Frequency Dispersion Effects on LWD Propagation Resistivity Measurements

Abstract

Abstract Measurements sensitive to the resistivity of earth formations acquired during and after the drilling of oil and gas wells can be subject to frequency dispersion effects. The frequency range of interest in this paper is from practically zero to two million cycles per second. The most common measurements are wireline induction (10 – 100 kHz) and LWD propagation resistivity (0.4 MHz – 2 MHz). Methods suggested in the literature to analyze data subject to this effect range from simply assuming Rt is the deep 2 MHz attenuation resistivity to applying a CRIM (complex refractive index method) or other mixing law such as the Hanai-Bruggeman model. No physical basis was given by the authors who recommend using the 2 MHz attenuation resistivity. In addition, the attenuation resistivity depends on a dielectric assumption which varies between service companies as does the spacing for the deep measurement. On the other hand, the mixing models appear to be impractical because they depend on material properties such as the formation fluid content, pore microstructure, clay content, grain size, porosity, tortuosity, etc. Published log examples consistently indicate that dispersion effects occur in formations with anomalously large apparent dielectric constants. By definition, a medium with a large apparent dielectric constant is readily electrically polarized. This paper applies the accepted knowledge that polarization effects over the frequency range of interest tend to be dominated by interfacial relaxation within the rock-pore system. On this basis, an equivalent electric circuit model is used to determine the low frequency limit for the conductivity and dielectric constant based on LWD propagation measurements. Log examples will be presented where the algorithm is applied to data from a dual frequency LWD propagation resistivity tool with three fully compensated spacings. As expected, the low frequency limit conductivity from data at each spacing is shown to be higher than the dielectric-independent resistivity values used to compute the parameters of the circuit model. The low frequency limit dielectric constant is also higher than the apparent dielectric constants used in computing circuit parameters. The algorithm and its underlying theory are discussed in detail. The possibility of applying it to anisotropic and inhomogeneous cases is also discussed.