07_Sw in Shaly Formation

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(05/96)

Contents

G1.0 WATER SATURATION IN SHALY SANDS ...................................................................................1G1.1 INTRODUCTION.....................................................................................................................1G1.2 THE DUAL WATER MODEL...................................................................................................1G1.3 DUAL WATER MODEL FORMULAE:......................................................................................6G1.4 PROCEDURE FOR USING THE DUAL WATER MODEL.........................................................7G1.5 DWQL Pass One ...................................................................................................................8

Input....................................................................................................................................8Output.................................................................................................................................8

G1.6 DWQL Pass Two..................................................................................................................10Input..................................................................................................................................10Output...............................................................................................................................10

G1.7 CYBERLOOK QUALITY CHECKS ........................................................................................16

G2.0 WORK SESSION.......................................................................................................................17

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Introduction to Open Hole Logging

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G1.0 Water Saturation in Shaly Sands

G1.1 INTRODUCTIONSince the introduction of CSU wellsite sur-

face instrumentation to well logging, the dual-water model has been applied as a means ofquick, effective interpretation of basic logs.This technique has been extended to theMAXIS 500 wellsite surface instrumentationand more recently to IBM-compatible PCsthrough QLA Quick Log Analysis program(version 2).

This section discusses the dual-water modelas it applies to Cyberlook wellsite openholeevaluation and QLA version 2.

G1.2 THE DUAL-WATER MODELIn 1972, the dual-water model was the sub-

ject of an SPE paper "The Theoretical and Ex-perimental Basis for the Dual Water Model forthe Interpretation of Shaly Sands" by Clavier,Coates and Dumanoir. Although this sectiondiscusses the important basic ideas about themodel, reference should be made to this paperif a more detailed explanation is necessary.

The dual-water model is an improvement overthe Waxman-Smits model presented in 1967and better fits their experimental data. TheWaxman-Smits model proposed that a shalyformation behaved like a clean formation ofthe same porosity, tortuosity and fluid contentexcept that the water appears to be more con-ductive than expected from its bulk salinity.The excess conductivity is due to additionalcations held loosely captive in a diffuse layersurrounding the clay particles to compensatefor the deficiency of electrical charges in the

clay crystal. This model did not take into ac-count the exclusion of salt from part of thepore volume near the shaly surface. Ion distri-bution near a clay surface should be as shownin Figure G1.

In other words, the layer of water bound tothe shale surface contains more positive (Na+)ions than negative (Cl–) ions. This fact is nec-essary to balance the negative internal chargedistribution of the shale particles. The thick-ness of the diffuse layer of positive (Na+) ionsX

d is related to the salinity of formation water,

being smaller for more saline waters. Hence,conduction of current flow through this boundwater is mainly by positive ion transport.

Figure G1: Schematic of Diffuse LayerIonic Concentration

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Introduction to Openhole Logging

Actually, the positive (Na+) ions are keptsome distance from the clay surface by the hy-dration water around each cation and the waterabsorbed on the clay surface (see Figure G2).

As a consequence, the diffuse layer thicknesscannot be less than X

d. However, X

d = X

h when

the connate water is saline enough. In otherwords, when the formation water has deficientsalinity, the resistivity of the bound water isrelatively constant.

For sodium clays, the distance Xh is about

6Å and the Na+ ions will be stacked in theHelmoltz plane whenever the resistivity of thebrine in the pores is less than 0.425 at 75 oF[24oC].

This thin sheet of salt-free water (the claywater) is important because clays have tre-mendous surface area, as much as 91071ha/m3 compared to 1.5 to 3.0 ha/m3 for a typi-cal sand, and the volume of clay water is farfrom negligible in comparison with the totalpore volume.

We can now make certain definitions in rela-tion to bound water, free water, the volumesthey occupy and their saturations.

a. Bound Water: This is the water adheredto shales as described. In addition to thebound layer, shales may contain watertrapped within the structure and not ex-pelled by the rock compaction. This waterdoes not have the same ion distribution asthe surface bound water and so it has adifferent conductivity. In the event that theresistivity of bound water defined here asR

WB is derived from 100% shale zones,

the value of RWB

is affected by this trappedwater.

Hence, when RWB

is used as the resistivityof bound water for the shale contained innearby reservoirs it could be incorrect. Inpractice, this is not found to be too muchof a problem, and generally R

WB derived

from shales may be used in adjacent beds.

b. Free Water: All water that is not bound isfree water. Although free water, normallyassociated with the pore space, is not nec-essarily producible. It contains the fractionof water that is irreducible.

c. Total porosity φT: Total porosity is the

fraction of unit volume of formation oc-cupied by fluids, that is, bound water,free water and hydrocarbons.

Figure G2: Schematic View of Outer Helmoltz Plane

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d. Effective porosity φe: It is the fraction

of unit volume of formation occupiedby free water and hydrocarbons. It canbe derived from the total porosity byremoving the bound water per unitvolume of formation.

e. Total-Water Saturation SWT

: It is de-fined as the fraction of total porosityoccupied by bound and free water.

f. Bound-Water Saturation SWB

: It is de-fined as the fraction of total porosityoccupied by bound water.

g. Free-Water Saturation SWF

: It is de-fined as the fraction of total porosityoccupied by free water.

h. Effective Water Saturation SWE

: It isdefined as the fraction of effective po-rosity occupied by free water. It can bederived from the total-water saturation.

The relationship between these terms isshown diagrammatically in Figure G3. Be-cause we have separated the surface-layer wa-ter from shales we are left with a dry colloidfraction. As a formation becomes increasinglyshaly the colloid plus bound water fraction in-creases until we have a 100% shale formationconsisting of a certain fraction of bound waterand the remainder of dry colloids. Under thedefinition of total porosity φ

T, a pure shale

therefore has porosity filled with bound water(S

WB = 1, S

WF = 0). The effective porosity, φ

e,

as defined is, of course, zero. The evolution ofa formation with increasing shaliness is shownin Figure G4.

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Water Saturation Graphical Definitions

Figure G3

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Evolution of φT with Shaliness

Figure G4

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G1.3 DUAL WATER MODELFORMULAS

The main objective of the dual-water ap-proach whether it’s through Dual-Water QuickLog (DWQL), QLA software, or otherwise, isto reconstruct the wet formation resistivity R

0.

Consider a wet shaly formation where:

C0 = wet true conductivity

CWB

= bound-water conductivity

(Shale)C

WF = free-water conductivity

(connate water)φ

F= volume of free water

φB = volume of bound water

φT = total porosity.

Given these, then φT

= φB

+ φF

and hence

φW B

SWB

=

φT

Because φB represents the volume of bound

water, which thus represents the proportion ofshale out of the total volume. Therefore, S

WB is

in effect the volume of shale in the formationunder investigation.

By definition:

φWF

+ φW B

1) SWT

=

φT

φW B

2) SWB

=

φT

3) φT =

φ

WF + φ

WB + φ

H

(If hydrocarbon is present).

From the Archie relationships:

F = 1/φT

2 and F = Ro/R

w

(Note: For simplicity of derivation, a = 1 and m = 2, although they couldbe other specific values.)

Rw = φ

T2 R

0

which givesC

0 = φ

T2 C

W

where:C

W is the conductivity of the bound- and

free-water mixture.

Considering volumes, we have

φTC

W = φ

WBC

WB + φ

FC

WF

φBC

WB φ

FC

W F

CW = +

φT

φT

= SWB

CWB

+ (1 – SWB

)CWF

∴ C0 = φ

T2[S

WBC

WB + (1 – S

WB) C

WF]

or, in resistivity terms

RWF

RWB

R0 =

φT

2[SWB

RWF

+ (1 – SWB

)RWB

]

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Displayed graphically, our results are as fol-lows (Figure G5):

Figure G5

Water Saturation and Effective Porosity:

SWT

= R /R0 t

φe = φ

Τ (1 – S

WB)

vbwe

= φe S

w

G1.4 PROCEDURE FOR USINGDUAL-WATER MODEL

a) To evaluate a shaly formation using the dualwater model, four parameters must be de-termined:

1. RWF

: from the SP, Rwa

technique, waterresistivity catalog or known value.

2. RWB

: generally calculated from the shalesurrounding the zone using the R

WA

technique.

RWB

= φTSH

2 × RtSH

φNSH

+ φDSH

1 φ

T = and F =

2 φT

2

3. φT: total φ

from average of φ

N and φ

D

after correction for gas effect, if neces-sary.

4. SWB

: related to VSH

and for our purposescan be equated to V

SH.

Therefore SWB

= VSH

.

To this point, we have calculated Rw and V

SH

for our example and have determined a gascorrected φ

T. All that is now required is to

calculate RWB

. This can be done with thesame φ

NSH and φ

D SH values determined in

our previous section, along with a value forR

SH at the same point(s) on the log.

Utilizing all of this data, a value for wet re-sistivity, R

0, can be determined from

1 1R

0 = ×

φT

2 1 - VSH

+ VSH

RWF

RWB

using

R0

SWT

2 = R

t

where Rt = R

ILD corrected for

environmental effects as requi

To arrive at effective water saturation Swe

one more step is required:

SWT

– SWB

SWE

= where VSH

= SWB

1 – SWB

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We have now taken a shaly sand, corrected thelog data for the effects of shale on both resis-tivity and porosity, as well as gas effect on po-rosity, and determined the effective S

w and

hence SHYC

.

BVWeff

= Swe

× φe

b) In using software, the dual-water model isusually presented in two passes. The firstpass is used to perform simple correctionsto certain measurements and act as an aid topicking parameters for the second pass.Pass two performs the main output calcula-tions.

G1.5 DWQL PASS ONE

Input1. mud weight2. desired output matrix3. recorded CNT matrix4. bit size5. optional SP baseline drift correction6. logs—CNL/Litho-Density tool and

deep resistivity (RIDPH

, RLLD

, or RT from

tornado chart if necessary).

Output (see Figures G6 and G9)1. SP—optionally baseline drift corrected2. GR—borehole corrected if caliper

available3. apparent grain density

ρB

– φTA

ρGRA

= 1

– φ

TA

4. apparent fluid resistivityR

FA = R

T × φ

TA2

5. φN and φ

D in desired matrix

6. apparent total porosityφ

TA = F(φ

N, φ

D)

φNLS

– φDLS

φTA

= 2

7. RT for correlation

8. MP1, MP2, and MP3 - Mineral pro-portions from the three-mineral Litho-Density model.

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Figure G6

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G1.6 DWQL PASS TWO

Input1) All inputs used for pass one.2) Clean and shale parameters for GR

and/or SP and/or optionally φN

RHOB, MP3. GR – GR

CL

MSIGR

= GR

SH – GR

CL

SP – SPCL

MSISP

= SP

SH – SP

CL

3) Free- and bound-water resistivities.- R

WF = R

FA in a clean, wet for-

mation.- R

WB = R

FA in a good shale

formation.4) Maximum total porosity φ

MAX.

φMAX

= highest φTA

in good hole.a. eliminates computation in bad

hole.b. determines S

WB – MSI rela-

tionship.5) Expected clean grain density – ρ

GEX

If ρGA

< ρGEX

a minor correction ismade to total porosity based on either:

a. grain density orb. hydrocarbon volume and gas

density.

Output (see Figures G7 and G10)1) Shale index – minimum of indicators

chosen.2) Grain density.3) R

0 – reconstructed 100%-wet forma-

tion resistivity.4) Water saturation.5) Differential caliper – caliper-bit size.6) Effective porosity φ

e.

φT is φ

TA corrected for light hydrocar-

bon effect, φT

≥ φTA

.7) Water volume V

BWF.

8) Flags- Producibility – shading

between R0 and R

T

9) MP1, MP2, and MP3 as for pass one.

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Figure G7

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Figure G8

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Figure G9: Cyberlook Pass 1 for the Basic Log Set used in Sections B, C and D

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Figure G10: Cyberlook Pass 2 for the Basic Log Set used in Sections B, C and D

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Figure G11: Computational parameters for the Cyberlook using the Basic Log Set found in Sections B, C and D

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G.1.7 CYBERLOOK QUALITYCHECKS

1. R0 and R

T should overlay in clean, wet

zones (if not Rwf

is incorrect).

2. R0 and R

T should overlay in shale

zones (if not, RWB

is incorrect).

3. Sw should approach 100% in wet

zones.

4. φe must be comparable with log po-

rosity considering shale, matrix andgas effects.

5. Differential caliper must compare tolog.

6. VSH must appoach 0% in clean zonesand 100% in shales.

7. Grain density must conform to localknowledge in clean zones and ap-proach 3000 kg/m3 in shales.

8. Are shows on pass 1 also shows onpass 2?

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G2.0 Work Session

1. Calculate SWE on the shaly sand example (Figures F10 – F13).

Hint: Use the R0 equation developed in this section.

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07_Sw in Shaly Formation