Borehole Corrections for a Thick Resistivity Probe

Abstract

The electrical resistivity contrast between the borehole fluid and the surrounding rock can be very large during borehole logging in crystalline rock. In resistivity logging we are in general interested in acquiring information about the true resistivity of the rock. The fluid will cause an unwanted deflection of the measured apparent resistivity from the sought rock resistivity. The nonconducting probe and its finite dimensions will also affect the measurements. By assuming homogeneous rock and concentric geometry, the Laplace equation has been solved for a thick resistivity probe with normal electrode configuration. The resulting cosine-integral can be calculated numerically with the digital filter method. The corresponding solution for other types of electrode configurations can be found by superposition of results for the normal configuration. The inverse solution that is needed to correct the data is found by fitting calculated values in a least-squares sense to a low-order polynomial. The correction method has been tested on data from a deep hole in granitic rock in south-eastern Sweden. Significant variations in both borehole diameter and fluid resistivity are present in the hole. The assumptions of homogeneous rock and concentric geometry were not valid for the data. In spite of this it was possible to correct the data in a proper way. The resulting estimates of the rock resistivity were about the same for both the normal and the lateral logs. Also, no significant level shifts appeared in the corrected data where there was an abrupt change in borehole diameter. The large volume bulk resistivity of the rock mass was estimated from the corrected data and was found to be in accordance with estimates from ground-based geophysics. By supporting the logging data with petrophysical measurements on core samples it was possible to get reasonable estimates of the rock porosity along the borehole.