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 = R 0 / R w . • The formation factor varies as the inverse square of the porosity. F = 1 / φ 2 . • The saturation index in a reservoir (I R = R t / R 0 ) varies as the inverse square of the saturation. I = 1 / S w 2 .
ARCHIE’S “Clean Sand” Equation Effective DC Resistivity Response
Use of Archie formulae (late ‘40s)
F = R 0 / R w F = 1 / φ φ
m
I R = R t / R 0 = 1 / S w n
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
1
1 m n σ t = σ w Sw = σ w φ Sw F a 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 form where a ~ 1 and m ~2
•
m is
called the formation factor exponent • sandstones a = .81, m=2 or ‘Humble’ formula •
carbonates a = 1, m > 2 F=
a m
φ
Archie’s First Law • Ideally the Formation Factor is purely a function of pore space geometry. It is giving us information about porosity and the porosity distribution. • In practice ionic conduction is dependent on ion-type, concentration and temperature. • In shaly rocks we do not measure the Formation Factor and are dependent on a rock model eg. 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 3
.
2
0
.
5 1 1 φi
2
.
0
1
.
5
1
.
0
0
.
s
=
o
.
0
0
.
2
2 .
.
5
. 0
5
5
.
7
0
1 5
.
1 .
0
2 0
.
5
vugs
5
fractures
5 0
.1 8
2
6 φ,
p
8 o
1 r
0 o
s
i
2
0
t
y
3
04
50
0
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 φ φ = 47% and m = 1.95. On the right, a moldic bioclastic packstone with 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 EXPERIMENT Low Frequency Behavior of Heterogeneous Media •Spatial Scale of Measurement Becomes a Central Issue •Effect of Clay Component •Effect of Clay-Bound Water •Effect of Capillary-Bound Water •Anisotropy
V + I
+ + + +
? R
-
V R= I
ELECTRICAL PROPERTIES OF SHALY SANDS
Water-Wet Hydrocarbon-Bearing Rock Formation Water
Oil
Matrix
Dry Clay
ClayBound Water
Capillary Bound Water
Mobile Water
Hydrocarbon
Water Adsorption by Clays [Cation-Exchange-Capacity (CEC) Mechanism]
Oil-Wet Hydrocarbon-Bearing Rock Formation Oil
Water
Matrix
Dry Clay
ClayCapillary Bound Bound Water Water/Oil
Mobile Water
Hydrocarbon
Saturation Exponent: Water-Wet vs. Oil Wet
The Case of Heavy Oil
Matrix and Fluid Distributions
Matrix
Dry Clay
Heavy Oil ClayBound Water
CapillaryBound Water
Mobile Water
Solid HC
Water-Wet Hydrocarbon-Bearing Carbonates
Matrix and Fluid Distributions
Matrix
Dry Clay
ClayClayBound Water
Capillary Bound Water
Mobile Water
Hydrocarbon
Vugs
The Effect of Wettability and Surface Texture on the ‘n’ Exponent Data from Sweeney and Jennings (1960)
Data from Diederix (1982)
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
AC ELECTRICAL RESISTIVITY EXPERIMENT Frequency Behavior of Heterogeneous Media •Spatial Scale of Measurement Becomes a Central Issue •Effect of Clay Component, Clay-Bound Water •Capillary Effect •Anisotropy
