Deducing Electrical Permittivity of Formations From LWD Resistivity Measurements

The electrical permittivity (epsilon) of rock has been measured and applied in petrophysical evaluation for decades. With the new-generation tools the popularity and application of epsilon has increased in the past years. One of the advances of the new-generation tools is measurement of epsilon at multiple frequencies (f), also known as dispersive permittivity (epsilon(f)). Drawbacks with these tools are that they respond to the invaded zone and the data must be acquired on wireline and therefore is not always accessible. Logging-while-drilling (LWD) propagation resistivity records the phase shift and attenuation between two receivers and responds differently to electromagnetic rock properties (resistivity, permittivity and permeability). The characteristic of the phase shift and the amplitude decay can therefore, under given conditions, be used to extract both electrical permittivity and resistivity from the measurements. The purpose with this paper is to show that electrical permittivity and its dispersion can be extracted from LWD resistivities. The work is motivated by the fact that information about epsilon and epsilon(f) is hidden in the LWD resistivities, so why not extract it and use it? The permittivity can be used in the petrophysical evaluation, it is acquired in real time and can be used to identify bypassed zones, as geological marker and for geosteering. The LWD resistivity accuracy will also be improved by replacing the empirical-based assumption about epsilon with the more correct value on epsilon in the LWD processing. This improvement in accuracy of LWD resistivity will be significant in rocks with large permittivity, e.g., organic-rich source rocks. This paper applies classical electromagnetic theory and shows how to extract permittivity from LWD resistivity. Examples are illustrated based on results from different LWD tools. The examples show that LWD permittivity and its dispersion fit very well with data from commercial wireline tools. Limitations of the presented techniques and further application of LWD permittivity and dispersion will be discussed.