Publication History: This article is based on Chapter 8 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986  Updated 2004 and 2017. This webpage version is the copyrighted intellectual property of the author.

Do not copy or distribute in any form without explicit permission.

Water Saturation From SIGMA and FNXS Logs
Logs that come under this designation are the Thermal Decay Time (TDT) or Neutron Lifetime (NLL)  Logs. They are also called Pulsed Neutron (PNL) or Pulsed Decay Time (PDK) Logs. The primary measurement is the formation capture cross section ISIGMA). Some tools provided a compensated neutron porosity (TPHI) derived from the ratio of the near to far detector count rates.

Newer induced gamma ray spectroscopy tools also provide  SIGMA and TPHI, and a recent tool gives a new measurement called fast neutron cross section (FNXS).

Both SIGMA and FNXS can be transformed into water saturation.

On very old logs, the primary derived value from the pulsed neutron device is the neutron decay time (TAU), for Schlumberger logs and the Neutron Half Life (LIFE) for Dresser logs. These are related to the formation capture cross section (SIGMA), by the following equation:
      1: SIGMA = 4550 / TAU for the Schlumberger tool
      2: SIGMA = 3150 / LIFE for the Dresser tool

On modern logs, and many older ones, the SIGMA curve is displayed and the above calculation is not needed.

Water Saturation from TDT log.
Here is the log response equation for the SIGMA measurement with only hydrocarbon and water in the porosity:

3: SIGMA= PHIe * Sw * SIGw (water term)
                    + PHIe * (1 - Sw) * SIGh (hydrocarbon term)
                    + Vsh * SIGsh (shale term)
                    + (1 - Vsh - PHIe) * Sum (Vi * SIGi) (matrix term)
Where:
  SIGh = log reading in 100% hydrocarbon
  SIGi = log reading in 100% of the ith component of matrix rock
  SIGMA = log reading
  SIGsh = log reading in 100% shale
  SIGw = log reading in 100% water
  PHIe = effective porosity (fractional)
  Sw = water saturation in reservoir (fractional)
  Vi = volume of ith component of matrix rock
  Vsh = volume of shale (fractional)

This equation is solved for Sw by assuming all other variables are known or previously calculated:
      4:  SIGw = 22.0 + 0.000404 * WS(ppm)
      5: SIGm = Sum (Vi * SIGi)
      6: PHIe = TPHI from log if available and no gas OR from open hole logs
      7: SWtdt = ((SIGMA - SIGm) - PHIe * (SIGh – SIGm) - Vsh * (SIGsh - SIGm))
                    / (PHIe * (SIGw - SIGh))

Solving the fast neutron response equation with CO2 instead o hydrocarbon gives:
      8: FNXSm, = Sum (Vi * FNXSi)
      9: SWfnxs = ((FNXS-FNXSm)-PHIe*(FNXSco2-FNXSm)-Vsh*(FNXSsh-FNXSm))
                    / (PHIe * (FNXSw - FNXSco2))


NUMERICAL EXAMPLE:
1. Assume data as follows:
PHIe = 0.28
SIGw = 84 cu
SIGm = 10 cu
SIGh = 22 cu
SIGMA = 25.5 cu
Vsh = 0.20
SIGsh = 37 cu
SWtdt = ((25.5 - 10) - 0.28 * (10 - 22) - 0.20 * (37 - 10)) / (0.28 * (84 - 22)) = 0.39

2. If zone contained gas:
SIGh = 9 cu
SWtdt = ((25.5 - 10) - 0.28 * (10 - 9) - 0.20 * (37 - 10)) / (0.28 * (84 - 9)) = 0.49
 

Porosity from TDT LOGS
In the case of the dual detector devices, porosity from the TDT log (TPHI or PHItdt) is calculated from the ratio of the near and far count rate. This is the same approach that is used for the open hole compensated neutron log (CNL). Like  the CNL, gas effects must be taken into account.


Limits to use of OLDER tdt for saturation calculations
The capture cross section is relatively inaccurate in low salinity, low porosity situations. The chart shown below is used to determine under what conditions the log can be used. The C/O curve on modern tools often helps locate hydrocarbon zones in fresher water situations.


Find useful range of TDT log here

To overcome this inaccuracy problem, older logs were run in multiple passes and the SIGMA curves summed to reduce statistics. Typically, five runs were summed. More modern tools have better signal to noise ratio and do not need multiple passes. However, saturation may still be inaccurate when salinity is less than 50,000 ppm. Check with the service company for useful salinity / porosity ranges on current tools as specifications are constantly changing

The current Schlumberger tool is called the Reservoir Saturation Tool (RST) and the term TDT may disappear as newer tools replace older ones.

RECOMMENDED Parameters - 2015 LIST

Material

Sigma

(c.u.)

TPHI

FNXS (1/m)

Quartz

4.55

–0.03

6.84

Calcite

7.08

0.00

7.51

Dolomite

4.70

0.03

8.51

Orthoclase

15.82

–0.05

6.33

Albite

7.65

–0.04

6.69

Anhydrite

12.45

–0.03

7.14

Pyrite

90.53

0.01

6.60

Bituminous Coal

15.79

0.68

7.72

Dry Illite

20.79a

0.22

8.06

Wet Illite

21.00 a

0.34

8.02

Dry Smectite

14.36 a

0.29

8.36

Wet Smectite

19.23 a

0.68

8.60

Water

22.20

1.00

7.80

Kerogen (CH 1.3g/cm3)

20.18

0.98

9.07

CH4 (0.05 g/cm3)

2.50

–0.05

0.67

CH4 (0.15 g/cm3)

7.50

0.21

2.01

CH4 (0.25 g/cm3)

12.50

0.47

3.36

Oil (C3H8 0.5g/cm3)

18.21

0.78

5.44

Oil (C3H8 0.6g/cm3)

21.85

0.97

6.53

Diesel (CH1.8 0.89 g/cm3)

23.30

1.08

7.98

CO2 (0.6 g/cm3)

0.03

–0.12

2.24

Water 0 ppm

22.2

1.00

7.800

Water 200,000 ppm

97.2

0.90

7.36

 

  Parameters - 1982 LIST

Some good legacy data here from early sources.

SIGMAwater (SIGW) is best derived from water salinity, which in turn can be derived from water resistivity:
      10: WS = 400000 / FT1 / ((RW@ET) ^ 1.14)
      11:
SIGw = 22.0 + 0.000404 * WS

Where:
  BHT = bottom hole temperature (degrees Fahrenheit or Celsius)
  BHTDEP = depth at which BHT was measured (feet or meters)
  DEPTH = mid-point depth of reservoir (feet or meters)
  FT = formation temperature (degrees Fahrenheit or Celsius)
  FT1 = formation temperature (degrees Fahrenheit)
  RW@FT = water resistivity at formation temperatures (ohm-m)
  SUFT = surface temperature (degrees Fahrenheit or Celsius)
  WS = water salinity (ppm NcCl)

SIGMA for hydrocarbon (SIGh) ranges between 0 and 23, with a default of 22 cu for typical oil and 9 cu for gas. See graphs below.


SIGMA values for oil, gas, and water

SIGMA values for shale (SIGsh) ranges between 20 and 45. You can look at a depth plot of your log, find the nearest, fairly thick, shale as observed on the gamma ray log and read the average of the SIGMA curve over the same interval. If GR is not a good shale indicator, try density neutron separation or shallow resistivity

A crossplot of GR vs SIGMA will do the same thing (as long as radioactivity is a function of shale minerals and not uranium). Find the cluster of high GR values representing shale and pick the corresponding SIGMA shale.

SIGMA for matrix rock (SIGm) can be taken from chartbook tables or can be calculated from the SIGMA log curve if porosity is known from conventional log analysis. The values in the chartbook tables do not work well because real rocks are not pure minerals. A method for finding SIGMAM from the log data itself uses the following equation:
      9. SIGm = (SIGMA - PHIe * SIGw) / (1 - PHIe)

This eliminates the salt in the water in the porosity (SIGMA salt = 770) and accounts for any other minerals in the sandstone (for example an iron rich cement where SIGMA iron = 220). Most real rocks have SIGMA larger than the values in the tables in chartbooks. You can vary SIGMA matrix point by point or take an average of several calculated values.

Where:
  SIGm = capture cross section of matrix (capture units)
  SIGMA = capture cross section log reading (capture units)
  SIGw = capture cross section of water (capture units)
  PHIe = effective porosity (fractional)

This should be done in a clean porous interval containing water.

MATRIX PARAMETERS FOR PURE MINERALS
Caution: these values are for pure minerals and values for real rocks are often higher.

MINERAL SIGm
Quartz SiO2 4.3
Calcite CaCO3 7.3
Dolomite CaCO3.MgCO3 4.8
Feldspars  
Albite NaALSi3O8 7.6
Anorthite CaALSi2O8 7.4
Orthoclase KAlSi3O8 15.0
Evaporites  
Anhydrite CaSO4 13.0
Gypsum CaSO4.2H2O 19.0
Halite NaCl 770
Sylvite KCl 580
Carnallite KCl.MgCl2.6H2O 370
Borax Na2B4O7.10H2O 9000
Kermite Na2B4O7.4H2O 10500
Coal  
Lignite 30 +/-5
Bituminous coal 35 +/-|
Anthracite 22 +/-5
Iron-Bearing Minerals  
Iron Fe 220
Geothite FeO(OH) 89.0
Hematite Fe2O3 104
Magnetite Fe3O4 107
Limonite FeO(OH).3H2O 80.0
Pyrite FeS2 90.0
Siderite FeCO3 52.0
Iron-Potassium Bearing Minerals  
Glauconite (green sands) 25 +/-5
Chlorite 25 +/-15
Mica (Biotite) 35 +/-1
Illite Shale 37 +/-5
Others  
Pyrolusite MnO2 440
Manganite MnO(OH) 400
Cinnabar HgS 7800
 
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