The "m" cementation exponent is the adimensional power
parameter for porosity in the Archie water saturation equation, the Simandoux equation,
the Indonesia equation,
and others. The higher the m, the higher SW water saturation.
This parameter m depends upon the pore space structure connectivity, the matrix
consolidation, and the grains shape (more than the size). Historically, m
has been called cementation exponent, but the term
porosity exponent is also used.
When the tortuosity factor "a" is fixed to 1.0, a default value of
m=2 is usually used (also with n=2), but this is more representative
for carbonates. For clastic sandstones, the m value ranges from around 1.3 for
completely unconsolidated sands, to 2.2 for very well consolidated or cemented
sandstones. Typical values for water wet consolidated sandstones range 1.5-1.9.
The lower the m value, less free movable water saturation is calculated for the rock.
The Archie equation involves four variables: SW, φ,
Rw (formation water resistivity), and
Rt (true -deep non invaded- formation resistivity),
and three parameters:
a, m, and n (the saturation exponent).
That means that in the well logging practice, some assumptions must be made or
the system would be undetermined.
—However, if representative water samples with
are available, electro-chemical computations of salinity and Rw are usually more reliable and preferred—
Since the Archie equation works well for
non shaly rocks, the easiest way to estimate some unknowns is to work in
clean zones (Vsh=0) embedded in SW=100% water,
and collect (φ, Rt) log data to solve the unknowns.
In some reservoirs, the irreducible
water saturation SWirr can be reasonably well known
(for example, around 15%) to work with clean rocks in fully oil impregnated zones.
The most used methods to estimate parameters from the Archie equation,
are the Hingle, the Pickett Plot, and the
apparent cementation exponent methods:
Hingle method assumes that
a, m, and n, are known, and solves Rw
from the log porosity φ and the formation resistivity Rt in
a clean, water bearing zone.
The method produces the best, most stable and precise estimate of Rw
from log data.
This is the mathematical analog of averaging the apparent water formation
resistivity Rwa values in a clean, water bearing zone:
The apparent water saturation curve yields the correct value of Rw in clean, water bearing
zones, but yields an overestimated value in hydrocarbon bearing zones.
Better than a direct examination of high deep resistivity Rt values,
Rwa provides a correction for porosity, so it is a very effective
and popular screening technique to detect
Pickett Plot method assumes that a, and n, are known,
and simultaneously solves Rw and m
in a clean, water bearing zone from the log porosity φ
and the formation resistivity Rt. However, it requires
enough heterogeneous porosity rocks. This condition usually fails in many reservoirs
with homogeneous rocks in the water bearing zone. Use it judiciously with caution.
To overcome the problem of dealing with clean rocks, we recommend to use a
modified Pickett Plot
equation specifically designed to work with
shaly rocks (Vsh > 0). This easily increases the rock's sample size,
avoiding the problem of an almost nil variance on porosity that produces
a unstable, underestimated value of m.
Apparent cementation exponent method assumes that
a, and n, are known. But also that Rw
is known from other source different than Hingle or Rwa to avoid
any mathematical circularity. Typically, Rw is estimated
form ion chemical water analysis lab samples. Then, solving the Archie equation
for m, and setting SW=1 for a clean, water bearing zone, yields:
The apparent cementation exponent curve yields the correct value of m
in clean, water bearing zones, but yields an incorrect value in hydrocarbon
The equation also proves that Rw < Rt for rocks with
non conductive matrix. Otherwise the equation could yield a negative
estimate for m.
From the hands-on logging practice point of view, an anomalous case where
Rt < Rw usually indicates either the presence of conductive
minerals, a variable Rw zone not considered in the petrophysical
interpretation, unreliable values for Rw, Rt, or a bad
deep resistivity tool signal.
If the rock matrix is conductive (has metals
or semi-conductor minerals like pyrite FeS2) the
Archie equation and some of the formation evaluation theory dealing with
water saturation equations is not applicable and corrections must be applied
to deal with a conductive matrix (like the excess of conductivity for shaly
The Indonesia equation can be rewritten to provide an explicit correction
for shale content:
Don't hesitate to prefer to use this equation to estimate m in moderately shaly sands (say VSH < 25%)
instead of the traditional Pickett plot technique. It usually works well and provides the correct theoretical
framework to estimate m for shaly rocks. Notice that if Vsh=0 the equation reduces algebraically
to the former Archie m apparent equation.
Is there an easy way to determine the water saturation exponent
n from well logs? Not really. The basic problem is that a log independent
knowledge of SW would be required, and core lab water saturation data
is not often reliable or accurate. A default value of n=1.9 to n=2.1 is usually
an useful approximation implicitly used in many well logging equations and theory.
The figure below shows the GeolOil panel to estimate the Rwa apparent water resistivity curve in a shaly sand
Resistivity fails to detect water oil contact, but apparent water resistivity does, confirmed by production