Invaded Zone Water Saturation From SHALLOW Resistivity
Calculate invaded zone water saturation (Sxo) using the same method as used to calculate water saturation in the un-invaded zone (Sw). To do this, replace the following terms in any water saturation equation given earlier in this Chapter:

  RESD by RESS
  RW@FT by RMF@FT
  RSH by RSHS
  Sw by Sxo

Where:
  RESD = deep resistivity (ohm-m)
  RESS = shallow resistivity (ohm-m)
  RMF@FT = mud filtrate at form temperature (ohm-m)
  RSH = resistivity of shale on deep log (ohm-m)
  RSHS = resistivity of shale on shallow log (ohm-m)
  RW@FT = water resistivity at form temperature (ohm-m)
  Sw = water saturation in the invaded zone (fractional)
  Sxo = water saturation in the invaded zone (fractional)

COMMENTS:
Most analysts assume RSHS = RSH.

Invaded zone water saturation is used to find the amount of hydrocarbon flushed by the invasion process. The hydrocarbon thus moved is called the moveable hydrocarbon saturation, and that left behind is the residual hydrocarbon saturation. A simple empirical formula relating water saturation and invaded zone water saturation is:
      1: Sxo = Sw ^ (1/5)

This is a traditional relationship and local knowledge may provide different results.

Invaded Zone Water Saturation from Electromagnetic Logs
The electromagnetic propagation log measures the travel time and attenuation of microwaves propagated along the borehole wall. The analysis concept is similar to a sonic log, but the frequencies involved are microwave (electromagnetic) in the gigahertz range instead of acoustic in the kilohertz range. The travel time is largely influenced by the amount of water in the formation and does not depend too greatly on other components, such as hydrocarbon or matrix rock. Because of its shallow investigation, the log measures the water volume of the flushed zones.

The response equation for the electromagnetic propagation log follows the classical form:
      1: TP = PHIe * Sxo * TPw (water term)
              + PHIe * (1 - Sxo) * TPh (hydrocarbon term)
              + Vsh * TPsh (shale term)
             + (1 - Vsh - PHIe) * Sum (Vi * TPi) (matrix term)

Where:
  TPh = log reading in 100% hydrocarbon
  TPi = log reading in 100% of the ith component of matrix rock
  TP = log reading
  TPsh = log reading in 100% shale
  TPw = 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)

The hydrocarbon does not contribute any signal, so the equation is solved directly for water filled porosity, assuming Vsh = 0.0. This is then compared to the total porosity, after shale volume corrections, based on data derived from the dual water method described in Section 8.11.
 

Water Satuation from EPT Method
Calculate loss free propagation time from measured propagation time.
      1: Tpo = (TPL ^ 2 - ((ATTN - 50)) ^ 2 / 3604) ^ 0.5

The value of Tpw varies with temperature and is given by:
      2: FT1 = SUFT + (BHT - SUFT) / BHTDEP * DEPTH)
      3: IF LOGUNITS$ = "METRIC"
      4: THEN FT1 = 9 / 5 * FT1 + 32
      5: Tpw = 20 * (710 - FT1 / 3) / (444 - FT1 / 3)

Calculate water filled porosity from propagation time.
      6: PHIept = (Tpo - TPM) / (Tpw - TPM)

Calculate water saturation of invaded zone.
      7: IF Vsh < 1.0
      8: THEN SWept = (PHIept - BVWSH * Vsh) / (PHIt - BVWSH * Vsh)
      9: OTHERWISE SWept = 1.0

Where:
  ATTN = measured attenuation time of formation (db/m)
  BHT = bottom hole temperature (degrees Fahrenheit or Celsius)
  BHTDEP = depth at which BHT was measured (feet or meters)
  BVWsh = bulk volume water in 100% shale (fractional)
  FT1 = formation temperature (degrees Fahrenheit or Celsius)
  PHIept = total porosity from electromagnetic log (fractional)
  PHIt = total porosity from any total porosity (fractional)
  SUFT = surface temperature (degrees Fahrenheit or Celsius)
  SXOept = invaded zone saturation (fractional)
  TPL = measured propagation time of formation (nsec/m)
  TPM = loss free propagation time of matrix (nsec/m)
  Tpo = loss free propagation time of formation (nsec/m)
  Tpw = loss free propagation time of water (nsec/m)
  Vsh = volume of shale (fractional)

COMMENTS:
In tar sands and heavy oil, SXOept will equal SW since there is no invasion in these reservoirs. This is also true in oil reservoirs drilled with genuine oil base mud. There may be a bit of invasion, but it does not change SW very much.

Note that this value of SXOept does not depend on any knowledge of resistivity log data or assumed fluid resistivities.

This is a thin bed tool as it sees zones of 3-4 inches in thickness

Shale volume can be calculated from the EPT attenuation curve in a fashion similar to the gamma ray. This helps to resolve laminated shaly sands.

A graphical solution exists but is more complicated to use than these simple formulae.

RECOMMENDED PARAMETERS:
Material	Relative Dielectric Permitivity	TPM Loss-Free Propagation Time ns/m
Gas or Air	1.0	3.3
Oil	2.2	4.9
Water	56 - 80	25 - 28
Quartz	4.7	7.2
Limestone	7.5	9.6
Dolomite	6.9	8.7
Anhydrite	6.5	8.4
Dry Clay	5.7	8.0
Halite	5.6 - 6.3	7.9 - 8.4
Gypsum	4.2	6.8
Shale	5.0 - 25	7.5

The value for water varies with temperature - see Step 5 for more precise values.

NUMERICAL EXAMPLE:
1. Given a zone with:
ATTN = 200 db/m
FT = 43 degrees C = 109 degrees F
TPL = 15 nsec/m
TPM = 7.2 nsec/m (sandstone)
BVWSH = 0.30
Vsh = 0.33
PHIe = 0.11
Tpo = (15 ^ 2 - ((200 - 50) ^ 2) / 3604) ^ 0.5 = 11.9
Tpw = 20 * ( 710 - 109 / 3) / (444 - 109 / 3) = 33.0
PHIept = (11.9 - 7.2) / (33.0 - 7.2) = 0.182
SWept = (0.182 - 0.30 * 0.33) / (0.11) = 0.75

This is a reasonable number for Sxo in a sand such as Sand D.