Science and Engineering of Level Measurement

Intro

Level measurement is required in a wide range of applications and can involve the measure of solids in the form of powders or small particles as well as liquids. While some applications require levels to be measured to a high degree of accuracy, other applications only need approximate indication of level. A wide variety of instruments are available to meet these differing needs.

Simple devices such as dipsticks or float systems are relatively inexpensive. Although o offering limited measurement accuracy, they are entirely adequate for applications and f widespread use. A number of higher accuracy devices are also available for applications require a better level of accuracy. The list of devices in common use that offer good measured accuracy includes pressure-measuring devices, capacitive devices, ultrasonic devices, rad devices, and radiation devices. A number of other devices used less commonly are also available. All of these devices are discussed in more detail below.

Dipsticks

Dipsticks offer a simple means of measuring the level of liquids approximately. The ordinary dipstick is the least expensive device available. This consists of a metal bar on which a scale is etched. The bar is fixed at a known position in the liquid containing vessel. A level measurement is made by removing the instrument from the vessel and reading off how far up the scale the liquid has wetted. As a human operator is required to remove and read the dipstick, this method can only be used in relatively small and shallow vessels. One common use is in checking the remaining amount of beer in an ale cask.

The optical dipstick is an alternative form that allows a reading to be obtained without removing the dipstick from the vessel and so is applicable to larger, deeper tanks. Light from a source is reflected from a mirror, passes round the chamfered end of the dipstick, and enters a light detector after reflection by a second mirror. When the chamfered end comes into contact with liquid, its internal reflection properties are altered and light no longer enters the detector. By using a suitable mechanical drive system to move the instrument up and down and measure its position, the liquid level can be monitored.

Float Systems

Float systems are simple and inexpensive and provide an alternative way of measuring the level of liquids approximately that is widely used. The system consists of a float on the surface of the liquid whose position is measured by means of a suitable transducer. They have a typical measurement inaccuracy of _1%. The system using a potentiometer is very common and is well known for its application to monitoring the level in motor vehicle fuel tanks. An alternative system, which is used in greater numbers, is called the float-and-tape gauge (or tank gauge). This has a tape attached to the float that passes round a pulley situated vertically above the float. The other end of the tape is attached to either a counterweight or a negative-rate counterspring. The amount of rotation of the pulley, measured by either a synchro or a potentiometer, is then proportional to the liquid level. These two essentially mechanical systems of measurement are popular in many applications, but the maintenance requirements of them are always high.

--- Pressure transducer; Flow of gas; Differential pressure transducer; Differential pressure transducer

Pressure-Measuring Devices (Hydrostatic Systems)

Pressure-measuring devices measure the liquid level to a better accuracy and use the principle that the hydrostatic pressure due to a liquid is directly proportional to its depth and hence to the level of its surface. Several instruments are available that use this principle and are widely used in many industries, particularly in harsh chemical environments. In the case of open-topped vessels (or covered ones that are vented to the atmosphere), the level can be measured by inserting a pressure sensor at the bottom of the vessel. The liquid level, h, is then related to the measured pressure, P, according to h=P/rg, where r is the liquid density and g is acceleration due to gravity. One source of error in this method can be imprecise knowledge of the liquid density. This can be a particular problem in the case of liquid solutions and mixtures (especially hydrocarbons), and in some cases only an estimate of density is available. Even with single liquids, the density is subject to variation with temperature, and therefore temperature measurement may be required if very accurate level measurements are needed.

Where liquid-containing vessels are totally sealed, the liquid level can be calculated by measuring the differential pressure between the top and the bottom of the tank.

The differential pressure transducer used is normally a standard diaphragm type, although silicon based microsensors are being used in increasing numbers. The liquid level is related to the differential pressure measured, dP, according to h=dP/rg. The same comments as for the case of the open vessel apply regarding uncertainty in the value of r. An additional problem that can occur is an accumulation of liquid on the side of the differential pressure transducer measuring the pressure at the top of the vessel. This can arise because of temperature fluctuations, which allow liquid to alternately vaporize from the liquid surface and then condense in the pressure tapping at the top of the vessel. The effect of this on the accuracy of the differential pressure measurement is severe, but the problem is avoided easily by placing a drain pot in the system.

A final pressure-related system of level measurement is the bubbler unit shown.

This uses a dip pipe that reaches to the bottom of the tank and is purged free of liquid by a steady flow of gas through it. The rate of flow is adjusted until gas bubbles are just seen to emerge from the end of the tube. The pressure in the tube, measured by a pressure transducer, is then equal to the liquid pressure at the bottom of the tank. It’s important that the gas used is inert with respect to the liquid in the vessel. Nitrogen, or sometimes just air, is suitable in most cases. Gas consumption is low, and a cylinder of nitrogen may typically last 6 months. This method is suitable for measuring the liquid pressure at the bottom of both open and sealed tanks.

It’s particularly advantageous in avoiding the large maintenance problem associated with leaks at the bottom of tanks at the site of pressure tappings required by alternative methods.

Measurement uncertainty varies according to the application and condition of the measured material. A typical value would be _0.5% of full-scale reading, although _0.1% can be achieved in some circumstances.

Capacitive Devices

Capacitive devices are widely used for measuring the level of both liquids and solids in powdered or granular form. They perform well in many applications, but become inaccurate if the measured substance is prone to contamination by agents that change the dielectric constant. Ingress of moisture into powders is one such example of this. They are also suitable for use in extreme conditions measuring liquid metals (high temperatures), liquid gases (low temperatures), corrosive liquids (acids, etc.), and high-pressure processes. Two versions are used according to whether the measured substance is conducting or not. For nonconducting substances (less than 0.1 mmho/cm^3), two bare-metal capacitor plates in the form of concentric cylinders are immersed in the substance. The substance behaves as a dielectric between the plates according to the depth of the substance. For concentric cylinder plates of radius a and b (b > a), and total height L, the depth of the substance, h, is related to the measured capacitance, C, by ...

[…]

...where E is the relative permittivity of the measured substance and Eo is the permittivity of free space. In the case of conducting substances, exactly the same measurement techniques are applied, but the capacitor plates are encapsulated in an insulating material. The relationship between C and h, then has to be modified to allow for the dielectric effect of the insulator. Measurement uncertainty is typically 1-2%.

Ultrasonic Level Gauge

Ultrasonic level measurement is one of a number of noncontact techniques available. It’s used primarily to measure the level of materials that are either in a highly viscous liquid form or in solid (powder or granular) form. The principle of the ultrasonic level gauge is that energy from an ultrasonic source above the material is reflected back from the material surface into an ultrasonic energy detector. Measurement of the time of flight allows the level of the material surface to be inferred. In alternative versions (only valid for liquids), the ultrasonic source is placed at the bottom of the vessel containing the liquid, and the time of flight between emission, reflection off the liquid surface, and detection back at the bottom of the vessel is measured.

Ultrasonic techniques are especially useful in measuring the position of the interface between two immiscible liquids contained in the same vessel or measuring the sludge or precipitate level at the bottom of a liquid-filled tank. In either case, the method employed is to fix the ultrasonic transmitter-receiver transducer at a known height in the upper liquid.

This establishes the level of the liquid/liquid or liquid/sludge level in absolute terms. When using ultrasonic instruments, it’s essential that proper compensation is made for the working temperature if this differs from the calibration temperature, as the speed of ultrasound through air varies with temperature. Ultrasound speed also has a small sensitivity to humidity, air pressure, and carbon dioxide concentration, but these factors are usually insignificant. Temperature compensation can be achieved in two ways. First, the operating temperature can be measured and an appropriate correction made. Second, and preferably, a comparison method can be used in which the system is calibrated each time it’s used by measuring the transit time of ultrasonic energy between two known reference points. This second method takes account of humidity, pressure, and carbon dioxide concentration variations as well as providing temperature compensation. With appropriate care, measurement uncertainty can be reduced to about _1%.

Radar (Microwave) Sensors

Level-measuring instruments using microwave radar are an alternative technique for noncontact measurement. Currently, they are still very expensive (_$6000), but prices are falling and usage is expanding rapidly. They are able to provide successful level measurement in applications that are otherwise very difficult, such as measurement in closed tanks, where the liquid is turbulent, and in the presence of obstructions and steam condensate. They can also be used for detecting the surface of solids in powder or particulate form. The technique involves directing a constant amplitude, frequency-modulated microwave signal at the liquid surface. A receiver measures the phase difference between the reflected signal and the original signal transmitted directly through air to it. This measured phase difference is linearly proportional to the liquid level. The system is similar in principle to ultrasonic level measurement, but has the important advantage that the transmission time of radar through air is almost totally unaffected by ambient temperature and pressure fluctuations.

However, as the microwave frequency is within the band used for radio communications, strict conditions on amplitude levels have to be satisfied, and the appropriate licenses have to be obtained.

Nucleonic (or Radiometric) Sensors

Nucleonic, sometimes called radiometric, sensors are relatively expensive. They use a radiation source and detector system located outside a tank in the manner. The noninvasive nature of this technique in using a source and detector system outside the tank is particularly attractive. The absorption of both b and g rays varies with the amount of material between the source and the detector, and hence is a function of the level of the material in the tank. Cesium-137 is a commonly used g-ray source. The radiation level measured by the detector, I, is related to the length of material in the path, x, according to ...

[…]

... where Io is the intensity of radiation that would be received by the detector in the absence of any material, m is the mass absorption coefficient for the measured material, and r is the mass density of the measured material.

Radiation follows a diagonal path across the material, and therefore some trigonometrical manipulation has to be carried out to determine material level h from x. In some applications, the radiation source can be located in the center of the bottom of the tank, with the detector vertically above it. Where this is possible, the relationship between radiation detected and material level is obtained by directly substituting h in place of x in Equation (2). Apart from use with liquid materials at normal temperatures, this method is used commonly for measuring the level of hot, liquid metals and also solid materials in a powdered granular form.

Unfortunately, because of the obvious dangers associated with using radiation sources, very strict safety regulations have to be satisfied when applying this technique. Very low activity radiation sources are used in some systems to overcome safety problems, but the system is then sensitive to background radiation and special precautions have to be taken regarding the provision of adequate shielding. Because of the many difficulties in using this technique, it’s only used in special applications.

Other Techniques

Vibrating Level Sensor:

The principle of the vibrating level sensor. The instrument consists of two piezoelectric oscillators fixed to the inside of a hollow tube that generate flexural vibrations in the tube at its resonant frequency. The resonant frequency of the tube varies according to the depth of its immersion in the liquid. A phase-locked loop circuit is used to track these changes in resonant frequency and adjust the excitation frequency applied to the tube by the piezoelectric oscillators. The liquid level measurement is therefore obtained in terms of the output frequency of the oscillator when the tube is resonating.

Laser Methods:

One laser-based method is the reflective level sensor. This sensor uses light from a laser source that is reflected off the surface of the measured liquid into a line array of charge-coupled devices. Only one of these will sense light, according to the level of the liquid. An alternative, laser-based technique operates on the same general principles as the radar method described earlier but uses laser-generated pulses of infrared light directed at the liquid surface. This is immune to environmental conditions and can be used with sealed vessels, provided that a glass window is at the top of the vessel.

Intelligent Level-Measuring Instruments

Most types of level gauges are now available in intelligent form. Pressure-measuring devices are obvious candidates for inclusion within intelligent level-measuring instruments, and versions claiming 0.05% inaccuracy are now on the market. Such instruments can also carry out additional functions, such as providing automatic compensation for liquid density variations.

Microprocessors are also used to simplify installation and setup procedures.

Choice between Different Level Sensors

The first consideration in choosing a level sensor is whether it’s a liquid or a solid that is being measured. The second consideration is the degree of measurement accuracy required.

If it’s liquids being measured and a relatively low level of accuracy is acceptable, dipsticks and float systems would often be used. Of these, dipsticks require a human operator, whereas float systems provide an electrical output that can be recorded or output to an electronic display as required.

Where greater measurement accuracy is required in the measurement of liquid level, a number of different devices can be used. These can be divided into two distinct classes according to whether the instrument does or does not make contact with the material whose level is being measured. The advantage of noncontact devices is that they have a higher reliability than contact devices for a number of reasons. All pressure-measuring devices (hydrostatic systems) fall into the class of a device that does make contact with the measured liquid and are used quite frequently. However, if there is a particular need for high reliability, noncontact devices such as capacitive, ultrasonic, or radiation devices are preferred. Of these, capacitive sensors are used most commonly but are unsuitable for applications where the liquid may become contaminated, as this changes its dielectric constant and hence the capacitance value. Ultrasonic sensors are less affected by contamination of the measured fluid but only work well with highly viscous fluids. Radar (microwave) and radiation sensors have the best immunity to changes in temperature, composition, moisture content, and density of the measured material and so are preferred in many applications. However, both of these are relatively expensive. Further guidance on this can be found in elsewhere.

In the case of measuring the level of solids (which must be in powdered or particle form), the choice of instrument is limited to the options of capacitive, ultrasonic, radar (microwave), and radiation sensors. As for measuring the level of liquids, radar and radiation sensors have the best immunity to changes in temperature, composition, moisture content, and density of the measured material and so are preferred in many applications. However, they both have a high cost. Either capacitive or ultrasonic devices provide a less expensive solution. Capacitive devices generally perform better but become inaccurate if the measured material is contaminated, in which case ultrasonic sensors are preferred out of these two less expensive solutions.

Calibration of Level Sensors

The sophistication of calibration procedures for level sensors depends on the degree of accuracy required. If the accuracy demands are not too high and a tank is relatively shallow, a simple dipstick inserted into a tank will suffice to verify the output reading of any other form of level sensor being used for monitoring the liquid level in the tank. However, this only provides one calibration point. Other calibration points can only be obtained by putting more liquid into the tank or by emptying some liquid from the tank. Such variation of the liquid level may or may not be convenient. However, even if it can be done without too much disturbance to normal use of the tank, the reading from the dipstick is of very limited accuracy because of the ambiguity in determining the exact point of contact between the dipstick and the meniscus of the liquid.

If the dipstick method is not accurate enough or is otherwise unsuitable, an alternative method of calibrating the level is to use a calibration tank that has vertical sides and a flat bottom of known cross-sectional area. Tanks with circular bottoms and rectangular bottoms are both used commonly. With the level sensor in situ, measured quantities of liquid are emptied into the tank. This increases the level of liquid in the tank in steps, and each step creates a separate calibration point. The quantity of liquid added at each stage of the calibration process can be measured either in terms of its volume or in terms of its mass. If the volume of each quantity of liquid added is measured, knowledge of the cross-sectional area of the tank bottom allows the liquid level to be calculated directly. If the mass of each quantity of liquid added is measured, the specific gravity of the liquid has to be known in order to calculate its volume and hence the liquid level. In this case, use of water as the calibration liquid is beneficial because its specific gravity is unity and therefore the calculation of level is simplified.

To measure added water in terms of its volume, calibrated volumetric measures are used. If a 1-liter measure is used, this has a typical inaccuracy of 0.1%. Unfortunately, errors in the measurement of each quantity of water added are cumulative, and therefore the possible error after 10 quantities of water have been added increases 10-fold to 1.0%. If 20 quantities are added to create 20 calibration points, the possible error is 2.0% and so on.

Better accuracy can be obtained in the calibration process if the added water is measured in terms of its mass. This can be done conveniently by mounting the calibration tank on an electronic load cell. The typical inaccuracy of such a load cell is _0.05% of its full-scale reading. So, the inaccuracy of the level measurement when the tank is full is 0.05% if the load cell is chosen such that it’s giving its maximum output mass reading when the tank is full. Because the total mass of water in the tank is measured at each point in the calibration process, measurement errors are not cumulative. However, errors do increase for smaller volumes of water in the tank because measurement uncertainty is expressed as a percentage of the full-scale reading of the load cell. Therefore, when the tank is only 10% full, the possible measurement error is +-0.5%. So, calibration inaccuracy increases for smaller quantities of water in the tank but measurement uncertainty is always less than the case where measured volumes of water are added to the tank even for low levels.

Wherever possible, liquid used in the calibration tank is water, as this avoids the cost involved in using any other liquid and it also makes the calculation of level simpler when the quantities of water added to the tank are measured in terms of their volume. Unfortunately, liquid used in the tank often has to be the same as that which the sensor being calibrated normally measures.

E.g., the specific gravity of the measured liquid is crucial to the operation of both hydrostatic systems and capacitive level sensors. Another example is level measurement using a radiation source, as the passage of radiation through the liquid between the source and the detector is affected by the nature of the liquid.

Summary

We have seen that level sensors can be used to measure the position of the surface within some type of container of both solid materials in the form of powders and of liquids. We have looked at various types of level sensors, following which we considered how the various forms of level sensors available could be calibrated.

One very important observation made at the start of our discussion was that the accuracy requirements during level measurement vary widely, which has an important effect on the type of sensor used in any given situation and the corresponding calibration requirements. So, if the surface level of a liquid within a tank used for cooling purposes in an industrial process is being monitored, only a very approximate measurement of level is needed to allow a prediction about how long it will be before the tank needs refilling. However, if the level of liquid of a consumer product within a container is being monitored during the filling process, high accuracy is required in the measurement process.

Where only approximate measurements of liquid level are needed, we saw that dipsticks provide a suitable, low-cost method of measurement, although these require a human operator and so cannot be used as part of an automatic level control system. Float systems are also relatively low-cost instruments and have an electrical form of output that can be used as part of an automatic level control system, although the accuracy is little better than that of dipsticks.

Our discussion then moved on to sensors that provide greater measurement accuracy. First among these were hydrostatic systems. These are widely used in many industries for measuring the liquid level, particularly in harsh chemical environments. Measurement uncertainty is usually about +-0.5% of full-scale reading, although this can be reduced to +-0.1% in the best hydrostatic systems. Because accurate knowledge of the liquid density is important in the operation of hydrostatic systems, serious measurement errors can occur if these systems are used to measure the level of mixtures of liquids, as the density of such mixtures is rarely known to a sufficient degree of accuracy.

Moving on to look at capacitive level sensors, we observed that these were widely used for measuring the level of both liquids and solids in powdered or granular form, with a typical measurement uncertainty of 1-2%. They are particularly useful for measuring the level of difficult materials such as liquid metals (high temperatures), liquid gases (low temperatures), and corrosive liquids (acids, etc.). However, they become inaccurate if the measured substance is prone to contamination by agents that change the dielectric constant.

Next on the list of devices studied was the ultrasonic level sensor. We noted that this is one of a number of noncontact techniques available. It’s used primarily to measure the level of materials that are either in a highly viscous liquid form or in solid (powder or granular) form.

We also observed that it’s particularly useful for measuring the position of the interface between two immiscible liquids contained in the same vessel, and also for measuring the sludge or precipitate level at the bottom of a liquid-filled tank. The lowest measurement uncertainty achievable is _1%, but errors increase if the system is not calibrated properly, particularly in respect of the ambient temperature because of the changes in ultrasound speed that occur when the temperature changes.

The discussion then moved on to radar sensors, another noncontact measurement technique.

We saw that this, albeit very expensive, technique provided a method for measuring the level in conditions that are too difficult for most other forms of level sensors. Such conditions include measurement in closed tanks, where the liquid is turbulent, and in the presence of obstructions and steam condensate. Like ultrasonic sensors, they can also measure the level of solids in powder or granular form.

We then looked at nucleonic sensors. These provide yet another means of noncontact level measurement that finds niche applications in measuring the level of hot, molten metals and also in measuring the level of powdered or granular solids. However, apart from the high cost of nucleonic sensors, it’s necessary to adhere to very strict safety regulations when using such sensors.

Having then looked briefly at two other less common level sensors, namely the vibrating level sensor and laser-based sensors, we went on to make brief comments about intelligent level sensors. We noted that most of the types of level sensors discussed were now available in an intelligent form that quoted measurement uncertainty values down to _0.05%.

The final subject covered in this section was that of level sensor calibration. We noted that devices such as a simple dipstick could be used to calibrate sensors that were only required to provide approximate measurements of level. However, for more accurate calibration, we observed that it was usual to use a calibrated tank in which quantities of liquid were added, measured either by weight or by volume, to create a series of calibration points. We concluded that greater accuracy could be achieved in the calibration points if each quantity of liquid was weighed rather than measured with volumetric measures. We also noted that water was the least expensive liquid to use in the calibration tank but observed that it was necessary to use the same liquid as normally measured for certain sensors.

Quiz

+++1. How do dipsticks and float systems work and what are their advantages and disadvantages in liquid level measurement?

+++2. Sketch three different kinds of hydrostatic level measurement systems. Discuss briefly the mode of operation and applications of each.

+++3. Discuss the mode of operation of the following, using a sketch to aid your discussion as appropriate: capacitive level sensor and ultrasonic level sensor.

+++4. What are the merits of microwave and radiometric level sensors? Discuss how each of these devices works.

+++5. What are the main things to consider when choosing a liquid level sensor for a particular application? What types of devices could you use for an application that required (a) low measurement accuracy, (b) high measurement accuracy where contact between the sensor and the measured liquid is acceptable, or (c) high measurement accuracy where there must not be any contact between the sensor and the measured liquid?

+++6. Discuss the range of devices able to measure the level of the surface of solid material in powdered form contained within a hopper.

+++7. What procedures could you use to calibrate a sensor that is only required to provide approximate measurements of liquid level?

+++8. What is the best calibration procedure to use for sensors required to give high accuracy in level measurement?

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