Pe/Neutron/Density/Sonic Crossplot

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.