Alimoradi Et Al - Methods of Water Saturation Estimation: Historical Perspective
Alimoradi Et Al - Methods of Water Saturation Estimation: Historical Perspective
Alimoradi Et Al - Methods of Water Saturation Estimation: Historical Perspective
= =
0
(7)
application is limited in clean formations. This is because
in the first kind of the Worthigton equations it is
assumed that shale and sand are independent from each
other in conducting the electrical current and shale
has not been affected by hydrocarbon. In situation of
Table 1. The values of X according to different values of
ma
t (Kamel and Mabrouk, 2002)
Matrix
) / ( ft s t
ma
X
Silica 55.5 1.60
Calcite 47.6 1.76
Dolomite 43.5 2.00
scattered shale, hydrocarbon will influence the shale.
According to interaction between shale and sand (or
shale and saturation), a third parameter will appear in the
model (Models 4, 5 and 6). A classic example of the
fourth kind of Worthington model is Indonesian equation
introduced by Poupon and Leveaux (Equation 8). This
equation is empirical and is valid for most shaly
reservoirs in Indonesia (Poupon and Leveaux, 1971).
2 ) 2 ( 2
) 2 ( 2
2
W sh
V
sh W
sh
V
sh W W W
t
S C V S
F
C V C
F
S C
C
sh
sh
+ + =
(8)
Although all these methods could potentially detect the
effect of shale and yield more realistic values of the
formation conductivity and water saturation, a major
obstacle remains in these methods due to their strong
dependency on cores and logs analyses which are costly
and time consuming. Opposite to shaly sands, there are
not any highlighted works on the estimation of water
saturation in carbonate formations. A few have worked
on the effect of pore size and distribution in the
evaluation of water saturation in these kind of rocks
(Alger et al., 1989; Obeida et al., 2005; Lucia, 2007)
perhaps the most significant contribution is the equation
by Lucia.
c b
W
H a S = (9)
In this equation, H is the reservoir height (vertical
thickness of the reservoir zone), a, b, and c are constant
coefficients which are the functions of rock type and grain
size. Unfortunately, Lucia formula does also depend on
the analyses of cores and logs. To treat the problem of
dependency of water saturation estimation on core
analysis, Kamel and Mabrouk (2002, 2003) proposed
using rock physics and arrived at an improved model of
water saturation estimation. Their method is based on
two equations as follows:
i) A first equation to determine the water saturation using
a combination of Archie and Raiga formulas with two logs
Alimoradi et al. 47
of acoustic and electrical resistivity (Kamel and Mabrouk,
2002) as follows:
t
m
X
ma P
W
W
R
t V
R
S
(
(
|
.
|
\
|
=
1
6
10
1
(10)
Where V
P
is P-wave velocity in rock obtained from
acoustic log,
ma
t is the acoustic wave transition time in
rock matrix, and X is a parameter obtained from
ma
t
using Table 1.
ii) A second equation to determine shale volume in shaly
sands using a combination of three porosity logs of
neutron, density, and acoustic (Kamel and Mabrouk,
2003).
0 )
100
2 (
) 2 ( ) (
2
=
+ +
tsh tma tf
tma t
ma f
ma b
N
sh
tma tf
tma tsh
ma f
ma sh
ma f
ma b
N sh
ma f
ma sh
V V
(11)
In this equation,
sh
is density of shale,
ma
is density
of rock matrix,
f
is density of fluid,
N
is Notron log
porosity,
b
is total density,
tsh
is acoustic wave time
in rock matrix,
tf
is acoustic wave transition time in
transition time in shale,
tma
is acoustic wave transition
time in rock matrix,
tf
is acoustic wave transition time in
rock fluid, and
t
is total transition time of acoustic
wave. The roots of Equation 11 are the values of shale
volume.
Kamel and Mabrouks (2002 to 2003) procedures give
reasonably good results of water saturation estimation
especially in shaly sands.
A review of literature, as documented here, shows that
most valuable contributions to date have been focused
on determination of water saturation using well logs and
cores data. Graphically illustrated, the process of
reservoir characterization will much benefit from more
detailed studies in the first part of the process which
involves seismic data, as is shown in Figure 1.
There seems to be a lack of coherent methodologies to
48 J. Petroleum Gas Eng.
Figure 1. Reservoir characterization chain.
Table 2. Two kinds of error in seismic attributes selection (Kalkomey, 1997).
Decision Property and attribute are uncorrelated Property and attribute are correlated
Keep seismic attribute as a predictor Type I Error Correct decisio (no error)
Reject seismic attribute as a predictor Correct decision (no error) Type II Error
incorporate seismic data into water saturation evaluation
instantly; alternatively such procedures could be used to
determine only the necessary well logs that could help
estimation of water saturation level to complete the first
part of the chain in Figure 1.
Seismic attributes in reservoir characterization
Generally, the three most important aspects of seismic
reservoir characterization are considered to be quality of
seismic data, determination of proper seismic attributes,
and existence of a physical relationship between
attributes and the reservoir property of interest. Kalkomey
(1997) introduced two kinds of errors which may occur
during selection of seismic attributes. Table 2 illustrates
these errors.
A Type I Error will occur if no relationship exists
between the seismic attribute of choice and the reservoir
property of interest, yet we opt to use the seismic
attribute as a predictor. On the other hand, a Type II Error
occurs when a physical relationship exists between the
seismic attribute and the reservoir property of interest,
but we fail to consider the seismic attribute as a predictor.
The cost of a Type I Error is inaccurate prediction biased
by the attribute and the cost of a Type II Error is less
accurate prediction than if we would have used the
seismic attribute.
After selecting the proper attributes, the next step is
integration of the attributes to predict reservoir property of
interest.
Pan and Ma (1997) introduced three kinds of
techniques for integrating seismic attributes:
1. Techniques based on statistical relationships, such as
correlation and cross plotting.
2. Techniques based on expert experience and
information.
3. Techniques which use artificial neural networks, fuzzy
logic, and genetic algorithms to find the relationship
between seismic attributes and the reservoir property of
interest.
Seismic attributes in water saturation estimation
A review of previous studies on correlation between
seismic attributes and water saturation is presented next.
Seismic attributes such as amplitude, instantaneous
amplitude, and impedance are shown generally well-
correlated with water saturation. There also seem to be a
consensus amongst researchers on applicability of
prestack seismic data and AVO to provide reliable
information about liquids and their identification in
reservoirs (Van, 2000; Varela, 2003; Li et al., 2007; Zhou
et al., 2009). Some of the findings are as follows:
Investigation of oil saturation in a sand stone formation in
China using 3D seismic data (Pan and Ma, 1997). Their
result is presented in Figure 2. Pan and Ma use real
values of oil saturation from three wells, with interpolation
throughout the reservoir using 3D seismic data that
makes their final results highly dependent on the output
of limited number of wells.
Balch et al. (1999) predicted the water saturation in a
sandstone reservoir in Mexico using artificial intelligence
and seismic attributes. The reservoir in their study had
two zones of hydrocarbon (L and K). Three dimensional
seismic data and values of water saturation at 19 wells
were used first step in a fuzzy logic algorithm to detect
five attributes (reflection coefficient, frequency,
instantaneous phase, amplitude and energy) that were
strongly correlated with water saturation. Then, a back-
propagating artificial neural network was used to find the
relationship between these attributes and the value of
water saturation. The results of training the network is
Alimoradi et al. 49
0.4
0.4
0.5
0.6
0.6
0.4
0.4
0.5
0.6
0.6
0.7
0.5
0
500
500
1500
1500 2500
2500
3500
2000
2000 1000
1000
3000
3000 4000
Distance (m)
D
i
s
t
a
n
c
e
(
m
)
Figure 2. Oil saturation values (Pan and Ma, 1997).
Predicted values of S
W
R
e
a
l
v
a
l
u
e
s
o
f
S
W
Predicted values of S
W
Training results for zone K R = 0.83 Training results for zone L R = 0.84
R
e
a
l
v
a
l
u
e
s
o
f
S
W
Figure 3. Correlation coefficient between real and predicted values of water saturation in zone "L" (left
panel) and K (right panel), from Balch et al. (1999).
shown in Figures 3. The main contribution in the study by
Balch et al. (1999) is using seismic attributes for water
saturation estimation.
Boadu (2001) studied the effect of change in oil
saturation level on seismic wave velocities and their ratio
in a laboratory experiment. He applied changes to the
temperature and values of oil saturation and observed a
relationship between these variables and the values of P
and S wave velocities and their ratio. He used an artificial
neural network to express this relationship.
One of the most interesting studies in this field is the
work done by Mu and Cao. They created a physical
model of a sandstone reservoir in laboratory scales (Mu
and Cao, 2004). They isolated the model and drilled two
holes (injecting and discharging) in it. Saturating the
sandstone layer with water, oil, CO
2
and CH
4
from 10 to
100 percents respectively, they succeeded in simulating
seismic surveying by application of ultrasonic data acqui-
sition; therefore, creating an environment to study the
effect of change in the fluids type and saturation value on
P-wave amplitude and absorption coefficient (Figures 4
and 5). The outcome of their study was an expression for
determining absorption coefficient profile using Biot
theory and reflection amplitude spectrum. They applied
this formula for a sandstone reservoir in China (Figure 6)
and reliably detected the gas zones (Figure 7) that could
50 J. Petroleum Gas Eng.
70
Llquld saLuraLlon ()
10 20 30 40 30 60 80
30
0
100
130
200
230
-
w
a
v
e
a
m
p
l
l
L
u
d
e
CP
4
CC
2
Cll
WaLe
100 90
Figure 4. The relationship between amplitude of P-wave reflected from top of the
sandstone layer and saturation values of different liquids (Mu and Cao, 2004).
80 30 10 20
Llquld saLuraLlon ()
100
0
2
4
6
8
10
12
-
w
a
v
e
a
b
s
o
r
p
L
l
o
n
70 30 40 60
CP
4 CC
2
Cll
WaLe
90
Figure 5. The relationship between P-wave absorption coefficient in sandstone layer
and saturation values of different liquids (Mu and Cao, 2004).
not be seen on the initial seismic section in Figure 6. It is
clear from Figure 7 that Mu and Caos formula had
detected other zones as gas; further drillings indicated
that these zones in fact belonged to the coal seems that
lied underneath the gas layer. This potentially presents a
problem in the discrete gas and coal detection
methodology of Mu and Cao.
Kitamura et al. (2006) studied the effect of water and
gas saturation on P and S wave velocity values in
sandstone samples. They changed the temperature at
restricted pressure value to 130 MPa for each saturation
degree and determined the P and S wave velocities for
each temperature. Their results are shown in Figure 8.
CONCLUSIONS
Water saturation is one of the most important parameters
in reservoir characterization procedure. This parameter
can be either predicted from core data, well logs, or
seismic attributes directly or can be estimated from an
intermediate parameter such as shale volume in sand
Alimoradi et al. 51
Figure 6. Seismic profile of the reservoir h8 is a zone of gas (Mu and Cao, 2004).
Figure 7. Black zones are zones of high absorption coefficient and indicate the existence of gas in the formation (Mu
and Cao, 2004).
52 J. Petroleum Gas Eng.
0
0
30 30 100 100 130 200 200 130
2.3
3
3.3
4
2.3
3
2
1.3
4.3
3
1emperaLure (C) 1emperaLure (C)
-
w
a
v
e
v
e
l
o
c
l
L
y
(
k
m
/
s
)
S
-
w
a
v
e
v
e
l
o
c
l
L
y
(
k
m
/
s
)
Without pore fluid (Pp=0)
H2O (Pp=70 Mpa)
Ar-Gas (Pp=70Mpa)
Figure 8. The P and S wave velocity values for dry, saturated with water, and saturated with gas samples (Kitamura et al.,
2006).
stone reservoirs. Over the past decades, we have
witnessed developments in using well log data to
estimate water saturation. This process was started from
Archie formula in 1942 and progressed by the works of
Patnode and Wyllie (1950), Winsauer and McCardell
(1953), Wyllie and Southwick (1954), Waxman and Smith
(1968), Poupon and Leveaux (1971), Clavier et al.
(1984), Worthington (1985).
To treat the problem of dependency of water saturation
estimation on core analysis in previous works, Kamel and
Mabrouk (2002, 2003), proposed using rock physics and
arrived at an improved model of water saturation
estimation. All of the proposed procedures till that time
reveal the superior progress in second part of the
reservoir characterization chain (from well logs to water
saturation estimation).
More recently, interpreters have used seismic attributes
to evaluate water saturation values directly or estimating
proper rock physical properties such as shale volume
which are useful in water saturation estimation process
(Pan and Ma, 1997; Balch et al., 1999; Boadu, 2001; Mu
and Cao, 2004; Kitamura et al., 2006; Lucia, 2007).
These methods apply artificial intelligence computational
agents such as fuzzy logic, genetic algorithms and
neural networks or statistical approaches to detect
unknown non-linear relationships between different
seismic attributes and the reservoir property of interest
which is here the water saturation value.
ACKNOWLEDGMENTS
A review paper spanning more than six decades cannot
be a one- or two-man job. The authors therefore acknow-
ledge the advice, support, and suggestions given by
many prominent individuals, some of whom were actually
involved in the development of the methods of reservoir
characterization. The many constructive comments and
advice received from Professor Majid Nabi Bidhendi of
Geophysics Institute of University of Tehran, Dr. Iraj
Abdollahi Fard and Mr. Torabi of National Iranian Oil
Company, Dr. Misaghi from Research Institute of
Petroleum Industry, Dr. Iraj Pirouz and Dr. Abolghasem
Kamkar Rouhani from the department of mining,
petroleum and geophysics engineering of Shahrood
University of Technology is appreciated. The authors also
would like to gratefully acknowledge their sponsor: NIOC,
Exploration Directorate for their support.
Nomenclature
Sw, water saturation; Sh, hydrocarbon saturation;
tortuosity factor; Rw, water resistivity; , porosity; R
t
,
corrected total electrical resistivity of formation; m,
cementation exponent; n, saturation exponent; C
t
, total
conductivity of fully saturated sand; C
w
, water conduc-
tivity;
n
w
S , water saturation of non-shaly sand;
s
w
S , water
saturation of shaly sand; s, saturation exponent for shaly
sand; X, additional conductivity added by clay; F,
formation factor; V
sh
, shale volume; C
sh
, shale
conductivity; H, reservoir height; V
p
, P-wave velocity;
tma
, Acoustic wave transition time in rock matrix
tsh
,
Acoustic wave transition time in shale;
tf
, Acoustic
wave transition time in rock fluid;
t
, Total transition time
of acoustic wave;
sh
, shale density;
ma
, rock matrix
density;
f
, fluid density;
b
, total density;
N
, notron
log porosity.
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