Hydrostatic Pressure Type Level Measurement (Hydrostatic interface level measurement)

Hydrostatic pressure sensors may be used to detect the level of a liquid-liquid interface, if and only if the total height of liquid sensed by the instrument is fixed. A single hydrostatic-based level instrument cannot discriminate between a changing interface level and a changing total level, so the latter must be fixed to measure the former.

One way of fixing total liquid height is to equip the vessel with an overflow pipe and ensure that drain flow is always less than incoming flow (forcing some flow to always go through the overflow pipe). This strategy naturally lends itself to separation processes, where a mixture of light and heavy liquids is separated by their differing densities:

Here we see a practical application for liquid-liquid interface level measurement. If the goal is to separate two liquids of differing densities from one another, we need only the light liquid to exit out the overflow pipe and only the heavy liquid to exit out the drainpipe. This means we must control the interface level to stay between those two piping points on the vessel. If the interface drifts too far up, the heavy liquid will be carried out the overflow pipe; and if we let the interface drift too far down, the light liquid will flow out of the drainpipe. The first step in controlling any process variable is to measure that variable, and so here we are faced with the necessity of measuring the interface point between the light and heavy liquids.

Another way of fixing the total height seen by the transmitter is to use a compensating leg located at a point on the vessel always lower than the total liquid height. In this example, a transmitter with remote seals is used:

Since both sides of the differential pressure transmitter “see” the hydrostatic pressure generated by the liquid column above the top connection point (γ2h3), this term naturally cancels:

(γ1h1 + γ2h2 + γ2h3) − (γ4h4 + γ2h3)

γ1h1 + γ2h2 + γ2h3 − γ4h4 − γ2h3

γ1h1 + γ2h2 − γ4h4

The hydrostatic pressure in the compensating leg is constant (γ4h4 = Constant), since the fill fluid never changes density and the height never changes. This means the transmitter’s sensed pressure will differ from that of an uncompensated transmitter merely by a constant offset, which may be “calibrated out” to have no impact on the measurement:

γ1h1 + γ2h2 – Constant

At the first, it may seem as though determining the calibration points (lower- and upper-range values: LRV and URV) for a hydrostatic interface level transmitter is impossibly daunting given all the different pressures involved. A recommended problem-solving technique to apply here is that of a thought experiment, where we imagine what the process will “look like” at lower-range value condition and at the upper-range value condition, drawing two separate illustrations:

For example, suppose we must calibrate a differential pressure transmitter to measure the interface level between two liquids having specific gravities of 1.1 and 0.78, respectively, over a span of 3 feet. The transmitter is equipped with remote seals, each containing a halocarbon fill fluid with a specific gravity of 1.09. The physical layout of the system is as follows:

As the first step in our “thought experiment,” we imagine what the process would look like with the interface at the LRV level, calculating hydrostatic pressures seen at each side of the transmitter:

We know from our previous exploration of this setup that any hydrostatic pressure resulting from the liquid level above the top remote seal location is irrelevant to the transmitter since it is “seen” on both sides of the transmitter and thus cancels out. All we must do, then, is calculate hydrostatic pressures as though the total liquid level stopped at that upper diaphragm connection point.

First, calculating the hydrostatic pressure “seen” at the high port of the transmitter:

P high = 4.5 feet of heavy liquid + 4.5 feet of light liquid

P high = 54 inches of heavy liquid + 54 inches of light liquid

P high ”W.C. = (54 inches of heavy liquid )(1.1) + (54 inches of light liquid )(0.78)

P high ”W.C. = 59.4 ”W.C. + 42.12 ”W.C.

P high = 101.52 ”W.C.

Next, calculate the hydrostatic pressure “seen” at the low port of the transmitter:

P low = 9 feet of fill fluid

P low = 108 inches of fill fluid

P low ”W.C. = (108 inches of fill fluid )(1.09)

P low = 117.72 ”W.C.

The differential pressure applied to the transmitter in this condition is the difference between the high and low port pressures, which becomes the lower range value (LRV) for calibration:

P LRV = 101.52 ”W.C. − 117.72 ”W.C. = − 16.2 ”W.C.

As the second step in our “thought experiment,” we imagine what the process would look like with the interface at the URV level, calculating hydrostatic pressures seen at each side of the transmitter:

P high = 7.5 feet of heavy liquid + 1.5 feet of light liquid

P high = 90 inches of heavy liquid + 18 inches of light liquid

P high ”W.C. = (90 inches of heavy liquid )(1.1) + (18 inches of light liquid )(0.78)

P high ”W.C. = 99 ”W.C. + 14.04 ”W.C.

P high = 113.04 ”W.C.

The hydrostatic pressure of the compensating leg is exactly the same as it was before: 9 feet of fill fluid having a specific gravity of 1.09, which means there is no need to calculate it again. It will still be 117.72 inches from the water column. Thus, the differential pressure at the URV point is:

P URV = 113.04 ”W.C. − 117.72 ”W.C. = − 4.68 ”W.C.

Using these two pressure values and some interpolation, we may generate a 5-point calibration table (assuming a 4-20 mA transmitter output signal range) for this interface level measurement system:

Interface Level (ft)	Percentage of Range (%)	Differential Pressure at Transmitter (“WC)	Transmitter Output (mA)
4.5	0	-16.2	4
5.25	25	-13.32	8
6.0	50	-10.44	12
6.75	75	-7.56	16
7.5	100	-4.68	20

 When the time comes to bench-calibrate this instrument in the shop, the easiest way to do so will be to set the two remote diaphragms on the workbench (at the same level), then apply 16.2 to 4.68 inches of water column pressure to the low remote seal diaphragm with the other diaphragm at atmospheric pressure to simulate the desired range of negative differential pressures.

The more mathematically inclined reader will notice that the span of this instrument (URV − LRV) is equal to the span of the interface level (3 feet, or 36 inches) multiplied by the difference in specific gravities (1.1 − 0.78):

Span in ”W.C. = (36 inches)(1.1 − 0.78)

Span = 11.52 ”W.C.

Looking at our two “thought experiment” illustrations, we see that the only difference between the two scenarios is the type of liquid filling that 3-foot region between the LRV and URV marks.

Therefore, the only difference between the transmitter’s pressures in those two conditions will be the difference in height multiplied by the difference in density. Not only is this an easy way for us to quickly calculate the necessary transmitter span, but it also is a way for us to check our previous work: we see that the difference between the LRV and URV pressures is indeed a difference of 11.52 inches of water column just as this method predicts.

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Hydrostatic Pressure Type Level Measurement (Tank expert systems)

An alternative to using a compensating leg to subtract gas pressure inside an enclosed vessel is to simply use a second pressure transmitter and electronically subtract the two pressures in a computing device:

This approach enjoys the distinct advantage of avoiding a potentially wet compensating leg but suffers the disadvantages of extra cost and greater error due to the potential calibration drift of two transmitters rather than just one. Such a system is also impractical in applications where the gas pressure is substantial compared to the hydrostatic (elevation head) pressure. If we add a third pressure transmitter to this system, located a known distance (x) above the bottom transmitter, we have all the pieces necessary for what is called a tank expert system. These systems are used on large storage tanks operating at or near atmospheric pressure, and can measure infer liquid height, liquid density, total liquid volume, and total liquid mass stored in the tank:

The pressure difference between the bottom and middle transmitters will change only if the liquid density changes since the two transmitters are separated by a known and fixed height difference.

Algebraic manipulation shows us how the measured pressures may be used by the level computer (LY) to continuously calculate liquid density (γ):

P bottom − P middle = (P gas + γh) − [P gas + γ(h − x)]

P bottom − P middle = P gas + γh − P gas − γ(h − x)

P bottom − P middle = P gas + γh − P gas − γh + γx

P bottom − P middle = γx

P bottom − P middle/x = γ

Once the computer knows the value of γ, it may calculate the height of liquid in the tank with great accuracy based on the pressure measurements taken by the bottom and top transmitters:

P bottom − P top = (P gas + γh) − P gas

P bottom − P top = γh

P bottom − P top/γ = h

With all the computing power available in the LY, it is possible to characterize the tank such that this height measurement converts to a precise volume measurement (V ), which may then be converted into a total mass (m) measurement based on the mass density of the liquid (ρ) and the acceleration of gravity (g). First, the computer calculates mass density based on the proportionality between mass and weight (shown here starting with the equivalence between the two forms of the hydrostatic pressure formula):

ρgh = γh, => ρg = γ

Then, ρ = γ / g

Armed with the mass density of the liquid inside the tank, the computer may now calculate the total liquid mass stored inside the tank: m = ρV

Dimensional analysis shows how units of mass density and volume cancel to yield only units of mass in this last equation:

[kg] = [kg / m³] / m³

Here we see a vivid example of how several measurements may be inferred from just a few actual process (in this case, pressure) measurements. Three pressure measurements on this tank allow us to compute four inferred variables: liquid density, liquid height, liquid volume, and liquid mass.

The accurate measurement of liquids in storage tanks is not just useful for process operations, but also for conducting business affairs. Whether the liquid represents raw material purchased from a supplier, or a processed product ready to be pumped out to a customer, both parties have a vested interest in knowing the exact quantity of liquid bought or sold. Measurement applications such as this are known as custody transfer because they represent the transfer of custody (ownership) of a substance exchanged in a business agreement. In some instances, both buyer and seller operate and maintain their own custody transfer instrumentation, while in other instances there is but one instrument, the calibration of which is validated by a neutral party.

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Hydrostatic Pressure Type Level Measurement (Compensated leg systems)

The simple and direct relationship between liquid height in a vessel and pressure at the bottom of that vessel is ruined if another source of pressure exists inside the vessel other than hydrostatic (elevation head). This is virtually guaranteed to be the case if the vessel in question is unvented.

Any gas or vapor pressure accumulation in an enclosed vessel will add to the hydrostatic pressure at the bottom, causing any pressure-sensing instrument to falsely register a high level:

A pressure transmitter has no way of “knowing” how much of the sensed pressure is due to liquid elevation and how much of it is due to pressure existing in the vapor space above the liquid. Unless a way can be found to compensate for any non-hydrostatic pressure in the vessel, this extra pressure will be interpreted by the transmitter as an additional liquid level.

Moreover, this error will change as gas pressure inside the vessel changes, so it cannot simply be “calibrated away” by a static zero shift within the instrument. The only way to hydrostatically measure liquid level inside an enclosed (non-vented) vessel is to continuously compensate for gas pressure.

Fortunately, the capabilities of a differential pressure transmitter make this a simple task. All we need to do is connect a second impulse line (called a compensating leg), from the “Low” port of the transmitter to the top of the vessel, so the “Low” side of the transmitter experiences nothing but the gas pressure enclosed by the vessel, while the “High” side experiences the sum of gas and hydrostatic pressures. Since a differential pressure transmitter responds only to differences in pressure between “High” and “Low” sides, it will naturally subtract the gas pressure (P gas ) to yield a measurement based solely on hydrostatic pressure (γh):

The amount of gas pressure inside the vessel now becomes completely irrelevant to the transmitter’s indication, because its effect is canceled at the differential pressure instrument’s sensing element. If gas pressure inside the vessel were to increase while liquid level remained constant, the pressure sensed at both ports of the differential pressure transmitter would increase by the exact same amount, with the pressure difference between the “high” and “low” ports remaining constant with the constant liquid level. This means the instrument’s output signal is a representation of hydrostatic pressure only, which represents liquid height (assuming a known liquid density γ).

Unfortunately, it is common for enclosed vessels to hold condensable vapors, which may over time fill a compensating leg full of liquid. If the tube connecting the “Low” side of a differential pressure transmitter fills completely with a liquid, this will add a hydrostatic pressure to that side of the transmitter, causing another calibration shift. This wet leg condition makes level measurement more complicated than a dry leg condition where the only pressure sensed by the transmitter’s “Low” side is gas pressure (P gas):

Gas pressure still cancels due to the differential nature of the pressure transmitter, but now the transmitter’s output indicates a difference of hydrostatic pressures between the vessel and the wet leg, rather than just the hydrostatic pressure of the vessel’s liquid level. Fortunately, the hydrostatic pressure generated by the wet leg will be constant, so long as the density of the condensed vapors filling that leg (γ2) is constant. If the wet leg’s hydrostatic pressure is constant, we can compensate for it by calibrating the transmitter with an intentional zero shift, so it indicates as though it were measuring hydrostatic pressure on a vented vessel.

Differential pressure = γ1h1 – Constant

We may ensure a constant density of wet leg liquid by intentionally filling that leg with a liquid known to be denser than the densest condensed vapor inside the vessel. We could also use a differential pressure transmitter with remote seals and capillary tubes filled with liquid of known density:

Remote seals are very useful in applications such as this, for the wet leg never requires re-filling.

An actual level transmitter installation using two remote seals (in this case, a Foxboro IDP10 differential pressure transmitter) appears in this photograph:

The vessel itself is insulated and covered in sheet aluminum to protect the thermal insulation from impact and weather-related damage. White-painted flanged “nozzles” protrude from the vessel through the insulation to provide places for the level-sensing instrument to connect. You can see the two flanged remote seals (painted blue) where the armored (stainless steel) capillary tubes terminate. Note how the long capillary tube on the “wet” leg is neatly coiled to reduce the possibility of damage by snagging on a nearby moving object.

An accessory commonly used with non-sealed (non-capillary) “wet leg” systems is a sealed pot. This is a chamber at the top of the wet leg joining the wet leg line with the impulse line to the upper connection point on the process vessel. This “seal pot” maintains a small volume of liquid in it to allow for occasional liquid loss during transmitter maintenance procedures without greatly affecting the height of the liquid column in the wet leg:

Regular operation of the transmitter’s three-valve manifold (and drain valve) during routine instrument maintenance inevitably releases some liquid volume from the wet leg. Without a seal pot, even a small loss of liquid in the wet leg may create a substantial loss in liquid column height within that tube, given the tube’s small diameter. With a sealed pot, the (comparatively) large liquid volume held by the pot allows for substantial liquid loss through the transmitter’s manifold without substantially affecting the height of the liquid column within the wet leg.

Seal pots are standard on-level measurement systems for boiler steam drums, where steam readily condenses in the upper impulse tube to naturally form a wet leg. Although steam will condense over time to refill the wet leg following a loss of water in that leg, the level measurements taken during that re-fill time will be in error. The presence of a sealed pot practically eliminates this error as the steam condenses to replenish the water lost from the pot since the amount of height change inside the pot due to a small volume loss is trivial compared to the height change in a wet leg lacking a sealed pot.

The following example shows the calibration table for a compensated-leg (wet) hydrostatic level measurement system, for a gasoline storage vessel and water as the wet leg fill fluid. Here, I am assuming a density of 41.0 lb/ft³ for gasoline and 62.4 lb/ft³ for water, with a 0-to-10-foot measurement range and an 11-foot wet leg height:

Gasoline Level (ft)	Percentage of Range (%)	Differential Pressure at Transmitter (PSI)	Transmitter Output (mA)
0	0	-4.77	4
2.5	25	-4.05	8
5.0	50	-3.34	12
7.5	75	-2.63	16
10.0	100	-1.92	20

 Note that due to the superior density and height of the wet (water) leg, the transmitter always sees a negative pressure (pressure on the “Low” side exceeds the pressure on the “High” side).

With some older differential pressure transmitter designs, this negative pressure was a problem. Consequently, it is common to see “wet leg” hydrostatic transmitters installed with the “Low” port connected to the bottom of the vessel and the “High” port connected to the compensating leg. In fact, it is still common to see modern differential pressure transmitters installed in this manner, although modern transmitters may be ranged for negative pressures just as easily as for positive pressures. It is vitally important to recognize that any differential pressure transmitter connected as such (for any reason) will respond in reverse fashion to increases in the liquid level. As the liquid level in the vessel rises, the transmitter’s output signal will decrease instead of increase:

Either way of connecting the transmitter to the vessel will suffice for measuring liquid level, so long as the instrumentation receiving the transmitter’s signal is properly configured to interpret the signal. The choice of which way to connect the transmitter to the vessel should be driven by fail-safe system design, which means to design the measurement system such that the most probable system failures – including broken signal wires – result in the control system “seeing” the most dangerous process condition and therefore taking the safest action.

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Hydrostatic Pressure Type Level Measurement (Transmitter suppression and elevation)

A very common scenario for liquid level measurement is where the pressure-sensing instrument is not located at the same level as the 0% measurement point. The following photograph shows an example of this, where a Rosemount model 3051 differential pressure transmitter is being used to sense hydrostatic pressure of colored water inside a (clear) vertical plastic tube:

Consider the example of a pressure sensor measuring the level of liquid ethanol in a storage tank. The measurement range for liquid height in this ethanol storage tank is 0 to 40 feet, but the transmitter is located 30 feet below the tank:

This means the transmitter’s impulse line contains a 30-foot elevation head of ethanol, so the transmitter “sees” 30 feet of ethanol when the tank is empty and 70 feet of ethanol when the tank is full. A 3-point calibration table for this instrument would look like this, assuming a 4 to 20 mA DC output signal range:

Ethanol Level in Tank (ft)	Percentage of Range (%)	Pressure (inches of water)	Pressure (PSI)	Output (mA)
0	0	284	10.3	4
20	50	474	17.1	12
40	100	663	24.0	20

Another common scenario is where the transmitter is mounted at or near the vessel’s bottom, but the desired level measurement range does not extend to the vessel bottom:

In this example, the transmitter is mounted exactly at the same level as the vessel bottom, but the level measurement range goes from 4 feet to 9 feet (a 5-foot span). At the level of castor oil deemed 0%, the transmitter “sees” a hydrostatic pressure of 1.68 PSI (46.5 inches of water column), and at the 100%, castor oil level the transmitter “sees” a pressure of 3.78 PSI (105 inches water column). Thus, these two pressure values would define the transmitter’s lower and upper range values (LRV and URV), respectively.

The term for describing either of the previous scenarios, where the lower range value (LRV) of the transmitter’s calibration is a positive number, is called zero suppression. If the zero offset is reversed (e.g. the transmitter mounted at a location higher than the 0% process level), it is referred to as zero elevation.

If the transmitter is elevated above the process connection point, it will most likely “see” a negative pressure (vacuum) with an empty vessel owing to the pull of liquid in the line leading down from the instrument to the vessel. It is vitally important in elevated transmitter installations to use a remote seal rather than an open impulse line, so liquid cannot dribble out of this line and into the vessel:

In this example, we see a remote seal system with a fill fluid having a density of 58.3 lb/ft³, and a process level measurement range of 0 to 11 feet of seawater (density = 64 lb/ft³). The transmitter elevation is 6 feet, which means it will “see” a vacuum of -2.43 PSI (-67.2 inches of water column) when the vessel is completely empty. This, of course, will be the transmitter’s calibrated lower range value (LRV). The upper range value (URV) will be the pressure “seen” with 11 feet of seawater in the vessel. This much seawater will contribute an additional 4.89 PSI of hydrostatic pressure at the level of the remote seal diaphragm, causing the transmitter to experience a pressure of +2.46 PSI.

List of Prominent Manufacturers: Aquas, Ametek, Anderson Negele, Aplisens, Autosen, BCM Sensor, Endress + Hauser, Flowtech, HolyKell, Huba Control, Jiucheng, Keller, LEEG, LTH Electronics, Nivelco, Noshok, Piezus, Prisma, Scaime, VEGA, ZHYQ

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