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Standardizing Characterization of Electromagnetic Water Content Sensors

Part 1. Methodology

^a Dep. of Plants, Soils and Biometerology, Utah State University, Logan, Utah
^b University of Connecticut, Dep. of Civil and Environmental Engineering, Storrs, CT

View larger version (21K): [in a new window]   Fig. 1. Frequency dependent permittivities from (upper) network analyzer measurements of different soil minerals demonstrating mild and strong relaxation as a function of the volumetric moisture contents indicated in parentheses and (lower) real ('), imaginary ('') and complex (*) permittivities fit to measured real and imaginary permittivities of sodium bentonite using Eq. [9]. Model parameters are s = 40.0, = 6.50, dc = 0.055 S m–1, = 0.3, and frel = 6.37 x 107 Hz.

View larger version (16K): [in a new window]   Fig. 2. Example of sensor measurement frequency determination by relating TDR measured permittivity (Ka) to the Cole–Cole modeled network analyzer data (symbols), yielding what is termed the maximum passable frequency for travel time instruments.

View larger version (16K): [in a new window]   Fig. 3. Measured and fitted static permittivity (obtained from s in Eq. [9]) of water–2-isopropoxyethanol mixtures as a function of volume fraction of the latter. Data from Kaatze et al. (1996) are compared with our network analyzer (NA) measurements. A polynomial equation was fit to the network analyzer (N.A. Measured) data and is presented in the text as Eq. [14].

View larger version (29K): [in a new window]   Fig. 4. Modeled (Eq. [9]) real and imaginary permittivities of various dielectric liquids and mixtures thereof (numbers in Part a indicate volume fraction of 2-isopropoxyethanol–water). In the left-hand panels (real) and (imaginary), relaxation occurs beyond 1 GHz, outside the frequency range of many EM sensors. On the right, relaxations occur within the megahertz frequency range where EM sensors operate. The broader relaxation spectrum of Brasso (polishing compound) is due to its complex liquid makeup and mixture of fine suspended solids.

View larger version (16K): [in a new window]   Fig. 5. Network analyzer measured real and imaginary permittivities measured in a 0.6 fraction mixture of 2-isopropoxyethanol and water as a function of solution electrical conductivity. The effect of salinity on the imaginary component is two to three times greater at 0.1 GHz as compared with data at 1 GHz.

View larger version (17K): [in a new window]   Fig. 6. Temperature dependent permittivities of pure water and a 0.6 mixture of 2-isopropoxyethanol and water. A linear equation was fit to the measured mixture permittivities shown.

View larger version (25K): [in a new window]   Fig. 7. Cross section of the modeled sampling area of a 2-conductor, looped TDT sensor (Acclima TDT, Blonquist et al., 2005). The electromagnetic energy storage density was modeled using the ATLC model of (Kirkby, 1996) with normalized contour lines ranging from 0 to 1 at increments of 0.1. The two center rods are connected and the two outer rods form a separate connection. In (a) the energy storage density is independent of background permittivity, while in (b) there is an order of magnitude difference between the background permittivity of the top and bottom half of the cross section resulting in a significantly different distribution.