3D-FEM modeling of F/TDR sensors for clay-rock water content measurement in combination with broadband dielectric spectroscopy

The use of electromagnetic sensors such as Time Domain Reflectometry (TDR) probes has gained increasing importance for long term monitoring of the water content in radioactive waste repositories. TDR probes are sensitive to changes in electromagnetic properties of the surrounding material, a clay rock in our case. Prior to the in situ application, it is mandatory to have an accurate relationship between the electromagnetic properties of the intact host clay rock and the water content. For this purpose, the dielectric properties of intact clay rock samples were systematically studied at frequencies from 1 MHz to 10 GHz with network analyzer technique in combination with coaxial transmission line cells. Samples were conditioned to achieve a water saturation range from 16 % to nearly saturation. The relaxation behavior was quantified based on a generalized fractional relaxation model under consideration of an apparent direct current conductivity assuming three relaxation processes: a high-frequency water process and two interfacial processes which are related to interactions between the aqueous pore solution and mineral particles (adsorbed/hydrated water relaxation, counter ion relaxation and Maxwell-Wagner effects). In a second step, these data are introduced 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 rode based TDR-probe embedded in the clay rock. The results are analyzed with classical travel time analysis (onset/inflection) which under/overestimates the value of the permittivity compared to effective permittivity at 1 GHz. Indeed, apparent permittivity contains not only the water-content contribution but also effects due to water-mineral interaction processes. The results demonstrate the capabilities of a combined TD/FD analysis procedure for the monitoring of physical and chemical properties of materials with high frequency electromagnetic sensor techniques.