Summary
An existing theory describes how electrical anisotropy in the formationaffects the response of resistivity logging tools. We have related this theory to the processing of logging while drilling (LWD) induction logs and are thus able to calculate the anisotropic resistivities directly from the logs.
The method has been demonstrated by application to logs from a horizontal well section. Anisotropy ratios of 2 to 5, and occasionally higher values, were obtained for this formation. We also addressed the accuracy of these numbers by using independent sets of input logs. The results indicate that the logs are influenced by factors like invasion, in addition to the anisotropy.
Our approach provides a fast and efficient computer algorithm. The output is calculated at the depths of the input logs; hence, the resulting anisotropy becomes a depth-dependent formation property.
Introduction
Electrical anisotropy has gained considerable attention in recent years. If present in the formation, neglection of this property when interpreting resistivity logs may lead to erroneous saturation estimates and may thus have great consequences upon development and production strategies and the overall economic situation.
Electrical anisotropy denotes that the resistivity shows directional dependence. In sedimentary formations, it is commonly assumed that the anisotropy is caused by the deposition process, which yields different small-scale (grain and pore-size scale) structural properties in the vertical and horizontal directions. Anisotropy may also occur on a lithology scale[i.e., as a result of thin layers (compared to the extension of the electricfield) having individual isotropic properties]. Because the effect is determined by the sedimentary structure, a formation can be expected to show anisotropy in several properties, such as electric, acoustic, and fluid-flow resistance (permeability) properties, simultaneously.
A common way of describing anisotropy is to distinguish between the vertical direction and directions in the horizontal plane. In this paper, we shall denote the resistivities in these directions by RV andRH, respectively. However, the terms "vertical" and"horizontal" refer to the original deposition process and may no longer correspond to the actual orientation of the formation owing to small- or large-scale geological activity. For dipping beds, it is common practice to assume one resistivity (R H) in the bedding plane and one (RV) in the direction normal to the bed, unless evidence of intrabed disturbances suggests other orientations of the anisotropy.
Numerous publications have addressed the influence of electrical anisotropy on resistivity logs. Among the effects that have been studied are anisotropy in dipping and thinly laminated formations1–3 and in crossbedded formations.4 Effort has been put on theoretical tool response modeling and simulation 5–7 and on anisotropy corrections to logs.8,9 From field cases, anisotropy ratios(RV/R H) up to the order of 5 to 10 have been reported.7,8,10
In this paper, we demonstrate a method for calculating the electrical anisotropy directly from well logs, based on the theory developed by Hagiwara.6 The method has been implemented and applied to log data from a horizontal North Sea well.
Theory
Hagiwara6 has analyzed the resistivity log's response in anisotropic formations. According to this reference, two different measurements are sufficient to determine the anisotropy unambiguously, as long as the anisotropy orientation is known. The measurements may differ with respect to one or more of the following:antenna spacing (which is a prerequisite for phase- and attenuation-derived resistivity),frequency, ordeviation angle between tool axis and anisotropy orientation.
In our work, we consider the LWD induction response. For this instrument class, Hagiwara shows that the complex voltage V recorded by one transmitter-receiver pair of electrodes isEquation 1
where i=the imaginary unit (i=-11/2) and L=the antenna spacing. Further,Equation 2
where a2= RH/RV is the anisotropy ratio between horizontal and vertical resistivitiesRH and RV, and ?=the deviation of tool direction from the R V direction. Notice the interpretation of the terms "vertical" and "horizontal," as discussed in the introduction.
The wave number k is defined byEquation 3
where ?=the measurement angular frequency, µ=the magnetic permeability, andeH=the horizontal dielectric constant. In this study, we used the free space magnetic permeability µ=µ0=4p×10–7 N/A, and approximated eH from the logged resistivity through an empirical relation. Both these approximations are considered to have negligible influence on the results.
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