Resistivity of partially saturated carbonate rocks with microporosity

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Abstract
Simple Archie's relations relate average conductivity to average porosity and average saturation, and seem to work when the fluctuations of local porosity and local saturation are small. In general, carbonates are extremely inhomogeneous and Archie's relations fail—the saturation exponent n can depend on saturation itself, and n can be anomalously large or small. The resistivity of rocks with a mixture of micropores, macropores, and vugs is computed using effective medium theories. Quantitative mathematical modeling is used to study the influence of textural details. Geometries that lead to an anomalously high value of saturation exponent are contrasted with those with an anomalously low value of saturation exponent. The resistivity becomes anomalously large when the conducting water phase is trapped in isolated regions. The resistivity becomes insensitive to the volume fraction of water if the configuration of the major current‐carrying paths changes little with saturation. Simple examples with differences in wettability are considered.

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