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Electrical Properties
Archie’s Law
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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
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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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• 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
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Formation Factor - Example Core Data
From J. Jensen, PETE 321 Lecture Notes
a 1.0
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• 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
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• 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
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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
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R0 Appears in Both Equations
nwo
t
mw
o
S
1RR
aRR
when Sw = 100%
when = constant
From NExT, 1999
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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
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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)
Transition
Zone
Uninvaded Zone(Rt)Invaded
Zone (Rxo)
Uninvaded Zone(Rt)
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GRC0 150
SPCMV-160 40ACAL
6 16
ILDC0.2 200
SNC0.2 200
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
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Laboratory Resistance
From J. Jensen, PETE 321 Lecture Notes
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Laboratory Resistivity
• Resistivity
mLmAohms
IV
metersohmR
2*)(
From J. Jensen, PETE 321 Lecture Notes