Simulating complex conductivity in carbonate rocks: using digital carbonate rocks and comparison to laboratory measurements

Digital rock physics involves the modern microscopic imaging of geomaterials, digitalization of the microstructure, and numerical simulation of physical properties of rocks. This physics-based approach can give important insight into understanding properties of reservoir rocks, and help reveal the link between intrinsic rock properties and macroscopic geophysical responses. Our focus is the simulation of the complex conductivity of carbonate reservoir rocks using reconstructed 3D rock structures from high-resolution X-ray micro computed tomography (micro-CT). Carbonate core samples with varying lithofacies and pore structures from the Cambro-Ordovician Arbuckle Group and the Upper Pennsylvanian Lansing-Kansas City Group in Kansas were used in this study. The wide variations in pore geometry and connectivity of these samples were imaged using micro-CT. A two-phase segmentation method was used to reconstruct a digital rock of solid particles and pores. We then calculated the effective electrical conductivity of the digital rock volume using a pore-scale numerical approach. The complex conductivity of geomaterials is influenced by the electrical properties and geometry of each phase, i.e., the solid and fluid phases. In addition, the electrical double layer that forms between the solid and fluid phases can also affect the effective conductivity of the material. In the numerical modeling, the influence of the electrical double layer is quantified by a complex surface conductance and converted to an apparent volumetric complex conductivity of either solid particles or pore fluid. The effective complex conductivity resulting from numerical simulations were compared to results from laboratory experiments on equivalent rock samples. In general, simulated σ'eff values were below laboratory measurements, while numerical σ''eff values were within reasonable range. The imaging and digital segmentation technique, fundamental rock characteristics, and model assumptions all play an important role in the simulation process