Error Analysis of Clay-Rock Water Content Estimation with Broadband High-Frequency Electromagnetic Sensors—Air Gap Effect

Abstract

Broadband electromagnetic frequency or time domain sensor techniques present high potential for quantitative water content monitoring in porous media. Prior to in situ application, the impact of the relationship between the broadband electromagnetic properties of the porous material (clay-rock) and the water content on the frequency or time domain sensor response is required. For this purpose, dielectric properties of intact clay rock samples experimental determined in the frequency range from 1 MHz to 10 GHz were used as input data in 3-D numerical frequency domain finite element field calculations to model the one port broadband frequency or time domain transfer function for a three rods based sensor embedded in the clay-rock. The sensor response in terms of the reflection factor was analyzed in time domain with classical travel time analysis in combination with an empirical model according to Topp equation, as well as the theoretical Lichtenecker and Rother model (LRM) to estimate the volumetric water content. The mixture equation considering the appropriate porosity of the investigated material provide a practical and efficient approach for water content estimation based on classical travel time analysis with the onset-method. The inflection method is not recommended for water content estimation in electrical dispersive and absorptive material. Moreover, the results clearly indicate that effects due to coupling of the sensor to the material cannot be neglected. Coupling problems caused by an air gap lead to dramatic effects on water content estimation, even for submillimeter gaps. Thus, the quantitative determination of the in situ water content requires careful sensor installation in order to reach a perfect probe clay rock coupling.

Spatial Retrieval of Broadband Dielectric Spectra

“…The broadband three-phase CRIM model used includes water relaxation, interfacial relaxation, as well as losses due to direct-current conductivity. From a practical point of view, the supposed model is sufficient for most soils and rocks in the considered frequency range from 1 MHz–10 GHz [ 25 , 26 , 44 , 47 ].…”

“…This issue is not considered in available TD solvers. In contrast, FD solvers overcome this inconsistency by solving the set of equations at a specific frequency, which allows the incorporation of the appropriate material properties without any restriction [ 44 , 45 ].…”

A TDR Array Probe for Monitoring Near‐Surface Soil Moisture Distribution

“…Thus, the relative EM field distribution of the TDR array (Fig. 3) was investigated by means of a commercial finite element method solver for EM structures—Ansys HFSS high‐frequency EM field simulator (Ansys Inc.) as applied in several previous studies (Wagner et al, 2007, 2014; Bore et al, 2016). For simplification, the rod length in the model was set to 12 cm without considering the air gap.…”

Dielectric spectroscopy measurements on kaolin suspensions for sediment concentration monitoring

“…Moreover, the correction of temperature on apparent permittivity computed from TDR waveform with empirical calibration remains challenging[57,58]. Relaxation models have been widely used for soils[59,60] or suspensions[61] to model the spectrum as a sum of relaxation processes along the frequency bandwidth. The parameters for each process are computed by matching the spectrum and the model.…”