Formation Electrical Anisotropy Derived From Induction-Log Measurements in a Horizontal Well
- Jon Bang (Sintef Petroleum Research) | Arne Solstad (Sensorlink AS) | Svein Mjaaland (Sintef Petroleum Research)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2001
- Document Type
- Journal Paper
- 483 - 488
- 2001. Society of Petroleum Engineers
- 5.6.1 Open hole/cased hole log analysis, 4.3.4 Scale, 1.12.1 Measurement While Drilling, 2.4.3 Sand/Solids Control, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 1.6 Drilling Operations, 3.3.1 Production Logging, 5.1 Reservoir Characterisation, 1.12.2 Logging While Drilling
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An existing theory describes how electrical anisotropy in the formationaffects the response of resistivity logging tools. We have related this theoryto the processing of logging while drilling (LWD) induction logs and are thusable to calculate the anisotropic resistivities directly from the logs.
The method has been demonstrated by application to logs from a horizontalwell section. Anisotropy ratios of 2 to 5, and occasionally higher values, wereobtained for this formation. We also addressed the accuracy of these numbers byusing independent sets of input logs. The results indicate that the logs areinfluenced by factors like invasion, in addition to the anisotropy.
Our approach provides a fast and efficient computer algorithm. The output iscalculated at the depths of the input logs; hence, the resulting anisotropybecomes a depth-dependent formation property.
Electrical anisotropy has gained considerable attention in recent years. Ifpresent in the formation, neglection of this property when interpretingresistivity logs may lead to erroneous saturation estimates and may thus havegreat consequences upon development and production strategies and the overalleconomic situation.
Electrical anisotropy denotes that the resistivity shows directionaldependence. In sedimentary formations, it is commonly assumed that theanisotropy is caused by the deposition process, which yields differentsmall-scale (grain and pore-size scale) structural properties in the verticaland 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 isdetermined by the sedimentary structure, a formation can be expected to showanisotropy in several properties, such as electric, acoustic, and fluid-flowresistance (permeability) properties, simultaneously.
A common way of describing anisotropy is to distinguish between the verticaldirection and directions in the horizontal plane. In this paper, we shalldenote the resistivities in these directions by RV andRH, respectively. However, the terms "vertical" and"horizontal" refer to the original deposition process and may no longercorrespond to the actual orientation of the formation owing to small- orlarge-scale geological activity. For dipping beds, it is common practice toassume one resistivity (R H) in the bedding plane and one (RV) in the direction normal to the bed, unless evidence ofintrabed disturbances suggests other orientations of the anisotropy.
Numerous publications have addressed the influence of electrical anisotropyon resistivity logs. Among the effects that have been studied are anisotropy indipping and thinly laminated formations1-3 and in crossbeddedformations.4 Effort has been put on theoretical tool responsemodeling and simulation 5-7 and on anisotropy corrections tologs.8,9 From field cases, anisotropy ratios(RV/R H ) up to the order of 5 to 10 havebeen reported.7,8,10
In this paper, we demonstrate a method for calculating the electricalanisotropy directly from well logs, based on the theory developed byHagiwara.6 The method has been implemented and applied to log datafrom a horizontal North Sea well.
Hagiwara6 has analyzed the resistivity log's response inanisotropic formations. According to this reference, two different measurementsare sufficient to determine the anisotropy unambiguously, as long as theanisotropy orientation is known. The measurements may differ with respect toone or more of the following: (a) antenna spacing (which is a prerequisite forphase- and attenuation-derived resistivity), (b) frequency, or (c) deviationangle between tool axis and anisotropy orientation.
In our work, we consider the LWD induction response. For this instrumentclass, Hagiwara shows that the complex voltage V recorded by onetransmitter-receiver pair of electrodes is
where i=the imaginary unit (i=-11/2) and L=the antenna spacing. Further,
where a2= RH/RV is theanisotropy ratio between horizontal and vertical resistivitiesRH and RV, and ?=the deviation of tooldirection from the R V direction. Notice the interpretationof the terms "vertical" and "horizontal," as discussed in the introduction.
The wave number k is defined by
where ?=the measurement angular frequency, µ=the magnetic permeability, andeH=the horizontal dielectric constant. In this study, we usedthe free space magnetic permeability µ=µ0=4p×10-7 N/A,and approximated eH from the logged resistivity through anempirical relation. Both these approximations are considered to have negligibleinfluence on the results.
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