# Log analysis: lithology

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Series Development Geology Reference Manual Methods in Exploration Wireline methods Difficult lithologies Khaled Hashmy, Mark Alberty Web page AAPG Store

The term difficult lithologies, as addressed here, refers to a formation composed of two or more mineralogies. The presence of two or more minerals significantly increases the difficulty of determining both porosity and lithology from wireline logs. This article reviews some common techniques that can be used to solve for lithology and porosity. It also addresses some commonly encountered lithologies and their characteristics relative to log responses.

## Identifying the occurrence of difficult lithologies

Figure 1 M-N crossplot for mineral identification. © Schlumberger Well Services, 1979.

The occurrence of difficult lithologies can be identified from the following sources:

• Local knowledge of formations in the area
• Cuttings from the well
• Mudlogs of the well
• Conventional core analysis
• Sidewall percussion core analysis
• Sidewall rotary core analysis
• Analysis of log responses

The methods to determine the occurrence of difficult lithologies from the first six sources just listed are not covered in this article. (For information on these sources, see Mudlogging: drill cuttings analysis and Mudlogging: the mudlog; also see Core description.)

Identifying the occurrence of difficult lithologies from logs can be formidable. Two crossplot techniques are commonly used to identify the occurrence of mineralogies: (1) the M-N crossplot and (2) the MID crossplot.

### M-N crossplot

The M-N crossplot uses the density, compensated neutron, and compressional sonic logs to identify binary and ternary mixtures of minerals. The terms M and N are defined as follows:

$M={\frac {\Delta t_{{{\rm {fl}}}}-\Delta t_{{{\rm {log}}}}}{\rho _{{{\rm {b}}}}-\rho _{{{\rm {fl}}}}}}\times 0.01$
$N={\frac {\phi _{{N{{\rm {fl}}}}}-\phi _{{N\log }}}{\rho _{{{\rm {b}}}}-\rho _{{{\rm {fl}}}}}}$

These values are crossplotted in Figure 1. Binary mixtures of minerals plot along a line connecting the two mineral points. Ternary mixtures of minerals plot in a triangle connecting the three minerals points. Arrows indicate the effects of gas, salt, sulfur, secondary porosity, and shaliness.

### MID crossplot

Figure 2 UMAA determination chart. © Schlumberger Educational Services, 1989.

The MID or matrix identification crossplot uses the apparent volumetric cross section (UMAA) and the apparent matrix grain density (RHOMAA) to identify minerals. UMAA represents the projection of the volumetric photoelectric absorption index, U (the product of Pe and electronic density), to the value at zero porosity. RHOMAA results from a mathematical projection of the bulk density of an interval to its value at zero porosity. These projections to zero porosity effectively eliminate variance due to porosity, resulting in a variance mainly due to lithology.

This method requires that an estimate of total porosity be determined first. Typically, this can be done from a density-neutron crossplot (see Standard interpretation). Using this porosity, an apparent matrix density is determined from the following equation:

${\mbox{RHOMAA}}={\frac {\rho _{{{\rm {log}}}}-\phi \cdot \rho _{{{\rm {fl}}}}}{1.0-\phi }}$
Figure 3 MID plot for mineral identification. © Schlumberger Educational Services, 1989.

UMAA can be determined from the chart in Figure 2. Start by marking the Pe value on the photoelectric portion of the horizontal axis (left side), then go vertically to the bulk density value. Next, move horizontally to the apparent total porosity, and then down to the UMAA value.

Now you can cross plot the RHOMAA and UMAA values on the chart in Figure 3. Binary mixtures of minerals plot along a line connecting the two mineral points. Ternary mixtures of minerals plot in a triangle connecting the three mineral points. Arrows indicate the affects of gas, secondary porosity, salt, barite, and heavy minerals.

## Techniques for analyzing difficult lithologies

Each logging measurement can be expressed in a response equation that relates the recorded log to the volumetric components of lithology and fluids. (For these response equations expressed in their most basic configuration, see Standard interpretation.) These basic equations can be expanded to include any number of mineralogies and fluids.

All the logging response equations can then be set up for each measurement, such as the density, neutron, and sonic. The unknowns must be less than or equal to the number of equations for a unique solution to be obtained. A paramount fact that must be kept in mind is that the number of variables that are being computed cannot exceed the number of equations. For example, if the density, neutron, and sonic logs are being used, the total number of equations that can be set up is four—one for each of the measured logs and the fourth for the material balance equation (exemplifying that the sum of all constituents equals 100% of the volume of the rock). Thus, in this case, only four variables can be computed. Assumptions and local knowledge can be used to constrain the problem by reducing the amount of unknown knowledge.

Once these logging relationships are established for the difficult lithology being addressed, a number of methods are available to solve these equations effectively for a solution. The more commonly used methods are

• Graphical crossplots
• Linear matrix solutions
• Weighted least squares minimization

### Graphical crossplots

A wide variety of crossplots are used for analysis. Basically, these crossplots are designed for use with two porosity measurements and are all generally published in vendor chartbooks. The three most common crossplots are discussed here.

#### Density-compensated neutron crossplot

This type of crossplot is used for binary mixtures of sandstone and limestone, limestone and dolomite, dolomite and anhydrite, and sandstone and shale.

#### Sonic-compensated neutron crossplot

Two versions of the sonic-compensated neutron crossplot exist, one that uses the Wyllie time average equation and the other the Raymer-Hunt-Gardner equation for the sonic porosity relationship. These are used typically for binary mixtures of sandstone and limestone or limestone and dolomite. However, the sonic-compensated neutron crossplot is not particularly useful in fractured or vuggy formations.

#### Density-sonic crossplot

Two versions of the density-sonic crossplot also exist, one using the Wyllie time average equation and the other the Raymer-Hunt-Gardner equation for the sonic porosity relationship. These are used typically for binary mixtures of sandstone, limestone, or dolomite with gypsum, trona, salt, or sylvite. This plot is not particularly useful in fractured or vuggy formations nor for sandstone and limestone or limestone-dolomite mixtures.

#### Linear matrix solutions

Linear matrix solutions are almost always performed on a computer. A matrix is developed for each of the unknowns with the response equations used to describe the relationship between each element of the matrix. The computer uses a matrix solver to find the unique solution to the problem. The response equations must be linear for this system to work. This drawback leads to oversimplification of the response equations, which can result in degradation of the answers.

### Weighted least squares minimizations

The weighted least squares minimization method is always performed on a computer. A number of commercial packages exist, including Global and Elan from Schlumberger, Optima from Western Atlas, ULTRA from Halliburton, and Probe from Scientific Software. Although these software packages are similar in general principle, they differ in individual methods of implementation, flexibility, and assignment of uncertainty.

This methodology uses an algorithm to search the range of possible answers to the problem to find the single answer that best fits the response equations and the measured logs. The equations are not required to be strictly linear, although as the response equation become somewhat nonlinear, the search becomes more difficult and time consuming. An incoherence function is output which is usually a useful indicator of the reliability of the answer (low incoherence is good). These programs are usually very flexible in the input of assumptions and allow virtually any type of mineralogy to be solved.

## Types of difficult lithologies

The more commonly encountered difficult lithologies include

### Shaly sandstones

The interpretation method best suited for shaly sandstones is dependent upon the distribution of shale, the clay type, the mineralogy of the silt fraction, and the resistivity of water within the sandstones. The classic approach is the sand-silt-shale method introduced by Poupon et al.[1] An approximate correction for a single heavy mineral was provided for in this approach. Silt is considered to be primarily quartz. Volume of clay, volume of silt, and porosity are determined from interpolation of the density-neutron crossplot. Matrix response points are defined for sand and silt, water, and dry clay minerals. A wet clay point is defined on the dry clay minerals-100% water line. A shale point was defined on the quartz-wet clay line. The model can then determine porosity, shale volume, and silt index from interpolation in this framework. Water saturation can be determined using an appropriate shaly sandstone resistivity equation. This method does not adequately address the more complex case of shaly sandstones with variable volumes of feldspar, mica, or carbonate material. This model can be solved using the graphical, linear matrix, or least squares minimization method.

The solution for the complex case of sandstones with feldspar, mica, and carbonate material was resolved after log analysts became comfortable with the new spectral gamma ray (K, Th, and U) and photoelectric (Pe) measurements. The spectral gamma ray log is helpful in sandstones containing potassium feldspars or thorium-bearing clays. The natural gamma ray spectra, Pe, density, and neutron expanded response equations can be combined to solve for porosity and to estimate volumes of calcite, quartz, dolomite, clay, feldspar, anhydrite, and salt. Once porosity is determined, saturation can be estimated from the appropriate shaly sandstone resistivity equation. This model is too complex to address using graphical methods and must be done using the linear matrix or least squares minimization method.

The distribution of shale and the salinity of formation water can significantly affect the resistivity of the formation. A variety of saturation models have been developed over the years to describe the influence of these factors. Some commonly used equations are as follows:

Simandoux:
$C_{{{\rm {t}}}}={\frac {C_{{{\rm {w}}}}}{F}}S_{{{\rm {w}}}}^{{2}}+S_{{{\rm {w}}}}V_{{{\rm {sh}}}}C_{{{\rm {sh}}}}$

Indonesia:

$C_{{{\rm {t}}}}={\frac {C_{{{\rm {w}}}}}{F}}S_{{{\rm {w}}}}^{{2}}+{\sqrt {{\frac {C_{{{\rm {w}}}}V_{{{\rm {sh}}}}C_{{{\rm {sh}}}}}{F}}}}S_{{{\rm {w}}}}^{{2}}+S_{{{\rm {w}}}}^{{2}}V_{{{\rm {sh}}}}^{{2}}C_{{{\rm {sh}}}}$

Dual water:

$C_{{{\rm {t}}}}={\frac {C_{{{\rm {w}}}}}{F_{{{\rm {o}}}}}}S_{{{\rm {w}}}}^{{2}}+{\frac {(C_{{{\rm {bw}}}}-C_{{{\rm {w}}}})V_{{{\rm {sh}}}}Q_{{{\rm {v}}}}}{F_{{{\rm {o}}}}}}S_{{{\rm {w}}}}$

Waxman and Smits:

$C_{{{\rm {t}}}}={\frac {C_{{{\rm {w}}}}}{F^{{*}}}}S_{{{\rm {W}}}}^{{n}}+{\frac {BQ_{{{\rm {v}}}}}{F^{{*}}}}S_{{{\rm {w}}}}^{{n-1}}$

For a more complete explanation of water saturation equations and their terms, refer to Worthington[2] or Patchett and Herrick.[3] The Simandoux and Indonesia equations were designed mainly for relatively salty formation waters and moderate amounts of dispersed clay. The dual water and Waxman and Smits equations were designed for all water salinities and moderate amounts of dispersed clays.

Recommended logs to use for interpreting shaly sandstones are

### Carbonates and evaporites

Carbonates and evaporites can complicate the interpretation process through the occurrence of fractures and vugs. The three primary porosity devices—the density, compensated neutron, and sonic—respond differently to the presence of fractures and vugs. The density investigates one side of the borehole, while the compensated neutron averages the formation properties around the borehole. The sonic generally does not respond to the secondary porosity associated with either fractures or vugs. This unequal response to these properties can lead to significant problems in determining lithology from any of the methods, as they generally presume that all the porosity devices see a common porosity and lithology.

Binary mixtures of carbonates or evaporites can be evaluated using graphical crossplot approaches. The density-neutron is generally the most used approach. This method will solve for sandstone-limestone, limestone-dolomite, or dolomite-anhydrite mixtures.

More complicated mixtures are best handled using the linear matrix or preferably the weighted least squares minimization technique. Additional minerals can be identified by incorporating the photoelectric, spectral gamma ray, and sonic logs. Some log measurements do not provide any relevant information in a given section. If the K, Th, and U values are uniformly low in the evaporite minerals, these logs have no resolving ability and are of little help in determining the rock constituents. If dolomite contains uranium, the uranium log is diagnostic.

Recommended logs to use for interpreting carbonates and evaporites are

• Dual laterolog or dual induction
• Density with photoelectric effect
• Compensated neutron
• Compensated sonic
• Spectral gamma ray

### Metamorphic, igneous, and volcanic sequences

The approach to the interpretation of these sequences is similar to that of the carbonate sequences. Evaluation of tuffites and tuffaceous sandstones has been successful using compensated sonic, density, and compensated neutron crossplots on which the minerals form a Uthologic triangle of silica, light tuffite, and heavy tuffite. Models can easily be established for igneous and metamorphic sequences using the linear equations or the weighted least squares minimization approaches. The methods require the identification of the appropriate mineral matrix responses. Table 1 lists the log matrix responses of common minerals.

Table 1 Logging tool responses in sedimentary minerals
Name Formula ρlog g/cc φsnp p.u. φcnl p.u. Δtc μs/ft Δts μs/ft Pe barn/elect U barn/cc ε farads/m tp nsec/m GR APR units Σ c.u.
SILICATES
Quartz SiO2 2.64 1. 2. 56.0 88.0 1.81 4.79 4.65 7.2 4.26
β -Cristobalite SiO2 2.15 2. 3. 1.81 3.89 3.52
Opal (3.5% H2 O) SiO2 (H2 O)1209 2.13 4. 2. 58. 1.75 3.72 5.03
Garnet Fe3 AI2 (SiO4 )3 4.31 3. 7. 11.09 47.80 44.91
Hornblende Ca2 NaMg2 Fe2 AISi8 O22 (O,OHopen hole)2 3.20 4. 8. 43.8 81.5 5.99 19.17 18.12
Tourmaline NaMg3 AI6 B3 Si6 O2 (OHopen hole)4 3.02 16. 22. 2.14 6.46 7449.82
Zircon ZrSiO4 4.50 –1. 3. 69.10 311. 692
CARBONATES
Calcite CaCO3 2.71 0 –1. 49.0 88.4 5.08 13.77 7.5 9.1 7.08
Dolomite CaCO3 MgCO3 2.85 2. 1. 44.0 72. 3.14 9.00 6.8 8.7 4.70
Ankerite Ca(Mg,Fe)(CO3 )2 2.86 0 1. 9.32 26.65 22.18
Siderite FeCO3 3.89 5. 12. 47 14.69 57.14 6.8 – 7.5 88 91 52.31
OXIDATES
Hematite Fe2 O3 5.18 4. 11. 42.9 79.3 21.48 111.27 101.37
Magnetite Fe3 O4 5.08 3. 9. 73. 22.24 112.98 103 08
Geothite FeO(OHopen hole) 4.34 50 + 60 + 19.02 82.55 85 37
Limonite FeO(OHopen hole)(H2 O)2 05 3.59 50 + 60 + 56.9 102.6 13.00 46.67 9.9–10.9 10.5–11.0 71.12
Gibbsite AI(OHopen hole)3 2.49 50 + 60 + 1.10 23.11
PHOSPHATES
Hydroxyapatite Ca5 (PO4 )3 OHopen hole 3.17 5. 8. 42. 5.81 18.4 9.60
Chlorapatite Ca5 (PO4 )3 CI 3.18 1. 1. 42. 606 19.27 130.21
Fluorapatite Ca5 (PO4 )3 F 3.21 1. 2. 42. 5.82 18.68 8.48
Carbonapatite (Ca5 (PO4 )3 )2 CO3 H2 O 3.13 5. 8. 5.58 17.47 9.09
FELDSPARS-Alkali
Orthoclase KAISi3 O8 2.52 2. 3. 69. 2.86 7.21 4.4–6.0 7.0–8.2 ~220 15.51
Anorlhoclase KAISi3 O8 2.59 2. 2. 286 7.41 4.4–6.0 7.0–8.2 ~220 15.91
Microciine KAISi3 O8 2.53 –2. –3. 2.86 7.24 4.4–6.0 7.0–8.2 ~220 15.58
FELDSPARS-Plagioclase
Albite NaAISi3 O8 2.59 – 1. –2. 49. 85. 1.68 4.35 4.4–6.0 7.0–8.2 7.47
Anorthite CaAl2 Si2 O8 2.74 –1. 2. 45. 3.13 8.58 4.4–6.0 7.0–8.2 7.24
MICAS
Muscovite KAl2 (Si3 AIO10 )(OHopen hole)2 2.82 12. 20. 49. 149. 2.40 6.74 6.2–7.9 8.3–9.4 ~270 16.85
Glauconite K2 (Mg,Fe)2 Al6 (Si4O10)3(OHopen hole)2 ~2.54 ~23. ~38. 6.37 16.24 24.79
Biotite K(Mg,Fe)3 (AISi3 O10 (OHopen hole)2 ~2.99 ~11. ~21. 50.8 224. 6.27 18.75 4.8–6.0 7.2–8.1 ~275 29.83
Phlogopite KMg3 (AISi3 O10 (OHopen hole)2 50. 207. 33.3
CLAYS
Kaolinite AI4 Si4 O10 (OHopen hole)8 2.41 34. 37. 1.83 4.44 ~5.8 ~8.0 80–130 14.12
Chlorite (Mg,Fe,AI)6 (Si,AI)4 O10 (OHopen hole)8 2.76 37. 52. 6.30 17.38 ~5.8 ~8.0 180–250 24.87
llite K1.15 Al4 (Si76.5 AI11.5 )O20 (OHopen hole)4 2.52 20. 30. 3.45 8.73 ~5.8 ~8.0 250–300 17.58
Montmorillonite (Ca,Na),(AI,Mg,Fe)4 (Si, AI)8 O20 (OHopen hole)4 (H2 O)n 2.12 40. 44. 2.04 4.04 ~5.8 ~8.0 150–200 14.12
EVAPORITES
Halite NaCI 2.04 –2. –3. 67.0 120. 4.65 9.45 5.6 – 6.3 7.9–8.4 754.2
Anhydrite CaSO4 2.98 1. 2. 50. 5.05 14.93 6.3 8.4 12.45
Gypsum CaSO4 (H2 O)2 2.35 50 + 60 + 52. 3.99 9.37 4.1 6.8 18.5
Trona Na2 CO4 NaHCO3 H2 O 2.08 24. 35. 65. 0.71 1.48 15.92
Tachydrite CaCl2 (MgCI2 )2 (H2 O)t2 1.66 50 + 60 + 92. 3.84 6.37 406.02
Sylvite KCI 1.86 –2. 3. 8.51 15.83 4.6–4.8 7.2–7.3 500 + 564.57
Carnalite KCIMgCI2 (H2 O)6 1.57 41. 60 + 4.09 6.42 ~220 368.99
Langbenite K2 SO4 (MgSO4 )2 2.82 1. 2. 3.56 10.04 ~290 24.19
Polyhalite K2 SO4 MgSO4 (CaS04 )2 (H2 O)2 2.79 14. 25. 4.32 12.05 ~200 23.70
Kainite MgSO4 KCI(H2 O)4 2.12 40. 60 + 3.50 7.42 ~245 195.14
Kieserite MgSO4 H2 O 2.59 38 43. 1.83 4.74 13.96
Epsomite MgSO4 (H2 O)2 1.71 50 + 60 + 1.15 1.97 21.48
Bischofite MgC12 (H2 O)6 1.54 50 + 60 + 100. 2.59 3.99 323.44
Barite BaSO4 4.09 –1. 2. 266 82 1091. 6.77
Celestite SrSO4 3.79 –1. –1. 55.19 209. 7.90
SULFIDES
Pyrite FeS2 4.99 –2. 3. 39.2 62.1 16.97 84.68 9010
Marcasite FeS2 4.87 –2 3. 16.97 82.64 88.12
Pyrrhotite Fe7 SB 4.53 2. –3. 20.55 93.09 94.18
Sphalerite ZnS 3.85 3. 3. 35.93 138.33 7.8–8.1 9.3–9.5 25.34
Chalopyrite CuFeS2 4.07 2. 3. 26.72 108.75 102.13
Galena PbS 6.39 3. 3. 1631.37 10424. 13.36
Sulfur S 2.02 2. –3. 122. 5.43 10.97 20.22
COALS
Anthracite CHchoke358 N009 KOkicked off022 1.47 37. 38. 105. 0.16 0.23 8.65
Bituminous CHchoke793 N015 O078 1.24 50 + 60 + 120. 0.17 0.21 14.30
Lignite CHchoke849 N015 O211 1.19 47. 52. 160. 0.20 0.24 12.79

Recommended logs to use for interpreting metamorphic and igneous sequences are

• Dual laterolog or dual induction
• Density with photoelectric effect
• Compensated neutron
• Compensated sonic
• Spectral gamma ray