WATER SATURATIONS

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Water saturation
The saturation of a formation represents the amount of a
given fluid present in the pore space
S w = S w irr + S w "free"

water S o = S oresidual + S o"free"

oil

Matrix

The porosity logs react to the pore space.

The resistivity logs react to the fluids in the pore space.
The combination of the two measurements gives the
saturation
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Water saturation – Archie equation
Rw = resistivity of water in the pore space.
Define Ro = resistivity of a rock totally filled with water.
Ro
F
Rw
F: Formation Factor.
At constant porosity F is constant.
As porosity increases, Ro decreases and F decreases.
Experiments have shown that F is inversely proportional to
m. a
F 
 m

m: is called the "cementation exponent".

a: is called the "lithology" constant.
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Water saturation – Archie equation
Archie show the formation
factor F and porosity φ on
the log chart and this is
relationship between two
parameters

m varies from 1.8 to 2.15,

this is the slope of trend line
and a varies from 0.62 to 1

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Water saturation – Archie equation
Table 1. Different coefficients and exponents used to calculate formation factor (F)

Table 1 illustrates the range of values for a and m. In first-pass or

reconnaissance-level interpretations, or where there is no knowledge of
the local parameters, the following values can be used to achieve an
initial estimate of water saturation: a = 1.0; m = n = 2.0
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Water saturation – Archie equation
In VietNam

White Tiger Field

Oligocene a = 0.71 and m = 1.86
Miocene a=1 and m = 1.8
DaiHung Field
Sandstone a=1 and m = 1.74
Limestone a=1 and m = 1.84

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Water saturation – Archie equation
In experiment rock sample saturation with a part of
hydrocarbon and get a linear coefficients is resistivity index

Rt resistivity of rock is saturated with a part of hydrocarbon

Ro resistivity of rock is saturated with water 100%

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Water saturation – Archie equation
On the log chart, I and Sw have a relationship

White Tiger Field

Oligocene b = 1.04 and n = 2.19

DaiHung Field
Sandstone
b = 1 and n = 1.93
Limestone
b = 1 and n = 2.21
Sw increase

Rt decrease

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Water saturation
Saturation can be expressed as a ratio of the resistivities:
Ro
S  n
w
Rt
where n is the "saturation exponent", an empirical
constant.
FRw
Substituting for Ro: S 
n
w
Rt

a Rw
Substituting for F: S n
w  m
 Rt

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Water saturation
a Rw
S n
w  m
 Rt
The Archie equation is hence very simple. It links porosity
and resistivity with the amount of water present, Sw.
Increasing porosity,, will reduce the saturation for the
same Rt.
Increasing Rt for the same porosity will have the same
effect.
n, m, a, b determine from core analysis
Rw and Rt, porosity determine from well-log

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Water saturation
Determine parameters a and m

Logarithm equation
log F = log a – m logφ
When φ = 100%
=> log F = log a

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Water saturation
Determine parameters n
Rt 1
 n
Ro S w
Logarithm equation
Rt
log  n log S w
Ro

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Water saturation
Example 1. Determine parameter a and m
NN F φ
1 140 0.06
2 76 0.11
3 51 0.12
4 40 0.13
5 37 0.13
6 37 0.13
7 30 0.15
8 27 0.16
9 25 0.17
10 22 0.15
11 22 0.17
12 15 0.21
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Water saturation
Example 1. Determine parameter n

NN F φ Sw Rt/Ro NN F φ Sw Rt/Ro
1 25.9 0.169 0.564 2.46 3 27.4 0.165 0.5 1.51
0.301 5.87 0.287 4.28
0.245 10.3 0.234 13.8
0.199 14.5 0.22 22.3
0.17 27.8 0.21 41.2
0.136 57.2
2 22.4 0.169 0.478 2.87 4 29 0.153 0.426 2.75
0.273 4.85 0.311 3.3
0.21 8.64 0.251 5.42
0.18 11.8 0.197 10.5
0.151 35.5 0.155 17.3
0.122 47.8 0.131 44.3

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Water saturation
Invaded Zone
The same method can be applied to the invaded
zone. The porosity is identical, the lithology is assumed to
be the same, hence the constants a, n, m are the same.
The changes are the resistivities which are now Rxo
and Rmf.
Rmf is measured usually on surface and Rxo is
measured by the MSFL tool.
The equation is then:
aRmf
S n

xo
 Rxom

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Water saturation
Dividing for Sxo and Sw, with n set to 2
1

Sw  Rxo Rt  2
 
S xo R R 
 mf w 
Observations suggest:
1
S xo  S w 5

5
Hence:  Rxo Rt  8
Sw   
R R 
 mf w 
providing a quick look saturation answer when porosity is
not available.
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Water saturation
Rw = resistivity of connate water.
m = "cementation factor", set to 2 in the simple case.
n = "saturation exponent", set to 2 in the simple case.
a = constant, set to 1 in the simple case.
All the constants have to be set.
Two common sets of numbers for these constants are:
In a simple carbonate, the parameters are simplified to:
m = 2, n = 2, a=1
In a sandstone the following values are often quoted:
m = 2.15, n = 2, a = 0.62
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Water saturation
Rw determination
Rw is an important parameter.
Sources include:
Client.
Local tables / knowledge.
SP.
Resistivity plus porosity in water zone.
RFT sample.
From Rxo and Rt tools.

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Water saturation
Rw from Rwa
If Sw = 1, the saturation equation can become:

R  R
w
2
t

Assuming simple values for a, m, n.

Procedure is to:
Compute an Rwa (Rw apparent) using this
relationship.
Read the lowest value over a porous zone which
This is the method employed by all computer based
interpretation systems.

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Water saturation
Rw from resistivity
In a water zone Sw = 1, thus the alternative saturation
equation becomes:

The value of Rmf is measured;

Rxo and Rt are measured, the value of Rw can be calculated.

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Water saturation
Other Archie Parameters
The constants a, m, n are an integral part of Archie's
saturation equation.

They can, and do, vary.

They are usually taken from local knowledge if at
all possible.
n is dependent on the wettability of the rocks; in the
common water wet case it is usually close to 2.
a and m are dependent on the lithology and pore
systems of the rock.

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Water saturation
Effects of parameters
Example of variations in the Archie parameters
a Rw
S n
w  m
 Rt
The following are measurements
 = 25%, Rt = 5 ohm-m, Rw = .02 ohm-m
Assuming a simple formation with
a = 1, m = 2, n = 2
Sw = 25%
Changing n to 2.5, changes the Sw to 33%
Changing m to 3 changes Sw to 50%
Hence the choice of these constants is important
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Water saturation
Computing Saturation
The standard saturation equation can be used with special attention
taken to obtain the correct value for the cement exponent ‘m’.
In vuggy formations this will be greater than 2. The resistivity logs
see read higher as the “pathway” is more tortuous.
Saturations calculated with an ‘m’ of 2 will show too much
hydrocarbon
In fractured formations ‘m’ will be less than one as the resistivity
pathways are straight.
In this case saturations computed with ‘m’ = 2 will show too much
water.

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Water saturation
Variation of m
m reflects the tortuosity of the formation, the pathway for
electrical current flow
Carbonates have complex porosities and hence current
pathways an values of m

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Water saturation
Variation of m
Hence in a carbonate the major problem is the
determination of ‘m’
There are two methods of determining m using logs
1) In a water zone, rearranging Archies formula
Log Rt = - m log + log (aRw)
Slope will give m, and the intercept a
The assumption is that m is constant through the entire
reservoir.

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Water saturation
Variation of m
line , slope = m

cloud of points in water zone

Perfect plot

log Rt

log 

line , slope = m

Alte rnate line s

More common
output
log Rt

cloud of points in water zone Cloud of points

with no obvious
lines
log 

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Water saturation
Variation of m
2) In a clean formation the following are measured by the
standard methods:
porosity, 
water resistivity, Rw, Rmf
formation resistivity, Rt, Rxo
The saturation Sw, Sxo, m and n are unknown (a is taken as
1)
Assume that n is 2 , (valid in most circumstances)
If the saturation isaformula) the only unknown is m.

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Water saturation
Variation of m
The Electromagnetic Propagation Tool, EPT, is used
This measures Sxo independently of Archies Equation

The advantage is that m is calculated over the entire

reservoir and variations taken into account

The disadvantage is that the tool only measures in the

invaded zone hence the assumption that this is the same as
the virgin zone.

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Water saturation
Variation of m Secondary Porosity
0 'm'
25 Limestone

2 7 Dolomite

Residual h.c.

Moved h.c.

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Water saturation
Archie’s experiments showed that the resistivity of a water-filled
formation (Ro) could be related to the resistivity of the water (Rw)
filling the formation through a constant called the formation resistivity
factor (F):

Archie’s experiments also revealed that the formation factor (F) could
be related to the porosity of the formation by the following formula:

where m is the cementation exponent whose value varies with grain

size, grain-size distribution, and the complexity of the paths between
pores (tortuosity), and a is the tortuosity factor

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Water saturation
Water saturation (Sw) is determined from the water filled resistivity (Ro)
and the actual (true) formation resistivity (Rt) by the following
relationship:

where:
Sw = water saturation of the uninvaded zone
Rw = resistivity of formation water at formation temperature
Rt = true formation resistivity (i.e., deep induction or deep laterolog
corrected for invasion)
φ = porosity
a = tortuosity factor
m = cementation exponent
n = saturation exponent
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Water saturation

The first cross plot technique to be considered is the Hingle plot. In this
case, assuming that a porosity measurement is available, even if the
matrix values are unknown, a plot can be constructed which will give
porosity and water saturation directly. To see the logic behind the
Hingle plot, note that the simplified saturation expression of Eq. 23.1,
with m = n = 2, indicates that φ will vary as 1/√Rt at a fixed value of
water saturation, assuming, of course, that the water resistivity is
constant. This leads to the construction of a plot, shown in Fig below,
inverse square root of resistivity versus porosity

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Water saturation
It is clear that the 100%
water-saturated points will
fall on a straight line of
maximum slope. Less-
saturated points, at any fixed
porosity, must have a larger
resistivity and thus fall
below this line. Once these
points have been identified
and ignored, the line
corresponding to Sw = 100%
can be drawn, as shown in.

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Water saturation
The Hingle plot, which combines resistivity and porosity (in this case
the Δt measurement) to estimate water saturation. In constructing the
chart, implicit use is made of the square-root saturation relation and in
this case of the relation F = 1/φ2

The implication is that at a porosity of 10 p.u. the indicated value of

Ro will be 100 times the value of Rw. For the example given, the
value of Ro at 10 p.u. is 12 ohm-m, which indicates that the water
resistivity is 0.12 ohm-m.

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Water saturation
The second useful graphical technique is the result of work by Pickett.
A knowledge of porosity is required, but the values of m, Rw, and Sw
can be obtained. In this method, the power law expression for
saturation is exploited by plotting on log–log scales. Starting with the
general saturation expression:

taking the log of both sides of the equation and rearranging results in:

If we consider the value of a to be unity, then we can write:

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Water saturation
which represents the line of 100% water saturation. In this case the intercept at the
100% porosity point gives the value of Rw directly. For values of Sw less than 100%,
the relationship between φ and Rt will be represented by lines parallel to the 100%
saturation case but displaced to the right.

A log–log representation of resistivity and porosity attributed to Pickett. It is useful

for determining the cementation exponent that best describes a given formation.
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Water saturation
The uninvaded zone’s water saturation (Sw), determined by the Archie
equation, is the most fundamental quantity used in log evaluation. But
merely knowing a zone’s water saturation (Sw) does not provide enough
information to completely evaluate a zone’s potential productivity. A
geologist must also determine
if:
• the water saturation is low enough for a waterfree completion
• the hydrocarbons are moveable
• the zone is permeable
• there is an commercial volume of recoverable hydrocarbon
reserves

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