Multi-Frequency Interpretation of Electric Resistivity and Dielectric Permittivity Measurements for Simultaneous Assessment of Porosity, Water Saturation, and Wettability

ABSTRACT

Broadband electric resistivity and dielectric permittivity measurements are affected by combined effects of rock fabric, composition, fluid saturation and distribution, and interfacial polarization mechanisms. An integrated multi-frequency interpretation of electrical measurements can provide information about the dominant polarization mechanisms, which are linked to grain size, solid-fluid interfacial properties, porosity, fluid saturations, and wettability. In this work, we propose to narrow down the knowledge gap in interpretation of broadband dielectric measurements in water-, oil-, and mixed-wet formations by introducing a new interpretation workflow for simultaneous assessment of porosity, fluid saturations, and wettability. The objectives of this paper include (a) to introduce a new rock physics model for broadband characterization of dielectric measurements incorporating the combined effects of grain size, porosity, water saturation, wettability, and interfacial polarization, and (b) to develop a new interpretation workflow based on an inversion algorithm capable of simultaneously estimating porosity, water saturation, and wettability of the formation uniquely from multi-frequency electrical resistivity and dielectric permittivity measurements.

We introduce a rock-physics model for broadband characterization of permittivity measurements by integrating a mechanistic model of electrolyte-solid interfacial polarization, on water- and oil-wet grains, with bulk properties of fluids and grains. Then, we develop a new interpretation workflow for estimating porosity, fluid saturations, and wettability of the formation. These properties are obtained by minimizing an objective function using a combination of downhill gradient-descent and evolutionary methods.

We successfully applied the introduced interpretation workflow to multi-frequency electrical resistivity/permittivity measurements performed on different rock samples at different wettability conditions and different levels of water saturation. The experimental measurements of complex resistivity/permittivity, performed in the frequency interval from 100 Hz to 10 MHz, were in agreement with values obtained from the proposed analytical workflow. Finally, wettability, saturation, and porosity of the samples were simultaneously estimated by applying the new interpretation workflow. It should also be noted that all the parameters required by the introduced workflow are associated with physical mechanisms at microscopic-and pore-scale domains or realistic and quantitative pore geometry features of the rock. A unique contribution of the new workflow is that it honors rock fabric and minimizes the need for extensive calibration efforts.