This document discusses the volumetric model used to characterize pore space in geological formations. It describes how the total pore volume can be divided into volumes occupied by shale, clay, silt, and matrix rock as well as mobile and residual fluids like oil, gas, and water. Effective porosity refers to the interconnected pore space that contains movable fluids, while total porosity includes both effective porosity and water bound in the shale. Permeability is related to porosity and describes fluid flow within the pore network which is influenced by grain size and sorting. Log responses can be modeled based on these volumetric proportions.

1. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Formation Evaluation
Fluids in Pore Space
Source of image: www.careerfirst.lk
Petroleum Engineering Department PE 363
KNUST

2. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
t: - total porosity
Vclay: -volume of clay
Vsilt: - volume of silt
Vsh: - volume of shale
e: - effective porosity
Vrock: - volume of matrix rock
The formation rock/fluid model is comprised
of Vrock,Vsh and e, by definition:
Vrock+Vsh + e=1
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock

3. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 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.

4. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 Vsh:
 Shale solids can be classified further into:
- one or more clays (Vcl1, Vcl2, … )
-silt (Vsilt)
 CBW – clay bound water, the sum of the three
water volumes:
- water trapped into the shale matrix due to lack of
sufficient permeability to escape
- water locked onto the surface of the clay minerals
- water absorbed chemically into the molecules of the
clay minerals
 By definition：
Vsh = Vcl + Vsilt + CBW

5. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 e:
 Effective porosity is the sum of:
- bulk volume water (BVW), free water, including
irreducible (capillary-bound) water
- bulk volume hydrocarbon (BVH)
 t:
 Total porosity is the sum of:
- CBW
- e
 By definition：
t = e +CBW

6. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 BVH:
 Hydrocarbon volume can be
classified into:
- mobile hydrocarbon (BVHm)
- residual hydrocarbon (BVHr)
 Swt:
 Total water saturation is the ratio of:
- total water volume (BVW + CBW) to
- total porosity

7. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 Swe:
 Effective water saturation is
the ratio of:
- free water volume (BVW) to
- effective porosity
 This is the standard definition
of “water saturation”

8. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 Swir
 Irreducible water
saturation is the ratio of:
- immobile or irreducible water
volume (BVI) to
- effective porosity
 Sor
 Residual oil saturation is
the ratio of:
- immobile oil volume (BVHr) to
- effective porosity

9. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Formation model - a volumetric model
mobile
residual
mobile
irreducible
oil and/or gas
free water
bound water
dry solids
dry clay
silt
1
2
3
trapped in shale
locked on surface
locked in molecule
rock type 1
rock type 2
rock type 3
rock type 4
e
t
Vsh
Vclay
Vsilt
Vrock=1-Vsh-e
shale
porosity
matrix rock
 Sxo
 The water saturation in flushed
zone 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.
 Constraints
 t  e
 Swt  Swe
 t = e when Vsh = 0
 Swt = Swe when Vsh = 0

10. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 The Log Response Equation
LOG = e * Sxo * Lw (water term)
+ e * (1 - Sxo) * Lh (hydrocarbon term)
+ Vsh * Lsh (shale term)
+ (1 - Vsh - e) *  (Vi * Li) (matrix term)
LOG = log reading
Lh = log reading in 100% hydrocarbon
Li = log reading in 100% of the ith component of matrix rock
Vi = volume of ith component of matrix rock
Lsh = log reading in 100% shale
Lw = log reading in 100% water

11. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Sandstone Porosity - measured by various methods
quartz
(framework)
small
pores
isolated
pores
large, Interconnected
pores
clay surfaces
& interlayers
clay
layers
irreducible or
immobile water
hydration or
bound water
hydrocarbon
pore volume
structural
water
rock
matrix
total porosity - neutron log
total porosity - density log
absolute or total porosity
oven-dried core analysis porosity
humidity-dried
core analysis porosity
capillary
water
Vsh
(modified from Eslinger and Pevear, 1988)

12. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Permeability - Henry Darcy 1856 , laminar flow
1
l
Q
2
𝑢 =
𝑄
𝐴 𝑡
=
𝑘
𝜂
𝜎1 − 𝜎2
𝑙
=
𝑘
𝜂
Δ𝜎
𝑙
=
𝑘
𝜂
∇σ
𝑘 = 𝜂
𝑢
∇𝜎
 k – permeability
 u – volume flow density
 Q – fluid volume
 t – time
 A – cross section
 η – dynamic viscosity
  – fluid pressure

13. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Permeability - influence of grain shape & size

14. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Permeability vs porosity
Core samples from three
sandstone reservoirs,
Gulf Coast Field
Colorado Field
California Field

15. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Permeability vs porosity & grain size
Chilingar, 1969
coarse & very coarse
coarse & medium coarse
fine grained
silty
clayey

16. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Summary sketch
- impact of grain size, sorting, clay, & interstitial cements upon permeability-porosity
trends
porosity (linear scale)
permeability
(logarithmic scale)
(Nelson, 1994)

17. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Absolute & relative permeability
 absolute permeabilty - single fluid
 effective permeability - two or three fluids
 relative permeability - effective permeability
absolute permeability

18. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Specific internal surface
Stotal=
Spor=
Stotal = Spor
Unit: m2/m3 = m-1 usually µm-1
surface area of pores
total volume
surface area of pores
pore volume

19. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Specific internal surface
 Depends on
– Size and shape of the pores
– Microstructure and morphology
of the interface matrix-pore
 Related to properties like
– cation exchange capacity (CEC)
– NMR T2 signal

20. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Relationships between , k, & Spor
based on models
r
l
L
L
L
L
l
T
r
l
r
l
r
S
L
l
r
por 











2
2
2
3
2



porosity specific surface tortuosity

21. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Fluids in Pore Space
 Summary
 Porosity, permeability, & specific internal surface are most
important pore space parameters. They show a correlation,
but express different physical properties:
– porosity characterizes pore space volume (scalar property)
– specific internal surface characterizes surface of pore space (scalar
property)
– permeability expresses fluid flow ability (tensor)
– porosity correlates to density (and nuclear, acoustic, or electrical
properties).
– permeability correlates to porosity (pore diameter or grain size
dependent)
– specific internal surface links porosity & permeability - (“surface -
sensitive” properties like Sw,irr or NMR allow permeability derivation)

22. Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
THANKS FOR
ATTENTION!!!