Calibration Measurements of Dielectric Properties of Porous Media
Authors: Nguyen Buu-Long , Geels Amanda M. , Bruining Johannes , Slob Evert C. 
Published: December 2007

Calibration Measurements of Dielectric Properties of Porous Media Buu-Long Nguyen, SPE, Amanda M. Geels, SPE, Johannes Bruining, SPE, Evert C. Slob, Department of Petroleum Engineering & Applied Geophysics, Delft University of Technology

Abstract
We present a specially designed experimental set-up for accurate measurements of the frequency-dependent relative complex dielectric permittivity (RCDP) in porous media. The set-up operates on the principles of steady-state flooding and time-domain reflectometry (TDR). The steady-state flooding technique allows for a well-controlled uniform saturation distribution in the sample. The TDR technique enables on-line measurement of the dielectric response. We derive the equations for the propagation and reflection of an electromagnetic (EM) signal along a coaxial transmission line consisting of a standard coaxial cable, a transition unit and the sample holder. The RCDP at different oil saturations are calculated by means of frequency analysis of the scattered signal.
We present the RCDP obtained from experiments in sand samples at different saturations. We compare the obtained results with those calculated with a number of existing mixing models, including the Complex Refractive Index (CRI) model and the classical Rayleigh's formula.
The experimental method has proved to be suitable for online measurement of dielectric properties of porous media with varying fluid saturation. It turns out that small saturation difference can be discerned in the measurements. We have found that the RCDP calculated with the CRI model (refractive index exponent =0.75) show the best agreement with those obtained from the experiments.

Introduction
The interpretation of data obtained with the Electromagnetic Propagation Tool (EPT) or Ground Penetrating Radar (GPR) requires knowledge of the dielectric properties of water- and oil-saturated porous media. Existing mixing models of dielectric properties give strongly divergent results. To examine the applicability of existing mixing models it is necessary to have accurate calibration data.
Numerous researchers have performed calibration measurements in laboratory experimental setups. Most of the measurements suffer from an inhomogeneous distribution of fluids. In many cases the setup had no special construction to reduce fluid inertia effects at the inlet or capillary end effects at the outlet.
In the next section we explain the principles of Time Domain Reflectometry (TDR) which we use to measure the dielectric response of porous media. Subsequently we describe the experimental setup and procedure. Finally we present and discuss the obtained results.
Appendix A presents the derivation of multiple reflection coefficient for an EM signal traveling along a multisection coaxial line. Appendix B describes the procedure we use for the frequency analysis of the measured scatter functions. Appendix C gives a brief summary on the empirical mixing models for multicomponent materials with which we compare the results of our measurements.
The Time Domain Reflectometry (TDR) Technique Basic Principles. The theoretical background of the TDR technique is described in [5]. When an EM wave is launched into a (coaxial) cable, any change in the electrical and dielectric properties of the cable will cause a partial or total reflection of the wave. Changes in the electrical and dielectric properties cause change in the impedance. Waves reflected on a discontinuous boundary either are in phase or in counter phase with the in-coming wave. The voltage amplitude of the reflected waves is a function of the change in impedance which causes the reflection (see App. A for detailed description). If the EM wave encounters an increase in impedance the reflected wave will be in phase with the in-coming wave. If the EM wave encounters a decrease in impedance the reflected wave will be counter phase with the in-coming wave.
A standard TDR device consists of a signal generator, a sampler and an oscilloscope. The signal generator launches the EM wave into the cable. P. 13^