CHAPTER
NINE: CALCULATING
LITHOLOGY
Table
Of Contents

9.00 Introduction To This Chapter
9.01 Visual Methods of Lithology Identification
9.02 Lithology from Matrix Density
9.03 Lithology from Matrix Travel Time
9.04 Secondary Porosity
9.05 Lithology from Mlith-Nlith Method
9.06 Lithology from Alith-Klith Method
9.07 Elastic Constants from Sonic and Density
Logs
9.08 Lithology from PE-Density-Neutron
9.09 Lithology from Spectral Gamma Ray
9.10 Simultaneous Equation Solutions
9.11 Probabilistic Solutions
9.12 Principal Component Solutions
9.13 Coding Lithology on Plots
9.14 Lithology Identification Routines
9.15 Calibrating Lithology to Core and Sample
Data
9.16
Igneous and Metamorphic Rock Properties
9.17
Tables of Mineral
Properties
Table 9.01 Radioactive and Acoustic
Table 9.02 Radioactive - Expanded List
Table 9.03 Density, Acoustic, Elastic
Properties
9.18 In Conclusion
9.19 Exercises For Chapter Nine
9.20 Bibliography For Chapter Nine
SPECIAL
FEATURE: Guest Chapters by Dr Zoltan Barlai
Principal Components
Analysis (PCA)
Statistical Lithology
Models
Continue
to NEXT CHAPTER
Publication
history: This Chapter formed Chapter Nine of The Log Analysis
Handbook published by Pennwell (1986). Extensive revisions were
added for this electronic edition in June 2002 (Sections 9.08
through 9.12, 9.15). Section 9.00 updated Oct 2003, Jan 2008. Section 9.16
and 9.17 added Oct 2004, updated Jan 2008..
CHAPTER
NINE: CALCULATING
LITHOLOGY
9.00
Introduction To This Chapter
This Chapter deals in detail with lithologic analysis, based
first on visual observation of the logs, and second by evaluation
of computed matrix values. As discussed in earlier Chapters, none
of the logs measures what we really want to know, so visual or
mathematical analysis is needed. The use of crossplots for matrix
identification is discussed in Chapter Eleven.
In
oil field applications of logs, interest is primarily directed
to definition of the amount and type of fluids in the formations.
These determinations require that matrix effects be defined and
accounted for through appropriate assumptions about the mineralogy
of the reservoir or by combinations of logging measurements that
automatically compensate for mineral effects. In addition, we
have found that a knowledge of the mineral composition of the
reservoir aids in understanding its depositional environment, porosity
distribution, production characteristics, and exploitation potential.
In
coal, evaporite, and mineral exploration, the primary interest
is in the identification of the minerals - porosity is usually
negligible. Mathematically, the oil-field and mining situations
are identical, so the methods described here apply to both disciplines.
Before
proceeding, we need to define the nature of rocks more clearly.
An element is a primary component of a chemical compound.
Familiar elements are iron (Fe), calcium (Ca), carbon (C), and
oxygen (O).
A
mineral is a naturally occurring inorganic compound with a specific chemical
formula and a defined crystal structure. Many naturally occurring
minerals are impure, so their chemical makeup varies slightly.
Familiar mineral compounds are quartz SiO2) and calcite (CaCO3).
A rock is made from a mixture of minerals, although one
mineral may dominate. For example, some sandstones are mostly quartz
(SiO2) but many other minerals may also be present. Other sandstones
may be mostly feldspar with little quartz. Limestone is a rock
containing mostly calcite (CaCO3) but other minerals may be mixed
with it. Most rocks have a wide range of minerals and the fraction
of each mineral in a rock may vary widely from one sample to
another.
Minerals are often described by, and hand samples identified
by, their hardness, magnetic response, colour, luster, streak,
cleavage, crystal form, specific gravity, reaction to acid, or even
their taste and smell. These terms are useless for petrophysical log
analysis, which relies on physical properties that can be measured
remotely in a well bore, such as density, acoustic velocity, neutron
and gamma ray response, or electrical resistivity.
Minerals are classified into groups and sub-groups.
Silicate minerals have silicon and oxygen in their composition. There are four
types of silicate minerals:
-
Single chain
silicate (eg. augite)
-
Double chain
silicate (eg. hornblende)
-
Sheet silicate
(eg. micas and clays)
-
3-D framework
silicate (eg. feldspars, quartz)
Silicates are also divided into two groups based on their
color and density. Light (nonferromangesian) silicates are light in
color and have a specific gravity around 2.7. Light silicates
contain various amounts of aluminum, potassium, calcium and sodium.
Dark (ferromagnesian) silicates are dark in color and have a
specific gravity ranging from about 3.2 to 3.6. They contain mostly
iron and magnesium.
All other minerals are put into the non-silicate group, then
broken down into six subgroups:
-
Carbonates -
minerals that contain carbon and oxygen
-
Oxides -
minerals with an oxygen base
-
Sulfides -
minerals that contain sulfur
-
Sulfates -
minerals that contain sulfur and oxygen
-
Halides -
minerals that contain a metal and a halogen element
-
Native metals -
copper, silver, gold, zinc, iron, and nickel
Because
the earth has an active surface, minerals (in the form of rocks) are
under constant change. Molten rock from the interior of the earth
can be exposed at the surface from volcanos or mid-ocean ridges.
When molten these rocks are called lava flows and when cool they are
called igneous rocks.
As
igneous rocks are eroded by weather and water, they become lose
grains or dissolved in water. When deposited, they become soil or
sediment, and later under the pressure of overburden, turn into
sedimentary rocks.
If
sedimentary rocks are forced deep enough, heat and pressure modify
the rock structure. These are called metamorphic rocks.
All
three kinds of rocks can contain porosity that can hold economic
quantities of oil and gas, although sedimentary reservoirs are much
more common. Any of these rock types can re-enter the mantle and
become molten again, by subduction at the edges of tectonic plates.
This cycle of igneous – sedimentary – metamorphic is called the rock
cycle.
The majority of this
Chapter deals with sedimentary rocks because the majority of
petrophysical analysis is performed on sedimentary rocks. However,
igneous and metamorphic rocks do form important reservoirs. See
Section 9 .17.
Sedimentary rocks are an accumulation of fragments of many pre-existing rocks. Weathering
is a process by which rocks are broken down into sediments. There
are two types of weathering:
-
Mechanical -
weathering in which physical process such as frost wedging and
unloading break down rocks.
-
Chemical -
weathering in which chemical processes such as oxidation break
down rocks.
Transport describes the process by which sediments are moved
across the surface. Types of transport include fluvial, glaciers,
wind (aolean), and gravity.
Depositional environments describes where
sediment comes to
rest, The three main groups however are:
-
Continental -
deserts, lakes, river beds, swamps, and caves
-
Continental and
Marine - deltas
-
Marine - ocean
Lithification is the process by which sediments come together to form a sedimentary
rock. There are three ways in which this is done:
-
Compaction –
the intense weight and compression caused by the weight of
overburden welds sediments together to form a sedimentary rock
-
Cementation -
sediments are cemented together by precipitation. Of other
minerals
-
Crystallization
- process where an existing solution creates a sedimentary rock.
The
texture of a rock is based on the size, shape, and arrangement of the grains and
other parts of the rock. Sedimentary rocks can be broken down into
five different textures:
-
Clastic -
consists of broken fragments of preexisting rock.
-
Bioclastic
- consists of the remains of organic material.
-
Crystalline
(Nonclastic) - minerals are in a pattern of interlocking
crystals.
-
Amorphous -
no crystal structure .
-
Oolitic -
made of small round particles of calcium carbonate.
Mineral
composition in sedimentary rocks varies widely.
-
Silica
-
Carbonate
-
Clay Minerals
-
Organic Matter
-
Evaporites
-
(Volcanic) Rock
Particles
-
Heavy Minerals
-
Feldspar
Many
descriptive terms are used to define rock samples, most cannot be
determined directly from petrophysical logs. Shape, sorting, bedding
type and bed thickness are common terms. Size of the sedimentary
particles is a semi-quantitative approach to sample description and
assists the petrophysicist in understanding the rock texture. Terms
used are:
-
Clay - <1/256mm
-
Silt - 1/256mm
– 1/16mm
-
Sand - 1/16mm –
2mm
-
Pebble- 2mm –
64mm
-
Cobble - 64mm –
256mm
-
Boulder - >256mm
The
kinds of rocks we can identify with well logs depend on the logging tools
that have been run in the well bore,
the rock mixtures present, and local zone knowledge. In clastic
and carbonate sections, we can usually identify quartz, shale,
limestone, dolomite, anhydrite, coal, pyrite or glauconite or
siderite or
other heavy minerals, salt, potash, trona, sulphur, gypsum, and
a few rarer minerals like fluorite or barite, provided the minerals
occur as mixtures of only a few components and we have a full
modern log suite. Shale minerals, such as montmorillonite, illite,
and chlorite, can be distinguished if we have additional logs.
Kaolinite and feldspars can also be defined under certain conditions,
as can mica. Although not discussed in this Chapter, hardrock
minerals and uranium deposits can be evaluated with well logs.
The
mineralogy of unconventional reservoir rocks, such as granite,
metamorphic, and volcanic rocks, can be evaluated with the techniques
described here, provided the list of minerals is small and their
physical properties can be determined.
In
most carbonate reservoirs, the lithology is usually reasonably
well known from sample descriptions or can be determined from
log response. This is not true in sandstones because the mineral
makeup of the sand is NOT usually described in much detail. There
is a universal trend to give sandstones the physical properties
of pure quartz, but this is almost universally NOT appropriate.
Most sandstones contain other minerals such as mica, volcanic
rock fragments, calcite, dolomite, anhydrite, and ferrous minerals,
as well as the shale and clay described above. All of these minerals
have different density, acoustic, and neutron properties than
quartz. If a sandstone is assumed to be pure quartz when it is
not, the commonly used properties of quartz will provide pessimistic
porosity answers.
Thus,
authors and service company manuals that present mineral properties
for “sandstone” are misleading their audience into
believing these properties are constant. In more than 40 years
of petrophysical analysis, I have never seen a thin section or
XRD report that gave an assay of 100% quartz in any petroleum
reservoir. A 100% quartz sand is very rare. If anyone doubts this
statement, look at the PEF curve. If it reads more than 1.8, you
have “quartz plus other things” in your sandstone.
There
is a story (it may even be true) that reserves for the early North
Sea discoveries were seriously underestimated because the mica
in the sands was not accounted for properly. The engineers used
density log porosity without correcting for the real matrix density.
If true, good engineering practice would have undersized all the
offshore equipment and early cash flow and rate of return on investment
would have been significantly reduced. If the myth that sandstone
is pure quartz is perpetuated, there will be more economic blunders
of this type.
To
further confuse the uninitiated, many logs show data on a "porosity"
scale. These log curves are transforms of some measured physical
property to an approximate porosity based on some arbitrary parameters.
Examples are density, neutron, or sonic porosity on so-called
Sandstone, Limestone, or Dolomite porosity scales. Porosity as
defined by these transforms is only directly useful if there is
no shale, the scale matches the rock mineralogy. and there are
no accessory minerals. Real reservoirs are rarely this simple.
DO NOT use these porosity transforms without further analysis
unless all the arbitrary assumptions used to create them match
exactly the rock you are analyzing.
Some
people call these porosity curves an “interpretation”.
They are not. They are merely a transform of the raw data to a
more attractive scale. The difference between a transform and
an interpretation is critical. Interpretation infers some intelligent
thought went into creating and understanding the result. The service
company running the log does not provide interpretations. YOU
are the interpreter.
There
are endless cases where a transform to an inappropriate porosity
scale has caused millions in losses due to poorly informed analysts
who see “gas cross over” when there is no gas, or
who read porosity directly from the transform and either seriously
over estimate or under estimate reservoir effective porosity.
In
spite of these comments, a number of charts and tables in this
Chapter and elsewhere in this Handbook show the word "sandstone'
when they really should say "quartz". I have not edited
the charts and tables taken from common sources, such as service
company chart books, so the common usage of incorrect terminology
is repeated even here.
It
should be noted also that this book uses the term "matrix
rock" to mean the solid, non-shale portion of a porous or
non-porous rock. In petrographic descriptions, "matrix"
is the clay between rock grains.
9.01
Visual Methods of Lithology Identification
Visual identification of lithology depends on the relative values
between two or more log curves as well as absolute values of one
or more curves. It is the separation between density and neutron
data, for example, that helps identify both carbonates and shaly
sands. The absolute values of the log readings help identify evaporites,
coal, gypsum, and anhydrite.
When
a single porosity log is all that is available, it is difficult
and sometimes impossible to find a baseline that will indicate
lithology. Use a sample description or regional knowledge to define
rock matrix, then proceed to estimate porosity as described earlier.
FIGURE
9.01: Sandstone/Shale identification
Visual
identification of lithology is best explained by describing a
few examples. In Figure 9.01, the density neutron log and the
gamma ray are used to identify sandstone and shale as the basic
rock components. This is evident because the logs are recorded
on a sandstone scale, and the two logs read about the same porosity
in the clean (non-shaly) zones. Therefore, sandstone is indicated.
If the logs had been recorded on limestone scales, crossover of
6 to 7% porosity would have occurred - again indicating sandstone,
or a gas filled limestone.
If
some other minerals were present, such as limestone, coal, or
siderite beds, then the specific log characteristics for those
zones would stand out from the average sand and shale values.
For example, a limestone bed would be evident on the density log
by its apparent low or negative porosity (high density) when recorded
on a sandstone scale. Siderite, which is an iron rich mineral,
may show a low or negative porosity as well. It would be hard
to distinguish, by visual means alone, between it and a limestone
stringer in a sandstone sequence.
On
a sonic log in a sand-shale sequence, there may be a few tight
sandstones which will record values close to the matrix value
of sandstone, which is 55.5 microseconds per foot (or 182 microseconds
per meter). Such tight sandstones may not be present in a well
and therefore it would be difficult to prove that the sequence
is sand-shale just from the sonic log alone. Data from Figure
9.02, from Classic Example 1, does not show any baselines suitable
for identifying lithology.
A
more complex example is shown in Figure 9.03, in which coal and
dolomite appear as well as sands and shales.
FIGURE
9.02: Lithology from a single log is usually impossible
Figure
9.03 shows a carbonate sequence from Classic Example 2, logged
on a limestone scale with a density neutron log. Here the density
and neutron both read similar values in clean, non-shaly limestone.
There is a separation of 8 to 12 porosity units if the carbonate
is a pure dolomite and is fairly clean. Shale can also have this
kind of separation, so the gamma ray log is necessary to define
dolomite from shale. Anhydrite shows a separation of 12 to 20
porosity units.
FIGURE
9.03: Lithology assessment in a carbonate sequence
On
a limestone scale log, the rules for mineral identification are
pretty simple:
* PHIN near PHID, low GR = limestone or gas in dolomite
* PHIN - PHID > 0.10, low GR = dolomite
* PHIN - PHID > 0.15, low GR = anhydrite
* PHIN < PHID, low GR = sandstone or gas in limestone
* PHIN near PHID, both > 0.40 = coal
* PHIN > PHID, high GR = shale
Remember,
the above rules are for compatible scale density neutron logs
recorded on limestone units scale. Add 0.07 to all the separation
values if logs are recorded on sandstone scale.
A
neat tool developed by Yalcin Pekiner for learning the separation
rules is located HERE.
When
the photo-electric curve is available, the density neutron rules
can be enhanced by the following when GR is low (not too shaly):
*
PE near 2 = sandstone
* PE near 3 = dolomite
* PE near 5 = limestone or anhydrite
* PE < 1 = coal or bad hole
* PE > 7 = barite in mud, PE is probably useless everywhere
The
most ambiguous case is radioactive dolomite (PHIN > PHID, PE
near 3, high GR) as this is often mistaken for shale. The thorium
curve on a natural gamma ray spectral log can be used to differentiate
– dolomite has low thorium, shale has high thorium.
Radioactive
sandstone (feldspar sands, granite wash) has high GR but density
neutron separation and PE follow the rules given above. The thorium
curve will also help as feldspar sands have low thorium (and high
potassium) while shale has high thorium (and may have high potassium
as well).
Radioactive
limestones are usually fractured but otherwise they obey the normal
PE and separation rules since the radioactivity is from uranium
salts and not feldspar. Again the spectral gamma ray is helpful,
showing high uranium. If a uranium corrected gamma ray curve (CGR)
is available, compare it to the total gamma ray curve (SGR or
GR). CGR < SGR means uranium is present.
Crossplots
in Section 9.09 may help to honour these rules for radioactive
minerals.
FIGURES
9.04 and 9.05: Sonic and density-neutron logs in evaporite sequence
The
evaporite sequence shown in Figure 9.04 and 9.05 can be interpreted
by comparing the absolute log values to the data in Section
9.16, which contains usual log readings for the commonly encountered
sedimentary minerals. Lithology identification is aided materially
in evaporites by sonic log data (Figure 9.04).
The
matrix rock values for common sedimentary minerals is given in
Section 9.16 and for igneous and metamorphic
rocks in Section 9.17.
As
with shaly sand sequences, the sonic is not especially helpful
in carbonate sequences, as far as visual identification is concerned.
Another complex lithology example is shown in Figure 9.06; layers
are well defined by the density neutron separation.
Figure
9.06: Lithology analysis on density neutron log
The
most recent advances in visual identification of lithology make
use of the photoelectric effect (PE) curve of the lithodensity
log, in combination with the density and neutron log readings.
The rules were given earlier in this Section.
The
photoelectric effect for pure minerals are listed in Table 9.01,
and vary slightly with porosity and hydrocarbon type. The amount
of variation is shown in Figure 9.07.
Even
though literature suggests strongly that there is no porosity
effect, and most formulae make this assumption, the variation
in water filled high porosity can be as much as 15% of the PE
value. This is not trivial and should be considered when using
PE data for estimation of lithology in dual mineral situations.
It
is fortunate that the PE values for common minerals (quartz, calcite,
and dolomite) do not overlap, even with porosity effect, so interpretation
is relatively clear cut.
However,
anhydrite falls near calcite and must be distinguished by its
characteristic high density.
Shales
and shaly sands can fall anywhere in the PE spectrum depending
on the clay type and the amount of shale. A pure shale of illite
would fall near dolomite, but a pure shale of kaolinite or montmorillonite
would fall near sandstone. Chlorite shales have abnormally high
PE values and can usually be distinguished. Thus shaly sands can
fall anywhere between quartz (PE = 1.81) and chlorite (PE = 6.3)
depending on clay type and shale content.

FIGURE 9.07: PE vs water filled porosity in various minerals
The
visual overlay method for the neutron density and photoelectric
data works quite well for some two mineral situations. Again,
it is the separation between the curves that counts. A schematic
diagram, based on the data in Section 9.16, is shown in Figure
9.08.
FIGURE
9.08: PE values and density neutron separation help define lithology
Note
that the density neutron log is in limestone units and no gas
effect is present.
If
gas effect is present, then ambiguity still persists. If shale
is present, the overlay should not be used. An example of real
log data is provided in Figure 9.09. A similar example for shale
identification is shown in Figure 9.10.

FIGURE
9.09: PE and density neutron in various lithologies

FIGURE 9.10: PE and GR in shaly sections
9.02
Lithology from Matrix Density
The response equation for the density log follows the classical
form:
DENS = PHIe * Sxo * DENSw (water term)
+ PHIe * (1 - Sxo) * DENSh (hydrocarbon term)
+ Vsh * DENSsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * DENSi) (matrix term)
WHERE:
DENSh = log reading in 100% hydrocarbon
DENSi = log reading in 100% of the ith component of matrix rock
DENS = log reading
DENSHsh = log reading in 100% shale
DENSw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)
By
rearranging the density response equation, we can derive apparent
matrix density, based on the final effective porosity, shale volume,
and the density log reading. Sxo is assumed to be 1.0. The matrix
density thus derived can be compared to the data in Table 9.01
to find an approximate lithology.
If
PHIe is derived from a crossplot method (with or without the use
of the density data), or from any one-log shale corrected method,
the matrix density (DENSMA) can be back calculated as follows.
| NAME
- DENSma - Apparent Matrix Density |
|
Calculate
density log value from porosity log reading.
1: C = 2.71 - 0.06 * (IF LOGUNIT$ = "SANDSTONE")
2: DENS = PHID + (1 - PHID) * C
3: DENSSH = PHIDSH + (1 - PHIDSH) * C
4: DENSW = DENSW / (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))
Rearrange
the response equation to solve for DENSMA.
5: IF Vsh + PHIe < 0.95
6: THEN DENSma = (DENS - PHIe*DENSW - Vsh*DENSSH) / (1 - PHIe
- Vsh)
* (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))
7: OTHERWISE DENSma = DENS
WHERE:
C = matrix density corresponding to logging units (SS or LS)
DENS = density log reading (gm/cc or Kg/m3)
DENSma = calculated matrix density (gm/cc or Kg/m3)
DENSSH = density log reading in shale (gm/cc or Kg/m3)
DENSW = density log reading in water (gm/cc or Kg/m3)
PHID = porosity log reading (fractional)
PHIe = effective porosity from any method (fractional)
PHIDSH = porosity log reading in shale (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This equation will break down when PHIe plus Vsh approaches 1.0,
so we limit the use of the equation to those cases where PHIe
+ Vsh < 0.95.
The
matrix density will be too low in gas zones and in rough hole.
No obvious correction can be made to overcome this problem. Do
not use apparent matrix densities under these conditions.
The
standard density neutron crossplot can be used to determine matrix
density, as shown in Figure 9.11.

FIGURE 9.11: Density neutron crossplot to find DENSma
NAME:
DlithCODE$ - Density Lithology Codes
|
|
To
produce a lithology code on computer listings, we bracket the
DENSma values as follows:
DENSma DlithCODE$
< 2630 and bad hole HOLE
< 2630 and coal trigger set COAL
< 2630 and good hole GAS
2630 - 2659 QRTZ
** 2660 - 2699 LMSD
** 2700 - 2729 LIME
** 2730 - 2799 LMDL
2800 - 2879 DOLO
2880 - 3149 ANHY
3150 and above HEVY
no value computed ----
any value and Vsh > 0.85 SHLE
** Could be DLSD if PE < 3.0
Evaporites
require special handling in computer programs and the above codes
should be expanded to include:
DENSma DLITHCODE$
2500 - 2629 gas or bad hole as above
2300 - 2499 GYPS
2000 - 2299 and low sonic SALT
2000 - 2299 and high sonic SULF
1800 - 1999 SYLV
1500 - 1799 CARN
COMMENTS:
Bad hole codes override any lithology code created from density
data.
NAME:
VROCKd - Rock Volume from Matrix Density for Two Mineral
Mode
|
|
To
produce the fraction of each mineral present in a two-mineral
model, the computed matrix density is interpolated linearly between
the two end point densities. This is merely a rearrangement of
a response equation written in terms of matrix density, where
all terms go to zero except the matrix term.
1: Vrock = (1.0 - Vsh - PHIe)
2: V1 = (DENSma - DENS2) / (DENS1 - DENS2) * Vrock
3: V2 = Vrock - V1
WHERE:
DENSma = computed matrix density (gm/cc or Kg/m3)
DENS1 = density of first mineral (gm/cc or Kg/m3)
DENS2 = density of second mineral (gm/cc or Kg/m3)
PHIe = effective porosity (fractional)
Vrock = rock volume (fractional)
Vsh = volume of shale (fractional)
V1 = volume of first mineral (fractional)
V2 = volume of second mineral (fractional)
COMMENTS:
This solution ensures that the sum of all components equals one.
To obtain V1 and V2 as comparative volumes, set Vrock = 1 in equations
2 and 3.
PARAMETERS:
*
English Metric
* gm/cc Kg/m3
DENSSH
2.50 - 2.83 2500 – 2830
(choose from log)
KD
0.25 - 0.70 0.25 - 0.70
DENSW
Fresh drilling mud
1.00 1000
Salty drilling mud
1.10 1100
DENSMA
Clean Quartz
2.65 2650
Calcite
2.71 2710
Dolomite
2.87 2870
Anhydrite
2.95 2950
Gypsum
2.35 2350
Mica Muscovite
2.83 2830
Biotite
3.20 3200
Clay Kaolinite
2.64 2640
Glauconite
2.83 2830
Illite
2.77 2770
Chlorite
2.87 2870
Montmorillonite
2.62 2620
Barite
4.08 4080
NaFeld Albite
2.58 2580
Anorthite
2.74 2740
K-Feld Orthoclase
2.54 2540
Iron
Siderite 3.91 3910
Ankerite
3.08 3080
Pyrite
5.00 5000
Evaps Fluorite
3.12 3120
Halite
2.03 2030
Sylvite
1.86 1860
Carnalite
1.56 1560
Coal Anthracite
1.47 1470
Lignite
1.19 1190
NUMERICAL
EXAMPLE:
1. For Sand D in Classic Example 1:
PHID = 0.12
PHIe = 0.11
Vsh = 0.33
DENSW = 1000 Kg/m3
DENSMA = 2150 Kg/m3
C = 2.71 - 0.06 = 2.65
DENS = 0.12 + (1 - 0.12) * 2.65 = 2.452
DENSSH = 0.03 + (1 - 0.03) * 2.65 = 2.600
DENSW = 1000 / 1000 = 1.000
DENSma = (2.452 - 0.11 * 1.0 - 0.33 * 2.65) * 1000 / (1 - 0.11
- 0.33) = 2620 Kg/m3
2.
If we use the Vsh from the density neutron crossplot (Vsh = 0.59)
DENSma = (2.452 - 0.11 * 1.0 - 0.59 * 2.65) * 1000 / (1 - 0.11
- 0.59) = 4680 Kg/m3
This
is an impossible result which suggests that the shale volume or
the effective porosity is wrong. Calculated matrix density can
thus be used as a quality control indicator when it exceeds reasonable
bounds.
3.
Assume the two mineral model consists of quartz and dolomite and
the computed matrix density is 2680 Kg/m3. Then:
Vsh = 0.10
PHIe = 0.20
DENS1 = 2650 Kg/m3 (Sandstone)
DENS2 = 2870 Kg/m3 (Dolomite)
Vrock = 1 - 0.10 - 0.30 = 0.70
V1 = (2680 - 2870) / (2650 - 2870) * 0.70 = 0.60
V2 = 0.70 - 0.60 = 0.10
Note
that V1 + V2 + Vsh + PHIe = 1.0 and that V1 and V2 do not represent
the fraction of each matrix rock relative to each other, but to
the total bulk rock volume.
9.03
Lithology from Matrix Travel Time
The apparent matrix travel time can be calculated in a similar
fashion to the matrix density, again by rearrangement of the response
equation.
NAME:
DELTma - Apparent Matrix Travel Time |
|
1:
IF Vsh + PHIe < 0.95
2: THEN DELTms = (DELT - PHIe * DELTW - Vsh * DELTSH) / (1 - PHIe
- Vsh)
3: OTHERWISE DELTma = DELT
WHERE:
DELT = sonic log reading (usec/ft or usec/m)
DELTma = calculate matrix travel time (usec/ft or usec/m)
DELTSH = sonic log reading in shale (usec/ft or usec/m)
DELTW = sonic log reading in water (usec/ft or usec/m)
PHIe = effective porosity from any method (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This equation also breaks down with high values of PHIe + Vsh,
so we set DELTma = DELT when PHIe + Vsh > 0.95.
The
matrix travel time can be obtained graphically from the chart
in Figure 9.12.

FIGURE 9.13: Sonic neutron crossplot to find DELTma
NAME:
SlithCODE$ - Sonic Lithology Codes |
|
Lithology
codes are more difficult to generate with sonic data then with
density data.
| DELTma |
|
|
| English |
Metric |
SlithCODE$ |
| usec/ft |
usec/m |
|
| <
41 |
<
134 -- |
---- |
| 41
- 45 |
134
- 147 |
DOLO |
| 45
- 49 |
147
- 160 |
LIME |
| 49
- 51 |
160
- 167 |
ANHY |
| 51
- 58 |
167
- 190 |
QRTZ |
| 58
- 65 |
190
- 213 |
---- |
| 65
- 68 |
213
- 223 |
SALT |
| 68
- 72 |
223
- 236 |
---- |
| 72
- 76 |
236
- 249 |
SYLV |
| 76
- 80 |
249
- 262 |
CARN |
| 80
- 120 |
262
- 393 |
COAL
(only if trigger set) |
| 120
- 124 |
393
- 406 |
SULF |
| >
124 |
>
406 - |
--- |
| if
Vsh > 0.85 |
|
SHLE |
COMMENTS:
The bad hole code does not intervene in sonic calculations.
Should
not be used in shallow unconsolidated sandstones.
NAME:
VROCKs - Rock Volume from Matrix Travel Time for Two
Mineral Mode
|
|
Linear
interpolation of the DELTma value between the two end points of
a two mineral model can be accomplished in a fashion similar to
the matrix density described earlier.
1: Vrock = 1 - Vsh - PHIe
2: V1 = (DELTma - DELT2) / (DELT1 - DELT2) * Vrock
3: V2 = Vrock - V1
WHERE:
DELTma = computed matrix travel time (usec/ft or usec/m)
DELT1 = matrix travel time for first mineral (usec/ft or usec/m)
DELT2 = matrix travel time for second mineral (usec/ft or usec/m)
PHIe = effective porosity from any method (fractional)
V1 = volume of first mineral (fractional)
V2 = volume of second mineral (fractional)
Vrock = rock volume (fractional)
COMMENTS:
This solution guarantees that all components sum tp 1.00. To obtain
V1 and V2 as comparative volumes, set Vrock = 1 in equations 2
and 3.
PARAMETERS:
English Metric
usec/ft usec/m
DELTSH
60 - 150 190 – 480
KCP 1.0 - 1.4 1.0 - 1.4
KS 0.7 - 1.0 0.7 - 1.0
DELTW
Fresh drilling mud 200 656
Salty drilling mud 188 616
DELTMA
Clean Quartz 55.5 182
Calcite 47.3 155
Dolomite 44.0 144
Anhydrite 50.0 164
Gypsum 52.4 172
Mica Muscovite 47.3 155
Biotite 55.5 182
Clay Kaolinite 64.3 211
Glauconite 55.5 182
Illite 64.6
212
Chlorite 64.6 212
Montmorillonite 64.6 212
Barite 69.8
229
NaFeld Albite 47.3 155
This graph does not include shale corrections
Anorthite 45.1 148
K-Feld Orthoclase 68.9 226
Iron Siderite 44.0 144
Ankerite 45.7 150
Pyrite 39.6
130
Evaps Fluorite 45.7 150
Halite 67.0
220
Sylvite 63.8
242
Carnalite 78.0 256
Coal Anthracite 105 345
Lignite 160
525
NUMERICAL
EXAMPLE:
1. Assume Sand D in Classic Example 1.
DELT = 300 usec/m
DELTSH = 328 usec/m
Vsh = 0.33
DELTW = 616 usec/m
PHIe = 0.11
DELTma = (300 - 0.11 * 616 - 0.33 * 328) / (1 - 0.11 - 0.33) =
229 usec/m
This
value falls in the impossible area and is too high because the
sonic log reads high compared to effective porosity found from
the density neutron crossplot. If porosity was 0.16, the matrix
travel time would be 183 usec/ft (close to the sandstone value).
This
is another quality control indicator, and in this example demonstrates
a lack of coherence between the sonic and density neutron data,
when the matrix, shale and fluid assumption are as given above.
Either these parameters, or the log data, or the whole rock model
are in error.
9.04
Secondary Porosity
The sonic log does not always see vuggy (or secondary) porosity,
so this value can be found be comparing sonic and crossplot porosity.
However, the sonic porosity must be based on the same matrix as
the density neutron crossplot.
NAME:
PHIsec - Secondary Porosity |
|
Find
pseudo matrix travel time.
1: DENSma2 = DENSma / (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))
2: IF DENSma2 > 2.71
3: THEN DELTma2 = ( -5 * DENSma2 + 14.35) / 0.16 + 43
4: OTHERWISE DELTma2 = ( -7.5 * DENSma2 + 20.325) / 0.064 + 48
5: DELTma2 = DELTma2 * (1 + 2.28 * (IF DEPTHUNIT$ = "METRIC"))
These
formulae define a pseudo sonic matrix travel time used to calculate
sonic porosity with the same matrix as the density neutron porosity.
Calculate
sonic porosity.
6: PHIs2 = (DELT - (1 - Vsh) * DELTma2 – Vsh * DELTSH) /
(DELTW - DELTma2)
Compare
to density neutron crossplot porosity.
7: IF PHIs2 > 0
8: AND PHIs2 < PHIx
9: THEN PHIsec = PHIx - PHIs2
10: OTHERWISE PHIsec = 0.0
WHERE:
DELT = sonic log reading (usec/ft or usec/m)
DELTma2 = sonic matrix travel time to match DENSma2 (usec/ft or
usec/m)
DELTW = sonic log reading in water (usec/ft or usec/m)
DENSma2 = computed matrix density converted to English units (gm/cc)
PHIe = porosity from crossplot (fractional)
PHIsec = secondary porosity (fractional)
PHIs2 = porosity from sonic for secondary porosity calculations
(fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This calculation should be done only in carbonate sections since
secondary porosity is not found in sand shale sequences, although
the difference between sonic and density neutron porosity may
be present.
RECOMMENDED
PARAMETERS:
None.
NUMERICAL
EXAMPLE:
1. Assume a limestone with calculated properties of:
DENSma2 = 2.680 gm/cc
PHIe = 0.11
Vsh = 0.10
DELTSH = 100 usec/ft
DELTW = 189 usec/ft
DELT = 75 usec/ft
DELTma2 = (-7.5 * 2.680 + 20.325) / 0.064 + 48 = 51.5
PHIs2 = (75 - (1 - 0.10) * 51.5 - 0.10 * 100) / (189 - 51.5) =
0.135
Since
PHIs2 > PHIe, there is no secondary porosity and PHIsec = 0.0.
2.
Assume DENSma2 = 2.79 gm/cc and DELT = 65 usec/ft
DELTma2 = (-5.0 * 2.79 + 14.35) / 0.16 + 43 = 45.5
PHIs2 = (65 - (1 - 0.1) * 45.5 - 0.10 * 100) / (189 - 45.5) =
0.098
PHIsec = 0.11 - 0.098 = 0.012
9.05
Lithology from Mlith-Nlith Method
One method of numerically evaluating lithology is to use the Mlith-Nlith
method, which uses two formulae nearly independent of the porosity
of the rock. The input data to these algorithms must be shale
corrected, must be in limestone porosity units, and must be in
English units before processing begins.
An alternate version of this model can be made by replacing
Nlith with Plith = PE / (DENS - DENSW) - density in gm/cc. This
avoids the use of the neutron log in cases where it has little
lithology discrimination, such as in igneous rocks.
NAME:
Mlith/Nlith - Lithology from Mlith and Nlith |
|
1:
PHIdc = PHID - Vsh * PHIDSH
2: PHInc = PHIN - Vsh * PHINSH
3: PHIsc = (DELT - (1 - Vsh) * 47.3 - Vsh * DELTSH) / (188 - 47.3)
4: DENSc = PHIdc + (1 - PHIdc) * 2.71
5: DELTc = PHIsc * 188 + (1 - PHIsc) * 47.3
6: Nlith = (1.00 - PHInc) / (DENSc - DENSW)
7: Mlith = 0.01 * (DELTW - DELTc) / (DENSc - DENSW)
WHERE:
DELT = sonic log reading (usec/ft or usec/m)
DELTc = sonic log reading corrected for shale (usec/ft or usec/m)
DELTSH = sonic log reading in 100% shale (usec/ft or usec/m)
DELTW = sonic log reading in 100% water (usec/ft or usec/m)
DENS = density log reading (gm/cc or Kg/m3)
DENSc = density log reading corrected for shale (gm/cc or Kg/m3)
DENSW = fluid density (gm/cc or Kg/m3)
Mlith = sonic density lithology factor (fractional)
Nlith = neutron density lithology factor (fractional)
PHIdc = density porosity corrected for shale (fractional)
PHIDSH = density log reading in 100% shale (fractional)|
PHIN = neutron log reading (fractional)|
PHInc = neutron log porosity corrected for shale (fractional)
PHINSH = neutron log reading in 100% shale (fractional)
PHIsc = sonic log porosity corrected for shale (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
By comparing computed values of Mlith and Nlith with those in
the table below, or by plotting them on an Mlith - Nlith crossplot,
rock matrix can usually be identified. The method is relatively
independent of porosity, except for dolomite.
These
two variables are usually called M and N, but they can be confused
with the cementation exponent M and the saturation exponent N,
so we have changed their names to reduce confusion.
PARAMETERS:
*
PHINMA DENSMA DELTMA MLITH NLITH
PE UMA
Clean Quartz –
0.028 2650 182 0.802
0.623 1.82 4.8
Calcite
0.000 2710
155 0.822 0.585 5.09
13.8
Dolomite
0.005 2870 144
0.769 0.532 3.13 9.0
Anhydrite
0.002 2950 164
0.707 0.512 5.08 15.0
Gypsum
0.507 2350 172 1.002
0.365 4.04 9.5
Mica Muscovite
0.165 2830 155 0.768
0.456 2.40 6.8
Biotite
0.225 3200
182 0.601 0.352 8.59
27.5
Clay Kaolinite
0.491 2640 211 0.753
0.310 1.47 3.9
Glauconite
0.175 2830 182 0.723
0.451 4.77 13.5
Illite
0.158 2770
212 0.696 0.476 3.03
8.4
Chlorite
0.428 2870
212 0.658 0.306 4.77
13.7
Montmorillonite
0.115 2620 212 0.760
0.546 1.64 4.3
Barite
0.002 4080 229
0.383 0.324 261 1065
NaFeld Albite –
0.013 2580 155 0.889
0.641 1.70 4.4
Anorthite
– 0.018 2740 148
0.820 0.585 3.14 8.6
K-Feld Orthoclase –
0.011 2540 226 0.772
0.656 2.87 7.3
Iron Siderite
0.129 3910 144
0.494 0.299 14.3 56.2
Ankerite
0.057 3080
150 0.683 0.453 8.37
25.8
Pyrite
– 0.019 5000 130
0.370 0.255 16.4 82.2
Evaps Fluorite –
0.006 3120 150 0.670
0.475 6.66 20.8
Halite
– 0.018 2030 220
1.172 0.988 4.72 9.6
Sylvite
– 0.041 1860 242
0.295 0.270 8.76 16.3
Carnalite
0.584 1560
256 1.959 0.743 4.29
6.7
Coal Anthracite
0.414 1470 345 1.757
1.247 0.20 0.3
Lignite
0.542 1190
525 1.460 2.411 0.25
0.3
The
end points for the common minerals listed above are plotted in
Figure 9.14.

FIGURE 9.14: Mlith vs Nlith crossplot for two or three mineral
models
NAME:
VROCKm - Rock Volume from Mlith for Two Mineral Mode
|
|
If
the usual lithology is made up of two minerals, then the Mlith
and Nlith values can each be linearly interpolated to find the
fraction of the minerals.
1: Vrock = 1 - Vsh - PHIe
2: V1 = (Mlith - MLITH2) / (MLITH1 - MLITH2) * Vrock
3: V2 = Vrock - V1
WHERE:
Mlith = computed Mlith value of rock mixture
MLITH1 = Mlith of first mineral (fractional)
MLITH2 = Mlith of second mineral (fractional)
PHIe = effective porosity from any method (fractional)
V1 = volume of first mineral (fractional)
V2 = volume of second mineral (fractional)
Vrock = volume of rock (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This solution guarantees that all components sum to 1.00. To obtain
V1 and V2 as comparative volumes, set Vrock = 1 in equations 2
and 3.
NAME:
VROCKn - Rock Volume from Nlith for Two Mineral Mode
|
|
If
the usual lithology is made up of two minerals, then the Mlith
and Nlith values can each be linearly interpolated to find the
fraction of the minerals.
1: Vrock = 1 - Vsh - PHIe
2: V1 = (Nlith - NLITH2) / (NLITH1 - NLITH2) * Vrock
3: V2 = Vrock - V1
WHERE:
Nlith = computed Nlith value of rock mixture
NLITH1 = Nlith of first mineral (fractional)
NLITH2 = Nlith of second mineral (fractional)
PHIe = effective porosity from any method (fractional)
V1 = volume of first mineral (fractional)
V2 = volume of second mineral (fractional)
Vrock = volume of rock (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This solution guarantees that all components sum to 1.00. To obtain
V1 and V2 as comparative volumes, set Vrock = 1 in equations 2
and 3.
RECOMMENDED
PARAMETERS:
See above.
NAME:
VROCKmn - Rock Volume from Mlith and Nlith for Three
Mineral Model |
|
If
the usual lithology is made up of three minerals, then the Mlith
and Nlith values can be linearly triangulated to find the fraction
of the minerals.
1: D = (Mlith * (NLITH2 - NLITH1) + Nlith * (MLITH1 - MLITH2)
+ MLITH2 * NLITH1 - MLITH1 * NLITH2) / (MLITH1 * (NLITH3 - NLITH2)
+ MLITH2 * (NLITH1 - NLITH3) + MLITH3 * (NLITH2-NLITH1))
2: E = (D * (NLITH3 - NLITH1) - Nlith + NLITH1) / (NLITH1 - NLITH2)
3: V1 = MAX(0, 1 - D - E) / (MAX(0, 1 - D - E) + MAX(0, D) + MAX(0,
E)) * Vrock
4: V2 = MAX(0, E) / (MAX(0, 1 - D - E) + MAX(0, D) + MAX(0, E))
* Vrock
5: V3 = (1 - V1 - V2) * Vrock
WHERE:
Mlith = computed Mlith value of rock mixture
MLITH1 = Mlith of first mineral (fractional)
MLITH2 = Mlith of second mineral (fractional)
MLITH3 = Mlith of third mineral (fractional)
Nlith = computed Nlith value of rock mixture
NLITH1 = Nlith of first mineral (fractional)
NLITH2 = Nlith of second mineral (fractional)
NLITH3 = Nlith of third mineral (fractional)
PHIe = effective porosity from any method (fractional)
V1 = volume of first mineral (fractional)
V2 = volume of second mineral (fractional)
V3 = volume of third mineral (fractional)
Vrock = volume of rock (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This solution guarantees that all components sum to 1.00. To obtain
V1, V2, and V3 as comparative volumes, set Vrock = 1 in equations
3, 4, and 5.
An
alternate version of this model can be made by replacing Nlith
with Plith = PE / (DENS - DENSW) - density in gm/cc. This avoids
the use of the neutron log in cases where it has little
lithology discrimination, such as in igneous rocks.
RECOMMENDED
PARAMETERS:
See above.
NUMERICAL
EXAMPLE:
1. Assume data from 2135 - 2153 meters in Classic Example 2.
PHID = 0.015
PHIN = 0.15
DELTc = DELT = 190 usec/m = 61 usec/ft
DENSW = 1000 Kg/m3 = 1.00 gm/cc
DENSMA = 2710 Kg/m3 = 2.71 gm/cc
Vsh = 0.0
DENSc = 0.015 * 1.00 + (1 - 0.015) * 2.71 = 2.684
Nlith = (1.00 - 0.15) / (2.684 - 1.00) = 0.50
Mlith = 0.01 * (188 - 61) / (2.684 - 1.00) = 0.77
The
closest values in the table represent dolomite (Mlith = 0.778
and Nlith = 0.516), so this interval is very likely dolomite.
9.06
Lithology from Alith-Klith Method
The Alith-Klith method, like the Mlith-Nlith method, is used to
identify matrix lithology. The term A can be confused with the
tortuosity exponent A used in the water saturation equation, hence
we use the term Alith and Klith instead of A and K.
The
input data to these algorithms must be shale corrected, must be
in limestone porosity units and must be in English units before
processing begins.
NAME:
Alith/Klith - Lithology from Alith and Klith |
|
1:
PHIdc = PHID - Vsh * PHIDSH
2: PHInc = PHIN - Vsh * PHINSH
3: PHIsc = (DELT - (1 - Vsh) * 47.3 - Vsh * DELTSH) / (188 - 47.3)
4: DENSc = PHIdc + (1 - PHIdc) * 2.71
5: D |