Page 67 - The Geological Interpretation of Well Logs

- RESISTIVITY AND CONDUCTIVITY LOGS -

The basic equations of petrophysics Flushed zone saturation = the square root of the flushed
Below, the fundamental equations of petrophysics appear zone resistivity in a 100% water zone divided by the
in a specific order, followed by explanation and comment ftushed zone resistivity with possible residual hydrocar-
on their computation. In fact, these equations have bons. Residual hydrocarbon saturation, S, = 1 - $ |. The
applications beyond resistivity measurement, but their equation gives the saturation in unmoved or residual
use is not discussed here. Such information is found in hydrocarbons of the invaded zone. This is the same
logging company handbooks and specialist publications Archie Equation as above, but here uses the resistivity
(see references). ratio in the flushed zone. Comparison of S| and S., in a
hydrocarbon zone is considered to give movable hydro-
R= ER (1) carbons. S| — S, is equal to the fraction of movable
° Ww
hydrocarbons in the fonnation, The percentage volume in
Overall rock resistivity = the formation resistivity factor terms of the reservoir is given by multiplying the term by
X resistivity of the formation fluid (see ‘Rock resistivity’, the porosity, ic. % volume of reservoir with movable
p.44). Rock resistivity consists of two elements, the pas- hydrocarbons = (S,, - S,) (where ¢ = porosity).
sive but constricting formation and the conductive
formation fluids. As Wyllie said in 1956 (Wyllie, 1963), Formation resistivity factor-porosity relationships
This is perhaps the most important single relationship in
electric log interpretation and must be committed to a
memory. Pow (5)

where F = formation resistivity factor
i Nt
ou (2) tb = porosity
m = so-called cementation factor, dependent on
The resistivity index = the resistivity of a rock containing rock type, and more closely related to texture than
hydrocarbons divided by the resistivity of a rock with to cementation (Figure 6.5), and
100% water. The equation introduces the notion of the @=aconstant.
ratio (in one particular reservoir) of the resistivity when
The equation indicates that the formation resistivity factor
entirely water-saturated, as opposed to the resistivity in
is a function of porosity and rock type (mm). Archie discov-
ihe presence of hydrocarbons.
ered this relationship between F and porosity (see Figure
The Archie Equation 6.5) and equation (5) is the result. Subsequent research
and empirical] correlations show that the global relation-
a _ FR,
gta ship varies; average figures used for the relationship are:
w
R (3)
F= = in most sandstones (5a)

where $= water saturation;
n= Saturation exponent, usually 2.
F-R, = R, when the formation is 100% water-saturated
_ 0.62
Fe ee (best average for sandstones) (5b)
(see equation 1). Thus, equation (3) is usually written
— this is the Humble Formula
(3a)
Fe= ¥ compact formations, chalks (Se)
The water saturation (squared) = the rock resistivity with
100% water saturation divided by the rock resistivity with
possible hydrocarbons. The equation is more commonly
written Fe ¥ where m= variable (usually 1.8 to 3) (Sa)

The most frequently-used formula is (56) which is
(38,¢) applicable to sandstones. In Jimestones, the F-porosity
relationships are quite variable.
This equation, due to G.E. Archie of Shell, makes use of
Practical average Archie Equation
the ratio of resistivities from equation (2).
Invaded zone resistivities — movable hydrocarbons S = 0.62x R,
w PexRk
(6)
_ R(100% mud filtrate)

© ¥ R,, (with residual hydrocarbons) (4) This is the genera] equation for finding the water saturation,
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