flow glossary - · pdf fileflow glossary version 2 august 2011 . page 2 of 67 ... dead weight...

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Flow Glossary

Version 2

August 2011

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Contents Accuracy .............................................................................................................................................. 9

Acoustic Path Configurations .............................................................................................................. 9

Ambient Temperature ........................................................................................................................ 9

Amplification ....................................................................................................................................... 9

Annular Flow ....................................................................................................................................... 9

Asymmetry ........................................................................................................................................ 10

Attenuation ....................................................................................................................................... 10

Averaging Pitot .................................................................................................................................. 10

Bell Prover ......................................................................................................................................... 11

Bernoulli’s Equation .......................................................................................................................... 12

Bernoulli’s Principle .......................................................................................................................... 13

Beta ................................................................................................................................................... 13

Bluff (vortex shedding device) .......................................................................................................... 13

Bourdon Gauge ................................................................................................................................. 13

Bubble Flow ...................................................................................................................................... 14

Calibration ......................................................................................................................................... 14

Carbon Capture and Storage ............................................................................................................. 15

Cavitation .......................................................................................................................................... 15

Churn Flow ........................................................................................................................................ 15

Compressibility .................................................................................................................................. 16

Computational Fluid Dynamics ......................................................................................................... 16

Cone Meters ...................................................................................................................................... 16

Coriolis Effect .................................................................................................................................... 17

Coriolis Mass Flow Meters ................................................................................................................ 17

Cross Correlation............................................................................................................................... 18

Cryogenics ......................................................................................................................................... 19

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Dead Weight Tester .......................................................................................................................... 19

Decay (of Flow Disturbance) ............................................................................................................. 20

Density and Specific Volume ............................................................................................................. 20

Diagnostics ........................................................................................................................................ 20

Dimensionless Numbers ................................................................................................................... 21

Discharge Coefficient ........................................................................................................................ 21

Distortion (of the Velocity Profile) .................................................................................................... 21

Doppler Principle .............................................................................................................................. 22

Dual Energy Gamma Ray Absorption ................................................................................................ 22

Effective Range and Rangeability ...................................................................................................... 23

Electromagnetic Flow Meters ........................................................................................................... 24

Emulsion ............................................................................................................................................ 24

Error .................................................................................................................................................. 24

Falling Sphere Viscometer ................................................................................................................ 25

Filters................................................................................................................................................. 25

Flow Conditioners ............................................................................................................................. 25

Flow Disturbances ............................................................................................................................. 26

Flow Meter ........................................................................................................................................ 26

Flow Nozzles ...................................................................................................................................... 26

Flow Regime ...................................................................................................................................... 27

Fluid ................................................................................................................................................... 27

Flying Start and Stop Flow Calibration Process ................................................................................. 27

Fouling ............................................................................................................................................... 28

Froude Number ................................................................................................................................. 29

Gas .................................................................................................................................................... 29

Gas Entrainment ............................................................................................................................... 29

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Gas-Liquid Ratio ................................................................................................................................ 29

Gas-Oil Ratio ..................................................................................................................................... 29

Gas Void Fraction .............................................................................................................................. 29

Gas Volume Fraction ......................................................................................................................... 29

Heat Exchanger ................................................................................................................................. 29

Homogeneous Flow .......................................................................................................................... 30

Horizontal Flow ................................................................................................................................. 30

Humidity in Gases ............................................................................................................................. 30

Impulse Line ...................................................................................................................................... 30

Inferential Mass Flow Meters ........................................................................................................... 30

Insertion Meters ............................................................................................................................... 30

Inversion Region ............................................................................................................................... 31

K-Factor ............................................................................................................................................. 31

Laminar and Turbulent Flow ............................................................................................................. 31

Laser Doppler Velicometry (LDV) ...................................................................................................... 32

Linearity ............................................................................................................................................ 32

Liquefied Natural Gas ........................................................................................................................ 33

Liquid Hold-up ................................................................................................................................... 33

Lockhart-Martinelli Parameter ......................................................................................................... 33

Manometer ....................................................................................................................................... 34

Mass .................................................................................................................................................. 34

Mass Flowrate Measurement ........................................................................................................... 34

Mean Pipe Velocity Measurement ................................................................................................... 34

Measurement Standard .................................................................................................................... 34

Measurement Uncertainty................................................................................................................ 35

Mercury Seal Prover.......................................................................................................................... 35

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Meter Error ....................................................................................................................................... 35

Meter Factor ..................................................................................................................................... 36

Multiphase Flow................................................................................................................................ 36

Multiphase Flowrate ......................................................................................................................... 36

Multiphase Flow Separation ............................................................................................................. 36

Multiphase Velocity .......................................................................................................................... 37

Newtonian Fluids .............................................................................................................................. 37

Non-Newtonian Fluids ...................................................................................................................... 37

Oil ...................................................................................................................................................... 38

Oil-Water Separation ........................................................................................................................ 38

Orifice Plates ..................................................................................................................................... 39

Phase ................................................................................................................................................. 39

Phases and Phase Diagrams .............................................................................................................. 40

Phase Flowrate .................................................................................................................................. 40

Phase Area Fraction .......................................................................................................................... 40

Phase Mass Fraction ......................................................................................................................... 41

Phase Slip .......................................................................................................................................... 41

Phase Volume Fraction ..................................................................................................................... 41

Pipe Provers ...................................................................................................................................... 41

Plate Heat Exchangers ...................................................................................................................... 42

Platinum Resistance Thermometers ................................................................................................. 42

Plug Flow ........................................................................................................................................... 43

Point Velocity Measurement ............................................................................................................ 43

Positive Displacement Meter ............................................................................................................ 43

Pressure ............................................................................................................................................ 44

Pressure Drop ................................................................................................................................... 45

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Pressure-Volume-Temperature Equation ......................................................................................... 45

Produced Water ................................................................................................................................ 45

Relative Density/Specific Gravity ...................................................................................................... 46

Resolution ......................................................................................................................................... 46

Repeatability ..................................................................................................................................... 46

Reproducibility .................................................................................................................................. 46

Reynolds Number.............................................................................................................................. 46

Sampling ............................................................................................................................................ 47

Shell and Tube Heat Exchanger ........................................................................................................ 47

Signal Conditioning ........................................................................................................................... 47

Single Energy Gamma Ray Absorption .............................................................................................. 48

Slip Ratio ........................................................................................................................................... 48

Slip Velocity ....................................................................................................................................... 48

Slug Flow ........................................................................................................................................... 48

Snell’s Law ......................................................................................................................................... 49

Solubility of Air in Liquids .................................................................................................................. 49

Sonic Nozzles ..................................................................................................................................... 50

Standing Start and Stop Flow Calibration Process ............................................................................ 50

Steam ................................................................................................................................................ 51

Stokes’ Law ....................................................................................................................................... 52

Stratified Flow ................................................................................................................................... 52

Strouhal Number ............................................................................................................................... 53

Superficial Phase Velocity ................................................................................................................. 54

Swirl................................................................................................................................................... 54

Temperature ..................................................................................................................................... 54

Thermal Conductivity ........................................................................................................................ 54

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Thermal Expansion Coefficient ......................................................................................................... 54

Total Volume Measurement ............................................................................................................. 55

Traceability ........................................................................................................................................ 55

Tracer Methods for Flow Measurement ........................................................................................... 55

Transducers ....................................................................................................................................... 56

Transducer Configurations ................................................................................................................ 56

Transducer Frequency ...................................................................................................................... 57

Transfer Standard ............................................................................................................................. 57

Transit Time (time of flight) .............................................................................................................. 58

Transition Regions ............................................................................................................................. 58

Transmitters ...................................................................................................................................... 58

Triple Point Cell ................................................................................................................................. 58

Turbine Meter ................................................................................................................................... 59

Turbulence ........................................................................................................................................ 60

Turndown .......................................................................................................................................... 60

U-tube Viscometer ............................................................................................................................ 60

Valve Flow Coefficient ...................................................................................................................... 61

Variable Area Meters ........................................................................................................................ 62

Velocity Head .................................................................................................................................... 62

Velocity Profile .................................................................................................................................. 62

Venturi Tubes .................................................................................................................................... 63

Verification ........................................................................................................................................ 63

Vertical Flow ..................................................................................................................................... 63

Viscosity ............................................................................................................................................ 63

Void Fraction ..................................................................................................................................... 64

Volumetric Flowrate Measurement .................................................................................................. 64

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Vortex Meter ..................................................................................................................................... 65

Vortex Shedding ................................................................................................................................ 65

Water Cut .......................................................................................................................................... 66

Water-in-Liquid Ratio ........................................................................................................................ 66

Wedge Meter .................................................................................................................................... 66

Wet Gas ............................................................................................................................................. 67

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Accuracy This is the closeness of the agreement between the obtained measurement and the true

value of the measurement. Accuracy is a qualitative rather than quantitative term. So, for

example, it is perfectly correct to state that one instrument is more accurate than anther but

incorrect to ascribe a number to the accuracy.

Acoustic Path Configurations Ultrasonic meters tend to be available with a variety of path configurations. A selection of

commonly encountered path configurations is given below.

As a general rule, increasing the number of paths reduces the error, as an improved, more

accurate average velocity profile will be obtained. However increasing the number of paths

normally increases the cost of the meter.

Ambient Temperature Ambient temperature is a term which refers to the temperature in a room, or the temperature

which surrounds an object of interest. The value of the ambient temperature should be

quoted and not assumed to be a standard value.

Amplification Amplification is usually applied on data acquisition boards to improve the resolution of the

analogue-to-digital converter (ADC) by maximizing the analogue signal to match the ADC’s

voltage range. Amplification can also be applied to low voltage signals from the sensor.

This allows the signal to be amplified before it is affected by environmental noise; thus

increasing the signal-to-noise ratio.

Annular Flow This flow regime develops when the gas velocity is high. In annular flow, the gas (or lighter

phase) flows as a core in the centre of the pipe with the liquid forming a film on the pipe wall.

In horizontal flow, due to gravity, there will tend to be more liquid near the bottom of the pipe

than at the top.

A large fraction of the liquid phase may become entrained in the gas core, as droplets

travelling at velocities close to that of the gas. As the gas velocity increases further, the film

on the pipe wall may disappear completely, with the liquid becoming completely entrained in

the gas and the combined phases flowing as a mist.

single path double path double path four path nine path

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Asymmetry In long straight sections of pipe the flow (or velocity) profile will essentially be symmetrical

about the central axis of the pipe. However, in real pipe circuits the presence of a bend, a

flow meter, or a valve etc., will result in distortions to the flow profile.

Attenuation In relation to ultrasonic flow meters, attenuation is the reduction in signal amplitude

(strength) resulting from the beam passing through the fluid (and pipe wall in the case of

ultrasonic non-invasive meters). How strongly the transmitted signal reduces in amplitude

as a function of frequency is referred to as the attenuation coefficient. The value of the

coefficient will depend upon the media through which the ultrasound beam passes.

Averaging Pitot Averaging pitots are sometimes referred to as Annubars and contain multiple pressure

tappings to average the flow in order to try to compensate for a non ideal flow profile. The

averaging pitot tube is inserted across the pipe as indicated below. One side of the bar has

Annular Flow

Annular

Flow

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pressure taps facing the flowing fluid that are coupled into an averaging chamber that

measures the total (i.e. static + dynamic) pressure of the fluid.

There may be a single port (as shown) or multiple tapping ports on the opposite side of the

bar to measure the low static pressure in the downstream region. The difference between

the total and static pressures is effectively a measure of the fluid velocity head, which

together with the pipe area enables the volumetric flowrate to be determined.

Bell Prover The Bell Prover is the standard for calibrating low flow gas meters such as domestic meters.

A cylinder (or bell), open at the bottom and closed at the top, is lowered into a liquid bath.

The weight of the cylinder is supported by a wire, string or chain and counter balanced by

weights. A smaller counterbalance on a shaped cam arrangement (not shown in image) is

added to compensate for the changing buoyancy as the cylinder is submerged. By altering

the counterbalance weight, a pressure can be generated in the cylinder. A pipe passing

through the liquid is open to the trapped volume and, as the cylinder is lowered, gas is

displaced from the cylinder to the meter on test. By timing the fall of the cylinder and

knowing the volume/length relationship for the cylinder, the volume flow of gas through the

meter may be determined and compared with the meter reading. Most bell provers are filled

with low vapour pressure/low viscosity oil.

Low pressure

sideHigh

pressure

side

Static

pressure

port

Low

pressure

tube

Internal

averaging

tube

Total

pressure

ports

P

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Bernoulli’s Equation This equation describes the relationship between different energy types in a flow. Bernoulli

proved that the total energy at any given point within flow through a pipe is constant. That is,

it can be considered as a statement of the conservation of energy: energy per unit volume

before = energy per unit volume after. For example, in the diagram below energy at location

1 = energy at location 2 = energy at location 3.

In the above illustration:

hνhνhνΡ 3

2

32

2

21

2

11ρgρ

2

1ρgρ

2

1ρgρ

2

1

Where:

Ρ = Pressure energy

2ρν2

1= Kinetic energy per unit volume

ρgh = Potential energy per unit volume

Cylinder

Test meter

Gas

Pulley

Counter

weights

Water bath

Location 1

Location 2

Location 3

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Bernoulli’s Principle If a flowing fluid experiences a pressure drop there will be a corresponding and immediate

increase in the velocity of the flow (see Bernoulli’s Equation).

Beta Beta (β) is the ratio between the diameter of the orifice or throat of device (d) to that of the

pipe (D). Note: The lower the β value the smaller the diameter and the greater the pressure

loss.

Bluff (vortex shedding device) A bluff is the term referred to the body or obstruction used in vortex meters to generate the

vortices. Behind the obstruction to the fluid, a series of vortices is generated at a frequency

directly proportional to the fluid velocity. Externally or internally mounted sensors located

downstream on the pipe wall measure the frequency of the vortex shedding and from this the

velocity and volumetric flowrate can be determined.

Bourdon Gauge The Bourdon gauge is constructed using a metal tube with suitable elastic properties. It has

an oval cross section bent into a circular arc or coil and fixed at one end. As the fluid

pressure is applied to the inside of the tube it deforms to become circular and this in turn

causes the tube to straighten. Movement of the sealed free end of the tube is amplified and

coupled to a pointer via a linkage and gear mechanism thus indicating the pressure on a

dial.

Examples of vortex shedding device shapes

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Bubble Flow Bubble flow consists of a continuous liquid phase dispersed with small bubbles of gas. This

regime is observed when the ratio of gas flowrate to liquid flowrate is low. In horizontal flow,

due to the effect of gravity, the bubbles tend to collect in the upper part of the pipe.

Calibration Calibration is a comparison between the reading of a device and that of a standard (see

Measurement Standard). The process which establishes this relationship is a set of

interrelated measurements and operations which provide the comparison. Flow

measurement does not rely on a single operation and so neither does a flow based

calibration.

Measurement of the quantity of fluid depends on establishing the basic quantity and a

number of influence factors. The quantity of fluid may be expressed as a volume or a mass.

Bubble Flow

Bubble Flow

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The measurand (quantity that is being determined by measurement) may be the quantity or

the ‘rate’ i.e. the quantity per unit time (Kg/hr, l/s, m3/hr).

Carbon Capture and Storage Carbon Capture and Storage (CCS) is the process of capturing carbon dioxide (CO2) which

would otherwise be released to atmosphere and to thereafter store it permanently in a

suitable and safe geological storage site underground. The CCS chain involves three

defined stages:

Capture

Transportation

Storage (sometimes called sequestration)

Cavitation In a flowing liquid, if the pressure drop is large enough, a phenomenon known as cavitation

can occur. This can take two different forms:

In water and in liquefied gases cavitation generally occurs only when the pressure at some

point approaches the vapour pressure of the liquid. Then bubbles or pockets of vapour

appear, only to collapse as soon as they enter a region of higher pressure.

In oils and liquid fuels cavitation generally takes a different form. It begins at pressures

below atmospheric pressure, but well above the vapour pressure, and consists of the

release of bubbles of air from which the solution take quite a long time to re-dissolve.

Churn Flow As the gas velocity is increased beyond that for slug flow, a highly turbulent regime known

as churn flow develops. Irregular slugs of gas move up the centre of the pipe, generally

carrying droplets of liquid with them. The liquid rises and falls in an oscillatory manner

(hence the description churn flow), although the net flow remains upwards. Neither the gas

nor the liquid phase is continuous. Churn flow is a particular characteristic of large diameter

flow tubes, occurring over a wider range of flow conditions as the tube diameter is increased.

Churn

Flow

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Compressibility The compressibility of a fluid () is the fractional decrease in specific volume (or the

fractional increase in density) caused by unit increase of pressure. That is:

.p

ρ

ρ

1

p

V

V

1κ s

s

The compressibility of water is about 1/20,000 that of air at atmospheric pressure, and for

most purposes can be ignored. The compressibility of liquid petroleum products varies with

their composition, viscous oils being only a little more compressible than water and light

fuels being more than twice as compressible as water. In the large-scale commercial

metering of oils and fuels compressibility is generally taken into account when pressures

above about 2 bar are encountered, whist gases are very highly compressible at low

pressures; the opposite is true of gases at high pressures.

The humidity of a gas affects its density. For example, in the case of air at 1 bar and 23°C,

the density when dry is about 1 per cent greater than the density when saturated with water

vapour.

Computational Fluid Dynamics Computational Fluid Dynamics (CFD) is a powerful technique that utilises numerical

methods and algorithms (based around the Navier-Stokes equations) to predict the three

dimensional behaviour of fluid flows. CFD essentially integrates the disciplines of fluid

dynamics, mathematics and computer science. It is particularly dedicated to fluids that are

in motion and how the fluid behaviour influences flow related processes. This includes the

modelling of liquid, gas and multiphase flow through pipework and process components.

Either on its own or in conjunction with other analysis tools, experimentation and validation,

CFD can be used to:

Numerically model fluid flows (including heat transfer), particularly in situations where

it is not practical or feasible to undertake testing.

Predict flow properties without disturbance to the flow; something which is not always

possible with measuring instruments.

Devise and optimise laboratory test programmes.

Aid designers to optimise designs through numerical analysis, thus reducing the

number of prototypes for experimental testing.

Predict future flow issues and compatibility / durability of flow systems for aging

effects; for example erosion of valves and pipes, and other flow assurance issues.

Cone Meters Cone meters (e.g. V-cones) are a type of differential pressure meter which is essentially an

inverted Venturi tube. Instead of a contraction in the pipe, the fluid flows around a central

cone as shown below.

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Various designs are available and the downstream tapping can either be located in the base

of the cone or machined through the wall of the meter body at the widest part of the cone.

The upstream pressure tapping is located before the cone. Cone meters have proved

popular as it has been claimed that they require very little upstream straight pipework before

the meter to provide accurate measurements. This benefit is claimed to be due to the fluid

flowing around the cone which is described as conditioning the flow. Cone meters are not

covered by the standard ISO 5167 which describes the common differential pressure meter.

Coriolis Effect The Coriolis Effect was first reported in 1835 by the engineer Gustav Gaspard Coriolis, who

established relationships between forces present when a mass moves in a rotating plane. A

common example in nature is found in the motion of the atmosphere where large masses of

air flow from cold to hot regions on the earth’s surface. This mass flowing across the

rotating surface has forces acting on it to produce rotation of the air flows.

Coriolis Mass Flow Meters Coriolis mass flow meters exploit the Coriolis Effect by operating on the principle that inertia

forces are generated whenever a particle in a rotating body moves relative to that body in a

direction toward or away from the centre of rotation. This principle is shown below. A

particle of mass (m) moves with constant velocity (v) in a conduit which is rotating with

angular velocity () about a fixed anchor or pivot point. The particle acquires two

components of acceleration:

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A radial acceleration (ar) – Centripetal - equal to (2r) and directed towards the pivot.

A transverse acceleration (at) – Coriolis - equal to (2v) at right angles to (ar) and in

the direction shown.

To impart the Coriolis acceleration (at) to the particle, a force of magnitude (2v.m) is

required in the direction of (at). This comes from the conduit. The reaction of this force back

on the conduit is the Coriolis force (Fc = 2v.m).

From this illustration it can be seen that when a fluid of density () flows at a constant

velocity (v) along a rotating conduit, length (X), the tube experiences a transverse Coriolis

force of magnitude (Fc = 2v.A.X), where (A) is the cross sectional area of the conduit

interior. If the mass flowrate is (Qm), then since:

Qm = vA

and

Fc = 2.X.Qm.

Hence the measurement of the Coriolis force exerted by a flowing fluid on a rotating tube

can provide a direct measure of the mass flowrate. An additional advantage of Coriolis

meters is the ability to provide fluid density information.

The density is derived from the natural frequency of oscillation of the flow tube which varies

with mass. A change in the mass results in a change in frequency. As the volume of the

flow is constant the oscillation frequency is a function of fluid density.

Cross Correlation Cross correlation involves the measurement of some property of the flow at two separated

points along the flow direction. Typically this might be the response of a gamma-

densitometer, pressure, microwave or capacitance sensor to some transient effect in the

flow, such as the passage of a gas bubble or slug. The mean velocity of the flow is then

determined from the time lag between similar (correlated) sensor signals measured at the

two points.

Pivot/anchor ω

ar

at

Fr

Fc

δm

Generation of Coriolis force

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The time lag between correlated signals from an upstream (green) and downstream (red)

sensor to transient variations of the flow, is used to determine the mean flow velocity

between the two points.

Statistical correlation techniques are used to compare the signals from the upstream sensor

with those from the downstream sensor, allowing the mean transit time of the mixture

between the sensors to be derived. The measured transit time and the sensor spacing give

the bulk flow velocity.

Cryogenics Cryogenics is the generation of very low temperatures (below -150⁰C) and study of materials

and devices (including flow meters) at those temperatures. Examples of cryogenic fluids

include liquefied natural gas and liquefied nitrogen.

Dead Weight Tester The so called dead weight tester is an example of a primary pressure calibration standard.

A dead weight tester, or more precisely pressure balance, is a machine which generates a

known pressure from the force resulting from the placement of calibrated masses (weights)

on a very accurately machined piston located in a vertical, close fitting cylinder of known

cross sectional area. Testers are manufactured to operate with either dry gas or liquid,

usually oil, and the underlying principles are exactly the same.

Se

ns

or

Sig

nal

Time

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Hand pumpGauge

Connection

Oil

Reservoir

Schematic of Pressure Balance (Deadweight Tester)

Piston /

cylinder

Assembly

Decay (of Flow Disturbance)

Meters may be affected by one or more of the factors described in Flow Disturbances

to varying degrees. In most cases, the percentage error generated by flow disturbances

tends to remain constant, regardless of the flow rate. In general measurement errors

generated by flow disturbances tend to be of the order of 10% or less which means that

errors may be difficult to spot. However, some types of meter can be grossly affected by

swirl or velocity profile distortion.

Examples of decay lengths:

Distortion of axial velocity profiles generally decays to near zero in about 20 to 30 pipe

diameters (20 to 30D)

Single vortex swirl can persist for more than 100D. Double and multiple vortex swirl

decays within 20D (the more vortices, the quicker the decay rate)

Turbulence generally decays to fully developed levels in less than 20D

Density and Specific Volume The density of a fluid () is the ratio of its mass (m) to its volume (V) while the specific

volume (Vs) is its reciprocal. That is:

.V

m

V

1ρ

s

Densities vary widely according to the fluid and its temperature and pressure. As a rough

indication, the density of water is about a thousand times that of air at atmospheric pressure

and room temperature.

Diagnostics Improvements in digital signal processing techniques have allowed large amounts of data to

be processed and stored in real time. Modern flow meter devices such as ultrasonic meters

have taken advantage of these improvements and started to make better use of the

diagnostic information they can provide. Manufacturers have started using the diagnostic

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parameters to perform a ‘health-check’ of the meter in operation, which can help to diagnose

any potential problems with the measured fluid or the measurement systems.

Software is used to trend the diagnostic parameters over set time periods to give an

indication of the performance of the meter. Some use a ‘traffic light’ approach to warn users

of problems with the measurement.

Dimensionless Numbers Dimensionless quantities are widely used in mathematics, physics and engineering. A

dimensionless number is a quantity which describes a certain physical system but does not

have physical units associated with it. It has the same value regardless of the measurement

system used to calculate it (e.g. SI units or imperial units). Dimensionless numbers often

result from the process of simplification of terms having the same units or units of the same

dimension.

The value of dimensionless numbers can often determine the behaviour of system it

represents. High Reynolds number for example indicates turbulent flow whilst low Reynolds

number reflects laminar flow.

Discharge Coefficient The discharge coefficient (C) is a parameter that takes account of non-ideal effects,

including energy losses due to friction, when using differential pressure flow meters. The

discharge coefficient is the ratio of the actual to the measured mass flowrate.

The value of C is determined by flow calibration of the meters but for some meters, e.g.

orifice plates the values can be obtained from a standard.

Distortion (of the Velocity Profile) As a fluid moves through a long length of pipe the flow profile would be fully developed,

where the flow is fastest in the centre and slowest at the walls. If however, the fluid passes

through a valve, the flow will be skewed to one side of the pipe generating higher velocities

near the wall. Other disturbances may act to increase the velocity at the pipe centre and

decrease it near the walls creating a peaked velocity profile. The opposite may also occur

causing a flattened profile.

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Doppler Principle Ultrasonic flow meters operating on the Doppler principle require particulates or bubbles in

the flow. This metering technique utilizes the physical phenomenon of a sound wave that

changes frequency when it is reflected by moving particulates/bubbles in a flowing liquid.

Ultrasound with a single frequency is continuously transmitted into a pipe with flowing

liquids, and the discontinuities reflect the ultrasonic wave with a slightly different frequency

that is directly proportional to the rate of flow of the liquid.

Dual Energy Gamma Ray Absorption To gain information on the oil/water/gas ratio in a multiphase flow, the absorption of two

gamma ray lines (high energy and low energy) can be used to determine the phase

fractions. For low-energy gamma rays, the absorption probability in a fluid depends not only

upon its density but also upon its type (e.g. hydrocarbon, fresh water, saline water etc.).

When coupled with a high energy measurement (high energy gamma rays are sensitive only

to the total mass of material through which they have to pass), the resultant dual energy

gamma ray absorption sensor provides sufficient information to determine the full

composition of a three phase mixture; since there is now contrast between the oil and the

water phases as well as between the liquid and the gas. To determine both the gas volume

fraction (GVF) and the water cut of the fluid, the high and the low energy absorption

information is combined in a dual energy calculation, described by the diagram.

Flow v

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The transmitted count rate at low energy is plotted against the transmitted count rate at high

energy for any fluid passing through the sensor. In this plot, the pure phases (oil, water and

gas) form the corners of a triangle. Each point within the triangle represents a different

phase mixture. By interpolating along lines of constant GVF (parallel to the oil water axis)

and along lines of constant water cut (50% in this case) the composition of the mixture can

be determined. This technique is commonly used in multiphase flow meters.

Effective Range and Rangeability The effective range of an instrument is defined as the range over which it meets some

specified accuracy requirements. This definition is illustrated below, where the horizontal

lines A and B represent the permitted limits of accuracy, and the effective range is therefore

from Q1 to Q2. The ratio Q2/Q1 is often called the rangeability of an instrument or in the case

of a flow meter, its turndown ratio, or simply, turndown.

20% GVF

50% WC

I (ELOW)

I (EHIGH)

Wat

Oil

Gas

Mix20% GVF20% GVF

50% WC50% WC

I (ELOW)

I (EHIGH)

Wat

Oil

Gas

Mix

I (ELOW)

I (EHIGH)

Wat

Oil

Gas

Mix

A

B

Effective range

K F

acto

r 2 δK

Q1 Q2 Flowrate (Q)

Linearity = ±δK over range Q1 to Q2

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Electromagnetic Flow Meters Electromagnetic flow meters operate on the principle of Faraday’s law of electromagnetic

induction. When a conductor moves at right angles to a magnetic field a flow of charge is

induced which results in the creation of a potential difference (voltage). This potential

difference is at right angles to both the direction which the conductor is moving and to the

direction of the magnetic field.

The output voltage (or induced voltage) is directly proportional to the mean flow rate through

the flow meter.

kBDUV

Where:

V = Voltage

B = magnetic flux density

D = Internal pipe diameter

K = Constant

U = Mean axial velocity

Emulsion Colloidal mixture of two immiscible flows; one fluid dispersed in the form of droplets

(dispersed phase) within the other (continuous) phase.

Error Error is the difference between the measured value and the true value. Very often people

confuse error and uncertainty by using the terms interchangeably. Uncertainty is the margin

of doubt associated with a measurement.

Measurements should be fit for purpose. For example, if we are fitting curtains in a window

our measurement of the window space need not be very accurate. However if we are fitting

Magnetic field

Induced

voltage (v)

Flow

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a pane of glass in the same window our measurement should be more careful and have a

lower value of uncertainty.

Falling Sphere Viscometer With this type of viscometer a sphere of known size and density travels down a vertical glass

tube containing the test liquid. The terminal velocity of the sphere can be determined by the

time it takes to pass two marks or sensors on the tube. By knowing the size and density of

the sphere, its terminal velocity through the test liquid and the density of the test liquid, then

the viscosity of the fluid can be derived using Stokes’ law.

Filters These are electronic circuits designed to remove unwanted frequency components (such as

mains hum) in order to improve the measurement signal.

Flow Conditioners A flow conditioner is a device which avoids unwanted shifts in a flow meter calibration factor

by reducing the effect of upstream disturbances on the meter to an insignificant level.

Fdrag

Fgrav

Test fluid

Metallic sphere

Sensors

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Flow conditioners should fulfil the following requirements:

Low pressure drop across the device

Low fouling rate

Short operating length between the source of the flow disturbance and the conditioner

Short length for the conditioner itself

Short settling length downstream of the conditioner

Adequate robustness

Relatively inexpensive to manufacture

Easy to install

Flow Disturbances Most flow meters are designed to operate in ideal conditions. In practice, it is rarely possible

to achieve these conditions and the way in which the meter is installed is likely to generate a

measurement error. Common sources of installation effects that can result in flow

disturbances and hence flow meter errors include:

Pipe diameter contractions and expansions

Pipework mismatches, weld root intrusions and gaskets; any intrusions into the flow

Single bends and elbows

Double bends

Valves, open at different positions

Objects in pipeline

Flow Meter A flow meter is a device for measuring the flow of a fluid through a pipe or conduit. There

are a number of established technologies upon which flow meters are based and each has

its own advantages and disadvantages for particular applications.

Flow Nozzles Flow nozzles are mainly used in the electrical power generation industry. They have a

curved entry and a cylindrical throat, but no divergent outlet section. Therefore, the

discharge coefficient is similar to that of a Venturi tube, but the overall pressure loss is

similar to that of an orifice plate of comparable size used at an equivalent flowrate and

pressure difference.

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Flow Nozzles (a) Low and high long-radius nozzles (b) ISA 1932 nozzle

(c) Venturi nozzle.

The diagram shows some examples of nozzles. In order to reduce the pressure loss caused

by a nozzle, it can be fitted with a divergent section similar to that used for a Venturi, hence

becoming a Venturi nozzle, see (c) above.

Flow Regime The physical pattern or fluid distribution exhibited by a wet gas or multiphase flow in a

conduit, for example, stratified water/gas flow – liquid flowing at the bottom of the conduit

with the gas flowing above it (not usually at the same actual velocity).

Fluid A substance (gas and/or liquid) readily assuming the shape of the container in which it is placed.

Flying Start and Stop Flow Calibration Process This process is used to measure the flow through a meter in order to calibrate it against a

reference standard. With this process (sometimes called the diverter method) the flow

through the meter is not stopped but continues uninterrupted. The flow is physically diverted

between a return path to the liquid supply tank and the collection container. A switch on the

(a) Low-

(a) High-

(b)

(c)

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diverter mechanism starts and stops a timer and a pulse totaliser to quantify the flow through

the meter.

The key to accurate measurement is a clean separation between fluid entering the container

and fluid returning to the supply. This should be accomplished without any change of

flowrate through the device. For this reason the flow into the diverter is normally conditioned

by creating a long thin jet impinging on a splitter plate. This will be open to atmosphere

ensuring no change of pressure occurs when diverting and hence removing the potential for

a change in flowrate during a test. The diverter mechanism is operated as quickly as

possible to reduce timing errors to a minimum.

Fouling Fouling is the build up of extraneous material upon the transfer surface of a heat exchanger,

causing a gradual reduction in the operational performance of the heat exchanger.

Consideration therefore needs to be given at the design stage for the effect of fouling a)

through extra capacity and b) allow, if practical, provision for cleaning.

Fouling can also be used to describe the build up of material within pipes or other

equipment.

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Froude Number

Froude number is the ratio of the inertia force on an element of fluid to the weight of the fluid

element and can be expressed as:

g.d

vFr

Where:

v = flow velocity

g = acceleration due to gravity

d = water depth

Gas Gas - hydrocarbons in the gaseous state at ambient temperature and pressure.

Gas Entrainment

Flow meters can be highly susceptible to the presence of gas (often air) bubbles in a liquid.

Gas can be entrained into a liquid from a variety of sources, and in low viscosity fluids gas

bubbles rise rapidly and a settling tank or other equipment can be used to de-entrain gas.

However in heavy (high viscosity) oils the bubble rise velocity can be very low, especially for

small bubbles, and a settling tank is ineffective. Ideally any possible sources of gas

entrainment must be eliminated, quantified or at least minimised.

Gas-Liquid Ratio Gas-liquid ratio is the gas volume flow rate, relative to the total liquid volume flow rate at standard temperature and pressure.

Gas-Oil Ratio Gas-oil ratio is the gas volume flowrate, relative to the oil volume flow rate at standard

temperature and pressure.

Gas Void Fraction This is the fraction of gas occupied within a given volume of gas-liquid flow.

Gas Volume Fraction Gas volume fraction is the gas volume flowrate, relative to the total multiphase volume flow

rate, at the local temperature and pressure. Note: This is normally expressed as a

percentage.

Heat Exchanger Simply put, a conventional heat exchanger is a device that allows transfer of heat from a hot

fluid to a cold fluid while avoiding direct contact. There are two basic types of heat

exchanger; shell and tube, and plate. Heat exchangers are designed to minimise the

surface area of the barrier between the two fluids but at the same time limit any resistance to

the flow of the fluids. Classifications of heat exchangers with regard to their flow

arrangement include co-current flow, counter flow and cross flow. With co-current flow, as

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the name suggests, the fluids enter the heat exchanger at the same end and travel parallel

to one another. With counter flow the fluids enter at opposite ends and with cross fluid the

fluids flow at around 90 degrees to one another.

Homogeneous Flow A wet gas or multiphase flow in which all the phases are evenly distributed over the cross-

section of a closed conduit is described as homogeneous flow. Note: The composition is

the same at all points.

Horizontal Flow Flow of fluid(s) through a pipe positioned horizontally.

Humidity in Gases Gases may be either dry or humid (damp). This is because a gas at a given temperature is

capable of holding up to a certain maximum amount of water vapour; this maximum amount

increases as the temperature increases. When a gas is holding the maximum amount of

water vapour it is said to be saturated with water vapour. If it is unsaturated, its degree of

saturation may be expressed as a relative humidity.

Impulse Line An impulse line is a small-bore pipe that is used to connect a point in a pipe at which

pressure is to be measured to an instrument. In flow measurement using a primary device

such as an orifice plate, a nozzle, or a Venturi meter, impulse lines are used to connect

points upstream and downstream (or in the throat) of the meter to a secondary device for

measuring the differential pressure.

Inferential Mass Flow Meters Inferential mass flow meters may be divided into two groups:

Volumetric flow meters which are used in conjunction with knowledge of the fluid density to calculate the mass flowrate.

Critical nozzles, from which the mass flowrate may be inferred from knowledge of the condition of the flow upstream of the device.

Insertion Meters Insertion meters are used to estimate the flowrate by measuring the velocity at a single point

location in the duct and estimating the volumetric flow. The device used to measure the

point velocities may be a pitot tube, insertion turbine or an insertion electromagnetic meter.

Other types of insertion meters are available.

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To use this method, the installation and the positioning of the sensor has to be performed

accurately. The cross sectional area of the duct has to be known, and a good flow profile

present to allow the calculation of volume flow from the point velocity. Insertion meters can

be used by inserting them into an existing duct or pipe and this can be done without stopping

the process. This will allow an installed meter to be verified in-situ.

Inversion Region An oil/water mixture can be described as being oil-continuous or water-continuous. Oil-

continuous flow is characterised by water droplets surrounded by oil. Water-continuous flow

is oil droplets surrounded by water. The inversion region lies between oil-continuous and

water-continuous flow and is unpredictable as it can show characteristics of either oil-

continuous or water-continuous flow, changing from one moment to the next. Operating in

the oil/water inversion region can create difficulties for certain multiphase measurement

technologies.

K-Factor K-factor is a term used to describe the performance of meters, such as turbine meters,

whose output is in the form of a series of electrical pulses, and where the total pulse count,

(n) is nominally proportional to the volume (VT) passed, and the pulse frequency; (dn/dt) is

nominally proportional to the flowrate. It is defined as:

TV

nK

Characteristic curves for individual turbine meters customarily take the form of a graph of K-

factor against flowrate (see Linearity). The reciprocal of the K-factor is a factor of great

practical importance, since, when a meter is used, the meter pulse count (n) must be

multiplied by 1/K to derive the volume passed by the meter.

Laminar and Turbulent Flow The Reynolds number serves to classify the flow into different flow regimes. If the Reynolds

number is small (less than ≈ 2,000) then viscous forces dominate and the flow is described

as laminar. When the flow is laminar, it can be thought of as moving along in thin layers,

with no mixing between the layers.

Meter on test

Pitot traversing section Direction of flow

Borda inlet flow meter for flow indication

and good velocity profile

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If the Reynolds number is large (generally greater than ≈ 5,000) dynamic forces dominate

and the flow is described as turbulent. In turbulent flow the general motion is parallel to the

pipe axis, although mixing occurs readily between the different layers.

In between laminar and turbulent flow, the flow is described as transitional. In this regime,

the flow switches back and forth between laminar and turbulent behaviour and as such can

present significant difficulties in terms of flow measurement.

Laser Doppler Velicometry (LDV) LDV is a technique used for measuring the velocity of fluids. Essentially, the technique

involves crossing two beams of collimated laser light in the fluid flow. The two beams are

usually from a single source but split into two; thus ensuring beam coherency (in-phase

light). At the intersection of the two beams fringe lines are generated. As fluid particles pass

through the fringes they reflect light and the velocity is determined by measuring the

frequency shift of the scattered light.

Linearity The linearity of an instrument is a measure of the extent to which its performance over its

effective range departs from the ideal. In the figure below where the accuracy limits are

drawn 2K apart, the linearity is ±K. It is usually expressed as a percentage of the nominal

K-factor, Kn, that is, as 100 K/Kn per cent.

Laminar Flow Turbulent Flow

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Liquefied Natural Gas Liquefied Natural Gas (LNG) is natural gas cooled to a liquid state. At atmospheric

pressure, the boiling point of LNG is typically -160 ºC and the flash point is -187 ºC. When

natural gas is cooled to a temperature of approximately -160 ºC at atmospheric pressure, it

condenses to a liquid. During the liquefaction process, impurities that would freeze, such as

water, carbon dioxide, sulphur, and some of the heavier hydrocarbons are removed. The

volume of LNG is about 1/600th of the volume of natural gas. The density of LNG is about

45 per cent that of water and it is odourless, colourless, non-corrosive, and non-toxic.

Liquid Hold-up Liquid hold-up is the ratio of the volume of liquid in a pipe section to the volume of pipe

section at the same instant.

Lockhart-Martinelli Parameter To account for both the flow rates and densities of liquid and gas phases it is common

practice to define the wetness or liquid loading of the gas using the Lockhart-Martinelli

parameter (referred to as X). This parameter can be calculated from the mass or volumetric

flow rates and the density of the fluids.

DensityLiquid

DensityGas

FlowrateMassGas

FlowrateMassLiquidParameterMartinelliLockhart

Or

DensityGas

DensityLiquid

FlowrateVolumeGas

FlowrateVolumeLiquidParameterMartinelliLokhart

The Lockhart-Martinelli parameter is used to define a wet-gas flow with the value of X

between zero (i.e. completely dry gas) and about 0.3. Flows with a Lockhart-Martinelli

parameter above 0.3 are usually referred to as multiphase flows.

A

B

Effective range

K F

acto

r 2 δK

Q1 Q2 Flowrate (Q)

Linearity = ±δK over range Q1 to Q2

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Manometer A manometer is simply a column of liquid in a tube supported by the applied pressure.

Simple physics shows the pressure is proportional to the liquid density, local gravitational

acceleration and the column height.

The instrument is simple, relatively cheap and moderately accurate if used correctly. It does

have the disadvantage of being restricted in range to the height of the column sensibly

achieved and as such, manometers are customarily employed in a laboratory environment.

They are however used extensively elsewhere for low pressure measurements.

Mass Mass is the quantity of matter contained within a body.

Mass Flowrate Measurement Mass flowrate (Qm) is the passage of a given mass (M) of fluid in a given time (t), or

t

MQm

Some flow meters are designed to indicate mass flowrate directly. They are called mass

flow meters or true mass flow meters.

(Qm) is frequently determined by making simultaneous measurements of volumetric flowrate

(Qv) and density () and then employing the relationship

Qm = Qv

Mean Pipe Velocity Measurement Mean pipe velocity ( v ) is related to volumetric flowrate (Qv) and pipe cross-sectional area

(A) by the relationship:

A

Qv v

( v ) can be determined in three ways:

1. By measuring (Qv) and (A) and then employing the equation.

2. By measuring (v) at numerous points on one cross-section and then taking an

appropriately weighted mean.

3. Or, less accurately, by measuring the velocity at a point three-quarters of the way

between the pipe centre and the wall, since it is known that in fully developed

profiles the velocity there is approximately equal to the mean velocity.

Measurement Standard The comparison during a calibration is against a standard. The standard comprises the system of pumps, pipes, fluids, instrumentation, quantity reference measurement, calculations and operators. These all combined provide a measure of the quantity of fluid passing through the device or flow meter being calibrated.

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Measurement Uncertainty When making a measurement of a quantity the result obtained is not the actual true value of

the quantity, but only an estimate of the value. This is because no instrument is perfect;

there will always be a margin of doubt about the result of any measurement.

The uncertainty of a measurement is the size of this margin of doubt; in effect it is an

evaluation of the quality of the measurement. To fully express the result of a measurement

three numbers are required:

(1) The measured value. This is simply the figure indicated on the measuring

instrument.

(2) The uncertainty of the measurement. This is the margin or interval around the

indicated value inside which you would expect the true value to lie with a given

confidence level.

(3) The level of confidence attached to the uncertainty. This is a measure of the

likelihood that the true value of a measurement lies in the defined uncertainty

interval. In industry the confidence level is usually set at 95%.

Mercury Seal Prover For low flows, mercury seal provers use a very light displacer in a vertical glass tube. The

piston travels upwards in the tube and the seal is a mercury ring formed in a recess in the

piston. The use of a vertical piston and mercury seal reduces friction to a minimum. The

weight of the piston has to be counterbalanced by an external weight (not shown).

Meter Error Meter error (Δ) is a term often, but not exclusively, used in connection with volume meters of

the type that read directly in volume units, especially displacement meters. It is defined as:

T

TI

V

VVΔ

To atmosphere

Mercury vapour filter

Displacer

Mercury seal

Test meter

Detector unit

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Where, (VT) and (VI) denote true and indicated volume respectively. Meter error is normally expressed as a percentage of the true volume.

Meter Factor Meter factor (F) is a term mainly used in connection with meters used for measuring total

volume, and especially with turbine meters and positive displacement meters. Unfortunately

different operators use it in several different ways, and this has caused great confusion in

the past. It is now generally agreed that the correct definition should be:

I

T

V

VF

It is the factor by which the indicated volume ( IV ) should be multiplied in order to obtain the

‘true volume’ ( TV ).

Multiphase Flow Two or more phases flowing simultaneously in a conduit is defined as multiphase flow.

Multiphase Flowrate Multiphase flowrate is the total amount of the two or three phases of a multiphase flow

flowing through a cross-section of a conduit per unit time. Note: This may be specified as

being either mass or volume flowrate.

Multiphase Flow Separation Separators are generally used for the purpose of monitoring well production, also known as

well testing. The traditional approach to measuring multiphase flow is by separation.

Separators work by exploiting the differences in fluid properties of the multiphase

components for the separation to work.

In a two-phase separator, the liquid and gas will separate if given sufficient time in the

separator (residence time) because the gas has a much lower density than the liquid. The

gas and liquids (water and oil) are separated in a similar way in the three phase separator.

The oil and water will separate due to their immiscibility and the difference in densities and

viscosities of the two fluids.

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The outlet streams from the separator can then be measured using single phase flow

meters. In the case of a two phase separator a water cut monitor will also be required for

the oil outlet to determine the amount of water present.

Multiphase Velocity This is the flow velocity of a multiphase flow at a cross-section of a conduit.

Newtonian Fluids Newtonian fluids have a linear relationship between shear stress and shear rate at a given

temperature. If shear stress is plotted against shear rate then the slope of this graph is the

viscosity and will remain constant over a range of shear rates.

Non-Newtonian Fluids Unlike Newtonian fluids, non-Newtonian fluids have a non-linear relationship between shear

stress and shear rate. This means that the apparent viscosity of a non-Newtonian fluid will

change with varying shear rate. There are many different types of non-Newtonian fluids all

of which react differently to changes in shear rate.

Shear thinning or pseudoplastic fluids will reduce their apparent viscosity as the

shear rate increases.

Gas

From well

Water Oil

Sh

ea

r R

ate

Vis

co

sity

Shear Stress Shear Rate

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Shear thickening or dilatent fluids will increase their apparent viscosity as shear rate

increases.

Bingham plastic fluids will not flow until a yield stress is reached, above which they

will flow like a Newtonian fluid.

Oil Oil - hydrocarbons in the liquid state at ambient temperature and pressure.

Oil-Water Separation The first effect is the separation of the oil from the water to produce distinct layers. This

occurs in both stratified and slug flows.

In stratified flows at low velocities the separation is almost complete, with a sharp oil-water

interface. At increased velocities, the oil-water interface may remain smooth even though

oil-gas interface is rough or wavy. However, more generally the oil-water interface becomes

less distinct, with drops of oil visible within the water layer, until at some point there is no

longer any visible separation of the two liquids.

Oil and water separation also occurs in slug flow, but with several variations. The most

common effect is that the oil and water separate in the film region between slugs, giving rise

to an apparently stratified smooth flow with separate oil and water layers. The separate

layers are then seen to become mixed as a slug passes. In some cases a second slug

arrives before the film region has settled into layers again. As the slug frequency increases,

a point is reached where separation can no longer occur. At other conditions the slug does

not cause sufficient mixing to entrain the water layer, which can be seen to exist throughout

She

ar

Str

ess

Shear Rate Shear Rate Shear Rate

Rate

Vis

cosity

Vis

cosity

Yie

ld S

tress

Shear

thickening

Shear

thinning

Bingham plastic

Shear thinning

Shear

thickening

of 67

the slug. A further condition can occur where the water is undisturbed by the passage of a

slug, and the gathering of the oil layer into the slug can be quite clearly seen.

Visible separation of the water from the oil does not occur in bubble or annular flows, or in

any of the transition region flows.

Orifice Plates Orifice plates are the most common type of differential pressure meter and are basically a

machined metal plate with a hole. The plate has a sharp upstream edge and usually a

bevelled edge downstream of the flow. To allow the differential pressure to be measured, a

set of pressure tappings are located on pipework upstream and downstream of the plate.

When fluid passes through the hole of an orifice plate the pressure drops suddenly (see

Bernoulli’s Principle). The flow continues to contract and converges downstream of

the plate with the point of maximum convergence (or minimum area) called the Vena

Contracta. The fluid then expands and re-attaches to the pipe wall and the velocity profile

approaches that before the constriction. There is a relatively large net pressure loss across

the orifice plate which is not recovered; this should be taken into account in choosing a

meter as orifice plates are not suitable for applications where a large pressure drop is

undesirable.

Orifice plates are very sensitive to the velocity profile of the flow. If for example, the velocity

profile is asymmetrical or skewed this does affect the flow measurement. There are

specified requirements for using orifice plates which are detailed in the standard ISO 5167-2

for their use in dry gas and liquids.

Phase Within the bounds of wet gas or multiphase flow, the term refers to either oil, gas or water

flows in a mixture of any number of the three.

Plate thickness, E

Downstream face, B

Upstream face A

Bevel angle, F

Pipe axis

Direction of Flow

Orifice thickness, e

Pip

e d

iam

ete

r, D

Pipe internal

bore

Ori

fice

dia

me

ter,

d

Orifice platePipe

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Phases and Phase Diagrams A key factor in the understanding of the behaviour of fluids are phases and phase diagrams.

Simply put a phase can be another term for solid, liquid and gas. Oil floating on water

consists of two liquid phases whereas ice floating on water consists of one liquid phase and

one solid phase. In each case the surrounding air would constitute a third phase.

Knowledge on phase behaviour allows what is termed a phase diagram to be produced. A

phase diagram is constructed to determine what phases are present at any given

temperature and pressure. The example provided is for carbon dioxide (CO2) plotted over a

pressure range of 0 to 100 bar and -10 to 50 ºC. The green lines represents pure CO2 and it

can be seen from the diagram that there is a gas phase, liquid phase, a supercritical liquid

like phase and a supercritical gas like phase.

Phase Flowrate Phase flowrate is the amount of one phase of a multiphase flow flowing through a cross-

section of a conduit per unit time. Note: The phase flowrate may be specified as being

either ‘mass’ or ‘volume’ flow rate.

Phase Area Fraction The phase area fraction is the cross-sectional area occupied by one phase relative to the

total cross-sectional area of the pipe at that point.

The void fraction is the cross-sectional area of the pipe occupied with gas.

The hold-up is the cross-sectional area of the pipe occupied with liquid.

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Phase Mass Fraction The phase mass fraction is the mass flowrate of one component in relation to the total mass

flow rate of the multiphase mixture. That is:

FlowrateMassTotal

FlowrateMassGasFractionMassGas

Phase Slip The components of a multiphase mixture travel at different velocities. Generally speaking,

the velocity of the gas ( gv ) is much greater than the velocity of the liquid ( lv ). In some wells

it takes the gas a matter of hours to reach the well head but it can take the liquid days to

travel the same distance. This difference in velocities is known as phase slip ( Rv ).

Slip lgR vvv

Slip ratio l

g

v

vK

Gas volume fraction (GVF), gas void fraction (εg) and slip (K) are related to each other.

K

KGVF

gg

g

1

A multiphase mixture is considered to be a homogeneous flow when the liquid and gas are

travelling at the same velocity i.e. K = 1.

Phase Volume Fraction The phase volume fraction is the volumetric flow rate of one component in relation to the

total volumetric flow rate. That is:

FlowrateVolumetricTotal

FlowrateVolumetricGasFractionVolumeGas

Pipe Provers To calibrate flow meters in-situ without having to remove the meter, a device called a pipe

prover has been shown to fulfil most of the requirements for field proving. The basic pipe

prover comprises of a length of pipe fitted with switches so that the volume between the

switches is known. If a displacer is introduced to the flow, the time it takes to travel between

the switches will give a measure of the flowrate. If the switches are used to gate a pulse

counter, totalising pulses from a flow meter, a measure of the meter factor (pulse per litre)

can be found. Pipe provers can be uni or bi-directional.

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Plate Heat Exchangers Plate heat exchangers consist of a series of thin corrugated metal plates of large surface

area and fluid flow channels for effective heat transfer with the primary and secondary fluids

flowing through alternate channels. This stacked plate arrangement can be more effective in

a given space than a shell and tube heat exchanger. There are several different types of

plate heat exchanger including;

Plate and frame

Brazed plate

Welded plate

Plate and fin

Platinum Resistance Thermometers The electrical resistance of all metallic conductors changes with temperature. When

platinum metal is alloyed with a suitable dopant, this relationship becomes very predictable

and essentially linear over specified ranges and is the basis of the class of industrial grade

platinum resistance thermometers (PRTs).

Detectors

Displacer

sphere

Known volume

between detectors

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A practical thermometer can be made by using a sensing element made from fine platinum

alloy wire wound on an insulating former and enclosed within a metallic sheath. The usual

operating temperature range for these devices extends from -200 °C to +650 °C but specials

quality devices can be constructed to extend the range to +800 °C.

Plug Flow Plug flow is a regime where most of the gas moves as large bubbles (or plugs) along the top

of the pipe, which is otherwise liquid-filled. Small bubbles may still be present within the

continuous liquid phase but have the tendency to coalesce to form larger bubbles. Plug flow

differs from slug flow in that the gas bubbles are relatively smaller and slower moving.

Point Velocity Measurement Instruments are available with which the velocity of a fluid at a point can be measured.

These are often called anemometers if intended for use in free-flowing air, current meters if

intended for use in water and insertion meters if intended for use specifically inside a pipe or

duct.

Positive Displacement Meter Positive displacement or PD meters determine the volumetric flow rate of a fluid by

separating it into discrete measures of known volume and then counting the measures. It is

analogous to using a bucket to remove water from a pool; counting the number of times,

Plug Flow

Header housing terminal

block

Powder filled

Sheath

Platinum wire

element

Immersion depth

Former

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timing the operation and knowing the volume of the bucket is a simple positive displacement

meter. In practice, this principle must be realised using a continuous mechanism

appropriate to the rate of flow. While several types of PD meter exist, most consist of the

following three common components.

(a) A working chamber of constant volume.

(b) A displacer which is made, under the action of the flowing fluid, to transfer the fluid from

one end of the working chamber to the other.

(c) A register connected to the displacer to count the number of times the displacer moves

across the working chamber.

PD meters are fairly robust devices and are used to meter more viscous fluids. Also, they

require little upstream and downstream pipework.

This broad description covers a very wide range of meters operating on the displacement

principle; however, all meters operating on this principle must have some degree of sealing

preventing fluid from leaking past the displacer.

Pressure By definition, the pressure acting on a surface by a force normal to that surface is equal to the magnitude of the force divided by the area over which it is acting i.e. force per unit area.

The SI unit of pressure measurement, the Pascal (Pa) has the dimensions Newtons per square metre (N/m2). This is an impractically small measure for most purposes and the more familiar unit of bar is commonly used (1 bar = 105 N/m2) as are KPa and MPa. The more traditionally inclined (including the Americans) still favour the imperial pressure unit pounds force per square inch (psi).

Working chamber Displacer

Housing

Register

Working chamber Displacer

Housing

Register

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Atmospheric pressure is the pressure resulting from gravity acting upon the mass of atmospheric air above each unit of the earth’s surface area. This pressure varies with prevailing weather conditions and altitude. Many pressure measuring devices require correction for atmospheric pressure and many specifications call for a measure to be expressed in terms of a standard pressure. Standard pressure is defined as 101,325 Pa or 1.01325 bar or 1013.25 mbar (1 atm.).

When expressing pressure, it can be described as gauge (g) pressure when measured relative to atmospheric pressure or absolute (a) when measured relative to zero pressure or total vacuum. Most equations of state for gases require pressure to be stated in absolute terms so corrections for atmospheric pressure are commonly applied.

Pressure Drop When a fluid flows through a restriction, it accelerates to a higher velocity to conserve the

mass flow and, as a consequence of this, its static pressure drops.

Pressure-Volume-Temperature Equation The P-V-T equation relates the volume of a fluid to both its temperature and the pressure

acting on it. This relationship is normally important only for gases.

For a perfect gas the relation is:

T

PV = constant

Produced Water Produced water is a by-product of oil and gas production and with the increasing number of maturing fields water production is on the increase worldwide. Estimates of the amount of produced water vary but could be in the region of 250 million barrels per day. Produced water is a complex mixture consisting:

Oil content

Soluble organics

Salt

Production chemicals

Vacuum

Absolute

pressure

Gauge

pressure

Atmospheric

pressure

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Heavy metals

Radioactive material

Relative Density/Specific Gravity Relative density (or specific gravity) is the ratio of the density of a substance to density of a reference substance. Water is the reference substance for liquids and solids, with air or hydrogen being the reference for gases.

Resolution By international agreement the word resolution is used to describe the smallest change in

the display of an instrument which can be read. For example, the resolution of a digital

electronic timer reading in milliseconds is a hundred times as great as that of a digital

electronic timer reading in tenths of a second. Resolution must not be confused with

accuracy. Resolution tells you how many decimal places you read to; it tells you nothing

about how many of those decimal places you can rely upon.

Repeatability This is defined as the closeness of agreement between independent results obtained using

the same method on independent test material, under the same conditions (i.e. same

operator, same apparatus, same laboratory and after short intervals of time). Accuracy and

repeatability are often confused. Results that are accurate are also repeatable but results

that are repeatable may not necessarily be accurate.

Reproducibility A term related to repeatability is reproducibility. This is the ability of an instrument to give

the same result when it is used to measure the same quantity at different times and under

different conditions.

Reynolds Number The behaviour of fluids flowing through pipes can be said to be broadly governed by a

quantity known as Reynolds Number ( eR ). This is defined as follows:

Good accuracy

means good

repeatability

Poor repeatability

means poor accuracy

Good repeatability

doesn’t necessarily

mean good accuracy

of 67

DvR e

Where ( v ) is the mean velocity, () is dynamic viscosity and (D) is the pipe diameter and

( ) is density.

The Reynolds Number is a valuable concept in that it indicates which kind of forces will

predominate in the flowing fluid. When v D is relatively large eR will be large and dynamic

forces will prevail, but when () is relatively large Re will be smaller and viscous forces will

prevail.

Sampling For many production industries sampling can be a critical element to provide information for

quality assurance and for the management and optimisation of processes. Obtaining a

sample for analysis enables information on the composition of the fluids to be gained. This

information is essential to know exactly what is happening in the process. In the petroleum

sector sampling is required in many of stages from the extraction, transportation,

measurement, to the separation, refinement and trading of petroleum products.

Shell and Tube Heat Exchanger The simplest type of heat exchanger is one tube inside another tube; the inner tube may

have longitudinal fins on the outside. In practice however, there would be a number of inner

tubes placed within the outer tube, thus becoming a shell and tube heat exchanger.

This type of heat exchanger consists of a bundle of tubes contained within a cylindrical shell.

One fluid flows inside the tubes and the other flows over the tube bundle. Tubes can be low

finned to promote increased heat transfer.

Signal Conditioning Signal conditioning is the term given to the manipulations applied to the primary sensor’s

electrical signals to prepare them for measurement by the data acquisition system.

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Instrument transmitters perform signal conditioning by transforming the sensors output into a

4 to 20 mA current. In general common types of conditioning include amplification, isolation,

linearization and filtering.

Single Energy Gamma Ray Absorption In this method, gamma rays from a radio-isotope source are arranged to pass in a collimated

beam through the multiphase fluid. Some gamma rays will interact with atoms in the fluid

and be lost from the beam. Those gamma rays which undergo no interaction are counted by

a detector located on the opposite side of the pipe. The number removed depends upon the

nature of the fluid present.

Information on the composition of the fluid can be inferred from the absorption of the gamma

rays.

Slip Ratio This is the ratio between two phase velocities.

Slip Velocity This is the phase velocity difference between two phases.

Slug Flow The slug flow regime is characterised by a series of liquid slugs separated by relatively large

gas pockets, which almost entirely fill the cross section of the pipe. The slug itself may also

contain a considerable fraction of entrained gas. The nose of each gas slug is generally

very stable, but the area between successive slugs can be highly agitated and tends to

contain a dispersion of smaller bubbles.

DET

ECTO

R

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Snell’s Law

As an ultrasound beam passes between two acoustically different media the sound wave is

refracted. This means the angle at which the beam was first emitted will not be the same as

the angle that enters the flow. Snell’s law states that the angle of incidence of the sound

wave divided by the speed of sound in that medium is constant for all materials.

321

coscoscos

VoSVoSVoS

As the transducer angle (α) and the transducer velocity of sound (VoS1) will be known, the

ultrasonic beam propagation angle through the flowing fluid can be calculated.

Solubility of Air in Liquids Air is soluble in liquids, and its solubility is directly proportional to the absolute pressure. The

solubility of air in water is about 2% by volume at an absolute pressure of 1 bar, 4% at 2 bar,

1% at 0.5 bar, and so on. Air is very much more soluble in hydrocarbons: typical values at 1

bar are 8% in lubricating oil, 12% in kerosene and 16 per cent in gasoline. Dissolved air is

likely to be released from solution in oils and fuels if the pressure is allowed to fall

momentarily much below atmospheric. The resulting air bubbles in the liquid can cause

metering errors.

Pipe Wall

Fluid

Slug Flow

Slug Flow

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Sonic Nozzles Sonic nozzles are one of the most stable and accurate calibration and measurement

methods for gas flows. When sonic conditions are obtained at the nozzle throat, then it can

be shown that the mass flowrate through the nozzle depends only on the nozzle geometry,

the properties of the fluid and the upstream pressure (P) and temperature (T). Pressure

pulsations or changes cannot travel faster than the speed of sound meaning that variations

in downstream pressure cannot affect the mass flow through the nozzle while sonic

conditions are maintained. To achieve sonic or critical flow in the throat, a substantial

pressure drop across the nozzle must be generated.

Standing Start and Stop Flow Calibration Process This is the simplest method available for flow calibration and can be used for both high and

low accuracy flow meter calibrations. The flow system is filled, all air purged and the

required flowrate established, the flow then stopped using a fast acting valve. When the

container is empty, the drain valve is closed, the flow started and the container filled and

when the container is full the flow is stopped. The quantity collected is measured and

compared with the meter reading; the volume/mass of fluid and time to fill the container are

used to determine the flowrate.

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Steam The behaviour of water as it is heated and changes into steam can be illustrated by a

temperature-entropy diagram showing the phase change behaviour of steam. The x-axis

represents entropy and is a measure of the energy stored in the steam. The red line

describes the behaviour of the steam at atmospheric conditions. As heat is added to the

water its temperature increases up to 100 ºC. The heat content of the water at this point is

known as the sensible heat. Adding further heat causes the water to boil and the quality of

the steam defined by the mass fraction of vapour (x) increases. Steam whose quality is less

than 1 is known as saturated steam. Adding heat to saturated steam increases the quality of

the steam, but it does not change its temperature. Therefore if the pressure of saturated

steam is known its temperature is also known. As pressure is easy to control the

temperature of saturated steam can also easily be controlled.

If sufficient heat is added to saturated steam the quality increases to 1, and with further

heating it becomes superheated steam. Superheated steam can be regarded as a dry gas.

Unlike saturated steam, adding heat at a fixed pressure will cause an increase in

temperature. Superheated steam is used in steam turbine generators and in steam main

systems to avoid condensate problems. However, it is less efficient in heat transfer

applications and consequently most steam systems operate predominantly with saturated

steam.

Timer - counter

Flow measuring

device

Flow control

Stop valve

Weir

Container

Overflow

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Stokes’ Law Stokes’ Law (after George Gabriel Stokes) is a mathematical description of the force required to move a sphere through a viscous fluid at specified velocity.

Stokes’ law states that:

rF 6

Where:

F is the frictional (or drag) force generated by the sphere passing through the liquid

r is the radius of the sphere µ is the dynamic viscosity of the liquid v is the terminal velocity of the sphere through the liquid

Solving the above for dynamic viscosity gives:

9

2 2 gr s

Where:

ρs is the density of the sphere ρ is the density of the test liquid

Stratified Flow In this regime the gas and liquid flows in distinct layers within the pipe conduit. The heavier

liquid phase occupies the lower part of the pipeline and the gas the upper. The area of

interface between the gas and the liquid is lowest for this type of flow regime, irrespective of

the liquid content.

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When the flowrate of both phases is low, a smooth interface exists between the gas and the

liquid. As the flowrates increase (or in slightly upward inclines) the interface between the

stratified layers can become irregular, leading to stratified-wavy flow.

Strouhal Number

The first detailed experimental study into the generation of vortices behind a bluff body was

carried out by Strouhal in 1878 who showed that the frequency (f) of a vibrating wire of

diameter (d) placed in a cross-stream of air with a velocity past the wire of (U) was equal to

U/(6d).

Later, Rayleigh introduced the non-dimensional relationship;

fd/US

where the coefficient (S) became known as the Strouhal number. If S is constant, then for a

given diameter the frequency will be linearly related to velocity, which is an ideal relationship

for a flow meter.

Experimental work has shown that S is nominally constant over a range of Reynolds

numbers for most types of bluff bodies. However, the value of S, and the Reynolds number

range of linearity, is dependent on the shape of the body, as shown below, where the

Strouhal number has been plotted against Reynolds number for a circular and triangular rod

respectively. The latter is preferable as a flow metering device since the Strouhal number is

constant over a wider range of Reynolds number. This is because the sharp leading-edge of

the triangular body controls the point of separation much better than the cylinder.

Stratified Flow

Stratified Wavy Flow

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Superficial Phase Velocity The flow velocity a single phase of a multiphase flow would have, assuming that it occupies the whole conduit itself.

Swirl In fully developed flow all of the fluid travels parallel to the pipe walls. Some pipework

fixtures can impart rotational movement on the flow, generally referred to as swirl. Some

disturbances generate single vortex swirl, others double, triple or even quadruple swirl.

Temperature Temperature defines how hot or cold the fluid is.

Thermal Conductivity Thermal conductivity is the property of a fluid reflecting its ability to conduct heat.

Thermal Expansion Coefficient The thermal expansion coefficient of a fluid (), otherwise known as its coefficient of

volumetric expansion, is the fractional increase in specific volume (or the fractional decrease

in density) caused by a temperature increase of 1°C. That is:

T

ρ

ρ

1

T

V

V

1β s

s

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The thermal expansion coefficient of cold water is very small, 20 × 10-5/°C at 20°C, and is

usually disregarded except when very high accuracy is required, but it increases rapidly with

increasing temperature. The thermal expansion of oils and liquid fuels, however, is very

much higher than that of water, and is much less dependent on temperature. It cannot be

neglected if high accuracy measurement is required. Thermal expansion in gases is very

much greater still, and must always be taken into account.

Total Volume Measurement Some meters are designed to indicate directly the total volume passing through the meter;

they are sometimes called volume meters, or ‘bulk meters’, to distinguish them from flowrate

meters.

Traceability Traceability is the property whereby the result of a measurement or the value of a standard can be related to national or international standards, through an unbroken chain of comparisons with stated uncertainties. The UK National Measurement System (NMS) is controlled by the government through the National Measurement Office (NMO) and is delivered through a network of national laboratories, academic institutes and industrial establishments, as indicated.

Tracer Methods for Flow Measurement

Tracer methods are used in situations where a flow meter or calibration device cannot be

inserted in a process flow and the installed meter cannot be removed and calibrated

elsewhere. Tracer methods would normally be used to verify that a meter is operating within

an acceptable tolerance rather than providing a traditional calibration. They can also be

used to determine the flowrate of individual phases within multiphase flow.

of 67

Two recognised tracer methods are available.

For the transit time (velocity) method pulses of tracer fluid are injected into the main flow

stream, and the time taken for the tracer to pass between two detection points is noted. If

the volume of pipe between the detectors is known the volumetric flow can be determined.

At present, tracers used are usually radioactive isotopes, which can be generated on site,

with very short half lives.

The second technique is the dilution method where a tracer fluid which can be detected in

low concentrations, is injected into the flow at a known rate. If this injected flowrate is known

accurately, and a sample of the mainstream flow is taken downstream, the flowrate of the

main flow can be deduced from the concentration of dilutant.

Transducers Transducers are the key element in all ultrasonic metering technologies. They utilise the

piezoelectric properties of crystalline, ceramic, composite or polymer film materials which

exhibit a special electromechanical quality. The active element in the transducer is a

polarised material which has both positive and negative charges throughout. When a

current is applied across the material the positive and negative charges align with the

electric field which causes the material to change in size and shape; this is called

electrostriction. In the opposite direction, when an external influence acts on the material

and a current is produced, the effect is called piezoelectricity.

When a current is applied to a piezoelectric crystal the mechanical energy is produced in the

form of vibrations. Tailoring the current can produce vibrations of a chosen frequency and

this is the basis for all ultrasonic flow metering; including clamp-on and in-line meters.

By utilising this phenomenon, two different transducers can send and receive ultrasonic

pulses which can be used to decipher information about a flowing medium.

Transducer Configurations There are a number of practical transducer configurations for both clamp-on and in-situ

ultrasonic flow meters, including those shown.

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Transducer Frequency The frequency of the transmitted ultrasound is chosen as a compromise between signal

penetration, scattering magnitude and timing precision. Low frequencies provide good

signal penetration and reduced scattering from particles of small size whereas the use of

higher frequencies improves timing resolution but promotes scattering and increases

attenuation. Industrial ultrasonic meters typically use transducer frequencies between 0.5

and 5 MHz for liquids and in the 50 to 500 kHz range for gases.

Transfer Standard Transfer standard flow meter packages are the means used to compare the flow

measurement accuracy of different calibration laboratories or to relate the performance of a

meter in an industrial or commercial application to a recognised calibration standard. The

word ‘package’ is used advisedly since the transfer device must consist of the flow meter

itself together with sufficient lengths of upstream and downstream pipework (with sufficient

pressure and temperature tappings) and perhaps a flow straightener. For the period of the

transfer exercise the package should be maintained as a single construction, i.e. it should

not be dismantled into its component parts since re-assembly could result in a different

package through, for example, a ‘rougher’ section of pipe being placed adjacent to an orifice

plate pressure tapping when compared with the first set-up.

Retracted

Wetted

Retracted

Encapsulated

Intrusive

Wetted

External

(Clamp-on)

Retracted

Wetted

Retracted

Encapsulated

Intrusive

Wetted

External

(Clamp-on)

Flow conditioner Flow meter

Transfer Standard

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Note: In some cases more than one type of flow meter may be incorporated into the transfer

standard package.

Transit Time (time of flight) Transit-time ultrasonic flow meters utilize two transducers which function as both ultrasonic

transmitters and receivers. The transducers are clamped on the outside of a closed pipe at a

specific distance from each other. This type of flow meter operates by alternately

transmitting and receiving a frequency-modulated burst of sound energy between the two

transducers. The burst is first transmitted in the direction of fluid flow and then against the

fluid flow. Since sound energy in a moving fluid is carried faster when it travels in the

direction of flow (downstream) than it does when it travels against it (upstream), a difference

in the time of flight will occur. This is proportional to the velocity of the fluid.

Transition Regions Whether in vertical or horizontal flow, there are transition regions that may be observed

between the defined flow regimes (stratified and plug, slug and churn, churn and annular,

and bubble and annular flows). These transition regions exist since none of the flow pattern

boundaries are particularly sharp and all of the transition regions have properties which lie

between those of the adjacent flow patterns.

Transmitters Transmitters are instruments designed to be mounted adjacent to the point at which the

measurement is made. Pressure and differential pressure transmitters are connected to

the process fluid using suitable tapping points, isolation valves and small-bore piping,

whereas temperature transmitters are electrically connected to a temperature element.

These devices produce electrical signals, which represent the measured process variable,

in a form suitable for transmission over a long distance to remotely mounted monitoring

instruments.

Triple Point Cell A triple point cell is a device which is commonly used to calibrate high accuracy

thermometers at fixed points. The most common is the water triple point cell which when

correctly set up maintains a temperature defined as 0.01 ºC to within 0.1 mK for extended

periods. Other cells and fixed point devices, some employing highly refined metals, are

available to realise higher or lower fixed point temperatures. The method gives very good

accuracy but requires special laboratory equipment and very careful use.

Flow

L

v

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Turbine Meter Turbine flow meters are one of the most common flow meter types used for high accuracy

measurement of both liquids and gases. Within the oil sector, turbine meters are the first

choice for most liquid fiscal or custody transfer applications involving continuous or large

batch flows.

The turbine meter works on the principal that the speed of rotation of a bladed rotor is

proportional to the kinetic energy of the fluid flowing across the blades, which is in turn is

proportional to the mean axial velocity of the fluid. The result is a flow meter where the

speed of rotation of the rotor is proportional to the volumetric flowrate of the fluid passing

through it.

Pre

ssure

(b

ar)

Temperature (ºC)

Solid

(ice)

Liquid

(water)

Vapour

(steam)

0 0.01

0.006

1.01325

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Turbulence In nearly all cases of flow in pipes random turbulent fluctuations occur. In fully developed

flow these turbulent fluctuations are usually less than about 3% of the local mean fluid

velocity. Passing fluid through pipework fixtures effectively stirs up the flow, usually causing

increased turbulence.

Turndown The turndown of a flow meter is the ratio of the maximum to the minimum flowrate that can

be accurately measured. Ideally a large a turndown ratio is desirable to measure a wide

range of flowrates.

U-tube Viscometer The glass capillary viscometer consists of a U-shaped glass tube contained within a

temperature controlled environment. On one side of the U-tube is a reservoir beneath which

is a narrow bore capillary tube and on the other side of the U-tube is a second reservoir

located below the first reservoir. Through suction the liquid (of known density) is held in the

first reservoir at the initial liquid levels (marks). The liquid is then allowed to flow into the

second reservoir with the time taken to reach the final liquid levels (marks) being proportional

to kinematic viscosity.

Flow

Output to pulse

counter

Rotor Pulse pick-up

sensors

Rotor shaft and bearing assemblies Rotor supports

Meter body

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Valve Flow Coefficient As most control valves operate with turbulent flow through the valve, for a set valve position

the differential pressure across the valve is proportional to the flowrate squared, provided no

cavitation, flashing or choked flow occurs. This relationship is used as the basis for

expressing the capacity of a valve in terms of pressure drop and flowrate and is used to

derive the valve flow coefficient.

Valve coefficient is often expressed as Cv, Kv or Av depending on the units used. The Cv

valve flow coefficient is the most common definition (US units) and is in widespread use

worldwide.

A valve is often described in terms of its maximum valve coefficient, usually determined at

the fully open position. By determining Cv values at different stem openings a valve Cv

characteristic curve can be produced. An example curve is shown below, although its shape

can vary depending upon the type of control valve.

Valve stem position

Va

lve

co

eff

icie

nt (C

v)

Fully open

Closed

B2

B1

A1

A2

Upper reservoir

Capillary tube

Lower reservoir

of 67

Variable Area Meters Variable area meters operate at a constant differential pressure and the area changes with

the flowrate. The area will increase as the flowrate through the meter increases to preserve

a constant differential pressure. The most common design of variable area meter is the

cone-and-float type, which is also known as a rotameter. Variable area meters are widely

used for metering gas but different types are available for a variety of different fluids. A

buoyancy correction term is required for liquids and dense fluids.

Velocity Head The expression v ²/2g, where (g) is the acceleration of gravity, provides a convenient way of

indicating the amount of kinetic energy possessed by the fluid flowing in a pipe. It has the

dimensions of length, and is equal to the height (head) to which the fluid would rise if it were

projected vertically upwards at a velocity ( v ) in an ideal world where there was no such

thing as friction.

Velocity Profile The nature of the flow regime has a direct impact on the velocity profile of the flow. Velocity

profile is a term used to describe how fast the fluid is moving at different points over the

cross-section of the containing pipe. In reality, the pipe wall always creates some level of

friction, meaning that a thin layer of fluid next to the pipe wall will, in principle, not move at

all.

Moving away from the wall, the drag exerted by the pipe becomes less and less, and the

fluid moves at increasingly higher velocities, with the highest fluid velocity occurring in the

centre of the pipe. The precise way in which the velocity changes from the pipe wall to the

pipe centre, depends on the nature of the flow regime, and hence also on the Reynolds

number.

of 67

Venturi Tubes Venturi tubes are used extensively in industry and the design of a classical Venturi tube is

shown below. This type of meter has a gradual reduction in the pipe area, a parallel throat

section and then a gradual expansion back to the full pipe diameter. The long expansion

section (diffuser) enables an enhanced pressure recovery compared with that of an orifice

plate, which is useful in some metering applications.

The differential pressure is measured from the upstream tapping to the throat section, shown

by the high pressure and low pressure connections, respectively. Venturi meters are much

less susceptible to damage than orifice plates owing to their robust and solid design. They

are covered by a comprehensive standard (ISO 5167) and a value for the discharge

coefficient from the standard can be used.

Verification Confirmation that a flow meter is performing within specification; it is not a calibration in the

sense that no adjustments to the meter are made.

Vertical Flow Flow of fluid(s) through a pipe positioned vertically.

Viscosity The viscosity () of a fluid is a measure of its resistance to shearing at a constant rate. In

terms of the figure below:

γ

τμ

Where:

is the shear stress, and

is the rate of shear strain.

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Rate of Shear Strain: h

Vγ , Viscosity:

γ

τμ

The SI unit of viscosity is the Pascal second (Pa s), but it is more usual to express

viscosities in centipoise (cP), one cP being 10-3 Pa s. Viscosity is often referred to as

‘absolute viscosity’ or ‘dynamic viscosity’, to distinguish it from kinematic viscosity () the

latter brings in another factor, being the ratio of viscosity to density (/). The SI unit of

kinematic viscosity is m²/s, and the common unit is the centistoke (cSt), one cSt being

10-6 m²/s. Some values for common substances are given below. The values quoted are at

normal ambient temperatures.

Substance Approximate Viscosity (cP at 20 ºC)

Air 0.02

Water 1

Engine oil 100

Gear oil 1,000

Honey 10,000

Void Fraction The cross-sectional area locally occupied by the gaseous phase of a multiphase flow,

relative to the cross-sectional area of the conduit at the same local position.

Volumetric Flowrate Measurement Volumetric flowrate (QV) is defined as the passage of a given volume of fluid (V) in a given

time (t):

t

VQV

h Shear

stress,

Moveable plate

Fixed plate

Velocity (V)

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Many flow meters are designed to indicate directly the value of (QV) such meters are

sometimes referred to as ‘flowrate meters’.

Vortex Meter The vortex meter operates on the principle of a vortex shedding from a body or bluff

introduced into the main pipe. Behind the obstruction to the fluid, a series of vortices is

generated at a frequency directly proportional to the fluid velocity. Sensors placed

downstream on the pipe wall or internally measure the frequency of the vortex shedding and

from this the velocity and volumetric flowrate can be determined.

Whilst the principle of operation is basically the same for all types of vortex meter, the key

differences in operation and performance capabilities are largely determined by the method

of detection. There are a number of different types of vortex meters depending upon the

sensor types used and whether they are externally or internally mounted. Provided below is

a schematic representation of an ultrasonic based vortex meter.

Vortex Shedding When the fluid stream encounters a fixed obstruction the fluid must divide to pass around the

barrier. Because of viscous adhesion, the boundary layer (fluid moving along the surface of

the obstruction) moves slower than the outer layers. At very low flow rates, the viscous

forces dominate keeping the fluid attached to the wall of the body and the fluid recombines in

a symmetrical fashion behind it.

As the flow rate increases, however, there comes a point where the flow cannot withstand

the adverse pressure gradient along the surface of the body and the boundary layer duly

separates from it to form rotating vortices that are carried downstream with the mainstream

flow; this is often referred to as the wake region.

Amplifier and

signal processing

Oscillator

Transmitter

Receiver

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Water Cut Water cut (WC) is the water volume fraction of the liquid phase. That is:

FlowrateVolumetricLiquidTotal

FlowrateVolumetricWaterCutWater

and is usually expressed as a percentage.

Water-in-Liquid Ratio WLR is the water volume flow rate, relative to the total liquid volume flowrate at local

temperature and pressure. Note: This is normally expressed as a percentage.

Wedge Meter The wedge meter is a type of differential pressure meter, commonly employed for viscous

fluids or those carrying entrained solids, such as mud and slurry.

Based on similar principles to the Venturi meter, a restriction is arranged in the flow stream

across which the differential pressure drop is measured. In the wedge meter, however, the

restriction is created using a wedge or V-shaped segment, located within the meter body.

P1 P2

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Wet Gas In simple terms wet gas can be described as a gas with a small amount of liquid present.

There is no quantitative definition of a wet gas flow that is universally accepted and the

definition has been interpreted from a humid gas (i.e. gas saturated with liquid vapour) to

multiphase flows with a gas volume fraction of 90% or higher.

However, since the gas volume fraction is based on the volumetric flow rates of the liquid

and gas phases at actual conditions, no account has been made of the gas and liquid

densities. Liquids are considered as incompressible fluids and so the density does not tend

to change with a change in pressure. Gas on the other hand is a compressible fluid and the

density changes significantly with pressure. If the pressure of a system increases, the gas

density increases but the liquid density will not change. The fluid densities are an important

consideration in flow measurement as they relate to the actual mass quantities of the fluids

present.

The most commonly used parameter to describe wet gas flows is the Lockhart-Martinelli

parameter (see Lockhart-Martinelli Parameter). It is typically accepted in industry

that a Lockhart-Martinelli parameter of less than 0.3 is described as being a wet gas, above

this value it is multiphase flow.

Another common industry wet gas is steam (see Steam), when water is present in liquid

form.

Gas

Liquid

Liquid

hydrocarbon

Water

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