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