The Effect of Sonde Position in the Hole on Responses of Resistivity Logging Tools

Abstract

Theoretical relations exist in the literature for calculating the responses of electrode‐type resistivity logging tools when they are centered in the wellbore and the formations are thick and homogeneous (Fok, 1933; Stefanesco et al., 1929–32). These analyses are usually restricted to devices using dc or low‐frequency surveying currents, and they generally make use of the approximation of point electrodes. An analysis has also been made comparing the responses of such tools in anisotropic and isotropic formations (Kunz and Moran, 1958). In this paper, relations are derived for calculating the responses of electrode‐type logging tools when the sonde is not centered in the wellbore. Although similar relations could be applied to tilted sondes, the discussion in this paper is mainly restricted to the simple eccentered case in which the axis of the sonde is parallel to the axis of the hole. As will be shown, eccentering has a comparatively small effect on the responses of a normal device. On the other hand, certain types of focused‐log devices, in which a large proportion of the focusing current flows parallel to the hole, may exhibit an appreciable eccentering effect; this is particularly true when the contrast between formation resistivity and hole‐fluid resistivity is large. Spherically‐Focused‐Log (SFL*) resistivity devices (Schuster et al., 1971) have this type of current distribution, and, depending on electrode spacings, they may be appreciably influenced by eccentering. The applications shown in this paper will largely be done from SFL computations and measurements. The theoretical relations have been used in the development of a spherically focused tool less affected by eccentering. Tool responses predicted on the basis of the theoretical relations were found to be consistent with the results of test‐tank measurements made for one of the devices studied. Some field experiments have been made with centered and eccentered spherically focused tools, and more are to be done.

Large-Scale Electrical Resistivity and Bulk Porosity of the Oceanic Crust, Deep Sea Drilling Project Hole 504B, Costa Rica Rift

“…The same assumption is made in analyzing results from somewhat longer spaced versions of a large-scale DC resistivity log (e.g., Runge et al, 1969), but it is questionable with a conductive, seawater-filled borehole and the shorter electrode spacings used in Hole 504B. A much better approximation to in situ resistivity was obtained in this study by applying the analytic solution for the potential that arises from a point current source in a borehole penetrating a homogeneous medium (e.g., Kunz and Moran, 1958;Gianzero and Rau, 1977). At the center of a seawater-filled borehole of radius a, the potential at a vertical distance z from the current source is given by:…”

Large-Scale Electrical Resistivity and Bulk Porosity of the Upper Oceanic Crust at Hole 395A

“…For this study, a very close approximation to in-situ resistivities was obtained by applying the exact, analytic solution for the potential that arises from a point current source in a borehole that penetrates a locally homogeneous medium (e.g., Kunz and Moran, 1958;Gianzero and Rau, 1977). At the center of a seawater-filled borehole of radius a, the potential V at a vertical distance z from the current source / is given by:…”

Effects of formation anisotropy on resistivity‐logging measurements

“…This has been done, but-me details will not be given here. The important effects of eccentering have been covered by Gianzero and Rau (1977), and the introduction of anisotropy does not add anything interesting.…”