Publication History: This article was prepared especially for Crain's Petrophysical Handbook by E. R. Crain, P.Eng., in 2018. This webpage version is the copyrighted intellectual property of the author.

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

Two classes of tools are available for measuring the formation dielectric constant. The first one is low-frequency dielectric constant logging tools using coils on a mandrel, and more recently on a sidewall skid. They operate in the 50 to 200 megahertz range. The second type is high-frequency, 200 MHz to 1.1 GHz, using microwave antennae on a pad contact device.

The first type were known as dielectric logs (DLT). The high frequency tools became known as electromagnetic propagation (EPT) logs. Modern versions of both types that operate at multiple frequencies are called array dielectric tools. The Schlumberger tool scans 4 frequencies between 20 MHz and 1 GHz. The Baler tool covers 47 to 200 MHz.

EPT logs measure propagation time (TPLP and signal attenuation (ATTEN). Both are strongly affected by water so water filled porosity can be calculated from these values. As a 1 GHz tool, depth of investigation was very shallow. In heavy oil, where invasion is shallow, this water volume is close to the irreducible water. PHUept = PHIe only in water zones.

On low frequency DLT tools, curves presented varied considerably but might include attenuation, phase shift,  relative dielectric permittivity, or resistivity. The advantage of the DLT propagation log is that the lower frequency permits a larger depth of investigation and therefore an analysis of the undisturbed zone may be more likely.

Newer array dielectric logs measure at 4 different frequencies, giving a resistivity profile at 4 depths of investigation. They also measure signal phase shift, which  can be transformed into water filled porosity and presented on the log.

All these tools can be used to estimate invaded zone water saturation Sxo = PHIept / PHIt. Under the right conditions (shallow invasion, reasonably deep investigation) the Sxo may approach the undisturbed zone water saturation SWept. The measurement is relatively independent of water salinity at salinities above 10,000 ppm NaCl so it is a helpful guide to spotting hydrocarbons in fresh water environments.

Its major use is in in heavy oil wells, such as those in California and western Canada, and in EOR projects where water, CO2, and chemical floods have confused the original water resistivity regime.

 1. Electromagnetic Propagation - A New Dimension In Logging

    T.J. Calvert, R.N. Rau, L.E. Wells, AIME, 1977

Simplified log analysis of EPT is based on a time average equation similar to the sonic log Wyllie equations:
    1: TPo = (TPL^2 - ATTN^2 / 3604)^0.5
    2. PHIept = (TPo - (1 - Vsh) * TPma - Vsh * TPsh)
        / (TPw - TPma)

CAUTION: The porosity (PHIept) derived from these logs is the water filled porosity. This is the flushed or invaded zone water content which is not total or effective porosity, except in water zones.                
  ATTEN = EPT attenuation (db/m)
  TPL = EPT log reading (nsec/m)
  TPma = EPT matrix value (nsec/m)
  TPw = EPT water value (nsec/m)
  TPsh = EPT shale value (nsec/m)

In conventional oil and gas:
      3: Sxo = PHIept / PHIe
If shale corrections were ignored:
      4: Sxo = PHIept / PHIt

In very heavy oil, tar, or bitumen, where invasion is minimal:
      5: Sw = PHIept / PHIe
OR 6: Sw = PHIept / PHIt if shale corrections were ignored in finding PHIept.

Depth plots of both PHIept and PHIe are commonly shaded to show the difference, which is the hydrocarbon volume. This difference is helpful in locating hydrocarbons and oil water contacts in conventional oil, and may be close to actual hydrocarbon volume in heavier oils.

Charts are available to correct ATTEN and TPL for spreading, salinity, and temperature. Some computer software ignores the shale correct so you get water filled porosity plus clay bound water instead of just water filled porosity.

The EPT method is somewhat insensitive to water salinity and matrix properties as both terms have relatively narrow ranges (TPma ~~ 8 and TPw ~~ 70). It is especially useful in fresh water oil or gas reservoirs, where resistivity methods lack sufficient resolution to detect hydrocarbons easily.

More elaborate methods to solve for water filled porosity are encoded in commercial software, using the real and imaginary (phase and amplitude) information buried in the electromagnetic signal. The CRIM and CTA methods are documented in Schlumberger's "Log Interpretation Principals and Applications" manual. The dielectric constant of materials varies with the electromagnetic frequency of the logging tool, so these more exotic methods are required with dielectric (low frequency) logs, since propagation time is not recorded on these logs.


Porosity and Water Saturation From Dielectric Phase Shift
Modern dielectric logs measure both resistivity and phase shift between transmitted and received EM signals. The phase shift (PHZ) varies with the volume of each mineral and fluid in the formation. Like sonic travel time and density, the measured log value is the sum of these volumetric contributions.

These tools have relatively shallow depth of investigation so in conventional oil and gas they measure values in the flushed or invaded zone. In heavy oil and tar sands, invasion can be quite shallow, so the resistivity and phase shift usually represent the undisturbed zone. These comments must be considered in the choice of the fluid phase shift (PHZfl), as the values for water and hydrocarbon differ by a factor of 10 or more.

Dielectric Phase Responses Equation 200 MHz Tools
      1. PHZfl = SW * PHZw + (1 SW) * PHZhy
      2. PHZma = SUM (Vmin1 * PHZmin1 + Vmin2 * PHZmin2 + .)
      3. PHZ = (1 PHIe - Vsh) * PHZma + PHIe * PHZfl + Vsh * PHZsh

The above equation is often published without the shale term, but there is no reason to ignore the shale correction.

  PHZ = phase shift reading from log
  PHZfl = phase shift of fluid mixture in zone penetrated by EM signal
  PHZma = phase shift of rock matrix
  PHZsh = phase shift of shale
  PHZw = phase shift of water
  PHZhy = phase shift of hydrocarbon
  SW = water saturation (may be anywhere between flushed to undisturbed zone SW)

Dielectric Phase Shift Parameters

                      Degrees      Default
Gas                   18 20            18
Oil                     20 30            25
Water              60 450           250  See Graph ==>
Quartz               42 46            46
Dolomite           48 50            48
Limestone        50 52             52
Shale               45 65             55

Solving the response equation for water filled porosity, we get:
      4. PHIphz = (PHZ PHZma) / (PHZw PHZma)
      5. SXOphz = PHIphz / PHIt

CAUTION: The porosity (PHIphz) derived from these logs is the water filled porosity. This is the flushed or invaded zone water content which is not total or effective porosity, except in water zones.

  PHIphz = porosity from dielectric phase shift
  Rept = resistivity from deep dielectric log
  SXOphz = invaded zone water saturation
  PHIt = total porosity from conventional log analysis

NOTE: The service company will display a porosity derived from phase shift on the log. However, this will be based on default parameters. You may need to recompute with the fluid, matrix, and shale properties based on actual lithology.

TEXTURAL PARAMETER "W"  From Dielectric Phase Shift
Traditionally, the Archie parameters M and N are assumed or determined in the laboratory. The former method is prone to error and the latter may be impossible due to no core samples or results arrive too late to be useful. An alternate textural parameter, dubbed W by Baker Hughes and MN by Schlumberger, can be derived from the dielectric porosity and resistivity.
      6. W = log (Rmf / Rxo) / log (PHIphz)

Using the Archie equation:
      7. SWphz = ((RW / RESD) / PHIt^W)) ^ (1/W)

  SWphz = water saturation using M = N = W
The above assumes M = N = W. Since W cam be calculated continuously over an interval, it can be helpful in refining SW  in carbonates with varying pore geometry. In unconventional reservoirs where M and N are considerably less than 2.0, it may help to set N = W and M = 0.8 * W.

RESD may be from conventional array induction or from deepest dielectric resistivity if invasion is shallow enough. This log has excellent bed resolution, so it is worth trying to use porosity and resistivity from it if possible.

Porosity CROSSPLOTS FoR Dielectric LOG
These crossplots, courtesy of Baker Hughes, show dielectric phase porosity on a limestone scale versus other porosity tools.

Conventional density vs neutron crossplot (left) compared to dielectric phase shift vs neutron crossplot (right)

Lithology effects on phase porosity are minor.


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