Instrumentation and control

Principles of Level Measurement & Theory . . . . . . . . . . . . . . . . . . 163

Important Level Measurement Technologies . . . . . . . . . . . . . . . . . 164

• Differential Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

• Bubblers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

• Displacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

• Floats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

• RF Admittance & Capacitance . . . . . . . . . . . . . . . . . . . . . . . . 165

• Ultrasonic/Sonic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

• Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

• Nuclear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

• Table Comparing Level Measurement Technologies . . . . . 167

• Time Domain Reflectometry (TDR) . . . . . . . . . . . . . . . . . . . . 167

• Magnetostrictive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

• Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

• Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

• Float Switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Level Measurement Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Dielectric Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Weight of Water versus Temperature . . . . . . . . . . . . . . . . . . . . . . . 177

Sound Absorption Coefficient of a Material . . . . . . . . . . . . . . . . . . 179

Radiation Field Intensity in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

5Level Measurement

HB levelchap 5.qxd 3/2/2006 9:00 AM Page 161

Principles of Level Measurement

Instrument suppliers offer more than 20 different level measurementtechnologies. All work, when properly applied. However, each has itsstrengths and its weaknesses, and some are not suitable for certainapplications.

Theory

For a given acceleration of gravity, the liquid head in a tank or vesselgenerates a force per unit area or pressure (P) that is directly propor-tional to the liquid level (L) above the measurement point times theaverage density (ρ) of the liquid in the column. Solving for L:

L = P/ρ

While this formula is simple, its usage can be complicated. Virtually allapplications using pressure transmitters for liquid level include one ormore of the following issues:

• Transmitter is not located at the zero level point

• Transmitter is remote from the tank, above or below the primary pressure connection

• Transmitter is isolated from process fluid with a flange or sealsystem

• Tank is closed and, hence, subject to pressure or vacuum abovethe liquid

• The fluid above the liquid may be the vapor of the liquid itself oran outside sourced fluid, such as a nitrogen blanket

• Tank pressure reference connection is filled with a vapor (dry leg)

• Tank pressure reference connection is filled with liquid (wet leg)

• External wet legs can exist on both high and low pressure sidesof the transmitter

• Environmental conditions can be different for each of theseexternal legs

• Environmental conditions are usually different than tank conditions, e.g., a wet leg temperature might be very differentfrom the in-tank temperature

• Plus, changes in liquid and vapor densities.

Chapter 5/Level Measurement 163

Reference: Dudley Harelson and Jonathan Rowe, Foxboro Division, Invensys, Multivariable Transmitters:A New Approach to Liquid Level Measurement. Copyright 2004 by ISA. Presented at ISA 2004.


Important technologies used in level measurement include:

Differential Pressure

Among the most frequently used devices for measuring level, differen-tial pressure (d/p) transmitters do not measure level by themselves.Instead, they measure the head pressure that a diaphragm senses dueto the height of material in a vessel. That pressure measurement is mul-tiplied by a second variable, the product’s density. That calculationshows the force being exerted on the diaphragm, which is then trans-lated into a level measurement. Errors can occur, however, due to den-sity variations of a liquid, caused by temperature or product changes.These variations must always be compensated for if accurate measure-ments are to be made. DPs are primarily used for clean liquids andshould not be used with liquids that solidify as their concentrationsincrease, such as paper pulp stock.

Bubblers

This simple level measurement has a dip tube installed with the open endclose to the bottom of the process vessel. A flow of gas (usually air) passesthrough the tube. When air bubbles escape from the open end, the air pressure in the tube corresponds to the hydraulic head of the liquid inthe vessel. The air pressure in the bubble pipe varies proportionally with the change in head pressure. Calibration is directly affected by changes in product density, however. Because of this, it becomes amass measurement.

Displacers

When a body is immersed in a fluid, it loses weight equal to the liquidweight displaced (Archimedes Principle). By detecting the apparentweight of the immersed displacer, a level instrument can be devised. If thecross sectional area of the displacer and the density of the liquid is con-stant, then a unit change in level will result in a reproducible unit changein displacer weight. Displacers also are affected by changes in productdensity. They should only be used for relatively non-viscous, clean fluidsand work best for short spans.

Floats

Level measuring devices that use a float resting on the surface of themeasured process fluid are legion. Many commodes use a simple, float-driven, on/off switch, water-leveling apparatus. As the liquid in a processrises and falls in its vessel, the float rises and falls as well. Indicatorsadvise the operator and/or the automation links as to the liquid’s level. Thefloat may directly and mechanically trip a switch, push a magnet, pull alever, or raise a pointer. Floats are made of brass, copper, stainless steel,and many types of plastics, among other materials.

164 ISA Handbook of Measurement Equations and Tables


Float technology advantages include low cost, if remote reading isrequired; adaptability to wide variations in fluid densities; the ability to be used in extreme process conditions; unlimited tank height; and highaccuracy.

Disadvantages can include high maintenance requirements; vulnerabilityto particulate or product deposition; moving parts exposed to fluids; limited pressure rating; and not good for use in agitated vessels and forgranular products.

RF Admittance & Capacitance

For applications permitting contact with what’s being measured, radio fre-quency (RF) is perhaps the most versatile technology for continuous levelmeasurement. RF uses a constant voltage applied to a rod or cable (sens-ing element) in the process. The resulting RF current is monitored to inferthe level of the process material. RF technologies handle a wide range ofprocess conditions – from cryogenics to 1,000°F and from vacuum to 10,000psi pressure. It can withstand severe service in harsh corrosive environ-ments. RF also is the most preferred technology for point level measure-ment, able to achieve short span measurement accuracies many othertechnologies cannot achieve. As an intrusive technology, however, insu-lating granular measurements require special considerations, such asthe moisture range and location of the sensing element to minimizeerrors caused by probe movement.

Ultrasonic/Sonic

Ultrasonic transmitters send a sound wave from a piezoelectric transducerto the contents of the vessel. The device measures the length of time ittakes for the reflected sound wave to return to the transducer. A success-ful measurement depends on reflection from the process material in astraight line back to the transducer. Ultrasonic’s appeal is the transducerdoes not come in contact with the process material and does not containany moving parts. Ultrasonic technology was the first industriallyaccepted non-contact level measurement in the process control market.Today’s ultrasonic devices typically require no calibration and can providehigh accuracy level measurements in both liquid and solids applications.However, excessive process temperatures and pressure can be a limitingfactor. And, since ultrasonic technology is based on a traveling soundpressure wave, a constant velocity via its media (air) is required to assurea high degree of accuracy. Material such as dust, heavy vapors, surfaceturbulence, foam and even ambient noise can affect the returning signal.Because sound travels at a constant known velocity at a given tempera-ture, the time between the transmit burst and detection of the return echo



will be proportional to the distance between the sensor and the reflectingobject. The distance between the two can be calculated from:

Distance = Rate x Time

Radar

Radar technology broadened non-contact level technology options.Radar’s inherent accuracy with its ability to have a more narrow beamangle avoided many vessel internal obstructions from reflecting falselevel signals. Radar is unaffected by vapors, steams, and many of theundesired affects of condensation that can affect ultrasonic devices.Properly applied, radar is completely capable of measuring most liquidsand solids level applications. Frequency modulated continuous wave(FMCW) is fast enough for tank gauging, but normally too slow to meas-ure the turbulent surfaces encountered in agitated process applications.Like ultrasonic, radar does not require calibration.

Nuclear

Nuclear level controls are used for continuous measurements, typicallywhere most other technologies are unsuccessful. For example, they areextremely suitable for applications involving high temperatures and pres-sures, or corrosive materials within the vessel. No tank penetration isneeded. Radiation from the source penetrates through the vessel wall andprocess fluid. A detector on the other side of the vessel measures the radi-ation field strength and infers the level in the vessel. The basic unit of radi-ation intensity is the curie, defined as that source intensity which under-goes 3.70 x 1010 disintegrations per second. For industrial applications,radiation field intensity is normally measured in milliroentgens per hour.Radiation field intensity in air can be calculated from:

whereD = radiation intensity in milliroentgens per hour (mR/hr)Mc = source strength in millicuries (MCi)d = distance to the source in inchesK = source constant (0.6 for cesium 137; 2.0 for cobalt 60)

DKM

dc= 1000 2



Courtesy of Ametek Drexelbrook. M. Bahner, A Practical Overview of Level Measurement Technologies. Reprintedwith permission.

Other level measurement technologies include:

Time Domain Reflectometry (TDR)

Another contacting level measurement technology, TDR is also knownby trade names such as “guided wire radar,” “radar on a rope,” “reflexradar,” etc. TDR is a pulse time of flight measurement much like ultra-sonic and some radar techniques. Like radar, it transmits an electro-magnetic pulse that travels at the speed of light to the surface of thematerial to be measured. It has a more narrow beam, or pulse width,than radar since it is completely focused on a flexible wire or rod. Themeasurement is determined by the transit time divided in half. TDR alsodoes not require calibration.

Magnetostrictive

Magnetostrictive technology allows very high-accuracy level measure-ments of non-viscous liquids at ranges up to 50 feet. The technology isbased on a float with embedded magnets that rides on a tube that con-tains magnetostrictive wire pulsed with a low voltage, high current elec-tronic signal. When this signal intersects the magnetic field, generated bythe float, a torsional pulse is reflected back to the electronics. This createsa time of flight measurement. Magnetostrictive devices require no calibra-tion and no maintenance when properly applied.

Hydrostatic Pressure

A well-established level measurement method, hydrostatic pressuretechnology’s basic principle is measuring total head pressure above apressure-sensing diaphragm. Measuring water in below-ground wellsis a major application.


Technology Liquids Granulars Slurries Interfaces

RF Admittance O.K. Use Caution O.K. O.K.

Ultrasonic O.K. Use Caution O.K. Not Practical

Radar O.K. Use Caution O.K. Not Practical

Differential Pressure

O.K. Not Practical Use Caution Use Caution

Displacers O.K. Not Practical Use Caution Use Caution

Bubblers O.K. Not Practical Use Caution Not Practical

Nuclear O.K. Use Caution O.K. Use Caution


Conductance

Conductivity devices are primarily used for point level measurement.Materials being measured using conductivity switches must be conduc-tive. Typically, conductivity switches are used to measure high and/orlow level in liquids such as water, acids, conductive chemicals, etc. Theconductivity electrodes are connected to a relay to provide control andrequire little or no calibration.

Float Switch

One of the oldest methods of level measurement, float devices continueto be used because they are simple to apply and cost effective onappropriate applications. Because floats are a mechanical level switch,it is important to use them in applications where coating build up willnot occur. Clean, noncoating liquids are typically good applications forfloat measurement.

Variable Displacement Measuring Devices

whereV = volume of the displacerD = diameter of the displacerL = length of displacer

To Determine the Weight of the Displacer

whereWw = weight of displacerV = volume of displacerGv = volume of a gallon, H2OGw = weight of a gallon, H2O

References: 1. Ametek Drexelbrook brochure: Level Measurement Solutions …For Every Application.

2. Gillum, Donald R., Industrial Pressure, Level and Density Measurement , ISA—The Instrumentation,Systems, and Automation Society, 1995.

Wwv

wVG

G= ( )

VD

L=π 2

4( )



Hydrostatic Head Level Measurement

wherep = pressure on supporting sur-faceF = weight, H2OA = area of supporting surface

Open-Tank Head-Type LevelMeasurement

wherep = pressure corrected for atmosphere pressure

G = specific gravityh = vertical height of a columnF = weight, H2OA = area of supporting surface

Electrical Level Measurement,Total System Capacitance

where

CK l

Dd

p3

10

0 614=

. ( )( )

log

CK L

Dd

a2

10

0 614 1=

−. ( )

log

C C C CE = + +1 2 3

pFA

=

P pGh=

pFA

=


Principles of Level Measuring Devices


C1 = gland capacitanceC2 = vapor phase capacitanceC3 = liquid phase capacitanceKa = dielectric constant, vapor phaseKp = dielectric constant, liquid phaseL = vessel heightl = level heightD = diameter of vesseld = probe diameter


Hydrostatic Level Measurement in an Open Tank


Electrical Level Measurement

whereC = capacitance in microfaradsK = the dielectric constantA = the area of the platesD = the distance between plates

CKAD

=


Capacitor Probe in a Tank Probe

in Nonconductive Fluid

Equivalent Capacitance



Dielectric Constants of Solids

Acetic Acid (36°F) 4.1

Aluminum Phosphate 6.1

Asbestos 4.8

Asphalt 2.7

Bakelite 5.0

Barium Sulfate (60°F) 11.4

Calcium Carbonate 9.1

Cellulose 3.9

Cereals 3-5.0

Ferrous Oxide (60°F) 14.2

Glass 3.7

Lead Oxide 25.9

Lead Sulfate 14.3

Magnesium Oxide 9.7

Mica 7.0

Napthalene 2.5

Nylon 45.0

Paper 45.0

Phenol (50°F) 2.0

Polyethylene 4-5.0

Polypropylene 1.5

Porcelain 5-7.0

Potassium Carbonate (60°F) 5.6

Quartz 4.3

Rice 3.5

Rubber (hard) 3.0

Sand (Silicon Dioxide) 3-5.0

Sulphur 3.4

Sugar 3.0

Urea 3.5

Zinc Sulfide 8.3



Dielectric Constants of Granular and Powdery Materials

Material Loose Packed

Fly Ash 1.7 2.0

Coke 65.3 70.0

Oatmeal 1.47

Molecular 5A, Sieve Dry 1.8

Polyethylene 2.2

Polyethylene, Powder 1.25

Reclaimed Foundry Sand 4.8 4.8

Laundry Detergent 1.3 to 1.7 1.3 to 1.25



Dielectric Constants of LiquidsMaterial Temp. °F Constant

Acetone 71 21.4

Ammonia -30 22.0

Ammonia 68 15.5

Aniline 32 7.8

Aniline 68 7.3

Benzene 68 2.3

Bromine 68 3.1

Butane 30 1.4

Carbon Dioxide 32 1.6

Carbon Tetrachloride 68 2.2

Castor Oil 60 4.7

Chlorine 32 2.0

Chlorocyclohexane 76 7.6

Chloroform 32 5.5

Cumene 68 2.4

Cyclohexane 68 2.0

Dibromobenzene 68 8.8

Dibromohexane 76 5.0

Dowtherm 70 3.36

Ethanol 77 24.3



Dielectric Constants of Liquids (cont.)

Material Temp. °F Constant

Ethyl Acetate 68 6.4

Ethylene Chloride 68 10.5

Ethyl Ether -40 5.7

Ethyl Ether 68 4.3

Formic Acid 60 58.5

Freon-12 70 2.4

Glycerine 68 47.0

Glycol 68 41.2

Heptane 68 1.9

Hexane 68 1.9

Hydrogen Chloride 82 4.6

Hydrogen Sulfide 48 5.8

Isobutyl Alcohol 68 18.7

Kerosine 70 1.8

Methyl Alcohol 32 37.5

Methyl Alcohol 68 33.1

Methyl Ether 78 5.0

Naphthalene 68 2.5

Octane 68 1.96

Oil, Transformer 68 2.2



Dielectric Constants of Liquids (cont.)

Material Temp. °F Constant

Pentane 68 1.8

Phenol 118 9.9

Phenol 104 15.0

Phosphorus 93 4.1

Propane 32 1.6

Styrene (Phenylethene) 77 2.4

Sulphur 752 3.4

Sulphuric Acid 68 84.0

Tetrachloroethylene 70 2.5

Toluene 68 2.4

Trichloroethylene 61 3.4

Urea 71 3.5

Vinyl Ether 68 3.9

Water 32 88.0

Water 68 80.0

Water 212 48.0

Xylene 68 2.4



Weight of One Gallon (U.S.) of Water at Various Temperatures

Temp.°C

Wt. in VacuumGrams

Wt. in VacuumPounds

Wt. in AirGrams

Wt. in AirPounds

0 3784.856 8.34417 3780.543 8.33467

1 3785.078 8.34466 3780.781 8.33518

2 3785.233 8.34500 3780.953 8.33556

3 3785.326 8.34520 3781.060 8.33580

4 3785.355 8.34527 3781.105 8.33590

5 3785.325 8.34520 3781.090 8.33587

6 3785.235 8.34500 3781.015 8.33570

7 3785.089 8.34468 3780.884 8.33541

8 3784.887 8.34424 3780.698 8.33500

9 3784.633 8.34368 3780.358 8.33447

10 3784.326 8.34300 3780.167 8.33383

11 3783.966 8.34221 3779.821 8.33307

12 3783.557 8.34130 3779.426 8.33220

13 3783.099 8.34030 3778.983 8.33122

14 3782.597 8.33919 3778.495 8.33014

15 3782.049 8.33798 3777.962 8.32897

16 3781.458 8.33668 3777.415 8.32770

17 3780.824 8.33528 3776.764 8.32633

18 3780.148 8.33379 3776.103 8.32487

19 3779.430 8.33221 3775.398 8.32332

20 3778.672 8.33054 3774.653 8.32167

21 3777.873 8.32877 3773.868 8.31994

22 3777.035 8.32693 3773.044 8.31813

23 3776.158 8.32499 3772.180 8.31622

24 3775.243 8.32298 3771.279 8.31424



Weight of One Gallon (U.S.) of Water at Various Temperatures (cont.)

Temp.°C

Wt. in VacuumGrams

Wt. in VacuumPounds

Wt. in AirGrams

Wt. in AirPounds

25 3774.291 8.32088 3770.340 8.31217

26 3773.320 8.31870 3769.364 8.31001

27 3772.277 8.31644 3768.352 8.30778

28 3771.218 8.31410 3767.306 8.30548

29 3770.123 8.31169 3766.224 8.30309

30 3768.995 8.30920 3765.109 8.30063

31 3768.995 8.30664 3763.961 8.29810

32 3766.641 8.30401 3762.780 8.29550

33 3765.416 8.30131 3761.568 8.29283

34 3764.160 8.29854 3760.324 8.29008

35 3762.874 8.29571 3759.050 8.28728

40 3756.018 8.28059 3752.255 8.27230

45 3748.41 8.2638 3744.42 8.2550

50 3740.19 8.2457 3736.22 8.2369

55 3731.34 8.2261 3727.37 8.2174

60 3721.91 8.2054 3717.95 8.1966

65 3711.88 8.1832 3707.93 8.1745

70 3701.35 8.1600 3697.42 8.1514

75 3690.30 8.1357 3686.38 8.1270

80 3678.72 8.1101 3674.81 8.1015

85 3666.68 8.0836 3662.78 8.0750

90 3654.15 8.0560 3650.27 8.0474

95 3641.21 8.0274 3637.34 8.0189

100 3627.81 7.9979 3623.95 7.9894


Sonic and Ultrasonic Level Measurement

Sound Absorption Coefficient of a Material

whered = sound absorption coefficientSa = sound energy absorbedSs = sound energy incident upon the surface

Radiation Used in Level Measurement

Radiation Field Intensity in Air

whereD = radiation intensity in mR/hrMc = source strength in millicuried = distance to the source, inchesK = the source constant1.3 for radium 2260.6 for cesium 1372.0 for cobalt 60

DKM

dc= 1000 2

dSS

a

s=



Engineering

Instrumentation and control