Pe/Density 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 on Density/Pe Crossplot:

The Pe (photoelectric index) curve is a measure of a formation's effective adsorption cross-section for atomic particles. 'Pe' is well-tied 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 low-energy gamma-rays. 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.