8) saturation (1)

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



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




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


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


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



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



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



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



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



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




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




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




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




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 )




F-relations




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




Variation of m

m reflects the tortuosityof the formation thepathway for electrical

current flow Carbonateshave complex porositiesand hence currentpathways an values of m




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




Dual Water Model




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




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




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





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




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




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water




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)




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)




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)







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













F = R

0

R w

F = a

φm




Sw

n = R

0

R t

Sw

n = FR

w

R t



Substituting for Ro

Substituting for F

w

n

S = a

φ

m

R w

R t








w

n

S = a

φ m R w

R t



Invaded Zone



same


MSFL tool


Sxon = aR mf

φmR

xo



Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)
















F = R

0

R w

F = a

φm




Sw

n = R

0

R t

Sw

n = FR

w

R t



Substituting for Ro

Substituting for F

w

n

S = a

φ

m

R w

R t








w

n

S = a

φ m R w

R t



Invaded Zone



same


MSFL tool


Sxon = aR mf

φmR

xo



Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Sw

n = R

0

R t

Sw

n = FR

w

R t



Substituting for Ro

Substituting for F

w

n

S = a

φ

m

R w

R t








w

n

S = a

φ m R w

R t



Invaded Zone



same


MSFL tool


Sxon = aR mf

φmR

xo



Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)











w

n

S = a

φ m R w

R t



Invaded Zone



same


MSFL tool


Sxon = aR mf

φmR

xo



Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)






Invaded Zone



same


MSFL tool


Sxon = aR mf

φmR

xo



Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)






Other Relationships



bull Hence


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



Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)






Archie parameters







bull m = 2

bull n = 2

bull a = 1


bull m = 215

bull n = 2

bull a = 062

w

n

S =

a

φ m

R w

R t



Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)






Rw determination



bull Client


bull SP


bull RFT sample





Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Rw from Rwa







R w

= φ 2R

t




Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Rw from resistivity



calculated

Sw

Sxo

= R

xo R

t

R mf R w

⎛

⎝⎜

⎞

⎠⎟

1

2











systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)














systems of the rock




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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







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


φ





F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







F-relations
















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)



















Variation of m






Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Variable m (1)


of lsquomrsquo






entire reservoir




Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Dual Water Model






shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)









shale effect


equations




present









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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)












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 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





shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)








shaly sands





and universal





Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Dual water







model





hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)








hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unit

volume

Vclwet clayVdcl

φwb

φwf

φhyeffective

porosity

φe

totalporosity

φt

= φwf+ φhy




Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water






S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)









S wb = φ wb

φ t

S wf = φ wf

φ t

S hy = φ hy

φ t

S wt = S wf + S wb


S wt + S hy = 1









Si lifi d DWM (1)




Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)







Simplified DWM (1)

Swt

2

Rf

t

2R

t


where






Si lifi d DWM (2)





ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)








ndash Swt = 1

φt2Rt = Rf



ndash Swt = 1

φt

2




Simplified DWM (2)




8) saturation (1)

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