Dielectric Permittivity Dispersion Measurements in Downhole Conditions – Effect on Porosity Measurements

Abstract

The dielectric dispersion of porous media saturated with water and oil is described by the Havriliak–Negami curve in the frequency range 10 kHz – 50 MHz with characteristic values of polarization parameters. Laboratory data show the relationship between porosity and polarization parameters. This relationship allows us to determine porosity of water-and-oil saturated formation under downhole conditions, using borehole dielectric logging methods. In this study, a possibility of using borehole electromagnetic (EM) inductive measurements for determining dispersion of complex dielectric permittivity of the formation, including the invaded zone was investigated. The influence of the inductive measurement error when finding formation porosity when determining polarization parameters of the frequency dependence of complex dielectric permittivity (the Havriliak–Negami spectrum) was studied. For this study, a vertically oriented coil is placed in the well (along the borehole wall), creating a harmonic electromagnetic field. Several receivers that are aligned with the borehole axis measure this harmonic electromagnetic field. By using the magnetic field values on the well axis, we solve the inverse problem of determining complex dielectric permittivity of the formation, taking into account the invaded zone. Dielectric permittivity of the formation is calculated at different frequencies and is then used to restore the frequency dispersion curve, which enables us to find polarization parameters for the Havriliak-Negami polarization curve, taking into account the measurement error. Subsequently, these parameters can be used to find formation porosity. The proposed method of finding porosity uses inductive logging technology and is an alternative to the method based on the mixing formulae.

Numerical Simulation and Application of Response Characteristics of High-Frequency Dielectric Logging Instrument

“…In recent years, researchers have performed numerous theoretical simulations and laboratory tests of dielectric logging instruments. Accordingly, they have investigated the relationship between the properties of the rock and the high-frequency electromagnetic wave propagation characteristics [11][12][13]. In 2003, Liu and Sato used the finite difference time domain method to numerically simulate the electromagnetic response of formations with different thicknesses and multiple frequencies and built a dielectric logging instrument based on a vector network analyzer [14].…”