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Soil Science Society of America Journal 64:1922-1925 (2000)
© 2000 Soil Science Society of America

DIVISION S-1-SOIL PHYSICS

A Pore Water Conductivity Sensor

M.A. Hilhorst

IMAG-DLO, P.O. Box 43, NL-6700 AA Wageningen, The Netherlands

m.a.hilhorst{at}imag.wag-ur.nl


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Theory and methods
 Discussion and conclusions
 REFERENCES
 
The electrical permittivity and conductivity of the bulk soil are a function of the permittivity and conductivity of the pore water. For soil water contents higher than 0.10 both functions are equal, facilitating in situ conductivity measurements of the pore water. A novel method is described, based on simultaneous measurements of permittivity and conductivity of the bulk soil from which the conductivity of the pore water can be calculated. A prototype of a pore water conductivity sensor based on this method is presented. Validation results show that the method can be used for a broad range of soils and is valid for water contents between 0.10 and saturation and for the conductivity of the pore water up to 0.3 S m-1.

Abbreviations: ASIC, application-specific integrated circuit


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Theory and methods
 Discussion and conclusions
 REFERENCES
 
ONE METHOD of determining the conductivity of the pore water of soil, {sigma}p, is by extracting a sample of water from the soil matrix. This is a labor-intensive task and not well suited for automation. Additionally, it is not certain that all ions are collected in the extracted sample. Another way is to translate the electrical conductivity of the bulk soil, {sigma}b, to {sigma}p using methods, models, and estimates such as those described by Rhoades et al. (1990) or Mualem and Friedman (1991). The weakness of these methods is that they are empirical relationships.

The electrical permittivity of the bulk soil, {epsilon}b, is a function of both the soil water content, {theta}, and the permittivity of the pore water, {epsilon}p (e.g., Nyfors and Vainikainen, 1989). Soil water content, {theta}, is a quantity defined as the volume fraction of water in the soil. Similarly, {sigma}b is a function of both {theta} and {sigma}p.

Malicki et al. (1994) found a high degree of linear correlation between {sigma}b and {epsilon}b values measured using time domain reflectometry for a broad range of soil types. They found an attractive method to calculate {sigma}p from simultaneous measurements of {sigma}b and {epsilon}b. However, Malicki's method is still an empirical one. The aim of this work was to approach the problem from a slightly different angle to derive a more fundamental relationship between {sigma}b and {sigma}p.


   Theory and methods
TOP
 ABSTRACT
 INTRODUCTION
 Theory and methods
Discussion and conclusions
 REFERENCES
 
Bulk Soil Conductivity vs. Pore Water Conductivity
The relative electrical permittivity of a dielectric material, {epsilon}, is a complex quantity expressing the ability to polarize the material in an electric field (E-field) and is defined as

(1)
with . In this paper the dielectric can be either water, solids, or air, or a mixture of them. In the following, the superscript ' refers to the real part of {epsilon} and the superscript '' refers to the imaginary part of {epsilon}. For a static E-field the real part of the permittivity, {epsilon}', is usually referred to as dielectric constant. The imaginary part of the permittivity, {epsilon}'', represents the total energy absorption or energy loss. The energy losses include dielectric loss, {epsilon}''d, and loss by ionic conduction

(2)
where {sigma}i is the specific ionic conductivity of the material, and {omega} the radian frequency (rad s-1). The frequency (Hz) of the applied E-field is . The permittivity for free space is .

Let us consider the water that can be extracted from the pores of the soil matrix. The permittivity and conductivity of the pore water will be denoted by subscript p. The imaginary part of the complex permittivity of the pore water is {epsilon}''p. In soil science it is not customary to use {epsilon}''p. It is more practical to use the conductivity of the pore water, {sigma}p, which can be defined as

(3)
where {sigma}ip represents the ionic conductivity of the extracted pore water. Dielectric losses are frequency dependent and have a maximum at the relaxation frequency. The relaxation frequency of water is 17 GHz at 20°C (Kaatze and Uhlendorf, 1981). The operating frequency for most dielectric or conductivity sensors is <<1 GHz. At frequencies low with respect to the relaxation frequency of water, {epsilon}''dp is negligible and Eq. [3] can be reduced to

(4)

Frequently {sigma}p is referred to as the electrical conductivity (EC) of the pore water. Note that EC refers to the conductivity of the pore water and not to that of the bulk soil. Ionic conduction is a function of temperature. In the case of a NaCl–water mixture, the conductivity increases by 2.25% °C-1. Often the measured {sigma}p or EC is given corrected for temperature dependence to a temperature of 20°C. This temperature correction depends on the composition of the solution and will not be used here. The complex permittivity of the pore water, {epsilon}p, is equal to that of pure water. The real part of the complex permittivity of the pore water with a temperature coefficient of about –0.37°C-1 (Kaatze and Uhlendorf, 1981). By analogy with Eq. [1] we can write the following approximation for {epsilon}p

(5)

The permittivity and conductivity of the bulk soil will be denoted by subscript b. The complex permittivity of the bulk soil, {epsilon}b, is proportional to both {epsilon}p and a function of {theta}, g({theta}). This g({theta}) function includes soil type and frequency dependency. In the following we assume that {epsilon}b and {sigma}b are measured for the same frequency and soil type. For dry soil, there is no water to facilitate ionic conduction; that is, the conductivity of the bulk soil {sigma}b {approx} 0. However, dry soil material is still polarizable. Hence the permittivity for dry soil ; appears as an offset to {epsilon}b. Now it is reasonable to postulate the following form for the complex permittivity of the bulk soil

(6)

Note that is a complex value and includes dielectric and ionic loss. However, since {sigma}b {approx} 0 for dry soil, we may approximate by its real part . Note also that is the extrapolated intercept with the y axis from the linear part of the {epsilon}'b vs. {sigma}b plot. With this and Eq. [5] substituted in Eq. [6], {epsilon}b can be written as

(7)

An electric model for a dielectric, like soil, between two electrodes is a lossy capacitor. The admittance, Y, of this capacitor is a complex quantity that is proportional to {epsilon}b of the bulk soil. Y is the reciprocal of the impedance Z. For soil Y can be defined by

(8)
where {kappa} is a geometry factor that is determined by the distance between the electrodes and their areas in contact with the soil. Note that contact problems of the electrodes with the soil will be reflected in {kappa}. The equivalent circuit for such a lossy capacitor is a loss-free capacitor, C, with a conductor, G, in parallel. C represents the energy storage capability of the soil and is related to {epsilon}'b. G represents the energy loss and is related to {sigma}b. Y may be written in terms of C and G as

(9)

From Eq. [8] and [9], and with Eq. [1] to [7] in mind, the real and imaginary parts of Y can be found

(10)
and

(11)
or in terms of the measurable bulk quantities {sigma}b (dividing Eq. [10] by {kappa}) and {epsilon}'b (dividing Eq. [11] by {omega}{epsilon}0{kappa})

(12)
and

(13)

From Eq. [12] and [13] the ionic conductivity of the pore water can be written as

(14)

The model of Eq. [14] describes the relationship between {sigma}p of the pore water (the water that can be extracted from the soil) and the values {epsilon}'b and {sigma}b as measured in the bulk soil using a dielectric sensor. The offset can be calculated from the {epsilon}'b and {sigma}b values measured at two arbitrary free water content values.

The relationships between the bulk soil parameters {epsilon}'b and {sigma}b and the corresponding pore water parameters {epsilon}'p and {sigma}p is different when the water present is bound to the soil matrix rather than free water. The model of Eq. [14] cannot be used for the conduction due to ions moving through the lattice of ionic crystals in a dry or almost dry soil. Therefore, the model is only valid for the free water in the matrix. Thus is not the value for . For sand, the free water content corresponds with {theta} > 0.01, but for clay it can be {theta} > 0.12 (Dirksen and Dasberg, 1993). As a rule of thumb, the model applies for most normal soils and other substrates for growing, like rockwool, if {theta} > 0.10.

The Dielectric Sensor
For both {epsilon}'b and {sigma}b equally (see Eq. [12] and [13]), only g({theta}) will be affected to a major extent by the frequency, by the shape of the electrodes, by the contact between electrodes and soil, and by the soil composition. Due to the ratiometric form of Eq. [14] with respect to {epsilon}'b and {sigma}b, g({theta}) will be eliminated. Therefore, contact problems have only a minor effect on the conductivity measurement of the pore water. This allows development of a small sensor tip for easy insertion in the soil. In Fig. 1 , a prototype of a pore water conductivity sensor as developed by IMAG in Wageningen, the Netherlands, is shown. For a detailed description of the sensor electronics the reader is referred to Hilhorst et al. (1993) and Hilhorst (1998). The "T"-shaped sensor is commercially available from Delta-T Devices Ltd. (Cambridge, UK).



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  		Fig. 1 A prototype of a sensor for the measurement of the conductivity of the pore water in the soil matrix. A temperature sensor is located near the sensor tip. The measuring frequency of the sensor is 30 MHz. The drawing shows more details of the sensor tip

 
The sensor is built around an application-specific integrated circuit (ASIC) developed for dielectric sensors. It contains all analogue and digital electronics to measure {epsilon}'b and {sigma}b. The measuring frequency is 30 MHz, which was more or less arbitrarily chosen. The ASIC measures 4 by 4.5 mm. Therefore all the electronics can be conveniently placed in the cylinder at the top of the sensor rod. The sensor rod is 10 cm long and 5 mm in diameter. The rod ends in a sharp point to facilitate insertion of the electrodes into the soil. The sensor tip is {approx}15 mm long and split into two metal electrodes separated from each other by a thin sheet of isolating material. A temperature sensor is located close to the sensor tip to facilitate temperature measurements. The ASIC is embedded in a cylinder of hard polyurethane molding. The flexible polyurethane output cable contains the RS232 signal wires and power supply wires. This cable is connected to a PSION-Workabout that runs the software for further signal processing and contains the model of Eq. [14].

Validation of the Theory
Relationship Between Bulk Conductivity and Permittivity
First we will demonstrate the validity of the assumption that {epsilon}'b changes linearly with {sigma}b if {theta} is varied. Four samples of wet glass beads of 0.2 mm at arbitrary {theta} were prepared by slowly extracting solution from an initially saturated sample. Since {sigma}p is not allowed to change with {theta}, drying by evaporation was avoided. The measurements of {epsilon}'b and {sigma}b, and also the measurement of {sigma}p (in the water left on top of the samples), were performed using the sensor of Fig. 1. This sensor measures {epsilon}'b and {sigma}b, performs the calculations, and returns only {sigma}p. For this experiment a software facility was built in to export also the {epsilon}'b and {sigma}b. The measurement of {sigma}p was checked using a laboratory four-electrode conductivity meter at 1 kHz. Water content was determined by the gravimetric method. The experiment started with clean glass beads, and {sigma}p was measured before the solution was applied.

The result for the relationship between {epsilon}'b and {sigma}b is shown in Fig. 2 . From this data it followed that for glass beads . The {sigma} of the applied solution was 0.4 S m-1. With in Eq. [14] we found for the conductivity of the pore water of all glass bead samples within ± 0.1 S m-1.



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  		Fig. 2 The linear relationship between the real part of the permittivity, {epsilon}'b, as a function of the conductivity of the bulk, {sigma}b, for glass beads. The conductivity of the applied water was 0.4 S m-1

 
Model Evaluation
The model of Eq. [14] was evaluated for five different soils, glass beads of 0.2-mm diam. and a slab of rockwool. The soils were samples from the Dirksen and Dasberg (1993) experiment. Their compositions are listed in Table 1 . The salinity of the soil samples was left as it appeared. The salinity of the rockwool slab and the glass beads were adjusted to and , respectively, using water–NaCl solutions. Sufficient water was left on top of the saturated samples to measure {sigma}p of the soil solution. The measurements of {epsilon}'b and {sigma}b, and also the measurement of {sigma}p (in the water left on top of the samples), were performed using the sensor of Fig. 1. This sensor measures {epsilon}'b and {sigma}b, performs the calculations, and returns only {sigma}p. The measurement of {sigma}p was checked using a laboratory four-electrode conductivity meter at 1 kHz.


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  		Table 1 Soil composition and validation results

 
Each material was dried in 10 steps by slowly extracting solution from an initially saturated and thoroughly mixed sample. In this way 10 water contents between and saturation were created. The change in {theta} was measured using a balance. Since the salinity of the pore water is not allowed to change with {theta}, drying by evaporation was avoided. The experiment was carried out at a temperature of 20°C. The measured {sigma}p values are listed in the eighth column of Table 1. The average values with their standard deviations for {sigma}p, at the 10 {theta} steps, calculated according to Eq. [14], are listed in the last two columns. The seventh column lists the measured {sigma}p of a pore water extract. Comparison of the {sigma}p values measured in the soil solution and the {sigma}p values calculated from {epsilon}'b and {sigma}b justifies the model of Eq. [14]. The values found for are listed in the sixth column.


   Discussion and conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Theory and methods
 Discussion and conclusions
REFERENCES
 
The relationship between simultaneously measured values of the real part of the permittivity, {epsilon}'b, and the electrical conductivity of the bulk soil, {sigma}b, measured at the same frequency, is to a major extent linear. {epsilon}'b and {sigma}b are equally affected by the shape of the electrodes, by the contact between electrodes and soil, and by the soil composition. In general this applies for any soil where the water content {theta} > 0.10. In addition at low water contents, thus at low {epsilon}'b values, the method becomes sensitive to the term in Eq. [14].

The intercept with the y axis, , of the linear part of the {epsilon}'b vs. {sigma}p plot is not the value one would expect for . In case of the glass beads of Fig. 2, at and , but for dry glass beads we measured . Thus, there should be a bending of the {epsilon}'b vs. {sigma}p curve near the y axis. This bending was not observed in this research. Therefore, further research on as a function of temperature and {sigma}p for different materials is desired.

Due to the linear relationship between {epsilon}'b and {sigma}b, the ionic conductivity of the pore water in the soil, {sigma}p, can be found from a simultaneous measurement of {epsilon}'b and {sigma}b independently of {theta}. Contact problems have only minor effect on {sigma}p measurements. To facilitate calibration can be used as an average. In this case, calibration of the sensor for {sigma}p is not required if {theta} > 0.1.

The presented sensor has a measurement limit at a bulk conductivity of 3 mS cm-1, but this is not the limit of the method. For high salt concentrations or for bound water {epsilon}'p may deviate from that of free water. However, as long as the actual {epsilon}'p of the pore water is known Eq. [14] can still be used.


   ACKNOWLEDGMENTS
 
The funding of this research was supported, in part, by the European Commision, project WATERMAN, number FAIR1 PL95 0681.

Received for publication June 25, 1999.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Theory and methods
 Discussion and conclusions
 REFERENCES
 




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