Fig. B-9--Determination of apparent matrix parameters from readings should, of course, be depth matched and cor-
bulk density or interval transit time and apparent total porosity;
fluid density = 1. rected for hole effect, etc. The need for such corrections
can often be seen from the trend of the plotted points
The crossplot of the apparent matrix interval transit on the MID plot (Fig. 6-10).
time and apparent grain density on the MID plot will
identify the rock mineralogy by its proximity to the label- emu= vs. lJ,, MID PLOT
ed points on the plot. On Chart CP-15 the most com- Another crossplot technique for identifying lithology uses
mon matrix minerals (quartz, calcite, dolomite, data from the Litho-Density log. It crossplots the. ap-
anhydrite) plot at the positions shown (Fig. 6-10). Mineral parent matrix grain density, emarr.and the apparent
mixtures would plot at locations between the correspon- matrix volumetric cross section, U,, (in barns per cubic
ding pure mineral points. Lithology trends may be seen centimeter).
by plotting many levels over a zone and observing how The apparent matrix grain density is obtained as
they are grouped on the chart with respect to the mineral previously described in the MID plot discussion. Charts
points. CP-1 and -14 are used for its determination.
The presence of gas shifts the plotted points to the The apparent matrix volumetric cross section is com-
northeast on the MID plot. Secondary porosity shifts puted from the photoelectric cross section index and bulk
points in the direction of decreased t,,,,, . i . e., to the left. density measurements
For the SNP log, shales tend to plot in the region to the
CJ pee, - ho uf
right of anhydrite on the MID plot. For the CNL log,
shales tend to plot in the region above the anhydrite point.
mm= 1 - hc? , (Eq. 6-12)

6-8
LOG INTERPRETATION PRINCIPLES/APPLICATIONS

where
P, is photoelectric absorption cross section index,

e, is electron density

and
e, =
eb + 0.1883
1.0704
Table 6-3

b 1.810
5.080
3.140
5.050
9p.9r
2.65
2.71
2.85
2.96
@bLOG
2.64
2.71
2.65
U
4.780
13.800
9.000
14.900
4.650 2.17 :::: 9.680

T-l-
&a is apparent total porosity. 14.700 3.94 3.89 55.900
17.000 5.00 4.99 82.100
267.000 4.48 4.09 1065.000
The apparent total porosity can be estimated from the 0.358 1.00 1.00 0.398
density-neutron crossplot if the formation is liquid filled.
Chart CP-20 solves Eq. 6-12 graphically. A simplified 0.734 1.06 1.05 0.850
version is shown in Fig. 6-11. 1.120 1.12 1.11 1.360
0.119 e, 1.22e,-.118 0.136 e,
0.095 eg .33 Q-.188 0.119 e,

Fig. E&11-Matrix identification plot; emaa vs. U,,,. ,.

-
t 3 Kadiniie 0
OJ 3.1 lllite 0
2
Table 6-3 lists the photoelectric absorption cross sec-
2 4 6 8 10 12 14 16
tion index, the bulk density, and the volumetric cross sec- U,,,, Apparent Matrix Volumetric
tion for common minerals and fluids. For the minerals, Cross Section Earns/cm?
the listed value is the matrix value (emor (I,&; for the
fluids, it is the fluid value (Qf, U,). Chart CP-21 (Fig.
6-12) shows the location of these minerals on a emoo ver- Fig. 6-12-Matrix identification plot.
sm umaa crossplot. The triangle encompassing the three
common matrix minerals of quartz, calcite, and dolomite COMPLEX LITHOLOGY MIXTURES
has been scaled in the percentages of each mineral. For Mathematically, the transformation of the basic measure-
example, a point exhibiting an apparent matrix grain den- ment of a porosity or other appropriate log into porosi-
sity of 2.76 g/cm3 and volumetric cross section of 10.2 ty and/or lithology and/or pore fluid identification is
barns/cm3 would be defined by the crossplot as 40% simply the solution of one or more simultaneous equa-
calcite, 40% dolomite, and 20% quartz provided no other tions. When the rock matrix contains only a single known
minerals exist and the pores are liquid saturated. mineral and the saturating fluid is also known, any one
On this crossplot, gas saturation displaces points up- of the porosity logs can be used for porosity identifica-
wards on the chart and heavy minerals displace points tion. In other words, a single equation (single log
to the right. Clays and shales plot below the dolomite measurement) is sufficient to solve for a single unknown
point. (in this case, the porosity).

6-9
 LITHOLOGY AND POROSITY DETERMINATION

If, however, in addition to porosity, the rock matrix (i.e., its Qma and o,,r,, characteristics). It is presumed that
is an unknown mixture of two known minerals, then two e mnand hna are known for most minerals expected to
independent equations (two log measurements) are need- be encountered in sedimentary rocks.
ed to solve for the two unknowns (in this case, the porosi- When more unknowns exist, such as in a rock matrix
ty and the mineral fractions). For example, in a limestone- made up of three minerals, another independent equa-
dolomite mixture, the combination of neutron and den- tion (or log measurement)is required. The soniclog might
sity logs could be used. Their responses to porosity and be added to the neutron-density combination. The equa-
lithology are tions become for a limestone-dolomite-quartz mixture:~
eb = @ef eb = 4er
+ c1 - 4) cLemaL + oemoD) (Eq. 6-13) + (1 - 4) (LemoL-t Demon+ se,,, (Eq. 6-15)
and

+ (1 - 4) WmoL + mm&J 5 (Eq. 6-14)

+ (1 - 4) @&,L + mt,, + S&‘,,) (Eq. 6-17)
where
l=L+D+S. (Eq. 6-18)
eb and +N are the measured bulk density and apparent
limestone porosity from the density and neutron logs, Simultaneous solution of these four equations yields
respectively; values for the four unknowns (L, D, S, and 4). The M-
N plot (Chart CP-8), the Q,,, versus t,, MID plot
of and +.are the density and hydrogen index of the fluid
(Chart CP-15), and the emoaversus U,, Matrix Iden-
saturating the pores investigated by the density and
tification plot (Chart CP-21) are graphical solutions to
neutron logs;
four unknowns, four equation systems.
4 is the porosity; Even more complex mixtures can be unraveled by ad-
ding more equations (log measurements).Of course, the
emnL and emoD are the grain densities of limestone and
additional log measurementsmust respond to the same,
dolomite, respectively;
but not necessarily all, unknown petrophysical
4 l?IoL and Q,, are the hydrogen indices of limestone parameters; they should not introduce additional
and dolomite; unknowns into the problem.
It is not easy to develop graphical techniquesthat can
and
solve systemsof five, six, and more simultaneousequa-
L and D are the fractions of limestone and dolomite in tions for a large number of unknown petrophysical
the rock matrix mixture. parameters. These problems are best handled by com-
Three unknowns exist in the above two equations; they puter programs. One such program is Litho-Analysis*.
are 4, L, and D. However, since the mineral fractions
of the rock matrix must total unity, the dolomite frac- LITHO-ANALYSIS PROGRAM
tion could be expressed in terms of the limestone frac- This program usesthe uranium, thorium, and potassium
tion as D = 1 - L, thereby reducing the number of concentration measurementsfrom the NGS log; the
unknowns in the above equations to two; or a third bulk density and photoelectric cross section index meas-
material balance equation of L + D = 1 could be in- urements from the Litho-Density log; and the apparent
cluded. In either event, solution for 4, L, and D is possi- porosity measurementfrom the CNL log. Lithology
ble since the number of equations (and independent log mixtures containing quartz (sandstone), calcite (lime-
measurements) equals the number of unknowns. stone), dolomite, anhydrite, halite (salt), two shales
The several crossplot charts that plot one log measure- (low- and high-potassiumclays), feldspar, and mica can
ment against another are simply approximate graphical be unraveled into the fractions of each mineral present.
solutions of the responses of two log measurements for Response equations and parameter selections are
porosity and lithology determination. Charts CP-1, -2, obtained from the comparison of thorium and potassi-
-7, -16, and -17 are examples. These charts can also be um measurementsand from the apparent matrix densi-
used when the rock matrix is composed of a single, but ty and apparent volumetric photoelectric cross sec-
unknown, mineral. The problem is the same; it is one tion index (Chart CP-21). The thorium and po-
of two equations and two unknowns. The unknowns, tassium response equations are used to estimate the
in this situation, are porosity and mineral identification volumes of clays, mica, and feldspar. The apparent

6-10
LOG INTERPRETATION PRINCIPLES/APPLICATIONS

matrix density (e,,,) and volumetric cross section (U,,,) 1 = WCl, + WC12 + whlat + WFel 9 (E% 6-z2)
data can then be corrected for clay, mica, and feldspar.
A three-mineral analysis is then done using the corrected with WC1 as a known function of Th and K. The model
e mm and Urn, data. A test ensures that the clay correc-
is shown by Fig. 6-14. The resulting mineral weight frac-
tion is within the limits for the assumed lithology model. tions can readily be converted to volume fractions.
If it is not within limits, either the estimate of clay volume The Litho-Density measurements of bulk density and
or the lithology model, or both, are changed. effective photoelectric cross section are sensitive to the
The general case of two clays and feldspar can be presence of any of the six sedimentary categories: car-
modeled by observing the rather close proximity of the bonates, evaporites, silicates, clays, micas, feldspar.
100% kaolinite, montmorillonite, and chlorite clay points Chart CP-21 presents a crossplot of U,, versus emOO.
on Chart CP-19. This suggests defining (1) a low- The locations of the various mineral points represent
potassium clay point, Cl,; (2) a high-potassium clay theoretical locations based upon the chemical composi-
point, Cl,, which is generally illite; and (3) a low- tions of the various minerals.
thorium, high-potassium point; i.e., feldspar, Fel; and The fundamental Litho-Density interpretation problem
(4) a clean matrix point, Mat. This model is depicted by is the correction of the apparent matrix volumetric cross
Fig. 6-13. The line connecting the two clay points is call- section and apparent matrix density for the presence of
ed the clay line, and the line from the origin through the feldspar, mica, or clay. The presence of evaporites must
feldspar point is called the feldspar line. WC, is obtain- also be considered. Assuming the type of clay is known
ed by linear interpolation between the clay and feldspar and assuming, for discussion, that initially no evaporites
lines. exist, the Litho-Density variables are corrected for the
The following four-mineral natural gamma ray spec- presence of feldspar and clay. This problem can be ex-
tral interpretation model is assumed: pressed mathematically as

WC1 = WCl, + WClz (Eq. 6-19) emon - P4e4 - PSe,

= qe, + Pze, + P3e3 (Eq. 6-23)
Th = Thcl, WI, + Thclz Wclz
+ That WM,, + Th wFei @I. 6-W u mw - P,lJ, - P,U,
= P,U* + P,U, + P,U,, (Eq. 6-24)
K = Kq WCI, + Kc12 WCI~
+ Khlat --Mat + KF~I wF.9 (Eq. 6-21) 1 - P4 - Ps = P, + Pz + P3, (Eq. 6-25)

Fig. 6-13-Estimation of total clay percentage.

6-11
 LITHOLOGY AND POROSITY DETERMINATION

Constant Percentage

Fel -

Fig. 6-l4-Four-mineral spectral model.

where This probability logic is rather complex. It is sufficient

to say, for example, that the probability of anhydrite or
Q, is the density of mineral 1,
salt increases as the emonversus Um, point moves away
P, is the proportion of mineral 1 in formation matrix, from the calcite, quartz, dolomite triangle towards the
anhydrite or salt point, and the neutron porosity
and
decreases. However, the probability of anhydrite or salt
U,is the volumetric cross section of mineral 1. decreases with increasing clay fraction.
A Litho-Analysis computation is shown in Table 6-4
Indices 1,2, and 3 correspond to the three selected matrix with corresponding X-ray diffraction data.
minerals (say, quartz, calcite, and dolomite) and form
the vertices of the chosen triangle of Chart CP-21. In-
Table 6-4
dices 4 and 5 correspond to the feldspar and clay correc- Comparison of Litho-Analysis data with X-ray diffraction on
tions obtained from the spectral measurement of Th and cores.
K.
There are now three unknowns (P,, Pz, and P3) and
three equations. Minimum and maximum amounts of
clay can be set by not ‘allowing a negative PI.

PRESENCE OF EVAPORITES
Eqs. 6-19 through 6-25, with some constraints on the pro- Limestone 0% 19% 12% 8% Litho-Analysis
portion of clay, define the basic Litho-Analysis model. 0 19 3 3 X-ray diffraction
However, a test must be applied to detect evaporites- Dolomite 0% 0% 0% 0% Litho-Analysis
anhydrite and salt. The Litho-Analysis model accepts the 0 0 0 0 X-ray diffraction
existence of two models: (1) a calcite, quartz, dolomite Feldspar 0% 0% 0% 0% LithoAnalysis
(plus the allowance of a clay/feldspar correction) model; Trace 1 0 Trace X-ray diffraction
and (2) an aahydrite, salt, dolomite model. Then, the pro- Siderite - - - - Litho-Analysis
bability of each model is computed. The fmal estimates Trace 0% 1% 1% X-ray diffraction
of calcite, quartz, dolomite, anhydrite, and salt are just
IIke 0% 0% 0% 0% Litho-Analysis
those. obtained from the Litbo-Density measurements 2 1 2 4 X-ray diffraction
(with Model 1 corrected for clay, feldspar) for each of
Clay 2 15% 6% 6% 13% Lithc-Analysis
the two models. However, they are weighted in accor- 7 6 8 14 X-ray diffraction
dance with the probability of the respective models.
1557.86
b12
LOG INTERPRETATION PRINCIPLES/APPLICATIONS

FLUID IDENTIFICATION 4. Sem, O., Baldwin, J., and Quirein, J.: “Theory, Interpretation,
and Practical Applications of Natural Gamma Ray Spectroswpy,”
Most of the discussion to this point has involved the use Trans., 1980 SPWLA Annual Logging Symposium, paper Q.
of porosity logs in determining porosity when the rock 5. Gaymard, R. and Poupon, A.: “Response of Neutron and Fw
lithology is not known or when the rock matrix consists mation Density Logs in Hydrocarbon-Bearing Formations,” The
of two or more known minerals in unknown proportions. Log Anu/y.vt (Sept.-Oct. 1968).
6. Burke, J.A., Campbell, R.L., Jr., and Schmidt, A.W.: “The
These techniques generally require that the fluid Litho-Porosity Crossplot,” The Log Ana(ysr (Nov.-Dec. 1969).
saturating the rock pores is known and is a liquid. 7. Haasan, M. and Hossin, A.: Contribudon a L’efude des Cm-
Similar combinations of porosity logs can be used to portemenrs du Thorium ef du Pofmium Dam /es Roches Sedimen-
determine porosity when the fluid or fluids saturating the tories, C. R. Acad. Sci., Paris (1975).
pores are unknown but the rock lithology is known. In 8. Edmundson, H. and Raymer, L.L.: “Radioactive Logging
Parameters for Common Minerals,” TheLog Analyst (Sept.-On.
this case, the tool response equation for the density log is 1979).
9. Suau, .I. and Spurfin, J.: “Interpretation of Micaceous Sandstones
eb = 4 [s, eh + (1 - sh) e,l in the North Sea,” Trans., 1982 SPWLA Annual Logging
+ (1 - 4) emo, (Eq. 6-26) Symposium.
10. Quirein, J.A., Gardner, J.S., and Watson, J.T.: “Combined
where Natural Gamma Ray Spectral/Lithe-Density Measurements Ap-
plied to Complex Lithologies,” paper SPE 11143 presented at the
S,, is hydrocarbon saturation in the zone investigated by 1982 SPE Annual Technical Conference and Exhibition.
the density log 11. Delfiner, P.C, Peyret, O., and Sara, 0.: “Automatic Determina-
tion of Lithology From Well Logs,” paper SPE 13290 presented
and at the 1984 SPE Annual Technical Conference and Exhibition.
12. Log Interpretaiion Chnns, Schlumberger Well Services, Houston
Qh is hydrocarbon density. (1989).
Similar tool response equations can be written for the
neutron and sonic logs.
To determine porosity from Eq. 6-26, the density, and
hence the nature, of the saturating hydrocarbon and/or
the fractions of hydrocarbon and water saturation must
be known. If only one of these parameters is known, the
other can be found by combining the density log with
another porosity log--usually the neutron log. Chart
CP-5 graphically solves the density log response equation
(Eq. 6-26) and a similar neutron log response equation
when the nature of the saturating hydrocarbon is known
approximately. Porosity and gas saturation or water
saturation can be determined.
If the nature of the saturating hydrocarbon is not
known but its fraction of saturation is known, the chart
(CP-9) “Porosity Estimation in Hydrocarbon-Bearing
Formations” permits the estimation of porosity from a
comparison of the density and neutron logs. Hydrocar-
bon saturation can be estimated from a microresistivity
or shallow dielectric measurement. The density of the
hydrocarbon saturation can be estimated from Chart
CP-10.

REFERENCES
1. Raymer,L.L.andBiggs,W.P.: “Matrix Characteristics Defined
by Porosity Computations,” Trans., 1963 SPWLA Annual Log-
ging Symposium.
2. Poupon, A., Hoyle, W.R., and~schmidt, A.W.: “Log Analysis
in Formations with Complex Lithologies,” J. Pef. Tech. (Aug.
1971).
3. Gardner, J.S. and Dnmanoir, J.L.: “Litho-Density Log Interpreta
don,” Trans., 1980 SPWLA Annual Logging Symposium, paper
N.

6-13