Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo‐analytic formulas

Abstract

Downhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo‐analytic solution for eccentric coaxial and tilted‐coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging‐while‐drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well‐established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging‐while‐drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.

Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications

“…On the other hand, the pseudo-analytical method is efficient to deal with the tool response in cylindrical multilayered formation. Some study has been performed for generally tilted and/or co-axial coil antennas in eccentric respect to the borehole [27]- [31]. Loss of cylinder symmetry, their expressions involve all order harmonics of EM field that couple each other and are usually very complex.…”