An Effective-Medium Saturation Model for Carbonate Rock

With the development of the Symmetrical Anisotropic Theory On Resistivity Interpretation (SATORI) in the late nineties, a generic class of saturation models became available for the determination of hydrocarbon saturations from resistivity logs using Effective Medium theory. From the generic "SATORI source theory", tailor-made models can be distilled for specific rock types. Such models are particularly suitable to describe the resistivity behavior of rock with multiple conductivity mechanisms. Examples are SATORI models for shaly sands and dual porosity sandstones that were successfully applied in a number of complex formations. The present paper describes the challenging attempt to develop a SATORI model for carbonate reservoirs. Given the enormous diversity in carbonates, the first such model was tailored to a specific Middle East field with a large spread in formation properties. In the developed model, the rock is characterized by a non-conductive matrix with three types of porosity: microscopic matrix porosity, mesoscopic matrix porosity, and macroscopic porosity (or vugs). These three volume fractions can in principle be derived from Nuclear Magnetic Resonance (NMR) logs run in boreholes, with verification through laboratory NMR and Scanning Electron Microscopy (SEM) measurements. After a brief outline of the SATORI concept, we describe the carbonate model for our field and demonstrate that it performs well against a (limited) set of Special Core Analysis measurements. A single set of parameters sufficed to describe the large variation in resistivity behavior observed between the samples, implying that the variation in resistivity behavior is largely determined by the different porosity type volume fractions. For the samples tested, the porosity type volume fractions derived from laboratory NMR and SEM measurements are in good agreement supporting the potential for an NMR + SATORI based field approach.