Estimating Hydraulic Permeability in Dual Porosity – Dual Permeability Media Using Joint Inversion of Electrical Resistivity and Acoustic Data: Effective Medium Theory, Surface Electrical Conductivity and Sensitivity Analysis (Part I)

This study establishes a link between electrical and acoustic properties using effective medium theory to estimate permeability in porous-fractured media. The proposed method, applicable across diverse geological formations, employs the T-matrix approach to model elastic moduli, electrical conductivity, and hydraulic conductivity within a dual – porosity dual – permeability framework. The model incorporates micro- and macro-scale structural parameters—including void alignment, concentration, and aspect ratio—while accounting for electrochemical fluid-mineral interactions that influence surface conductivity. A novel tortuosity metric is introduced, defined as the ratio of the longest electrical flow path along a void’s surface to its axial length in the flow direction. Results show tortuosity decreases along elongating axes but increases perpendicularly. The surface area-to-volume ratio declines with increasing α₁ and α₂ axes but rises with α₃, particularly in micro-voids where α₁ expansion sharply reduces the ratio if α₃ is large. Macro-voids follow similar trends, with α₃ playing a dominant role. Surface conductivity depends on the interplay between tortuosity and surface area-to-volume ratio, leading to non-universal electrical conductivity trends. Permeability is highly sensitive to α₃: in micro-voids, it drops rapidly as α₃ shortens, while macro-voids show increased principal permeabilities (κ₁, κ₂) with decreasing α₃ and rising κ₃ with α₃ elongation. Although the model assumes elastic isotropy, void geometry variations induce electrical and hydraulic anisotropy. Acoustic velocities are minimized when α₁ is small and α₂ large (or vice versa), with extreme α₃ values shifting velocity minima to maximal α₁ and α₂. These insights advance predictive capabilities for heterogeneous reservoirs by integrating multi-physical property relationships.