Process Instrumentation and Control (English)

Process instrumentation and control

Sensors

General properties of the sensors

A sensor is a device able to measure a particular physical variable in a system. The part of the sensor which transforms the mechanic signal into an electric one is called transducer. The transducers take their names by the input variable because the output one is always electric. Particular transducers which involve direct current are called transmitters; they are able to transmit signal for long distance. The measured entity is the physical quantity which is measured by the sensor. The set of values that the sensor is able to measure is called measuring range; it’s between the range [x_min; x_max]. The maximum value is called full scale and the difference is called span.

The most important properties of the sensors are:

• Accuracy estimates the closeness of the measure to the real value. The are three ways to express the accuracy, they are:

(x_m - x_v) = 100ε·f(x_FS)

(x_m - x_v) = 100ε·a(x_v)

(x_m - x_v) = Bias = x ^{± 1°C}

• Repeatability is the ability to provide a measured value with a deviation as small as possible with respect to a true value.
• Calibration is a procedure or method of adjusting parameters of the sensor in order to improve the accuracy.
• Rangeability is the ratio between the full scale and the infimum of the measuring.
• Static characteristic is represented by a diagram or an analytic form of the relation between the measured variables and the output signal: y = f(u).
• Sensitivity is represented as the ratio: Δy/Δu.
• Resolution is the smallest change of the measured value which can be detected by the sensor.
• Sensitivity threshold is the resolution at the minimum of the measuring range.
• Hysteresis is the maximum difference between values of the output signal in a "going and return" calibration procedure.
• Dynamic characteristic describes how the instrument responds to a variation in the measured entity. It is expressed by a characteristic time called response time.

The parameters that can distinguish a sensor are:

• The measured variable (Pressure, Temperature, Voltage);
• The physical principle on which they are based;
• The energetic behaviour (active and passive sensors);

Two categories of sensor which have been introduced in the last years are:

• Smart sensors that are measuring devices able to process signal into a digital one, transmit information to external environment, memorize and provide the configuration;
• Soft sensors which are software-implemented algorithm where several measurements are processed together.

Temperature measurements

The temperature control is fundamental in process engineering; for this reason, it is indispensable to have instrumentation able to measure this variable with accuracy, repeatability and short response time. The common devices used for this operation are based on thermomechanical and thermoelectric principles:

• Thermomechanical sensors are: liquid-in-glass thermometer;
• Thermoelectric sensors are: thermocouples, resistance thermometers, thermistors, solid state sensors, pyrometers.

Thermocouples

The so-called Seebeck effect is a thermoelectric principle which involves conductors submitted to a temperature gradient which causes a voltage E between the conductors' terminals.

E = ∫_T1^T₂ σ(T) dT; σ = SEEBECK COEFFICIENT

An occurrent problem linked to the Seebeck effect is represented by the difficulty of the voltage measurement of the hot junction. To solve this problem, we use two conductors connected to the hot point and we use the voltmeter to measure the voltage between the two cold junctions.

E = ∫_Tc^T_h σ(T) dT - σ(T_c)

The electromotive force depends on the cold junction temperature which is not fixed and subject to variability, even unpredictable. We transform the cold junction into a reference junction and keep it at reference temperature (for example, 0°C). That could not be easy, in particular in the industries. We can remedy this using the law of intermediate temperatures:

E(T_h, T_c) = [E(T_h, 0) - E(T_c, 0)]

The practical measure is obtained in this way:

• The reference temperature is measured by a small semiconductor dedicated sensor;
• The reference temperature is converted into the corresponding voltage;
• The reference voltage is algebraically added to the measured voltage in order to obtain the reference voltage of a thermocouple with the cold junction at 0°C;
• The voltage is converted into the corresponding measured temperature using the reference tables.

Usually, the cold junction is far from the voltage measurement device, so we use wires to connect them:

• Extension wires consist of wires made of the same material as the thermocouple material;
• Compensation wires consist of wires made of a different material, but equivalent to the constructive material of the TC.

The thermocouples are made of materials which present: high electrical conductivity, constancy of the characteristic, ductility, low cost, resistance to aggressive and hot environment, large T range. The static characteristic of a thermocouple can be easily obtained in a laboratory placing the cold junction at 0°C.

The common configurations of thermocouples are:

• Bare hot junction These present very short response time, but they are unsuitable for aggressive environment.
• Grounded hot junction In this type of realization, the hot junction is an integral part of the protection stealth.
• Insulated hot junction The hot junction is completely insulated from the protection stealth.

Resistance temperature detector (RTD)

This kind of device is based on the temperature dependence of the electrical resistance of a conductor. The materials involved are platinum, copper, and nickel. RTDs present a greater accuracy than the TC: in the range ±0.02°C between -50 and 150°C. The transduction of the resistance value in voltage is performed by a Wheatstone bridge.

Thermistors

Thermistors are devices which use the principle of the electrical resistance variation in a non-conductor with temperature; the materials usually involved are:

• Semiconductors;
• Metal Oxides.

We can distinguish two types of thermistors looking at the dependence with the temperature that, in both cases, is non-linear:

• NTC Thermistors (Negative Temperature Coefficient);
• PTC Thermistors (Positive Temperature Coefficient).

In both cases, the temperature range is between -50 and 250°C with an absolute accuracy of ±0.1°C.

Infrared temperature measurement

Contact-based temperature sensors have demonstrated great accuracy. However, there are many applications and settings where they are not practical. In those cases, engineers can turn to non-contact temperature measurement devices, many of which are based on measuring infrared radiation (Pyrometer).

Typical costs

The typical costs of temperature measurement devices are:

• Thermocouples: 40-50 euros;
• RTD: 90-100 euros.

Pressure measurements

In order to be clear in the following definitions, it’s useful to give preliminary definitions of pressure:

• Absolute pressure Pressure referenced to the perfect vacuum.
• Barometric pressure Pressure exerted from the atmosphere on the Earth’s surface (it can change). The standard atmospheric pressure is measured at sea level, at 0°C and with average weather conditions. The values in terms of the most important units are:
  • 101325 Pa;
  • 1 atm;
  • 760 mmHg;
  • 14.6959 psi.
• Differential pressure Pressure difference between two different points.
• Gauge pressure Difference between the absolute and the barometric pressure.
• Residual pressure Absolute pressure that is referred to the perfect vacuum and it’s below the atmospheric pressure.
• Vacuum Pressure measured from the barometric pressure to the down.

Pressure sensors

Quite often all pressure sensors are improperly called manometers; here we distinguish the pressure sensors:

Classification

The pressure measurement devices are classified according to the measuring principle:

• Variation of a liquid level;
• Deformation of an elastic element (Macro-deformation);
• Change of an electromagnetic quantity (Micro-deformation).

Liquid column manometer

Stevin’s law: P_A = P_atm + ρgΔh

Measuring range: 0.01-2 bar. This kind of device presents disadvantages such as:

• Usable only with low differential pressure;
• Almost exclusively with gas and vapor;
• It’s a local indicator, not part of automatic controls.

Bourdon pressure gauge

It consists of a closed-end elastic tube shaped as an arc with a fixed terminal. The free terminal moves because of the stress given by the pressure. This device is usually involved as a local indicator in piping systems. The assembling accessories for this kind of measurement device are:

• Quadrant Ø 40mm: Quadrant with double graduation in psi and kg/cm²;
• Quadrant Ø 50mm: Quadrant with double graduation in bar and psi.

Capacitive pressure transducers

The measurement principle of this device is the change of the capacity:

A = ε_rε₀ / d

We can also distinguish two cases:

• Capacitive cells with ceramic membranes;
• Ceramic cells with metallic diaphragm.

Another configuration, used to measure a differential pressure, is:

• Capacitive cells with double compensator.

(In all cases, the transduction is operated by a Wheatstone bridge)

Electrical resistance-based pressure transducers

Strain-Gauge Piezoelectric Transducer: It operates on the variation of an electrical resistance due to the change of the length and the cross-sectional diameter: R = l₀ / (ρA₀).

Piezoelectric transducer: The electrical resistance and the voltage across the sensible element, which is a crystal or another solid material, changes directly because of the deformation.

Accuracy: 0.1%

Rangeability: (75/100):1

Measuring range: 0-14000 bar

Inductive differential pressure transducers

The measuring principle involved by this kind of device is the variation of the inductance. The pressures acting on the two sides of the device produce a deformation of the metallic diaphragm and a consequent translation of two units of ferrite with respect to two fixed coils. The deformation occurring as a consequence of the pressure difference is transduced in an inductance variation through a Wheatstone bridge.

Resonators on silicon

The measuring principle of this device is the resonant frequency induced in a double diapason of a resonant silicon mono-crystal immersed in a permanent magnetic field. They are usually named MEMS (Micro ElectroMechanical Systems). Resonant frequency depends on the transverse deformation produced by the measuring pressure. The advantages are:

• No Attrition;
• No AC/DC converter;
• Better performances and stability with time.

Flow rate measurements

Within the class of flow meters, we can distinguish three different kinds of device:

• Volumetric flow meter;
• Mass flow meter;
• Molar flow meter.

Another classification could be based on the measuring principle:

• Differential pressure;
• Variable area;
• Velocity;
• Direct mass measurements;
• Rotary.

Contraction-based flow meters

The contraction-based flow meters are devices which use contraction in the section of the pipe to establish a differential pressure in the pipeline in order to evaluate the flow rate. The position of the pressure sensors determines different evaluations of the flow rate; the possible configurations are:

• At vena contracta;
• On the carrier ring;
• On the pipeline.

There are several configurations of this class of flow meter, in particular:

• Orifice plates Devices used for the evaluation of the volumetric flow rate of gas and liquids through a sharp reduction of the cross-sectional area of the fluid flow. Usually, the diaphragm is thin and the orifice can assume different configurations:
  • Off-axis;
  • Semi-circular;
  • Grooved.

The main conditions for the installation are:

• Re > 500;
• Horizontal position;
• Undisturbed straight pipeline 20D upstream and 5D downstream (where D is pipe diameter).

• Flow nozzles Devices used for the evaluation of the pressure drop before and after a contraction by means of a differential manometer. The advantage of this type of device is the easy substitution and the possibility of different values of β.
• Venturi meter This device consists of a converging and diverging section. The initial decrease of section determines an increase in velocity (because of the continuity equation). The venturi meter shows a better repeatability than the other contraction-based flow meters because it is less scratched by the solid particles transported by the fluid. With the same contract ratio venturi meter has also greater accuracy and lower pressure drop, but is more expensive. It’s also important to take into account cavitation in the design and construction.

Variable area flow meter - Rotameter

The Rotameter consists of a transparent pipe, slightly conical and graduated. Inside there is a body (float) having a greater density than the fluid which flows in the pipe. Measurement is performed by the observation of the position of the float on the graduated scale. The hypotheses for the rotameter are:

• Steady state;
• Local and distributed pressure drop negligible;
• Surfaces for pressure forces are projected areas: A₁ = A₂.

The flow equation of the rotameter is obtained in this way:

• Force balance equation: P₁A₁ - P₂A₂ - ρ₀V₀g = 0 → P₁A₁ - P₂A₂ - ρ₀V₀g = 0
• Continuity equation: A₁V₁ = A₂v₂ → v = A₂V₁ / A₁ → h = V₂ / A₁ Δh
• Bernoulli’s equation: (P₁ - P₂)/ρ₂ = (v₂² - v₁²)/2 + gh → (v₂² - v₁²)/2 = gΔh
• (p₂/ρ₂ - p₁/ρ₁)/(1- (A₁/A₂)²) = gΔh

The geometric dependence of the surface area of the throttling section on the height of float lifting is:

A(H) = π/4 [Θ(D + tanΘ(H)) + Θ₀(tanΘ(H) + tanΘ₀)]

The volumetric flow rate of a rotameter is expressed in normal-liters per hour for the calibration condition; in a different condition, the measurements need correction as:

V_m = V_n√(ρ₀/ρ)_calibration = V_n√(ρ_n/ρ)

For an ideal gas:

PV = nRT → ρ = MP/RT → V_m = V_n√(T₀/T) → V_n√(P/P_n)

The accuracy for the rotameter is:

• ±1% of the measurement at 100% of the flow rate and ±3/10% of the measurement at 10% of the max flow rate.

The measuring range is up to 30 kg/s for water and up to 1 kg/s for air.

The advantages consist of:

• Linear relation flow rate-float position;
• Constant pressure drop across the float;
• Easy to read.

The disadvantages are:

• Need of calibration;
• Only vertical installation;
• Reinforced model for high-pressure pipe, which needs an electromagnetic display to be read.

Flowmeter – Measurement of velocity