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Updated 30 June 2005

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