PETROPHYSICAL MODELS - DEFINITIONS
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
DEFINITIONS OF PETROPHYSICAL PROPERTIES
Here are the definitions that derive from the rock/fluid model
shown above.
DFN
1: |
The
formation rock-fluid model is comprised of: |
|
-
the minerals that make up the matrix rock (Vrock) |
|
-
the pore space (or porosity) within the
formation (PHIe) |
|
-
the shale content of the
formation (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 of hydration, locked into the molecules of the clay minerals |
The
sum of the three water volumes in a particular rock is called clay bound water (CBW).
CBW varies with shale volume and is zero when Vsh = 0.
By
definition, Vsh = Vcl + Vsilt + CBW. Sometimes Vsilt is
considered to be part of Vrock, especially in fine grained
unconventional reservoirs.
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% |
|
shale.
|
|
|
|
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)
The term "free water" is used to distinguish it from clay
"bound water" - free water may not be maveable water. |
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.