Permittivity Spectrum of Low-Loss Liquid and Powder Geomaterials Using Multipoint Reentrant Cavities

Permittivity is a useful tool to characterize the composition and quality of many geomaterials. In general, the non-resonant permittivity measurement methods exhibit a higher degree of uncertainty than their resonant counterparts. In resonant measurements, the reduction in uncertainty comes typically with a loss in broadband. This article describes the theory, design, and application of multipoint coaxial reentrant resonant cavities applied to low-loss geomaterials at different temperatures. Specifically, a full-wave method based on circuit analysis is developed and applied for a circular corrugated waveguide. Moreover, the mode-matching method is applied to calculate the generalized admittance matrix (GAM). Two multipoint cavities and software were built and validated. The first cavity has five resonant frequencies, between 170 MHz and 2.3 GHz, and the second has four resonant frequencies, between 1.3 and 8.6 GHz. Thus, this method allows for “broadband-resonant” measurements. The permittivity values of liquid hydrocarbons, powdered kerogen, and pyrite are shown.