Publication History: This article is based on Chapter 7 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.

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Material Balance (Maximum Porosity)
Material balance for porosity is needed to prevent too high a porosity in very shaly sections or in bad hole conditions. It can also be used in shaly sands as a porosity method, when only a GR or SP log is available with no porosity indicating logs:
      1: IF PHIe < 0
      2: THEN PHIe = 0
      3: AND PhiNEG = PhiNEG + 1
      4: IF PHIe > (1.00 - Vsh) * PHIMAX
      5: THEN PHIe = PHIMAX * (1.00 - Vsh)
      6: AND PhiPOS = PhiPOS + 1

  PHIe = porosity from any method (fractional)
  Vsh = shale content from any method (fractional)
  PHIMAX = maximum expected porosity in clean rock (fractional)
  PhiPOS = counter for porosity greater than PHIMAX
  PhiNEG = counter for porosity less than zero
Don't fail to use this routine. It makes computer output look pretty nice even with poor logs.

This material balance prevents the sum of shale volume, porosity and rock matrix from exceeding 100%.

Normal values for PHIMAX:
Very high porosity sandstone (and tar sands) PHIMAX = 0.36 to 0.42
High to medium porosity PHIMAX = 0.25 to 0.36
Low or shaly medium porosity PHIMAX = 0.18 to 0.25
Very low porosity, PHIMAX = 0.10 to 0.18

Porosity from Maximum Porosity Method
PHIMAX is also useful for estimating porosity in shaly sands where only an SP or gamma ray log is available, since it provides a porosity value based only upon the shale content and the analyst's assumed maximum possible porosity. With offset well data or core data for control, this is not a bad approach for wells with a very limited log suite. It is often used in computer analysis of ancient logs. Because of its gross assumptions, a warning note should be annotated on the results, if the method is used.
      1: PHImx = PHIMAX * (1.00 - Vsh)

  PHImx = porosity from maximum porosity (fractional)
  Vsh = shale content from any method (fractional)
  PHIMAX = maximum expected porosity in clean rock (fractional)

This method has been very successful where good control of Vsh and PHIMAX are possible, based on core data and density neutron porosity in offset wells.

Choose from core and density neutron data in offset wells. Plot VSH vs PHIe to extrapolate to zero Vsh.

1. For example, if Vsh = 0.65 and PHIe = 0.30, this would mean the sand fraction has 85% porosity, which is unreasonable. The sand fraction porosity is derived as follows:
PHIsd = PHIe / (1 - Vsh) = 0.30 / (1 - 0.65) = 0.85

Using the PHIMAX equation with a PHIMAX of 0.30:PHIe = (1 - 0.65) * 0.30 = 0.105 which indicates the sand fraction has a porosity of 0.30 by edict of the analyst. This is more reasonable than the value of 0.85 derived earlier.

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