1.Introduction

The measurement of liquid level is very important for nuclear safeguards as well as process monitoring, control, and storage of materials used for safety and profitability, in many ordinary industrial processes [1-8]. Level measurement techniques can be classified into three categories: mechanical, electromechanical, and electronic [1]. Float, dip probes, sight gauge glasses, and a tape system, are used in mechanical methods, while a displacer, magnetostrictive device, resistance tape, rotation suppression method, and servo powered level gauge, are used in electromechanical methods. Electronic methods can be divided into two subclasses: electronic contact and electronic non-contact methods. Vibrating fork switches, a capacitance or conductivity method, a thermal dispersion technique, an ultrasonic gap sensor, and guided wave radar, are used in the electronic contacting method; whereas time domain reflectometry, non-contacting radar, and a gamma-ray radiation absorption method are used in the electronic non- contacting method. All of these methods have their own limitations [9]. For example, electromechanical displacers based on the Archimedes’ principle are easily affected by the operating conditions, such as temperature, pressure, composition, and density. In a non-contacting radar technique, the medium and surface conditions affect the measurements, and the bubbles present in the liquid can influence the results significantly. Thus, special care should be taken in the selection of a method after considering the characteristics of the processes and the applicability of each technique under each process condition.

There are three types of well-known pressure-based liquid level measurement methods: a hydrostatic pressure method, differential pressure method, and bubbler [5-8]. In the hydrostatic pressure method and differential pressure method, the pressure sensors are in direct contact with the liquid while the bubblers use the tubes immersed in the liquid, and therefore, the tubes instead of the sensors have direct contact with the liquid. If the liquids are chemically reactive or hot enough to damage the pressure sensors and tubes, pressure-based methods cannot be used. Moreover, the major disadvantages of all three conventional pressure- based methods are a dependency on the density, inhomogeneity, and conditions of the liquid medium.

In this study, we propose a new pressure-based liquid level measurement technique that can be used under extreme conditions, i.e., very hot, corrosive, and highly radioactive environments, by minimizing the damage or contamination of the tubes by liquids and the effects of the process conditions. In addition, the technique does not depend on the bulk liquid conditions such as the temperature, density, composition, and homogeneity of the liquids. Our new dynamic tube pressure method detects the liquid surface directly through the abrupt internal pressure changes inside the tube. As a preliminary study, our prototype liquid level measurement system was investigated using water at room temperature under the air conditions. In the very near future, measurements of the liquid level of molten salts at high temperatures under harsh conditions will be performed in order to examine the applicability of our in-house manufactured system, which will be installed inside the argon-atmosphere glove box.

2.Experiments

The dynamic tube pressure measurement system, as depicted in Fig. 1, consists of a linear stepper motor, a stainless steel tube connected to an air compressor, and a pressure sensor. All experiments were performed at room temperature. Ordinary tap water was placed into the cylindrical vial with a diameter of 26.3 mm and a length of 92.2 mm. The tube is brought to the surface of the water in the vial operated at room temperature by means of a stepper motor (EMS24- C1036, E-Motor, Republic of Korea) for precise positioning control. The stepper motor is controlled by a programmable logic controller (XGB Cnet I/F, LS Industrial Systems Co., Republic of Korea). A stepper motor with a resolution of 1.8°/pulse drives a stainless steel tube in downward directions at speeds of 0.125 – 5.0 mm/s. The stepper motor angular increment of 1.8°/pulse resulted in a longitudinal resolution of 2.5 μm per pulse. As soon as it touches the water surface, the tube moves back to its original position. The flow and pressure of air through the tube is controlled by a needle valve. The pressures inside the tube were monitored using a differential pressure switch and transmitter (PTA 202D-D2-D300P, CSC Co., Republic of Korea). In the first step, the tube pressure in an ambient air atmosphere is monitored at the zero position (z = 0). If the ambient pressure at z = 0 is stable with a pressure variation of less than 5 Pa for 10 seconds, the last pressure value is set as an ambient base pressure (P_a), and the tube then starts to move downward until the pressure difference between the measured tube pressure (P_t) and the ambient base pressure (P_a) exceeds the preset value of ΔP_L, which indicates that the tube touches the liquid surface. As shown in Fig.2, using a simple relation in Eq. (1), the liquid level (H) was determined from the length between z = 0 and the bottom of the vessel (L₂), the length between z = 0 and the tube tip (L₁), and the travel distance from the tube tip to the liquid surface (D) [2].

where L₂ and L₁ can be predetermined directly using rulers. However, it is very difficult to measure these two values accurately, especially in many field processes.

Four tubes of different diameters (d) and lengths (l) (see Fig. 3) were used to examine the effects of the tube dimension on the accuracy of the measurements. The effects of the ambient base pressure and the descending speed of the tube on the accuracy of the measurement were investigated. To increase the liquid level of the water samples accurately, a gravimetric method was adopted. In the gravimetric calibration method, various amounts of water were weighed using a digital balance with a 0.001 g readability, and added into the vial. The gravimetric calibration method can provide a methodology for the determination of the amount of liquid in a vessel without measurements of the hard-to-measure L₁ and L₂.

3.Results and Discussion

The purpose of this study is to determine the optimum conditions for the liquid level measurement of molten salts using an in-house manufactured prototype instrument. First, four different-sized tubes, as shown in Fig. 3, were used to examine the effect of the ambient base pressures at some arbitrary fixed experimental conditions, i.e., at a descending speed of 0.250 mm/s using 20 g of water. The tube tip-to- water surface distance was adjusted to ca. 70 mm for all four tubes using a lab jack, because the absolute liquid level values are not important in this experiment, and the relative values of the travel distance give sufficient information to examine the effect of the tube size and ambient base pressures. As shown in Table 1, the minimum ambient base pressures at which the measurement can be started, increase as the tube size decreases because the tube pressure should be high enough to generate gas bubbles from the tube immersed in the liquid. Higher base pressures are required for a smaller tube according to the following Young-Laplace equations in Eq. (2).

where R is the radius of the tubes, γ is the surface tension of the water, and ΔP is the pressure difference between the tube pressure and the hydrostatic pressure. The tube pressures represent the air flow rate. The higher the pressure, the higher the flow rate. In the case of a 0.26-mm tube, the initial ambient tube pressure (P_a) should be higher than 1,200 Pa to start the experiment, whereas 150 Pa is enough to measure the liquid level for a 0.98-mm tube. If P_a increases from 150 Pa up to 1,000 Pa, the distance (D) traveled from z = 0 to the liquid surface increases significantly owing to the strong gas flows from the tube. As P_a increases, the standard deviation of the 10-repetitive measurements also worsens from 0.03 mm to 0.24 mm owing to the large bubbles by the strong gas flows. All three other tubes exhibited better accuracy and precision, although the minimum P_a increased as the tube diameter decreased. Over the same range of P_a, D does not depend on P_a when using a 0.85-mm tube, and its standard deviation was also within 0.03 mm. Likewise, 0.34-mm and 0.26-mm tubes show good accuracy and precision at P_a up to 2,700 Pa. A larger tube can avoid clogging by dust or any other contaminants, and the base pressure can be controlled precisely through a simple needle valve, whereas it is much more difficult to control the base pressure in a very small tube. In our present measurement system, a 0.98-mm tube and 250 Pa as the base pressure were selected as the optimum conditions for further studies. In the second experiment, the effect of the descending speed of the tube on the liquid level measurement was investigated using a 0.98-mm tube and 250 Pa as the base pressure. Table 2 shows that the high-speed movement of the tube increases the D values. In field applications, the measurement time is the key to the efficient monitoring of the processes. If the speed of the moving tube increases from 0.125 mm/s to 2.5 mm/s, D is increased by around 1 mm. A tube speed of 0.25 mm/s is selected as a reasonable speed for a level measurement because it is possible to measure the liquid level with sub-millimeter accuracy and precision, which is one of our major concerns in the pyroprocess application.

In general, information on the liquid level is required to determine the amount of liquid in the vessel or to monitor any variation in the volume of the liquid in the process vessel. For such purposes, it is not necessary to measure the absolute liquid level. In fact, our present system is not appropriate for a direct measurement of the liquid level, as shown in Fig. 1. However, the measurement of the tip-tosurface distance (D) is enough, for monitoring purposes, to detect the process faults. The liquid level (H) can be calculated from the direct measurement of L₁, L₂, and D. However, the direct measurement of L₁ and L₂ is one of the major sources of the measurement errors. Instead, we propose a gravimetric calibration method for an accurate determination of the liquid weight. Fig. 4 shows the water weight vs. distance (D) curve using a 0.98-mm tube at a tube speed of 0.25 mm/s and a base pressure of 250 Pa with 15 - 45 g of water corresponding to a liquid level of ca. 2.8 - 8.3 cm calculated from the vial diameter by assuming that the vial is a perfect cylinder. The calibration curve shows a very good linear relationship between the water weight and distance (D) with a coefficient of determination (R²) of 0.9999. The standard deviations of the 10 repetitive measurements were less than 0.07 mm for all samples in Fig. 4. These values are very satisfactory compared to the conventional level gauges, whose accuracies are frequently over 1 mm. Instead of the direct measurement of L₁ and L₂ for a determination of the liquid level (H), the concept of a “calibration-free” technique is quite useful in terms of the process monitoring, because the accurate measurement of L₂ and L₁ are sometimes very difficult in field processes. By adopting the concept of a calibration-free technique, a precise determination of distance (D) is only enough to monitor and control the amount of liquids in a field process.

4.Conclusions

In conventional pressure-based methods such as the hydrostatic method, differential pressure, and bubbler methods, the major source of measurement errors is the temperature inside the liquid solutions throughout the measurement because the temperature variation influences the liquid density and the hydrostatic pressure values the actual liquid level not being changed. The liquid density is also dependent on the process conditions, e.g., compositional changes, phase separation, presence of suspended particles, and bubbles. However, our present dynamic tube pressure method which detects the surface through abrupt pressure changes at the gas/liquid surface, does not depend on such process conditions of the melts.

As a preliminary study for the development of a liquid level measurement system suitable for high- temperature pyrochemical application, a prototype measurement system was investigated using a simple, single tube controlled by a stepper motor for the water samples. Experimental parameters such as the gas flow rate, descending speed of the tube, and critical pressure level were determined carefully for the best results. In general, the measurement errors were less than 0.1 mm. The smaller the diameter of the tube, the higher the gas flow rate required for better results. However, when the gas flow rate is too high, the accuracy becomes worse. The effect of the descending speed of the tube is not significant within the range examined in this study. We also developed a methodology for determining the weight of the liquid in the vessels measuring the travel distance from the tube tip-to-liquid surface. In most applications, the information on the travel distance is enough in the process monitoring.

In a further study, our prototype of the liquid measurement system will be improved to measure the density and surface tension, as well as the liquid level, of high-temperature molten salts inside the glove box with an electric furnace. In the case of a high-temperature application, special care should be taken because the molten salts are very hot and corrosive. The time of contact with the molten salt should be minimized.