Sonic/Neutron 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 program solves the neutron (either sidewall or compensated) and compensated sonic log crossplot. It uses these equations: ``` Stt1*V1 + Stt2*V2 + Sttfluid*Porosity = SttLog Nma1*V1 + Nma2*V2 + Nmafluid*Porosity = NtnLog 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 neutron and density logs, with optional shale-correction based upon the gamma-ray curve, using Larionov's equations. 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. 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: you can and will get multiple valid compositions for many data points! For example: if the Schlumberger Comp. neutron porosity is 15% and the sonic travel time is 70 microsec/ft, you will get the following compositions: ``` Pass 1: 93.25% LS, -8.899% DOLO, 15.649% XPOR (gas/gyp, sec por) Pass 2: 75.58% LS, 9.036% SS, 15.384% XPOR Pass 3: 44.486% SS, 41% DOLO, 14.514% XPOR ``` Which run is accurate? They all are, pending more information. You can try correcting the input values for shale effect, or better yet, check other sources of information, like your zone's sample descriptions on a mud log, to pin things down. Also note that while the presence of gas tends to decrease the neutron porosity, it doesn't generally affect the sonic unless the zone is unconsolidated. This makes the sonic-neutron crossplot (and the sonic-density crossplot, for that matter) inferior to the neutron-density crossplot for identifying gas effects.