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 on Density/Pe Crossplot:
The Pe (photoelectric index) curve is a measure of a
formation's effective adsorption crosssection for atomic
particles. 'Pe' is welltied to lithology: quartz, dolomite,
and calcite are distinctly separated:
Quartz: Pe=1.806
Calcite: Pe=5.084
Dolomite: Pe=3.142
However, Pe has some drawbacks. Here are three:
1) The Pe value for Dolomite can become confused with
other things that also hover around a Pe value of 3.0:
average shale: Pe=3.42
"dirty" sandstone: Pe=2.7
Gypsum: Pe=3.42
2) Anydrite can slip in for Calcite:
Calcite: Pe=5.084
Anhydrite: Pe=5.055
3) Pe is enormously sensitive to elements with a high
atomic number, like barium. This is unfortunate, because barite
(Pe=266.8) is a common drilling mud additive, and barite is
very good at absorbing lowenergy gammarays. A rugose borehole
and lots of barite in the mud will render the Pe curve useless.
The ideal setting for a Pe curve is a smooth borehole with no
mudcake or invasion.
Because Pe is proportional to the photoelectric
cross section per electron, you can't just plug Pe matrix
values into a set of volumetric fraction equations to arrive at
rock composition. Pe values mix according to electron density,
or mass fraction, instead of volume fractions. For this reason
the program multiples Pe times density, to turn the reading
into something that combines volumetrically. So the program
solves this set of equations:
Rho1*V1 + Rho2*V2 + Rhofluid*Porosity = RhoBulk
Pe1*Rho1*V1 + Pe2*Rho2*V2 + Pef*Rhofl*Porosity = PeLog*RhoB
1*V1 + 1*V2 + 1*Porosity = 1
and returns three possible rock compositions with
crossplotted porosities, each flagged with an [ok] or
[invalid]. Potential salt or anhydrite zones are also noted.
