Autonomous Sensors for Measuring Continuously the Moisture and Salinity of a Porous Medium

Abstract

The article describes a new field sensor to monitor continuously in situ moisture and salinity of a porous medium via measurements of its dielectric permittivity, conductivity and temperature. It intends to overcome difficulties and biases encountered with sensors based on the same sensitivity principle. Permittivity and conductivity are determined simultaneously by a self-balanced bridge, which measures directly the admittance of sensor electrodes in medium. All electric biases are reduced and their residuals taken into account by a physical model of the instrument, calibrated against reference fluids. Geometry electrode is optimized to obtain a well representative sample of the medium. The sensor also permits acquiring a large amount of data at high frequency (six points every hour, and even more) and to access it rapidly, even in real time, owing to autonomy capabilities and wireless communication. Ongoing developments intend to simplify and standardize present sensors. Results of field trials of prototypes in different environments are presented.

Keywords: autonomous sensors; electrode admittance; permittivity measurement; profile of soil moisture, salinity and temperature; sample volume; self-balanced bridge; vadose zone; wireless network.

Figure 1

Prototypes developed in the laboratory with same physical principles. (a) multi-channel sensor for vertical profile owing to stacked electrodes; (b) one-channel sensor derived from the multi-channel one; (c) low cost sensor; and (d) one-channel simplified sensor.

Figure 2

Successive conversions from sensor signals, bridge voltages $V_G$ and $V_C$, to the water content of a porous medium, ${\theta }_v$, and its salinity ${\sigma }_{ion}$. A previous system relied on a direct current-voltage measurement. G and C are, respectively, the capacitance and the conductance of the electrodes embedded in the medium, while ${\epsilon }_r$ and $\sigma$ are its apparent electric permittivity and conductivity.

Figure 3

Schematic diagram of the self-balanced bridge. The current $i_x$ flowing through the admittance to be measured, $Y_x=G_x+\mathbf{j}{C}_{x}2\pi f$, under bridge oscillator voltage $v_{osc}$ at frequency f, is balanced by the current $i_{eq}$. It is generated by the bridge owing to a feed back loop, multipliers and fixed components, conductance $G_{eq}$ and capacitance $C_{eq}$. The feed back loop provides the direct voltages $V_G$ and $V_C$.

Figure 4

Instrument imperfections (in complex notation), as included in a physical model of the sensor: bridge interferences between G and C branches (${\phi }_Y$), parasitic admittance ($Y_p$) and impedance ($Z_s$) due to leads, and electrode inductance ($L_{el}$).

Figure 5

Calibration of a sensor with air and water at different concentrations of KCl salt as references (black lines). (a) sensor conductivity against measurements by the conductivity-meter C931 of the firm Consort (Belgium); (b) sensor permittivity against water permittivity. At high conductivity, adjustments depend tightly on inductances of leads and electrodes, the latter being fixed. The last point is affected by bridge voltage $V_G$ exceeding 3.5 V; sensor sensitivity was $G_{eq}=24$ mS·V⁻¹.

Figure 6

Comparison of the outputs of a GS3 Decagon sensor with known values using the same procedure as in Figure 5. (a) sensor conductivity against conductivity measurements by the conductivity meter C931; (b) sensor permittivity against air and water permittivity.

Figure 7

Time series of data from a multi-channel sensor in a dry sand. From data dispersion, the accuracy on permittivity and conductivity at low values is: ${\epsilon }_r=3.30\pm 0.05$ and $\sigma =0\pm 1$ $\mathsf{\mu }$S·cm⁻¹ (with sensor parameters $G_{eq}=5$ mS·V⁻¹ and $g=0.12$ m). Compaction of sand by shaking its container reduces air presence close to electrodes, and, therefore, ${\epsilon }_r$ differences between channels. Low temperature sensitivity of the sensor is demonstrated by varying external temperature at the end of the trial.

Figure 8

Electrodes of the multi-channel sensor in Figure 1a, with dimension symbols: $\mathsf{\Phi }$ is the electrode diameter ($\mathsf{\Phi }=50$ mm here), D the distance between their axes ($D=100$ mm) and h their height ($h=50$ mm).

Figure 9

Cross sections in the dimensionless plane $x^{*}=2x/D$ $y^{*}=2y/D$ of the spatial distribution of sensor sensitivity in medium. Distribution is deduced from the expression of electrical field for the electrode design in Figure 8. Each contour corresponds to points in which sensitivity normalized by its maximum value has a value $\eta$, with $\eta =0.40$ (filled with magenta color), $\eta =0.25$ (purple) and $\eta =0.10$ (blue), respectively. The distribution depends on the sensor geometry factor $\alpha =\mathsf{\Phi }/D$, where D is the electrode spacing and $\mathsf{\Phi }$ their diameter. Distributions are reported for (a) $\alpha =0.12$; (b) $\alpha =0.25$; (c) $\alpha =0.50$.

Figure 10

Schematic view of a wireless network of autonomous sensors as developed in our laboratory.

Figure 11

Time series of data recorded by a multi-channel sensor (f at 20 MHz) in sand with low clay content during summer 2015. Fluctuations of medium permittivity and conductivity of each channel are correlated to diurnal cycles of soil temperature at the same level. Data at depth 5–10 cm (red), at depth 10–15 cm (dark) and at depth 15–20 cm (green).

Figure 12

Time series recorded by a one-channel sensor (f at 10 MHz) during a cold spell in January 2017. Apparent medium permittivity and conductivity decreased towards low values as temperatures fell below 0 °C. Water in soil was progressively frozen. Rain and air temperature were provided by other sensors.

Figure 13

Series of data recorded by a one-channel sensor (Figure 1b; f at 20 MHz; a point every 10 min.) in a clayey calcareous soil at the end of 2015. (a) apparent medium permittivity, conductivity and temperature along with data from a rain gauge; (b) conversion into water content and salinity (see text).

Figure 14

Data from Figure 11 for the channel at depth 5–10 cm. (a) apparent medium permittivity, conductivity and temperature; (b) conversion into water content and salinity (see text).

Figure 15

Time series recorded by a one-channel sensor (f at 20 MHz) in the same soil as in Figure 11 and Figure 14, just after a large amount of rain. (a) apparent medium permittivity, conductivity and temperature; (b) conversion into water content and salinity (see text).

Figure 16

Zoom in on the series in Figure 13. (a) apparent medium permittivity, conductivity and temperature; (b) conversion into water content and salinity (see text).