Permittivity measurements using dual open ended coaxial probes
The motivation for this study has been to conduct a feasibility study on a measuring device to monitor hydrate formation close to the inner surface of a pipe where a multiphase hydrocarbon fluid mixture is flowing. This measurement device is supposed to measure both the permittivity and the conductivity of the fluid mixture, and estimate the hydrate layer thickness formed on the inner surface of the pipe.
The permittivity was calculated using a Bilinear Calibration Procedure (BCP) based on reflection measurements within the frequency range of 10 MHz - 13 GHz using two different open-ended coaxial probes. Measurements on fluids with known permittivity were used to verify the sensitivity and reproducibility of the measurement device. Two open ended coaxial sensors with different geometries mounted into the pipe wall may be a suitable technique for performing hydrate monitoring by measuring the changes of permittivity and corresponding thickness. The objective of this work was to examine if a dual probes system is suitable for measuring both permittivity and thickness of fluid layers with sufficient accuracy to be applied for hydrate monitoring. The main conclusion of this work is that a two-probe system (small and large) with different geometries and sensitivity depths can be employed to determine both the permittivity and the layer thickness using the BCP and an empirical exponential model. The mounted sensor system on the pipe wall can be a suitable technique for gas hydrate monitoring by measuring the changes of permittivity and corresponding hydrate layer thickness. In this work, the open ended coaxial sensors, used as non-intrusive permittivity sensors, have been investigated and the basic principles of permittivity measurement on fluid layers have been revealed. A test material of unknown permittivity can be placed in aperture of the sensor where the reflection coefficient will be measured using a network analyzer. The BCP together with a simple capacitance model has been used to determine the broadband complex permittivity from recorded reflection coefficients. The broadband complex permittivity spectrum contains information about static permittivity, high frequency permittivity, dispersion frequency, etc. It is found that the apparent static permittivity for an increasing thickness of unknown sample is in good agreement with an empirical model of the open ended coaxial sensors. This empirical model relates the apparent permittivity, the thickness and permittivity of the layer. By applying two coaxial probes with different geometries in an ideal condition for a permittivity known sample, the sensitivity depths and constants of the probes are obtained. The thickness detection is applicable for layers thinner than the sensitivity depth of the large probe. The permittivity measurement is however the most accurate for layers with thickness larger than the sensitivity depth of the small probe. It is found that the thicknesses of the layers can be predicted within minimum 78.23% accuracy (mean accuracy is 89.85%) for layers thinner than the sensitivity depth of the large probe and also it is found that the permittivity of the layers can be calculated within minimum 94.3% accuracy (mean accuracy is 97.4%) for layers thicker than approximately 1.5 mm. Further on, it is also observed that the relaxation frequency obtained from the broadband complex permittivity spectrum increases as the conductivity of the dispersed phase increases.