dual water model

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Dual Water Model

Intellectual Property

This presentation is sole the property

of the INDONESIA TRAININGCENTRE.

It is not to be duplicated or used byanyone other than the individual for

personal use who has attended thecourse.


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Dual Water Model

Dual Water Model

Schlumber er 1999


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Dual Water Model

Shale and Saturation

The Archie equation has to be changed to takeaccount of the shale effect.

The shale looks like low resistivity so anotherterm is added to the equations.

The result is an equation which will can be usedto compute water saturation in shaly sands.

All these equations return to Archies equation ifthere is no shale present.


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Dual Water Model

Saturation Equations

Indonesia Equation

Nigeria Equation

Waxman-Smits Equation

Dual Water Equation

1

Rt=

Sw2

F*Rw

+ BQvSw

F*

Ct = tmSwtn

aCw +

Swb

SwtCwb Cw( )

Sw = 1

Vcl

1Vcl2

Rcl

+ eR

w

* 1

Rt

1

Rt=

Vcl1.4

Rcl+

em

2

aRw

2

Swn


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Dual Water Model

Saturation equations 2

One of the difficulties is the number ofequations available for shaly sands.

They are often country oriented, Nigeria,Venuzeula..

The choice of equation was (is) dictated bylocal practice.

Waxman-Smits (WS) and Dual Water(DW) approach the problem fromexperiments on the clay properties and are

thus more realistic and universal.


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Dual Water Model

Dual water

The Dual Water Model takes the basic work ofWaxman Smits and expands it for use with loggedinformation

It divides the formation into solids and fluids.

It splits the clay into dry clay and its associated

water, called bound water

The standard definitions for porosity andsaturation to describe the fractions of fluids in theformation are expanded to include the new model.


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Dual Water Model

Dual water model definitions

hydrocarbon

far

water

bound

water

dry

clay

clean

matrix

fluids

solids

unitvolume

Vcl

wet clayVdcl

wb

wf

hyeffectiveporosity

etotal

porosity

t

= wf+ hy


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Dual Water Model

Clean to Shale

t

t

t

t

Matrix

Matrix

Matrix

Dry Colloid

Dry Colloid

Bound water

Far Water


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Dual Water Model

Dual Water definitions 2

the porosities are combined to give the saturations of thefluids present

Swb = wb

t

Swf =

wf

t

Shy =hy

t

wt = wf + wb

t =e + wb = t1 Swb( )+ tSwb

wt + hy =1

Vcl = Vdcl + t wb

saturation of bound water

saturation of far water (this is Sw)

Hydrocarbon saturation

Total water saturation is the sum

of the saturations of the two waters

total water saturation plushydrocarbon saturation must beone

wet clay volume includes the volume

of bound water

The total porosity is given by


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Dual Water Model

Simplified DWM

Swt2

=Rf

t2Rt

Archie Equation can be generalized into the following form;

where;

Swt - total water saturation

ft - total porosity

Rt - true formation resistivity

Rf - resistivity of the water(s)

The equation can be solved if Rf is known.


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Dual Water Model

Simplified DWM 2

1) Clean water bearing zone

Swt = 1

t2Rt = Rf

This is Rwf, the resistivity of Far water

2) Clean 100% shale zone

Swt = 1

t2Rt = Rf

This is Rwb, the resistivity of Bound water

These are the two end points. To give a universalsolution they are combined linearly using thevolume of shale.


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Dual Water Model

Practical DWM 2

Ct=

t

mSwt

n

aC

wf+

Swb

Swt

Cwb

Cwf

( )

The standard equation for the water saturationis expressed in terms of the conductivity, as it islinear.

This equation is in terms of measured quantities,porosity and resistivity and parameters that canbe found, the far and bound water conductivities.


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Dual Water Model

DWM Saturation solution

Swt =x + x2

+CtF0

Cw

x = Swb Cw Cwb( )2Cw

Fo = a m

The solution to the equation is

where

and


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Dual Water Model

Practical outputs

The equations give total water saturation Swtand total porosity t. These have to betransformed into effective saturation, Sw andeffective porosity, wf (or e)

Sw = Swt Swb

1 Swb

wf = t Swt Swb( )


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Dual Water Model

Dual water equation solution

This derivation of the Dual Water equations isvalid for any rock with any mixture of fluids

It is possible to use the Dual Water Model tomake a manual computation of a shaly zone.

However computer programs are bestequipped to handle the calculations.

The selection of key parameters is essential toobtain the correct answers,

Cwf - free water conductivity

Cwb - bound water conductivity

Swb - bound water saturation

t - total porosity


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Dual Water Model

Rwa-GR crossplot

10.00

3.16

1.00

.32

.10

.03

Hydrocarbon Sands

FREQUENCY PLOT

Shales

Water Sands

Gamma Ray API

1500 30 60 90 120

Rwb

Rw

R =wa

tm

aR

t

in clean zones R = Rwa w

in shale zones R = Rwa wb

Rwa


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Dual Water Model

Appendix

This appendix contains a brief introduction to thebehaviour of clays in the formation.

Full details are available in the relevant technicalpapers.


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Clays

Clays are usually present as sheet like particles

with very large surface areas compared to theirvolume

There is an excess negative charge inside thesheet due to atoms with 3 units of positivecharge (e.g. Al) being substituted by atoms

with 2 (e.g. Mg)The system is balanced by positive counterionson the surface of the clay sheets

This is measured by the Cation ExchangeCapacity - CEC

the units are milli-ion equivalent per 100gr ofdry clay material

It is different for each clay type

Montmorillonite - 1.00 meq/gr

Illite - 0.20 meq/gr

Kaolinite - 0.05 meq/gr


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Dual Water Model

Clay charge

When the clays are immersed in water (as in areservoir)

- the force keeping the counterions on the claysurface are reduced by the dielectric propertiesof the water

- the counterions leave the clay surface- they move in a layer of water close to thesurface

- they contribute to the electrical conductivityof the rock


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Dual Water Model

Diffuse layer

The sodium ions (Na+) from the salt water areat a high concentration close to the clay surface

This decreases until far away they reachequilibrium with the chlorine

The negative chlorine (Cl-) behaves in theopposite sense

The thickness of the layer where the positiveions are at a higher concentration is governedby the Gouy model and depends on the salinityof the water


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Dual Water Model

Exclusion Layer

The simple situation is complicated by the finitesize of the molecules involved.

There is a layer of water molecules adsorbed onthe clay surface and a shell around the sodiumion

This gives a minimum thickness of the layer atthe Outer Helmholtz Plane of xH

This distance at standard temperatures andpressures is 6.18 angstroms ()


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Dual Water Model

Diffuse layer thickness

The diffuse layer thickness, xd has its minimumof xH at a water resistivity, Rw of 0.245 ohm-m(at standard temperature and pressure)

Above this resistivity

xd = xHwhere depends on the resistivity (salinity),i.e.

= 1= , if Rw < 0.245 ohm-mxd

xH

dual water model

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