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

摘要

So called Archie rocks are characterized by a resistivity index versus water saturation that plots as a straight line on a log-log scale, the slope of the line being equal to -n where n is the saturation exponent. All rocks for which the resistivity index presents a curvature qualify as non-Archie rocks. Negative curvatures are observed for rocks that tend to remain more conductive at low saturations compared to Archie equation. That is the case for example of shaly sands and of some micritic carbonates. Positive curvatures are typical of strongly oil-wet rocks such as some carbonates. This paper presents a model in which a small term is introduced in Archie equation to correct for water connectivity effects. This water connectivity correction term takes positive values for positive curvatures, and negative values for negative curvatures. It is equal to zero for Archie rocks. The introduction of this term helps to stabilize the single exponent in the model called the conductivity exponent – equivalent to the case n=m in Archie equation. For example for rocks made strongly oil-wet in laboratory experiments – for which Archie’s saturation exponent n can exceed 10 – normal conductivity exponent values around 2 can be used in the model with the introduction of a small positive water connectivity correction term. Effective medium theory is used with a modified CRIM mixing law to model the water connectivity correction index as a function of conductive structures and fluid parameters in the rock. The model is shown to match the predictions of Waxman-Smits and Dual-Water models for shaly sands (negative curvature) as well as experimental data obtained on strongly oil-wet rocks (positive curvature). For example we show that the water connectivity correction index is a linear function of the volume fraction of oil-wet zones in the rock. This prediction is confirmed from wettability measurements on carbonate cores. The connectivity theory provides a simple explanation for why some rocks follow Archie’s equation and why some don’t. It leads to a simple equation that has – like Archie equation - only two parameters and it reverts back to the Archie equation when the water connectivity correction index is equal to 0.