Theory of induced‐polarization logging in a borehole

Abstract

Currently, there is interest by the petroleum well‐logging industry in the potential use of induced polarization (IP) measurements to improve formation evaluation in shaly sands. Shell Development Company has constructed an experimental four‐electrode IP and resistivity logging tool to obtain downhole measurements in shaly sands. This study contributes to the theoretical understanding and interpretation of the dynamic (i.e., time‐dependent) response of this type of downhole IP logging device. A low‐frequency (e.g., 32 Hz or less) electric current oscillating at a single fixed frequency is applied between a pair of current electrodes in a borehole. The resulting voltages induced between pairs of potential measuring electrodes in the borehole are calculated by solving the time‐dependent Maxwell’s equations. Inductive electromagnetic (EM) coupling contributions to apparent (e.g., measured) IP phase angles are automatically taken into account. The model is applied to the study of normal logging arrays for which the voltage measuring electrodes are interior to the current electrodes. The model responses are calculated for normal arrays in both infinitely thick noninvaded formations and infinitely thick invaded formations. EM coupling contributions to apparent IP phase angles have an approximately universal dependence on a scaling parameter defined here. The scaling relationship permits the quantitative estimate of EM coupling effects for specific tool parameters (i.e., electrode spacings and frequencies) and formation characteristics (i.e., apparent conductivities). Therefore, scaling relationships of this type should be useful in the design of IP tools. An inverse method, developed for determining true formation IP phase angles and resistivities from apparent values measured by an IP tool, utilizes data from multiple pairs of voltage‐measuring electrodes and exploits the fact that, for the systems of interest, the inverse resistivity and IP problems can be “decoupled.” The assumption that IP phase angles have a logarithmic dependence on frequency over a decade frequency interval leads to a nonlinear relationship between percent frequency effect (PFE) and IP phase angle. This nonlinear relationship agrees well with experimental data.