Dynamic calibration method for a trace moisture analyzer based on the quick response of a ball surface acoustic wave sensor

Figure 1(a) shows a schematic diagram of the static calibration system. The calibration gas is prepared by two-step dilution of saturated water vapor generated in a saturator. The saturator is controlled at the pressure of 400 kPa and the temperature of 25 °C. First, the flow ratio between wet gas passing through the saturator and dry gas is controlled by a mass flow controller (MFC) 1 and MFC 2 to dilute the wet gas in the range of 1–200 times. Next, the diluent gas is further diluted in the range of 1–200 times by MFC 3 and MFC 4. Then, the conditioned gas is introduced into a sensor cell at a flow rate controlled by MFC 5. Here, the pressure in the sensor cell is 100 kPa. The flow rate of gas passing through MFC 3 should not be larger than total amount of gas passing through MFC 1 and MFC 2, and the excess gas is exhausted by an automatic pressure regulator (APR) 1. Similarly, the flow rate of gas passing through MFC 5 should not be larger than total amount of gas passing through MFC 3 and MFC 4, and the excess gas is exhausted by APR 2. In this way, this system can change the moisture concentration around the sensor and calibrate in the range of frost point from −87 to 4 °C.

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Figure 1(b) is an example of the ball SAW sensor response when the moisture concentration is changed stepwise using this system. This graph shows the temporal variation of the attenuation α as the response of the ball SAW sensor in 10 h when the moisture concentration evaluated as the frost point (FP) was changed in steps from −76 °C to −17 °C. From this data, a calibration curve of the relationship between the FP and the attenuation α can be obtained.

In figure 2(a), the relationships between the FP and the attenuation α of the ball SAW sensor obtained by the static calibration system are plotted as open circles. Here, we found that the relationship indicated as a dotted curve can be expressed as a function of α given by

$$\begin{equation}{\text{FP}} = A\alpha + B - {10^{C\alpha + D}},\end{equation} \tag{ 1 }$$

where A, B, C, and D are coefficients, which are characteristics of each sensor. That is, the calibration of the ball SAW sensor means the determination of these coefficients. When the FP is above −25 °C, the FP can be approximated to be almost linear to α neglecting the exponential term of equation (1) as

$$\begin{equation}{\text{FP}} = A\alpha + B.\end{equation} \tag{ 2 }$$

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Therefore, the coefficients A and B can be determined by a least squares fitting of the data in the high concentration range. Furthermore, equation (1) can be transformed to

$$\begin{equation}{\log _{10}}\left( {A\alpha + B - {\text{FP}}} \right) = C\alpha + D,\end{equation} \tag{ 3 }$$

expressing the exponential term of equation (1) as a linear function. Figure 2(b) shows the relationship between α and the values on the left-hand side of equation (3) using data in the low FP range. Therefore, the coefficients C and D can be determined by a least squares fitting. By using these coefficients, we can obtain the calibration curve for this sensor as

$$\begin{equation}{\text{FP}} = 1.279\alpha - 182.8 - {10^{ - 0.1776\alpha + 21.56}}.\end{equation} \tag{ 4 }$$

Furthermore, since it was found that each coefficient is almost linear to the sensor temperature near room temperature, it can be expressed by a linear function of the sensor temperature. Therefore, the coefficients for temperature compensation can be determined by fitting each coefficient from the relationship between the FP and the attenuation by changing the sensor temperature. In this paper, since the measurement was performed at a constant temperature, the explanation for the coefficient related to temperature compensation is omitted.

A schematic diagram of the system we developed is shown in figure 3. This system is composed of a saturated water vapor generator and a flow-controlled gas line leading to a moisture sensor. This line has an inlet to inject saturated water vapor upstream of the sensor. When the saturated water vapor is injected, the water vapor is carried to the moisture sensor by diffusion and drifting through the piping, and a sensor response is obtained, which varies with time owing to the change in moisture concentration.

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As a saturated water vapor generator, we use a sampling gas bag for gas analysis, whose inner surface was inactivated, as shown in figure 4(a). The size of the gas bag is 1 l. After purging the gas bag with nitrogen gas, pure water is injected into the bag and the bag is saturated with water vapor at room temperature controlled by an air conditioner. As an injector, we use a gas-tight syringe, with which we can control the injection volume using its scale. The saturated water vapor is extracted from the gas bag and injected into the inlet provided 170 mm upstream of the ball SAW sensor connected to the nitrogen pipe by manual operation of the gas-tight syringe. The dry nitrogen gas line is shown in figure 4(b). The sensor is in a small cell whose volume is 1.4 ml. The nitrogen gas flow is controlled using a mass flow controller. This injection is used both for the evaluation of response time and for a dynamic calibration, which will be described in section 4.

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We installed a ball SAW sensor into the system we developed and measured the attenuation by injecting saturated water vapor. The injection volume was 1 ml and the flow rate of the background gas was 100 ml min⁻¹. At this time, the room temperature was 21.6 °C. Response time was evaluated as the time within which a 10%–90% increase in the FP was observed after the injection of saturated water vapor.

Figure 5(a) shows a temporal variation of the FP due to the injection of saturated water vapor measured using the ball SAW sensor. The FP increased immediately after injection and then decreased gradually. The decrease took about 10 min and is considered to represent a process at which the water adsorbed on the pipe surface was gradually desorbed. The expanded view of the peak is shown in figure 5(b). The response time taken for 10%–90% of the FP change from −70 °C to 10 °C was only 0.64 s. It is considered to be the shortest response time of the trace moisture analyzer reported so far.

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Furthermore, since the response time is less than 1 s, it can be regarded that the equilibrium between the water concentration within the sensitive film and that in the atmosphere is rapidly reached at any instance of the dynamic calibration process, which takes 10 min. This rapid equilibrium is the basis for the validity of the dynamic calibration process.

First, to obtain a reference data for dynamic calibration, we install a ball SAW sensor calibrated by the static method described in section 2 into the developed system and measure the temporal variation of the attenuation by the injection of saturated water vapor. The temporal variation of the FP can be obtained by substituting the attenuation α at each time in equation (4).

Next, the ball SAW sensor is replaced with a new sensor to be calibrated, and the temporal variation of the attenuation α is measured for 10 min under the same conditions as when the reference data was measured. The calibration curve of this sensor is derived as the relationship between the attenuation α and the FP of the reference data at the same time. Finally, the sensor is calibrated again by the static method and the calibration curve obtained is compared with that obtained by the dynamic calibration method.

The measurement result for the reference data is shown in figure 6 at a background gas flow rate of 10 ml min⁻¹, a saturated water vapor injection volume of 1 ml, and a room temperature of 21 °C. From the temporal variation of the attenuation α after the injection of saturated water vapor, as shown in figure 6(a), that of FP was obtained using the calibration curve obtained using equation (4), as shown in figure 6(b). Since the rising part of the peak changes rapidly, it is not used for the calibration, and the gradually decreasing part of the curve shown in red is used as reference data.

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The attenuation α of a new sensor under the same condition as the measurement for the reference data is shown by the black curve in figure 7(a). Using the reference data shown by the red curve at the same time, we obtained the FP at the right axis. Figure 7(b) shows the relationship between the attenuation α and the FP in the high concentration range as shown by closed circles. Since this relationship is almost linear, the coefficients of calibration curves A and B were determined to be A = 1.188 and B = −94.41 by a least squares fitting. On the other hand, figure 7(c) shows the relationship between the attenuation α and the function on the left-hand side of equation (3) in the low concentration range as shown by open circles. Since this relationship is also linear, coefficients C and D were determined to be C = −0.1983 and D = 11.88 by a least squares fitting. Therefore, the calibration curve of this sensor obtained by the dynamic calibration method is given by

$$\begin{equation}{\text{FP}} = 1.188\alpha - 94.41 - {10^{ - 0.1983\alpha + 11.88}}.\end{equation} \tag{ 5 }$$

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On the other hand, the calibration curve of the same sensor obtained by the static calibration method is given by

$$\begin{equation}{\text{FP}} = 1.257\alpha - 101.3 - {10^{ - 0.1994\alpha + 11.86}}.\end{equation} \tag{ 6 }$$

In figure 8, the result of dynamic calibration curve using equation (5) is shown as a solid curve and that of the static calibration curve using equation (6) is shown as a dotted curve. These two curves look nearly identical.

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