Modifying the generalized effective-medium theory of induced polarization model in compacted rocks

Abstract

The generalized effective-medium theory of the induced polarization model (GEMTIP) is a mathematical-physical model derived from the Maxwell equations based on the effective-medium approach. Compared to the Cole-Cole model, the GEMTIP parameters are better related to the structural parameters of reservoir rocks, such as rock composition, mineral particle size, porosity, and specific surface; therefore, it can better describe the induced polarization (IP) characteristics of tight oil and gas reservoirs. However, GEMTIP is not suitable for high-resistivity perturbed media, and it does not account for interfacial polarization, which occurs between two media that share the same resistivity. Starting from the theoretical assumptions of the GEMTIP model, we derived an extended GEMTIP model (MGEMTIP) by adding an equivalent surface current term into the Maxwell equations for a heterogeneous medium. The complex resistivity parameters predicted by two models are compared through numerical simulation, and the results demonstrate that MGEMTIP can more accurately predict the DC resistivity and the chargeability of heterogeneous media. MGEMTIP is suitable for characterizing the polarization phenomena of rock with high salinity, low porosity, low hydraulic permeability, and a disseminated perturbed medium. Furthermore, the testing of rock samples for the inversion of IP parameters with MGEMTIP revealed that the predicted chargeability is higher than the inverted chargeability from the experimental data. This difference is strongly correlated with rock hydraulic permeability. MGEMTIP provides a petrophysical basis for the forward modeling and inversion of IP parameters of compacted rocks. The quantitative relationships between model IP parameters and reservoir parameters also provide a theoretical foundation for predicting reservoir permeability using electromagnetic methods.