Design and analysis of time domain reflectometry probes for measuring water content and bulk electrical conductivity under steady and transient flow conditions

Abstract

A time domain reflectometry (TDR) instrument includes an EM pulse generator, transmission lines to deliver the pulse to the point of measurement, and proves to guide the pulse through the medium. Standard, continuous-rod probes are comprised of two or three parallel metal rods that are pushed into the medium. The velocity of propagation of the pulse along the rods defines the relative dielectric permittivity of the medium. Given the large contrast in the relative dielectric permittivities of water (81), air (1) and soil solids (3-5), the relative dielectric permittivity of a soil sample is highly correlated with its water content. In addition, the pulse loses energy through electrical conduction as it travels along the rods. These energy losses can be related to the bulk electrical conductivity (EC) of the medium in the sample volume of the probe.

The bulk EC of a porous medium is a function of the water content and of the EC of the pore water. If the pore water chemistry is dominated by a single electrolytic solute, the pore water EC can be related to the solute concentration at a given water content. As a result, TDR offers the possibility of measuring both the water content and the solute concentration simultaneously, allowing for rapid, nondestructive monitoring of flow and transport n partially saturated media.

Standard, continuous-rod TDR probes have been shown to measure the length-weighted average water content along their length, even if the water content varies along the probe. The distribution of probe sensitivity in the plane perpendicular to the rods has only been described for homogenous distributions and under restrictive heterogenous conditions. A numerical model is used here to define the spatial distribution of probe sensitivity in the plan transverse to standard continuous-rod probes. The results show that the size of the sample area is directly related to the rod separation; an increase in the rod diameter results in a more uniform distribution of sensitivity in the transverse plane. A three-rod design has a far smaller sample area than a two-rod probe with the same separation of the outermost rods. Regardless of the probe configuration, the probe sensitivity is not uniform in the transverse plane. Therefore, the rods should be installed in a manner that minimizes water content variations between them to ensure that the measured relative dielectric permittivity correlates with a representative average water content in the sample volume.

Direct current EC measurements show a nonlinear dependence of the bulk EC on the water content. The results of a laboratory experiment conducted in a sand-filled column show that the TDR-measured EC follows the same relationship shown for direct current measurements. The relationship applies to both two-rod probes with and without baluns and three-rod probes. Results from the experiment also demonstrate that probe calibrations can be conducted in a saline solutions. In contrast to the laboratory results, a field experiment showed a linear dependence of the bulk EC on the water content. This result is critical for solute concentration monitoring if the water content varies along the rods. A method of probe calibration is presented and used to monitor the advance of a solute step under steady-state flow.

The ability of continuous-rod probes to measure the water content and solute concentration in their sample volume has been demonstrated. However, these probes face limitations for profiling the water content and solute concentration with depth, measuring the water content very near the ground surface, and measuring the water content in electrically conductive media. Several alternative probes have been designed to address these shortcomings. Analytical and numerical analyses are presented to describe the response of these probes to changing water contents and to define their sample areas in the transverse plane. The results can be summarized generally based on the geometry of the metal rods and nonmetallic probe components for a given probe design. Any probe that places the probe materials in series with the medium, such as coated continuous-rod probes, will have a sensitivity that varies with the water content of the surrounding medium. As a result, the sample areas will not be constant, usually decreasing with increases in the soil water content. In addition, the measured relative dielectric permittivity will not be related uniquely to the average water content along the rods if the water content varies along the probe. Probes that place their components in parallel with the surrounding medium avoid these problems, showing sensitivities that are independent of the water content and measuring the correct length-weighted average water content along their length. The numerical approach can also be used to investigate the sensitivity of the response and sample area of an alternative probe on each of its parameters, allowing for efficient optimization of the design.

An alternative TDR probe is presented that was designed to measure both the water content and the bulk EC over limited depth intervals. The probe is shown to produce water content profiles comparable to those measured with a neutron probe to 2m depth. The EC response is calibrated to measure the solute concentration under temporally variable water content and solute concentrations, providing a unique ability to profile the resident solute concentration during transport under transient flow conditions in the field. Unfortunately, given that the probe materials are placed in series with the surrounding medium, the probe will not measure the correct length-weighted average water content of bulk EC if these properties vary along the probe. Therefore, the measurement interval should be as short as possible to limit the spatial variability of the water content and solute concentrations in the sample volume of the probe.

The results of numerical calibrations of published alternative probes consistently differ from physical probe calibrations. This may demonstrate errors in the methods of physical calibration. Poorly understood influences from the connection of the transmission line to the probe or from the field distribution at the ends of the rods may also add to the discrepancies between the measured and modeled probe responses. Further investigation of the causes of these differences will lead to greater understanding of the behavior of TDR probes, allowing for further improvements in their design.