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