General comments on Porosity Crossplots
This crossplot solves a subset of equations listed below:
Density: D1*V1 + D2*V2 + D3*V3 + D4*V4 + Dfluid*Por = DBulk
Neutron: N1*V1 + N2*V2 + N3*V3 + N4*V4 + Nfluid*Por = NLog
Sonic: S1*V1 + S2*V2 + S3*V3 + S4*V4 + Sfluid*Por = SLog
Pe: P1*D1*V1+ P2*D2*V2 +P3*D3*V3 +P4*D4*V4 +Pf*Df*Por = PLog*D
Volumes: 1*V1 + 1*V2 + 1*V3 + 1*V4 + 1*Por = 1
where:
V1,V2,V3,V4 = end members Por=volume frac void space
D=bulk density Dbulk=log's density reading
N=neutron apparent matrix effect NLog=log's neutron reading
S=sonic travel time SLog=log's sonic reading
P=Photoelectric index fluid=log's fluid response
The program assumes that the response of a log is the sum of
the individual responses of the rock constituents times their
respective volume fractions. (The photoelectric index curve,
Pe, is multiplied by density to make it conform to volumetric
mixing rules.) The acceptable porosity range=-1% to 41%, and
the acceptable end member range =-1% to 101% (with +- 1% for
statistical error). Each calculated composition is evaluated
and flagged as [ok] or labeled with possible effects ([gas],
[shale], etc.).
Comments specific to this crossplot:
This four-mineral crossplot, and the other three-mineral
crossplots, give you many possible choices. Many potential end
members have values that land on top of each another. You
probably won't get much information from a crossplot that uses
Kaolinite (den=2.41), Illite (den=2.52), and quartz (den=2.65)
for end members. The values are just too close together. While
the Pe curve may peg dolomite at 3.142, that is uncomfortably
close to Illite at 3.45, and gypsum at 3.42, and also to many
shales and shaley sands. Calcite may have a Pe of 5.08, but
anhydrite comes in at a Pe of 5.05, and so on.
Let this be a warning to you.
Crossplotted compositions and porosities are guides, not
ironclad conclusions. If you have lab data from core or well
cuttings that rule out certain minerals, then you can use this
program with a bit more confidence. It will often be the case
that no combination of end members gives a valid composition.
Even after resorting to shale correction, you still may not be
able to generate a rock composition that the program flags as
"[ok]." The program is juggling quite a few parameters for you,
and, ultimately, you have to face the fact that
default mineral values are no more than
averages, and may not apply in your case.
Watch what happens to the computed porosities as you modify the
rock composition from run to run. You may develop a feel for
how much the porosity can be expected to vary, should certain
minerals crop up, and you should notice that some minerals will
have a far more pronounced effect upon porosity than others.
For shale correction: I prefer using the gamma-ray for Vshale
because the neutron and density logs don't respond to the same
kinds of shale in the same way. The gamma-ray responds to high
cation exchange capacity (CEC) shales, which are the main ones
of interest.
Sample run:
Using a Schlumberger Compensated neutron log run on a limestone
matrix, I chose a point that read 15% porosity. The density log
showed a bulk density of 2.45 for the same interval, a
Pe reading of 4, and a sonic travel time of 70. Entering these values into the program gives:
%Quartz=18.38
%Calcite=60.174
%Dolomite=5.908
%Gypsum=0.539
%XPorosity=14.999
Comments: [ok]
If you are worrying about rock compositions to this level of
detail, I'd suggest sending a bag of cuttings to your local
x-ray diffraction lab... As always, check other sources of
information, like your zone's sample descriptions on a mud log,
to narrow the lithology choices.
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