This paper narrows down the knowledge gap in interpretation of electrical resistivity measurements in oil-wet and mixed-wet formations by analytically deriving a new resistivity model that can reliably estimate hydrocarbon reserves at different levels of wettability. The objectives of this paper include (a) to quantify the influence of wettability on electrical resistivity measurement, (b) to develop a new analytical resistivity model that takes into account the impacts of wettability on electrical resistivity, and (c) to improve the assessment of hydrocarbon saturation by introducing a wettability-dependent parameter into a new resistivity method. The new resistivity model not only incorporates wettability of the rock, but also a directionally conducting fractional pore network to honor rock fabric.
The aforementioned features are quantitatively evaluated from the three-dimensional (3D) pore-scale images, taken from each rock type in the formation. We apply a semianalytical streamline numerical model to estimate pore-network connectivity in the 3D binary images. The resistivity and the calculated geometry-related parameters are used as inputs to the new model in order to estimate water saturation. To test the performance of the introduced method at different levels of wettability and water saturation, we synthetically saturate the porescale images with water and oil at different wettability configurations and water saturation, honoring the physics of intermolecular interactions between different fluid and solid components.
The results obtained from the new method are compared against the actual saturation. We successfully applied the introduced method to carbonate rock samples with wettability ranging from strongly oil-wet to strongly water-wet. The electrical resistivity results obtained from numerical simulations were in agreement with the resistivity estimates from the new method. The results also showed that wettability has a significant influence on electrical resistivity of the rocks at water saturation levels below 50%. Moreover, we demonstrated that the proposed model provides reliable results when applied to field data. The outcomes of this paper are promising for well-log-based applications of the new method in complex mixed-wet formations.