Effect of Sonde Eccentricity on Responses of Conventional Induction-Logging Tools

This paper develops the mathematical analysis for calculating the responses of a typical induction-logging tool in usual conductive drillings muds, when it is positioned at a certain standoff distance from the nearest side of the borehole wall. A complete investigation, including skin effect, reveals that the contribution of the skin effect is adequately compensated for by boosting the induction-log signal by the amount of skin effect that would be expected if the sonde were surrounded by a homogeneous medium. Thus a geometrical-factor-type theory is sufficiently general to account for the effect of eccentricity of the sonde position in the borehole. The theoretical equations developed are applied to a focused induction-logging tool with a medium depth of investigation (ILm) and a focused induction-logging tool with deep investigation (ILd). The results are found to be in fair agreement with experimental results. Some disparity in the two sets of results can be attributed to the effect of the finite size of the mandrel, which is not taken into account in the theoretical development.