Pore combination modeling (PCM) is a technique to model the influence of pore geometry on resistivity and permeability. PCM is consistent with Archie's equation, including the saturation dependence (Myers, 1989, 1991). It is an extension allowing the effect of multiple pore systems to be modeled including their saturation dependence. Myers (1991) developed quantitative relationships between thin section point counts and Archie's parameters for different pore systems (vuggy, intergranular, and microporosity) associated with a global carbonate dataset.
The commonly used interpretation methods (CRIM, CTA, TPO) for dielectric-constant measurements usually fail in carbonate reservoirs. The dispersion in clean carbonates is attributed to the Maxwell-Wagner effect. This has two immediate implications: that the dispersion scales with the measured brine conductivity, and that it is proportional to the volume fraction of the materials present. Myers (1996) developed a mixing law which proposed that the interfacial polarization term and the high-frequency limit are additive, i.e. assuming that there are no interaction terms. In the model, the first two terms are the Maxwell-Wagner terms quantifying contributions due to the multiple pore systems (intergranular and vugs) and saturation. The last addition is the high frequency limit term, which is described by the Hanai-Bruggeman equation.
Combining the PCM, brine dielectric constant model, and carbonate dielectric-constant model, we propose an integrated technique to jointly model resistivity and dielectric-constant measurements for dual-porosity carbonates. The technique has been applied on synthetic carbonate well logs. Then, we developed a stochastic global optimization algorithm (Very Fast Simulated Annealing, VFSA) to invert the multi-frequency dielectric array as well as resistivity well logs. The outcomes of joint inversion are the water-filled vuggy and intergranular porosity, salinity, lithology exponents of each pore structure, and matrix dielectric constant. Water saturation is a natural byproduct of the algorithm assuming total porosity is known using density and/or neutron logs. We include the temperature, salinity, and frequency dependence of dielectric constant of the saturating brine.
Future work will include inverting multi-frequency dielectric constant, micro-, medium-, and deep-resistivity logs. This will include the geometric factor of each tool, assuming a piston-like invasion profile representing the salinity of the invaded zone and the salinity of connate water.