Triaxial Induction Logging: Theory, Modeling, Inversion and Interpretation

Abstract
Thinly laminated sand-shale formations represent a difficult challenge for petrophysical evaluation. The conductive shale laminations have a profound effect on the traditional induction log, causing it to read the shale laminations significantly lower than the high-resistivity sand layers. This misreading leads to pessimistic computations of water saturation and estimations of reserve. The newly developed triaxial induction logging tool provides much more information than the conventional induction logging measurement. It is not only sensitive to the effective horizontal resistivity, which is dominated by the conductive shale layers, but it is also sensitive to the effective
vertical resistivity, which is determined by the conductive shale and the resistive sand, at any dip angle.

A key challenge of developing the triaxial induction array is the large borehole effect on coplanar couplings when the tool is eccentered in the transverse direction in water-base mud boreholes. To reduce the borehole effect to a manageable level, a new design with multiple electrodes has been implemented. Tank experiments and numerical modeling results show the borehole effect is reduced dramatically by using this design.

A parametric inversion algorithm to simultaneously determine the horizontal resistivity, vertical resistivity, formation dip, and azimuthal angle and bed boundary position from the triaxial induction logging data will be presented. The inversion problem is solved by employing a weighted, constrained, and regularized Gauss-Newton minimization scheme. To archive the practical application of the inversion
algorithm, a fast Jacobian matrix computation is implemented to improve the efficiency. Furthermore, a multiplicative regularization technique is used to automatically determine the regularization coefficient. Synthetic examples will be presented to indicate the robustness of the algorithm.

A quantitative interpretation method of water saturation in laminated shale-sand formation will be presented. Shale anisotropy is taken into account for building the interpretation model. Two field examples demonstrate the laminated shales and analysis improves the estimate of hydrocarbons in place.

Introduction
Formation electrical anisotropy has been recognized for many years.1 It is critical to measure the formation electrical property for accurate formation evaluation. In a laminated shale-sand sequence, the horizontal resistivity that is parallel to the formation bedding plane is much smaller than the vertical resistivity that is perpendicular to the formation bedding, when the sand formation is hydrocarbon-bearing. Since the standard induction logging only measures the horizontal resistivity in vertical wells, the interpretation based on that data will either miss the pay-zone or overestimate the water saturation. To address the problem, the recently developed triaxial induction tool provides both horizontal resistivity and vertical resistivity. It also produces deep, robust formation dip and azimuth angle and accurate formation bed boundary position information2,3 .

Theoretical study of triaxial induction logging was performed by Moran and Gianzero4 in 1979. They concluded that, in principle, by using a coplanar system with a magnetic moment parallel to the formation bedding plane, the vertical conductivity can be measured. But, because of the large borehole effect, it was impractical to build such system. A multielectrode tool design was built to reduce the borehole effect to a manageable level5.

In this paper, we will cover the theory, modeling, inversion, and interpretation of triaxial induction logging. In the theory part, we will present the sensitivity of triaxial induction measurement to formation dip, azimuth, horizontal conductivity, vertical conductivity, and bed boundary position in transverse isotropic formations and layered formations. Current distribution will also be presented in this section to
explain the solution to develop the practical triaxial induction tool. In the modeling section, we will compare the numerical simulation and measurement when the tool is located in a test facility, an experimental water tank. In the inversion part, we will describe the processing technique of triaxial induction logging data. In the interpretation part, we will present the petrophysics model to calculate the water saturation in laminated shale-sand sequence. Finally, two field examples will be discussed to show the impact of triaxial induction
logging tool on formation evaluation.