Water Saturation From Pulsed Neutron Logs
Logs that come under this designation are the Thermal Decay Time Log (TDT) or the Neutron Lifetime Log (NLL). They are also called Pulsed Neutron Logs (PNL). They are primarily affected by the presence of chlorine and hence can differentiate between salt water and hydrocarbons. They do this by generating a burst of neutrons and monitoring the decay time of the neutrons.

The tool emits a burst of neutrons and the decay time of the neutrons are recorded by measuring the neutron count rate zt the detectors versus time. This process is repeated as the tool is moved up the borehole. 

Pulsed neutron devices usually have a series of `gates' for measuring count rates at different times after the neutron burst has taken place. This method is used to measure borehole and background effect, and correct for them.

Since the neutrons are generated, rather than emitted by a radioactive chemical source, the tool is very attractive to those who fear the consequences of losing a radioactive source in a producing well.

The new generation of dual spacing detector devices minimize the effects of casing and tubing, so that no corrections are necessary.

On older 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.

  SIGMA = capture cross section (capture units)
  TAU = neutron decay time (usec)
  LIFE = neutron half life (usec)

The capture cross section SIGMA is defined as the relative ability of a material to "capture" or absorb free thermal neutrons. Chlorine has a high capture cross section and hydrogen has a low capture cross section.

Water saturation is based on the sum of the capture cross sections, in a mathematical treatment similar to the sonic, density and neutron logs.

The response equation for the thermal decay time log follows the classical form:

      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)

  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 un-invaded zone (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.

SWtdt - Water Saturation from TDT log.
SIGW = 22.0 + 0.000404 * WS
      5: IF PHIe > 0
      6: THEN SWtdt = ((SIGMA - SIGMAM) - PHIe * (SIGHY - SIGMAM) - Vsh * (SIGSH - SIGMAM))
                               / (PHIe * (SIGW - SIGHY))
      7: OTHERWISE SWtdt = 1.0

  PHIe = effective porosity (fractional)
  SIGMA = TDT capture cross section log reading (capture units)
  SIGMAM = capture cross section matrix value (capture units)
  SIGW = capture cross section for water (capture units)
  SIGHY = capture cross section for hydrocarbons (capture units)
  SIGSH = capture cross section for shale (capture units)
  SWtdt = water saturation from TDT (fractional)
  Vsh = shale volume (fractional)
  WS = water salinity (ppm NaCl)

1. Assume data as follows:
PHIe = 0.28
SIGW = 84 cu
SIGMAM = 10 cu
SIGHY = 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:
SIGHY = 9 cu
SWtdt = (25.5 - 10) - 0.28 * (10 - 9) - 0.20 * (37 - 10)) / (0.28 * (84 - 9)) = 0.49

Nomograph for water saturation from TDT log

Porosity from TDT LOGS
In the case of the dual spacing devices, the ratio of the corrected, or net, count rate from each detector is calculated. This is the same approach that is used for the CNL and, like the CNL, porosity can be derived from the pulsed neutron ratio. Similarly, gas effects must be taken into account.

The illustration below shows how porosity can be derived from the TDT ratio curve. Equations to represent this chart are available but are complex and seldom used. Most modern TDT logs present a porosity curve equivalent to a CNL style neutron log. There was a short period when TDT porosity in dolomite was badly in error. Always compare TDT porosity to other sources.

Porosity from TDT log

Limits to use of 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.

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

  BHT = bottom hole temperature (degrees Fahrenheit or Celcius)
  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 Celcius)
  FT1 = formation temperature (degrees Fahrenheit)
  RW@FT = water resistivity at formation temperatures (ohm-m)
  SUFT = surface temperature (degrees Fahrenheit or Celcius)
  WS = water salinity (ppm NcCl)

SIGMAhydrocarbon (SIGHY) 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

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.

SIGMAmatrix (SIGMAM) can be taken from chartbook tables or can be calculated from the SIGMA log chrve 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. SIGMAM = (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.

  SIGMAM = 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.

Caution: these values are for pure minerals and values for real rocks are often higher.

Quartz SiO2 4.3
Calcite CaCO3 7.3
Dolomite CaCO3.MgCO3 4.8
Albite NaALSi3O8 7.6
Anorthite CaALSi2O8 7.4
Orthoclase KAlSi3O8 15.0
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
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
Pyrolusite MnO2 440
Manganite MnO(OH) 400
Cinnabar HgS 7800
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