Modeling of triaxial induction logging responses in multilayered anisotropic formations

Triaxial induction logging tools have been widely applied to formation characterization due to its 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 the H components are nonzero. For a tool in a vertical well in transversely isotropic and biaxially anisotropic formations, only the diagonal components of H 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.

Quantitative method for determining the solution error of the inverse problem in the electrometry of oil and gas wells

Determining the quantitative degree of connection between logging error and the corresponding error of oil and gas wells electrometry inverse problem solving is considered. A quantitative method to determine the magnitude of the error of solving the inverse problem depending on the magnitude of the logging error for a given model of a single layer or section as a whole is described. Examples of determining the error of the inverse problem for real well materials, taking into account the actual measurement error, are given. A method for determining the characteristics of the spatial resolution of electrometry methods is described. Examples of its use for low-frequency induction logging equipment are given. The proposed methods allow to determine the areas of equivalent solutions and the areas of existence of stable / unstable solutions of the inverse electrometry problem.