Summary

Advances in multicomponent induction logging data acquisition and processing make possible the characterization of biaxially anisotropic formations. However, understanding of induction response in a biaxially anisotropic formation lags behind. In this paper, analytic formulas are proposed that allow us to quickly model multicomponent induction responses in a biaxially anisotropic formation. The formula is accurate for the coaxial component and the ones for the coplanar components are reasonably accurate over the entire range of relative dip angles. The theory suggests that for a tool tilted in the xoz plane, the XX- and YY-responses are affected primarily by Rx and Rz and have little dependence on Ry, the resistivity normal to the tool deviation plane. An immediate observation made from the theory is that in a vertical and near vertical well, a full tensor measurement may not be sufficient to resolve a biaxially anisotropic formation. Measurements at higher frequencies must be made to resolve the ambiguity.

Introduction

In their classic paper, Moran and Gianzero (1979) provided an analytic formula for predicting induction logging response in an anisotropic formation. The formula aids in the understanding of tool response as a function of relative dip in a transversely isotropic (TI) formation. However, the formula is limited to a coaxial-coil array. Zhadnov et al. (2001) extended Moran and Gianzero’s work to coplanar arrays. Much insight has been derived from those formulas. The formulas by Moran and Gianzero (1979) and Zhdanov et al. (2001) apply only to a TI formation that has different resistivities parallel and normal to the bedding plane. No analytic formulas are available to describe induction responses in a biaxially anisotropic function. A biaxially anisotropic formation has three distinct resistivity values. Such a medium can form when a thinly layered rock is fractured in a direction normal to the bedding plane. Depending on the resistivity of materials filling the fractures, the bulk horizontal resistivity will demonstrate azimuthal variation. The horizontal resistivities parallel to and normal to the fracture planes will be different. Both are different from the vertical resistivity. Understanding of multicomponent induction responses (Krieghäuser et al., 2000) in such a medium helps interpret logging measurements for the distinct resistivity values. The multicomponent induction measurement technique (Krieghäuser et al., 2000) was developed to characterize thinly-bedded reservoir rocks whose individual bed thicknesses are beyond the resolution capability of conventional resistivity logs. Significant progress has been made in applying the new technique to characterize anisotropic formations. One important application now is definition of formation dip and azimuth (Rabinovich et al., 2005). This application proves to be particularly valuable in wells drilled with oil based muds where borehole resistivity imaging logs are not always acquired or where poor borehole conditions prevent collection of quality borehole imaging logs. With the advances in instrumentation and data processing, interpretation of multicomponent induction data for biaxial anisotropy now becomes a reality. However, the theory for a biaxially anisotropic formation lags behind. We have attempted to provide basic functions to predict multicomponent induction responses in a biaxially anisotropic formation.

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