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 Sonic/Density Crossplot:
This program solves the density and compensated sonic log
crossplot. It uses these equations:
Stt1*V1 + Stt2*V2 + Sttfluid*Porosity = SttLog
Rho1*V1 + Rho2*V2 + Rhofluid*Porosity = RhoLog
1*V1 + 1*V2 + 1*Porosity = 1
where:
V1=volume fraction of end member #1
V2=volume fraction of end member #2
The program evaluates inputs for the sonic and density logs,
with optional shalecorrection based upon the gammaray curve,
using Larionov's equations.
For shale correction: I prefer using the gammaray for Vshale
because the neutron and density logs don't respond to the same
kinds of shale in the same way. The gammaray responds to high
cation exchange capacity (CEC) shales, which are the main ones
of interest.
The program assumes metric units are in use if the fluid travel
time is over 600. It solves the simultaneous equations and
returns three successive answer sets. Each set is labeled for
feasibility, giving possible reasons if the results seem
unlikely.
KEEP IN MIND: this crossplot is less helpful than the others
because the limestone, sandstone, and dolomite curves are
squeezed very close together on a plot of sonic versus density
data. They are close enough to be affected by normal data
scatter, so points can have dramatically different porosities
and compositions. A point with a bulk density of 2.45 and a
travel time of 70 gives:
Pass 1: 73.13% LS, 10.668% DOLO,16.203% XPOR
Pass 2: 54.459% LS, 31.44% SS, 14.101% XPOR
Pass 3: 123.143% SS, 31.115% DOLO, 7.972% XPOR
(gas/lt min, sec por)
which is an 8% spread for crossplotted porosity! Faced with
this kind of uncertainty, I'd look for a better logging suite
in an offset well. Note that while the presence of gas causes
the density to decrease, it usually doesn't affect the sonic
unless the formation is uncompacted. This makes a sonicdensity
crossplot (and a sonicneutron crossplot, for that matter)
inferior to a neutrondensity crossplot for identifying gas
effects.
As always, check other sources of information, like your zone's
sample descriptions on a mud log, to narrow lithology choices.
