Numerical Study on Anisotropic Permeability Inversion From Dipole Seismoelectric Logging in Fluid-Saturated Porous Formations

In situ determination of permeability anisotropy is important for unconventional reservoir productivity, such as in the evaluation of hydraulic fracturing effectiveness. We investigate a method of permeability-anisotropy inversion using dipole seismoelectric logging. A 3-D numerical algorithm combining finite-difference and -element methods in cylindrical coordinates is proposed to simulate dipole seismoelectric logging in fluidsaturated porous formations with transversely isotropic (TI) permeability. Calculation results reveal that the flexural-waveinduced electric field (Ef wave) exhibits high sensitivity to permeability variations, and its amplitude and phase delay increase significantly as the porosity and permeability decrease. Wave attenuation from the θ0 = 0° dipole source effectively inverts horizontal permeability (κH). Crucially, wave attenuation from the θ0 = 90° source reliably inverts vertical permeability (κV) unless the borehole is nearly parallel to the symmetry axis. Using the radial electric field component of the Ef wave provides a significantly higher inversion accuracy for both κH and κV, especially in low-porosity and -permeability formations, compared with those using the flexural wave. As the difference between the horizontal and vertical permeabilities increases, the relative inversion errors increase significantly. The greater the difference between κH and κV, the larger could be their inversion errors. Furthermore, a new relationship is identified where the amplitude ratio Ez(θ0)/Ez(90°) approximates either κrr(90°)/κrr(θ0) (when κH > κV) or κrr(κ0)/κrr(90κ) (when κH < κV). Accordingly, an equation for estimating the anisotropic permeability orientation is derived, achieving relative errors of less than 12%. Even at high noise levels, it can maintain good robustness. We conclusively demonstrate the significant advantages of dipole seismoelectric logging for accurately inverting anisotropic formation permeability.