PressureSensors

Authors: (09/14/06 / Date Revised: 09/20/06 ) Wen Chung Lim, James Bennett, Jamila Grant, Ajay Bhasin

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Introduction
Pressure must be considered when designing many chemical processes. Pressure is defined as force per unit area and is measured in English units of psi and SI units of Pa. There are three types of pressure measurements: There are various types of pressure sensors that are available in the market today for use in industry. Each functions best in a certain type of situation.
 * 1) Absolute pressure - atomospheric pressure plus gauge pressure.
 * 2) Gauge Pressure - absolute pressure minus atmospheric pressure.
 * 3) Differential Pressure - pressure difference between two locations.

Sensor Selection Criteria
In order for a pressure controlled system to function properly and cost-effectively, it is important that the pressure sensor used be able to give accurate and precise readings as needed for a long period of time without need for maintenance or replacement while enduring the conditions of the system. Several factors influence the suitability of a particular pressure sensor for a given process: the characteristics of the substances being used or formed during the process, the environmental conditions of the system, the pressure range of the process, and the level of precision and sensitivity required in measurements made.

Process
The pressure sensing element (elastic element) will be exposed to the materials used in the process, therefore materials which might react with the process substances or degrade in corrosive media are unsuitable for use in the sensor. Diaphragms are optimal for very harsh environments.

Environment
The environment (as in the system -- pipes, vibrations, temperature, etc.) in which the process is carried out also needs to be considered when choosing a suitable pressure sensor. Corrosive environments, heavy vibrations in the piping units, or extreme temperatures would mean that the sensors would have to have an added level of protection. Sealed, strong casing materials with interior liquid containing glycerine or silicone are often used to encase the internal components of the sensor (not including the sensing element), protecting them from very harsh, corrosive environments or frequent vibrations.

Pressure Range
Most processes operate within a certain pressure range. Because different pressure sensors work optimally in different pressure ranges, there is a need to choose pressure gauges which are able to function well in the range dictated by the process.

Sensitivity
Different processes require different levels of precision and accuracy. In general, the more precise the sensor, the more expensive it is, thus it is economically viable to choose sensors that are able to satisfy the precision desired. There is also a compromise between precision and the ability to detect pressure changes quickly in sensors, hence in processes in which the pressure is highly variable over short periods of time, it is unadvisable to use sensors which take a lot of time to give accurate pressure readings, although they might be able to give precise pressure values.

Pressure Measuring Methods
Several pressure measuring methods have been developed and utilized; these methods include visual inspection of the height of liquid in a column, elastic distortion, and electrical methods.

Height of Liquid in Column
The height of a liquid with known density is used to measure pressure. Using the equation $$P = \rho g h$$, the gauge pressure can be easily calculated. These types of pressure measuring devices are usually called manometers. Units of length may be used to measure the height of the liquid in the column as well as calibrated pressure units. Typically water or mercury is used as the liquid within these columns. Water is used when you desire greater sensitivity (its density is much less than liquid mercury, so its height will vary more with a pressure change). Mercury is used when you desire higher pressure measurements and not as great sensitivity.

Elastic Distortion
This pressure measuring method is based on the idea that deformation of an elastic material is directly proportional to the pressure being measured. There are mainly three sensor types that are used in this method of measuring pressure: Bourdon-tubes, diaphragms and bellows. (refer to “Types of Sensors” Section)

Electrical Methods
Electrical methods used for measuring pressure utilize the idea that dimensional changes in a wire affect the electrical resistance to the conductor. These devices that use the change in resistance of the wire are called strain gauges. Other electrical sensors include capacitive sensors, inductive pressure transducers, reluctive pressure transducers, potentiometric transducers, piezoresistive transducers and piezoelectric sensors. (refer to “Types of Sensors” Section)

Types of Sensors
There are many different pressure sensors to choose from when considering which is most suitable for a given process, but they can generally be placed into a few categories, namely elastic sensors, electrical transducers, differential pressure cells and vacuum pressure sensors. Listed below each general category are specific internal components, each functioning best in a certain situation.

Elastic Sensors
Most fluid pressure sensors are of the elastic type, where the fluid is enclosed in a small compartment with at least one elastic wall. The pressure reading is thereby determined by measuring the deflection of this elastic wall, resulting in either a direct readout through suitable linkages, or a transduced electrical signal. Elastic pressure sensors are sensitive; they are commonly fragile and susceptible to vibration, however. In addition, they tend to be much more expensive than manometers, and are therefore preferentially used for transmitting measured data and measuring pressure differences. A wide variety of flexible elements could conceivably be used for elastic pressure sensors; the majority of devices use some form of a Bourdon tube, bellows, or diaphragm.


 * Bourdon Tube Gauges

The principle behind all Bourdon tubes is that an increase in pressure on the inside of the tube in comparison to the outside pressure causes the oval or flat shaped cross-section of the tube to try to achieve a circular shape. This phenomenon causes the tube to either straighten itself out in the c-type or spiral cases or to unwind itself for the twisted and helical varieties. This change can then be measured with an analog or digital meter connected to the tube. Tube materials can be changed accordingly to suit the required process conditions. Bourdon tubes can operate under a pressure range from 0.1-700 MPa. They are also portable and require little maintenance; however,they can only be used for static measurements and have low accuracy.

Types of Bourdon tubes include C-type, spiral (a more coiled C-type tube), helical and straight tube Bourdon tubes. C-type gauges can be used in pressures approaching 700MPa; they do have a minimum recommended pressure range, though -- 30 kPa (i.e., it is not sensitive enough for pressure differences less than 30 kPa).


 * Bellows

Bellows elements are cylindrical in shape and contain many folds. They deform in the axial direction (compression or expansion) with changes in pressure. The pressure that needs to be measured is applied to one side of the bellows (either inside or outside) while atmospheric pressure is on the opposite side. Absolute pressure can be measured by evacuating either the exterior or interior space of the bellows and then measuring the pressure at the opposite side. Bellows can only be connected to an on/off switch or potientiomenter and are used at low pressures, <0.2 MPa with a sensitivity of 0.0012 MPa.


 * Diaphragms

Diaphragm elements are made of circular metal discs or flexible elements such as rubber, plastic or leather. The material from which the diaphragm is made depends on whether it takes advantage of the elastic nature of the material, or is opposed by another element (such as a spring). Diaphragms made of metal discs utilize elastic characteristics, while those made of flexible elements are opposed by another elastic element. These diaphragm sensors are very sensitive to rapid pressure changes. The metal type can measure a maximum pressure of approximately 7 MPa, while the elastic type is used for measuring extremely low pressures (.1 kPa - 2.2 MPa) when connected to capacitative transducers or differential pressure sensors. Examples of diaphragms include flat, corrugated and capsule diaphragms. As previously noted, diaphragms are very sensitive (0.01 MPa). They can measure fractional pressure differences over a very minute range (say, inches of water) (elastic type) or large pressure differences (approaching a maximum range of 207 kPa) (metal type).

Diaphragm elements are very versatile -- they are commonly used in very corrosive environments or with extreme over-pressure situations.

Examples of these elastic element pressure sensors are shown here.

Electric Sensors
Sensors today are not neccessarily only connected to a gauge meter needle pointer to indicate pressure, but may also serve to convert the process pressure into an electrical or pneumatic signal, which can be transmitted to a control room from which the pressure reading is determined. Electric sensors take the given mechanics of an elastic sensor and incorporate an electrical component, thus heightening the sensitivity and increasing the amount of instances in which you could utilize the sensor. The types of pressure transducers are capacitive, inductive, reluctive, piezoelectric, strain gauge, vibrating element, and potentiometric.


 * Capacitive

A capacitive sensor consists of a parallel plate capacitors coupled with a diaphragm that is usually metal and exposed to the process pressure on one side and the reference pressure on the other side. Electrodes are attached to the diaphragm and are charged by a high frequency oscillator. The electrodes sense any movement of the diaphragm and this changes the capacitance. The change of the capacitance is detected by an attached circuit which then outputs a voltage according to the pressure change. This type of sensor can be operated in the range of 2.5 Pa - 70MPa with a sensitivity of 0.07 MPa.

An example of a capacitive pressure sensor is shown on the right.


 * Inductive

Inductive pressure sensors are coupled with a diaphragm or a Bourdon tube. A ferromagnetic core is attached to the elastic element and has a primary and 2 secondary windings. A current is charged to the primary winding. When the core is centered then the same voltage will be induced to the two secondary windings. When the core moves with a pressure change, the voltage ratio between the two secondary windings changes. The difference between the voltages is proportional to the change in pressure.

An example of an inductive pressure sensor utilizing a diaphragm is shown below. For this kind of pressure sensor, taking Chamber 1 as the reference chamber with a reference pressure P1 coming into the chamber and the coil being charged with a reference current. When the pressure in the other chamber changes, the diagphragm moves and induces a current in the other coil, which is measured and gives a measure of the change in pressure.

These may be used with any elastic element (though, it is typically coupled with a diaphragm or a bourdon tube). The pressure reading generated will be determined by voltage calibration. Thus, the range of pressure in which this sensor may be used is determined by an associated elastic element but falls in the range of 250 Pa - 70 MPa.


 * Reluctive

Reluctive pressure sensors also charge a ferromagnetic core. When the pressure changes, the flexible element moves a ferromagnetic plate, leading to a change in the magnetic flux of the circuit which can be measured. The situations in which one would use a reluctive electric element is one in which the inductive sensor does not generate a precise enough measurement. The pressure range is 250 Pa - 70 MPa with a sensitivity of 0.35 MPa.

An example of a reluctive pressure sensor can be seen on the right.


 * Piezoelectric

Piezoelectric sensors use a crystal sensor. When pressure is applied to the crystal, it deforms and a small electric charge is created. The measurement of the electric charge corresponds to the change in pressure. This type of sensor has a very rapid response time to constant pressure changes. Similar to reluctive electric element, the piezoelectric element is very sensitive, but responds much, much faster. Thus, if time is of the essence, a piezoelectric sensor would be desired. The pressure range is .021 - 100 MPa with a sensitivity of 0.1 MPa.

On the right is an example of a piezoelectric pressure sensor.


 * Potentiometric

Potentiometric sensors have an arm mechanically attached to the elastic pressure sensing element. When pressure changes, the elastic element deforms, causing the arm to move backwards or forwards across a potentiometer and a resistance measurement is taken. These sensing elements do posess an optimum working range, but are seemingly limited in their resolution by many factors. As such, they are low end sensors that aren't used for much. With a low sensitivity and working range, they may be best suited as a cheap detector evaluating a coarse process.The pressure range is 0.035 - 70 MPa with a sensitivity of 0.07 -0.35 MPa.

An example of a potentiometric pressure sensor is shown on the right.


 * Strain Gauge

The strain gauge detects changes in pressure by measuring the change in resistance of a Wheatstone bridge circuit. In general, this circuit is used to determine an unknown electrical resistance by balancing two sections of a bridge circuit such that the ratio of resistances in one section ($$\frac{R_3}{R_2}$$) is the same as that in the other section($$\frac{R_4}{R_1}$$), resulting in a zero reading in the galvanometer in the center branch. One of the sections contains the unknown component of which the resistance is to be determined, while the other section contains a resistor of known resistance that can be varied. The Wheatstone bridge circuit is shown below:



The strain gauge places sensors on each of the resistors and measures the change in resistance of each individual resistor due to a change in pressure. Resistance is governed by the equation $$R = \rho \frac {L}{A}$$ where $$\rho$$ = resistivity of the wire, L = length of the wire, and A = cross-sectional area of the wire. A pressure change would either elongate or compress the wire, hence a compression sensor is needed on one resistor and an elongation sensor on the other. To control the effects of temperature (a wire would also either elongate or compress with a change in temperature), a blank sensor would be placed on the remaining two resistors. These gauges are frequently a type of semiconductor (N-type or P-type). Thus, their sensitivity is much greater than their metal counterparts; however, with greater sensitivity comes a more narrow functional range: the temperature must remain constant to obtain a valid reading. These gauges are affected greatly by variations in temperature (unlike the other types of electrical components). The pressure range is 0 - 1400 MPa with a sensitivity of 1.4 - 3.5MPa.

An example of an unbonded strain gauge is shown below. This makes use of strain-sensitive wires one end fixed to an immobile frame and the other end attached to a movable element, which moves with a change in pressure. An example of a bonded strain gauge can be seen below. This is placed on top of a diaphragm, which deforms with change in pressure, straining the wires attached to the diaphragm.


 * Vibrating Element

Vibrating element pressure sensors function by measuring a change in resonant frequency of a vibrating element. A current is passed through a wire which induces an electromotive force within the wire. The force is then amplified and causes oscillation of the wire. Pressure affects this mechanism by affecting the wire itself: an increase in pressure decreases the tension within the wire and thus lowers the angular frequency of oscillation of the wire. The sensor is housed in a cylinder under vacuum when measuring absolute pressures. These absolute pressure measuring sensors are very efficient: they produce repeatable results and are not affected by temperature greatly. They lack sensitivity in meausurement, though, so they would not be ideal for a process in which minute pressures need monitoring. The pressure range is 0.0035 - 0.3 MPa with a sensitivity of 1E-5 MPa.

A vibrating wire pressure sensor is shown below. A vibrating cylinder pressure sensor (for absolute pressures) is shown below.

Differential Pressure Cells
Differential pressure cells are used with various kinds of sensors in which measurement of pressure is a result of a pressure differential such as orifice plates, flow nozzles, or venturi meters. The differential pressure cell converts the pressure differential into a transmittable signal. Where the differential pressure (DP) cell is placed depends on the nature of the fluid stream that is being measured. A typical DP cell is minimally invasive (an external component attached across the point of measurement); it is commonly employed with a capacitive element paired with a diaphragm that allows the capacitive body to separate or move together, generating a signal (via change in capacitance) that can be interpreted to a pressure drop. They are often used to detect small differences in large pressure drops. Its placement is similar to connecting a voltmeter in parallel to a resistor to measure its voltage "drop" (analgous to the pressure drop).

An example of a differential pressure cell using bellows can be found here: http://www.tpub.com/fluid/ch2s.h49.gif

The range of pressure measured and sensitivity of a differential cell depends upon the electric and elastic components used in the cell itself. It is a great sensor to use when measuring a pressure drop; however, for all other applications, it is fairly useless.

Vacuum Sensors
Such sensors are able to measure extremely low pressures or vacuum, referring to pressures below atmospheric pressure. Besides diaphragm and electric sensors designed to measure low pressures, there are also thermal conductivity gauges and ionization sensors.


 * Thermal Conductivity Gauges

The principle involved here is the change in gas thermal conductivity with pressure. However, due to deviation from ideal gas behavior in which the relationship between these two properties is linear, these kind of gauges, which are also called Pirani gauges, can only be used at low pressures, in the range of (0.4E-3 to 1.3E-3) MPa. They are amazingly sensitive elements as well (can detect changes of 6E-13 MPa).

In these gauges, a coiled wire filament has a current flowing through it, which heats up the coil. A change in pressure changes the rate of heat conduction away from the filament, thereby causing its temperature to vary. These changes in temperature can be detected by thermocouples in the gauge, which are also connected to reference filaments in the gauge as part of a Wheatstone bridge circuit.

An example of a Pirani gauge can be found here: http://www.bama.ua.edu/~surfspec/vacbasics_files/image046.jpg


 * Ionization Gauges

There are two categories for these types of gauges: hot cathode and cold cathode. For hot cathode gauges, electrons are emitted by heated filaments, while for the cold cathode gauges electrons are released from the cathode due to collision of ions. Electrons hit the gas molecules entering the gauge forming positive ions, which are collected and cause an ion current to flow. The amount of cation formation is related to the gas density and consequently the pressure to be measured, as well as the constant electron current used, hence the ion current flow is a direct measure of the gas pressure. These both are highly sensitive instruments and thus most suited for fractional pressures. The hot cathode gauges are even more sensitive than cold cathode gauges and are able to measure pressures near 10-8Pa. Their sensitivity ranges from (1E-16 to 1E-13) MPa

An example of an ionization gauge can be found here: http://www.bama.ua.edu/~surfspec/vacbasics_files/image049.jpg

Semi-batch Reactor Problem
Suppose you have a semi-batch reactor (1,000 L) with 50 kg of zinc within the reactor at 1 atm pressure and 25 C. 6M hydrochloric acid is flowing in at 1 L / min to react with the zinc to produce zinc chloride for use in another process.

A) What factors should be considered?

B) Say the valve fails at an operating pressure of 4 atm (i.e., it will not close and the reactor will be flooded with HCl) At what pressure would you (safely) set the shutdown point?

C) What type of sensor should be used?

Ans:

The factors that should be considered are:
{1000 L}$$ = 0.073 atm / min.
 * 1) Process
 * 2) Hydrochloric acid is very, very caustic (especially at such a high molarity), and thus whatever sensor you choose, it should be able to withstand the corrosive nature of hte process.
 * 3) Range of pressures
 * 4) Initially the reactor is at 1 atm of pressure. Considering the reaction 2 HCl(aq) + Zn(s) --> H2(g) + ZnCl2(aq), you're producing one mole of hydrogen gas in addition to the existing air pressure in the vessel. As the reaction proceeds, the pressure would increase substantially within the vessel. Modeling the pressure of H2(g) ideally, $$P = nRT/V$$
 * 5) $$P = \frac{(6M HCl) (1 L / min) (1 mol H_{2(g)}/ 2 mol HCl_{(aq)}) (0.08206 Latm / molK) ((25 + 273) K)}
 * 1) After about 1 hour, the pressure of H2(g) would increase to 4.38 atm, putting the total pressure in the vessel at 5.38 atm (past failing pressure for the valve).
 * 2) Environment
 * 3) There is no danger of high temperatures or excessive vibration due to high flow / reaction.
 * 4) Sensitivity
 * 5) Since this is a moderately dangerous process, we need to have the sensor output to a computer so an engineer can monitor the process as a fail-safe. We assume the sensor will signal the HCl valve to close once the operating pressure becomes 3 atm, however devices do fail from time to time. We also need high sensitivity, so electric components will be preferrable (i.e., we don't want the process to runaway as it potentially could if the sensor isn't highly sensitive to incremental changes).

The shutdown point
Considering the rapid increase in pressure, as evaluated in (2), and the failure of the valve at 4 atm, the shutdown point should be approximately 3 atm.

The type of sensor:

 * 1) Considering the types of sensors discussed, we can automatically eliminate vacuum sensors as they operate at very low pressures (almost vacuum, hence the name). We can also eliminate differential pressure sensors as we are not looking for a pressure drop across the vessel.
 * 2) Since we desire high sensitivity, we would like to use electric components. Considering the range of pressures (3 atm max ~ .3 MPa) a capacitive element would be optimal because it is robust and functions well in low pressure system.
 * 3) Noting the corrosiveness of the HCl in the system, a diaphragm is likely to be used as the elastic element. Diaphragms are also fairly robust and offer quick response times.
 * 4) This combination is likely to be filled in a strong, sealed, glycerine/silicone filled case so as to protect the sensor from degradation.

So, overall, the sensor we choose will utilize a diaphragm as the elastic component, a capacitive element as the electrical component, and an anti-corrosive body.

Worked out Example 2
Your supervisor told you to add a pressure sensor to a very expensive and important piece of equipment. You know that the piece of equipment is operating at 1MPa and at a very high temperature. What sensor would you choose?

Solution

Because the piece of equipment that you are dealing with is very expensive, you need a sensor that has the greatest sensitivity. An electric sensor would be desired because you could have it connected to a computer for quick and easy readings. Also, you need to pick a sensor that will operate at 1 MPa and a sensor that will be able to withstand high temperatures. From the information given in this article you know that there are many sensors that will operate at 1 MPa, so you need to decide on the other factors. One of the most sensitive electric sensors is the capacitive sensor. It has a sensitivity of 0.07MPa. The capacitive sensor usually has a diaphragm as the elastic element. Diaphragms have a rapid response time, are very accurate and work at 1 MPa.

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