electrical properties archie’s law. rtrt roro rwrw resistivity cube of water having resistivity, r...

Electrical Properties

Archie’s Law

Rt

Ro

Rw

Resistivity

Cube of waterhaving resistivity,

Rw

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

Rw

Rock containing pores saturatedwith water and hydrocarbons

= 100%Sw = 100%

= 20%Sw = 100%

= 20%Sw = 20%

Formation Factor Equation

Saturation Equation

• 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

• Archie’s 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=1From NExT, 1999

Formation Factor - Example Core Data

From J. Jensen, PETE 321 Lecture Notes

a 1.0

• F=a·-m

a = constant 1.0 for most formationsm = 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

• Power Law Model

IR=Rt/R0=Sw-n

– Each curve for a specific core sample

– No conductive materials (clay) present

Saturation Equation

Rock type 1

Rock type 2

1000

100

10

1.01 .1 1.0

Sw

I R =

Rt

R0

From NExT, 1999

Laboratory Determination of Saturation Exponent, n

100

10

10.1 1.0

Sw (fraction)

Rt /

Ro

n = Slope

From J. Jensen, PETE 321 Lecture Notes

R0 Appears in Both Equations

nwo

t

mw

o

S

1RR

aRR

when Sw = 100%

when = constant

From NExT, 1999

Archie’s Equation (Combined)

n

t

mw

w

R

RaS

Water saturation, fraction

wSResistivity of formation water, -mwR

True formation resistivity, -m

tRPorosity, fraction

Empirical constant (usually near unity)

a

Saturation exponent (also usually near 2)

n Cementation exponent (usually near 2)

m

From NExT, 1999

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

Effect of Filtrate Invasion -Rnear_well Rt (permeability present)

Modified from J. Jensen, PETE 321 Lecture Notes

Wellbore

Mud(Rm)

Mud Cake(Rmc)

Transition

Zone

Uninvaded Zone(Rt)Invaded

Zone (Rxo)

Uninvaded Zone(Rt)

GRC0 150

SPCMV-160 40ACAL

6 16

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/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

Laboratory Resistance

From J. Jensen, PETE 321 Lecture Notes

Laboratory Resistivity

• Resistivity

mLmAohms

IV

metersohmR

2*)(

From J. Jensen, PETE 321 Lecture Notes