
Publication History:
This article is based on
Chapter 9 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986 Updated 2004.
This
webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
Lithology fRom SONIC, DENSITY, NEUTRON, PE LOGS
One method of numerically evaluating lithology is to use the MlithNlith
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. Various 2 and 3 mineral
models can be constructed from the available data  all
possible combinations are listed in this Chapter.
Lithology fRom MlithNlith
Methods
Shale correct all data:
1:
PHIdc = PHID  Vsh * PHIDSH
2: PHInc = PHIN  Vsh * PHINSH
3: PHIsc = (DTC  (1  Vsh) * 47.3  Vsh * DTCSH) / (188  47.3)
4: DENSc = PHIdc + (1  PHIdc) * 2.71
5: DTCc = PHIsc * 188 + (1  PHIsc) * 47.3
Calculate Mlith and Nlith
6: Nlith = (1.00  PHInc) / (DENSc  DENSW)
7: Mlith = 0.01 * (DTCW  DTCc) / (DENSc  DENSW)
2Mineral
Model Using Mlith
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.
8: Vmin1 = (Mlith  MLITH2) /
(MLITH1  MLITH2)
9: Vmin2 = 1.00  Vmin1
2Mineral
Model Using Nlith
10: Vmin1 = (Nlith  NLITH2) / (NLITH1  NLITH2)
11: Vmin2 = 1.00  Vmin1
3Mineral
Model Using Mlith and Nlith
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.
12: D = (Mlith * (NLITH2  NLITH1) + Nlith * (MLITH1  MLITH2)
+ MLITH2 * NLITH1  MLITH1 * NLITH2) / (MLITH1 * (NLITH3  NLITH2)
+ MLITH2 * (NLITH1  NLITH3) + MLITH3 * (NLITH2  NLITH1))
13: E = (D * (NLITH3  NLITH1)  Nlith + NLITH1) / (NLITH1  NLITH2)
14: Vmin1 = MAX(0, 1  D  E) /
(MAX(0, 1  D  E) + MAX(0, D) + MAX(0, E))
15: Vmin2 = MAX(0, E) / (MAX(0, 1
 D  E) + MAX(0, D) + MAX(0, E))
16: Vmin3 = (1.00  Vmin1  Vmin2)
Where:
DTC = sonic log reading (usec/ft)
DTCc = sonic log reading corrected for shale (usec/ft)
DTCSH = sonic log reading in 100% shale (usec/ft)
DELTW = sonic log reading in 100% water (usec/ft)
DENS = density log reading (gm/cc)
DENSc = density log reading corrected for shale (gm/cc)
DENSW = fluid density (gm/cc)
Mlith = sonic density lithology factor (fractional)
MLITH1 = Mlith of first mineral (fractional)
MLITH2 = Mlith of second mineral (fractional)
MLITH3 = Mlith of third mineral (fractional)
Nlith = neutron density lithology factor (fractional)
NLITH1 = Nlith of first mineral (fractional)
NLITH2 = Nlith of second mineral (fractional)
NLITH3 = Nlith of third mineral (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)
Vmin1 = relative volume of first mineral (fractional)
Vmin2 = relative volume of second mineral (fractional)
Vmin3 = relative volume of third mineral (fractional)
COMMENTS:
NOTE:
all log data must be converted to English Units before use  usec/m
* 0.3048 = usec/ft and kg/m3 * 0.001 = g/cc.
All Vmin results must be multiplied by Vrock to get true mineral
volumes (V1, V2, V3) from relative mineral volumes. Vrock = 1.00
 PHIe  Vsh.
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.
The
end points for the common minerals are plotted below.
Mlith vs Nlith crossplot for two or three mineral
models
NUMERICAL
EXAMPLE:
1. Assume data from 2135  2153 meters in Classic Example 2.
PHID = 0.015
PHIN = 0.15
DTCc = DTC = 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.
Lithology from AlithKlith
Methods
The AlithKlith method, like the MlithNlith 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.
Shale correct raw data:
21: PHIdc = PHID  Vsh * PHIDSH
22: PHInc = PHIN  Vsh * PHINSH
23: PHIsc = (DELT  (1  Vsh) * 47.3  Vsh * DELTSH) / (188  47.3)
24: DENSc = PHIdc + (1  PHIdc) * 2.71
25: DTCc = PHIsc * 188 + (1  PHIsc) * 47.3
Calculate Alith and Klith:
26: Alith = (DENSc  DENSW) / (1.00  PHInc)
27: Klith = 0.01 * (DTCW  DTCc) / (1.00  PHInc)
2Mineral
Model Using Alith
If the usual lithology is made up of two minerals, then the Alith
and Klith values can each be linearly interpolated to find the
fraction of the minerals.
28: Vmin1 = (Alith  ALITH2) /
(ALITH1 AMLITH2)
29: Vmin2 = 1.00  Vmin1
2Mineral
Model Using Klith
30: Vmin1 = (Klith  KLITH2) / (KLITH1  KLITH2)
31: Vmin2 = 1.00  Vmin1
3Mineral
Model Using Alith and Klith
If
the usual lithology is made up of three minerals, then the Alith
and Klith values can be linearly triangulated to find the fraction
of the minerals.
32: D = (Alith * (KLITH2  KLITH1) +
Klith * (KLITH1  ALITH2)
+ ALITH2 * KLITH1  ALITH1 * KLITH2) / (ALITH1 * (KLITH3  KLITH2)
+ ALITH2 * (KLITH1  KLITH3) + ALITH3 * (KLITH2  KLITH1))
33: E = (D * (KLITH3  KLITH1) 
Klith + KLITH1) / (KLITH1  KLITH2)
34: Vmin1 = MAX(0, 1  D  E) /
(MAX(0, 1  D  E) + MAX(0, D) + MAX(0, E))
35: Vmin2 = MAX(0, E) / (MAX(0, 1
 D  E) + MAX(0, D) + MAX(0, E))
36: Vmin3 = (1.00  Vmin1  Vmin2)
Where:
Alith = density neutron lithology factor (fractional)
DTC = sonic log reading (usec/ft or usec/m)
DTCc = sonic log reading corrected for shale (usec/ft or usec/m)
DTCSH = sonic log reading in 100% shale (usec/ft or usec/m)
DTCW = 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)
Klith = sonic neutron 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:
Note that Alith is the inverse of Nlith and that Klith is the
ratio Mlith/Nlith. The data for common minerals is plotted
below.
To
calculate 2 or 3 mineral models, use the same math as the
MlithNlith Section, but replace Mlith with Alith and Nlith with
Klith.
NUMERICAL
EXAMPLE:
1. Assume the same data as before:
PHID = 0.015
PHIN = 0.15
DELT = 190 usec/m = 61 usec/ft
DENSc = 0.015 + (1.0  0.015) * 2.71 = 2.684
Klith = 0.01 * (188  61) / (1  0.15) = 1.52
Alith = (2.684  1.00) / (1  0.15) = 1.98
Again,
these values are close to the dolomite point, so the rock is assumed
to be dolomite.
Lithology from
MlithPlith
Method
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.
Shale correct all data:
1:
PHIdc = PHID  Vsh * PHIDSH
2: PEc = PE  Vsh * PESH
3: PHIsc = (DTC  (1  Vsh) * 47.3  Vsh * DTCSH) / (188  47.3)
4: DENSc = PHIdc + (1  PHIdc) * 2.71
5: DTCc = PHIsc * 188 + (1  PHIsc) * 47.3
Calculate Mlith and Plith
6: Plith = PEc / (DENSc  DENSW)
7: Mlith = 0.01 * (DTCW  DTCc) / (DENSc  DENSW)
2Mineral
Model Using Mlith
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.
8: Vmin1 = (Mlith  MLITH2) /
(MLITH1  MLITH2)
9: Vmin2 = 1.00  Vmin1
2Mineral
Model Using Plith
10: Vmin1 = (Plith  PLITH2) / (PLITH1  PLITH2)
11: Vmin2 = 1.00  Vmin1
3Mineral
Model Using Mlith and Plith
If
the usual lithology is made up of three minerals, then the Mlith
and Plith values can be linearly triangulated to find the fraction
of the minerals.
12: D = (Mlith * (PLITH2  PLITH1) +
Plith * (MLITH1  MLITH2)
+ MLITH2 * PLITH1  MLITH1 * PLITH2) / (MLITH1 * (PLITH3  PLITH2)
+ MLITH2 * (PLITH1  PLITH3) + MLITH3 * (PLITH2  PLITH1))
13: E = (D * (PLITH3  PLITH1) 
Plith + PLITH1) / (PLITH1  PLITH2)
14: Vmin1 = MAX(0, 1  D  E) /
(MAX(0, 1  D  E) + MAX(0, D) + MAX(0, E))
15: Vmin2 = MAX(0, E) / (MAX(0, 1
 D  E) + MAX(0, D) + MAX(0, E))
16: Vmin3 = (1.00  Vmin1  Vmin2)
Where:
DTC = sonic log reading (usec/ft)
DTCc = sonic log reading corrected for shale (usec/ft)
DTCSH = sonic log reading in 100% shale (usec/ft)
DTCW = sonic log reading in 100% water (usec/ft)
DENS = density log reading (gm/cc)
DENSc = density log reading corrected for shale (gm/cc)
DENSW = fluid density (gm/cc)
Mlith = sonic density lithology factor (fractional)
Plith = PE density lithology factor (fractional)
PHIdc = density porosity corrected for shale (fractional)
PHIDSH = density log reading in 100% shale (fractional)
PE = photo electric log reading (fractional)
PEc = photo electric log corrected for shale (fractional)
PESH = photo electric log reading in 100% shale (fractional)
PHIsc = sonic log porosity corrected for shale (fractional)
Vsh = volume of shale (fractional)
COMMENTS:
This
model is very effective in granite reservoirs.
To
calculate 2 or 3 mineral models, use the same math as the
MlithNlith Section, but replace Nlith with Plith.
MATRIX
ROCK PARAMETERS
