Technical Information TI 1-50aMarch 2016

Density Measurement Methods for Liquids and Liquid Slurries

GeneralDensity is defined as weight per unit volume. Specific gravity of a liquid is the unitless ratio of the density of that liquid to the density of water at some standard temperature.

The measurement (and control) of liquid density is critical to a great many industrial processes. Although density can be of interest, it is usually more important as an inference of composition, of concentration of chemicals in solution, or of solids in suspension.

There are many methods to determine concentration. They include measurement of changes in electrolytic conductivity and of rise in boiling point. This Technical Information (TI) Sheet deals with common industrial methods of measuring density continuously. Application of instruments for other methods is discussed in separate publications. Several of the more common density and specific gravity scales, with conversions, are listed in TI 5-1j.

Density Measurement Principles

Nearly all industrial liquid density instruments utilize the effect of density changes on weight as a measurement. Such instrumentation falls into three major categories; weight, buoyancy, and hydrostatic head, defined by the principles employed. Two other categories, radiation and vibration methods, are also discussed.

Density Measurement Using WeightThe actual weighing of a sample of known volume is a simple but seldom practical application of this principle. Various methods for continuous weighing have been devised. The most successful involves the use of a horizontal “U”- shaped tube with flexible couplings at a pivot point. The weight measured at the end of the tube varies with the density of the liquid flowing through the tube. Another method, usually requiring customized equipment, is periodic weighing of tanks when filled with process liquid.

Density Measurement Using BuoyancyBuoyancy transmitters based upon Archimedes’ principle may be readily adapted to the measurement of liquid density or specific gravity.

For density measurement, a cylindrical displacer is located so as to be fully submerged. The buoyant force on the displacer changes only as a function of changing liquid density and is independent of changing liquid level in the vessel.

The output of the 17B (pneumatic) or E17B (electronic) buoyancy transmitters is directly proportional to density or specific gravity within the calibrated span.

The buoyancy method may be used on either vented or pressurized tanks. It offers the following advantages:

1. It eliminates any need for constant liquid level in the vessel.

2. It eliminates external wet or dry leg piping and related problems.

3. It eliminates the need for a pressure repeater in pressurized tanks where pressure and/or level may vary.

Density Measurement Using Hydrostatic HeadThe hydrostatic head method, which continuously measures the pressure variations by a fixed height of liquid, has proven suitable for many industrial processes. Briefly, the principle, illustrated in Figure 1, as follows:

The difference in pressure between any two elevations (A and B) below the surface is equal to the difference in liquid head pressure between these elevations. This is true regardless of variation in liquid level above elevation B. This difference in elevation is represented by dimension H. Dimension H must be multiplied by the specific gravity (G) of the liquid to obtain the difference in head (ΔP) in inches or metres of water, which are standard units for instrument calibration.

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Figure 1. Hydrostatic Head Principle (The difference in pressure between elevations A and B is a function of liquid density.)

To measure the change in head resulting from a change in specific gravity from G1 to G2, it is necessary only to multiply H by the difference between G2 and G1. Expressed mathematically:

ΔP = (H) (G2 - G1)

The change in head, ΔP, is differential pressure in inches or metres of water, G1, is minimum specific gravity, and G2 is maximum specific gravity.

It is common practice to measure only the span of actual density changes. Therefore, the instrument “zero” is “suppressed” to the minimum head pressure to be encountered; this allows the entire instrument measurement span to be devoted to the differential caused by density changes. For example, if G1 is 1.0 and H is 100 inches, the zero of the measuring device must be suppressed 100 inches of water (H X G1). For a second example, if G1 is 0.6 and H is 3 metres, the zero suppression value should be 1.8 metres of water.

The two principal relationships which must be considered in selecting a measuring device are:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (G1)

For a given instrument span, a low specific gravity span requires a greater H dimension (a deeper tank). For a given specific gravity span, a low span measuring device permits a shallower tank. H vs specific gravity span values are plotted in Figure 2.

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Figure 2. Relationships of Specific Gravity Span to Distance H Between Measurement Points for

Hydrostatic Head Method

Density Measurement Using RadiationDensity measurements by this method are based on the principle that absorption of gamma radiation increases with increasing specific gravity of the material measured.

The principal instrumentation includes: a constant gamma source (usually radium), a detector, and an indicating or recording instrument. Variations in radiation passing through a fixed volume of flowing process liquid are converted into a proportional electrical signal by the detector.

Density Measurement Using VibrationDamping of a vibrating object in contact with the process fluid increases as the density of the process fluid increases. This principle is applied to industrial density measurement. The object which vibrates (from externally applied energy) is usually an immersed reed or plate. Sometimes the vibrating object is a tube or a cylinder filled with the process fluid. Density can be inferred from one of two measurements: changes in the natural frequency of vibration when energy is applied constantly, or changes in the amplitude of vibration when the object is “rung” periodically, in the “bell” mode.

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Temperature Effects and ConsiderationsThe density of a liquid varies with expansion due to rising temperature, but all liquids do not expand at the same rate. Although a specific gravity measurement must be corrected for temperature effects to be completely accurate in terms of standard reference conditions for density and concentration, in most practical cases this is not necessary, unless the temperature changes are rather wide. See Figure 3.

Figure 3. Temperature vs % Density Change for Liquids (For most liquids, temperature effects are relatively small and usually within operating tolerances over narrow temperature spans.)

For applications where specific gravity measurement is extremely critical, it may be necessary to control temperature at a constant value. The necessary correction to the desired base temperature can then be included in the density instrument calibration.

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d/p Cell Transmitter Methods

GeneralThere are a variety of system arrangements for hydrostatic head density measurements with d/p Cell transmitters. Although flange-mounted d/p Cell transmitters are often preferred, pipe-connected transmitters can be used on liquids where crystallization or precipitation in stagnant pockets will not occur.

These d/p Cell transmitter methods are usually superior to those using bubble pipes. They can be applied wherever the vessel is high enough to satisfy the minimum transmitter span. They are also well suited for pressure and vacuum applications.

d/p Cell Transmitter with Overflow TankConstant level, overflow tanks permit the simplest instrumentation, as shown in Figure 4. Only one d/p Cell transmitter is required. With H as the height of liquid above the transmitter, the equations are still:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (G1)

Figure 4. Constant Level, Open, Overflow Tank (Requires only one d/p Cell transmitter for density measurement.)

d/p Cell Transmitter with a Wet LegApplications with level and/or static pressure variations require compensation. There are three basic arrangements for density measurement under these conditions. First, when a seal fluid can be chosen that is always heavier than the process fluid and will not mix with it, the method shown in Figure 5 is adequate. This method is used extensively on hydrocarbons with water in the wet leg.

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Figure 5. Open or Closed Tank with Wet Leg (With varying level and/or pressure, a wet leg can be filled with seal fluid heavier than the process liquid.)

For a wet leg fluid of specific gravity Gs, an elevated-zero transmitter must be used. The equations become:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (Gs - G1)

When there is no suitable wet leg seal fluid, but the process liquid will tolerate a liquid purge, the method shown in Figure 6 can be used. To ensure against process liquid entering the purged wet leg, piping to the process vessel should include an appropriate barrier, either gooseneck or trap, as shown in Figure 7. Zero elevation or suppression of the transmitter will depend on the difference in specific gravity of the seal and process liquids. Here, the equations are:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (G1 - Gs), when G1 > Gs

Zero Suppression Value = (H) (Gs - G1), when Gs > G1

Ideally, the purge liquid will have a specific gravity equal to G1, which will eliminate the need for either suppression or elevation.

Figure 6. Open or Closed Tank with Liquid Purge (With varying level and/or pressure, a liquid purge can be used.)

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Figure 7. Goosseneck and Trap Piping Configurations (Used to keep a purged wet leg free of process

liquid.)

d/p Cell Transmitter with a Pressure RepeaterWhen no seal or purge liquid can be tolerated, there are ways to provide a “mechanical seal” for the low pressure leg, or for both legs if needed. Figure 8 shows the use of a pressure repeater for the upper connection. In one form (the 13R Repeater), this instrument will reproduce any pressure existing at the B connection from full vacuum to 240 kPa (35 psi) positive pressure. In another form (the 17R Repeater), this instrument will reproduce any pressure from 7 kPa (1 psi) to 700 kPa (100 psi). The repeater transmits the total pressure at elevation B to the low pressure side of the d/p Cell transmitter. In this way, the pressure at elevation B is subtracted from the pressure at elevation A. The lower transmitter, therefore, measures density (or H X G, where G is the specific gravity of the liquid.) The equations for the lower transmitter are:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (G1)

The equation for the repeater is:

Output (maximum) - (dBmax) (G2) + Pmax

where dB is the distance from elevation B to the liquid surface and P is the status pressure on the tank, if any.

Figure 8. Open or Closed Tank with Pressure Repeater (With varying level and/or pressure, where seal fluid or liquid purge is not suitable, a pressure repeater [13R Repeater shown] can be used.)

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Special consideration must be given when the repeater method is desired for vacuum applications, where the total pressure on the repeater is less than atmospheric. In some instances the density measurement is still possible. The vacuum application necessitates biasing of the repeater signal or furnishing a vacuum source for the repeater relay. In this case, there are restrictions on allowable specific gravity spans and tank depths.

d/p Cell Transmitter with Matched Pressure SealsFigure 9 illustrates an alternate method for measuring density in a pressurized vessel where wet leg seal fluids and purges are intolerable. A d/p Cell transmitter with matched pressure seals is used. The seal diaphragms are flange-mounted in the appropriate positions on the vessel. The pressure at points A and B are conducted via closed pressure seals to the transmitter, and external leg piping is avoided. Operating pressures from full vacuum to full flange rating of the seal flanges can be accommodated. Here, the equations are:

Span = (H) (G2 - G1)

Zero Suppression Value = (H) (G1 - Gs), when G1 > Gs

Zero Suppression Value = (H) (Gs - G1), when Gs > G1

Figure 9. Open or Closed Tank Pressure Seals (With varying level and/or pressure, a remote, sealed 13DMP, E13DMP, or 823MP d/p Cell transmitter can be used.)

For vacuum applications, the transmitter must be mounted at, or below, tap “A” in Figure 9.

d/p Cell Transmitter with Flanged or Extended DiaphragmThe standard flanged and extended diaphragm transmitter application is illustrated in Figure 10. An extended diaphragm transmitter may be desirable in order to place the capsule flush with or inside the inner wall of the tank. With this instrument, pockets in front of the capsule where buildup may occur are eliminated.

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Figure 10. Flanged and Extended Diaphragm d/p Cell Transmitters

Other Process ConsiderationsAgitation in a process tank where density measurement is made must be sufficient to ensure uniformity of the liquid.

Velocity effects must be avoided; agitation should be enough to maintain a uniform mixture without affecting head pressure at measurement points.

Transmitter locations should be as high as possible above the bottom of the tank. The process liquid can then be drained below this level for removal and maintenance of the transmitter.

Gamma Gauge MethodsSeveral manufacturers furnish gamma source and detector systems with specific gravity output signals compatible with our instrumentation.

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ISSUE DATESFEB 1985MAR 2016

Vertical lines to the right of text or illustrations indicate areas changed at last issue date.

Invensys Systems, Inc.38 Neponset AvenueFoxboro, MA 02035United States of Americahttp://www.fielddevices.foxboro.com

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Invensys, Foxboro, and d/p Cell are trademarks of Invensys Limited, its subsidiaries, and affiliates. All other trademarks are the property of their respective owners.

Invensys is now part of Schneider Electric.

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