CONNECTIVITY THEORY – A NEW APPROACH TO MODELING'NON-ARCHIE' ROCKS

摘要

So called Archie rocks are characterized by a resistivityindex versus water saturation that plots as a straight lineon a log-log scale, the slope of the line being equal to -nwhere n is the saturation exponent. All rocks forwhich the resistivity index presents a curvature qualifyas non-Archie rocks. Negative curvatures are observedfor rocks that tend to remain more conductive at lowsaturations compared to Archie equation. That is thecase for example of shaly sands and of some micriticcarbonates. Positive curvatures are typical of stronglyoil-wet rocks such as some carbonates. This paperpresents a model in which a small term is introduced inArchie equation to correct for water connectivityeffects. This water connectivity correction term takespositive values for positive curvatures, and negativevalues for negative curvatures. It is equal to zero forArchie rocks. The introduction of this term helps tostabilize the single exponent in the model called theconductivity exponent – equivalent to the case n=m inArchie equation. For example for rocks made stronglyoil-wet in laboratory experiments – for which Archie’ssaturation exponent n can exceed 10 – normalconductivity exponent values around 2 can be used inthe model with the introduction of a small positivewater connectivity correction term.Effective medium theory is used with a modified CRIMmixing law to model the water connectivity correctionindex as a function of conductive structures and fluidparameters in the rock. The model is shown to matchthe predictions of Waxman-Smits and Dual-Watermodels for shaly sands (negative curvature) as well asexperimental data obtained on strongly oil-wet rocks(positive curvature). For example we show that thewater connectivity correction index is a linear functionof the volume fraction of oil-wet zones in the rock.This prediction is confirmed from wettabilitymeasurements on carbonate cores. The connectivitytheory provides a simple explanation for why somerocks follow Archie’s equation and why some don’t. Itleads to a simple equation that has – like Archieequation - only two parameters and it reverts back tothe Archie equation when the water connectivitycorrection index is equal to 0.