# CALIBRATING TOROIDAL CONDUCTIVITY SENSORS

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1 Application Data Sheet ADS October 2010 Theory CALIBRATING TOROIDAL CONDUCTIVITY SENSORS BACKGROUND A toroidal conductivity sensor consists of two wire wound toroids encased in a plastic body. When an alternating voltage is applied to one of the toroids, it induces an ionic current in the surrounding the sensor. The ionic current, in turn, induces an electronic current in the second toroid, which the analyzer measures. The current in the second toroid depends on the number of turns of wire on each toroid and on the conductance of the. The conductance depends on the total ion concentration (the conductivity) and the area and length of the ionic current flows through. The physical dimensions of the sensor determine the dimensions of the current path. Because the purpose of the measurement is to get information about the total concentration of ions in, i.e., the conductivity, the effect of sensor dimensions and windings has to be accounted for. The correction factor is the cell constant. Conductivity is equal to the measured conductance multiplied by the cell constant. The cell constant is simply a calibration factor that converts conductance (measured in ms) to conductivity (measured in ms/cm). The units of cell constant are 1/cm. Figure 1 illustrates the relationship. Note that the slope of the calibration line is the cell constant. conductivity, ms/cm conductance, ms m = 1/cm (cell constant) FIGURE 1. Graphical representation of the cell constant. The analyzer measures the conductance (x-axis) and converts the result to conductivity (y-axis) using the calibration line. The slope of the calibration line is the cell constant. The cell constant is also influenced by the nearness of the vessel walls to the sensor, the so-called wall effect. Conductive and non-conductive walls have opposite effects. Metal walls increase the amount of induced current, which leads to an apparent increase in conductance and a corresponding decrease in cell constant. Plastic walls have the opposite effect. As the Figure 2 shows, the magnitude of the wall effect also depends on the orientation of the sensor with respect to the walls. % increase in conductivity flat face approaches wall cylindrical face approaches wall distance from wall, inches FIGURE 2. Wall effects in a flat-sided metal container. Nearness of the flat face of the toroids to the wall has a much greater influence on conductance than nearness of the curved sides. Wall effects generally disappear when the distance between the sensor and wall is about ¾ of the diameter of the sensor. Because nearly every installation involves some degree of wall effect, there is little value in calibrating toroidal sensors at the factory. Instead, they must be calibrated in the field. Typically, the sensor is calibrated in place in the process piping. CALIBRATION METHODS There are two basic ways to calibrate a toroidal sensor: against a or against a referee meter and sensor. A referee meter and sensor is an instrument that has been previously calibrated and is known to be accurate and reliable. The referee instrument can be used to perform either an in-process or a grab sample calibration. In-process calibration involves connecting the process and referee sensors in series and measuring the conductivity of the process liquid simultaneously. Grab sample calibration involves taking a sample of the process liquid and measuring its conductivity in the laboratory or shop using the referee instrument. No matter which calibration method is used, the analyzer automatically calculates the cell constant once the known conductivity is entered.

2 Calibration against a Calibration against a requires removing the sensor from the process piping. It is practical only if wall effects are absent or the sensor can be calibrated in a container identical to the process piping. The latter requirement ensures that wall effects during calibration, which are incorporated into the cell constant, will be exactly the same as the wall effects when the sensor is in service. Toroidal conductivity sensors are normally used to measure liquids having fairly high conductivity, so s having similarly high conductivity are generally most suitable for calibration. Standard s having conductivity as high as 200,000 us/cm (at 25 C) are commercially available. High conductivity s can also be prepared in the laboratory following procedures in ASTM D1125 or Standard Methods International Electrotechnical Commission Standard 746-3, Appendix B, Tables BI, BII, and BIII also contains procedures for preparing high conductivity s. The calibration procedure is fairly straightforward. Immerse the rinsed sensor in the and adjust the analyzer reading to match the conductivity of the. For an accurate calibration several precautions are If wall effects are absent in the installation use a sufficiently large container to ensure that wall effects are also absent during calibration. To check for wall effects, fill the container with and place the sensor in the center submerged at least ¾ of the way up the stem. Note the reading. Then move the sensor small distances from the center and note the reading in each position. The readings should not change. If wall effects are present, be sure the vessel used for calibration has exactly the same dimensions as the process piping. Also, ensure that the orientation of the sensor with respect to the piping is exactly the same in the process and calibration vessels. See Figure 3. will be used. However, toroidal conductivity sensors have good linearity, so any greater than about 5000 us/cm at 25 C is adequate. Turn off automatic temperature compensation in the analyzer. Almost all process conductivity analyzers feature automatic temperature compensation in which the analyzer applies one of several temperature correction algorithms to convert the measured conductivity to the value at a reference temperature, typically 25 C. Although temperature correction algorithms are useful for routine measurements, they should not be used during calibration. There are two reasons. First, no temperature correction algorithm is perfect. If the assumptions behind the algorithm do not perfectly fit the being measured, the temperaturecorrected conductivity will be in error. Second, if the temperature measurement itself is in error, the corrected conductivity will be in error. The purpose of calibrating the sensor is to determine the cell constant. To minimize the error in the cell constant, all sources of avoidable error i.e., temperature compensation, should be eliminated. Use a for which the conductivity as a function of temperature is known. The information will usually be on the bottle label. If not, it can often be calculated if the identity and concentration of the electrolyte is known. Use a good quality calibrated thermometer to measure the temperature of the. The thermometer error should be less than ±0.1 C. Allow adequate time for the and sensor to reach thermal equilibrium. If the sensor is being calibrated in an open beaker, keep the thermometer far enough away from the sensor so it does not introduce wall effects. If the sensor is being calibrated in a pipe tee or similar vessel, it will probably be impractical to place the thermometer in the. Instead, put the thermometer in a beaker of water placed next to the calibration vessel. Let both come to thermal equilibrium with the ambient air before continuing the calibration. See Figure blank flange thermometer flow sensor in process piping pipe tee identical to process pipe tee sensor being calibrated FIGURE 3. Calibrating sensor in a container identical to the process piping. The calibration vessel is a pipe tee exactly the same size as the process pipe tee. Note that the sensor orientation is the same in both cases. The opening faces the pipe wall. Ideally, the conductivity of the should be close to the middle of the range over which the sensor pipe tee FIGURE 4. Measuring the temperature during calibration. Avoid wall effects by keeping the thermometer at least ¾ of the toroid diameter away from the sensor. If it is impractical to place the sensor in the, put it in a container of water placed next to the calibration vessel. Allow ample time for thermal equilibration. If the conductivity of the is known only at 25 C, the temperature of the must be adjusted to 25.0 ± 0.1 C before completing the cali- 2 Rosemount Analytical

5 LIMITATIONS There are two important facts to keep in mind about calibration methods described above. First, the calibration is done at a single point. There is no certainty that the cell constant calculated at the calibration point will be exactly the same at other conductivity values. However, toroidal conductivity sensors are usually highly linear. Therefore, as long as the sensor is used in the recommend conductivity range, the cell constant will be reasonably close to the value at the calibration point. For example, when a Model 228 sensor is used with a Model 1056 analyzer between and 1500 ms/cm, the expected variability in the cell constant is ±1%. Second, the analyzer and sensor are calibrated as a unit. Thus, any error in the conductance (at the calibration point) measured by the analyzer is automatically incorporated into the cell constant. When the sensor is used with a different analyzer, which may have a slightly different error at the calibration point, the cell constant may be slightly in error. ACCURACY The accuracy of the calibration depends on the calibration method. For calibration against a, the accuracy depends on the accuracy of the itself and the accuracy of the temperature measurement. For routine work using a good quality and thermometer, the uncertainty is probably between 0.5 and 1.0%. For calibration against a referee instrument, either in-process or using a grab sample, the errors are greater. Error in the conductivity measured by the referee instrument, which includes the uncertainty in the conductivity of the used to calibrate it, and the variability of the cell constant over the operating range of the referee sensor are the major causes of the increased error. Of course, if the in process calibration is done at the same conductivity the referee instrument was calibrated, the error will be less. For calibration using a grab sample, the error will be even greater. The additional uncertainty arises from temperature measurement errors and failure of the temperature correction algorithm to perfectly correct for conductivity changes caused by temperature. The right people, the right answers, right now. ON-LINE ORDERING NOW AVAILABLE ON OUR WEB SITE 8 Credit Cards for U.S. Purchases Only. Emerson Process Management 2400 Barranca Parkway Irvine, CA USA Tel: (949) Fax: (949) Rosemount Analytical Inc. 2010

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