Sonic/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 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 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: 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 sonic-density crossplot (and a sonic-neutron crossplot, for that matter) inferior to a neutron-density 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.