Modeling of triaxial induction logging responses in multilayered anisotropic formations

Abstract

Triaxial induction logging tools have been widely applied to formation characterization due to their sensitivity to electric anisotropy. To model triaxial induction logs in multilayered general anisotropic formations, where the anisotropy can be arbitrary, an analytical method is applied to compute the tool responses. For the analytical method, Maxwell’s equations in the spectral domain are written into a compact first-order differential equation. The equation is solved to obtain the spectral-domain fields, which are transformed to the spatial domain through the inverse Fourier transform. The singular issue for the tool located in highly deviated wells is handled by subtracting the singular term in the spectral domain. The singularity treatment makes the integrands in the inverse Fourier transform decay faster, thus making the infinite integration computation faster. Formations with isotropic, transversely isotropic, biaxially anisotropic, and general anisotropic conductivity are modeled and compared to investigate the effects of anisotropy on the tool responses. For a tool in a general anisotropic formation, all of the [Formula: see text] components are nonzero. For a tool in a vertical well in transversely isotropic and biaxially anisotropic formations, only the diagonal components of [Formula: see text] are nonzero. For a tool located in a deviated well, the effects of tool deviation and electric anisotropy are coupled. The diagonal components are more sensitive to the electric anisotropy than the off-diagonal components, and the off-diagonal ones can clearly indicate bed boundaries.