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Electrical Properties

Archies Law

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Rt

Ro

Rw

Cube of water

having resistivity,

Rw

Non-shaly rock, 100% saturatedwith water having resistivity,

Rw

Rock containing pores saturated

with water and hydrocarbons

= 100%Sw = 100%

= 20%

Sw = 100%

= 20%

Sw

= 20%

Formation Factor

Equation

SaturationEquation

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The formation factor (F) depends on

Porosity of the formation,

Pore geometry - tortuosity

Lithology of the formation

Degree of cementation, and

Type and amount of clay in the rock

Formation Factor

From J. Jensen, PETE 321 Lecture Notes

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Archies equation for formation factor is a

power law model:

F=R0/Rw=a-m

Formation Factor Equation

Rock type 1

Rock type 2

1000

100

10

1.01 .1 1.0

F

Note: Sw=1 From NExT, 1999

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Formation Factor - Example Core Data

From J. Jensen, PETE 321Lecture Notes

a 1.0

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F=a-ma = constant 1.0 for most formations

m = cementation factor 2 for most formations

Other commonly used values

Sandstones:

F = 0.8/2 (Tixier)

0.62/2.15 (Humble)

Carbonates

F = 0.8/2

Formation Factor

From J. Jensen, PETE 321 Lecture Notes

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Power LawModel

IR=Rt/R0=Sw-n

Each curve for aspecific core

sampleNo conductive

materials (clay)present

Saturation Equation

Rock type 1

Rock type 2

1000

100

10

1.01 .1 1.0

Sw

IR=

Rt

R0

From NExT, 1999

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Laboratory Determination of

Saturation Exponent, n

From J. Jensen, PETE 321 Lecture Notes

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R0 Appears in Both Equations

n

wo

t

m

w

o

S

1

R

R

a

R

R

when Sw = 100%

when = constant

From NExT, 1999

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Archies Equation (Combined)

n

t

mw

w

R

Ra

S

Water

saturation,

fraction

wS

Resistivity of

formation water,-mw

R

True formation

resistivity, -mt

R

Porosity,fraction

Empirical constant

(usually near unity)

a

Saturation

exponent

(also usually

near 2)

n Cementationexponent

(usually near 2)

m

From NExT, 1999

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IDEALIZED

LOG SET = 0.30

= 0.35

= 0.07

R = 0.4

R = 0.3

R = 4

R = 8

Sand

Shale

From J. Jensen, PETE 321 Lecture Notes

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Effect of Filtrate Invasion -

Rnear_well Rt (permeability present)

Modified from J. Jensen, PETE 321 Lecture Notes

Wellbore

Mud

(Rm)

Mud Cake

(Rmc)

Uninvaded

Zone

(Rt)Invaded

Zone (Rxo)

Uninvaded

Zone

(Rt)

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GRC0 150

SPCMV-160 40ACAL

6 16

ILDC0.2 200

SNC0.2 200MLLCF

0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15DTus/f150 50

001) BONANZA 1

10700

10800

10900

EXAMPLE LOG WITH RESISTIVITY

Deep

Resistivity

Log (ILDC), Rt

SNC

0.2 200

MLLCF

0.2 200

ILDC

0.2 200

From NExT, 1999

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Laboratory Resistance

From J. Jensen, PETE 321 Lecture Notes

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Laboratory Resistivity

Resistivity

mL

mAohmsI

V

metersohmR

2*)(

From J. Jensen, PETE 321 Lecture Notes