THE PETROPHYSICAL MODEL
This article is based
on Crain's Petrophysical
Pocket Pal" by E. R. (Ross) Crain, P.Eng.
Copyright
2018 by the author. Copying or distribution in any form without
express written permission is prohibited.
The rockfluid 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 RockFluid 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 rockfluid 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. Nonuseful 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 nonuseful
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 byproduct. 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 uninvaded zone. 
The
amount of free water in the invaded zone is usually higher than
in the uninvaded zone, when oil or gas is present. Thus Sxo >=
Swe. The water saturation in the invaded zone between the flushed
and uninvaded 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 