Towards a Petrophysically Consistent Implementation of Archie’s Equation for Heterogeneous Carbonate Rocks

Abstract

Archie’s empirical resistivity-saturation relation of 1942 is widely applied in the petroleum industry. Despite its shortcomings, Archie’s equation is the basis for inferring water saturation, even in carbonates with complex pore structure, albeit with empirical tuning of cementation and saturation exponents. Industry literature is replete with examples of why this approach leads to erroneous estimates of the water saturation, and methods have been proposed where the range of saturation present in the reservoir has been subdivided into segments, each having a different set of exponents. Here, based on a homogenization methodology, we propose an effective resistivity model of an inter- and intragranular vuggy carbonate, when the pore sizes in the subsystems are well separated. The model is applied both for water-wet and mixed-wet rocks with appropriate modifications. Methodologies for apportioning pore fractions and their sizes depend on the openhole logs and/or core data. Computed results show significant deviations from Archie correlations in microporous or vuggy intervals. Results are verified on several Middle East carbonate formations against core and evidence from nuclear logs.