Evaluation of Relative Permeability From Resistivity Data for Fractal Porous Media

The characteristics of multiphase ow in porous media are of great significance to various applications, such as reservoir evaluation and engineering geology. The analogy between fluid flow and electric ow provides a new idea for studying multiphase ow properties from geophysical resistivity data. However, a theoretical relationship between relative permeability and resistivity index, which is the key to the successful joint interpretation of multiphase ow and rock electric characteristics in porous media, is poorly understood. Based on fractal theory, a relative permeability-resistivity index model is developed to accurately describe the link between the rock electric and multiphase ow characteristics. The relative permeability is found not only to be related to fluid saturation and resistivity index, but also to be affected by structural parameters, such as the tortuosity fractal dimension, pore fractal dimension, water-phase fractal dimension, and tortuosity ratio. The proposed model reveals the significant effect of structural parameters on the resistivity index and relative permeability, on the other hand, the study provides an effective method to calculate the relative permeability from the resistivity data. By applying the relative permeability-resistivity index model to real cases, it shows that the predicted relative permeability results calculated by our model are in good agreement with experimental data.