Pseudo-random renormalization group forward and inverse modeling of the electrical properties of some carbonate rocks

• Electrical properties of carbonate rocks were investigated experimentally in the frequency domain (100 Hz to 100 kHz).
• Asymmetric mixture laws cannot describe electrical behaviour of heterogeneous rocks in that frequency range.
• A theoretical Pseudo random renormalization group (PRNG) method was developed to model electrical behaviour of rock mixtures.
• With appropriately chosen coatings of phases, PRNG method can reasonably model the electrical properties of rock mixtures.

Electrical properties of carbonate rocks from North Sinai, Egypt, were investigated experimentally in the frequency domain (100 Hz to 100 kHz). Changes between electrical properties were attributed to changes in mineral composition and texture of samples. Asymmetric mixture laws cannot describe electrical behavior of heterogeneous rocks in the mentioned frequency range. A theoretical pseudo-random renormalization group (PRNG) method was developed to model electrical behavior of rock mixtures. The main goal of this paper is to make forward and inverse modeling using PRNG method for the electrical properties as a function of frequency for carbonate rocks with texture.In PRNG method four phases were used to take into account the texture in the samples. Four phases are the best that we could use in the model. We are trying to increase the competence of the model in the near future. In these four phases mainly conducting constituents (silt and clay) and mainly insulating constituents (sand, air and carbonate) may coat each other. With appropriately chosen coatings for the four phases, the PRNG method can reasonably model the electrical properties of the samples in the measured frequency range. Thus, an inverse problem is used to find the detailed structure of the four phases, which leads to the measured electrical properties of the samples, taking into account the measured concentrations of the different constituents of the samples. The inverse problem is based on minimizing the misfit between the measured frequency response for the conductivity and the dielectric constant and those obtained theoretically from the PRNG method. It was shown that the texture plays an important role in determining the A.C. electrical properties of heterogeneous samples.