dP-Cell Level Measurement

3D.    Differential Pressure Level Measurement

 OBJECTIVES

1.      Calculate the required differential pressure range for a given dp level measurement application.

2.      Select and describe applications for wet and dry legs, chemical seals and purge or bubbler systems.

3.      Explain problems that may be encountered due to change in ambient temperature and some solutions.

4.      Sketch a typical installation for a dp cell and give reasons for the method used.

THEORY

Liquid level can be measured by measuring the pressure it exerts due to its gravitational attraction to the earth.

            P  =  rog h                   ro-  density of the fluid

                                                g  -  gravity

                                                h  -  height of liquid column

                                                P  -  pressure exerted

If the density of the fluid is constant then the pressure exerted by a column of liquid will be directly proportional to the fluids height or level.  In other words, differential pressure level measurement measures the pressure due to a column of liquid and infers the level from this.

Example:

Note:  The fluid level is directly related to the pressure measured by the dp cell.

The pressure measured by the dp cell needs to be related to the fluids height for proper operation.  This is accomplished by determining the P that the dp cell would see when the fluid level is at the Lower Range Valve (LRV) and determining the P that the dp cell would see when the fluid level is  at the Upper Range Valve (URV).  This gives the necessary calibration range (DP @ the LRV to DP @ the URV) for the dp cell so that its output will be proportional to the fluids level.

Setting up a differential pressure transmitter for level measurement

There are many different methods used to measure level using a differential pressure transmitter (dp cell).  Selecting the appropriate method for a given application will be covered later in this module.  However, the basic steps required to properly set up the dp cell to measure level are similar and presented here.

1.         The calibration range required for a particular application must be determined.  The transmitters installed location must be know to be able to perform this calculation.

2.         The dp cell must be properly calibrated using an appropriate pressure standard.

3.         The transmitter is installed in its proper location and the connection lines are “bleed” to ensure that there is no air pockets in the line that may effect the pressure being measured. (Air pocket will cause measurement errors due to surface tension especially when measuring low pressures)

Following these steps will result in proper level measurement.

Atmospheric vessels using a standard dp cell

For vessels operated at atmospheric pressure, the high side of the  dp  cell is connected to the bottom of the vessel and the low side is vented to atmosphere.

Example:

Process fluid RD  =  .750                               Assume g  =  9.81 m/s2

Calculating the required calibration range:

P  seen by the dp cell when fluid is at its LRV

            PH  =  (.750)(1000 kg/m3)(9.81 m/s2)(.2m) + Patm

            PH  =  1.4715 kPag + Patm

            PL  =  Patm

            P =  PH - PL  =  (1.4715 kPag + Patm) - Patm = 1.4715 kPag

Calculation (continued)

P  seen by the dp cell when fluid is at its URV

            PH  =  (.750)(1000 kg/m3)(9.81 m/s2)(1.2m) + Patm

            PH  =  8.829 kPag + Patm

            PL  =  Patm

            P =  PH - PL  =  (8.829 kPag + Patm) - Patm = 8.829 kPag

Therefore, the calibration range is  1.4715 to 8.829 kPag

Calibration procedure:

This transmitter would now be calibrated for this P range by using the appropriate pressure standards. 

Installation:

The dp cell is generally connected to the process with ½ inch tubing or ½ inch pipe.  A block valve should be installed between the vessel and the dp cell to allow for isolation and maintenance of the dp cell without having to shut down the process and drain the vessel.  The preferred location for the transmitter is below the connection point.

Differential pressure transmitters come with two connection points to each of the high side and low side.  This allows the installation to be “bleed” to ensure no air pocket exist in the connection line and that the line is not plugged.  The connection point not connected to the vessel is opened allowing the process fluid to “bleed” through the connecting line.

Note, this type of installation would only be practical on those applications where the connection line will not plug and the process fluid will not freeze or congeal in the lines.

Operation:

If the output of the transmitter was 12.000 mA this means that the level in the tank from the LRV is       

     

 

          

or by calculation

            PH  =  (.75)(1000 kg/m3)(9.81 m/s2)(0.7 m) + 0 kPag=5.150 kPag

            PL  =  0 kPag

            P =  (5.150 kPag) - (0 kPag) = 5.150 kPag

With proper calibration  and installation the output of the transmitter is directly related to the level in the vessel.

Notes:

1. If the inlet connection was 0.1 m from the bottom of the tank then the level in the vessel from the bottom of the tank would be .7 + .1 = 0.8 m  or

Pressure Sensors and Transmitters

Measuring instruments can be functionally broken down into four general blocks.  (Appreiate NAIT canada) 

The  sensor receives some energy from the measured medium and converts this energy into another form that is compatible to the next part of the instrument.  This may involve one step or several steps with transmission of the energy between them.  The variable manipulation step allows the signal to be changed so that it can be delivered or presented in a meaningful way.  This step also allows for the calibration of the signal.

For example:  Pressure gauge

The Bourdon tube is the sensor.  It receives the pressure energy and converts it to a movement.  The links and levers perform the variable manipulation function.  The links and levers also, allow for zero, span, and angularity calibration.  The scale performs the data presentation function.

Strain Gauge Pressure Transducers

The strain gauge is a device for measuring mechanical surface strain.  It is used for a wide variety of applications, making it possibly the most used transducer in the measurement field.  Strain is defined as the ratio of length extension of a conductor to its original length.

Strain is the elastic movement of a material due to an applied force.  If the strain is positive, then we say the material is under tension.  If the strain is negative, then we say the material is under compression.

A strain gauge then is a device that measures this change in length or strain.

The resistance strain gauge is based on the principle that the resistance of a conductor is a function of its dimensions.

The resistance of the original length of conductor is:

The resistance of the stretched length of conductor is:

Since L2>L2  and  D2<D1  the resistance of the conductor will be increased when stretched, i.e. when strained.

A strain gauge can be a length of very thin wire wound back and forth.

If the gauge is put in tension or compression in the y-axis, there will be virtually no change in length (opens and closes like an accordion) and therefore no change in resistance. 

A strain gauge measures strain only along one axis.

A strain gauge pressure transducer can be made by bonding a strain gauge to an element, which undergoes strain when exposed to pressure. 

 As the pressure increases, the diaphragm will deflect, bending the thin beam (stretching it).  The strain gauge bonded to the beam will experience this strain and change the resistance.

The pressure is being converted to a change in resistance by the strain gauge.  (strain gauge pressure transducer).  For this to work, the bonding must transfer the strain from the beam to the strain gauge and it must electrically isolate the strain gauge from the beam. 

Types of Strain Gauges

Many different types of resistance strain gauges have been developed since the first bonded strain gauge was introduced in 1936.  Currently, the most commercially used gauge is the bonded foil gauge, but this could change in the future.  This gauge uses a thin foil of metal alloy to sense strain.  The bonded semiconductor strain gauge uses silicon or germanium to sense strain. 

Two other types of gauges eliminate the problems of adhesive bonding by molecularly bonding the gauge to the surface being measured.  The diffused semiconductor strain gauge diffuses an impurity such as boron into a semiconductor transducer diaphragm to form a strain gauge, and the thin-film strain gauge molecularly deposits metal alloy directly on a metallic structure such as the beam or diaphragm of a transducer element.

Typical Accuracy:

±0.25% of span (uncompensated strain gauge transducer)

Process Temperature Range:

-54 °C to 121 °C

Capacitance Pressure Transducer

In a typical capacitive pressure transducer, a change in pressure causes the distance between the two parallel plates to change, thus changing the electric capacitance between the plates. This capacitance change can then be amplified and used to adjust the output of the transmitter.

Electronic Theory:

This change in capacitance must be converted to a change in current or voltage before it can be used by the rest of the circuit.  This change can then be manipulated by electronic circuitry to provide the standard 4 to 20 mA signal.

Capacitance pressure transducers are commonly found with differential pressure transducers.

An increase in pressure on the high side will push the sensing diaphragm toward the low side. This will increase the capacitance C₂ (Capacitance between sensing diaphragm and fixed on low side) and decrease capacitance C₁ (Capacitance between sensing diaphragm and fixed on high side).

Typical circuit operation:

The electronics keeps Iref constant via a negative feedback circuit.

From equation 8, it is seen that a change in DP results in a proportional change in the current Idiff.   Idiff can then be manipulated by more electronic circuitry to provide the 4 to 20 mA standard signal.

Note:

·      The dielectric constant between the plates has no effect as long as it is the same on both sides.

·      The transducer usually has a liquid fill which will change its volume due to thermal expansion & contraction.  This will have no effect if even on both sides (i.e. does not change position of sensing diaphragm).

·      High static pressures may cause a zero or span shift. The zero shift may result due to diaphragm area differences between high and low side. The span shift may result due to changes in how far the sensing diaphragm move for a given DP.

Typical Accuracy:  ±.25%

Temperature Range:  -40 to 120 °C

Resonant Wire Pressure Transducer

Principle of Operation

A wire under tension is caused to oscillate at its resonant (or natural) frequency, and changes in pressure are converted to changes in this frequency.  The approximation of the resonant frequency f_n of a wire in a vacuum is:

Simplifying, and assuming the length, density, and area remain constant in the range of tension applied to the wire, the frequency becomes a function of the square of the wires tension.

A typical resonant wire sensor for differential pressure or liquid-level measurement is illustrated on the previous page. A wire under tension is located in the field of permanent magnet. The wire is an integral part of an oscillator that causes the wire to oscillate at is resonant frequency.  One end of the wire is connected to the closed end of the metal tube. The tube is fixed to the sensor body by the electrical insulator. The other end of the wire is connected to the low-pressure diaphragm and loaded in tension by the preload spring.

The spaces between the diaphragms and the backup plates, the fluid transfer port, and the metal tube are all filled with fluid.  An increasing pressure on the high-pressure diaphragm tends to move the diaphragm toward it backup plate, causing fluid displacement. The displaced fluid moves through the fluid transfer port and tends to push the low-pressure diaphragm away from its backup plate. This increases the tension the wire, raising its resonant frequency, and increases the output signal of the transducer.

Elevated-Zero Ranges for a Resonant Wire Pressure Transducer:

An elevated-zero is one that starts below zero and has a negative lower range-value. A typical elevated-zero range application is a wet leg liquid-level measurement on a closed tank. Since the higher pressure must always be applied to the high-pressure diaphragm (to ensure tension on the wire), the low pressure diaphragm must face the tank. This is necessary because the wet leg head is always greater than the tank head. In order that an increasing level will provide an increasing output signal, it is also necessary to place the output action jumpers in the reverse “R” position.  An elevated-zero range application is therefore handled by transforming the transmitter into a suppressed-zero range application and reversing the output signal of the transmitter.

Optical Pressure Transducers

Principle:

A vane is fixed to a diaphragm or small helical Bourdon tube.  This vane blocks a light source from a detecting photo diode.  The output of the photo diode will vary proportionally with the amount of light it receives.

V = hkA

h - light intensity

k - sensitivity factor

A - area of exposure

The signal will vary with the light intensity from the LED which will vary with temperature and time. In addition, the sensitivity factor for the photo diode will vary with temperature. These must be compensated for in an  optical pressure transducer. This can easily be done using a reference photo diode and measuring the difference between it and the measuring photo diode.

Piezoelectric Pressure Transducers

When certain asymmetrical crystals are elastically deformed along specific axes, a voltage is produced in the crystal which causes a flow of electric charge.  This charge is converted into a voltage signal using a capacitor.  E = Q/C

An increase in pressure produces a voltage seen across capacitor C.  The capacitor will slowly discharge (RC time constant), thus changing the output voltage seen (E).  Therefore, the circuit measuring this voltage must have a very high input resistance.

This transducer is particularly suitable for dynamic pressure measurement such as vibration measurement and less appropriate for static pressure measurement.

Magnetic Pressure Transducers

Principle:

The inductance of a coil will change with the position of it's magnetic core.  A magnetic pressure transducer uses pressure to position the magnetic core.  A change in core position causes a change in inductance, which is then converted into a standard instrument signal.

N - number of turns

            - permeability of core

            A - area of core

            - length of core

LVDT (Linear Variable Differential Transformer)

Alternating current is supplied to the primary coil, which produces magnetic flux lines distributed by the core.  This induces a voltage in coils A and B.  Changing the core position will result in different mutual inductance in A and B.

·         Coils A and B are connected in series so that the are "bucking" each  other.

·         If the core is centered, both coils will have equal induced voltages but will be 180 degrees out of phase, resulting in zero output.

·         If the core is moved, then one coil (A or B) will be larger than the other, resulting in an output voltage

·         This change in output voltage per unit in movement is a linear relationship for a fixed amount of movement.

This transformer can be designed in a circular way as well, called RVDT (Rotational Variable Differential Transformer).

PROBLEMS

1.         Draw and label a block diagram of a transmitter.

2.         Describe what strain is.

3.         Explain what elastic movement is.

4.         Explain why a strain gauge works in one direction only with the aid of a sketch.

5.         What effects a strain gage other then strain and how it can be compensated.

6.         Explain how high static pressure may effect a differential pressure transducer.

7.         Briefly explain the principle of operation of the following pressure transducers with the aid of a sketch.

            (a)        LVDT

            (b)        piezoelectric sensor

            (c)        resonant wire sensor