The rock-fluid model used for the analysis methods described in this Handbook is shown in the illustration below. From this model, we can generate a series of equations that can be used to calculate the petrophysical properties of a rock. These equations have been derived by many researchers across a long period of years. Some equations are tuned to local areas, and may not be universally applicable. The mathematical algorithms selected for inclusion in this Handbook were chosen for their universal applicability, although many regionalized variations probably exist for most of them. Because you might need to modify existing models, or develop a new one of your own, the basic reservoir model should always be in the back of your mind.

The Rock-Fluid Model for Petrophysical Analysis


Here are the definitions that derive from the rock/fluid model shown above.

DFN 1: The formation rock-fluid model is comprised of:
  - the matrix rock (Vrock)
  - the pore space (or porosity) within the matrix rock (PHIe)
  - the shale content of the matrix rock (Vsh)

By definition, Vrock + PHIe + Vsh = 1.00

DFN 2: The matrix rock component (Vrock) can be subdivided into two or more constituents
  (Vmin1, Vmin2, ….), such as:
  - limestone, dolomite, and anhydrite or
  - quartz, calcite cement, and glauconite

The mineral mixture can be quite complex and log analysis may not resolve all constituents.

DFN 3: The shale component (Vsh) can be classified further into:
  - one or more clays (Vcl1, Vcl2, …)
  - silt (Vsilt)
  - water trapped into the shale matrix due to lack of sufficient permeability to allow
  the water to escape
  - water locked onto the surface of the clay minerals
  - water absorbed chemically into the molecules of the clay minerals

The sum of the three water volumes is called clay bound water (CBW). CBW varies with shale volume and is zero when Vsh = 0.

By definition, Vsh = Vcl + Vsilt + CBW

DFN 4: Bulk volume water of shale (BVWSH) is the sum of the three water volumes listed
  above in the definition of shale and is determined in a zone that is considered to be 100%
  By Definition, CBW = BVWSH * Vsh

DFN 5: Total porosity (PHIt) is the sum of:
  - clay bound water (CBW)
  - free water, including irreducible water (BVW)
  - hydrocarbon (BVH)

DFN 6: Effective porosity (PHIe) is the sum of:
  - free water, including irreducible water (BVW)
  - hydrocarbon (BVH)

DFN 7: Effective porosity is the porosity of the reservoir rock, excluding clay bound water (CBW).
  PHIe = PHIt – CBW
OR PHIe = PHIt – Vsh * BVWSH

Some of the “free water” is not free to move - it is, however, not “bound” to the shale.

DFN 8: Free water (BVW) is further subdivided into:
  - a mobile portion free to flow out of the reservoir (BVWm)
  -- an immobile or irreducible water volume bound to the matrix rock by surface
  tension (BVI or BVWir)

BVI is sometimes called “bound water”, but this is confusing (see definition of clay bound water above), so “irreducible water” is a better term. Note that BVWm = BVW – BVI.

DFN 9: Hydrocarbon volume (BVH) can be classified into:
  - mobile hydrocarbon (BVHm)
  - residual hydrocarbon (BVHr)

DFN 10: Free fluid index (FFI) is the sum of BVWm, BVHm, and BVHr. It is also called
  moveable fluid (BVM) or useful porosity (PHIuse).
  PHIuse = BVM = FFI = BVWm + BVHm + BVHr
OR PHIuse = PHIe – BVI
OR PHIuse = PHIe * (1 – SWir)

This definition is needed for the nuclear magnetic log (NMR, CMR, etc), since it cannot see BVWir. Non-useful porosity also occurs as tiny pores that do not connect to any other pores. They are almost invariably filled with immoveable water and do not contribute to useful reservoir volume or energy. Such pores occur in silt, volcanic rock fragments in sandstones, and in micritic, vuggy, or skeletal carbonates. The NMR may see some of this non-useful porosity – the jury is still out.

DFN 11: Total water saturation (SWt) is the ratio of:
  - total water volume (BVW + CBW) to
  - total porosity (PHIt)
  SWt = (BVW + CBW) / PHIt

DFN 12: Effective water saturation (SWe) is the ratio of:
  - free water volume (BVW) to
  - effective porosity (PHIe)
  SWe = BVW / PHIe

This is the standard definition of “water saturation”. Older books use this term to define total water saturation. Since all interpretation methods described here correct for the effects of shale, we are not normally interested in the total water saturation, except as a mathematical by-product. As effective porosity approaches zero, the water saturation approaches one (by edict, if not by calculus).

DFN 13: Useful water saturation (SWuse) is the ratio of:
  - useful water volume (BVW - BVI) to
  - useful porosity (PHIuse)
  SWuse = (BVW – BVI) / PHIuse

DFN 14: Irreducible water saturation (SWir) is the ratio of:
  - immobile or irreducible water volume (BVI) to
  - effective porosity (PHIe)
  SWir = BVI / PHIe

DFN 15: Residual oil saturation (Sor) is the ratio of:
  - immobile oil volume (BVHr) to
  - effective porosity (PHIe)
  Sor = BVHr / PHIe

DFN 16: The water saturation in the flushed zone (Sxo) is the ratio of :
  - free water in the flushed zone, to
  - effective porosity, which is assumed to be the same porosity as in the un-invaded zone.

The amount of free water in the invaded zone is usually higher than in the un-invaded zone, when oil or gas is present. Thus Sxo >= Swe. The water saturation in the invaded zone between the flushed and un-invaded zone is seldom used.

DFN 17: Further constraints that should be remembered are:
  PHIt >= PHIe >= PHIuse
  SWt >= SWe >= SWuse.
  PHIt = PHIe when Vsh = 0
  SWt = SWe when Vsh = 0

All volumes defined above are in fractional units. In tables or reports, log analysis results are often converted to percentages by multiplying fractional units by 100.

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