Moisture Content Estimation of Wet Sand from Free- Space Microwave Techniques

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1 213 Seventh International Conference on Sensing Technology Moisture Content Estimation of Wet Sand from Free- Space Microwave Techniques Sean Richards, Adrian Tan, Ian Platt, Ian Woodhead Lincoln Agritech Ltd, Christchurch, New Zealand Abstract Dielectric models are used with permittivity measurements of material for translation from permittivity to moisture content. A dielectric model for pure sand was developed based on fundamental physical properties such as the permittivity and geometry of the host material particles, and the frequency dependent processes that determine the permittivity of water. The measurement of sand using the short-circuited reflection method is discussed as is the processing of the measured data to extract permittivity values. Measured data in the 1 6 GHz frequency range for sand with a volumetric moisture content of 6.35 and 11.47% and thickness of 1 and 2mm is compared with the dielectric model. Keywords-sand; dielectric; microwave; time-gating I. INTRODUCTION Extraction of volumetric moisture content from material permittivity measurements requires the use of a dielectric model to relate the measured permittivity to the material moisture content. Dielectric models for various soil types include empirical models such as Topp [1] and Wang & Schmugge [2] and theoretical models such as the well known Looyenga model [3], [4]. Measurement of mass and moisture content of sand is necessary both during extraction and in industrial processes. This paper describes the derivation of a dielectric model for wet pure sand based on the fundamental physical properties such as the permittivity of the host material, geometry and size of the sand particles, and the frequency dependent processes that determine the permittivity of water. We will assume a nonporous host material and characterise the permittivity based on dry host and film water which is then related to the specific surface area (SSA), in turn related to the particle size distribution (PSD). A saturation model is then used to calculate the water permittivity which is then compensated for frequency effects and combined with the host permittivity using a mixing model. Permittivity data for a variety of rock types has been reviewed. Ulaby [5] investigated the dielectric properties of 8 rock samples in the microwave frequency range (.5 18GHz) and reported that ' was found to be approximately independent of frequency and the loss factor " in general is negatively correlated with frequency with values in the range of.1 to.1. This frequency independence of ' has been confirmed over the range 1 1GHz [6]. The dry bulk density of rock and the chemical composition are strongly correlated with ' [5],[7] while " shows no correlation with bulk density at any frequency. Zheng [7] lists permittivity values for a range of rock types measured at 973 MHz. Hunger [8] discussed the calculation of specific surface area SSA for sand samples with equal (mono-sized) and from a particle size distribution where this is available. Based on the analysis, a shape factor that is related to particle geometry of samples is introduced. Jones and Friedman [9] related the complex permittivity to shape factors and suggest a 1:1 ratio between the dimensions of a particle before shape (and isotropy) becomes a significant contributor. Hence an assumption of spherical particles would seem quite valid considering the natural and machine based mechanical processes that reduced the parent rock to particulates. Friedman [1], [11] defines an equation for calculation of water shell thickness based on PSD and an associated saturation model to determine mean water permittivity. II. DIELECTRIC MODEL FOR SAND In this section we will derive the dielectric model for sand. For mono-sized samples SSA ) can be calculated by (1) where d is the diameter of a sand particle and h is the host material density which may be taken as 27 kg/m 2 if the value is unknown. When a PSD is available, (2) can be used where are respectively the diameter and volume fraction of each particle size. Bulk density packing density The average water shell thickness (1) (2) of the sand material is calculated from the and the host density., is where is volumetric moisture content. The static permittivity of water, mixed with sand is (3) (4) (5) This research project is funded by the Ministry of Business, Innovation and Employment of New Zealand (Contract No.: LVLX81) /13/$ IEEE 974

2 213 Seventh International Conference on Sensing Technology where is the static permittivity of free water. = where T is the temperature in degrees Celsius, is the high frequency water permittivity; 5.5 is proposed by Friedman based on experimental work by several others, and 1/ is the scaling length for soil minerals. Friedman chose the value ( for but Friedman, et al. used, based on the.28 nm diameter of a water molecule and usefully related to the hygroscopic water content of soil based on Dirksen & Dasberg. Hence sand with.1% moisture content yields a value for of 73,.1% is 79 and 1% yields 8, the value used for. Although the effect is small for sand, a smaller grain size and hence increased SSA would decrease the permittivity at low moisture content, dramatically so for fine grained soils. Next we compensate for the primary relaxation of water using the first two terms in (6) ' m '' m y = GHz 4 y = GHz Fig. 2. Imaginary part of permittivity where is the angular frequency and is the relaxation time. A = 8.28ps value is used, based on the analysis by Kaatze. Near-surface water relaxation can be ignored due to large size of the sand particles and correspondingly small amount of near-surface water. The third term in (6) describes water permittivity due to conduction processes and can be related back to the low frequency conductivity, often measured at 1 khz. The final part of the model is to convert the mixture, volume fractions and individual permittivity's into a composite permittivity for the mixture, :.2 x = Fig. 1. Real part of permittivity.2 x = (6) where is the permittivity of the host, the shape factor equal to 1/3 for spherical particles and is a free parameter that corrects for the slope when using the Looyenga model. Note that while it seems counter-intuitive that the mixture permittivity can increase at a greater rate than the addition of water ( ), series models and percolation models demonstrate the effect, as does the Topp, et al model. Fig. 1 and Fig. 2 show respectively the real and imaginary permittivity calculated by the model for 2 to 6 GHz and from to.3. III. MEASUREMENT THEORY Experimental data was measured using the free-space shortcircuited reflection (SCR) method. This is based on transmission line theory where the complex reflection coefficient S 11 is given by (8) where Z is the wave impedance of the Material Under Test (MUT) normalised to the impedance of free-space (9) and is the phase constant (9) in the MUT while d is the thickness and the complex permittivity of the MUT. Since cannot be expressed explicitly in terms of S 11 and d, it needs to be solved numerically,. Free-space measurements (Fig. 3) require translation of the measurement plane to the front face of the MUT before solving with (8) which can be achieved in free space by normalising the S 11 measurement data with an S 11 measurement of a metal reflector positioned at the front face of the MUT,,. Free-space measurements taken in a less than ideal environment contain the response from both the environment and non-ideal components in the signal path such as cables, antenna and connectors. Time gating is used to remove unwanted responses from the desired signal,,,. The frequency. The frequency domain signal is transformed into a Fourier Fourier domain impulse response using an Inverse Fourier Transform; the impulse response is then gated over the expected signal interval using a window function then Fourier Transformed to recover the original frequency domain signal minus the unwanted components. Pre-processing of the frequency domain data involves windowing and zero-padding padding with the inverse of these operations required after time gating. Windowing is performed on the measured S11 signal to reduce spectral leakage, and associated Gibb's effect Gibb's effect (ringing artifacts). The choice of shape parameters for the window function is a trade-off between reduction in spectral leakage and limiting band edge effects created when applying the inverse window to the gated impulse response. Similarly for time-gating the choice of gate function (7) (8) (9) /13/$ IEEE 975

3 S Seventh International Conference on Sensing Technology and associated parameters is a trade-off between well-defined gate edges and data truncation. The experimental setup is shown in Fig. 3. S 11 measurements were taken for the flat aluminium reflector backed MUT S sand ( ) and of an aluminium reference reflector placed directly at the front of the MUT S reflector ( ) using a A- INFO LB-18 ridged horn antenna (Fig. 4) and Hewlett Packard (now Agilent) 8753D vector network analyser (VNA). These signals are then processed using the processing scheme described and translation of the measurement plane to the front face of the MUT is achieved (1) in free space by normalising S sand ( ) with S reflector ( ),, as shown in (1). (1) Fig. 5 shows the comparison between the raw and processed S11 measurements for 1mm sand with = 6.35%. Variations between the processed data and ideal data can in a large part be ascribed to the data pre-processing especially the choice of window and gate functions and gate positioning raw S11 gated S11 HP 8753D VNA x 1 9 Fig. 5. Raw and gated S11 for 1mm sand with = 6.35% 55 Aluminium plate PORT 1 Antenna Incident wave MUT Fig. 3. Experimental setup Permittivity values may be extracted from S11 measurements by inverting (8) and (9). We applied Muller's method using initial values generated from the dielectric model. Fig. 6 Fig. 8 show the inversion results for three samples with sample details in Table 1. The agreement between the dielectric model and the processed measurements demonstrate the utility of the process and agreement with values from the literature, viz., for sand provide validation. Table 1. Extraction of moisture content Measurement Sand Thickness (mm) Actual θv (%) Extracted θv (%) 1 sample A sample A sample B Fig. 4. A-INFO LB-18 ridged horn antenna IV. RESULTS AND DISCUSSION S11 measurements of a 1 to 2mm thick sand samples 8mm x 8mm with a volumetric moisture contents 1 of 6.35, and 11.47% were taken from 1 to 6GHz in steps of 3.125MHz and processed using the processing regime described in III. 1 Determined using standard gravimetric methods /13/$ IEEE 976

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