Electrical Petrophysics
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Transcript of Electrical Petrophysics
Lecture PresentationPGE368
Fall 2001 SemesterSeptember 24, 26, and 28,
and October 5
Electrical Properties of Porous Rocks
Carlos Torres-Verdín, Ph.D.Assistant Professor
Water Saturation• Definition:
– The fraction of the pore space containing waterSw = Vw / f
Porosity• Definition:
– The volume fraction of the rock occupied by pore space
φφφφ= Vp / VR * 100 %
THEORY REALITY
Composite Porous MediaSpatial Scale is Important!
Water-Wet Hydrocarbon-Bearing Rock Formation
Wilcox SandOklahoma City
1 cm
Close-Up
Clay
Water-Wet Hydrocarbon-Bearing Rock Formation
Thin Sections
1 cm
POROSITY
• TOTAL WATER SATURATION?
• BOUND-FREE (MOVABLE) WATER?
• IRREDUCIBLE WATER SATURATION (i.e. clay-bound water and capillary-bound water)?
WATER SATURATION
• TOTAL POROSITY?
• EFFECTIVE POROSITY?
FORMATION EVALUATION (PETROPHYSICS)• DIRECT: Core Analysis
• INDIRECT: Well Logging (In Situ)
• Electrical Resistivity• Spontaneous Potential• Acoustic Velocity• Radioactive Emissions• Nuclear Magnetic Resonance• Gravity• Etc.
EFFECTIVE MEDIUM THEORY
+ -
++++
----
V
R
DC ELECTRICAL RESISTIVITY EXPERIMENT(low frequency behavior)
I
R =VI
Electric Field Lines
DC ELECTRICAL RESISTIVITY EXPERIMENTA more realistic E-field line behavior
+ -
++++
----
V
R
I
R =VI
Electric Field Lines
DC ELECTRICAL RESISTIVITY EXPERIMENTApproximate Equivalent Circuit
R =VI
1R
1Rm
1Rf
= +
+ -V
RmI
Rf
Rock Matrix
Pore Fluid
ELECTRICAL RESISTIVITY OF ROCK CONSTITUENTS
ELECTRICAL CONDUCTIVITY AND RESISTIVITY
ELECTRICAL RESISTIVITY OF ROCK CONSTITUENTS
ELECTRICAL RESISTIVITY OF NaCl and KCl SOLUTIONSAT 200C
ELECTRICAL RESISTIVITY OF ROCKS:MAIN TENDENCIES
Shale-Free Electrical Model
•• Archie (1942)Laminated Shale Electrical Model
•• Poupon-Leveaux (Indonesian))
“Double-Layer” Dispersed Clay Electrical Models
•• Waxman-Smits
•• Dual-WaterMixed Dispersed-Clay / Laminar-Shale Electrical Model
•• Patchett-Herrick
Several Water Saturation Models
GUS ARCHIE (Circa 1942)
Testing Archie by Experiment
ELECTRICAL RESISTIVITY OF CLEANPOROUS ROCKS
Archie (1942)• In clean sandstones with saline brines, the resistivity
of the rock is proportional to the salinity of the saturating brine. The constant of proportionality is called the ‘formation factor’. F = R0 / Rw .
• The formation factor varies as the inverse square of the porosity. F = 1 / φ2 .
• The saturation index in a reservoir (IR = Rt / R0 ) varies as the inverse square of the saturation. I = 1 / Sw
2.
ARCHIE’S “Clean Sand” EquationEffective DC Resistivity Response
Use of Archie formulae (late ‘40s)
F = R0 / Rw F = 1 / φφφφ m
IR = Rt / R0 = 1 / Swn and permeability too
LOG-LOG PLOT: F vs. Porosity
FORMATION FACTOR vs. POROSITY
Formation Factor – Porosity Relationships
RESISTIVITY: Influence of Water Saturation
LOG-LOG PLOT: Resistivity Index (I) vs. Water Saturation
Mean Value of Saturation Exponent
Archie may be written in terms of electrical conductivities
• Standard form
• In conductivity notation
σ t = 1
FσwSw
n = 1a
σwφmSw
n
Archie 1
Archie 1
Archie 2
Summary Archie 1• Archie valid at high
salinities > 100ppk at 200°F
• Archie also valid if there are no conductive materials (clays).
• In very fresh water surface conductance of ordinary grains can also be a problem
Archie 1 OK in Clean Sands
• General formwhere a ~ 1 and m ~2
• m is called the formation factor exponent
• sandstones a = .81, m=2or ‘Humble’ formula
• carbonates a = 1, m > 2
F = a
φm
Archie’s First Law• Ideally the Formation Factor is purely a function
of pore space geometry. It is giving us informationabout porosity and the porosity distribution.
• In practice ionic conduction is dependent onion-type, concentration and temperature.
• In shaly rocks we do not measure the FormationFactor and are dependent on a rock modeleg. SEN (1986)
Archie 1 fails in shaly sands
Archie 2 also fails when there is clay
Archie 2 not so good in carbonates
m in carbonates, vugs and fractures
0 . 5 0 . 8 1 2 6 8 1 0 2 0 3 0 4 0 5 0
φ, p o r o s i t y
3 . 0
2 . 5
2 . 0
1 . 5
1 . 0
φi s o = 0 . 51 . 0
1 . 5
2 . 55 . 0
7 . 51 0 . 0
1 2 . 5
2 . 0
vugs
fractures
Formation Factor in Carbonates
General form of Archie 1
• Formation Factor generally, the ‘m’ exponent are often a function of porosity.
• Variable ‘m’ technique has been successful in carbonates.
Carbonate Texture
On the left, a crystalline dolomite with φφφφ = 47% and m = 1.95. On the right, a moldic bioclastic packstone with φ φ φ φ = 36% and m = 3.27. This large variation in m illustrates the importance of rock texture on petrophysical evaluation. Environmental scanning electron microscope images, scale bar is 100 mm at left and 200 mm at right.
DC ELECTRICAL RESISTIVITY EXPERIMENTLow Frequency Behavior of Heterogeneous Media
+ -
++++
----
V
R
I R =VI
?
•Spatial Scale of Measurement Becomes a Central Issue•Effect of Clay Component•Effect of Clay-Bound Water•Effect of Capillary-Bound Water•Anisotropy
ELECTRICAL PROPERTIES OF SHALY SANDS
MatrixMatrix DryDryClayClay
Clay-Clay-BoundBoundWaterWater
MobileMobileWaterWater
CapillaryCapillaryBoundBoundWaterWater
HydrocarbonHydrocarbon
Oil
Water
Water-Wet Hydrocarbon-Bearing Rock Formation
Water Adsorption by Clays[Cation-Exchange-Capacity (CEC) Mechanism]
Water
Oil
MatrixMatrixMatrix DryDryClayClay
Clay-Clay-BoundBoundWaterWater
MobileMobileWaterWater
CapillaryCapillaryBoundBound
Water/OilWater/OilHydrocarbonHydrocarbon
Oil-Wet Hydrocarbon-Bearing Rock Formation
Saturation Exponent: Water-Wet vs. Oil Wet
Matrix DryClay Clay-
BoundWater
MobileWaterCapillary-
BoundWater
SolidHC
Heavy Oil
The Case of Heavy Oil
Matrix and Fluid Distributions
MatrixMatrix DryDryClayClay
ClayClay--BoundBoundWaterWater
MobileMobileWaterWater
CapillaryCapillaryBoundBoundWaterWater
HydrocarbonHydrocarbon VugsVugs
Water-Wet Hydrocarbon-Bearing Carbonates
Matrix and Fluid Distributions
The Effect of Wettability and Surface Texture on the ‘n’ Exponent
Data from Diederix (1982)Data from Sweeney and Jennings (1960)
Archie 2 Summary
• In water-wet rocks estimations of water saturation from resistivity logs are generally pessimistic
We need to account for the conductivity of clay
I (f)
AC ELECTRICAL RESISTIVITY EXPERIMENTFrequency Behavior of Heterogeneous Media
++++
----
V(f)
Z(f)
Z(f) =V(f)I(f)
?
•Spatial Scale of Measurement Becomes a Central Issue•Effect of Clay Component, Clay-Bound Water•Capillary Effect•Anisotropy
Time-Varying Voltage Source
Electrical Impedance (Ohmic conductivity + dielectric permittivity)
LABORATORY SAMPLESBrine-Water Saturation
Coarse Grains andDispersed Clay
CoarseGrains
StackedGrains
Super-FineSand Grains
Fine Grains
Photograph courtesy of Prof. Jon Olson
WHEN DOES THEORY BREAK DOWN?
Example of Microfracturing
ACKNOWLEDGEMENTSBaker Atlas
SchlumbergerTony Bermudez