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

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.