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7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 128
1copy 2006 Weatherford All rights reserved
Noviembre 2006
Angel Meso
Interpretacioacuten de Perfiles de Pozo
Saturation Computation
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 228
copy 2006 Weatherford All rights reserved
Saturation
bull The saturation of a formation represents the amount of a given fluid present in the porespace
bull The porosity logs react to the pore space
bull The resistivity logs react to the fluids in the pore space
bull The combination of the two measurements gives the saturation
Matrix
water
oil
Sw = Sw irr + Sw fr ee
So = Soresidual + Sofree
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 328
copy 2006 Weatherford All rights reserved
Saturation Basics (1)
bull Rw = resistivity of water in the pore space
bull Define Ro = resistivity of a rock totally filled with water
ndash F Formation Factor
ndash At constant porosity F is constant
ndash As porosity increases Ro decreases and F decreases
bull Experiments have shown that F is inversely proportional to φm
ndash m is called the cementation exponent
ndash a is called the lithology constant
F = R
0
R w
F = a
φm
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 428copy 2006 Weatherford All rights reserved
Saturation can be expressed as a ratio of the resistivities
Sw
n = R
0
R t
Sw
n = FR
w
R t
Saturation Basics (2)
where n is the saturation exponent an empirical constant
Substituting for Ro
Substituting for F
w
n
S = a
φ
m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 528copy 2006 Weatherford All rights reserved
Archiersquos Saturation Equation
bull The Archie equation is hence very simple It links porosity and resistivity with the
amount of water present Sw
bull Increasing porosity φ will reduce the saturation for the same Rt
bull Increasing Rt for the same porosity will have the same effect
w
n
S = a
φ m R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 228
copy 2006 Weatherford All rights reserved
Saturation
bull The saturation of a formation represents the amount of a given fluid present in the porespace
bull The porosity logs react to the pore space
bull The resistivity logs react to the fluids in the pore space
bull The combination of the two measurements gives the saturation
Matrix
water
oil
Sw = Sw irr + Sw fr ee
So = Soresidual + Sofree
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 328
copy 2006 Weatherford All rights reserved
Saturation Basics (1)
bull Rw = resistivity of water in the pore space
bull Define Ro = resistivity of a rock totally filled with water
ndash F Formation Factor
ndash At constant porosity F is constant
ndash As porosity increases Ro decreases and F decreases
bull Experiments have shown that F is inversely proportional to φm
ndash m is called the cementation exponent
ndash a is called the lithology constant
F = R
0
R w
F = a
φm
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 428copy 2006 Weatherford All rights reserved
Saturation can be expressed as a ratio of the resistivities
Sw
n = R
0
R t
Sw
n = FR
w
R t
Saturation Basics (2)
where n is the saturation exponent an empirical constant
Substituting for Ro
Substituting for F
w
n
S = a
φ
m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 528copy 2006 Weatherford All rights reserved
Archiersquos Saturation Equation
bull The Archie equation is hence very simple It links porosity and resistivity with the
amount of water present Sw
bull Increasing porosity φ will reduce the saturation for the same Rt
bull Increasing Rt for the same porosity will have the same effect
w
n
S = a
φ m R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 328
copy 2006 Weatherford All rights reserved
Saturation Basics (1)
bull Rw = resistivity of water in the pore space
bull Define Ro = resistivity of a rock totally filled with water
ndash F Formation Factor
ndash At constant porosity F is constant
ndash As porosity increases Ro decreases and F decreases
bull Experiments have shown that F is inversely proportional to φm
ndash m is called the cementation exponent
ndash a is called the lithology constant
F = R
0
R w
F = a
φm
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 428copy 2006 Weatherford All rights reserved
Saturation can be expressed as a ratio of the resistivities
Sw
n = R
0
R t
Sw
n = FR
w
R t
Saturation Basics (2)
where n is the saturation exponent an empirical constant
Substituting for Ro
Substituting for F
w
n
S = a
φ
m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 528copy 2006 Weatherford All rights reserved
Archiersquos Saturation Equation
bull The Archie equation is hence very simple It links porosity and resistivity with the
amount of water present Sw
bull Increasing porosity φ will reduce the saturation for the same Rt
bull Increasing Rt for the same porosity will have the same effect
w
n
S = a
φ m R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 428copy 2006 Weatherford All rights reserved
Saturation can be expressed as a ratio of the resistivities
Sw
n = R
0
R t
Sw
n = FR
w
R t
Saturation Basics (2)
where n is the saturation exponent an empirical constant
Substituting for Ro
Substituting for F
w
n
S = a
φ
m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 528copy 2006 Weatherford All rights reserved
Archiersquos Saturation Equation
bull The Archie equation is hence very simple It links porosity and resistivity with the
amount of water present Sw
bull Increasing porosity φ will reduce the saturation for the same Rt
bull Increasing Rt for the same porosity will have the same effect
w
n
S = a
φ m R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 528copy 2006 Weatherford All rights reserved
Archiersquos Saturation Equation
bull The Archie equation is hence very simple It links porosity and resistivity with the
amount of water present Sw
bull Increasing porosity φ will reduce the saturation for the same Rt
bull Increasing Rt for the same porosity will have the same effect
w
n
S = a
φ m R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 628copy 2006 Weatherford All rights reserved
Invaded Zone
bull 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
bull The changes are the resistivities which are now Rxo and Rmf measured by the
MSFL tool
bull The equation is then
Sxon = aR mf
φmR
xo
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 728copy 2006 Weatherford All rights reserved
Other Relationships
bull Dividing for Sxo and Sw with n set to 2
bull Observations suggest
bull Hence
bull providing a quick look saturation answer when porosity is not available
Sw
Sxo
= R
xo R
t
R mf
R w
⎛
⎝
⎜ ⎞
⎠
⎟
1
2
Sxo
asymp Sw
1
5
Sw =
R xo
R t
R mf
R w
⎛
⎝⎜
⎞
⎠⎟
5
8
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 828copy 2006 Weatherford All rights reserved
Archie parameters
bull Rw = resistivity of connate water
bull m = cementation factor set to 2 in the simple case
bull n = saturation exponent set to 2 in the simple case
bull a = constant set to 1 in the simple case
bull Two common sets of numbers for these constants are
ndash In a simple carbonate the parameters are simplified to
bull m = 2
bull n = 2
bull a = 1
ndash In a sandstone the following values are often quoted
bull m = 215
bull n = 2
bull a = 062
w
n
S =
a
φ m
R w
R t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 928copy 2006 Weatherford All rights reserved
Rw determination
bull Rw is an important parameter
ndash Sources include
bull Client
bull Local tables knowledge
bull SP
bull Resistivity plus porosity in water zone
bull RFT sample
bull From Rxo and Rt tools
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1028
copy 2006 Weatherford All rights reserved
Rw from Rwa
bull If Sw = 1 the saturation equation can become
bull Assuming simple values for a m n
bull Procedure is to
bull Compute an Rwa (Rw apparent) using this relationship
bull Read the lowest value over a porous zone which contains water
bull This is the method employed by all computer based interpretation systems
R w
= φ 2R
t
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1128
copy 2006 Weatherford All rights reserved
Rw from resistivity
bull In a water zone Sw = 1 thus the alternative saturation equation becomes
bull The value of Rmf is measured Rxo and Rt are measured the value of Rw can be
calculated
Sw
Sxo
= R
xo R
t
R mf R w
⎛
⎝⎜
⎞
⎠⎟
1
2
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1228
copy 2006 Weatherford All rights reserved
Other Archie Parameters
bull The constants a m n are an integral part of Archies saturation
equation They can and do vary They are usually taken from
local knowledge if at all possible
ndash n is dependent on the wettability of the rocks in the
common water wet case it is usually close to 2
ndash a and m are dependent on the lithology and pore
systems of the rock
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1328
copy 2006 Weatherford All rights reserved
F Relation chart25 5 10 20 50 100 200 500 1000 2000 5000 1000
25 5 10 20 50 100 200 500 1000 2000 5000 1000
1
2
3
4
5
6
7
89
10
15
20
25
30
40
50
FR=1
oslash2
FR=062
oslash215
FR=081
oslash2
FR=1
oslashmm
2 8
2 5
2 2
2 0
1 8
1 6
1 4
copySchlumberger
FR Formation Resistivity Factor
φ
P o r o s i t y ( p u )
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1428
copy 2006 Weatherford All rights reserved
F-relations
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1528
copy 2006 Weatherford All rights reserved
Computing Saturation
The standard saturation equation can be used with special
attention taken to obtain the correct value for the cement
exponent lsquomrsquo
In vuggy formations this will be greater than 2 The
resistivity logs see read higher as the ldquopathwayrdquo is more
tortuous Saturations calculated with an lsquomrsquo of 2 will showtoo much hydrocarbon
In fractured formations lsquomrsquo will be less than one as theresistivity pathways are straight In this case saturations
computed with lsquomrsquo = 2 will show too much water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1628
copy 2006 Weatherford All rights reserved
Variation of m
m reflects the tortuosityof the formation thepathway for electrical
current flow Carbonateshave complex porositiesand hence currentpathways an values of m
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1728
copy 2006 Weatherford All rights reserved
Variable m (1)
Hence in a carbonate the major problem is the determination
of lsquomrsquo
There are two methods of determining m using logs
1) In a water zone rearranging Archies formula
Log Rt = - m log φ + log (aRw)
Plotting on a log-log scale slope will give lsquomrsquo and the
intercept lsquoarsquo The assumption is that m is constant through the
entire reservoir
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1828
copy 2006 Weatherford All rights reserved
Dual Water Model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 1928
copy 2006 Weatherford All rights reserved
Shale and Saturation
bull The Archie equation has to be changed to take account of the
shale effect
bull The shale looks like low resistivity so another term is added to the
equations
bull The result is an equation which will can be used to compute water
saturation in shaly sands
bull All these equations return to Archies equation if there is no shale
present
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2028
copy 2006 Weatherford All rights reserved
Saturation Equations (1)
bull Indonesia Equation
bull Nigeria Equation
bull Waxman-Smits Equation
bull Dual Water Equation
1
R t
= S w
2
F R w
+ BQ v S w
F
C t = φ t
m S wt n
aC w +
S wb
S wt C wb minus C w( )⎡
⎣⎢⎤
⎦⎥
S w = 1
V cl
1 minus V cl
2
⎛
⎝⎜⎜
⎞
⎠⎟⎟
R cl
+ φ e
R w
1
R t
1
R t
= V cl
1 4
R cl
+ φ e
m2
aR w
⎛
⎝⎜
⎞
⎠⎟
2
S wn
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2128
copy 2006 Weatherford All rights reserved
bullOne of the difficulties is the number of equations available for
shaly sands
bullThey are often ldquocountryrdquo oriented Nigeria Venezuela
bullThe choice of equation is dictated by local practice
bullWaxman-Smits (WS) and Dual Water (DW) approach the problem
from experiments on the clay properties and are thus more realistic
and universal
Saturation Equations (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2228
copy 2006 Weatherford All rights reserved
Dual water
bullThe Dual Water Model takes the basic work of Waxman Smits and
expands it for use with logged information
bullIt divides the formation into solids and fluids
bullIt splits the clay into dry clay and its associated water called boundwater
bullThe standard definitions for porosity and saturation to describe the
fractions of fluids in the formation are expanded to include the new
model
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2328
copy 2006 Weatherford All rights reserved
Dual water model definitions
hydrocarbon
far
water
bound
water
dry
clay
clean
matrix
fluids
solids
unit
volume
Vclwet clayVdcl
φwb
φwf
φhyeffective
porosity
φe
totalporosity
φt
= φwf+ φhy
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2428
copy 2006 Weatherford All rights reserved
Clean to Shale
t
t
t
t
Matrix
Matrix
Matrix
Dry Colloid
Dry Colloid
Bound water
Far Water
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2528
copy 2006 Weatherford All rights reserved
Dual Water definitions
the porosities are combined to give the saturations of the fluids present
S wb = φ wb
φ t
S wf = φ wf
φ t
S hy = φ hy
φ t
S wt = S wf + S wb
φ t = φ e + φ wb = φ t 1 minus S wb( ) + φ t S wb
S wt + S hy = 1
V cl = V dcl + φ t S wb
saturation of bound water
saturation of free water (this is Sw)
Hydrocarbon saturation
Total water saturation is the sumof the saturations of the two waters
total water saturation plus hydrocarbon saturationmust be one
wet clay volume includes thevolume of bound water
The total porosity is given by
Si lifi d DWM (1)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2628
copy 2006 Weatherford All rights reserved
Simplified DWM (1)
Swt
2
Rf
t
2R
t
Archie Equation can be generalized into the following form
where
Swt - total water saturation
φt - total porosity
Rt - true formation resistivity
Rf - resistivity of the water(s)
The equation can be solved if Rf is known
Si lifi d DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2728
copy 2006 Weatherford All rights reserved
bull 1) Clean water bearing zone
ndash Swt = 1
φt2Rt = Rf
ndash This is Rwf the resistivity of Free water
bull 2) Clean 100 shale zone
ndash Swt = 1
φt
2
Rt = Rf ndash This is Rwb the resistivity of Bound water
bull These are the two end points To give a universal solution they are
combined linearly using the volume of shale
Simplified DWM (2)
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
7242019 8) Saturation (1)
httpslidepdfcomreaderfull8-saturation-1 2828
copy 2006 Weatherford All rights reserved
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