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University of Huddersfield Repository
University of Huddersfield Repository
Crabtree, Michael Anthony
Industrial flow measurement
Original Citation
Crabtree, Michael Anthony (2009) Industrial flow measurement. Masters thesis, University of
Huddersfield.
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INDUSTRIAL FLOW MEASUREMENT
MICHAEL ANTHONY CRABTREE
A thesis submitted to the University of Huddersfield
in fulfilment of the requirements for the degree of
Master of Science by Research
The University of Huddersfield
June 2009
2
To my wife Pam, without whose encouragement I
would never have started and without whose help I
would never have finished.
3
4
Abstract
This thesis discusses the intrinsic worth of a published work, ‘Industrial Flow
Measurement’ (Appendix A), a handbook written and revised by the author over a
period of 30 years. The author first discusses the need to measure flow and then
moves on to the raison d’être of the handbook before looking at a brief history of flow
measurement. Although not claiming that any single attribute of the handbook is
unique, the author nonetheless postulates that because it incorporates several
distinctive features, at a number of different levels, these agents combine to make it
one-of-a- kind.
The author moves on to an overview of existing flow metering technologies discussed
within the handbook. Finally, he looks at what he considers is a major gap in the
collected body of knowledge – the field of multiphase and water-cut metering and
provides a justification, not only for its inclusion in the future but for future
investigation.
5
6
Table of contents
Section No.
1.
2.
3.
4.
5.
6.
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.
7.1
7.1.1
7.1.2
7.1.3
7.2
8.
Appendix A
Title
Abstract
Acknowledgements
Author’s résumé
Introduction
Why measure flow?
Background
History of flow measurement
The book: ‘Industrial flow measurement’ (Appendix A)
Conclusions
Pros, cons and limitations of existing technologies
Positive displacement (Chapter 2 of Appendix A)
Inferential (Chapter 3 of Appendix A)
Oscillatory (Chapter 4 of Appendix A)
Differential pressure (Chapter 5 of Appendix A)
Electromagnetic (Chapter 6 of Appendix A)
Ultrasonic (Chapter 7 of Appendix A)
Mass flow (Chapter 8 of Appendix A)
Open channel (Chapter 9 of Appendix A)
Future directions
The need for multiphase flow metering
Multiphase flow
Separation-type flow metering
In-line multiphase flow metering (MPFM)
Water-cut metering
Bibliography
Industrial Flow Measurement
Page No.
5
9
11
12
14
15
17
19
21
21
22
23
23
24
27
28
29
30
31
31
33
34
34
35
37
39
List of diagrams
Diagram 1. Illustration showing how the delivery of oil and gas decreases over the
life of the well, with a commensurate increase in the delivery of water.
Diagram 2. A typical horizontal 3-phase separator.
Diagram 3. Flow regimes can be broadly grouped into: dispersed flow (bubble flow);
separated (stratified and annular) and intermittent (piston and slug flow).
Diagram 4. Spectral properties of two crude oils compared with condensate and water
(courtesy Weatherford).
Word count (excluding Appendix A)
8121
7
8
Acknowledgements
Dr. Rakesh Mishra, for his critical comments and suggestions.
Professor Andrew Ball, for his inspiration, help, support, and encouragement.
Dr. Lesley Crawford Campbell, who put me on the road.
Professor Ian Jandrell, who suggested it in the first place.
9
10
Author’s résumé
As a high-school drop-out Michael (Mick) Crabtree
claims he was ‘saved’ from total ignominy by joining the
Royal Air Force as an apprentice at the age of 16.
Trained in aircraft instrumentation and guided missiles
he completed a Higher National Certificate in Electrical
Engineering, (with distinction in Mathematics) and
concluded his service career seconded to the Ministry of
Defence.
In 1966 he moved to South Africa where he was involved in the sales of industrial
equipment and process control instrumentation. He later moved to a systems
integration company, working at the forefront of technology on a variety of projects.
In 1981 he was appointed Editor and Managing Editor of South Africa's leading
monthly journal dedicated to the process control instrumentation industries. In 1989
he founded his own company – specialising in feature writing, articles, and general
PR for the industrial process control sector.
During this period he also wrote and
published seven technical handbooks on industrial process control: ‘Flow
Measurement’, ‘Temperature Measurement’, ‘Analytical On-line Measurement’;
‘Pressure and Level Measurement’; ‘Valves’; ‘Industrial Communications’ and ‘The
Complete Profibus Handbook’.
For the last twelve years he has been involved in technical training and consultancy
and has run workshops on industrial instrumentation and networking throughout the
world. During this period he has led more than 4500 engineers, technicians and
scientists on a variety of practical training workshops covering the fields of Process
Control (loop tuning), Process Instrumentation, Data Communications and Fieldbus
Systems, Safety Instrumentation Systems, Project Management, On-Line Liquid
Analysis, and Technical Writing and Communications.
After nearly 35 years spent in South Africa, he now lives in Wales, just outside
Cardiff, having relocated to Britain about nine years ago.
11
1
Introduction
Over the past 60 years, the importance of flow measurement has grown, not only
because of its widespread use for accounting purposes, such as the custody transfer of
fluid from supplier to consumer, but also because of its application in manufacturing
processes. Throughout this period, performance requirements have become more
stringent – with unrelenting pressure for improved reliability, accuracy1, linearity,
repeatability and rangeability.
These pressures have been caused by major changes in manufacturing processes and
because of several dramatic circumstantial changes such as the increase in the cost of
fuel and raw materials, the need to minimise pollution, and the increasing pressures
being brought to bear in order to adhere to the requirements for health and safety.
Industries involved in flow measurement and control include:
¾ food and beverage;
¾ medical;
¾ mining and metallurgical;
¾ oil and gas transport;
¾ petrochemical;
¾ pneumatic and hydraulic transport of solids;
¾ power generation;
¾ pulp and paper; and
¾ distribution.
1
In the field of process instrumentation the term ‘accuracy’ is generally defined as
the ratio of the error to the full-scale or actual output, expressed as a percentage.
Strictly speaking the term should be confined to generalised descriptions and not to
specifications – where the term ‘error’ is preferred. However, the vast majority of
instrumentation manufacturers continue to use the term ‘accuracy’.
12
Fluid properties can vary enormously from industry to industry. The fluid may be
toxic, flammable, abrasive, radio-active, explosive or corrosive; it may be singlephase (clean gas, water or oil) or multi-phase (for example, slurries, wet steam, wellhead petroleum, or dust laden gases). The pipe carrying the fluid may vary from less
than 1 mm to many metres in diameter. Fluid temperatures may vary from close to
absolute zero to several hundred degrees Celsius and the pressure may vary from high
vacuum to many thousands of bar.
Because of these variations in fluid properties and flow applications, a wide range of
flow metering techniques has been developed with each suited to a particular area.
However, of the numerous flow metering techniques that have been proposed in the
past, only a few have found widespread application and no one single flowmeter can
be used for all applications.
13
2
Why measure flow?
There is of course no single answer. Flow measurement is normally concerned with
the question of ‘how much’ – how much is produced or how much is used. For small
quantities this can normally be achieved by volumetric measurement (e.g. pulling a
pint of beer). But as the amount grows larger this becomes impractical and, for
example, it becomes necessary to measure volumetric flow (e.g. dispensing fuel from
a garage petrol pump).
However, most petrol pump calibration is carried out using a test measuring can,
which is a purely volumetric measurement. On this basis, during hot weather, it would
be prudent to purchase petrol early in the morning when the temperature is low so that
you would end up with more mass per litre. Alternatively, a more practical and
consistent approach would be to make use of a mass flow metering system.
A further use of a flow measuring system is to control a process. In closed loop
regulatory control, there are several instances where the prime consideration is
repeatability rather than accuracy. This is particularly true in a cascaded system
where the prime objective is not to control the inner loop to an absolute value but
rather to increment up or down according to the demands of the master. Another
instance of where absolute accuracy is relatively unimportant is in controlling the
level of a surge tank. Here, the requirement is to allow the level to vary between an
upper and lower value and absorb the upstream surges – thus preventing them from
being passed downstream.
Accuracy is of prime importance in automatic blending control, batching and, of
course, custody transfer and fiscal metering. In fluid measurement, custody transfer
metering involves the sale, or change of ownership, of a liquid or gas from one party
to another. On the other hand, fiscal measurement involves the levering of taxes –
again relating to the production or sale of a liquid or gas.
14
3
Background
The book, ‘Principles and Practice of Flow Meter Engineering’ by L.K. Spink [1],
first published in 1930, is generally recognised as the first, and for many years the
only, definitive collected ‘body of knowledge’ appertaining to industrial flow
measurement. Undergoing nine revisions, the last addition was printed in 1978 – 21
years after Spink’s death.
In the flyleaf of this last addition the publishers lay claim to the book covering “… the
latest developments in flow measurement”. A weighty tome, by anyone's standards,
the book comes in at 575 pages. However, in essence ‘Principles and Practice of Flow
Meter Engineering’ is a eulogy “…devoted primarily to the characteristics of flow
rate measurement based on a differential pressure generated by the flow of liquid
through a restriction (such as an orifice) inserted in a line.”
Only a single page is devoted to the magnetic flow meter. A single page is likewise
devoted to the turbine meter. And barely a single paragraph is used to allude to
ultrasonic, thermal, and vortex-shedding meters – already key players in the field of
flow measurement.
Barely a single page is dedicated to the electrical pressure transmitter (already in
common use in 1978) – contrasting noticeably with long descriptions covering a
variety of mechanical-pneumatic type transmitters.
Readers, lured into purchase of the 9th edition of his book by the flyleaf promise of
“new data on the target meter”, might be disappointed to discover less than two pages
devoted to the subject. A similar enticement extends to the promise of new data on
the Lo-Loss tube, which is similarly dismissed in approximately a page and a half.
15
Of course, it could be said of Spink’s work that he spent most of his life in the oil and
gas industries and was instrumental in the early work of the American Gas
Association. In the oil and gas industry, in particular, conservatism is rife. A case in
point is that in the USA, most graduate facility engineers are taught in, and make use
of, the metric SI system (abbreviated from the French Le Système International
d'Unités). And yet, because of their mentoring program, they will have a reverted
back to fps (the imperial ‘foot-pound-second’ system used extensively in USA) within
a few years.
Generally regarded as the heir apparent to Spink, R.W. Miller’s ‘Flow Measurement
Engineering Handbook’ [2] weighs in at over 1000 pages. Although still referenced as
a standard for orifice plate sizing, the 2nd Edition, published in 1989 still devoted less
than 15 pages in total to the combined technologies of magnetic, ultrasonic and
Coriolis metering.
Too many process engineers, having had extensive experience with measuring
instruments and systems that have stood the test of time, see no reason to change.
Consequently, they will cling to the familiar, despite numerous shortcomings when
compared with the benefits offered by newer systems. And so, more than 50 years
after Spink’s death, the orifice plate still reigns supreme – not because of its
technological superiority but because of the industry’s unwillingness to accept and
implement new ideas and new technologies.
16
4
History of flow measurement
Early flow measurement was centred round the question of disputation: ‘how much
has he got’ versus ‘how much have I got’. As early as 5000 BC flow measurement
was used to control the distribution of water through the ancient aqueducts of the
early Sumerian civilisations from the Tigris and Euphrates rivers. Such systems were
very crude, based on volume per time: e.g. diverting flow in one direction from dawn
to noon, and diverting it in another direction from noon to dusk. And although not
fully comprehending the principles, the Romans devised a method of charging for
water supplied to baths and residences, based on the cross sectional areas of pipes.
The first major milestone in the field of flow technology occurred in 1738 when the
Swiss physicist Daniel Bernoulli published his Hydrodynamica [3] in which he
outlined the principles of the conservation of energy for flow. In it he produced an
equation showing that an increase in the velocity of a flowing fluid increases its
kinetic energy while decreasing its static energy. In this manner a flow restriction
causes an increase in the flowing velocity and a fall in the static pressure – the basis of
today’s differential pressure flow measurement.
The word ‘turbine’ is derived from the Latin spinning top and although the ancient
Greeks ground flour using horizontal turbine wheels, the idea of using a spinning
rotor or turbine to measure flow did not come about until 1790 when the German
engineer, Reinhard Woltman, developed the first vane-type turbine meter for
measuring flow velocities in rivers and canals.
Other types of turbine meter followed. In the late 1800’s Lester Pelton built the first
Pelton water wheel that turned as a result of water jets impinging on buckets attached
around the outside of the wheel. And in 1916 Forrest Nagler designed the first fixedblade propeller turbine.
A third milestone occurred in 1832 when Michael Faraday attempted an experiment to
use his laws of electromagnetic induction to measure flow.
With the aim of
measuring the water flow of the River Thames, Faraday lowered two metal electrodes,
17
connected to a galvanometer, into the river from Waterloo Bridge. The intent was to
measure the induced voltage produced by the flow of water through the earth’s
magnetic field. The failure of Faraday to obtain any meaningful results was probably
due to electrochemical interference and polarization of the electrodes.
It was left to a Swiss Benedictine monk, Father Bonaventura Thürlemann, working in
a monastery in Engelberg, to lay the foundations of this technology, with the
publication
of
his
scientific
work,
‘Methode
zur
elektrischen
Geschwindigkeitsmessung in Flüssigkeiten.’ (Method of Electrical Velocity
Measurement in Liquids), [4] in 1941.
Unfortunately, although his work was sound, the technology of the time was
insufficient to develop a practical system. Consequently, it was not until the mid
1950s that sufficient progress had been made in electronics to make it possible to
produce a low voltage, interference free, measuring amplifier that was sufficiently
sensitive and drift free. Despite the many advantages of this technology2, initial
conservatism slowed down its acceptance for use in industrial applications. The
impetus required to initiate further research and general acceptance, came in 1962
when J. A. Shercliff published his decisive book (‘The theory of electromagnetic
flow-measurement’[5]), setting down a firm theoretical foundation on the principles
of magnetic flowmeters.
The last milestone occurred only three years after Faraday conducted his original
experiment when, in 1835, Gaspar Gustav de Coriolis, made the discovery of what is
now termed the Coriolis effect, which led, nearly a century and a half later, to the
development of the highly accurate direct measurement mass flow Coriolis meter.
2
See Chapter 6, Section 6.14 (‘Conclusions’) of Appendix A for further details.
18
5
The book: ‘Industrial flow measurement’ (Appendix A)
In 1979 the author wrote a handbook entitled ‘Industrial Flow Measurement – a
definitive guide to the principles, selection and practice of industrial flow metering’.
Published in South Africa, it sought to provide a complete body of knowledge for
both the specialist and non-specialist instrumentation practitioner and to redress the
apparent shortcomings prevalent in most of the available books dealing with flow
measurement.
No single attribute of the handbook is unique. However, because it incorporates
several distinctive features, at a number of different levels, these agents combine to
make it one-of-a- kind.
During the last 30 years the handbook has been revised eight times and was last
published as ‘Mick Crabtree’s Flow Handbook’. The use of the author’s name sought
to capitalize on his credibility and his positive reputation for objectivity within the
South African marketplace. The current (last revised in April 2009), unpublished,
version (Appendix A) is entitled ‘Industrial Flow Measurement’ and represents some
thirty years wealth of experiential knowledge gleaned from the author's experience
working within a systems integration company and also feedback from more than
4000 technicians and engineers who have attended the author’s workshops.
The handbook makes use of a building block approach and is presented in a form
suitable for two distinct classes of reader: the beginner, with no prior knowledge of
the subject; and the more advanced technician.
The complete text is suitable for the advanced reader. However, those parts of the
text, which involve a mathematical treatment which are not required by the beginner,
are indicated by a mark (X) at the beginning and (W) at the end. Consequently, for
the beginner the text may be read, with full understanding, by ignoring the marked
sections.
19
In this manner two complete books are available at two different levels for two
distinct classes of reader. This avoids a purely mathematical treatment in favour of a
progressive journey that allows the reader a choice to firmly establish a knowledge
foundation. Moving from knowledge, to comprehension, to application the handbook
allows the reader to conduct a technical evaluation of the options based on rigid
analysis. Ultimately, what the author achieved is a handbook that gets to grips with
each technology in turn – explaining it in a detailed but understandable language. This
enables specifiers to examine the choices and make an informed recommendation
based on facts rather than vendors’ sales pitches.
Another feature of the published handbook is that it carried advertising.
Consequently, it was not sold directly to the public but was sent, free of charge, to
nearly 5000 subscribers of a South African trade journal called ‘Electricity and
Control’. Income was thus generated by a combination of advertising revenue and
direct sales of approximately 500 copies. The advantage of this approach to the
advertisers is that they were offered a guaranteed target market and circulation. They
were also offered, free of charge, a number of ‘Product editorials’ – short editorial
items of approximately 200 words. The benefit accruing to the author was that he was
fully appraised of all the latest products and technologies newly introduced into the
market. On the downside, there were vendors (actually only two) who attempted to
use their advertising ‘clout’ to influence the objectivity of the editorial. With the
backing of the publisher, this pressure was ruled as inappropriate and their
advertisements removed from the journal. Although drawing heavily on commercial
literature and publications, the handbook was, nonetheless, able to seek and find an
objectivity that was unavailable from vendor-resourced literature.
A further feature of the handbook lies in the more than 200 explanatory line drawings
and graphs, which, with only a few exceptions, were originated and drawn, or
redrawn, by the author.
20
6
Conclusions
The basis of this thesis, ‘Industrial Flow Measurement’, is to address the complete
range of modern flow measuring technologies in an easily accessible format.
Although the situation is changing, there is still a scarcity of literature collected in a
single body of knowledge that allows technicians and engineers to access a single
usable up-to-date reference point.
Two notable exceptions include: ‘Flow Measurement Handbook’ by Roger C. Baker
[6] and ‘Fluid Flow Measurement – A Practical Guide to Accurate Flow
Measurement’ by E. Loy Upp and Paul J. LaNasa [7]. Bakers book is particularly
comprehensive and covers a number of technologies and additional material that is
not found in Appendix A. However last published in 2000 and 2002 respectively,
both publications necessarily exclude some of the advances in flow technology (high
accuracy Coriolis; ultrasonic custody transfer; conditioning orifice plate; high
accuracy magnetic flowmeters with signature analysis) that are addressed in Appendix
A.
6.1
Pros, cons and limitations of existing technologies
Many attempts have been made to categorise flow metering technologies. Several,
including Spink, have merely split the technologies into two divisions: head-loss
metering and non head-loss metering – a simple enough categorisation but one that is
not only far too simplistic but one that is also somewhat dismissive of many of the
modern additions to the technology as a whole.
Another approach, used by Dr. Jesse Yoder, Flow Research, Inc. [8] is to classify the
technologies into:
¾ new-technology flow meters; and
¾ traditional-technology flow meters.
21
In its way, this approach is equally dismissive of the traditional technologies that
include head-loss meters. In some instances considerable work has been carried out
to dramatically improve the shortcomings of these previously restricted technologies.
In Appendix A, (Industrial Flow Measurement) the author has used neither of these
two approaches, seeking rather to look at each technology in turn and to weigh them
according to their importance in industry as a whole, rather than any specific sector.
To this effect the technologies are discussed in the following categories:
¾ Positive displacement.
¾ Inferential.
¾ Oscillatory.
¾ Differential pressure.
¾ Electromagnetic.
¾ Ultrasonic.
¾ Mass flow.
¾ Open channel.
When examined in detail these eight divisions encompass a total of 33 different
technologies. In the following discourse the author will briefly discuss each one of
these technologies in turn.
6.2
Positive displacement (Chapter 2 of Appendix A).
Positive displacement meters separate defined volumes of the medium from the flow
stream and move them from the inlet to the outlet in discrete packages. By totalising
the number of packages, the total volume passed in a given time is provided. With
moving parts that are subject to wear, positive displacement meters are, with a few
exceptions, part of a shrinking market sector. One of these exceptions, and one most
commonly met, is the nutating disc or ‘wobble’ meter which is used extensively,
particularly in the USA, for residential water service metering.
Because of their high accuracy, positive displacement meters are also to be found in
another major market sector: custody transfer and fiscal metering applications in the
oil and gas industries.
22
In spite of their high accuracy; the need for a clean medium; their high expense; and,
as mentioned previously, their susceptibility to wear; positive displacement meters
being are gradually being replaced by other ‘modern’ approaches such as turbine,
ultrasonic and Coriolis meters.
6.3
Inferential (Chapter 3 of Appendix A)
This group, which includes turbine, propeller, and impeller type meters, infers the
displacement of undefined volumes of the flowing medium as it passes from the inlet
to the outlet. Unlike the positive displacement meter, the volume is not geometrically
defined. Typically, the flowing fluid impinges on a blade or paddle causing it to rotate
at an angular velocity that is directly proportional to the fluid flow rate.
The
rotational velocity is measured by a proximity transducer (usually magnetic) that
produces an output pulse for each passage of a blade – with each pulse representing a
distinct volume of the displaced fluid.
Again, expensive, and subject to wear, the turbine meter is commonly used in custody
transfer applications in the oil and gas industry. However, the need for an on-site
meter prover calibration skid, to compensate for variations in the viscosity of the
medium, has caused a decline in its market share – slowly giving way to ultrasonic
and Coriolis metering. Many users, however, cling to the ‘tried, true and tested’
technologies of yesteryear for the very reason that an on-site meter prover skid is
available and that calibration can be verified immediately.
6.4
Oscillatory (Chapter 4 of Appendix A)
This group includes vortex, vortex precession, and fluidic type meters – all involving
different physical principles. The common denominator, however, is that in all three,
the primary device generates an oscillatory motion of the fluid whose frequency is
detected by a secondary measuring device that produces an output signal that is
proportional to fluid velocity.
23
Since their introduction by Eastech in 1969 [9] and subsequently by Yokogawa in
1972 [10] the vortex flow meter has made huge strides in market penetration –
especially in the field of steam metering where other technologies such as ultrasonic
and Coriolis fall short due to the high temperatures encountered.
However, unlike magnetic, ultrasonic and Coriolis based meters, vortex meters are
intrusive, with the bluff body producing an unrecoverable pressure drop – albeit a
small one. Another problem is the requirement for comparatively long straight runs
of piping after a discontinuity such as an elbow or a valve – typically a minimum of
40 pipe diameters. A further problem that plagued early models was their sensitivity
to external vibration. This has largely been overcome through the use of digital signal
processing but remains an area of concern.
6.5
Differential pressure (Chapter 5 of Appendix A)
Often referred to as ‘head loss’ meters, differential pressure flow meters encompass a
wide variety of meter types that includes: orifice plates; V-cone, venturi tubes and
nozzles; Lo-Loss tubes (that encompass the Dall tube); target meters, pitot tubes and
variable area meters. Indeed, the measurement of flow using differential pressure is
still the most widely used technology.
An important advantage of differential type meters over other instruments is that the
measurement is based on the accurately measurable dimensions of the primary device
and they do not necessarily require direct flow calibration. In addition, they offer
excellent reliability, reasonable performance and modest cost. Furthermore,
differential type meters can be used on liquid or gas applications3.
3
For gas flow applications account should be taken of the gas expansion factor (= 1
for liquid). See Chapter 5, Section 5.2.3 (‘Gas flow’) of Appendix A for further details.
24
A long-held bias towards this technology, exemplified by the orifice plate, remains in
force throughout the world despite a myriad of disadvantages:
¾ high permanent pressure head loss;
¾ poor accuracy – typically 2 to 3% at best;
¾ low turndown ratio4 – typically from 3:1;
¾ accuracy is affected by fluctuations in the density, pressure and viscosity and by
erosion and physical damage to the restriction;
¾ long straight pipe runs are required – for custody transfer applications, for
example, the American Gas Association (AGA) requires 95 pipe diameters of
straight pipe upstream of the measurement point;
¾ the output is not linearly related to flowrate – thus entailing square root extraction;
and
¾ there are a large number of potential leakage points5.
Even some of the perceived advantages, such as simple construction and relatively
low cost, do not hold up well when examined a little closer. Yes, construction of the
primary element, the orifice plate, is relatively simple. And yes, the primary element
is relatively inexpensive. However, there is a lot of ancillary equipment associated
with the primary element: the isolation valves; the impulse tubing; the 3- or 5-way
valve manifold valve; and the differential pressure transmitter itself [11].
On relatively small pipelines, of 100 mm diameter (DN 100) or less, these costs, taken
together as a system, can well exceed the cost of alternative technologies such as a
magnetic or vortex metering.
4
The turn-down ratio is the ratio of the maximum flow rate to the minimum flow
rate. See Chapter 1, Section 1.9.2 of Appendix A for further details.
5
See Chapter 5, Section 5.9.2 (‘Multiple leakage points’) of Appendix A for further
details.
25
However, several vendors have been at pains to address some of the issues.
Companies including Honeywell [12], Emerson (Rosemount) [13], and ABB [14]
have introduced Multivariable Pressure Transmitters that provide direct simultaneous
measurement of not only of the differential pressure but also static pressure, and
temperature. Built-in processing provides direct calculation of mass flow [15] and
extends the turndown ratio to 10:1.
Another radical innovation, introduced by Emerson, is the Conditioning Orifice Plate
[16]. In place of the conventional concentric round hole (orifice) through which the
liquid flows the Conditioning Orifice Plate makes use of four equally spaced holes
that are arranged in such a fashion as to leave a metal section of the plate in the centre
of the pipe. This causes the flow to condition5 itself as it is forced through the four
holes. The arrangement reduces swirl and irregular flow profiles and removes the
requirement for a flow conditioner to the extent that only a total of 4 pipe diameters
(2D up-stream and 2D down-stream) is required.
Furthermore, the discharge
coefficient uncertainty (UCd), a major factor in determining accuracy, is in many cases
reduced to ±0.5% from a typical value of ±1.0%.
A further innovation in the field of head loss metering is the V-Cone Flowmeter from
McCrometer – a patented technology that features a centrally-located cone inside the
flow tube that interacts with the fluid and creates a region of lower pressure
immediately downstream of the cone. The pressure difference is measured between
the upstream static line pressure tap, placed slightly upstream of the cone, and the
downstream low pressure tap located in the downstream face of the cone.
5
Flow conditioning ensures that the flow regime is a fully developed turbulent
profile, free of swirl. See Chapter 1, Section 1.3.3 of Appendix A for further details.
26
Major features of the V-Cone Flowmeter include:
¾ 0 to 3 diameters of upstream straight run piping and 0 to 1 diameters downstream;
¾ primary element accuracy of ±0.5% of reading with a repeatability of ±0.1% or
better;
¾ turndown ratio 10:1 with Reynolds numbers as low as 8000; and
¾ suitable for use with dirty fluids.
6.6
Electromagnetic (Chapter 6 of Appendix A)
A period of some 120 years elapsed from Faraday’s early experiments to measure the
flow rate of the River Thames in 1832 to the introduction of the first practical
electromagnetic flow meter by Tobimeter [17] in 1952. Since then more than 30
manufacturers have entered the arena and this type of meter generates more revenue
than any other type. Magnetic flow meters are widely used in the potable water,
wastewater and chemical industries. And because they can conform to sanitary
requirements they are also widely used in the food and beverage and pharmaceutical
industries.
Magnetic flow meters are almost the ideal flow meter. Positive features include:
¾ unrestricted pipe and therefore no pressure drop;
¾ short inlet/outlet sections (5D/2D);
¾ linear relationship between flow and measurement (no square root extraction
required);
¾ insensitive to axisymmetrical flow profile changes (laminar to turbulent);
¾ turndown ratio of 40:1 or better;
¾ inaccuracy of better than ±0.1% of actual flow over full range;
¾ no recalibration requirements;
¾ bi-directional measurement;
¾ no taps or cavities; and
¾ not limited to clean fluids.
But, there is one major drawback to electromagnetic flow meters – they require a
conductive fluid. This precludes their use to measure gases, steam, ultrapure water,
and all hydrocarbons.
27
Huge strides have been made in reducing the limit for conductivity. For most modern
d.c. field driven instruments the minimum conductivity was about 1 μS/cm.
However modern instruments employ a variety of technologies, including capacitively
coupled meters that can be used on liquids with conductivity levels down to 0.05
µS/cm. Although this is close to the upper hydrocarbon limit of 0.0017 µS/cm for
crude oil it falls far short of even jet fuel (150 – 300 pS/cm).
Another disappointment is in the flow measurement of pure and ultrapure water. The
conductivity of ultrapure water extends down to 0.1 µS/cm and would therefore
appear to be covered by the extended range down to 0.05 µS/cm. However in order to
meet these requirements use is made of very high input impedance amplifiers in the
range 1013 to 1014 Ω or even more and these are very susceptible to electrical noise.
Unfortunately water, being a bipolar vibratory molecule, produces relatively large
amplitudes of electrical noise that tend to swamp the amplifiers used to gain this
sensitivity.
Development effort is mainly centred on producing better reliability; better accuracy
(already down to ±0.1%); and better automatic diagnostics to the correct functioning
of the meter, based on signature analysis of the signal.
6.7
Ultrasonic (Chapter 7 of Appendix A)
First introduced in 1963 by Tokyo Keiki [18] there are now more than 35
manufacturers. Some of the earliest meters were based on the Doppler shift method
and generally proved to be most unsatisfactory – with inaccuracies of up to 10%. The
introduction of the transit time meter gave a well needed boost to the technology –
albeit that the measurement was restricted to clean liquids. Early models used only a
single path through the pipe, making the measurement extremely susceptible to
variations in the flow profile – a measurement variation of up to 33% could be
expected with a change from laminar to turbulent flow. The use of dual-path meters
reduced the laminar/turbulent dependency to less than 1% but was offset by the
increased cost.
28
However it was the only when Krohne [19] introduced their five-beam custodytransfer system into the oil and gas industry, following three years of trials, that the
technology started to be taken seriously.
The system was capable of providing
accuracies of down to ±0.15% on liquids. Subsequently, several other companies have
produced ultrasonic custody transfer meters making use of four to six beams.
The last observation, regarding ultrasonic flow meters, is that despite claims from a
number of manufacturers, clamp-on meters have generally failed to produce any
meaningful or consistent results. Indeed, their shortcomings have been so apparent
that they have tended to tarnish the reputation of the ultrasonic technology as a whole.
Because the ultrasonic beam must not only traverse the medium, but also the pipe wall
plus any external coatings, each interface contributes an unspecified amount of
refraction. Consequently, positioning the downstream transducer, in order to obtain a
meaningful signal, proves very difficult indeed. Furthermore, any change in the
characteristics of the liquid, which affects the speed of sound, will have a direct effect
on the refraction angle.
6.8
Mass flow (Chapter 8 of Appendix A)
In the chemical industry, most reactions are realised on a stoichiometric basis which
stresses the relationship between the relative quantities of the substances taking part in
a reaction, rather than the volume. And thus a system that measured mass flow
directly was a major breakthrough.
Traditionally the measurement of mass flow entailed measuring the volumetric flow
rate and multiplying it by the measured density. Density measurement is normally
achieved through the use of a nuclear gamma-ray based densitometer that is generally
regarded as being expensive, imprecise, and potentially dangerous. The Coriolis
meter measures mass flow directly, to a very high accuracy (better than ±0.1%). It is
also capable of providing a direct read out of density. Indeed, in many applications,
particularly the food and beverages industries, the measurement of density is often the
prime measurement.
29
The two major challenges currently facing the manufacturers of Coriolis meters are
pipeline size and pressure containment. Currently the largest pipeline size available is
DN 300 (12 inches), available from Rheonik [20] making use of dual curved (Ωshaped) shaped flow tubes. However, at this size the pressure is limited to 60 bar. A
lot of research has also been aimed at further developing straight-tube technology. To
this end, Krohne recently introduced a straight-tube model suitable for DN 250 (10
inch) and pressures up to 80 bar [21].
6.9
Open channel (Chapter 9 of Appendix A)
Little future development is expected in this field. Ninety percent of all applications
make use of specialised ultrasonic level sensors capable of providing level
measurement accuracy down to ±0.25%. Built-in software is now available that
translates the level measurement into flow rate according to the discharge equation
that is specific to the primary measuring element e.g. a weir or flume [22].
30
7
Future directions
A major gap in this collected a body of knowledge is specific to the oil and gas
industry – the field of multiphase and water-cut metering. The remainder of this
section details why this is such a crucial Issue.
7.1
The need for multiphase flow metering
During the life of an oil well the output components change dramatically. This is
illustrated in Diagram 1 which shows how the delivery of oil and gas decreases over
the life of the well with a commensurate increase in the delivery of water. In its early
life a typical well might deliver 90% oil and less than 10% water. Ideally the gas cap
forces the produced fluids out under pressure for some period of time. In midlife, as
the gas cap pressure falls, pumps may be required to bring the fluids to the surface,
which might now comprise about 50% oil and 50% water. In later life, with almost
no gas, artificial lift is required in order to raise fluid to the surface and obtain
maximum oil recovery which may now possibly comprise less than 20% oil and 80%
or more water. Artificial lift systems include: rod pumping using a pumping jack
(often referred to as a nodding donkey) as a prime mover; gas lifting (gas injection);
hydraulic pumping (water injection); and centrifugal pumping. A combination of gas
and/or water injection and pumps might be required to bring the fluid to the surface.
Diagram 1. Illustration showing
Volume (%)
100
0
Gas
how the delivery of oil and gas
Oil
decreases over the life of the well
with a commensurate increase in
er
Wa t
the delivery of water.
Time (years)
At the well-head surface, the three constituents (oil, gas, and water) are separated
using a series of 2, 3 or more separators. A typical separator (as illustrated in Diagram
2) involves three principles to realise physical separation: momentum, gravity settling,
and coalescing [23].
31
Gas
Inlet
baffle
Gravity
section
Coalescing
section
Mist
extractor
Oil/gas/water
inlet
Overflow baffle
GAS
Vortex breaker
OIL
WATER
OIL
Sump
Water
Oil
Diagram 2. A typical horizontal 3-phase separator.
In the representative system shown, the flow through the inlet nozzle impinges on a
diverter baffle that produces an abrupt change of direction. Since the momentum of
the heavier oil/water phase particles is greater than that of the gas, they cannot turn as
rapidly and separation occurs.
Enhanced separation of the entrained droplets occurs in the gravity section where the
gas moves at a relatively low velocity – with little turbulence. If the gravitational
force acting on the droplet is greater than the drag force of the gas flowing around the
droplet, liquid droplets will settle out of a gas phase.
In the coalescing section, a mist extractor (normally comprising a series of vanes or a
knitted wire mesh pad) removes the very small droplets of liquid from the gas by
impingement on a surface where they coalesce.
And finally, oil-water separation occurs in the sump where, using an overflow baffle,
the two immiscible liquid phases (oil and water) separate within the vessel by virtue
of their differences in density.
A critical factor that determines the efficacy of this process is that sufficient retention
time be provided in the separator to allow for gravity separation to take place. This
can vary from 30 seconds up to three minutes – depending on the size of the separator,
the inflow, the gas/oil ratio (GOR) and the oil/water ratio.
32
The oil output from a first stage separator should typically contain 1 - 3% water with
(possibly) up to 0.5% gas. The water output should typically contain less than 300
ppm of oil. In order to achieve this balance, tight control of the three component
outflows must be applied which must be balanced against the inflow. And this, quite
simply, is where the problem lies – accurate and reliable, simultaneous measurement
of the input multiphase flow.
7.1.1
Multiphase flow
A multiphase mixture of three different components (oil, water and gas) is a complex
phenomenon producing a variety of flow regimes whose distribution, in both space
and time, differ from each. Several different types of flow regimes are illustrated in
Diagram 3 and can be broadly grouped into: dispersed flow (bubble flow); separated
(stratified
and
annular)
and
intermittent (piston and slug flow)
Bubble flow
Piston flow
[24].
Because they are dynamic,
these flow regimes usually fall
outside the control of an engineer
or operator and are difficult to
Stratified flow
predict and model.6
Annular
bi-directional
flow
Semi-slug flow
Diagram 3. Flow regimes can be
broadly grouped into: dispersed
flow
(bubble
(stratified
and
flow);
separated
annular)
and
Slug flow
Oil
6
Gas
intermittent (piston and slug flow).
Water
Akio Tomiyama, Masahiro Tanaka, et al, (Kobe University, Tokyo) have been
working in the field of multiphase flow for the last 10 years. In recent computational
work [25] they have demonstrated an ability to accurately model the three
dimensional structure of multiphase flows – including time dependent variations in
the shapes and sizes of the individual gas bubbles.
33
It should be stressed that the flow regime illustrated in Diagram 3 showing annular bidirectional flow is only one of several possibilities. Generally, the liquid velocity in
the film (which is likely to be a homogeneous mixture of oil and water) is in the
upward direction adjacent to the gas – decreasing with increasing radial position so
that it may be in the downward direction adjacent to the pipe wall.
7.1.2
Separation-type flow metering
The technology required to measure any one of these regimes is already complex. A
further complicating consideration is that the multiphase mixture pressure may vary
from almost 0 to 2000 bar and the temperature can vary from -40 to 200° C.
For a single technology to cover them all, borders on the insurmountable. On this
basis, the traditional method is to split the multiphase steam into discrete phases,
using a test separator, with the measurement taking place on a single phase (or in the
case of oil-water mixtures, two phase) stream [26]. The compact upstream separation
device provides a relatively liquid-free gas stream and a liquid stream – with each
metered separately. The metering methods most commonly used are:
Gas: orifice plate; turbine
Liquid: orifice plate; turbine; Coriolis
A major problem with this method lies in separating the production stream into its
component parts. Indeed, rarely can complete phase separation occur and entrapment
of phases within each other is common [27].
7.1.3
In-line multiphase flow metering (MPFM)
Generally, full multiphase stream measuring systems make use of two or more sensors
that combine the data to yield individual phase flow rates. A major difficulty in
exploring the technologies used in multiphase flow metering is that manufacturers are
inclined towards a high degree of secrecy in order to preserve their competitive edge
in what could prove to be a highly rewarding and lucrative market. Estimates indicate
that installed costs of a single MPFM can range from US$100,000 to US$500,000 –
depending on size and application [28].
34
One such system, PhaseWatcher, from Schlumberger, comprises a Venturi tube
combined with a nuclear dual energy fraction meter [29]. The Venturi tube is fitted
with differential pressure, static pressure, and temperature measuring transducers for
temperature corrected flow measurement. The nuclear measuring section comprises a
Barium source and dual-energy fraction detector used to measure two different photon
energy levels – high energy for measuring density and low energy to calculate the
water-oil ratio.
Other technologies include: a combination of microwave sensor and positive
displacement flowmeter (Agar), capacitance and inductance sensors (FlowSys,
Roxar), and venturi tube and nuclear densitometers (Schlumberger, Haimo, Roxar).
Extensively tested by a large number of oil companies, conventional wisdom indicates
that, despite claims by the vendors, no one solution appears to be totally satisfactory.
The author’s spot opinion poll, conducted amongst more than twenty current, and
former facilities (topside offshore platforms) engineers and operational staff indicates
a deep cynicism regarding the claims by many vendors and that often calibration is
referenced back to both the empirical experience, and sometimes even priori feelings
and instincts of, the operational staff.
7.2
Water-cut metering
Water-cut meters measure the water content (cut) of an oil/water mixture, expressed
in % by volume, and are typically used in the oil and gas industry to measure: the
water-cut of oil flowing from a well; produced oil from a separator; crude oil transfer
in pipelines and in loading tankers. As with MPFM, several technologies are available
including: oscillatory; capacitive; microwave dielectric; and infrared (IR).
One such system, from Phase Dynamics [30], makes use of ‘oscillator load pull 7’ in
which an RF oscillator (150 to 500 MHz) sets up a standing wave within a resonant
chamber through which the oil/water mixture flows.
7
‘Oscillator load pull’ is a measure of how much an oscillator changes its frequency
when the load that is connected to it changes.
35
Because the relative permittivity (εr) of water (68 - 80) and oil (2.5) are very different,
changes in the water-cut vary the velocity of the RF, which in turn, changes the phase.
Ultimately, the phenomenon of ‘oscillator load pull’ changes the oscillator frequency
itself – depending on the water content.
Another system from Weatherford [31] relies on the preferential absorption of
infrared radiation in the ‘near’ region in which, at the operating frequency of the
sensor, water is the transmitting phase while oil is the attenuating medium (Diagram
4).
4
Diagram 4. Spectral properties
Crude A
Crude B
of two crude oils compared
Optical density
3
with condensate and water
Water
2
(courtesy Weatherford).
Condensate
1
0
400
600
800
1000
1200
Wavelength (nm)
1400
1600
Red Eye meters measure the volumetric proportion of oil in a mixture of oil and water
by passing a beam of infrared light through the stream. Accuracy is maintained under
a wide range of conditions by taking into account not only the directly transmitted
beam, but also light scattered forward and backward across the gap. Water transmits
close to 100% of the emitted radiation while crude oil typically transmits less than
10% of the light.
The Red Eye Water-Cut Meter claims not to be affected by variation or changes in the
properties of the water since the NIR radiation does not interact with the components
of field-produced brine.
36
8
Bibliography
[1] L.K. Spink, ‘Principles and Practice of Flow Meter Engineering’, Ninth Edition,
The Foxboro Company, Foxboro, Massachusetts. USA. 1978.
[2] R.W. Miller, ‘Flow Measurement Engineering Handbook’, Second Edition,
McGraw-Hill Publishing Company, 1989.
[3] Bernoulli, Daniel ‘Hydrodynamica’, Sive de viribus et motibus fluidorum
commentarii, Strasbourg, Johann Reinhold Dulsseker, 1738
[4] Thürlemann, B. ‘Methode zur elektrischen Geschwindigkeitsmessung in
Flüssigkeiten.’ (Method of Electrical Velocity Measurement in Liquids), Helv. Phys.
Acta 14, pp. 383-419, 1941.
[5] J. A. Shercliff, ‘The Theory of Electromagnetic Flow-Measurement’, Cambridge
University Press, 1962.
[6] Roger C. Baker, ‘Flow Measurement Handbook: Industrial Designs, Operating
Principles, Performance, and Applications’, 2nd Edition, Cambridge University Press,
2000.
[7] E. Loy Upp, Paul J. LaNasa, ‘Fluid Flow Measurement: A Practical Guide to
Accurate Flow Measurement’, 2nd Edition, Gulf Professional Publishing, 2002.
[8] Dr. Jesse Yoder, ‘The Paradigm Case Method of Selecting Flowmeters’, Flow
Research, Inc. 2007.
[9] United Kingdom Patent, GB1263614, Published 1972-02-16, Eastech (US)
1,263,614. ‘Measuring fluid-flow. Eastech Inc. May 21, 1969 (May 27, 1968),
No.25939/69. Heading G1R.
[10] United Kingdom Patent, GB19730015259 19730329 1387380 Measuring fluidflow Yokogawa Electric Works Ltd, 29 March 1973 (27 April 1972) 15259/73.
Heading G1R.
[11] Appendix A. Chapter 5, Section 5.3.4, 2009.
[12] Honeywell, ‘SMV 3000 Smart Multivariable Transmitter’, Technical
Information, 34-SM-03-01, 2009.
[13] Rosemount 3095 MultiVariable Mass Flow Transmitter, Product Specification
Sheet: 00815-0100-4716, Rev AA, August 2005
[14] ABB, ‘267CS Multivariable Transmitters’, Product Specification Sheet: Data
Sheet, SS/267CS/269CS, 2007.
[15] Appendix A. Chapter 5, Section 5.17.1, 2009.
[16] Rosemount 1595 Conditioning Orifice Plate, Product Data Sheet: 00813-01004828, Rev EB, 2007.
[17] F. Cascetta, ‘Short history of flowmetering’, Published by Elsevier Science Ltd.,
Copyright © 1995.
37
[18] M. Mohitpour, J. Szabo, T. Van Hareveld, ‘Pipeline Operation and Maintenance
– a practical approach’, ASME Press, USA, 2005.
[19] Krohne, ‘Altosonic V 5 - Beam ultrasonic flowmeter for custody transfer of
liquid hydrocarbons’, Technical Datasheet© Krohne 7.02330.23.00, 04/2006.
[20] Rheonik, ‘RHM 160 - 12 Coriolis Mass Flowmeter’, Page 5 of 5, v6, April 2006.
[21] Krohne, ‘Optimass bulk flowmeter’, Datasheet:4000228103, 03/2009
[22] Appendix A. Chapter 9, 2009.
[23] Gas Processors Suppliers Association (GPSA), ‘Engineering Data Book’, FPS
version, Volume I & II, Sections 1-26, 1998.
[24] Agar Corporation, ‘Not All Multiphase Flowmeters Are Created Equal’,
Revision 7, 2004.
[25] Masahiro Tanaka, Kosuke Hayashi, Akio Tomiyama, ‘Hybrid multiphase-flow
simulation of bubble-driven flow in complex geometry using an immersed boundary
approach’, Multiphase Science and Technology, Volume 21, 2009.
[26] John M. Campbell, ‘Gas conditioning and processing. Volume 1: The Basic
Principles’, Chapter 9, Multiphase Flow Measurement, Eight Edition, February 2004.
[27] Dr. Atef Al-Allah, ‘Field experience to optimize gas lift well operations’,
Academic Focus, Egypt Oil, Issue 10, October 2007.
[28] ‘Market Prospects for Multiphase Technology’, THERMIE Programme action
No: HC 6.3, The Petroleum Science and Technology Institute PSTI, For the European
Commission Offshore Technology Park, Directorate-General for Energy (DG XVII),
1998.
[29] Mohammed N. Al-Khamis and Abdulaziz F. Al-Bassam, (Saudi Aramco); Zaki
Bakhteyar and Muhammad N. Aftab, (Schlumberger) ‘Evaluation of PhaseWatcher
Multiphase Flow Meter (MPFM) Performance in Sour Environments’, Offshore
Technology Conference, Copyright 2008.
[30] Phase Dynamics, Inc. http://www.phasedynamics.com/technic.html#faq1
[31] Weatherford, ‘Red Eye® 2G Water-cut Meter’, Brochure 5313.00, 2008.
38
APPENDIX A
INDUSTRIAL FLOW MEASURMENT
39
Industrial Flow Measurement
Contents
INDUSTRIAL FLOW MEASUREMENT
Author: Michael A. Crabtree
Copyright © Crabtree Controls Ltd.
11 Stallcourt Avenue
Llantwit Major
CF 61 1TE
UK
All rights to this publication and to any associated workshop are reserved.
No part of this publication or associated software may be copied, reproduced, transmitted or stored in any form
or by any means (including electronic, mechanical, photocopying, recording or otherwise) without prior written
permission from Crabtree Controls Ltd.
Disclaimer
Whilst all reasonable care has been taken to ensure that the description, opinions, programs, listings, software
and diagrams are accurate and workable, Mick Crabtree Associates UK does not accept any legal responsibility
or liability to any person, organisation or other entity for any direct loss, consequential loss or damage, however
caused, that may be suffered as a result of the use of this publication or any associated workshop or software.
40
Industrial Flow Measurement
Contents
TABLE OF CONTENTS
1. BASIC PROPERTIES OF FLUIDS
Basic fluid properties
Non-Newtonian fluids
1.2.1. The ideal plastic
1.2.2. Pseudoplastic
1.2.3. Dilatant
1.3. Velocity profiles
1.3.1. Ideal profile
1.3.2. Laminar flow
1.3.3. Turbulent flow
1.4. Reynolds number
1.5. Disturbed flow profiles
1.6. Flow measurement
1.6.1. Volumetric flow rate
1.6.2. Velocity
1.6.3. Point velocity
1.6.4. Mean flow velocity
1.7. Mass flow rate
1.8. Flow range and rangeability
1.8.1. Flow range
1.8.2. Turndown ratio
1.8.3. Span
1.8.4. Rangeability
1.8.5. Accuracy
1.9. Pipe sizes
43
45
47
48
48
48
48
48
49
49
51
52
53
53
53
53
53
55
55
55
56
56
56
56
58
2.
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
2.7.
2.8.
2.9.
POSITIVE DISPLACEMENT METERS
Introduction
Sliding vane
Oval gear meters
Lobed impeller
Oscillating piston
Nutating disc
Fluted rotor meters
Wet-type gas meters
General summary
59
61
61
62
64
65
66
67
69
70
3.
3.1
3.2
INFERENTIAL METERS
Introduction
Turbine meters
71
73
73
1.1.
1.2.
41
Industrial Flow Measurement
Contents
3.2.1 K-factor
3.2.2 Selection and sizing
3.2.3 Application limitations
3.2.4 Advantages
3.2.5 Disadvantages
3.3 Woltman meters
3.4 Propeller-type flow meters
3.5 Impeller meters
3.5.1 Application limitations
3.6 Installation recommendations
74
75
75
76
76
77
78
78
80
81
4 OSCILLATORY FLOW METERS
4.1
Introduction
4.2
Vortex flow meters
4.2.1 Formation of vortices
4.2.2 Strouhal factor
4.2.3 Shedder designs
4.2.3.1 Cylindrical
4.2.3.2 Rectangular bodies
4.2.3.3 Rectangular two-part bodies
4.2.3.4 Delta-shaped bodies
4.2.3.5 Delta-shaped two-part bodies
4.2.3.6 T-shaped bar
4.2.4 Sensors
4.2.4.1 Thermal sensing
4.2.4.2 Mechanical sensor
4.2.4.3 Capacitive sensor
4.2.4.4 Piezoelectric sensor
4.2.4.5 Strain-gauge sensor
4.2.4.6 Ultrasonic sensing
4.2.5 Application guidelines
4.2.5.1 Viscosity
4.2.5.2 Low flow
4.2.5.3 Batching operations
4.2.5.4 Measuring range
4.2.5.5 Process noise
4.2.5.6 Accuracy
4.2.5.7 Effects of erosion
4.2.5.8 Low density gases
4.2.5.9 Orientation
83
85
85
86
86
87
88
88
88
89
89
89
89
90
91
91
92
92
93
94
94
94
94
95
95
96
96
96
97
42
Industrial Flow Measurement
Contents
4.2.5.10 Pressure drop
4.2.5.11 Multi-phase flow
4.2.5.12 Material build-up
4.2.5.13 Piping effects
4.2.5.14 Mass measurement
4.2.5.15 Avoiding problems
4.3
Vortex precession
4.4
Fluidic flow meters
97
97
97
97
98
99
100
101
5 DIFFERENTIAL PRESSURE METERS
5.1
Introduction
5.2
Basic theory
5.2.1 Equation of continuity
5.2.2 Bernoulli’s equation
5.2.3 Gas flow
5.3
Orifice plate
5.3.1 Orifice plate configurations
5.3.2 Tapping points
5.3.3 Orifice plate sizing
5.3.4 Orifice plates – general
5.3.4.1 Advantages
5.3.4.2 Disadvantages
5.3.4.2.1 Straight pipe run requirements
5.3.4.2.2 Multiple leakage points
5.3.4.2.3 Orifice plate thickness
5.4 Conditioning orifice plate
5.5 Segmental wedge meter
5.6 V-cone meter
5.7 Venturi tube meter
5.8 Venturi nozzle meters
5.9 Flow nozzle meters
5.10 The Dall tube
5.11 Target meter
5.12 Pitot tube
5.13 Point averaging meter
5.14 Elbow meter
5.15 Trouble shooting
5.16 Variable area meters
5.16.1 Operating principle
5.16.2 Floats
5.16.3 Float centring methods
5.16.4 Float shapes
103
105
105
105
106
110
111
113
113
116
116
116
117
117
119
119
120
121
122
123
124
125
125
126
127
129
130
131
132
132
133
133
135
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Industrial Flow Measurement
Contents
5.16.5 Metering tube
5.16.6 Conclusion
5.17 Differential pressure transmitters
5.17.1 Multivariable transmitters
5.17.2 Special transmitters
136
137
138
139
140
5 ELECTROMAGNETIC FLOW METERS
6.1.
Introduction
6.2.
Measuring principle
6.3.
Construction
6.4.
Electrodes
6.5.
Conductivity
6.6.
Capacitive coupled electrodes
6.7.
Field characterisation
6.8.
Measurement in partially filled pipes
6.9.
Empty pipe detection
6.10. Field excitation
6.11. The pulsed d.c. field
6.12. Bipolar pulse operation
6.13. Meter sizing
6.14. Conclusion
141
143
143
144
146
148
150
151
152
156
157
158
159
161
162
7.
ULTRASONIC FLOW METERS
7.1
Introduction
7.2
Doppler method
7.3
Transit time meter
7.4
Flow profile
7.5
Frequency difference
7.6 Clamp-on instruments
7.7
Velocity of sound measurement
7.7.1 Factors influencing the velocity of sound
7.8
Beam scattering
7.9
Summary
7.9.1 Advantages
7.9.2 Disadvantages
7.9.3 Application limitations
163
165
165
167
170
172
174
175
176
176
177
177
177
177
44
Industrial Flow Measurement
Contents
8.
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
MASS FLOW MEASUREMENT
Introduction
The Coriolis force
A practical system
Multiple phase flow
Density measurement
Loop arrangements
Straight through tube
Summary of Coriolis mass measurement
8.8.1 Advantages
8.8.2 Drawbacks
8.9
Thermal mass flow meters
8.9.1 Heat loss method
8.9.2 Temperature rise method
8.9.3 External temperature rise method
8.9.4 Capillary-tube method
8.9.5 Liquid mass flow
181
183
183
186
188
188
189
190
192
192
192
193
193
196
197
197
199
9.
OPEN CHANNEL FLOW MEASUREMENT
9.1.
Introduction
9.2.
The weir
9.2.1. Rectangular weir
9.2.2. Trapezoidal weir
9.2.3. Triangular V-notch
9.2.4. Application limitations
9.3.
The flume
9.3.1. Flume flow considerations
9.3.2. Venturi flume
9.3.3. Parshall venturi flume
9.3.4. Palmer Bowlus
9.3.5. Khafagi flume
9.4.
Level measurement
9.4.1. Float measurement
9.4.2. Capacitive
9.4.3. Hydrostatic
9.4.4. Bubble injection
9.4.5. Ultrasonic
9.5. Linearization
9.5.1. Non-linear scale
9.5.2. Mechanical cam
9.5.3. Software
201
203
203
204
205
205
206
207
207
207
208
209
210
210
210
211
211
212
213
213
213
213
214
45
Industrial Flow Measurement
Contents
10. COMMON INSTALLATION PRACTICES
10.1. Introduction
10.2. Environmental influences
10.2.1. Fluid temperature
10.2.2. Pressure pulsations
10.2.3. Vibration
10.3. Flow conditioning
10.4. General installation requirements
10.5. Torquing
10.6. Grounding and Earthing
215
217
217
217
217
218
218
219
221
222
11. SELECTION CHARTS
12. MEASUREMENT OF STEAM
13. STANDARDS ORGANISATIONS
227
231
235
46
Industrial Flow Measurement
Contents
Bibliography
[1]. W Hogrefe, U. Kirchhof, E. Mannherz, W. Marchewka, U. Mecke, F. Otto, K.H.
Rakebrandt, A. Thöne, H.J. Wegener, 'Guide to Flowmeasurements', Bailey-Fischer &
Porter.
[2]. J.G. Olin, 'An Engineering Tutorial: Thermal mass flowmeters', Sierra Instruments,
INTECH, August 1993
[3]. W S. Buzzard, 'Comparison of Flowmeter Accuracy Statements', Fischer & Porter.
[4]. L.K. Spink, 'Principles and Practice of Flow Meter Engineering', The Foxboro Company.
[5]. C.F. Cusick, 'Flow Meter Engineering Handbook', Honeywell Automation.
[6]. R. W. Miller, 'Flow Measurement Engineering Handbook', McGraw-Hill.
[7]. D. M. Considine, 'Process instruments and Control Handbook' McGraw-Hill.
[8]. 'Fundamentals of Flowmetering', Rosemount Inc.
[9]. J. Grimson, 'Mechanics and Thermodynamics of Fluids', McGraw-Hill
[10]. R. A. Furness, 'Fluid Flow Measurement', Longman in association with The Institute of
Measurement and Control, UK.
[11]. U. Endress, H. Häfelfinger, P Hafner, A. Jäggi, G. Kempf, M. Lang, A. Schinke, K.H.
Schulz, R. Silberman, K. Steiner, H. Thommen, P Tschabold, P. Wetzer, E. Zeller, 'Flow
handbook', Flowtec, Endress+ Hauser.
[12]. D.M. Grant and B. D. Dawson, 'Isco Open Channel Flow Measurement Handbook', Isco
Inc.
[13]. Dr J. Leitner,'Flow',1980 Winter School, University of Pretoria and SAIMC. 2.
[14]. 'Sewage treatment plants ⎯ measuring and control', Flowtec, Endress + Hauser.
[15]. L.K. Spink, 'Fundamental principles of orifice plates', The Foxboro Co.
[16]. B. Marks, 'The evolution of the magnetic flowmeter', Paper presented to SAIMC,
October 1976, Datatrol.
I17]. S. Elonka, A. R. Parsons, 'Standard Instrumentation Questions and Answers for
ProductionProcess Control. Vol I ', McGraw-Hill.
[18]. D. C. Giancoli, 'Physics, Principles with Applications', PrenticeHall Intemational, Inc.
[19]. J.P Bentley, 'Principles of measurement systems', 3rd Edition, Longman, 1995 Doebelin
O.E.,
[20]. 'Measurement systems, application and design', 4th Edition, McGraw Hill, 1990
[21]. T. Hausman, ‘Understanding Non-magnetic Impeller Flow Sensors’, Great Lake
Instruments Inc., Plant Engineering, February 1992.
[22]. A. Boersma, J. van Grootveld ‘Vortex flowmetering’, Fisher Rosemount, August 1999.
[23]. ‘Vortex shedding flowmeters’ Krohne, 1998.
[24]. D.J. Lomas ‘Vortex flowmetering challenges the accepted techniques’, Kent
Instruments, Control and Instrumentation, August 1975.
[25]. T.Cousins, S.A. Foster, P>A> Johnson, ‘A linear and Accurate Flowmeter using Vortex
Shedding’, Kent Instruments.
[26]. J. Gitelson, ‘Magnetic flowmeters without electrodes’, Electricity + Control, April 1999.
[27]. G. Weber, ‘An argument for calorimetric flow sensors’, Weber Sensortechnich GmbH,
Sensors, April 1989.
[28]. G. Weber, W.S. Krause, ‘The Calorimetric measuring principle on the test bed’, Weber
Sensors Group, Electricity + Control, April 1999.
[29]. V.C. Aird, F.P. Venter, ‘Open channel flow measuring devices’, Neuplast (Pty) Ltd.
[30]. A.S. Pogonowski, ‘On-line ultrasonic flowmetering’, Danfoss Industries.
[31]. J. Baumoel, ‘Performance of clamp-on ultrasonic flowmeter pipeline leak detection
systems’, Controlotron Corporation, API Pipeline Conference, 1994.
47
Industrial Flow Measurement
Contents
Foreword
This handbook is presented in a form suitable for two distinct classes of reader: the beginner,
with no prior knowledge of the subject; and the more advanced technician.
The complete text is suitable for the advanced reader. However, those parts of the text, which
involve a mathematical treatment which are not required by the beginner, are indicated by a
mark (X) at the beginning and (W) at the end. Consequently, for the beginner the text may be
read, with full understanding, by ignoring the marked sections.
In this manner two complete books are available at two different levels for two distinct classes
of reader.
48
Industrial Flow Measurement
Basic Properties of Fluids
Chapter 1. Basic properties of fluids
Industrial Flow
Measurement
49
Industrial Flow Measurement
Basic Properties of Fluids
50
Industrial Flow Measurement
Basic Properties of Fluids
Chapter 1
Basic properties of fluids
1.1
Basic fluid properties
One of the most important primary properties of a fluid (liquid or gas) is its viscosity — its
resistance to flow or to objects passing through it. Conceptually, viscosity might be thought of
as the ‘thickness’ of a fluid. In essence it is an internal frictional force between the different
layers of the fluid as they move past one another. In a liquid, this is due to the cohesive
forces between the molecules whilst in a gas it arises from collisions between the molecules.
Different fluids possess different viscosities: treacle is more viscous than water and gearbox
oil (SAE 90) is more viscous than light machine oil (for example 3-in-1). A comparison of
various fluids is shown in Table 1.1.
Table 1.1. Comparison of the viscosities of various fluids.
Fluid
Temperature
(°C)
Molasses
20
Glycerine
20
Engine oil (SAE 10) 30
Milk
20
Blood
37
Water
0
Ethyl alcohol
20
Water
20
Water
100
Air
20
Water vapour
100
Hydrogen
0
Viscosity μ
(Pa.s)
100
1.5
0.2
5 x 10 -3
4 x 10 -3
1.8 x 10 -3
1.2 x 10 -3
1 x 10 -3
0.3 x 10 -3
0.018 x 10 -3
0.013 x 10 -3
0.009 x 10 -3
If the fluid is regarded as a collection of moving plates, one on top of the other, then when a
force is applied to the fluid, shearing occurs and the viscosity is a measure of the resistance
offered by a layer between adjacent plates.
Figure 1.1 shows a thin layer of fluid sandwiched between two flat metal plates of area A —
the lower plate being stationary and the upper plate moving with velocity v. The fluid directly
in contact with each plate is held to the surface by the adhesive force between the molecules
of the fluid and those of the plate. Thus the upper surface of the fluid moves at the same speed
v as the upper plate whilst the fluid in contact with the stationary plate remains stationary.
Since the stationary layer of fluid retards the flow of the layer just above it and this layer, in
turn, retards the flow of the next layer, the velocity varies linearly from zero to V, as shown.
51
Industrial Flow Measurement
Basic Properties of Fluids
Moving plate
Velocity gradient
Stationary plate
X
Figure 1.1. When a thin layer of fluid is sandwiched between two flat metal
plates, shearing occurs and the upper surface of the fluid moves at the same
speed as the upper plate whilst the fluid in contact with the stationary plate
remains stationary.
The relative force acting on the layers is called the shear stress (the force per unit area).
In Figure 1.1, the fluid flows under the action of the shear stress due to the motion of the
upper plate. It is also clear that the lower plate exerts an equal and opposite shear stress to
satisfy a ‘no-slip’ condition at the lower stationary surface.
It follows, therefore, that at any point in the flow, the velocity at which the layers move
relative to each other, referred to as the shear rate, is directly proportional to the shear stress :
Shear rate ∝ Shear stress
Shear stress = μ. Shear rate
or:
where μ is the viscosity ⎯ the ratio of shear stress and shear rate.
These days, viscosity is expressed as absolute or dynamic viscosity measured in PascalSeconds (Pa.s).
Formerly, viscosity was expressed as relative viscosity – the ratio of the liquid’s absolute
viscosity with respect to the viscosity of water. Here, the unit of measurement was the
centipoise (cP) or, in the case of gases, micropoise (μP) where:
Viscosity
1 Pa.s = 1000 cP
As shown in Figure 1.2, the viscosity of a
fluid depends strongly on temperature and
generally decreases when the temperature
increases. Gases, however, show the
opposite behaviour and the viscosity
increases for increasing temperature.
Oil
Wate
r
Gas
Figure 1.2. The viscosity of fluids is
strongly dependent on temperature.
Temperature
52
Industrial Flow Measurement
Basic Properties of Fluids
Subsequently, Table 1.1 lists the viscosity of various fluids at specified temperatures – with
the viscosity of liquids such as motor oil, for example, decreasing rapidly as temperature
increases.
The viscosity of a fluid also depends on pressure but, surprisingly, pressure has less effect on
the viscosity of gases than on liquids.
A pressure increase from 0 to 70 bar (in air) results in only an approximate 5% increase in
viscosity. However, with methanol, for example, a 0 to 15 bar increase results in a 10-fold
increase in viscosity. Some liquids are more sensitive to changes in pressure than others.
Viscosity related to the density of a fluid is termed the kinematic viscosity. Kinematic
viscosity is given by:
v = μ/ρ
where:
v
=
kinematic viscosity measured in m2/s;
μ
=
dynamic viscosity measured in Pa.s; and
ρ
=
density of the liquid (kg/m3).
Kinematic viscosity was formerly measured in centistokes (cSt) where:
1 m2/s = 106 cSt
1.2
Non-Newtonian fluids
Shear stress
Most fluids used in engineering systems exhibit Newtonian behaviour in that, for a given
value of pressure and temperature, the shear stress is directly proportional to the shear rate.
Thus, if the shear stress is plotted against shear rate the result is a straight line passing
through the origin (Figure 1.3).
t ic
n
ia
as
l
n
p
to
al
w
e
e
Id
N
stic
dopla
u
e
s
P
t
an
li at
D
Yield
point
Shear rate
53
Figure 1.3. The shear stress
plotted against shear rate for a
number of materials.
For
Newtonian materials the shear
stress plotted against shear
rate results in a straight line
passing through the origin.
Industrial Flow Measurement
Basic Properties of Fluids
Certain fluids, however, do not exhibit this behaviour. Examples include: tar, grease,
printers’ ink, colloidal suspensions, hydrocarbon compounds with long-chain molecules, and
polymer solutions. In addition, some fluids, called viscoelastic fluids, do not immediately
return to a condition of zero shear rate when stress is removed.
1.2.1 The ideal plastic
The so-called Ideal plastics or Bingham fluids exhibit a linear relationship between shear
stress and shear rate. However, such substances only flow after a definite yield point has
been exceeded (Figure 1.3).
When at rest, these materials possess sufficient rigidity to resist shear stresses smaller than the
yield stress. Once exceeded, however, this rigidity is overcome and the material flows in
much the same manner as a Newtonian fluid.
Examples of materials exhibiting this type of behaviour include: tar; chewing gum; grease;
slurries; sewage slugs; and drilling muds.
1.2.2 Pseudoplastic
A pseudoplastic substance, such as printer’s ink, is characterised by polymers and
hydrocarbons which possess long-chain molecules and suspensions of asymmetric particles.
Although exhibiting a zero yield stress, the relationship between shear stress and shear rate is
non-linear and the viscosity decreases as the shear stress increases.
1.2.3 Dilatant
Dilatant materials also exhibit a non-linear relationship between shear stress and shear rate
and a zero yield stress. However, in this case, the viscosity increases as the shear stress
increases.
This type of behaviour is found in highly concentrated suspensions of solid particles. At low
rates of shear, the liquid lubricates the relative motion of adjacent particles, thereby
maintaining relatively low stress levels. As the shear rate increases, the effectiveness of this
lubrication is reduced and the shear stresses are increased. W
1.3
Velocity profiles
One of the most important fluid characteristics affecting flow measurement is the shape of the
velocity profile in the direction of flow.
1.3.1 Ideal profile
In a frictionless pipe in which there is no retardation at the pipe walls, a flat ‘ideal’ velocity
profile would result (Figure 1.4) in which all the fluid particles move at the same velocity.
54
Industrial Flow Measurement
Basic Properties of Fluids
Figure 1.4. A flat ‘ideal’ velocity
profile.
1.3.2
Laminar flow
We have already seen, however, that real fluids do not ‘slip’ at a solid boundary but are held
to the surface by the adhesive force between the fluid molecules and those of the pipe.
Consequently, at the fluid/pipe boundary, there is no relative motion between the fluid and the
solid.
At low flow rates the fluid particles move in straight lines in a laminar manner — with each
fluid layer flowing smoothly past adjacent layers with no mixing between the fluid particles
in the various layers. As a result the flow velocity increases from zero, at the pipe walls, to a
maximum value at the centre of the pipe and a velocity gradient exists across the pipe.
The shape of a fully developed velocity profile for such a laminar flow is parabolic, as shown
in Figure 1.5, with the velocity at the centre equal to twice the mean flow velocity. Clearly, if
not corrected for, this concentration of velocity at the centre of the pipe can compromise the
flow computation.
Figure 1.5. A laminar ‘parabolic’ velocity profile.
1.3.3 Turbulent flow
One of the earliest investigators into fluid flow was Osborne Reynolds (1842-1912) who
conducted a number of experiments using what is now termed a Reynolds instrument – a
device that injects ink into the flow stream (Figure 1.6).
Ink
Figure 1.6. Reynolds’s
instrument injects ink
into the flow stream in
order to observe the flow
regime (Courtesy
Emerson).
Fluid
55
Industrial Flow Measurement
Basic Properties of Fluids
For a given pipe and liquid, as the flow rate increases, the laminar path of an individual
particle of fluid is disturbed and is no longer straight. This is called the transitional stage
(Figure 1.7).
As the velocity increases further the individual paths start to intertwine and cross each other
in a disorderly manner so that thorough mixing of the fluid takes place. This is termed
turbulent flow.
Laminar flow
Transitional flow
Figure 1.7. Transition from laminar through to
turbulent flow.
Turbulent flow
Since the flow velocity is almost constant in all of the pipe cross section, the velocity profile
for turbulent flow is flatter than for laminar flow and thus closer approximates the 'ideal' or
'one dimensional' flow (Figure 1.8).
Figure 1.8. A turbulent velocity profile.
56
Industrial Flow Measurement
1.4
X
Basic Properties of Fluids
Reynolds number
The onset of turbulence is often abrupt and to be able to predict the type of flow present
in a pipe, for any application, use is made of the Reynolds number, Re — a dimensionless
number given by:
Re =
ρ ⋅v⋅d
μ
where:
ρ = density of fluid (kg/m3)
μ = viscosity of fluid (Pa.s)
v = mean flow velocity (m/s)
d = diameter of pipe (m).
Irrespective of the pipe diameter, type of fluid, or velocity, Reynolds showed that the flow is:
Laminar:
Re < 2000
Transitional:
Re = 2000 - 4000
Turbulent:
Re > 4000
From the foregoing it is seen that, in addition to viscosity, Re also depends on density.
Since most liquids are pretty well incompressible, the density varies only slightly with
temperature. However, for gases, the density depends strongly on the temperature and
pressure in which (for ideal gas):
PV
where:
P
V
T
m
R
Since:
ρ
=
mRT
=
=
=
=
=
pressure (Pa);
volume of the gas (m3);
temperature (K)
number of moles; and
universal gas constant (8,315 J/(mol.K))
=
m/V
=
P/RT
Most gases may be considered ideal at room temperatures and low pressures. Both, laminar
and turbulent flow profiles require time and space to develop. At an entrance to a pipe, the
profile may be very flat – even at low Re. And it may stay laminar, for a short time, even at
high Re.W
57
Industrial Flow Measurement
1.5
Basic Properties of Fluids
Disturbed flow profiles
Obstructions in a pipe, such as bends, elbows, reducers, expanders, strainers, control valves,
and T-pieces, can all affect the flow profile in a manner that can severely affect measurement
accuracy.
Such disturbed flow, which should not be confused with turbulent flow, gives rise to a
number of effects that include:
Swirl ⎯ fluid rotation about the pipe axis.
Vortices ⎯ areas of swirling motion with high local velocity which are often caused by
separation or a sudden enlargement in pipe area.
Asymmetrical profile ⎯ see Figure 1.9
Symmetrical profile with high core velocity ⎯ caused by a sudden reduction in pipe area.
Figure 1.9. Asymmetric flow profile due to disturbed flow.
Fl
ow
Ultimately the flow profile will be restored by the natural mixing action of the fluid particles
as the fluid moves through the pipe. However, the effect of such disturbances can have an
important bearing on accuracy for as much as 40 pipe diameters upstream of the measuring
device. Figure 1.10 shows the ongoing disturbance in a pipe following a simple elbow.
Figure 1.10. Ongoing disturbance in a pipe following a simple elbow.
58
Industrial Flow Measurement
1.6
Basic Properties of Fluids
Flow measurement
In flow measurement a number of parameters can be used to describe the rate at which a fluid
is flowing:
1.6.1
Volumetric flow rate
The volumetric flow rate, Q, represents the total volume of fluid flowing through a pipe per
unit of time and is usually expressed in litres per second (l/s) or cubic metres per hour (m3/h).
The measurement of volumetric flow rate is most frequently achieved by measuring the mean
velocity of a fluid as it travels through a pipe of known cross sectional area A (Figure 1.11).
Q = v• A
Thus:
Flow
Unit of Time
Area
Figure 1.11. The volumetric flow rate, Q, represents the total
volume of fluid flowing through a pipe per unit of time.
1.6.2
Velocity
The term velocity is often used very loosely to describe the speed at which the fluid passes a
point along the pipe. In reality, most modern flowmeters measure either the point velocity or
the mean velocity.
1.6.3
Point velocity
The point velocity is the flow velocity in a localised region or point, in the fluid and is,
generally of little use in practice. It is used mainly in research to determine, for example,
velocity profiles or flow patterns.
1.6.4
Mean flow velocity
X The mean flow velocity, v , can be obtained by measuring the volumetric flowrate, Q,
and dividing it by the cross-sectional area of the pipe, A:
v=
Q
A
Alternatively, if the velocity profile is known the mean flow velocity can be obtained by
averaging the velocity over the velocity profile, giving equal weight to equal annular regions.
An example of the calculation of the mean velocity of the flow conduit by area-weighting
point-velocity measurements is illustrated in Figure 1.12. As shown, a number of velocity
bands are scaled across the cross-sectional area of a 320 mm diameter conduit.
59
Industrial Flow Measurement
Basic Properties of Fluids
76 cm/s
107 cm/s
120 cm/s
130 cm/s
Radius
160 120 80
(mm)
40
A
B
C
D
Figure 1.12. Example of area weighted technique
for determining the mean velocity of a fluid.
The mean velocity can be determined using standard averaging techniques in which the
velocities of each band are summed and then divided by the number of bands:
VAV =
VA + VB + VC + VD
= 108.25
4
In the area-weighted technique, the scaled areas, velocities and products of each area, times
its local velocity, are tabulated for each velocity band (Table 1.2). The area-weighted mean
velocity is calculated by summing the velocity-area products, and dividing the sum of the
cross-sectional area of the flow conduit.
Table 1.2. Calculations for determination of area-weighted mean velocity
Band
Radius
(cm)
4.0
8.0
12.0
16.0
A
B
C
D
Total
V=
(Vn ⋅ An )
Total area
Velocity
(cm/s)
130
120
107
76
Area
(cm2)
50.26
150.80
251.33
351.86
804.25
= 97.31cm / s
The error thus obtained using the standard averaging technique is:
W
Error =
(V
AV
−V
V AV
) =10.11%
60
Vn . An
6533
18096
26892
26741
78262
Industrial Flow Measurement
1.7
Basic Properties of Fluids
Mass flow rate
Most chemical reactions are largely based on their mass relationship and, consequently, in
order to control the process more accurately, it is often desirable to measure the mass flow of
the product. The mass flow rate, W, gives the total mass of fluid flowing at any instant in
time. A knowledge of volume flow rate, Q and the fluid density, ρ, determines the mass flow
rate from:
W = Q. ρ (kg/s)
Some flowmeters, such as Coriolis meters, measure the mass flow directly. However, in
many cases, mass flow is determined by measuring the volumetric flow and the density and
then calculating the mass flow as shown above. Sometimes the density is inferred from the
measurement of the pressure and temperature of the fluid. This type of measurement is
referred to as the inferred method of measuring mass flow.
1.8
Flow range and rangeability
Whilst there is considerable confusion regarding basis terminology used in the field of
instrumentation in general, nowhere is this more evident than in the differences between the
terms flow range, turndown ratio, span, and rangeability. Whilst the following terms are
those prescribed by the ISA they are by no means adhered to either by different organisations
and manufacturers.
1.8.1
Flow range
The flow range is simply the difference between the maximum and minimum flow rate over
which a meter produces acceptable performance within the basic accuracy specification of the
meter. This is illustrated in Figure 1.13.
Minimum
Maximum
Flow rate
Flow range
Figure 1.13. The flow range is the difference between the maximum
and minimum flow rate over which a meter produces acceptable
performance within the basic accuracy specification of the meter.
For flowmeters that exhibit a minimum flowrate, the flow range is thus the interval from the
minimum flow rate to the maximum flowrate. If the meter does not exhibit a minimum flow
rate, the flow range is the interval from zero flow to maximum flow.
61
Industrial Flow Measurement
Basic Properties of Fluids
1.8.2
Turn-down ratio
The turn-down ratio is the ratio of the maximum flow rate to the minimum flow rate for a
measuring range that is within a stated accuracy. For example, the measuring range of a
magnetic flow meter might be 0.3 m/s to 12 m/s within an accuracy of 0.3%. This would thus
be stated as having a 40:1 turndown ratio (0.3 %). In addition the measuring range might
extend from 0.2 m/s to 12 m/s within an accuracy of 0.5%. In this case the turndown ratio is
60:1 (0.5%). It is, therefore, meaningless to express the turndown ration without a specified
accuracy.
1.8.3
Span
The term span relates to the flowmeter output signals and is the difference between the upper
and lower range values assigned to the output signal.
For example, for a Coriolis meter having a 4-20 mA analog output the upper and lower range
values might be assigned as:
Lower range value:
4 mA = 0 kg/h
Upper range value:
20 mA = 5000 kg/h
The span is thus the difference between the two values, i.e. 5000 - 0 = 5000 kg/h. The
minimum span is the lowest flowrate able to produce full-scale output and the maximum span
is equal to the maximum range of the sensor.
1.8.4
Rangeability
Rangeability is a measure of how much the flow range of an instrument can be adjusted and is
defined as the ratio of the maximum flow range (maximum span) and the minimum span.
The term rangeability is often confused with turndown ratio and users should be careful as to
what is actually meant when the terms are uses.
1.8.5
Accuracy
The accuracy of a flowmeter is the maximum deviation between the meter's indication and the
true value of the flow rate or of the total flow. Accuracy, also referred to as uncertainty, is the
interval within which the true value of the measured quantity can be expected to lie within a
stated probability (generally taken to be 95 % unless otherwise specified). Accuracy includes
the combined errors due to linearity, hysterisis and repeatability and can be expressed in any
one of three ways: as a percentage of span; as a percentage of a rate; or as a percentage of the
upper range value.
To illustrate this difference, consider three flowmeters: one with an accuracy of ±1 % of span;
one with an accuracy of ± 1 % of a reading; and one with an accuracy of ±1 % of URL
(Upper Range Limit). The URL is defined as the highest flowrate that a meter can be
adjusted to measure whilst the Upper Range Value (URV) is defined as the highest flowrate
that the meter is adjusted to measure. Each meter has a URL of 100 l/min, and is calibrated 0
to 50 l/min.
62
Industrial Flow Measurement
Basic Properties of Fluids
For the percentage of span instrument, the absolute error is determined at the 100 % span
reading, and then used to determine the accuracy at lower flow rates. Since the span is 50
l/min the absolute error would be ±1 % of 50, or ±0.5 l/min. The accuracy of the meter at 50
l/min would be 50 l/min ±0.5 l/min, or ±1 %. And at 25 l/min the accuracy at would be 25
l/min ±0.5 l/min, or ±2 % (Figure 1.14).
Accuracy = 1% of span
URL
100
l /min
Absolute error = 1% of 50 l /min = ±0.5 l /min
100% of
span
50 l /min ±0.5 l /min = 1%
Figure 1.14. In the percentage of
span instrument, the absolute
error is determined at the 100 %
span reading, and then used to
determine the accuracy at lower
flow rates.
25 l /min ±0.5 l /min = 2%
Span
For the percentage of reading instrument, the absolute error is determined at the actual
reading, and varies with flow rate. The absolute error at 50 l/min is ±1 % of 50, or ±0.5
l/min. The absolute error at 25 l/min is ±1 % of 25, or ±0.25 l/min. This means the meter
has a constant accuracy of ±1 % at all readings (Figure 1.15).
Accuracy = 1% of reading
URL
100% of
span
Span
100
l /min
Absolute error = 1% of 50 l /min = ±0.5 l /min
Absolute error = 1% of 25 l /min = ±0.25 l /min
Figure 1.15. In the
percentage
of
reading instrument,
the absolute error is
determined at the
actual reading, and
varies with flow rate.
For the percentage of URL instrument, the absolute error is determined at the URL and then
used to determine the accuracy at lower flow rates. The absolute error would be ±1 % of 100,
or ± 1 l/min. The accuracy of the meter at 50 l/min would be 50 l/min ±1 l/min, or ±2 %.
The accuracy at 25 l/min would be 25 l/min at ±1 l/min, or ±4 % (Figure 1.16).
63
Industrial Flow Measurement
Basic Properties of Fluids
Accuracy = 1% of URL
URL
100% of
span
Span
Absolute error of 100 l /min = ±1 l /min = 1%
Absolute error of ±1 l /min at 50 l /min = 2%
Absolute error of ±1 l /min at 25 l /min = 4%
Figure 1.16. In the percentage
of URL instrument of, the
absolute error is determined at
the URL and then used to
determine the accuracy at lower
flow rates.
In the above example, or three meters would have the same accuracy, ±1 %, when calibrated
at the URL, 100 l/min. Percentage of range meters are generally preferred when operating
over a wide flowrate range.
1.9
Pipe sizes
Pipes are rated according to their size and pressure ratings.
The size, the normal pipe diameter, is given according to a preferred series – either in inches
(ANSI specification) or in mm (DN series) where DN = nominal diameter according to Table
1.3.
Table 1.3. Nominal pipe diameters.
Pipe diameter in
inches (ANSI)
Pipe diameter in
mm (DN)
Pipe diameter in
inches (ANSI)
Pipe diameter in
mm (DN)
0.5
0.75
1
1.5
2
3
4
6
15
20
25
40
50
80
100
150
8
10
12
14
16
24
36
48
200
250
300
350
400
600
900
1200
64
Industrial Flow Measurement
Positive Displacement Meters
Chapter 2. Positive displacement meters
Industrial Flow
Measurement
65
Industrial Flow Measurement
Positive Displacement Meters
66
Industrial Flow Measurement
Positive Displacement Meters
Chapter 2
Positive Displacement Meters
2.1
Introduction
Positive displacement meters (sometimes referred to as direct volumetric totalisers) all operate
on the general principle where defined volumes of the medium are separated from the flow
stream and moved from the inlet to the outlet in discrete packages.
Totalising the number of packages provides the total volume passed and the total volume
passed in a given time provides the flow rate, for example, litres/min.
Because they pass a known quantity, they are ideal for certain fluid batch, blending and
custody transfer applications. They give very accurate information and are generally used for
production and accounting purposes.
2.2
Sliding vane
Used extensively in the petroleum industry for gasoline and crude oil metering, the sliding
vane meter is one of the highest performance liquid positive displacement meters. In its
simplest form it comprises a rotor assembly fitted with four spring-loaded sliding vanes so
that they make constant contact with the cylinder wall (Figure 2.1). The rotor is mounted on a
shaft that is eccentric to the centre of the meter chamber.
Figure 2.1. Sliding vane positive
displacement meter comprising a
rotor assembly fitted with four
spring-loaded sliding vanes.
As liquid enters the measuring chamber the pressure on the exposed portion of vane 1 causes
the rotor to turn. While the rotor turns on its shaft, vane 2 moves to seal off the inlet port —
rotating to occupy the position formerly occupied by vane 1.
This process is repeated, without pulsations, as the vanes move around the measuring
chamber — with 'packets' of fluid trapped and passed to the outlet manifold as discrete known
quantities of fluid.
67
Industrial Flow Measurement
Positive Displacement Meters
A mechanical counter register or electronic pulse counter is attached to the shaft of the rotor
so that flow volume is directly proportional to shaft rotation.
Close tolerances and carefully machined profiles of the casing ensure the blades are guided
smoothly through the measuring crescent to give high performance.
Advantages of the sliding vane meter include:
¾
¾
¾
¾
¾
¾
¾
suitable for accurately measuring small volumes;
High accuracy of ± 0.2%;
high repeatability of ± 0.05%;
turndown ratio of 20:1;
suitable for high temperature service, up to 180°C;
pressures up to 7 Mpa; and
not affected by viscosity.
Disadvantages of the sliding vane meter include:
¾ suitable for clean liquids only;
¾ limitations due to leakage; and
¾ high unrecoverable pressure loss.
2.3
Oval gear meters
Oval gear flow meters comprise two identical precision moulded oval rotors which mesh
together by means of gear teeth around the gear perimeter. The rotors rotate on stationary
shafts which are fixed within the measuring chamber (Figure 2.2).
Figure 2.2. Construction of the oval gear
meter (courtesy Emerson).
The meshed gears seal the inlet from the outlet flow, developing a slight pressure differential
across the meter that results in movement of the oval rotors.
When in the position shown in Figure 2.3(a), Gear A receives torque from the pressure
difference while the net torque on Gear B is zero. (b) Gear A drives Gear B. (c) As Gear B
continues to rotate, it traps a defined quantity of fluid until, in this position, the net torque on
Gear A is zero and Gear B receives torque from the pressure difference. (d) Gear B drives
68
Industrial Flow Measurement
Positive Displacement Meters
Gear A and a defined quantity of fluid is passed to the outlet. This alternate driving action
provides a smooth rotation of almost constant torque without dead spots.
A
A
B
B
(b)
(a)
A
A
B
B
(c)
(d)
Figure 2.3. Principle of the oval gear meter: (a) Gear A receives torque from the pressure
difference while the net torque on Gear B is zero. (b) Gear A drives Gear B. (c) As Gear
B continues to rotate it traps a defined quantity of fluid until in this position, the net
torque on Gear A is zero and Gear B receives torque from the pressure difference. (d)
Gear B drives Gear A and a defined quantity of fluid is passed to the outlet.
With flow through the meter, the gears rotate and trap precise quantities of liquid in the
crescent shaped measuring chambers. The total quantity of flow for one rotation of the pair of
oval gears is four times that of the crescent shaped gap and the rate of flow is proportional to
the rotational speed of the gears.
Because the amount of slippage between the oval gears and the measuring chamber wall is
minimal, the meter is essentially unaffected by changes in viscosity and lubricity of the
liquids.
An output shaft is rotated in direct proportion to the oval gears by means of a powerful
magnetic coupling. Oval gear meters find widespread use in the measurement of solvents,
with close tolerances ensuring that leakage is minimised.
69
Industrial Flow Measurement
Positive Displacement Meters
The major disadvantage of this meter is that the alternate driving action is not constant and, as
a result, the meter introduces pulsations into the flow.
Further, the viscosity of the fluid can affect the leakage or slip flow. If the meter is calibrated
on a particular fluid, it will read marginally higher should the viscosity increase.
Newer designs of this type of meter use servomotors to drive the gears. These eliminate the
pressure drop across the meter and the force required to drive the gear. This appliesmainly to
smaller sized meters and significantly increases the accuracy at low flows.
Advantages of the oval gear meter include:
¾
¾
¾
¾
¾
¾
high accuracy of ± 0.25%;
high repeatability of ± 0,05%;
low pressure drop of less than 20 kPa;
high operating pressures, up to 10 MPa;
high temperatures, up to 300°C; and
wide range of materials of construction.
Disadvantages of the oval gear meter include:
¾ pulsations caused by alternate drive action; and
¾ accuracy dependent on viscosity.
2.4
Lobed impeller
Similar in operation to the Oval meter, the lobed impeller type meter (Figure 2.4) is a noncontact meter comprising two high precision lobed impellers which are geared externally and
which rotate in opposite directions within the enclosure. For each revolution four measured
‘cups’ of the fluid are transferred through the meter with an accuracy of up to 0,2% under
controlled conditions. The lobed impeller meter is suitable for a wide range of fluids ranging
from LPG through to tar in the ranges from 4 litres to 200 kilo-litres/hr, process temperatures
up to 300 °C, and pressures up to 10 MPa.
The main disadvantages include:
¾ Poor accuracy at low flow rates.
¾ Temperature of process medium limited to about 60°C
¾ Bulky and heavy.
¾ Expensive.
¾ Pulsations caused by alternate drive action
¾ Accuracy dependent on viscosity
70
Industrial Flow Measurement
Positive Displacement Meters
Figure 2.4. Lobed impeller meter (courtesy Tokico Ltd).
2.5
Oscillating piston
The oscillating or rotating piston meter consists of a stainless steel housing and a rotating
piston as shown in Figure 2.5. The only moving part in the measuring chamber is the
oscillation piston which moves in a circular motion.
Divider
plate
Inlet port
Outlet port
Circular
track
Slotted
piston
Figure 2.5. Basic layout of
oscillating or rotating piston
meter.
Eccentric
centre pin
To obtain an oscillating motion, movement of the piston is restricted in two ways. First, the
piston is slotted vertically to accommodate a partition plate which is fixed to the chamber.
This plate prevents the piston from spinning around its central axis and also acts as a seal
between the inlet and outlet ports of the chamber. Secondly, the piston has a centre vertical
pin which confines the piston's movement to a circular track which is part of the chamber.
Differential pressure across the meter causes the piston to sweep the chamber wall in the
direction of flow — displacing liquid from the inlet to the outlet port in a continuous stream.
The openings for filling and discharging are located in its base and thus in Figure 2.6 (a),
areas 1 and 3 are both receiving liquid from the inlet port (A) and area 2 is discharging
through the outlet port (B).
71
Industrial Flow Measurement
Area 1
Positive Displacement Meters
Area 2
Area 1
Area 2
Area 2
Area 1
Area 3
Area 3
Area 3
(a)
(b)
(c)
Figure 2.6. Oscillating or rotating piston meter showing principle of operation.
In Figure 2.6 (b), the piston has advanced and area 1, which is connected to the inlet port, has
enlarged; and area 2, which is connected to the outlet port, has decreased, while area 4, is
about to move into position to discharge through the outlet port.
In Figure 2.6(c), area 1 is still admitting liquid from the inlet port, while areas 2 and 3 are
discharging through the outlet port. In this manner known discrete quantities of the medium
have been swept from the inlet port to the outlet port.
The rotating piston meter is particularly suitable for accurately measuring small volumes and
its main advantages are:
¾ accuracy of ± 0.5%; and
¾ performance largely unaffected by viscosity (from heating oil to paste).
The main disadvantages of the oscillating piston meter are:
¾ leakage and maximum permissible pressure loss.
2.6
Nutating disc
The term nutation is derived from the action of a spinning top whose axis starts to wobble and
describe a circular path as the top slows down.
In a nutating disc type meter the displacement element is a disc that is pivoted in the centre of
a circular measuring chamber (Figure 2. 7). The lower face of the disc is always in contact
with the bottom of the chamber on one side, and the upper face of the disc is always in contact
with the top of the chamber on the opposite side. The chamber is therefore divided into
separate compartments of known volume.
72
Industrial Flow Measurement
Positive Displacement Meters
Figure
2.7.
Nutating disc meter
in
which
the
displacement
element is a disc
pivoted in the centre
of
a
circular
measuring
chamber.
Liquid enters through the inlet connection on one side of the meter and leaves through an
outlet on the other side — successively filling and emptying the compartments and moving
the disc in a nutating motion around a centre pivot. A pin attached to the disc's pivot point
drives the counter gear train.
Although there are inherently more leakage paths in this design, the nutating disk meter is
also characterised by its simplicity and low-cost.
It tends to be used where longer meter life, rather than high performance, is required, for
example, domestic water service. The meter is also suitable for use under high temperatures
and pressures.
2.7
Fluted rotor meters
The axial and radial fluted rotor meters work on the same principal.
The axial fluted rotor meter (Figure 2.8) makes use of two aluminium spiral fluted rotors
working within the same measuring chamber — with the rotors maintained in a properly
timed relationship with one another by helical gears.
The axial fluted rotor meter (Figure 2.8) makes use of two aluminium spiral fluted rotors
working within the same measuring chamber — with the rotors maintained in a properly
timed relationship with one another by helical gears.
Preamp
Pick off
Figure 2.8. Physical construction
of the axial radial fluted ‘Birotor’
meter courtesy Emerson).
Gear
chain
Rotors
73
Industrial Flow Measurement
Positive Displacement Meters
As the product enters the intake of the measuring unit chamber, (Figure 2.9) the two rotors
divide the volume being measured into segments; momentarily separating each segment from
the flowing inlet stream and then returning them to the outlet of the measuring unit chamber.
Liquid intake
Liquid transition
Liquid outlet
Figure 2.9. Operation of the axial radial fluted
‘Birotor’ meter (courtesy Emerson).
During this ‘liquid transition’, the segments of flow are counted and the results are transferred
to a totalising counter or other flow recording device by means of a gear train.
In the radial fluted rotor meter, Figure 2.10, two specially shaped hydraulically unbalanced
rotors are maintained in a properly timed relationship with one another by helical gears. The
rotors are neither in metal-to-metal contact with one another nor with the housing in which
they rotate. Again, as shown, as the product enters the intake of the measuring unit chamber
the two rotors divide the volume being measured into segments; momentarily separating each
segment from the flowing inlet stream and then returning them to the outlet of the measuring
unit chamber.
Liquid intake
Liquid transition
Liquid outlet
Figure 2.10. Operation of the radial fluted ‘Birotor’ meter (courtesy Emerson).
74
Industrial Flow Measurement
2.8
Positive Displacement Meters
Wet-type gas meters
The wet-type gas meter (Figure 2.11) comprises a gas-tight casing containing a measuring
drum, with four separate compartments, mounted on a spindle that is free to revolve. The
casing is filled to approximately 60% of its of volume with water or light oil.
Gas outlet
Gas discharging
Gas filling
Sight glass
Water
or oil
Gas inlet
Figure 2.11. The wet-type gas meter (courtesy Alexander Wright division of GH Zeal Ltd)
Under normal operation the gas passes through the measuring drum so that each compartment
of the drum must, in turn, be emptied of water and filled with gas ⎯ thus forcing the drum to
rotate. In an alternative arrangement the gas is introduced into the space above the water in
the outer casing and then passes through the drum to the outlet of the meter.
The calibration of the measuring drum (i.e. the quantity of gas passed for each revolution) is
determined by the height of the water in the casing. Consequently, the normal calibration
point is shown by a water-level indicating point that is visible in the sight box located on the
side of the meter casing.
The spindle on which the measuring drum is mounted is connected through gears to record
the quantity of gas passing through the meter.
Such meters are available in capacities ranging in size from 0.25 to 100 dm3 with an accuracy
down to ±0.25%.
75
Industrial Flow Measurement
2.9
Positive Displacement Meters
General Summary
Because of their high accuracy, positive displacement meters are used extensively in liquid
custody transfer applications where duty is applicable on such commodities as petrol, wines,
and spirits.
In use, some of the following application limitations should be noted:
¾ Owing to the mechanical contact between the component parts, wear and tear is a
problem. In general, therefore, positive displacement meters are primarily suited for clean,
lubricating and non-abrasive applications.
¾ In some cases, filters (down to 10 µm) may be required to filter debris and clean the fluid
before the meter. Such filters require regular maintenance. If regular maintenance is not
carried out, the added pressure drop may also need to be considered.
¾ Their working life also depends on the nature of the fluid being measured, especially in
regard to solids build-up and the media temperature.
¾ Positive displacement meters are an obstruction to the flow path and consequently
produce an unrecoverable pressure loss.
¾ Because many positive displacement meters have the same operating mechanisms as
pumps, they may be driven by a motor and used as dosing or metering pumps.
¾ One of the drawbacks of the positive displacement meter is its high differential pressure
loss. This, however may be reduced by measuring the differential pressure across the
meter and then driving it with a motor that is controlled by a feedback system.
¾ Positive displacement meters are limited at both high and low viscosities. Errors can
occur due to leakage (slippage) around the gears or pistons. Slippage may be reduced by
using viscous fluids which have the ability to seal the small clearances. However if the
fluid is too viscous then it can coat the inner chambers of the meter and reduce the volume
passed — causing reading errors. Thus, whilst low viscosities limit the use at low flows
(due to increased slippage), high viscosities limit the use at high flows due to the high
pressure loss.
¾ If slippage does occur, and is calibrated for, it can change with temperature as the
viscosity varies.
¾ Positive displacement meters can be damaged by over-speeding.
¾ In certain cases (e.g. the oval gear meter) positive displacement meters give rise to
pulsations. This may inhibit the use of this type of meter in certain applications.
¾ Positive displacement meters are primarily used for low volume applications and are
limited when high volume measurement is required.
76
Industrial Flow Measurement
Inferential Meters
Chapter 3. Inferential Meters
Industrial Flow
Measurement
77
Industrial Flow Measurement
Inferential Meters
78
Industrial Flow Measurement
Inferential Meters
Chapter 3
Inferential Meters
3.1
Introduction
Inferential meters, loosely referred to as ‘turbine meters’, are indirect volumetric totalisers, in
which packages of the flowing media are separated from the flow stream and moved from the
input to the output. However, unlike the positive displacement meter, the enclosed volume is
not geometrically defined.
Inferential meters have rotor-mounted blades in the form of a vaned rotor or turbine which is
driven by the medium at a speed proportional to the flowrate. The number of rotor
revolutions is proportional to the total flow and is monitored by either a gear train or by a
magnetic or optical pick-up.
Competing with the positive displacement meter for both accuracy and repeatability, the
turbine flowmeter is used extensively in custody transfer applications in the oil and gas
industries.
3.2
Turbine meter
Available in sizes from 5 to 600 mm, the turbine meter usually comprises an axially mounted
bladed rotor assembly (the turbine) running on bearings and mounted concentrically within
the flow stream by means of upstream and downstream support struts (Figure 3.1). The
support assembly also often incorporates upstream and downstream straightening sections to
condition the flow stream. The rotor is driven by the medium (gas or liquid) impinging on the
blades.
The simplest method of measuring the rotor speed is by means of a magnet, fitted within the
rotor assembly, that induces a single pulse per revolution in an externally mounted pick-up
coil. To improve the resolution, the externally mounted pick-up coil is integrated with a
permanent magnet and the rotor blades are made of a magnetically permeable ferrous
material. As each blade passes the pick-up coil, it cuts the magnetic field produced by the
magnet and induces a voltage pulse in the coil.
To improve the resolution even further, especially in large turbine meters (200 mm and
above) where the rotor operates at much lower angular velocities, small magnetic bars are
inserted in a non-magnetic rim that is fitted around the blades. This modification can improve
the pulse resolution by as much as ten times.
79
Industrial Flow Measurement
Thrust bearing
Inferential Meters
Pulse pick-up coil and
electrical connector
Figure 3.1. Turbine meter
consists of a bladed rotor
suspended in the flow stream.
Upper and lower straightening
vanes are normally included.
(Courtesy Rosemount).
Straightening and
support vanes
Turbine blades
3.2.1
K-factor
The number of pulses produced per unit volume is termed the K-factor.
Ideally, the meter would exhibit a linear relationship between the meter output and the flow
rate – a constant K-factor. In reality, however, the driving torque of the fluid on the rotor is
balanced by the influence of viscous, frictional and magnetic drag effects.
Since these vary with the flow rate, the shape of the K-factor curve (Figure 3.2) depends on
viscosity, flow rate, bearing design, blade edge sharpness, blade roughness and the nature of
the flow profile at the rotor leading edge. In practice, all these influences have differing
effects on the meter linearity and thus all turbine meters, even from the same manufacturing
batch, should be individually calibrated.
The linear relationship of the K-factor is confined to a flow range of about 10:1 – sometimes
extending up to 20:1.
At low flows, the poor response of the meter is due to bearing friction, the effect of fluid
viscosity and magnetic drag on the rotor due to the use of a magnetic pick-off. It is possible
to extend the lower limit of the meter’s response by using, for example, a radio pick-off
coupled with the use of high quality rotor bearings. The humping section of the curve
flattens as the viscosity decreases – with resultant increase in accuracy.
80
Industrial Flow Measurement
Inferential Meters
Meter K-factor (pulses/litre)
100
99
98.5%
+0.25%
-0.25%
98
Flattening of hump
with decrease in
viscosity
97
96
Minimum flow rate for ± 0.25 linearity
100
200
300
400
500
600
Flow rate Q (litres/min)
700
800
Figure 3.2. K-factor (the meter ‘constant’) should, ideally, be flat. The
actual plot exhibits a drop off at low flow rates and a viscosity hump.
At low flows, the poor response of the meter is due to bearing friction, the effect of fluid
viscosity and magnetic drag on the rotor due to the use of a magnetic pick-off. It is possible
to extend the lower limit of the meter’s response by using, for example, a radio pick-off
coupled with the use of high quality rotor bearings.
The humping section of the curve
flattens as the viscosity decreases – with resultant increase in accuracy.
3.2.2 Selection and Sizing
Although turbine meters are sized by volumetric flow rate, the main factor that affects the
meter is viscosity.
Typically, larger meters are less affected by viscosity than smaller meters. This may indicate
that larger meters would be preferred; in fact the opposite is true. By using a smaller meter,
operation is more likely to occur towards the maximum permitted flowrate, and away from
the non-linear ‘hump’ response at low flows.
Turbine meters are specified with minimum and maximum linear flow rates that ensure the
response is linear and the other specifications are met. For good rangeability, it is
recommended that the meter be sized such that the maximum flow rate of the application be
about 70 to 80% of that of the meter.
3.2.3
Application limitations
In liquids, the maximum flow rate is usually limited by the effect of cavitation that occurs
when the system pressure falls to a point at which the liquid itself and/or the dissolved gases
in the liquid ‘boil off’ at critical points in the meter where hydrodynamic forces cause a low
pressure region. Cavitation can be avoided by retaining a sufficiently high back pressure and
by keeping the pressure loss through the meter at a minimum.
81
Industrial Flow Measurement
Inferential Meters
Because the rotor, stator, measuring pipe and bearings all come in contact with the medium,
the meter’s resistance to aggressive fluids is dependent on the materials from which it is
constructed. Generally the measuring pipe, rotor and stator are fabricated from stainless steel,
whilst the bearings are made of ceramic materials such as aluminium oxide, or PTFE used in
conjunction with metal or other materials.
Density changes have little effect on the meters’ calibration.
Because turbine meters rely on the flow impinging on the rotor blades, they absorb some
pressure. As a result, the pressure drop is typically around 20 to 30 kPa at the maximum
flow rate and varies depending on the flow rate.
3.2.4
Advantages
Because the rotation of the turbine is measured by non-contact methods, no tapping points are
required in the pipe. The result is that, depending on pipe diameter and materials of
construction, pressures of up to 64 MPa can be applied.
When properly installed and maintained, turbine meters are capable of high accuracy (± 0.5 %
of flow) over a 10:1 range as well as excellent repeatability (± 0.05 %). Turbine meters also
exhibit a wide flow capacity range (from 4 litres/min – 800 klitres/min)
Temperature limitations are only imposed by the limitations of the materials of construction
and turbine flowmeters are capable of operation with very high process media temperatures
(up to 600 °C) as well as for use at very low temperatures (cryogenic fluids) down to -220 °C.
¾
¾
¾
¾
¾
¾
¾
¾
Suitable for pressures of up to 64 MPa.
High accuracy (up to ± 0.2 % of flow)
Excellent repeatability (± 0.05 %).
Wide rangeability up to 20:1
Wide range of temperature applications from -220 to 600 °C
Measurement of non-conductive liquids.
Capability of heating measuring device.
Suitable for very low flow rates.
3.2.5
Disadvantages
The main limitation of a turbine meter is that because it has a moving part (the rotor), it is
subject to wear. Consequently, it is unsuited to dirty fluids and requires regular maintenance
and calibration to maintain its accuracy. Another disadvantage is that because the K-factor is
dependent on the viscosity, the viscosity of the liquid must be known and each meter must be
calibrated for its application – especially at low flow rates.
Turbine meters are not suitable for use with high viscosity fluids since the high friction of the
fluid causes excessive losses – leading to excessive non-recoverable pressure losses.
82
Industrial Flow Measurement
¾
¾
¾
¾
¾
¾
¾
¾
¾
3.3
Inferential Meters
Not suitable for high viscous fluids.
Viscosity must be known.
10 diameter upstream and 5 diameters downstream of straight pipe is required.
Not effective with swirling fluids.
Only suitable for clean liquids and gases.
Pipe system must not vibrate.
Specifications critical for measuring range and viscosity.
Subject to erosion and damage.
Relatively expensive.
Woltman meter
The Woltman meter, used primarily as a water meter, is very similar in basic design to the
turbine meter. The essential difference is that the measurement of rotation is carried out
mechanically using a low friction gear train connecting the axle to the totalizer.
The Woltman meter is available in two basic designs – one with a horizontal turbine (Figure
3.3) and one with a vertical turbine (Figure 3.4). The vertical design offers the advantage of
minimal bearing friction and therefore a higher sensitivity resulting in a larger flow range.
Whilst the pressure drop of the vertical turbine meter is appreciably higher, because of the
shape of the flow passage, it is widely used as a domestic water consumption meter.
Figure 3.3. Horizontal turbine
Woltman meter.
Figure 3.4. Vertical turbine Woltman
meter.
In many designs, an adjustable regulating vane is used to control the amount of deflection and
thus adjust the meter linearity.
83
Industrial Flow Measurement
3.4
Inferential Meters
Propeller type
In the propeller type flowmeter (Figure 3.5) the body of the meter is positioned above the
flow path and only the propeller is in the flow line.
N
S
Figure 3.5. Propeller type
flowmeter with the meter
body positioned above the
flow path and only the
propeller in the flow line
(Courtesy Rhodes & Son).
With the bearings outside of the main flow, the effects of contamination flom dirty liquids are
eliminated or reduced to a minimum. The use of a three-bladed propeller with large
clearances between each blade, enables particles in suspension to pass with ease and, in
addition, the transmitter and all working parts can be removed and replaced in a few minutes,
without breaking the pipeline. Another advantage of this type of meter is that manufacturing
costs are significantly reduced.
On the negative side performance is correspondingly lower with the linearity typically ±2%
and repeatability typically ±1% of full scale.
3.5
Impeller meters
As opposed to the vane-axial blades of turbine-type models, the rotating blades of impellertype sensors are perpendicular to the flow-making them inherently less accurate than turbine
sensors. However, their typical 1% accuracy and excellent repeatability makes them ideal for
many applications.
Impeller sensors are especially suitable for measuring flow rates of low-viscosity liquids that
are low in suspended solids over line velocities of between 0.15 and 10 m/s (Figure 3.6).
84
Industrial Flow Measurement
Inferential Meters
Meter reading error
+
+
Cavitation
Figure 3.6. Reading vs. velocity
for a typical impeller type meter.
0.15
Velocity (m/s)
10
At lower flow rates, the fluid cannot maintain the force needed to overcome bearing friction,
impeller mass inertia, and fluid drag. And at flow rates above 10 m/s, cavitation can occur
and cause readings to increase more than the increase in flow velocity. As velocity continues
to increase under cavitation conditions, the reading eventually decreases with respect to true
velocity.
The most common form of impeller-type meter is the in-line insertion format in which the
main bearing is located out of the main flow stream and thus provides only a minimal
pressure drop. Figure 3.7 illustrates a Tee-mount flow sensor suitable for pipe sizes ranging
from 10 to 100 mm.
Tee-piece
Locking pin
Impeller
wheel
Figure 3.7. A Tee-mount
flow sensor suitable for
pipe sizes ranging from 10
to 100 mm (courtesy GLI
International).
Other versions are available for use with welded-on pipe threads that allow the same meter to
be used on pipe sizes ranging from 75 mm to 2.5 m diameter. This technique also allows its
use in a ‘hot tap’ mode whereby it may be removed and replaced on high pressure lines
without the need for a shutdown.
Another form of the impeller type meter, the Pelton wheel turbine (Figure 3.8), is able to
measure extremely low flow rates down to 0.02 litres/min, coupled with a turn-down ratio of
up to 50:1.
85
Industrial Flow Measurement
Inferential Meters
Pelton wheel
Figure 3.8. Cross-section
of Pelton wheel system.
Sensing
coil output
Ferrite magnets
Concentrating nozzle
The incoming low velocity fluid is concentrated into a jet that is directed onto a lightweight
rotor suspended on jewel bearings. The rotational speed is linear to flow rate and is detected
by means of ferrite magnets, located in the rotor tips, which induce voltage pulses in a sensing
coil. One drawback is that the nozzle can cause a rather large pressure drop.
3.5.1 Application limitations
As with turbine meters, most such sensors employ multiple blades with a permanent magnet
embedded in each blade. A pick-up coil in the sensor acts as a generator stator – generating
an electrical pulse each time the blade passes near it.
The use of such a magnetic pick-up, however, has some serious drawbacks. Firstly, the signal
is susceptible to interference by extraneous magnetic fields in the vicinity of the coil. In
addition, ferrous contamination, present in many industrial applications, causes particles to be
attracted to the magnets in each blade. This not only affects sensor accuracy, but can impede
or stop the impeller from rotating. Further, at low flows, the magnetic attraction between
each rotating blade and the pick-up coil increases the force required to turn the impeller –
resulting in poor linearity.
One method of overcoming this problem is shown in Figure 3.9 in which permanent magnets
embedded in the impeller blades pass close to a Hall-effect transducer.
Figure 3.9. The problem
of magnetic drag may be
overcome through the
use of a Hall-effect
transducer that picks up
the signal from magnets
embedded in the impeller
blades (courtesy FTE).
Hall-effect
transducer
Five bladed rotor
Permanent magnet
Ceramic shaft
Ceramic bearing
86
Industrial Flow Measurement
Inferential Meters
Another method of overcoming this problem is through the use of a non-magnetic ferrite rods
embedded in the impeller blades. Although the ferrites are not magnetic, they form a low
permeable path for a magnetic field.
As shown in Figure 3.10 the pickup comprises a composite transmitting and sensing coil. In
the absence of a ferrite rod the magnetic coupling is loose and the signal produced by the
receiving coil is small. However, in the presence of a ferrite rod, the magnetic coupling is
strong – resulting in a much larger output signal.
Pulsed 10 V d.c
Pulsed 10 V d.c
Pulsed 1 V d.c
Pulsed 9 V d.c
Transmitting Receiving
coil
coil
Transmitting Receiving
coil
coil
Weak magnetic coupling
Strong magnetic coupling
Figure 3.10. In the absence of a ferrite rod the magnetic coupling is loose and the signal
produced by the receiving coil is small. When a ferrite rod is present, the magnetic
coupling is strong resulting in a much larger output signal (courtesy GLI International).
Because permanent magnets are not used, there is no magnetic drag and no accumulation of
magnetic particles to degrade the accuracy or cause clogging.
3.6
Installation recommendations
In order to reap the benefits of high accuracy the following installation practices should be
observed:
¾ At least 10 pipe diameters of straight approach and 5 pipe diameters of straight outlet
piping are required.
¾ Turbines should never be subjected to a swirling flow
¾ Flow must not contain any solids – especially fibre.
¾ Do not exceed the measuring range.
¾ A turbine for liquids should never be subjected to gas flow (danger of over-speeding)
¾ Never clean with compressed air.
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Industrial Flow
Measurement
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Chapter 4
Oscillatory Flow Meters
4.1
Introduction
Oscillatory flow measurement systems involve three primary metering principles: vortex,
vortex swirl (precession) and Coanda effect. In all three, the primary device generates an
oscillatory motion of the fluid whose frequency is detected by a secondary measuring device
to produce an output signal that is proportional to fluid velocity.
4.2
Vortex flowmeters
Vortex flowmeters for industrial flow measurement were first introduced in the mid-1970s but
the technology was poorly applied by several suppliers. As a result, the technology
developed a bad reputation and several manufacturers dropped the technology. However,
since the mid-1980s many of the original limitations have been overcome and vortex
flowmetering has become a fast growing flow technology.
Vortex meters are based on the phenomenon known as vortex shedding that takes place when
a fluid (gas, steam or liquid) meets a non-streamlined obstacle – termed a bluff body.
Because the flow is unable to follow the defined contours of the obstacle, the peripheral
layers of the fluid separate from its surfaces to form vortices in the low pressure area behind
the body (Figure 4.1). These vortices are swept downstream to form a so-called Karman
Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency
that, within a given Reynolds number range, is proportional to the mean flow velocity in the
pipe.
Bluff body
Karman vortex street
Figure 4.1. The Karman vortex street – with vortices formed on
alternate sides in the low pressure area of bluff body.
In vortex meters, the differential pressure changes that occur as the vortices are formed and
shed, are used to actuate the sealed sensor at a frequency proportional to the vortex shedding.
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4.2.1 Formation of vortices
At very low velocities – the laminar flow region (Figure 4.2(a)) – the fluid flows evenly
around the body without producing turbulence. As the fluid velocity increases the fluid tends
to shoot past the body, leaving a low pressure region behind it (Figure 4.2(b)). As the fluid
velocity increases even further, this low pressure region begins to create a flow pattern as
shown in Figure 4.2(c) – the beginning of the turbulent flow region. This action momentarily
relieves the pressure void on one side of the low pressure region and the fluid forms into a
vortex. The interaction of the vortex with the main stream fluid releases it from the surface
of the body and it travels downstream. Once released, the low pressure region shifts towards
the other rear side of the body to form another vortex. This process is repeated, resulting in
the release of vortices from alternate sides of the bluff body as illustrated in Figure 4.1.
Figure 4.2. Formation of vortices: (a)
laminar flow region with fluid flowing
evenly around the body; (b) at higher
velocities a low pressure region starts
to form behind the bluff body; and (c)
beginning of turbulent flow region and
formation of vortex.
(a)
(b)
(c)
Vortex shedding occurs naturally throughout nature and can be observed in the whistling tone
that the wind produces through telephone wires or in a flag waving from a flagpole. Because
the flagpole acts as a bluff body, vortex shedding occurs. As the wind speed increases the
rate of vortex shedding increases and causes the flag to wave faster.
4.2.2 Strouhal factor
X In 1878 Strouhal observed that the frequency of oscillation of a wire, set in motion by a
stream of air, is proportional to the flow velocity. He showed that:
f =
St ⋅ v
d
where:
f = vortex frequency (Hz)
d = diameter of the bluff body (m)
v = velocity of liquid(m/s)
St = Strouhal factor (dimensionless)
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Unlike other flow sensing systems, because the vortex shedding frequency is directly
proportional to flow velocity, drift is not a problem as long as the system does not leave its
operating range. Further, the frequency is unaffected by the medium’s density, viscosity,
temperature, pressure, and conductivity, as long as the Reynolds number (Re) stays within
defined limits. Consequently, irrespective of whether the meter is used for measuring steam,
gas or liquids, it will have virtually the same calibration characteristic and the same meter
factor – although not necessarily over the same volumetric flow velocity ranges.
In reality, the Strouhal factor is not a constant but, as illustrated in Figure 4.3, varies with the
shape of the bluff body and the Reynolds number. The ideal vortex flowmeter would,
therefore, have a bluff body shape that features a constant Strouhal number over as wide a
measuring range as possible. W
Round bluff body
Delta bluff body
Strouhal factor
0,3
Figure 4.3.
Relationship between
Strouhal factor and
Reynolds number for
both a round and a
delta bluff body
(courtesy Endress +
Hauser).
0,2
0,1
100
1000
10 000
Reynolds number
10 000
Meters based on this relationship are shown to have a linearity of better than ±0.5 % over a
wide flow range of as high as 50: 1 for liquids and 100:1 for gases. The limits are determined
at the low-end by viscosity effects and at the upper end by cavitation or compressibility.
Another major advantage of the vortex meter is that it has a constant, long-term calibration
that does not involve any in-service adjustment or tuning. For a given size and shape of the
bluff body, the vortex shedding frequency is directly proportional to flow rate.
4.2.3 Shedder design
Meters differ only in the shape of the bluff body and in the sensing methods used – with each
manufacturer claiming specific advantages. Some of the bluff body shapes are shown in
Figure 4.4.
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(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.4. Various bluff
body shapes: (a) round;
(b) rectangular; and (c)
two-part rectangular; (d)
Tee-bar; (e) deltashaped (courtesy
Endress + Hauser).
Tests have shown that changes in the dimensions of the bluff body have a negligible effect on
calibration. For example, tests with a rectangular bluff body indicate that with a body-tometer bore ratio of 0.3, the body width can vary by as much as ±10 % to produce a change in
the meter factor of < 0.4 %. Similarly, radiussing the edges of the bluff body by as much as 4
mm will not cause the calibration to deviate outside the standard accuracy band.
(Compare this with an orifice plate where radiussing the sharp edge of the orifice by as little
as 0.4 mm produces a reading inaccuracy of approximately 4%.) The major benefit of this
insensitivity to dimensional changes of the bluff body is that the vortex meter is virtually
unaffected by erosion or deposits.
4.2.3.1
Cylindrical
Early bluff bodies were cylindrical. However, as the boundary layer changes from laminar to
turbulent, the vortex release point fluctuates backwards and forwards, depending on the flow
velocity, and the frequency is, subsequently, not exactly proportional to velocity.
As a result, use is made of bluff bodies having a sharp edge that defines the vortex shedding
point.
4.2.3.2
Rectangular bodies
Following the cylindrical body, the rectangular body was used for many years. However,
current research indicates that this body shape produces considerable fluctuation in linearity
in varying process densities.
4.2.3.3
Rectangular two-part bodies
In this configuration, the first body is used to generate the vortices and the second body to
measure them.
The two-part body generates a strong vortex (hydraulic amplification) that requires the use of
less complicated sensors and amplifiers. On the negative side, the pressure loss is almost
doubled.
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4.2.3.4
Delta-shaped bodies
The delta-shaped shedder has a clearly defined vortex shedding edge and tests (including
those carried out by NASA) indicate that the delta shape provides excellent linearity.
Accuracy is not affected by pressure, viscosity or other fluid conditions. Many variations of
the Delta shape exist and are in operation.
4.2.3.5
Delta-shaped two-part bodies
Claimed to combine the best features of modern technology, here, the delta-shaped bluff body
generates the vortices and the second body is used to measure them.
4.2.3.6
Tee-shaped bar
Also claimed to combine the best features of the delta-shaped body with a high hydraulic
amplification.
4.2.4 Sensors
X Since the shedder bar is excited by kinetic energy, the amplitude of the vortex signal
depends on the dynamic pressure of the fluid:
pd = ½ ⋅ ρ ⋅ v 2
where:
pd
ρ
v
=
=
=
dynamic pressure
fluid density
velocity
As shown, the sensor amplitude is thus proportional to the fluid density and to the square of
the velocity (Figure 4.5).
Amplitude
1000 kg/m3
700 kg/m3
500 kg/m3
0
10
20
30
40 50 60 70 80
Velocity (% of range)
90
100
Figure 4.5. Amplitude as a function of velocity and process density.
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Industrial Flow Measurement
Oscillatory flow meters
Consequently, the dynamic sensitivity range of the vortex sensor needs to be quite large. For
a turn-down ratio of 1:50 in flow velocity, the magnitude of the vortex signal would vary by
1:2500. This leads to very small signal levels at the low end of the measuring range.
While the vortex shedding frequency decreases as the size of the bluff body or meter
increases, the signal strength falls off as the size decreases – thus, generally, limiting the
meter size to within the range 15 to 200 mm bore. While there are several methods available
for measuring the vortex frequency, there is no sensor currently available that will suit all
operating conditions. W
Many vortex meters use non-wetted, external
sensors connected to internal parts that move
or twist due to vortex shedding. Formerly,
this technology was plagued by sensitivity to
pipeline vibration that produces a similar
motion to vortex shedding when there is no
flow in the pipe and can cause an erroneous
output at zero flow. However, modern
instruments have largely overcome this
problem and systems as illustrated in Figure
4.6 are insensitive to vibrations in each axis
up to at least 1 g covering the frequency
range up to 500 Hz.
Sensor
Delta
shedding bar
Sensor
bar
Figure 4.6. Use of separate mechanically
balanced sensor positioned behind the bluff
body (courtesy Endress + Hauser).
4.2.4.1
Thermal sensing
Thermal sensors (Figure 4.7) make use of electrically heated thermistors (heat-sensitive semiconductor resistors) with a high temperature coefficient and a rapid time response. As the
vortices are shed, on alternate sides of the fluff body, heat is convected away from the
preheated elements – resulting in a change in resistance that is in phase with the shedding
frequency.
Thermistor
Figure 4.7. Basic configuration of
thermal sensor (courtesy Endress +
Hauser).
Thermistor
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Industrial Flow Measurement
Oscillatory flow meters
Depending on their location, the thermistors are sensitive to dirt and are generally incapable
of withstanding temperature shocks. In addition, the upper frequency limit 500 Hz precludes
their use with small diameter pipes (e.g. 25 mm) particularly with gas where vortex
frequencies of 3300 Hz or more can be encountered.
4.2.4.2
Mechanical sensors
Sometimes called a shuttle ball sensor, a magnetic ball or disc moves from side to side, under
the influence of the vortices, along a lateral bore that connects both sides of the bluff body
(Figure 4.8). This movement is detected by a magnetic pick-up.
Figure 4.8. Shuttle ball or disc sensor (courtesy
Endress + Hauser).
The main problems with this sensor are that it is easily blocked by dirt and in saturated steam
the movement of the ball or disc can be slowed by condensation. Further, condensed water
can cause the ball or disc to adhere to one side or other.
4.2.4.3
Capacitive sensors
In the form illustrated in Figure 4.9, stainless steel diaphragms are welded onto the sides of
the bluff body and the assembly filled with oil and sealed. Since the oil is incompressible it
fully supports the diaphragms against high static pressure. However, under the influence of
an asymmetric differential pressure, as occurs during vortex shedding, the diaphragms deflect
and the oil transfers through the internal port from one side to the other. When the
diaphragms deflect there is a change in the capacitance between the diaphragms and the
electrodes ⎯ one side increasing and the other side decreasing..
Diaphragm (electrode)
Liquid fill
Figure 4.9. The vortices act on two
diaphragms. As the diaphragms
deflect the oil transfers through the
internal ports from one side to the
other ⎯ changing the capacitance
between the diaphragms and the
Diaphragm (electrode)
electrodes (courtesy Endress +
Fixed electrode
Hauser).
Since the capacitance is inversely proportional to the distance between the electrodes and
directly proportional to the plate area, pressure differences can be used to vary the plate
overlap area or the electrode distance. Modern capacitive sensors are available for use with
superheated steam for temperatures up to 427°C.
Ports
Leadouts
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Industrial Flow Measurement
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4.2.4.4
Piezoelectric sensor
Like the capacitive sensor, the alternating vortices,
shed on each side of the shedder, act on two
diaphragms mounted on each side of the sensor. In
this case, (Figure 4.10) the flexing motion is coupled
to a piezoelectric sensor, outside the flow line, which
senses the alternating forces and converts them to an
alternating signal.
Figure 4. 10. Use of piezoelectric sensor positioned
outside the flow line (courtesy Emerson).
Fo
se rce o
ns
or n
g
otin
v
i
P s
axi
Vo
sh rtex
for eddi
ce ng
The piezo elements produce a voltage output that is
proportional to the applied pressure. Whilst piezoceramic materials produce a high output for a given pressure (a high ‘coupling factor’) they
have a limited operating temperature range (about 250 °C).
The piezoelectric material Lithium Niobate (LiNbO3) offers only medium coupling factors
but can be operated at temperatures above 300 °C.
Generally, piezoelectric materials are unsuitable for temperatures below -40 °C since below
this point, the piezoelectric effect becomes too small.
Because the piezoelectric element produces an output that is affected by movement or
acceleration, it is also sensitive to external pipe vibration. This problem can be overcome by
using a second piezoelectric element to measure the vibration and use it in a compensating
circuit to ensure that only the clean vortex shedding frequency is obtained.
4.2.4.5
Strain gauge sensors
The vortices created by the bluff body cause the body itself to be mechanically displaced by
small amounts – of the order of 10 μm. This elastic movement can be detected using strain
gauges attached directly or indirectly to the bluff body. Movement of the body produces a
change in resistance of the strain gauges.
The main drawbacks of this technology are the upper temperature limitation of the strain
gauges (about 120°C) and the fact that diameters above 150 mm are sensitive to vibration.
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Industrial Flow Measurement
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4.2.4.6
Ultrasonic sensing
An ultrasonic detector system (Figure 4.11) makes use of an ultrasonic transmitter and
receiver placed behind the bluff body. The vortices modulate the ultrasonic beam and the
resultant output is the vortex signal.
Ultrasonic transmitter
Ultrasonic receiver
Figure 4.11. General configuration of the ultrasonic sensor (courtesy Endress + Hauser).
This sensor system has a good turn-down ratio and, since there is no mass associated with the
sensor that would experience a force under vibration, the sensor is virtually vibration
insensitive.
The main problem associated with this technique is that extraneous sound sources can affect
measurements.
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4.2.5 APPLICATION GUIDELINES FOR VORTEX FLOWMETERING*
* These application guidelines have been compiled from a series of notes supplied by
Krohne
In general, a vortex shedding flowmeter works well on relatively clean low viscosity liquids,
gases and steam to obtain specified accuracy.
4.2.5.1
Viscosity
The pipe Reynolds number should be above 30 000 minimum. This means vortex meters can
only be used on low viscosity liquids. Highly viscous fluids (>3 Pa.s (30 cP)) and slurries are
not recommended applications. As a rule of thumb, the viscosity should be 0.8 Pa.s (8 cP) or
less (a viscosity of 0.8 Pa.s would correspond to cooking oil). Higher viscosity fluids can be
metered, but at the expense of rangeability and head loss.
4.2.5.2
Low flow
The vortex meter cannot measure flow down to zero flow since, at low flow rates, vortex
shedding becomes highly irregular and the meter is totally inaccurate. This generally
corresponds to a Reynolds number between 5 000 and 10 000 and therefore depends on the
pipe diameter and the fluid viscosity. For water, typical minimum velocity flow rate values
would vary from about 2.4 m/s for a 15 DN pipe to 0.5 m/s for a 300 DN pipe.
Whilst the minimum Reynolds number requirement imposes a limitation on the usability of
the vortex meter, this is not a serious limitation for many applications. For example, water
flow in line sizes 25 DN and higher generally corresponds to Reynolds numbers in the tens of
thousands to hundreds of thousands. Gas and steam applications generally correspond to
Reynolds numbers in the low hundreds of thousands to the millions.
Most vortex meters include a low flow cut-in point, below which the meter output is
automatically clamped at zero (for example, 4 mA for analog output).
For many applications the low flow cut-off point does not pose a problem. However, it can
be a serious drawback for applications that see low flows during start-up and shutdown
operations (i.e., flows much lower than normal conditions, often by a factor of 10 or more).
While users may not want to measure flow accurately during such times, they may want to get
some indication of flow. The vortex meter is not a good choice for such an application.
4.2.5.3
Batching operations
Vortex meters may or may not be suitable for typical batching applications involving
intermittent (on/off) flow ⎯ especially if the pipe does not remain full at zero flow. The
vortex meter will not register flow as the fluid accelerates from zero to the low flow cut-in
value, and again when the flow decelerates from the low flow cut-in value to zero. This lost
flow may or may not create a significant error depending on the dynamics of the system, and
the size of the batch being measured. In addition, the vortex meter can only measure flow in
one direction. Any back flow through the meter (for example, the result of turning a pump
off) will not be measured and will not be deducted from the registered batch total. One way to
minimise errors on intermittent flows is to install check valves with the vortex meter on
horizontal lines to keep the line full during zero flow conditions.
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4.2.5.4
Measuring range
Note that in vortex meters, the measuring range is fixed for a given application and meter
size. Although it depends on the specific application it is generally > 20:1 on gases and
steam, and >10:1 on liquids.
A 50 mm vortex meter has, typically, a flow range over the range of 1 to 15 ℓ/s on water (15:
1 rangeability). If we need to measure over the range 0.5 to 3 l/s there is nothing that can be
done to the 50 DN meter to allow it to measure a lower range and it would be necessary to use
a 25 DN meter. For this reason, vortex meters are sized to the desired flow range, rather than
to the nominal pipe diameter. To get the proper measuring range (Figure 4.12), it is often
necessary to use a smaller diameter meter than the nominal diameter of the pipe.
50:25 mm
concentric
reducer
25 mm
vortex
meter
25 mm
upstream run
25:50 mm
concentric
expander
25 mm
downstream run
Figure 4.12. Use of reducer and expander to obtain the correct
measuring range (courtesy Krohne).
When buying a flow meter, the instrument engineer often does not know the exact flow range
and has to make an educated guess. Since vortex meter rangeability is fixed for a given line
size by the process conditions, a meter sized on an educated guess may not meet the process
conditions.
Consequently if the user does not have a good ‘ball park’ figure in regard to rangeability it is
often better to opt for a more forgiving technology such a magnetic flowmeter.
4.2.5.5
Process noise
Process noise from pumps, compressors, steam traps, valves, etc., may cause the meter to read
high, by triggering a higher than expected frequency output from the sensor, or by indicating
a false flow rate when the system is at zero flow. Process noise is generally not a problem on
liquids because the sensor's signal-to-noise ratio is at a maximum. However, gases and steam
produce a much weaker sensor signal, which may not be as easily discernible from process
noise at low flow.
Process noise cannot be quantified before the meter is installed and, therefore, it should
always be assumed that some process noise exists. It can be eliminated using built-in noise
filtering circuitry. However, this raises the threshold value of the low flow cut off. Thus, the
more filtering used to eliminate process noise, the less the net rangeability of the meter. To
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Industrial Flow Measurement
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avoid this, vortex flowmeters need to be sized properly to ensure the desired rangeability .
There are two general sizing guidelines that should be followed:
1. The user Upper Range Value (URV) must not be less than 20% of the meter Upper Range
Limit (URL).
Note. URL is the highest flow rate that a meter can be adjusted to measure whilst the URV
is the highest flowrate that a meter is adjusted to measure. The URV will always be equal
to or lower than the URL.
2. The minimum desired flow rate must be > 2 times the value of the meter's low flow cut-in
rate
4.2.5.6
Accuracy
Vortex meter accuracy is based on the known value of the meter factor (K-factor), determined
from a water calibration at the factory. Accuracy for liquids is typically stated as ± 0.5% of
flowrate for Reynolds numbers above 30 000.
Water calibration data cannot precisely predict K-factor values for gases and steam, which
can flow at Reynolds numbers well outside the test data range. For this reason, gas and steam
accuracy is typically stated as ±1.0% of flowrate for Reynolds numbers above 30 000.
Long term accuracy depends on the stability of the internal dimensions of the flow-tube and
shedder body. Only significant changes in these dimensions (due to corrosion, erosion,
coatings, etc. ) can affect accuracy with time. Whilst vortex meter K-factors can only be
determined by wet calibration, the dimensions of the flow-tube inside diameter and bluff body
thickness can be used as a 'flag' to determine if recalibration is necessary. Prior to installation,
inspect the flow-tube and carefully measure and record the two reference dimensions. After a
period of time in service, the meter can be removed, cleaned, and re-measured. The meter
does not require recalibration if there has been no significant change in the two reference
dimensions.
4.2.5.7
Effects of erosion
Although vortex shedding flowmeters are primarily designed for measuring the flow of clean
liquids and gases, they can still be used if small amounts of foreign matter are present. Since
there are no moving parts, or ports with active flow, there is little concern for erosion,
physical damage or clogging. The effect of erosion on the salient edges of the bluff body is
small and often poses no significant accuracy degradation.
4.2.5.8
Low density gases
Measuring gas flows can be a problem when the process pressure is low (i.e. low density
gases) because a vortex produced under such conditions does not have a strong enough
pressure pulse to enable a sensor to distinguish it from flow noise. For such applications,
minimum measurable flow becomes a function of the strength of the pressure pulse (a
function of the product of fluid density and the square of fluid velocity) rather than Reynolds
number. Low-density gases can be measured with a vortex meter; however, minimum
measurable flow may correspond to a high fluid velocity, and rangeability may be
significantly less than 20:1.
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4.2.5.9
Orientation
Vortex meters can be installed vertically, horizontally or at an angle. However, for liquid
measurements the meter must be full at all times. The meter should also be installed to avoid
formation of secondary phases (liquid, gas or solid) in the internal sensor chambers.
4.2.5.10 Pressure drop
If the inside meter diameter is the same as the nominal diameter of the process piping (i.e. a
50 DN meter is used in a 50 DN line), then the pressure drop will normally be less than 40
kPa on liquid flow at the URL (usually in the 14 to 20 kPa range at the user's URV).
However, when downsizing the vortex meter to achieve a desired rangeability, the
unrecoverable pressure loss through the meter is increased.
It must be ensured that this increased pressure loss is not enough to cause a liquid to flash or
cavitate within the pipe. Flashing and cavitation have an adverse effect on meter accuracy,
and can cause damage to the meter itself.
4.2.5.11 Multi-phase flow
Measurement of two- or three-phase flow (for example, water with sand and air, or 'wet'
steam with vapour and liquid) is difficult and if multi-phase flow is present the vortex meter
will not be as accurate.
Because the vortex meter is a volumetric device, it cannot distinguish which portions of the
flow are liquid and which portions of the flow are gas or vapour. Consequently, the meter will
report all the flow as gas, or all the flow as liquid, depending on the original configuration of
the device. Thus, for example, if the meter is configured to measure water in litres, and the
actual water has some entrained air and sand mixed in, a litre registered by the meter will
include the water, air and sand that is present. Therefore if the area of interest were the
amount of water, the reading from the meter would be consistently high, based on the
proportions of air and sand present. A user would, consequently, need to separate the phases
prior to metering or live with this inherent error.
4.2.5.12 Material build-up
Fluids that tend to form coatings are bad applications for vortex meters. Coating build-up on
the bluff body will change its dimensions, and therefore, the value of the K-factor.
4.2.5.13 Piping effects
The specification for vortex meter accuracy is based on a well developed and symmetrical
fluid velocity profile, free from distortion or swirl, existing in the pipe. The most common
way to prevent errors is to provide sufficient lengths of straight, unobstructed pipe, upstream
and downstream of the meter, to create a stable profile at the meter site.
Generally, vortex meters require similar amounts of upstream and downstream pipe runs to
orifice plates, turbine meters and ultrasonic meters. Vortex meters are not usually
recommended for 'tight' piping situations, with limited runs of straight pipe, unless
repeatability is more important than accuracy. Typical manufacturers' recommendations are
shown in Figure 4.13, when flow conditioners are not being used.
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Industrial Flow Measurement
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Oscillatory flow meters
5D
15D
Expander
40D
Reducer
40D
5D
5D
Two 90° bends
in the same plane
Single 90° bend
Two 90° bends
in different planes
40D
5D
5D
Valve fully open
35D
5D
Figure 4.13. Typical manufacturers’ recommendations for straight pipe lengths (courtesy
Emerson).
Most performance specifications are based on using schedule 40 process piping. This pipe
should have an internal surface free from mill scale, pits, holes, reaming scores, bumps, or
other irregularities for a distance of 4 diameters upstream, and 2 diameters downstream of the
vortex meter. The bores of the adjacent piping, the meter, and the mating gaskets must be
carefully aligned to prevent measurement errors.
For liquid control applications, it is recommended that the vortex meter be located upstream
of the control valve for a minimum of 5 diameters. For gas or steam control applications, it is
recommended that the vortex meter be located a minimum of 30 diameters downstream of the
valve. The only exception to this rule is for butterfly valves. In this instance the recommended
distances are increased to 10 diameters for liquids, and 40 to 60 diameters for gases and
steam.
4.2.5.14 Mass measurement
Pressure and/or temperature measurements are generally used in conjunction with a vortex
meter measurement when the user wants an output in mass.
¾ Pressure taps should be located 3.5 to 4.5 diameters downstream of the meter.
¾ The temperature tap should be located 5 to 6 diameters downstream of the meter, and the
smallest possible probe is recommended to reduce the chances of flow disturbance.
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4.2.5.15 Avoiding problems
The following guidelines will help prevent application and measurement problems with a
vortex meter and ensure premium performance:
¾
¾
¾
¾
¾
¾
¾
¾
¾
¾
¾
improper configuration;
improper sizing;
insufficient upstream/downstream relaxation piping;
improper meter orientation;
partially full piping;
accumulation of secondary phase ( gas, liquid or solid) inside the meter;
improper temperature/pressure taps;
flows below Reynolds numbers of 30000;
flows below the low flow cut-in;
process noise (at low flows or zero flow); and
presence of multiple phases.
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Industrial Flow Measurement
4.3
Oscillatory flow meters
Vortex precession
The 'Swirlmeter', a patented technology with manufacturing rights ceded to Bailey-Fischer &
Porter, is based on the principle known as vortex precession.
The inlet of the Swirlmeter (Figure 4.14) uses guide vanes, whose shape is similar to a
turbine rotor, to force the fluid entering the meter to spin about the centreline. This swirling
flow then passes through a venturi, where it is accelerated and then expanded in an expansion
chamber.
Inlet swirler
Piezoelectric sensor
Venturi section
Expansion
chamber
Figure 4.14. Basic principle of a vortex precession Swirlmeter (courtesy
Bailey Fischer & Porter).
The expansion changes the direction of the axis about which the swirl is spinning – moving
the axis from a straight to a helical path. This spiralling vortex is called vortex precession. A
flow straightener is used at the outlet from the meter. This isolates the meter from any
downstream piping effects that may affect the development of the vortex.
Above a given Reynolds number, the vortex precession frequency, which lies between 10 and
1500 Hz and is measured with a piezoelectric sensor, is directly proportional to the flow rate.
Although the Swirlmeter can be used with both gases or liquids, it finds its main application
as a gas flowmeter.
A major advantage of the vortex precession technique over that of vortex shedding is that it
has a much lower susceptibility to the flow profile and hence only three diameters of straight
line are required upstream of the meter. In addition, the Swirlmeter features: linear flow
measurement; rangeability between 1:10 and 1:30; no moving parts; and installation at any
angle in the pipeline.
Because of the higher tolerance in manufacture of this type of meter, it is more expensive than
comparative meters.
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Industrial Flow Measurement
4.4
Oscillatory flow meters
Fluidic flowmeter
The fluidic flowmeter is based on the wall attachment or 'Coanda' effect. Wall attachment
occurs when a boundary wall is placed in proximity to a fluid jet – causing the jet to bend
and adhere to the wall.
This effect is caused by the differential pressure
across the jet, deflecting it towards the
boundary (Figure 4.15). Here it forms a stable
attachment to the wall, which is little affected
by any downstream disturbances.
Figure 4.15. Explanation of the
Coanda effect – resulting in stable
attachment of the flow stream to the
wall.
In the fluidic meter (Figures 4.16 and 4.17), the flow stream attaches itself to one of the walls
– with a small portion of the flow fed back through a passage to a control port (Figure 4.16).
Sensor
Side wall
Figure 4.16. Once attached to one side of
the wall a feedback passage diverts a
portion of stream back onto the main
flow (courtesy Moore Products).
Feedback
passage
Control
port
Sensor
This feedback, diverts the main flow to
the opposite side wall where the same
feedback action is repeated (Figure 4.17).
Side wall
Figure 4.17. Main stream is diverted to
the other wall by the feedback control
action, and the procedure is then
repeated (courtesy Moore Products).
Feedback
passage
Control
port
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Industrial Flow Measurement
Oscillatory flow meters
The result is a continuous oscillation of the flow between the sidewalls of the meter body
whose frequency is linearly related to the fluid velocity. Flow in the feedback passage cycles
between zero and maximum which is detected by a built-in thermistor sensor.
The main benefit offered by the fluidic meter is that feedback occurs at much lower Reynolds
numbers and it may thus be used with fairly viscous media. In addition, since a fluidic
oscillator has no moving parts to wear with time, there is no need for recalibration during its
expected lifetime. Other benefits include:
¾ rugged construction;
¾ high immunity to shock and pipe vibration; and
¾ high turndown ratio.
The main drawback of the fluidic oscillator is its relatively high pressure loss and its poor
performance at low flow rates.
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Differential flow meters
Chapter 5. Differential Pressure Meters
Industrial Flow
Measurement
109
Industrial Flow Measurement
Differential flow meters
110
Industrial Flow Measurement
Differential flow meters
Chapter 5
Differential Pressure Meters
5.1
Introduction
Differential pressure flow meters encompass a wide variety of meter types that includes:
orifice plates, venturi tubes, nozzles, Dall tubes, target meters, pitot tubes and variable area
meters. Indeed, the measurement of flow using differential pressure is still the most widely
used technology.
One of the features of the differential flow meter, sometimes referred to as a ‘head’ or ‘head
loss’ meter, is that flow can be accurately determined from: the differential pressure;
accurately measurable dimensions of the primary device; and properties of the fluid. Thus, an
important advantage of differential type meters over other instruments is that they do not
always require direct flow calibration. In addition, they offer excellent reliability, reasonable
performance and modest cost.
Another advantage of orifice plates in particular, is that they can be used on liquid or gas
applications with little change.
5.2
Basic theory
Differential pressure flow rate meters are based on a physical phenomenon in which a
restriction in the flow line creates a pressure drop that bears a relationship to the flow rate.
X
This physical phenomenon is based on two well-known equations: the equation of
continuity and Bernoulli’s equation.
5.2.1
Equation of continuity
Consider the pipe in Figure 5.1 that rapidly converges from its nominal size to a smaller size
followed by a short parallel sided throat before slowly expanding to its full size again.
Further, assume that a fluid of density ρ flowing in the pipe of area A1, has a mean velocity v1
at a line pressure P1. It then flows through the restriction of area A2, where the mean velocity
increases to v2 and the pressure falls to P2.
Point 1
A1
Point 2
A2
v1
P1
D
d
Inlet Throat
section
v1
P1
D
Figure 5.1. Basic definition of terms.
Outlet
section
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Industrial Flow Measurement
Differential flow meters
The ratio of the diameters of the restriction (d) to the ID (inside diameter) (D) of the pipe is
called the beta ratio (β), i.e.
d
= β ……………………………………………………………….(5.1)
D
The equation of continuity states that for an incompressible fluid the volume flow rate, Q,
must be constant. Very simply, this indicates that when a liquid flows through a restriction,
then in order to allow the same amount of liquid to pass (to achieve a constant flow rate) the
velocity must increase (Figure 5.2).
Mathematically:
Q = v1A1 = v2A2
……………………………………………….(5.2)
where: v1 and v2 and A1 and A2 are the velocities and cross-sectional areas of the pipe at
points 1 and 2 respectively.
Q = v2. A2
Q = v1. A1
Figure 5.2. To
allow the same
amount
of
liquid to pass
the
velocity
must increase
i.e. Q = v1A1 = v2A2
5.2.2
Bernoulli’s equation
In its simplest form, Bernoulli's equation states that under steady flow conditions, the total
energy (kinetic +pressure + gravitational) per unit mass of an ideal incompressible fluid (i.e.
one having a constant density and zero viscosity) remains constant along a flow line.
where:
v2 P
+ + gz = k
2 ρ
……………………………………………….(3)
v = the velocity at a point in the streamline
P = the pressure at that point
ρ = the fluid density
g = the acceleration due to gravity
z = the level of the point above some arbitrary horizontal reference plane with the
positive z-direction in the direction opposite to the gravitational acceleration,
k = constant
In the restricted section of the flow stream, the kinetic energy (dynamic pressure) increases
due to the increase in velocity and the potential energy (static pressure) decreases.
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Industrial Flow Measurement
Differential flow meters
Relating this to the conservation of energy at two points in the fluid flow then:
v12 P1
v 22 P2
+
=
+
2 ρ
2 ρ
……………………………………………….(5.4)
Multiplying through by ρ gives:
1
1
⋅ ρ ⋅ v12 + P1 = ⋅ ρ ⋅ v22 + P2
2
2
or:
or:
1
1
⋅ ρ ⋅ v 22 − ⋅ ρ ⋅ v12
2
2
P1 − P2 =
ΔP =
1
1
⋅ ρ ⋅ v 22 − ⋅ ρ ⋅ v12
2
2
……………………………………….(5.6)
……………………………………….(5.7)
ΔP = P1 − P2
where:
……………………………………….(5.5)
……………………………………….(5.8)
Now from the continuity equation (2) we can derive:
v1 =
and:
v2 =
Q
A1
……….…………………..………………….……….(5.7)
Q
A2
……….……………………………………………….(5.8)
substituting in (6):
⎛Q⎞
⎛Q⎞
1
1
ΔP = ⋅ ρ ⋅ ⎜⎜ ⎟⎟ − ⋅ ρ ⋅ ⎜⎜ ⎟⎟
2
2
⎝ A2 ⎠
⎝ A1 ⎠
2
Solving for Q:
Q = A2
2
……………………………….(5.9)
2 ⋅ ΔP
ρ
⎛A ⎞
1 − ⎜⎜ 2 ⎟⎟
⎝ A1 ⎠
..….………………………….…….(5.10)
2
Since it is more convenient to work in terms of the diameters of the restriction (d) and
the ID (inside diameter) (D) of the pipe we can substitute for:
A1 =
and:
A2 =
π ⋅ D2
.…….……………………………..….(5.11)
4
π ⋅d 2
.…….………………………………...(5.12)
4
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Industrial Flow Measurement
Differential flow meters
Q=
π ⋅d
2 ⋅ ΔP
ρ
2
⎛d ⎞
1− ⎜ ⎟
⎝D⎠
4
..….…………………………….….(5.13)
2
1
⎛d⎞
1− ⎜ ⎟
⎝D⎠
The term:
2
....….……………………………..….(5.14)
is called the ‘Velocity of Approach Factor’ (Ev) and by substituting from (1):
Ev =
1 − (β )
1
....….……………………………..….(5.15)
2
Now, substituting in (13) we have:
Q = Ev ⋅ d 2
2 ⋅ ΔP
ρ
..……………………………...(5.16)
Unfortunately, equation (16) only applies to perfectly laminar, inviscid flows. In order to take
into account the effects of viscosity and turbulence a term called the ‘discharge coefficient’
(Cd) is introduced that marginally reduces the flow rate (Q).
The full equation for an incomprehensible fluid thus becomes:
Q = Cd ⋅ E v ⋅ d 2
2 ⋅ ΔP
ρ
..………………………..…….(5.17) W
In practice use is often made of a simplified formula that relates the difference between the
upstream static pressure and the pressure at or immediately downstream of the restriction, to
flow, with the following expression:
Q =kCd
2Δ P
ρ
..………………………..…….(5.18)
where k is a lumped constant.
X The discharge coefficient Cd is a function of the diameter ratio, the Reynolds number Re,
the design of the restriction, the location of the pressure taps and the friction due to pipe
roughness. Generally, for most orifices the discharge coefficient ranges from 0.6 to 0.9.
Reference texts and standards are available that list typical values and tolerances for Cd under
certain flows in standard installations.
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Industrial Flow Measurement
Differential flow meters
The discharge coefficient may also be calculated using the following (ISO) equation:
0 .8
6
⎛
⎛ 19000 β ⎞ ⎞⎟⎛ 10 ⎞
⎜⎜
⎟ β 3 .5 +
+ ⎜ 0.0188 + 0.0063⎜
⎟
⎟⎝ Re ⎟⎠
⎜
Re
⎝
⎠
⎠
⎝
1 .1
0 .8
4
⎛ 2L
⎛
⎞
⎛ 2 L2 ⎞ ⎞⎟ 1.3
2
⎜
⎜1 − 0.11⎛⎜ 19000 β ⎞⎟ ⎟ β
0
.
031
0
.
8
−
−
⎟
⎜
4
⎜ 1 − β ⎟ ⎟β
⎜
⎜1− β
⎝ Re ⎠ ⎟⎠ 1 − β
⎠ ⎠
⎝
⎝
⎝
⎛ 106 β
Cd = 0.5961 + 0.0261β 2 − 0.216 β 3 + 0.000521⎜⎜
⎝ Re
(0.043 + 0.08ε
−10 L1
− 0.123ε − 7 L1
)
⎞
⎟⎟
⎠
0 .7
0 .3
..………………………..…….(5.19)
where:
β
= diameter relation d/D
Re
= Reynolds number
L1 and L2 are functions of the tap type where:
L1= L2=0 for corner taps
L1=1 and L2 =0.47 for D and D/2 taps
L1 = L2 = 0.0254/D D (m) for 2.54 mm taps W
The foregoing formulae highlight two major limitations that are applicable to all differential
pressure systems:
¾ the square root relationship between differential pressure (ΔP) and flow (Q) severely
limits the turn-down ratio of such techniques to a maximum of 5:1 or less; and
¾ if density (ρ ) is not constant, it must be known or measured. In practice the effect of
density changes is not significant in the majority of liquid flow applications and needs
only to be taken into account in the measurement of gas flow.
A third limitation of meters based on differential pressure measurement is that, as shown in
Figure 5.3, they create a permanent pressure loss. This ‘head’ loss depends on the type of
meter and on the square of the volume flow (Figure 5.4).
Figure 5.3. Defining the ‘head’
loss.
P1
P2
P1
P3
P1 - P2 = DP
Permanent pressure
loss P1 -P3
P2
Vena Contracta
115
Industrial Flow Measurement
Differential flow meters
The point at which the minimum cross sectional area of the flow stream reaches a minimum
is known as the ‘vena contracta’ and occurs at, or just downstream of, the narrowest point of
the venturi. The ‘vena contracta’ (L., literally, contracted vein) is characterized by high
velocity, laminar flow.
100
90
Orifice with
flange taps
Permanent pressure loss (%)
80
70
60
Flow nozzle
50
40
30
Short cone venturi
20
10
0
Long cone venturi
Low-loss tube
0.4 0.5 0.6
0.7 0.8 0.9
β Ratio (d/D)
Figure 5.4. The permanent ‘head’ loss for various measurement techniques. The
orifice plate produces the most drop whilst the Low-loss tube causes the least
(courtesy Emerson).
0
0.1
0.2
0.3
5.2.3
Gas flow
X Vapour or gas flow through a restriction differs from liquid flow in that the pressure
decrease in the throat is accompanied by a decrease in density. Thus, for the mass flow to
remain constant, the velocity must increase to compensate for the lower density. The result is
that the formula for gas flow is slightly modified by the addition of the term Y1 gas
expansion factor (= 1 for liquid);
Q = Cd ⋅ Ev ⋅ Y1 ⋅ d 2
2 ⋅ ΔP
ρ
..………………………..…….(5.20)
The gas expansion factor is based on the determination of density at the upstream of the
restriction. Tables and graphs are available for the expansion factor as a function of the
pressure ratio across the restriction and the specific heat of the gas (BS 1042). Alternatively,
the expansion factor may be calculated by standard equations listed in BS 1042. The mass
flow rate for both liquids and gases is found by multiplying the theoretical mass flow equation
by the expansion factor and the appropriate discharge coefficient. W
116
Industrial Flow Measurement
5.3
Differential flow meters
Orifice plate
The orifice plate is the simplest and most widely used differential pressure flow measuring
element and generally comprises a metal plate with a concentric round hole (orifice) through
which the liquid flows (Figure 5.5). An integral metal tab facilitates installation and carries
details of the plate size, thickness, serial number, etc. The plate, usually manufactured from
stainless steel, Monel, or phosphor bronze, should be of sufficient thickness to withstand
buckling (3 - 6 mm). The orifice features a sharp square
upstream edge and, unless a thin plate is used, a bevelled
downstream edge.
UNI฀ ฀ ฀
฀฀r ฀฀s ฀฀฀฀
D฀a฀2
฀ mm
Figure 5.5. Concentric orifice plate with integral metal tab.
A major advantage of the orifice plate is that it is easily fitted between adjacent flanges that
allow it to be easily changed or inspected (Figure 5.6).
Figure 5.6. Orifice plate fitted
between adjacent flanges.
It is commonly assumed that, since the orifice is essentially fixed, its performance does not
change with time. In reality the orifice dimensions are extremely critical and although the
uncertainty may be as low as 0.6% for a new plate, this measurement accuracy is rapidly
impaired should the edge of the orifice bore become worn, burred or corroded.
Indeed, damaged, coated or worn plates that have not been examined for some time can lead
to dramatic measurement uncertainties as shown in Figure 5.7. Even radiussing the sharp
edge of the orifice by as little as 0.4 mm produces a reading inaccuracy of approximately 4%.
117
Industrial Flow Measurement
Lubricant: 24%
Differential flow meters
Warp: 9%
Wear: 1,3 mm 13%
Dirt: 11%
Damage or
nicks: 15%
Misalignment:
3%
Figure 5.7. Errors incurred as a result of wear and contamination on the orifice plate.
Independent tests carried out by Florida Gas Transmission Co. (courtesy Dieterich
Standard).
Although a correctly installed new plate may have an uncertainty of 0.6%, the vast majority
of orifice meters measure flow only to an accuracy of about ± 2 to 3%. This uncertainty is
due mainly to errors in temperature and pressure measurement, variations in ambient and
process conditions and the effects of upstream pipework.
An adaptation of the sharp, square edge is the quadrant edge orifice plate (also called quarter
circle and round edge). As shown in Figure 5.8 this has a concentric opening with a rounded
upstream edge that produces a coefficient of discharge that is practically constant for
Reynolds numbers from 300 to 25 000, and is therefore useful for use with high viscosity
fluids or at low flow rates.
Radius
r ± 0.001 d
45o
d ± 0.001 d W = 1.5 d < D
Figure 5.8. The quadrant edge orifice plate
with a rounded upstream edge.
The radius of the edge is a function of the diameters of both the pipe and the orifice. In a
specific installation this radius may be so small as to be impractical to manufacture or it can
be so large that it practically becomes a flow nozzle. As a result, on some installations it may
be necessary to change maximum differentials or even pipe sizes to obtain a workable
solution for the plate thickness and its radius.
118
Industrial Flow Measurement
Differential flow meters
5.3.1
Orifice plate configurations
Although the concentric orifice (Figure 5.9 (a)) is the most frequently used, other plate
configurations are used:
Figure 5.9. Various types of
orifice plate configurations:
(a) concentric; (b) eccentric;
and (c) segmental.
(a)
(b)
(c)
Eccentric
In the eccentric bore orifice plate (Figure 5.9 (b)), the orifice is offset from the centre and is
usually set at the bottom of the pipe bore. This configuration is mainly used in applications
where the fluid contains heavy solids that might become trapped and accumulate on the back
of the plate. With the orifice set at the bottom, these solids are allowed to pass. A small vent
hole is usually drilled in the top of the plate to allow gas, which is often associated with liquid
flow, to pass.
It should be noted, however, that the vent hole adds an unknown flow error and runs the risk
of plugging.
Eccentric plates are also used to measure the flow of vapours or gases that carry small
amounts of liquids (condensed vapours), since the liquids will carry through the opening at
the bottom of the pipe.
The coefficients for eccentric plates are not as reproducible as those for concentric plates, and
in general, the error can be 3 to 5 times greater than on concentric plates.
Segmental orifice plates
The opening in a segmental orifice plate (Figure 5.9 (c)) is a circular segment – comparable to
a partially opened gate valve. This plate is generally employed for measuring liquids or gases
that carry non-abrasive impurities, which are normally heavier than the flowing media such as
light slurries, or exceptionally dirty gases.
5.3.2
Tapping points
The measurement of differential pressure requires that the pipe is ‘tapped’ at suitable
upstream (high pressure) and downstream (low pressure) points. The exact positioning of
these taps is largely determined by the application and desired accuracy.
119
Industrial Flow Measurement
Differential flow meters
Vena contracta tapping
Because of the fluid inertia, its cross-sectional area continues to decrease after the fluid has
passed through the orifice. Thus its maximum velocity (and lowest pressure) is at some point
downstream of the orifice – at the vena contracta. On standard concentric orifice plates these
taps are designed to obtain the maximum differential pressure and are normally located one
pipe diameter upstream and at the vena contracta – about ½-pipe diameter downstream
(Figure 5.10).
D
1D
½D
Figure 5.10. For maximum differential pressure the high pressure tap is located one pipe
diameter upstream and the low pressure tap at the vena contracta – about ½-pipe diameter
downstream.
The main disadvantage of using the vena contracta tapping point is that the exact location
depends on the flow rate and on the orifice size – an expensive undertaking if the orifice plate
size has to be changed.
Vena contracta taps should not be used for pipe sizes under 150 mm diameter because of
interference between the flange and the downstream tap.
Pipe taps
Pipe taps (Figure 5.11) are a compromise solution and are located 2½ pipe diameters
upstream and 8 pipe diameters downstream. Whilst not producing the maximum available
differential pressure, pipe taps are far less dependent on flow rate and orifice size.
D
2½ D
8D
Figure 5.11. Pipe taps are far less dependent on flow rate and orifice size and
are located 2½ pipe diameters upstream and 8 x pipe diameters downstream.
120
Industrial Flow Measurement
Differential flow meters
Pipe taps are used typically in existing installations, where radius and vena contracta taps
cannot be used. They are also used in applications of greatly varying flow since the
measurement is not affected by flowrate or orifice size. Since pipe taps do not measure the
maximum available pressure, accuracy is reduced.
Flange taps
Flange taps are used when it is undesirable or inconvenient to drill and tap the pipe for
pressure connections. Flange taps are quite common and are generally used for pipe sizes of
50mm and greater. They are, typically, located 25
25 mm
mm either side of the orifice plate (Figure 5.12).
½” or ¾” NPT
pressure taps
Figure 5.12. Flange taps are located 25 mm
either side of the orifice plate.
Sheet or spiral
wound gaskets
Flange taps are not used for pipe diameters less than 50 mm, as the vena contracta starts to
become close to and, possibly, forward of the downstream tapping point.
Usually, the flanges, incorporating the drilled pressure tappings, are supplied by the
manufacturer. With the taps thus accurately placed by the manufacturer the need to
recalculate the tapping point, when the plate is changed, is eliminated.
Corner taps
Suitable for pipe diameters less than 50 mm, corner taps are an adaptation of the flange tap
(Figure 5.13) in which the tappings are made to each face of the orifice plate. The taps are
located in the corner formed by the pipe wall and the orifice plate on both the upstream and
downstream sides and require the use of special flanges or orifice holding rings.
Figure 5.13. Corner tap is made to each face of the
orifice plate.
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Industrial Flow Measurement
Differential flow meters
5.3.3
Orifice plate sizing
Whilst use can be made of the formulae detailed in the equations to 17, 19 and 20 the modern
practice is to make use of any one of a number of software sizing programs that are available
from a number of sources. Several, are detailed below:
http://www.flowcalcs.com/
http://www.osti.gov/energycitations/prod...
http://www.farrisengineering.com/Product...
http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm
http://www.flowmeterdirectory.com/flowmeter_orifice_calc.html
5.3.4
Orifice plates – general
At the beginning of this chapter it was stated that an important feature of differential type
meters is that flow can be determined directly – without the need for calibration. This is
particularly true for the orifice plate where there is a comprehensive range of standard designs
that require no calibration.
5.3.4.1 Advantages
¾ Simple construction.
¾ Inexpensive.
¾ Robust
¾ Easily fitted between flanges.
¾ No moving parts.
¾ Large range of sizes and opening ratios.
¾ Suitable for most gases and liquids as well as steam.
¾ Price does not increase dramatically with size.
¾ Well understood and proven.
The advantages listed above would normally be listed in most textbooks on the subject of
orifice plates. However, few observations regarding some of these ‘advantages’ are in order.
‘Expensive’ and ‘inexpensive’ are, of course, relative terms. Certainly the primary element,
the orifice plate itself, is relatively inexpensive compared with other flow measuring systems.
However, as shown in Figure 5.14 the orifice plate is only one part of a number of ancillary
components that includes: the flange plate assembly, the isolation valves, the impulse tubing,
the valve manifold, and the differential pressure transmitter.
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Industrial Flow Measurement
Isolation valve
Air vent
Differential flow meters
Orifice plate
tab
Figure 5.14. The orifice plate is only one
of a number of ancillary components that
includes the flange plate assembly, the
isolation valves, the impulse tubing, the
valve manifold, and the differential
pressure transmitter (not shown).
Valve
manifold
Designing, purchasing, installing, and commissioning an orifice plate based flow measuring
system can thus be a far more expensive proposal than first envisaged. In
Well understood and proven often has a negative connotation in that many technically
challenged instrumentation personnel would rather follow well-established instrumentation
solutions even if, as is often the case, they are extremely outdated.
5.3.4.2 Disadvantages
¾ Permanent pressure loss of head is quite high.
¾ Inaccuracy, typically 2 to 3%.
¾ Low turndown ratio, typically from 3 to 4:1.
¾ Accuracy is affected by density, pressure and viscosity fluctuations.
¾ Erosion and physical damage to the restriction affects measurement accuracy.
¾ Viscosity limits measuring range.
¾ Requires straight pipe runs to ensure accuracy is maintained.
¾ Pipeline must be full (typically for liquids).
¾ Output is not linearly related to flowrate.
¾ Multiple potential leakage points
5.3.4.2.1 Straight pipe run requirements
The inaccuracy with orifice type measurement is due mainly to process conditions and
temperature and pressure variations. Ambient conditions and upstream and downstream
piping also affect the accuracy because of changes to the pressure and continuity of flow.
The comparatively low turndown ratio is as a direct result for the need for square root
extraction which severely limits the range over which the instrument can operate.
Standard concentric orifice plate devices should not be used for slurries and dirty fluids, or in
applications where there is a high probability of solids accumulating near the plate. Halfcircle or eccentric bores can be used for these applications. With modern differential pressure
transducers, the rangeability can be substantially improved.
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Industrial Flow Measurement
Differential flow meters
The need for straight runs of piping both before and after the orifice plate flow element is
rarely met – often through ignorance; often through a ‘we’ll probably get away with it’
attitude; but, more often, because of the piping layout was designed well ahead of the
instrumentation requirements.
Without flow-straightening, a typical installation requires from 25 to 40 pipe diameters of
straight run piping before the element and about 4 or 5 pipe diameters downstream of the
element. These requirements vary quite considerably according to the upstream (and
downstream) discontinuities and the beta ratio. Typically:
β ratio of 0.5: 25 pipe diameters upstream and (25 D) and 4 pipe diameters downstream (4D).
β ratio of 0.7: 40 D upstream and 5 D downstream
The requirements for custody transfer applications are considerably more onerous:
The ASME (MFC 3M) requires up to 54 D upstream and 5 D downstream
AGA (Report Number 3) specifies up to 95 D upstream and 4.2 D downstream;
ISO 5167 specifies up to 60 D upstream and 7 D downstream.
The requirements for the API (RP550) are no less rigorous and specify the type of upstream
and downstream disturbance (e.g. valve, elbow, double elbow, etc.) as illustrated in Figures
5.15 and 5.16.
x
β-ratio
5D
x
Throttling valve
Pipeline
diameters
β-ratio
5D
Pipeline
diameters
0.8
20
0.8
50
0.7
14
0.7
39
0.6
10
0.6
31
0.5
8
0.5
25
0.4
7
0.4
22
0.25
6
0.25
19
Figures 5.15. API (RP550) straight-pipe run
lengths for a single upstream and
downstream elbow, for differing beta ratios.
124
Figures 5.16. API (RP550) straight-pipe
run lengths for an upstream valve
and a single downstream elbow.
Industrial Flow Measurement
Differential flow meters
5.3.4.2.2 Multiple leakage points
Figure 5.17 clearly illustrates the potential for multiple leakage points. Whilst many of these
can be eliminated using continuous welded impulse tubing, the risks associated with
blockages are increased.
Figure 5.17. Potential for multiple
leakage points.
5.3.4.2.3 Orifice plate thickness
As the differential pressure across the orifice increases, the plate tends to deform elastically
and, beyond a certain point, the deformation results in a shift in the meter characteristics and
an increase in the measurement uncertainty.
The thickness of an orifice plate should thus be sufficient to ensure that the deflection does
not exceed certain limits. The thickness is generally determined according to the guidelines
given by ISO-5167; ISA-RP-3.2; API-2530; and ASME-MFC-3M.
Theses are shown in Table 5.1.
Line size (DN)
< 150
> 200 < 400
> 450
Thickness in mm
3.18
6.125
9.53
Table 5.1. Orifice plate thickness
according to pipeline size.
In addition the AGA -3 Appendix- 2-F provides guidelines for using high differential for
measurement of natural gas. This maximum limit is dependent upon the thickness, diameter
and beta ratio. For a given line size, there is always a maximum allowable differential
pressure on the plate e.g. for 50 DN pipe, the maximum allowable ΔP is 1000 MPa in 2.5 bar
with minimum thickness of 3.2 mm.
125
Industrial Flow Measurement
5.4
Differential flow meters
Conditioning orifice plate
The ‘Conditioning Orifice Plate’ introduced several years ago by Emerson overcomes the
problem of upstream disturbances that cause swirl in a pipe and create an irregular flow
profile. In a conventional concentric orifice plate (Figure 5.18) these effects are amplified,
allowing the disturbance to impact measurement.
Figure 5.18 (a)conventional concentric orifice plate
and (b) ‘Conditioning Orifice Plate (courtesy
Emerson).
Conventional
Conditioning
The ‘Conditioning Orifice Plate’ is a differential pressure producer that differs from the
conventional orifice plate in using four equally spaced holes (Figure 5.18) that are arranged in
such a fashion as to leave a metal section of the plate in the center of the pipe. This causes the
flow to condition itself as it is forced through the four holes – thus eliminating swirl and
irregular flow profiles and removing the requirement for a flow conditioner.
The consequence of this arrangement is that the straight-run requirements are reduced to only
2 upstream and 2 downstream pipe diameters. Furthermore, the discharge coefficient (Cd) is
reduced to ± 0.5%. A further benefit is that the four-hole design minimizes liquid hold-up, as
compared with a standard orifice plate, without the need for an accuracy-reducing and
plugging-prone vent hole.
The sum of the area of the four bores is equivalent to the area of a bore ‘d’ in the standard
equation:
β = d/D ……………………………....……………………………...….…..(5.21)
for a schedule standard pipe.
The Conditioning Orifice Plate is designed with 2 standard bore sizes, one for high flow rates
and one for low flow rates having bores equal to betas of 0.4 and 0.65.
126
Industrial Flow Measurement
5.5
Differential flow meters
Segmental wedge meter
The segmental wedge element has a V-shaped restriction cast or welded into a flanged meter
body that creates a differential pressure. The restriction is characterized by the h/D ratio
(Figure 5.19), corresponding to the β ratio of an orifice plate, where (h) is the height of the
opening below the restriction (the only critical dimension) and (D) is the inside diameter of
the pipe.
Armoured
.
capillaries
Remote seals
Wedge
element
D
h
Figure 5.19. The segmental wedge element has a V-shaped restriction cast or welded into a
flanged meter body that creates a differential pressure.
The slanting upstream face of the wedge element is insensitive to wear and creates a sweeping
action that has a scouring effect that helps to keep it clean and free of build-up. Further,
because of the wedge does not restrict the bottom of the pipe, it can be used for a variety of
corrosive, erosive, and highly viscous fluids and slurries. The discharge coefficient (Cd) is a
stable for Reynolds numbers of less than 500 – allowing it to be used down to laminar flow
regimes. Further , because the discharge coefficient is highly insensitive to velocity profile
distortion and swirl, only 5 pipe diameters of relaxation piping is required upstream of the
meter for most common combinations of fittings and valves. An uncalibrated element has a
Cd uncertainty of 2 to 5% whilst for a calibrated system is 0.5%. The largest source of
measurement error is generally due to the variations in the density which, if not measured, is
taken as an assumed ‘normal’ value.
A typical segmental wedge meter is provided as a complete assembly combining the wedge
element and the pressure taps into a one-piece unit (Figure 5.20). The upstream and
downstream pressure taps are usually in the form of remote diaphragm seals – eliminating the
need for lead lines.
Figure 5.20. A typical segmental wedge meter is
provided as a complete assembly combining the
wedge element and the pressure taps into a onepiece unit (courtesy PFS Inc.).
Because of its as symmetrical design the primary
segmental wedge can be used to measure
bidirectional flow, but would require two differential
pressure transmitters.
127
Industrial Flow Measurement
5.6
Differential flow meters
V-Cone meter
The V-Cone Flowmeter from McCrometer is a patented technology that features a centrallylocated cone inside the flow tube that interacts with the fluid and creates a region of lower
pressure immediately downstream of the cone.
The pressure difference is measured between the upstream static line pressure tap, placed
slightly upstream of the cone, and the downstream low pressure tap located in the downstream
face of the cone (Figure 5.21).
ΔP transmitter
Upstream tap
Valve manifold
V-cone
Figure 5.21. The pressure
difference is measured between
the upstream static line pressure
tap, placed slightly upstream of
the cone, and the downstream
low pressure tap located in the
downstream face of the cone
(courtesy McCrometer).
Downstream tap
Because the cone is suspended in the center of the pipe, it interacts directly with the “high
velocity core” of the flow – forcing it to mix with the lower velocity flows closer to the pipe
walls. As a consequence, the flow profile is flattened toward the shape of a well-developed
profile – even under extreme conditions, such as single or double elbows out-of-plane
positioned closely upstream of the meter. (Figure 5.22). The V-Cone’s contour shaped cone
also directs the flow without impacting it against an abrupt surface. As a result, the beta edge
of the cone is not subject to wear by dirty fluids.
Changing shape of profile
Figure 5.22. The flow profile is flattened toward the shape of a well-developed profile –
even under extreme conditions, such as single or double elbows out-of-plane positioned
closely upstream of the meter (courtesy McCrometer).
Other major features of the V-Cone Flowmeter include:
¾
¾
¾
¾
0 to 3 diameters straight run piping upstream and 0 to 1 diameters downstream.
primary element accuracy of ±0.5% of reading with a repeatability of ±0.1% or better.
turndown ratio 10:1 with Reynolds numbers as low as 8000.
Suitable for use with dirty fluids
128
Industrial Flow Measurement
5.7
Differential flow meters
Venturi tube meter
The venturi tube (Figure 5.23) has tapered inlet and outlet sections with a central parallel
section, called the throat, where the low pressure tapping is located.
Figure 5.23. The venturi tube has
tapered inlet and outlet sections with
a central parallel section (courtesy
Emerson).
Shallow
Steep
inlet
Throat downstream
section
section
P1
P2
Generally, the inlet section, which provides a
smooth approach to the throat, has a steeper
angle than the downstream section. The
High
Low
shallower angle of the downstream section
pressure tap
pressure tap
reduces the overall permanent pressure loss
by decelerating the flow smoothly and thus minimising turbulence. Consequently, one of the
main advantages of the venturi tube meter over other differential pressure measuring methods
is that its permanent pressure loss is only about 10 % of the differential pressure (Figure 5.4).
At the same time, its relatively stream-lined form allows it to handle about 60 % more flow
than, for example, that of an orifice plate.
The venturi tube also has relatively high accuracy: better than ± 0.75 % over the orifice ratios
(d/D) of 0.3 to 0.75. This order of accuracy, however, can only be obtained as long as the
dimensional accuracy is maintained. Consequently, although the venturi tube can also be
used with fluids carrying a relatively high percentage of entrained solids, it is not well suited
for abrasive media.
Although generally regarded as the best choice of a differential type meter for bores over
1000 mm, the major disadvantage of the venturi type meter is its high cost – about 20 times
more expensive than an orifice plate. In addition, its large and awkward size makes it
difficult to install since a 1 m bore venturi is 4 - 5 m in length.
Although it is possible to shorten the length of the divergent outlet section by up to 35%, thus
reducing the high manufacturing cost without greatly affecting the characteristics, this is at
the expense of an increased pressure loss.
Advantages
¾ Less significant pressure drop across restriction.
¾ Less unrecoverable pressure loss.
¾ Requires less straight pipe up and downstream.
Disadvantages
¾ More expensive.
¾ Bulky – requires large section for installation.
129
Industrial Flow Measurement
5.8
Differential flow meters
Venturi nozzle meters
The venturi nozzle is an adaptation of the standard venturi that makes use of a 'nozzle' shaped
inlet (Figure 5.24), a short throat and a flared downstream expansion section. Whilst
increasing the permanent pressure loss to around 25 % of the measured differential pressure
of the standard venturi, the venturi nozzle is cheaper, requires less space for installation, and
yet still retains the benefits of high accuracy (± 0.75%) and high velocity flow.
Figure 5.24. The
venturi nozzle is an
adaptation of the
standard venturi using
a 'nozzle' shaped inlet.
5.9
Flow nozzle meters
The flow nozzle (Figure 5.25) is used mainly in high velocity applications or where fluids are
being discharged into the atmosphere. It differs from the nozzle venturi in that it retains the
'nozzle' inlet but has no exit section.
Figure 5.25. The flow nozzle is used mainly in
high velocity applications (courtesy Emerson).
The main disadvantage of the flow nozzle is that the permanent pressure loss is increased to
between 30 to 80% of the measured differential pressure – depending on its design.
Offsetting this disadvantage, however, accuracy is only slightly less than for the venturi tube
(± 1 to 1.5 %) and it is usually only half the cost of the standard venturi. In addition it
requires far less space for installation and, because the nozzle can be mounted between
flanges or in a carrier, installation and maintenance are much easier than for the venturi.
130
Industrial Flow Measurement
5.10
Differential flow meters
The Dall tube
Although many variations of low-loss meters have appeared on the market, the best-known
and most commercially successful is the Dall tube (Figure 5.26).
High pressure tap
Low pressure tap
Upstream buttress
Annular gap
Downstream
recovery section
Figure 5 .26. The Dall tube low-loss meter.
The Dall tube is virtually throatless and has a short steep converging cone that starts at a
stepped buttress whose diameter is somewhat less than the pipe diameter. Following an
annular space at the 'throat', there is a diverging cone that again finishes at a step.
A major feature of the Dall tube is the annular space between the 'liner' and tube into which
the flowing media passes to provide an average 'throat' pressure.
With a conventional venturi, upstream and throat tappings are taken at points of parallel flow
where the pressures across a cross section are constant. If the streamlines were curved the
pressure would not be constant over the cross section but would be greater at the convex
surface and less at the concave surface.
In the Dall tube, the upstream tapping is taken immediately before the buttress formed by the
start of the converging cone, where the convex curvature of the streamlines is at a maximum.
At the 'throat', where there is an immediate change from the converging to diverging section,
the 'throat' tapping is thus taken at the point of maximum concave curvature. This means that
a streamlined curvature head is added to the upstream pressure and subtracted from the 'throat'
pressure and the differential pressure is considerably increased. Thus, for a given differential
head the throat can be larger – reducing the head loss.
Because of the annular gap, no breakaway of the liquid from the wall occurs at the throat and
the flow leaves the 'throat' as a diverging jet. Since this jet follows the walls of the diverging
cone, eddy losses are practically eliminated, while friction losses are small because of the
short length of the inlet and outlet sections. The main disadvantages are: high sensitivity to
both Reynolds number and cavitation and manufacturing complexity.
131
Industrial Flow Measurement
5.11
Differential flow meters
Target meter
The target flowmeter is, in effect, an ‘inside out’ orifice plate used to sense fluid momentum.
Sometimes called a drag disc or drag plate, the target meter usually takes the form of a disc
mounted within the line of flowing fluid (Figure 5.27). The flow creates a differential
pressure force across the target and the resultant deflection is transmitted to a flexure tube –
with strain gauge elements mounted external to the flowing medium indicating the degree of
movement.
Strain
gauges
Target
Figure 5.27. The target flowmeter – an ‘inside out’ orifice plate.
The major advantages of the target meter include: ability to cope with highly viscous fluids at
high temperatures (hot tarry and sediment-bearing fluids); free passage of particles or
bubbles; and no pressure tap or lead line problems.
Disadvantages include: limited size availability; limited flow range; and high head loss.
132
Industrial Flow Measurement
5.12
Differential flow meters
Pitot tube
The Pitot tube is one of the oldest devices for measuring velocity and is frequently used to
determine the velocity profile in a pipe by measuring the velocity at various points.
In its simplest form the Pitot tube (Figure 5.28) comprises a small tube inserted into a pipe
with the head bent so that the mouth of the tube faces into the flow. As a result, a small
sample of the flowing medium impinges on the open end of the tube and is brought to rest.
Thus, the kinetic energy of the fluid is transformed into potential energy in the form of a head
pressure (also called stagnation pressure).
Pitot tube
Impact
hole
Figure 5.28. Basic Pitot tube illustrating
principle of operation.
X Mathematically this can be expressed by applying Bernoulli’s equation to a point in the
Static pressure
small tube and a point in the free flow region. From Bernoulli’s general equation:
P1 + ½ρv12 + ρgh1 = P2 + ½ρv22 + ρgh2 …….………………....….….…..(5.22)
we can write:
Ph/ρ + 0 + gh1 = Ps/ρ + v2/2 + gh2
…….………………....…..…..…..(5.23)
where:
Ps = static pressure
Ph = stagnation pressure
v = liquid velocity
g = acceleration due to gravity
h1 and h2 = heads of the liquid at the static and stagnation pressure measuring points
respectively
If h1 = h2 then:
v =
2 ( Ph − Ps )
ρ
…….…….……………....….………..(5.24)
133
Industrial Flow Measurement
Differential flow meters
Because the Pitot tube is an intrusive device and some of the flow is deflected around the
mouth, a compensatory flow coefficient Kp is required. Thus :
v = Kp
2 ΔP
ρ
…….…….……………....….………..(5.25)
For compressible fluids at high velocities (for example, > 100 m/s in air) a modified equation
should be used. W
By measuring the static pressure with a convenient tapping, the flow velocity can be
determined from the difference between the head pressure and the static pressure. This
difference, measured by a differential pressure cell, provides a measurement of flow that, like
a conventional differential pressure measurement, obeys a square root relationship to
pressure. Low flow measurement at the bottom end of the scale is thus difficult to achieve
accurately.
A problem with this basic configuration is that the flow coefficient Kp depends on the tube
design and the location of the static tap. One means of overcoming this problem is to use a
system as shown in Figure 5.29 that makes use of a pair of concentric tubes – the inner tube
measuring the full head pressure and the outer tube using static holes to measure the static
pressure.
Head or
stagnation
pressure
Static
pressure
Figure 5.29. Integrated Pitot tube system in which the inner tube measures the
head pressure and the outer tube uses static holes to measure the static pressure.
Both these designs of Pitot tube measure the point velocity. However it is possible to
calculate the mean velocity by sampling the point velocity at several points within the pipe.
Alternatively, provided a fully developed turbulent profile exists, a rough indication of the
average velocity can be obtained by positioning the tube at a point three-quarters of the way
between the centreline and the pipe wall.
134
Industrial Flow Measurement
5.13
Differential flow meters
Point averaging
Another method of determining the average velocity is with a point averaging Pitot tube
system (Figure 5.30).
Figure 5.30. Multiport ‘Annnubar’
Pitot averaging system (courtesy
Dieterich Standard).
Essentially, this instrument comprises two back-to-back sensing bars, that span the pipe, in
which the up- and down-stream pressures are sensed by a number of critically located holes.
The holes in the upstream detection bar are arranged so that the average pressure is equal to
the value corresponding to the average of the flow profile.
Because the point at which the fluid separates from the sensor varies according to the flow
rate (Figure 5.31) extreme care must be taken in positioning the static pressure sensing holes.
One solution is to locate the static pressure point just before the changing separation point.
Varying point
of separation
Head pressure
sensing port
Areas in which static
pressure adversely
affected
Static pressure
sensing ports
Figure 5.31.
Variation in flow
velocity can affect
point of separation
and the
downstream static
pressure
measurement.
Alternatively, a 'shaped' sensor (Figure 5.32) can be used to establish a fixed point where the
fluid separates from the sensor.
135
Industrial Flow Measurement
Differential flow meters
Fixed separation point
Figure 5.32. ‘Shaped’ bluff body establishes a
fixed separation point (courtesy Dieterich
Standard).
These multi-port averaging devices, commonly called ‘Annubars’ after the first design, are
used mainly in metering flows in large bore pipes – particularly water and steam. Properly
installed, ‘Annubar’ type instruments have a repeatability of 0.1% and an accuracy of 1% of
actual value.
Although intrusive, averaging Pitot type instruments offer a low pressure drop and
application on a wide range of fluids. Because they average the flow profile across the
diameter of the pipe bore, they are less sensitive to the flow profile than, for example, an
orifice plate and can be used as little as 2½ pipe diameters downstream of a discontinuity.
On the negative side, the holes are easily fouled if used on ‘dirty’ fluids.
On a conventional integrated Pitot tube, the alignment can be critical. Misalignment causes
errors in static pressure since a port facing slightly upstream is subject to ‘part’ of the
stagnation or total pressure. A static port facing slightly downstream is subjected to a slightly
reduced pressure.
5.14
Elbow
In applications where cost is a factor and additional pressure loss from an orifice plate is not
permitted, a pipe elbow can be used as a differential pressure primary device. Elbow taps
have an advantage in that most piping systems have elbows that can be used.
If an existing elbow is used then no additional pressure drop occurs and the expense involved
is minimal. They can also be produced in-situ from an existing bend, and are typically
formed by two tappings drilled at an angle of 45o through the bend (Figure 5.33). These
tappings provide the high and low pressure tapping points respectively. Whilst 45o tappings
are more suited to bi-directional flow measurement, tappings at 22.5o can provide more stable
and reliable readings and are less affected by upstream piping.
Ta
pp
in
g
pl
an
e
450
Figure 5.33. Elbow meter geometry
R
D
136
Industrial Flow Measurement
Differential flow meters
A number of factors contribute to the differential pressure that is produced and, subsequently,
it is difficult to predict the exact flow rate accurately. Some of these factors are:
¾
¾
¾
¾
¾
force of the flow onto the outer tapping;
turbulence generated due to cross-axial flow at the bend;
differing velocities between outer and inner radius of flow;
pipe texture; and
relationship between elbow radius and pipe diameter.
Generally, the elbow meter is only suitable for higher velocities and cannot produce an
accuracy of better than 5% . However, on-site calibration can produce more accurate results,
with the added advantage that repeatability is good.
Although the elbow meter is not commonly used, it is underrated since its low cost, together
with its application after completion of pipework, can be a major benefit for low accuracy
flow metering applications.
Suitable applications would include plant air conditioning, cooling water metering, site flow
checkpoints possibly with local indicators and check flow applications, where the cost of
magnetic meters is prohibitive.
For installation, it is recommended that the elbow be installed with 25 pipe diameters of
straight pipe upstream and at least 10 pipe diameters of straight pipe downstream.
5.15
Troubleshooting
One of the most common inaccuracies induced in differential pressure flowmeters is not
allowing enough straight pipe. When the flow material approaches and passes some change
in the pipe, small eddies are formed in the flow stream. These eddies are localised regions of
high velocity and low pressure and can start to form upstream of the change and dissipate
further downstream.
Flowmeter sensors detect these changes in pressure and consequently produce erratic or
inaccurate readings for flow rate.
137
Industrial Flow Measurement
5.16
Differential flow meters
Variable area meters
The variable area flowmeter is a reverse differential pressure meter used to measure the flow
rate of liquids and gases.
5.16.1 Operating principle
The instrument generally comprises a vertical, tapered glass tube and a weighted float whose
diameter is approximately the same as the tube base (Figure 5.34).
Tapered
glass
metering
tube
Fluid flow S
100
90
80
70
Buoyancy A
Scale
60
50
Equilibrium
40
30
Gravity W
Float
Figure
5.34.
Basic
configuration of a variable
area flowmeter (courtesy
Brooks Instrument).
20
10
0
In operation, the fluid or gas flows through the inverted conical tube from the bottom to the
top, carrying the float upwards. Since the diameter of the tube increases in the upward
direction the float rises to a point where the upward force on the float created by differential
pressure across the annular gap, between the float and the tube, equals the weight of the float.
As shown in Figure 5.34, the three forces acting on the float are:
¾ constant gravitational force W;
¾ buoyancy A that, according to Archimedes’ principle, is constant if the fluid density is
constant; and
¾ force S, the upward force of the fluid flowing past the float.
For a given instrument, when the float is stationary, W and A are constant and S must also be
constant. In a position of equilibrium (floating state) the sum of forces S + A is opposite and
equal to W and the float position corresponds to a particular flow rate that can be read off a
scale. A major advantage of the variable area flowmeter is that the flow rate is directly
proportional to the orifice area that, in turn, can be made to be linearly proportional to the
vertical displacement of the float. Thus, unlike most differential pressure systems, it is
unnecessary to carry out square root extraction.
The taper can be ground to give special desirable characteristics such as an offset of higher
resolution at low flows.
138
Industrial Flow Measurement
Differential flow meters
X In a typical variable area flowmeter, the flow q can be shown to be approximately given
by:
q=C A ρ
where:
q
C
A
ρ
=
=
=
=
…….…….……………....….………..(5.26)
flow
constant that depends mainly on the float
cross-sectional area available for fluid flow past the float
density of the fluid
Indicated flow, therefore, depends on the density of the fluid which, in the case of gases,
varies strongly with the temperature, pressure and composition of the gas.
It is possible to extend the range of variable area flowmeters by combining an orifice plate in
parallel with the flow meter.W
5.16.2 Floats
A wide variety of float materials, weights, and configurations is available to meet specific
applications.
The float material is largely determined by the medium and the flow range and includes:
stainless steel, titanium, aluminium, black glass, synthetic sapphire, polypropylene, Teflon,
PVC, hard rubber, Monel, nickel and Hastelloy C.
5.16.3 Float centring methods
An important requirement for accurate metering is that the float is exactly centred in
the metering tube. One of three methods is usually applied:
1. Slots in the float head cause the float to rotate and centre itself and prevent it sticking
to the walls of the tube (Figure 5.35). This arrangement led to the term 'Rotameter', a
registered trademark of KDG Instruments Ltd, being applied to variable area flow
meters. Slots cannot be applied to all float shapes and, further,
can cause the indicated flow to become slightly viscosity
dependent.
Slots in
head
Top view
Figure 5.35. Float centring in which a slotted float head
rotates and automatically centres itself.
Side view
139
Industrial Flow Measurement
Differential flow meters
2. Three moulded ribs within the metering tube cone (Figure 5.36), parallel to the tube
axis, guide the float and keep it centred. This principle allows a variety of float shapes
to be used and the metering edge remains visible even when metering opaque fluids.
Internal rib
Float
Conical
tube
Figure 5.36. Float centring in which the float is
centred by three moulded ribs parallel to the tube axis.
3.
Conical
tube
Internal rib
Float
A fixed centre guide rod within the metering tube (Figure 5.37 (a)) is used to guide the float
and keep it centred. Alternatively, the rod may be attached to the float and moved within
fixed guides (Figure 5.37 (b )). The use of guide rods is confined mainly to applications
where the fluid stream is subject to pulsations likely to cause the float to ‘chatter’ and
possibly, in extreme cases, break the tube. It is also used extensively in metal metering tubes.
Fixed guide
Guide rod
attached to float
Figure 5.37. Float is centred by (a) fixed
centre guide rod; or (b) guide rod attached to
the float (courtesy Bailey-Fischer & Porter).
Float moves up
and down on
guide rod
Fixed guide rod
Fixed guide
(a)
(b)
140
Industrial Flow Measurement
Differential flow meters
5.16.4 Float shapes
The design of the floats is confined to four basic shapes (Figure 5.38):
¾
¾
¾
¾
ball float;
rotating (viscosity non-immune) float;
viscosity immune float; and
float for low pressure losses.
(a)
(b)
(c)
(d)
Figure 5.38. (a) ball float; (b) rotating (viscosity non-immune) float; (c) viscosity
immune float; and (d) float for low pressure losses (courtesy Bailey-Fischer & Porter).
Indicated flow
Ball float
The ball float (Figure 5.38 (a)) is mainly used as a metering element for small flowmeters –
with its weight determined by selecting from a variety of materials. Figure 5.39 shows the
effect of viscosity on the flow rate indication. Since its shape cannot be changed, the flow
coefficient is clearly defined (1) and, as shown, exhibits virtually no linear region. Thus, any
change in viscosity, due often to small changes in temperature, results in changes in
indication.
3
Figure 5.39. Viscosity effect for various float
shapes(courtesy Bailey-Fischer & Porter).
2
1
1. Ball float
2. Rotating float
3. Viscosity immune float
Viscosity
141
Industrial Flow Measurement
Differential flow meters
Rotating float
Rotating floats (Figure 5.38 (b)) are used in larger sized meters and are characterised by a
relatively narrow linear (viscosity-immune) region as shown in Figure 5.39 (2).
Viscosity immune float
The viscosity immune float (Figure 5.38 (c)) is appreciably less sensitive to changes in
viscosity and is characterised by a wider linear region as shown in Figure 5.39 (3). Although
such an instrument is unaffected by relatively large changes in viscosity, the same size meter
has a span 25% smaller than the previously described rotating float.
Low pressure loss float
For gas flow rate metering, light floats (Figure 5.38 (d)) with relatively low pressure drops
can be used.
The pressure drop across the instrument is due, primarily, to the float since the energy
required to produce the metering effect is derived from the pressure drop of the flowing fluid.
This pressure drop is independent of the float height and is constant.
Further pressure drop is due to the meter fittings (connection and mounting devices) and
increases with the square of the flow rate. For this reason, the design requires a minimum
upstream pressure.
5.16.5 Metering tube
The meter tube is normally manufactured from borosilicate glass that is suitable for metering
process medium temperatures up to 200 °C and pressures up to about 2 - 3 MPa.
Because the glass tube is vulnerable to damage from thermal shocks and pressure hammering,
it is often necessary to provide a protective shield around the tube.
Variable area meters are inherently self-cleaning since the fluid flow between the tube wall
and the float provides a scouring action that discourages the build-up of foreign matter.
Nonetheless, if the fluid is dirty, the tube can become coated – affecting calibration and
preventing the scale from being read. This effect can be minimised through the use of an inline filter.
In some applications use can be made of an opaque tube used in conjunction with a float
follower. Such tubes can be made from steel, stainless steel, or plastic.
By using a float with a built-in permanent magnet, externally mounted reed-relays can be
used to detect upper and lower flow limits and initiate the appropriate action.
The temperature and pressure range may be considerably extended (for example up to 400 °C
and 70 MPa) through the use of a stainless steel metering tube. Again, the float can
incorporate a built-in permanent magnet that is coupled to an external field sensor that
provides a flow reading on a meter.
142
Industrial Flow Measurement
Differential flow meters
In cases where the fluid might contain ferromagnetic particles that could adhere to the
magnetic float, a magnetic filter should be installed upstream of the flowmeter. Typically
(Figure 5.40) such a filter contains bar magnets, coated with PTFE as protection against
corrosion, arranged in a helical fashion.
Figure 5.40. Typical magnetic filter (courtesy Krohne).
5.16.6 Conclusion
Generally, variable area flowmeters have uncertainties ranging from 1 to 3% of full scale.
Precision instruments are, however, available with uncertainties down to 0.4% of full scale
The variable area meter is an exceptionally practical flow measurement device. Its
advantages include:
¾
¾
¾
¾
¾
¾
¾
¾
¾
wide range of applications;
linear float response to flow rate change;
10 to 1 flow range or tumdown ratio;
easy sizing or conversion from one particular service to another;
ease of installation and maintenance;
simplicity;
low cost;
high low-flow accuracy (down to 5 cm3/ min); and
easy visualisation of flow
Its disadvantages are:
¾
¾
¾
¾
¾
¾
¾
limited accuracy;
susceptibility to changes in temperature, density and viscosity;
fluid must be clean, no solids content;
erosion of device (wear and tear);
can be expensive for large diameters;
operates in vertical position only; and
accessories required for data transmission.
143
Industrial Flow Measurement
5.17
Differential flow meters
Differential pressure transmitters
In modern process control systems, measurement of differential pressure is normally carried
out by a differential pressure transmitter whose role is to measure the differential pressure and
convert it to an electrical signal that can be transmitted from the field to the control room or
the process controlling system.
As illustrated in Figure 5.41, most industrial differential cells make use of isolation
diaphragms that isolate the transmitter. Movement of the isolation diaphragms is transmitted
via the isolating fluid (for example, silicon fluid) to the measuring diaphragm whose
deflection is a measure of the differential pressure.
Leads
Fixed electrodes
Seal diaphragm
Measuring diaphragm
(moving electrode)
P2
P1
Fill liquid
Ceramic insulator
Low pressure side
Low pressure side
Floating diaphragm
Figure 5.41. Basic construction of a floating cell capacitive differential pressure
sensor in which movement of the isolation diaphragms is transmitted via the
isolating fluid (for example, silicon fluid) to the measuring diaphragm whose
deflection is a measure of the differential pressure (courtesy Fuji Electric).
Measurement of the deflection of the measuring diaphragm may be carried out by a number
of methods including inductance, strain gauge, and piezoelectric. However, the most popular
method of measuring differential pressure, adopted by a large number of manufacturers, is the
variable capacitance transmitter.
As shown, the upstream and downstream pressures are applied to isolation diaphragms on the
high and low pressure sides, which are transmitted to the sensing diaphragm, which forms a
movable electrode. As the electrode changes its distance from the fixed plate electrodes, this
results in a change in capacitance.
144
Industrial Flow Measurement
Differential flow meters
Capacitance based transmitters are simple, reliable, accurate (typically 0.1% or better), small
in size and weight, and remain stable over a wide temperature range. The main advantage of
the capacitive transmitter is that it is extremely sensitive to small changes in pressure – down
to 100 Pa pressure.
Other manufacturers (including Honeywell) make extensive use of the piezoresistive
element, in which piezoresistors are diffused into the surface of a thin circular wafer of Ntype silicon and the diaphragm is formed by chemically etching a circular cavity – with the
unetched portion forming a rigid boundary and surface. Such silicon-on-insulator devices are
now capable of providing continuous operation at temperatures up to 225 ºC at pressures of
up to 7 MPa.
5.17.1 Multivariable transmitters
X At the beginning of this chapter it was shown that the differential pressure can be related
to flow by the expression:
Q = k Cd
where:
ΔP
ρ
…….…….……………....….………..(5.27)
Q = flow rate
k = constant
Cd = discharge coefficient
ΔP = differential pressure (P1 - P2)
ρ = density of fluid
In practice this expression is painfully inadequate ⎯ especially in applications involving, for
example, the mass flow of steam.
The most commonly used expression (AIME) for mass flow of liquids, gases and steam is:
Qm = N Cd Ev Y1 d 2 ΔP ρ
…….…….……………....….………..(5.28)
where:
Qm
N
Cd
Ev
Y1
d
DP
ρ
=
=
=
=
=
=
=
=
mass flow rate
units factor
discharge coefficient
velocity of approach factor
gas expansion factor (= 1 for liquid);
bore diameter
differential pressure; and
density of fluid.
Using this equation, the traditional approach has been to make use of three separate
transmitters to measure differential pressure, static pressure and temperature to infer the mass
145
Industrial Flow Measurement
Differential flow meters
flow. As shown in Figure 5.42 the density of a gas may be deduced from the measurement of
static pressure and temperature combined with the entry of certain known constants: i.e. the
compression factor, gas constant, molecular weight, and fluid constant.W
Isentropic exponent
Pressure
DP
Beta Ratio
Temperature
Gas Expansion Factor
Orifice bore
Units conversion factor
Qmass = N Cd Ev Y 1 d2
Discharge Coefficient
Beta Ratio
Pipe ID
Orifice Bore
Temperature
Velocity of Approach Factor
Beta Ratio
Temperature
Reynolds Number
Pipe ID
Velocity
Viscosity
Density
DP ρ
DP
Temperature
Data Entered
DP
Density
Compress. Factor
Gas Constant
Molecular Weight
Fluid Constants
Pressure
Temperature
Measured
Compress. Factor
Gas Constant
Pressure
Calculated
Figure 5.42. Computation of fully compensated mass flow requires the
measurement of DP, static pressure and temperature (courtesy Emerson).
In recent years both Honeywell and Emerson have developed a single transmitter solution that
makes simultaneous measurement of differential pressure, static pressure and temperature and
provides the on-board computation.
Apart from providing tremendous cost savings in purchase price as well as installation, such
multivariable transmitters provide accurate mass flow measurements of process gases
(combustion air and fuel gases) and steam, whether saturated or superheated. Other
applications include: DP measurement across filters and in distillation columns where the user
is concerned with the static pressure and temperature measurements to infer composition; and
in liquid flowrate applications where density and viscosity compensation is required due to
large temperature changes.
5.17.2 Special transmitters
Continued emphasis on safely shut-down systems in the petrochemical industries has lead to
the development of a new ‘Critical’ high availability transmitter from Moore which provides
complete hardware and software redundancy; comprehensive self testing and primary and
secondary current sources to ensure safe fault indication. These capabilities allow a single
‘Critical’ transmitter to be installed where two conventional transmitters are usually installed
on a critical application or two ‘Critical’ transmitters to be installed where three conventional
transmitters are required in a safety shutdown system.
146
Industrial Flow Measurement
Electromagnetic Flowmeters
Chapter 6. Electromagnetic Flowmeters
Industrial Flow
Measurement
147
Industrial Flow Measurement
Electromagnetic Flowmeters
148
Industrial Flow Measurement
Electromagnetic Flowmeters
Chapter 6
Electromagnetic Flowmeters
6.1
Introduction
Electromagnetic flowmeters, also known as ‘Magflows’ or ‘Magmeters’, have now been in
widespread use throughout industry for more than 40 years and were the first of modern
meters to exhibit no moving parts and zero pressure drop.
6.2
Measuring principle
The principle of the EM flowmeter is based on Faraday's law of induction that states that if a
conductor is moved through a magnetic field a voltage will be induced in it that is
proportional to the velocity of the conductor.
X
Referring to Figure 6.1, if the conductor of length (l) is moved through the magnetic field
having a magnetic flux density (B) at a velocity (v), then a voltage will be induced where:
e = B.l.v ..……………………………………………………………….(6.1)
and:
e
B
l
v
=
=
=
=
induced voltage (V);
magnetic flux density (Wb/m2);
length of conductor (m); and
velocity of conductor (m/s).
B
e
l
Figure 6.1. Illustration of
Faraday’s Law of
electromagnetic induction.
v
In the electromagnetic flowmeter (Figure 6.2) a magnetic field is produced across a
cross-section of the pipe – with the conductive liquid forming the conductor (Figure 6.3).
Two sensing electrodes, set at right angles to the magnetic field, are used to detect the voltage
that is generated across the flowing liquid and which is directly proportional to the flow rate
of the media.
149
Industrial Flow Measurement
Electromagnetic Flowmeters
B
Amplifier
Insulated
pipe
Sensing
electrode
l
Magnetic
field
Conductive
liquid
e
Sensing
electrode
Figure 6.2. Basic principle of
electromagnetic flowmeter.
Figure 6.3. The conductive liquid forms the
conductor in contact with the electrodes.
X It can thus be seen that since v is the flow rate (the parameter to be measured) the
generated voltage is limited by the length of the conductor (the diameter of the pipe) and the
flux density. In turn, the flux density is given by:
B = μ. H
where:
μ = permeability; and
H = magnetising field strength (ampere-turns/m).
Because the permeability of the magnetic circuit is largely determined by the physical
constraints of the pipe (the iron-liquid gap combination), the magnetic flux density B (and
hence the induced voltage) can only be maximised by increasing H – a function of the coil
(number of windings and its length) and the magnetising current.W
6.3
Construction
Because the working principle of the electromagnetic flowmeter is based on the movement of
the conductor (the flowing liquid) through the magnetic field, it is important that the pipe
carrying the medium (the metering tube) should have no influence on the field. Consequently,
in order to prevent short circuiting of the magnetic field, the metering tube must be
manufactured from a non-ferromagnetic material such as stainless steel or Nickel-Chromium.
It is equally important that the signal voltage detected by the two sensing electrodes is not
electrically short circuited through the tube wall. Consequently, the metering tube must be
lined with an insulating material. Such materials have to be selected according to the
application and their resistance to chemical corrosion, abrasion, pressure and temperature
(Table 6.1).
150
Industrial Flow Measurement
Electromagnetic Flowmeters
Table 6.1. Commonly used magnetic flowmeter liner materials
Material
General
Corrosion Abrasion Temperatur Pressure limit
resistance resistance e limit (°C)
(bar)
Excellent Fair
180
40
Teflon PTFE Warm deformable resin
with
excellent ant-stick
properties and suitable for
food and beverage
Teflon PFA Melt-processable resin with Excellent
better shape accuracy,
abrasion resistance and
vacuum strength than PTFE
Polyurethane Extreme resistance to wear Wide
and erosion but not suitable range
for strong acids or bases
Neoprene
Combines some of the
Wide
resistance to chemical attack range
of PTFE with a good degree
of abrasion resistance
Hard rubber Inexpensive – finds its main Fair to
(Ebonite)
application in the water and excellent
waste water industries
Soft rubber Mainly used for slurries
Fair
Modified
Developed for harsh
Very high
phenolic
environments containing
H2S/CO2 concentrations and
acids
Fused
Highly recommended for
Excellent
aluminium very abrasive and/or
oxide
corrosive applications.
Good
180
40
Excellent 50
250
Good to
excellent
80
100
Fair
95
250
Excellent 70
Good
200
64
Yield strength
of pipe
Excellent 180
40
Teflon PTFE
A warm deformable resin, Teflon PTFE is the most widely used liner material.
Characteristics include:
¾ very high temperature capability (180°C)
¾ excellent anti-stick characteristics reduce build-up
¾ inert to a wide range of acids and bases
¾ approved in food and beverage applications.
Teflon PFA
Teflon PFA is a melt-processable resin that offers:
¾ a better shape accuracy than PTFE;
¾ better abrasion resistance, since there are no bulges or deformations;
¾ better vacuum strength because of the ability to incorporate stainless steel reinforcement.
151
Industrial Flow Measurement
Electromagnetic Flowmeters
Polyurethane
Generally, Teflon PTFE/PFA does not have adequate erosion resistance for some applications
and, often, the best choice when extreme resistance to wear and erosion is required is
polyurethane. Other characteristics include:
¾ cannot be used with strong acids or bases
¾ cannot be used at high temperatures since its maximum process temperature is 40 °C.
Neoprene
¾ resistant to chemical attack
¾ good degree of abrasion resistance
¾ temperature of 80 °C.
Hard rubber
¾ inexpensive general purpose liner
¾ wide range of corrosion resistance
¾ main application in the water and waste water industries
Soft rubber
¾ relatively inexpensive
¾ high resistance to abrasion
¾ main application in slurries.
Modified phenolic
Developed by Turbo Messtechnik for harsh environments containing H2S/CO2 concentrations
and acids, this is a powder based line with high-resistant fillers and organic pigments. It is
suitable for high temperatures (200 °C) and high pressures.
Fused aluminium oxide
¾ highly recommended for very abrasive and/or corrosive applications
¾ high temperatures up to 180°C.
¾ used extensively in the chemical industry
6.4
Electrodes
The electrodes, like the liners, are in direct contact with the process medium and again the
materials of construction must be selected according to the application and their resistance to
chemical corrosion, abrasion, pressure and temperature. Commonly used materials include:
316 stainless steel, platinum/rhodium, Hastelloy C, Monel, and tantalum.
One of the main concerns is the need to ensure that there is no leakage of the process medium.
In the construction design shown in Figure 6.4, the electrode seal is maintained through the
use of five separate sealing surfaces and a coil spring. However, to ensure that the overall
integrity of the system is maintained, even if a process leak should occur past the liner/
electrode interface, the electrode compartment can also be separately sealed. Usually rated
for full line pressure, such containment ensures that in the event of a leak, no contamination
of the field coils occurs.
152
Industrial Flow Measurement
Electromagnetic Flowmeters
Figure 6.4. The electrode seal is
maintained through the use of
five separate sealing surfaces
and a coil spring (courtesy
Emerson).
Where heavy abrasion or contamination of the electrodes might occur, many manufacturers
offer the option of field replaceable electrodes (Figure 6.5).
SST tube
Tensioning washer
O-ring seal
Flowtube
liner
Field
replaceable
electrode
Electrode
housing
Nut
Insulator
Figure 6.5. Field replaceable electrode (courtesy Emerson).
Fouling of the electrodes by insulating deposits can considerably increase the internal
resistance of the signal circuit – changing the capacitive coupling between the field coils and
signal circuitry.
153
Industrial Flow Measurement
6.5
Electromagnetic Flowmeters
Conductivity
X The two main characteristics of the process medium that need to be considered are its
conductivity and its tendency to coat the electrode with an insulating layer. As shown in
Figure 6.6; to develop most of the electrode potential (e) across the input impedance (Ri) of
the meter amplifier, and to minimise the effect of impedance variations due to changes in
temperature, then Ri needs to be at least 1000 times higher than the maximum electrode
impedance Rs.
i
Figure 6.6. To develop most
of the electrode potential (e)
across the input impedance
(Ri) of the meter amplifier
the Ri needs to be at least
1000 times higher than the
maximum
electrode
impedance Rs.
Rs
Ri
V
e Magnetic
flowmeter
Modern high input impedance amplifiers are available in the range 1013 to 1014 Ω.
Consequently, with an amplifier having, for example, an input impedance of 1013 Ω, the error
due to impedance matching is less than 0.01% and a change in electrode impedance from 1 to
1000 MΩ will effect the voltage by only 0.001%.
The electrode impedance depends on fluid conductivity and varies with the size of the
metering tube. In older a.c. driven instruments the minimum conductivity of the fluid usually
lay between 5 - 20 μS/cm. For d.c. field instruments the minimum conductivity was about 1
μS/cm. However modern instruments employ a variety of technologies, including
capacitively coupled meters that can be used on liquids with conductivity levels down to 0.05
µS/cm. W
In some applications, coating of the electrodes is cause for concern and, over the years, a
number of solutions have been offered including a mechanical scraper assembly and
ultrasonic cleaning.
A solution offered by Turbo Messtechnik employs electrolytic electrode cleaning. If one or
more of the electrodes becomes isolated by gaseous slugs, sticky media or encrustation
(Figure 6.7 (a)), the instrument detects the abnormally low conductivity and applies 60 V a.c.
voltage across the electrodes. After approximately 1 minute the electrolytic action starts to
form microporous paths through the isolating ‘barrier’ (Figure 6.7 (b)). As these paths
become progressively larger, the isolating barrier starts to break away from the electrode
(Figure 6.7 (c))to re-establish contact with the process media. Normally a 2½ minute cycle is
sufficient for normal flow sensing.
154
Industrial Flow Measurement
Electrode
(a)
Electromagnetic Flowmeters
Sticky media or
encrustation
Figure 6.7. If the electrode is isolated by
encrustation (a) a 60 V a.c. voltage is applied
across the electrodes and electrolytic action
starts to form microporous paths through the
isolating 'barrier' (b). As these paths become
progressively larger, the isolating barrier
starts to break away from the electrode (c)
(courtesy Turbo Messtechnik).
Microporous paths
(b)
Localised paths
(c)
Most refinery products, and some organic products, have insufficient conductivity to allow
them to be metered using electromagnetic flowmeters (Table 6.2).
Table 6.2. Conductivities of some typical fluids.
Liquid
Carbon tetrachloride at 18°C
Toluene
Kerosene
Analine at 25°C
Soya bean oil
Distilled water
Acetone at 25°C
Phosphorous
Benzole alcohol at 25 °C
Acetic acid (1% solution)
Acetic acid (10% solution)
Latex at 25°C
Sodium silicate
Sulphuric acid (90% solution
Ammonium nitrate (10% solution)
Sodium hydroxide (10% solution)
Hydrochloric acid (10% solution)
Conductivity (μS/cm)
4 x 10–12
10-8
0.017
0.024
0.04
0.04
0.06
0.4
1.8
5.8 x 102
16 x 102
5 x 103
24 x 103
10.75 x 104
11 x 104
31 x 104
63 x 104
It should be noted that the conductivity of liquids can vary with temperature and care should
be taken to ensure the performance of the liquid in marginal conductivity applications is not
affected by the operating temperatures. Most liquids have a positive temperature coefficient
of conductivity. However negative coefficients are possible in a few liquids.
155
Industrial Flow Measurement
6.6
Electromagnetic Flowmeters
Capacitive coupled electrodes
The foregoing solutions do not solve the problem of 'electrode coating' in which an insulating
deposit effectively isolates the electrodes. These insulating deposits are often found in the
paper manufacturing industry and in sewage treatment applications where grease and protein
conglomerates can develop into thick insulating layers.
In the capacitive coupled flowmeter developed by Bailey-Fisher & Porter (Figure 6.8) the
electrodes, which are normally wetted by the process liquid, have been replaced by capacitive
plates buried in the liner as one of the plates; the meter lining acts as the dielectric; and the
second capacitive plate is formed by the metallic electrode that is embedded in the tube liner.
Spool body
Electrode screen
Figure 6.8. The electrodes have been a replaced by
capacitive plates buried in the liner.
Electrode
Insulating
liner
In an alternative solution offered by Krohne, the electrodes take the form of two large plates
bonded to the outside of a ceramic flowtube (Figure 6.9) – with the preamplifer mounted
directly on the flow tube. Capable of use with liquids with conductivity levels down to 0.05
µS/cm the capacitive coupled magnetic flow meter features: no gaps or crevices, no risk of
electrode damage due to abrasion; no leakage; and no electrochemical effects.
Capacitive electrode
Shielding
Routes and pads for
pre-amplifier
Figure 6.9. Capacitive electrodes formed by
two large plates bonded to the outside of a
ceramic flow tube (courtesy Krohne).
w
Flo
Ceramic flowtube
156
Industrial Flow Measurement
6.7
Electromagnetic Flowmeters
Field characterisation
X The purpose of a flowmeter is to measure the true average velocity across the section of
pipe, so that this can be related directly to the total volumetric quantity in a unit of time. The
voltage generated at the electrodes is the summation of the incremental voltages generated by
each elemental volume of cross-section of the flowing fluid as it crosses the electrode plane
with differing relative velocities.
Initially, designs assumed the magnetic field to be homogeneous over the measured crosssection and length of the pipe in order to achieve precise flow measurement. However, early
investigators showed that, for a given velocity, the medium does not generate the same
voltage signal in the electrodes at all points. Thus, for a given velocity (v) the medium
flowing at position A1 (Figure 6.10) does not generate the same voltage signal as that flowing
in position A2.
A2, v
A1, v
Figure 6.10. For a given velocity (v) the
medium flowing at position A1 does not
generate the same voltage signal as that
flowing position A2 (Courtesy Endress +
Hauser).
Rummel and Ketelsen plotted the medium flowing at various distances away from the
measuring electrodes (Figure 6.11) and showed how these contribute in different ways
towards the creation of the measuring signal. This shows that a flow profile that concentrates
velocity in the area of one electrode will produce eight times the output of that at the pipe
centre – leading to errors that cannot be overlooked.
0,65
0,85
Figure 6.11. Weighting factor distribution in
electrode plane (Rummel and Ketelsen).
8,0
5,0
2,0 1,2
1,0 1,2 2,0 5,0
0,85
0,65
0,5
157
8,0
Industrial Flow Measurement
Electromagnetic Flowmeters
One solution to this problem is to use a non- homogeneous field that compensates for
these non-linear concentrations.
Subsequent to his research, Ketelsen designed a magnetic flowmeter making use of a
‘characterised field’. As distinct from the homogeneous field in which the magnetic
flux density (B) is constant over the entire plane (Figure 6.12 (a)), the ‘characterised
field’ is marked by an increase in B in the x-direction and a decrease in the ydirection (Figure 6.12 (b)).
Because commercial exploitation of this design is limited in terms of a patent in the
name of B. Ketelsen, assigned to Fischer & Porter GmbH, a ‘modified field’ has
been developed in which the lines of magnetic flux, at any place in the electrodeplane, are characterised by an increase in B in the x-direction, from the centre to the
wall, but is constant in the y-direction (Figure 6.12 (c)). This ‘modified field’ is,
therefore, a compromise between the ‘characterised field’ and the ‘homogeneous
field’.
B (X)
X
B (Y)
X
B (X)
B (Y)
B (Y)
Y
Y
Y
(b)
(a)
W
6.8
X
B (X)
(c)
Figure 6.12. The three most common forms of magnetic fields: (a) the
homogeneous field in which B is constant over the entire plane (b) a
‘characterised field’ in which B increases in the x-direction but decreases in the
y-direction; and (c) the modified field in which B increases in the x-direction
but is constant in the y-direction.
Measurement in partially filled pipes
A fundamental requirement for accurate volumetric flow measurement is that the pipe should
be full. Given a constant velocity then, as the fill level decreases, the induced potential at the
electrodes is still proportional to the media velocity. However, since the cross sectional area
of the media is unknown it is impossible to calculate the volumetric flow rate.
In the water utility industry where large bore flowmeters are used and the hydraulic force is
based on gravity, the occurrence of a partially filled pipe, due to low flow, is quite frequent.
Although installing the flowmeter at the lowest point of the pipeline in an invert or U-section
(Figure 6.13) will combat this problem, there are still many situations where even the best
engineering cannot guarantee a full pipe – thus giving rise to incorrect volume readings.
158
Industrial Flow Measurement
Electromagnetic Flowmeters
(a)
(b)
Figure 6.13. Flowmeter installed in (a) an invert or (b) a U-section
can often ensure that the meter remains full when the media pipe
is only partially full (Courtesy ABB).
One answer to this problem would be to actually determine the cross-sectional area and thus
calculate the volumetric flow.
In the solution offered by ABB in their Parti-MAG, two additional electrode pairs are located
in the lower half of the meter to cater for partial flowrate measurements down to 10%. In
addition, the magnetic field is switched successively from a series to a reverse coil excitation.
The series excitation mode (Figure 6.14) corresponds to the excitation mode for a
conventional meter. As a result of this field, a voltage is induced in the electrode pairs that is
related to the media velocity.
E1
E1
E2
E2
E3
E3
159
Figure 6. 14. The series
excitation
mode
corresponds
to
the
excitation mode for a
conventional
meter
(Courtesy of ABB).
Industrial Flow Measurement
Electromagnetic Flowmeters
In the reverse excitation mode (Figure 6. 15) the induced voltages in the upper and lower
halves of the meter are of equal magnitude but opposite sign. Thus, in a full pipe the potential
would be zero at the electrode pair E1 and some definite value at the electrode pairs E2 and
E3. As the level falls, the signal contribution from the upper half decreases while that from
the lower half remains the same – resulting in a change in the potential at the various
electrode pairs that can be related directly to the change in media level. Microprocessor
technology is then used to compute the cross-sectional area and thus the volumetric flow.
E1
E1
E2
E2
E3
Figure 6.15.
In the reverse
excitation mode the induced
voltages in the upper and lower
halves of the meter are of equal
magnitude but opposite sign
(Courtesy of ABB).
E3
A slightly different scheme is used in Krohne’s TIDALFLUX meter. This instrument
combines an electromagnetic flowmeter with an independent capacitive level measuring
system.
The electromagnetic flow measuring section functions like a conventional electromagnetic
flowmeter, using a single set of electrodes that are placed near the bottom of the pipe as
shown in Figure 6.16. In this manner, even when the filling level falls to less than 10% of
the pipe diameter, the electrodes are still covered and capable of providing a flow velocityrelated output.
Figure 6.16. The two sensing electrodes are
positioned so that the electrodes are still covered
when the filling level falls to less than 10% of
the pipe diameter (Courtesy Krohne).
D
0,1D
160
Industrial Flow Measurement
Electromagnetic Flowmeters
The level measuring section makes use of a system of insulated transmission and detection
plates embedded in the flowmeter liner (Figure 6.17) in which the change in capacitive
coupling is proportional to the wetted cross-section.
Figure 6.17. The level measuring
section makes use of insulated
transmission and detection plates
embedded
in the flowmeter
(Courtesy Krohne).
Detection
plate
Transmission
plates
Using these two measured values it is now possible to compute the actual volumetric flow
(Figure 6.18) from:
Q = v.A ..…………………………………………………………...(6.2)
where:
Q = volumetric flow
v = velocity-related signal
A = wetted cross-sectional area.
Figure 6.18. The volumetric
flow is computed using the
two measured values of
velocity and cross-sectional
area (Courtesy Krohne).
Q = V. A
(V) Velocity
(A) Cross
sectional area
161
Industrial Flow Measurement
6.9
Electromagnetic Flowmeters
Empty pipe detection
In many cases, measurement of partially filled pipes in not required. Nonetheless, in order to
draw attention to this situation, many meters incorporate an `Empty Pipe Detection’ option.
In the most common system (Figure 6.19), a conductivity probe, mounted on top of the pipe,
senses the presence of the conductive medium. If the medium clears the sensor, due to partial
filling of the pipe, the conductivity falls and an alarm is generated.
Conductivity switch
To alarm
Conductivity sensor
electrically isolated
from pipe
Figure 6.19. Conductivity probe for
empty pipe detection.
Process pipe
An alternative scheme is to use a high frequency current generator across the flowmeter
sensing probes. Because normal flow measurement uses relatively low frequencies, the high
frequency signal used to measure the conductivity is ignored by the flow signal amplifier.
`Empty Pipe Detection’ is not only used to indicate that the volume reading is incorrect. For
example, in a two-line standby system, one line handles the process and the other line is used
for standby. Since the standby line does not contain any of the process medium, the
flowmeter sensing electrodes are `open circuit’ and the amplifier output signal will be subject
to random drifting. The resultant falsely generated inputs to any process controllers,
recorders, etc, connected to the system will give rise to false status alarms. Here, the `Empty
Pipe Detection’ system is used to ‘freeze’ the signal to reference zero.
Another application for `Empty Pipe Detection’ is to prevent damage to the field coils.
Magnetic flowmeters based on a `pulsed d.c.’ magnetic field, generate relatively low power to
the field coils – typically between 14 and 20 VA. This is usually of little concern regarding
heat generation in the field coils. However, flow sensors based on an `a.c generated’
magnetic fields, consume power in excess of a few hundred VA. In order to absorb the heat
generated in the field coils, a medium is required in the pipe to keep the temperature well
within the capability of the field coil insulation. An empty pipe will cause overheating and
permanent damage to the field coils and, consequently, this type of flowmeter requires an
`Empty Pipe Detection’ system to shut down the power to the field coils.
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Industrial Flow Measurement
6.10
Electromagnetic Flowmeters
Field excitation
The metallic electrodes in contact with the flowing liquid form a galvanic element that creates
an interfering electrochemical d.c. voltage. This voltage is dependent on the temperature, the
flow rate, the pressure and the chemical composition of the liquid as well as on the surface
condition of the electrodes. In practice, the voltage between the liquid and each electrode will
be different – giving rise to an unbalanced voltage between the two electrodes. In order to
separate the flow signal from this interfering d.c. voltage, an a.c. excitation field is used –
allowing the interfering d.c. voltage to be easily separated from the a.c. signal voltage by
capacitive or transformer coupling. Whilst a.c. electromagnetic flowmeters have been used
successfully for many years, the use of an alternating field excitation makes them susceptible
to both internal and external sources of errors.
Non-homogeneous conductivity
Although electromagnetic flowmeters are independent of liquid conductivity over a wide
range, it is assumed that the conductivity is homogeneous and is thus constant along the cross
section and along the length of the primary head. However, in many sewage and waste water
applications it is often found that, at low flow rates, layers of different density and
conductivity are formed. As a consequence the eddy current distribution that is created by the
time derivative of the induction, is completely deformed and therefore interference voltages
are produced, which cannot be fully suppressed in the converter.
Fouling of the electrodes
Fouling of the electrodes by insulating deposits can considerably increase the internal
resistance of the signal circuit – changing the capacitive coupling between the field coils and
signal circuitry.
Direct coupling
Because field excitation is derive directly from the mains voltage, it is impossible to separate
the signal voltage from external interference voltages.Interference voltages can be transferred
by either capacitive or inductive coupling from heavy current carrying cables laid in
proximity to the signal cable. Although these interference voltages may be largely suppressed
by multiple screening of the signal cable, they might not be completely eliminated.
Axial currents
Stray currents from other systems are occasionally carried by the pipeline and/or the flowing
media that generate voltages at the electrodes cannot be distinguished from the signal voltage.
Poor earthing
Earthing of the primary head as well as the pipeline by earthing rings or properly earthed
flanges, ensures that the liquid is at zero potential. If the earthing is not symmetrical, earth
loop currents give rise to interference voltages – producing zero-point shifts.
The result of these various interference voltages requires the use of a manually operated zero
control adjustment and the attendant problem of having to stop the flow to check the setting.
The a.c. electromagnetic flowmeter is a relatively low cost system having an accuracy in the
order of around 2%.
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Industrial Flow Measurement
6.11
Electromagnetic Flowmeters
The pulsed d.c. field
X The pulsed d.c. field is designed to overcome the problems associated with both a.c. and
d.c. interference. In the pulsed d.c. meter, the d.c. field is periodically switched on and off at
specific intervals. The electrochemical d.c. interference voltage is stored when the magnetic
field is switched off and then subtracted from the signal representing the sum of the signal
voltage and interference voltage when the magnetic field is switched on.
Figure 6.20 illustrates the voltage at the sensors in which the measured voltage Vm is
superimposed on the spurious unbalanced offset voltage Vu. By taking (and storing) samples
during the periods A and B, the mean value Vm may be obtained by algebraic subtraction of
the two values:
Vm = (Vu + Vm) – Vu ..……………………………………………………….(6.3)
Voltage across electrodes
e
Vm
Vu
A
Sample of Vu
B
Sample of Vu + Vm
t
Figure 6.20. The voltage at the sensors in which the measured voltage
Vm is superimposed on the spurious unbalanced offset voltage Vu.
This method assumes that the value of the electrochemical interference voltage remains
constant during this measuring period between the samples A and B. However if the
interference voltage changes during this period serious errors are likely to occur. Figure 6.21
shows the unbalanced offset voltage as a steadily increasing ramp. Here, the error is as high
as the amount by which the unbalanced voltage has changed during the measuring periods A
and B and could result in an induction error of as much as 100 %.
Voltage across electrodes
e
Measuring
error
Vm
Vu increasing
with time
Vu increasing
with time
A
Sample of Vu1
B
t
Sample of Vu2 + Vm
164
Figure 6.21.
With the
unbalanced offset voltage a
steadily increasing ramp, the
error is as high as the amount
by which the unbalanced
voltage has changed during
the measuring periods A and
B.
Industrial Flow Measurement
Electromagnetic Flowmeters
One method of overcoming this problem is by a method of linear interpolation as illustrated in
Figure 6.22. Prior to the magnetic induction the unbalanced voltage A is measured. During
the magnetic induction phase the value B (which is the sum of unbalanced voltage and flow
signal) is measured and then, after magnetic induction, the changed unbalanced voltage C is
measured.
e
B
C
Vm
(A+C)/2
A
Vu increasing
with time
A
Sample of Vu1
B
Sample of Vu2 + Vm
C
Sample of Vu3
t
Figure 6.22. The unbalanced voltage A is measured prior to the magnetic induction; the
value B (the sum of unbalanced voltage and flow signal) is measured during the induction
phase; and the changed unbalanced voltage C is measured after magnetic induction.
The mean value (A + C)/2 of the balanced voltage prior to and after magnetic induction is
electronically produced and subtracted from the sum signal measured during magnetic
induction. So, the exact flow signal:
Vm = B - (A + C)/2 ..……….…………………………………………(6.4)
is obtained which is free from the unbalanced voltage. This method corrects not only the
amplitude of the d.c. interference voltage, but also its change ,with respect to time.
6.12
Bipolar pulse operation
An alternative method of compensation is shown in Figure 6.23 using an alternating (or
bipolar) d.c. pulse. Under ideal or reference conditions, the values of V1 and V2 would be
equal and would both have the value Vm, the measured value. Thus:
V1 - V2 = (Vm) - (-Vm) = 2Vm ……………………………………….…(6.5)
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Industrial Flow Measurement
Electromagnetic Flowmeters
+e
Voltage across electrodes
V1
+ Vm
0
- Vm
V2
-e
Figure 6.23. Bipolar pulse compensation under ideal or reference conditions.
If, now, the zero or no-flow signal is off-set by an unbalanced voltage in, for example, a
positive direction (Figure 6.24) , then:
V1 = Vu + Vm ……………………..…………………………………(6.5)
and
V2 = Vu - Vm ……………………..…………………………………(6.6)
and
V1- V2 = (Vu +Vm) - (Vu - Vm) = 2Vm ……..………………..……(6.7)
V1
Voltage across electrodes
+e
No-flow signal
0
+Vu - Vm
Vu
t
+Vu + Vm
V2
-e
Figure 6.24. Bipolar pulse compensation eliminates error due to unbalanced offset
voltage.
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Industrial Flow Measurement
Electromagnetic Flowmeters
Again, linear interpolation methods may be applied as illustrated in Figure 6.25 where five
separate samples are taken during each measurement cycle. A zero potential measurement is
taken at the commencement of the cycle; a second measurement at the positive peak; a third at
zero potential again; a fourth at negative peak and finally another zero measurement at the
completion of the cycle. The result, in this case, will be:
2 Vm = (V1 - (Z1 + Z2)/2 - (V2 - (Z2 + Z3)/2) ……..……………………..……(6.8)
V1
Voltage across electrodes
+e
t
0
Z1
Z2
V2
-e
W
6.13
Z3
Figure 6.25. Bipolar pulse compensation with linear interpolation.
Meter sizing
Generally the size of the primary head is matched to the nominal diameter of the pipeline.
However, it is also necessary to ensure that the flow rate of the medium lies between the
minimum and maximum full scale ranges of the specific meter. Typical values of the
minimum and maximum full scale ranges are 0,3 and 12 m/s respectively.
Experience has also shown that the optimum flow velocity of the medium through an
electromagnetic flowmeter is generally 2 to 3 m/s – dependent on the medium. For example,
for liquids having solids content, the flow velocity should be between 3 to 5 m/s to prevent
deposits and to minimise abrasion.
Knowing the volumetric flowrate of the medium in, for example, cubic metres per hour, and
knowing the pipe diameter, it is easy to calculate and thus check to see if the flow velocity
falls within the recommended range. Most manufacturers supply nonograms or tables that
allow users to ascertain this data at a glance.
Occasionally, in such cases where the calculated meter size needs to be smaller than that of
the media pipe size, a transition using conical sections can be installed .The cone angle should
be 8 ° or less and the pressure drop resulting from this reduction can, again, be determined
from manufacturers' tables (Figure 6.26).
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Industrial Flow Measurement
Electromagnetic Flowmeters
d
D
8°
Figure 6.26. Conical section used to cater for reduced meter size.
6.14
Conclusion
The electromagnetic (EM) flowmeter is regarded by many users as the universal answer to
more than 90% of all flowmetering applications. Some of the many benefits offered by the
EM flowmeter include:
¾ no pressure drop;
¾ short inlet/outlet sections (5D/2D);
¾ relationship is linear (not square root);
¾ insensitive to flow profile changes (laminar to turbulent) including many non-Newtonian
liquids;
¾ rangeability of 30:1 or better;
¾ inaccuracy of better than ±0.2% of actual flow over full range;
¾ no recalibration requirements;
¾ bi-directional measurement
¾ no taps or cavities;
¾ no obstruction to flow;
¾ not limited to clean fluids;
¾ high temperature capabilities;
¾ high pressure capabilities;
¾ volumetric flow;
¾ can be installed between flanges; and
¾ can be made from corrosion resistance materials at low cost.
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Industrial Flow Measurement
Ultrasonic Flowmeters
Chapter 7. Ultrasonic Flowmeters
Industrial Flow
Measurement
169
Industrial Flow Measurement
Ultrasonic Flowmeters
170
Industrial Flow Measurement
Ultrasonic Flowmeters
Chapter 7
Ultrasonic Flowmeters
7.1
Introduction
Ultrasonic flowmeters, suitable for both liquids and gases, have been available for more than
twenty years and are currently the only truly viable non-intrusive measuring alternative to the
electromagnetic flowmeter.
Unfortunately, although originally hailed as a general panacea for the flow measurement
industry, lack of knowledge and poor understanding of the limitations of early instruments
(especially the Doppler method) often lead to its use in unsuitable applications.
Nonetheless, the ultrasonic meter is probably the only meter capable of being used on large
diameter pipes (above 3 m bore) at a reasonable cost and performance (around 1%).
In essence there are three basic principles used in ultrasonic metering: the Doppler method;
the time-of-flight method; and the frequency difference method.
7.2
Doppler method
Doppler flowmeters are based on the Doppler effect — the change in frequency that occurs
when a sound source and receiver move either towards or away from each other. The classic
example is that of an express train passing through a station. To an observer, standing on the
platform, the sound of the train appears to be higher as the train approaches and then falls as
the train passes through the station and moves away. This change in frequency is called the
Doppler shift.
In the Doppler ultrasonic flowmeter, an ultrasonic beam (usually of the order of 1 to 5 MHz)
is transmitted, at an angle, into the liquid (Figure 7.1). Assuming the presence of reflective
particles (dirt, gas bubbles or even strong eddies) in the flowstream, some of the transmitted
energy will be reflected back to the receiver. Because the reflective particles are moving
towards the sensor, the frequency of the received energy will differ from that of the
transmitted frequency (the Doppler effect).
v
f
θ
t
Figure 7.1. In the Doppler ultrasonic
flowmeter, an ultrasonic beam is
transmitted, at an angle, into the liquid.
C
This frequency difference, the Doppler shift, is directly proportional to the velocity of the
particles.
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Industrial Flow Measurement
Ultrasonic Flowmeters
X
Assuming that the media velocity (v) is considerably less than the velocity of sound in the
media (C), the Doppler frequency shift (Δf) is given by:
Δf =
2f t v cos θ
C
…………………………………………….(7.1)
where ft is the transmitted frequency.
From this it can be seen that the Doppler frequency, Δf, is directly proportional to flow rate.
The velocity of sound in water is about 1500 m/s. If the transmitted frequency is 1 MHz, with
transducers at 60°, then for a media velocity of 1 m/s the Doppler shift is around 670 Hz. W
Since this technique requires the presence of reflecting particles in the media, its use in ultraclean applications or, indeed, with any uncontaminated media, is generally, precluded.
Although some manufacturers claim to be able to measure ‘non-aerated’ liquids, in reality
such meter rely on the presence of bubbles due to micro-cavitation originating at valves,
elbows or other discontinuities.
In order for a particle to be ‘seen’, it needs to be approximately 1/10 larger than the
wavelength of the acoustic frequency in the liquid. In water, a 1 MHz ultrasonic beam would
have a wavelength of about 1,5 mm and so particles would need to be larger than 150 μm in
order to reflect adequately.
Whilst air, oil particle and sand are excellent sonic reflectors, the presence of too may
particles can attenuate the signal so that very little of the signal reaches the receive
transducer.
Probably the single biggest drawback of this technology is that in multiphase flows, the
particle velocity may bear little relationship to the media velocity. Even in single phase
flows, because the velocity of the particles is determined by their location within the pipe,
there may be several different frequency shifts — each originating at different positions in the
pipe. As a result, the Doppler method often involves a measurement error of 10 % or even
more.
In the insertion type probe shown in Figure 7.2, the reflective area is, to a large extent,
localised and the potential source of errors is thereby reduced.
Insertion probe
Figure 7.2. Insertion type probe Doppler
probe (courtesy Dynasonics).
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Industrial Flow Measurement
Ultrasonic Flowmeters
Generally, Doppler meters should not be considered as high performance devices and are cost
effective when used as a flow monitor. They work well on dirty fluids and typical
applications include sewage, dirty water, and sludge. Doppler meters are sensitive to velocity
profile effects and they are temperature sensitive.
7.3
Transit time meter
The ultrasonic transit time measuring method is based on the fact that, relative to the pipe and
the transducers, the propagation speed of an ultrasonic pulse travelling against the media flow
will be reduced by a component of the flow velocity. Similarly, the speed of propagation of
the pulse travelling downstream is increased by the fluid velocity. The difference between
these two transit times can be directly related to the flow velocity.
In practice, the meter comprises two transducers (A and B) mounted at an angle to the flow
and having a path length L (Figure 7.3) — with each acting alternately as the receiver and
transmitter. The transit time of an ultrasonic pulse, from the upstream to the downstream
transducer, is first measured and then compared with the transit time in the reverse direction.
A
Figure 7.3. In
the transit time
meter two
transducers (A
and B) each
act alternately
as the receiver
and
transmitter.
θ
L
v
C
B
X
Mathematically:
TAB =
L
(C vcosθ)
…………………………………………….….(7.2)
TBA =
L
(C+ vcosθ)
…………………………………………….….(7.3)
and:
where:
TAB
TBA
L
C
v
=
=
=
=
=
upstream travel time
downstream travel time
path length through the fluid
velocity of sound in medium
velocity of medium.
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Industrial Flow Measurement
Ultrasonic Flowmeters
The difference in transit time ΔT is:
ΔT = TAB − TBA
ΔT =
…………………………………………….….(7.4)
L
L
(C vcosθ) (C+ vcosθ) …………………………………………….….(7.5)
ΔT =
2Lvcosθ
(C2 v 2 cos2 θ)
…………………………………………….….(7.6)
Since the velocity of the medium is likely to be much less than the velocity of sound in the
medium itself (15 m/s compared to 1500 m/s), the term v2 cos2 θ will be very small compared
with C2 and may thus be ignored for all practical flow velocities. Thus:
ΔT=
2Lvcosθ …………………………………………….….(7.7)
(C2 )
ΔTC 2
…………………………………………….….(7.8)
v=
2Lcosθ
This shows that the flow velocity v is directly proportional to the transit time difference ΔT.
This also illustrates that v is directly proportional to C2 (the square of the speed of sound)
which will vary with temperature, viscosity, and material composition.
Fortunately, it is possible to eliminate the variable C2 from the equation:
C =
(T
L
TM
…………………………………………….….(7.9)
− TBA ) …………………………………………….….(7.10)
2
where: TM is the mean transit time given by:
TM =
AB
C =
Therefore:
(T
AB
and:
C =
2
(T
AB
now:
v
or:
− TBA )
…………………………………………….….(7.11)
− TBA )
…………………………………………….….(7.12)
2L
4 L2
2
= ΔT.4L2 / 2L cos θ (TAB + TBA)2 ………………………….(7.13)
v = k ΔT/(TAB + TBA)2 ……………….………………………….(7.14)
174
W
Industrial Flow Measurement
Ultrasonic Flowmeters
Since both the length L and the angle θ are likely to remain constant it is only necessary to
calculate the sum and difference of the transit times in order to derive the flow rate
independent of the velocity of sound in the medium.
As distinct from Doppler meters, transit time meters work better on clean fluids and typical
applications include: water, clean process liquids, liquefied gases and natural gas pipes.
The accuracy of measurement is determined by the ability of the instrument to measure
accurately the transit time. In a 300 mm diameter pipe, for example, with the transducers set
at 45 °, and the media flowing at 1 m/s, the transit time is about 284 μs and the time
difference ΔT is less than 200 ns. This means that in order to measure the velocity with a full
scale accuracy of 1 %, must be at the very least down to 2 ns. With smaller diameter pipes,
the measurement accuracy would need thus to be in the picosecond range.
Obviously, with longer path lengths, this stringent time measurement requirement becomes
easier to meet. Performance thus tends to be better with large bore pipes, and providing
multiple traverses as illustrated in Figure 7.4 can increase the path length.
Figure 7.4 Increasing the path length using a double traverse,
single ‘V’ path on the centre line.
These arrangements are frequently used for gas measurement in lines and gas flow measurement. The
double traverse, single path flow meter is frequently used for low-cost liquid measurement and
accurate real-time measurement of hazardous and non-hazardous gas flows in lines from 100
to 900 mm DN.
The 'U'-form meter as shown in Figure 7.5 can be used for very low flows.
Flow input
Flow output
Figure 7.5. The 'U'-form meter can be used for very low flows.
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Industrial Flow Measurement
7.4
X
Ultrasonic Flowmeters
Flow profile
V average =
∫ V . dx
The average velocity along an ultrasonic path (Figure 7.6) is given by:
where:
D
0
D = pipe internal diameter
X = distance across the pipe
x=D
V(x)
Vaverage
D
Figure 7.6. Average velocity
along an ultrasonic path.
x=0
Thus, with a single path across the flow, the average flow is made up of the sum of the
instantaneous velocities at each point across the diameter of the pipe.W
The transit time meter thus provides a picture of the total flow profile along the path of the beam.
However, the validity of the measurement can only be relied on if the flow profile is not subject
to an asymmetric velocity profile or symmetric swirl. In addition it is important to know the
flow profile. If, for example, the flow profile is not fully developed, then, as shown in Figure 7.7,
the laminar-to-turbulent error can be up to 33%.
Laminar
Pipe
flow profile
cross
section
Turbulent flow
profile
Beam
Figure 7.7. A single path produces a laminar-to-turbulent error up to 33% (courtesy Krohne).
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Industrial Flow Measurement
Ultrasonic Flowmeters
Using a dual path as shown in Figure 7.8, the laminar-to-turbulent error can be reduced to
0.5 %.
Laminar
flow profile
Turbulent flow
profile
Beam
Beam
Figure 7.8. A dual path reduces the laminar-to-turbulent error to 0.5% (courtesy Krohne).
An alternative method is shown in Figure 7.9. Here, internal reflectors, used to impart a
helical path to a single beam device, result in high accuracy measurement for a wide flow
range, from laminar to turbulent and even in the transitional region.
Figure 7.9. Single beam with helical
path produces high accuracy
measurement for a wide flow range
from laminar to turbulent (courtesy
Siemens).
In the Krohne multi-channel custody-transfer ultrasonic flowmeter, ten sensors form five
measurement paths located in the cross-section of the flow tube (Figure 7. 10).
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Industrial Flow Measurement
Ultrasonic Flowmeters
This approach provides a wealth of information on the flow profile (Figure 7.11) in laminar
and in turbulent flow conditions and provide highly accurate flow even in the presence of
non-symmetric flow profiles and swirl. — thus providing a measurement that is essentially
independent of the flow profile — with accuracies to 0.15% and repeatability down to 0.02%.
Another advantage of using multiple measurement channels is redundancy.
Beam Beam
Beam
Figure
7.10.
Five
measurement paths provide
a measurement that is
essentially independent of
the flow profile (courtesy
Krohne).
Beam Beam
Laminar flow
profile
Turbulent flow
profile
Figure 7.11. Determination of the flow profile
(courtesy Krohne).
7.5
Frequency difference
The frequency difference or ‘sing-around’ flowmeter makes use of two independent
measuring paths — with each having a transmitter (A and A’) and a receiver (B or B’) (Figure
7.6). Each measuring path operates on the principle that the arrival of a transmitted pulse at a
receiver triggers the transmission of a further pulse. As a result, a pair of transmission
frequencies is set up — one for the upstream direction and another for the downstream
direction. The frequency difference is directly proportional to the flow velocity.
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Industrial Flow Measurement
Ultrasonic Flowmeters
B1
B2
v
A1
A2
Figure 7.6. ‘Sing-around’ flowmeter makes use of two independent measuring
paths each having a transmitter (A and A’) and a receiver (B or B’).
X
Thus:
F1 =
and:
F2 =
(C
vcos θ) …..……………….………………………….(7.15)
L
(C+vcos θ)
…..……………….………………………….(7.16)
L
The frequency difference ΔF is given by:
ΔF= F1 F2 =
2v cos θ …..……………….………………………….(7.17)
L
and:
v=
W
ΔFL …..……………….………………………….(7.18)
2cosθ
The main advantage of this system is that because the frequency difference is directly
proportional to flow, no maths function is required. Further, the measurement is independent
of the velocity of sound in the medium.
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Industrial Flow Measurement
7.6
Ultrasonic Flowmeters
Clamp on instruments
Transducers that are clamped externally to the walls of the pipe provide portable nonintrusive flow measurement systems that can be installed within a few minutes to virtually
any pipe (Figure 7.13). Pipe materials include: metal, plastic, ceramic, asbestos cement and
internally and externally coated pipes.
Upstream sensor
Wedge
Oscillator
Pipe
θf
D
τ/2
Q
τ/2
Downstream
sensor
Figure 7.13. Clamp-on transducers must take into account the thickness
and material of construction of the pipe wall (courtesy Fuji Electric).
Clamp-on transducers are also often used in permanent installations that cannot justify a
permanent in-line meter but nonetheless require periodic metering.
Because the ultrasonic pulses must traverse the pipe wall and any coatings, the thicknesses
must be known. In addition, the presence of deposits on the inside pipe surface will affect the
transmitted signal strength and, therefore, performance.
Despite these obstacle, modern clamp-on ultrasonic meters, incorporating microprocessor
technology that allows the transducer mounting positions and calibration factors to be
calculated for each application, provide measuring accuracies of 1 to 3% — depending on the
application.
In conventional designs, a change in the characteristics of the liquid, which affects the speed
of sound, will have a direct effect on the refraction angle. With sufficient change in the
refraction angle, the signal from one transducer will not be received by the other. This
limitation is overcome with the wide beam approach (Figure 7.14) in which the pipe wall is
incorporated into the signal transmission system. During set-up, the meter selects a
transmission frequency that excites a natural acoustic waveguide mode of the pipe to induce a
sonic wave that travels axially down the pipe wall. In this manner the pipe itself becomes the
launching point of the acoustical signal and allows a much wider signal beam to be
transmitted from one transducer to the other. The result is that any change in the refraction
angle will have negligible effect on the strength of the received signal.
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Industrial Flow Measurement
Ultrasonic Flowmeters
Axial beam
injection
Upstream
transducer
θ
Refraction angle
Downstream
transducer
Figure 7.14. By selecting a transmission frequency that excites a natural acoustic
waveguide mode of the pipe, the pipe itself becomes the launching point of the
acoustical signal and allows a much wider signal beam to be transmitted from one
transducer to the other (courtesy Controlotron Corporation).
7.7
Velocity of Sound Measurement
Because ultrasonic meters measure volumetric flow which is, in most cases, not relevant for
plant operation purposes, their output is correlated to mass flow — assuming a fixed actual
density (reference density) under operating conditions. Consequently, deviations in actual
density will cause a misreading in mass flow which is inversely proportional to the deviation
compared with the reference density.
Since the velocity of sound is a characteristic property of a fluid, its measurement, in
conjunction with the temperature and pressure of the fluid, can be used as a
measure/indication of:
¾ actual flowing density
¾ concentration (e.g. for fluids consisting of two distinctive components);
¾ molecular weight (W pressure, temperature, Cp/Cv ratio and compressibility are known).
Furthermore, since deviations of the velocity of sound signal/range will indicate a change in
fluid composition, its output may thus be used as an ‘interface detector’ — alerting operators
to different plant operating conditions and/or feed stock changes or changes in composition
e.g. contamination in heavy crude.
Since the signal strength will also be measured, deviations in signal strength could indicate
viscosity changes, an increased level of solids (crystal formation, catalyst carry over) and/or
bubbles (flashing off of dissolved gases under changed pressure/temperature conditions) in
the fluid.
In applications where it is required to determine changes in the constituency of the medium,
the instrument should be capable of determining and displaying the speed of sound through
the medium as a separate parameter.
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Industrial Flow Measurement
7.7.1
Ultrasonic Flowmeters
Factors influencing the Velocity of Sound
Except in carbon dioxide gas service, the velocity of sound is independent of the ultrasonic
frequency. Generally the velocity of sound:
¾ increases with increasing density;
¾ decreases with increasing temperature for liquids; and
¾ increases with increasing temperature for gases.
An important exception is water which has a discontinuity in its relationship between velocity
of sound and temperature: For water below a temperature of 74 °C, the velocity of sound will
increase with increasing temperature. Above 74 °C the velocity of sound will decrease if the
temperature increases.
7.8
Beam scattering
As indicated earlier, beam scattering/dispersion may occur if the fluid contains too many
particles (crystals, catalyst particles). Further, as soon as the fluid ceases to be single phase,
beam scattering may occur under bubble flow or mist flow conditions.
At the frequency and intensity of the ultrasonic energy typically used in industrial
applications, propagation through liquids may be up to distances of 10 m. However, the
same energy will only propagate a few millimetres in air. Therefore, evenly distributed air
bubbles will disperse the energy by reflection from the liquid/air boundaries and cause
significant attenuation (Figure 7.15). The generally accepted upper limit for entrained gases
is about 1% by volume and for solids is 1 to 5%.
Liquid
molecules
Diaphragm
Large/heavy molecule
Damped
propagation
Figure 7.15. Sound propagation in a
mixed medium.
No
propagation
Bubble flow could appear with liquids
operating close to their boiling point
where only a marginal pressure decrease
could cause the liquid to evaporate and
form bubbles.
Discontinuity
(air bubble)
Elastic
bonds
Another flashing off phenomena (not so well recognised as boiling off) occurs if gas is
dissolved in liquid. Generally, as the pressure decreases or the temperature rises, the dissolved
gas can no longer be contained in the liquid and will flash off until a new equilibrium is
reached. Typical examples of gases soluble in liquid are:
¾ H2S in water
¾ H2S in DlPA (diisopropylamine)
¾ CO/C02 in water
¾ C02 in methanol
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Industrial Flow Measurement
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In order to minimise or prevent bubble flow, the meter should be moved to a location in the
line with a higher pressure, e.g. downstream of a pump
In immiscible mixtures (e.g. water/oil), beam scattering should be avoided by thorough
upstream agitation to ensure that no oil droplets in water or water droplets in oil are present at
the meter.
Product layering may also introduce beam scattering and should be avoided by proper mixing.
Product layering occurs not just as a result of poorly mixed products, but at locations where
cold and hot streams are mixed.Layering will most likely occur directly downstream of a tiein of a cold stream with a hot stream, of the same product, as a result of density differences.
To avoid product layering, the fluid should be thoroughly mixed upstream of the meter using
reducers (d/D ≤ 0.7) or static mixers.
7.9
Summary
Apart from not obstructing the flow, ultrasonic flowmeters are not affected by corrosion,
erosion or viscosity. Most ultrasonic flowmeters are bi-directional, and sense flow in either
direction.
7.9.1
¾
¾
¾
¾
¾
¾
¾
Suitable for large diameter pipes.
No obstructions, no pressure loss.
No moving parts, long operating life.
Fast response.
Weld-on transducers may be installed on existing pipe-lines.
Multi-beam systems can be used to eliminate the effects of profile
Not affected by fluid properties.
7.9.2
¾
¾
¾
¾
Advantages
Disadvantages
In single-beam meters the accuracy is dependent on flow profile.
Fluid must be acoustically transparent.
Expensive.
Pipeline must be full
7.9.3
Application limitations
For the transit time meter, the ultrasonic signal is required to traverse across the flow,
therefore the liquid must be relatively free of solids and air bubbles. Anything of a different
density (higher or lower) than the process fluid will affect the ultrasonic signal.
Turbulence or even the swirling of the process fluid can affect the ultrasonic signals. In
typical applications the flow needs to be stable to achieve good flow measurement, and
typically allowing sufficient straight pipe up and downstream of the transducers does this.
The straight section of pipe required upstream and downstream is dependent on the type of
discontinuity and varies for gas and liquid as shown in Tables 8.1 and 8.2.
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Industrial Flow Measurement
Ultrasonic Flowmeters
Table 8.1. Minimum straight line pipe lengths for general purpose liquid measurement
(Courtesy Fuji Electric)
Upstream
Downstream
≥10 D
Classification
90° bend
Detector
L≥10 D
L ≥5 D
Tee
≥10 D
Detector
L≥10 D
L≥50 D
Detector
≥10 D
Detector
≥1.5 D
Diffuser
≥0.5 D
Detector
L≥5 D
D
Detector
L≥30 D
Reducer
L≥5 D
L≥10 D
Detector
Detector
Valve
L≥10 D
L≥30 D
Detector
Detector
Pump
Check Stop
valve valve
P
L≥50 D
D = internal diameter of pipe
184
Industrial Flow Measurement
Ultrasonic Flowmeters
Table 8.2. Minimum straight line pipe lengths for general purpose gas measurement
(Courtesy Fuji Electric)
Classification
90° bend
Upstream
Downstream
L ≥10 D
L≥20 D
Detector
Detector
Valve
Detector
L≥20 D
Fan
L≥10 D
Detector
L≥30 D
10 D≥L
Detector
Detector
L≥40 D
Pump
P
Detector
D = internal diameter of pipe
185
Industrial Flow Measurement
Ultrasonic Flowmeters
186
Industrial Flow Measurement
Mass Flow Measurement
Chapter 8. Mass Flow Measurement
Industrial Flow
Measurement
187
Industrial Flow Measurement
Mass Flow Measurement
188
Industrial Flow Measurement
Mass Flow Measurement
Chapter 8
Mass Flow Measurement
8.1
Introduction
Most chemical reactions are based largely on their mass relationship. Consequently, by
measuring the mass flow of the product it is possible to control the process more accurately.
Further, the components can be recorded and accounted for in terms of mass.
Mass flow is a primary unit of flow measurement and is unaffected by viscosity, density,
conductivity, pressure and temperature. As a result it is inherently more accurate and
meaningful for measuring material transfer.
Traditionally, mass flow has been measured inferentially. Electromagnetic, orifice plate,
turbine, ultrasonic, venturi, vortex shedding, etc, all measure the flow of the medium in terms
of its velocity through the pipe (e.g. metres per second). However, because the dimensions
of the pipe are fixed, we can also determine the volumetric flow rate (e.g. litres per second).
Further, by measuring density and multiplying it by the volumetric flow rate, we can even
infer the mass flow rate. However, such indirect methods commonly result in serious errors
in measuring mass flow.
8.2
The Coriolis force
Possibly the most significant advance in flow measurement over the past few years has been
the introduction of the Coriolis mass flowmeter. Not only does this technology allow mass
flow to be measured directly but Coriolis meters are readily able to cope with the extremely
high densities of, for example, dough, molasses, asphalt, liquid sulphur, etc, found in many
industries.
The Coriolis meter is based on the Coriolis force – sometimes, incorrectly, known as
gyroscopic action. Consider two children, Anne and Belinda, sat on a rotating platform.
Anne is situated mid-way between the axis and the outer edge of the platform while Belinda
is sat at the outer edge itself (Figure 8.1). If Anne now throws a ball directly to Belinda,
Belinda will fail to receive the ball!
Rotating
platform
ω
Anne
Figure 8.1. If Anne throws a ball
directly to Belinda, Belinda will
fail to receive the ball due to the
Coriolis effect.
Belinda
Axis
Path of ball
189
Industrial Flow Measurement
Mass Flow Measurement
The reason will have nothing to do with Anne’s ability to throw a straight ball (we’ll assume
she’s a perfect pitcher) or Belinda’s ability to catch a ball (we’ll assume she’s a perfect
catcher). The reason is due to what is termed the Coriolis effect.
What Anne ignored is that although the platform is rotating at a constant angular speed (ω)
she and Belinda are moving at different circular or peripheral speeds. Indeed, the further you
move away from the axis, the faster your speed.
X
In fact, the peripheral speeds of each are directly proportional to the radius i.e.:
v = r.ω ……………………..………………………………….……(8.1)
where:
v = peripheral velocity
r = radius
ω = angular speed.
In this case, Belinda at the edge of the platform will have a peripheral speed of twice that of
Anne (Figure 8.2). Thus, when Anne throws the ball radially outwards towards Belinda, the
ball initially has not only the velocity (v) radially outwards, but also a tangential velocity vA
due to the rotation of the platform. If Belinda had this same velocity vA the ball would reach
her perfectly. But Belinda’s speed (vB) is twice that of vA. Thus when the ball reaches the
outer edge of the platform it passes a point that Belinda has already passed and so the ball
passes behind her.
Path of
ball
VA
Anne
VB
Figure 8.2. Belinda at the edge of
the platform will have a
peripheral speed of twice that of
Anne and thus the ball’s
peripheral speed needs to be
accelerated from vA to vB.
Belinda
Consequently, to move the ball from Anne to Belinda its peripheral speed needs to be
accelerated from vA to vB. This acceleration is a result of what is termed the Coriolis force,
named after the French scientist who first described it, and is directly proportional to the
product of the mass in motion, its speed and the angular velocity of rotation:
Fcor = 2mωv……………………..……………………………………(8.2)
where:
Fcor = Coriolis force
v = peripheral velocity
ω = angular speed
m = the mass of the ball
190
Industrial Flow Measurement
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Looking at this from another point, if we could measure the Coriolis force and knowing the
peripheral velocity and the angular speed, we could determine the mass of the ball.
How does this relate to mass measurement of fluids?
W
Consider a simple, straight liquid-filled pipe rotating around axis A, at an angular velocity ω
(Figure 8.3). With no actual liquid flow, the liquid particles move on orbits equivalent to
their distance r from the axis of rotation. Thus, at distance r1, the tangential velocity of a
particle would be r1.ω whilst at double the distance r2, the tangential velocity would also
double to r2.ω.
r1ω
r2ω
ω
r1
Figure 8.3. As the liquid flows
away from the axis A, each mass
particle will be accelerated by an
amount
equivalent
to
its
movement along the axis from a
low to a higher orbital velocity.
r2
If now, the liquid flows in a direction away from the axis A, at a flow velocity v, then as each
mass particle moves, for example, from r1 to r2 it will be accelerated by an amount equivalent
to its movement along the axis from a low to a higher orbital velocity. This increase in
velocity is in opposition to the mass inertial resistance and is felt as a force opposing the
pipe's direction of rotation – i.e. it will try to slow down the rotation of the pipe. Conversely,
if we reverse the flow direction, particles in the liquid flow moving towards the axis are
forced to slow down from a high velocity to a lower velocity and the resultant Coriolis force
will try to speed up the rotation of the pipe.
Thus, if we drive the pipe at a constant torque, the Coriolis force will produce either a braking
torque or an accelerating torque (dependent on the flow direction) that is directly proportional
to the mass flow rate.
Although the possibility of applying the Coriolis effect to measure mass flow rate was
recognised many years ago, it is little more than twenty years since the first practical design
was devised.
During this development period, many pipe arrangements and movements have been devised
– with the major drawback of early systems lying in their need for rotational seals. This
problem was overcome by using oscillatory movement rather than rotational.
191
Industrial Flow Measurement
8.3
Mass Flow Measurement
A practical system
One of the simplest arrangements that incorporates all the positive features of a Coriolisbased mass flow meter is illustrated in Figure 8.4. Here, a tubular pipe, carrying the liquid, is
formed in a loop and vibrated around the z axis. The straight parts of the pipe, A-B and C-D,
oscillate on the arcs of a circle and without any flow will remain parallel to each other
throughout each cycle.
B
C
A
Z-axis
Figure 8.4.
A pipe, formed
in a loop, is vibrated around
the z axis so that the straight
parts of the pipe, A-B and CD, oscillate on the arcs of a
circle.
D
Z-axis
If a liquid now flows through the tube in the direction shown, then the fluid particles in
section A-B will move from a point having a low rotary velocity (A) to a point having a high
rotary velocity (B). This means that each mass particle must be accelerated in opposition to
the mass inertial resistance. This opposes the pipe's direction of rotation and produces a
Coriolis force in the opposite direction. Conversely, in section C-D, the particles move in the
opposite direction – from a point having a high rotary velocity (C) to a point having a low
rotary velocity (D).
The resultant effect of these Coriolis forces is to delay the oscillation in section A-B and
accelerate it in section C-D. As a result section A-B tends to lag behind the undisturbed
motion whilst section C-D leads this position. Consequently, the complete loop is twisted by
an amount that is directly and linearly proportional to the mass flow rate of the fluid – with
the twisting moment lent to the pipe arrangement being measured by sensors. Figure 8. 5
shows a practical arrangement in which two tubes are vibrated in opposition to each other.
Electromagnetic
Drive coil velocity detector
Tube
oscillation
Electromagnetic
velocity detector
Figure 8.5. Typical arrangement of a Coriolis type instrument (Courtesy Micro Motion)
192
Industrial Flow Measurement
Mass Flow Measurement
Figure 8.6 shows the oscillatory motion applied to a single tube whilst Figure 8.7 shows the
forces acting on the tube in which there is fluid flow. As a result, the complete loop is twisted
by an amount that is directly and linearly proportional to the mass flow rate of the fluid
(Figure 8.8) – with the twisting moment lent to the pipe arrangement being measured by
sensors.
Tube
oscillation
Figure 8.6. Oscillatory motion
applied to a single tube (courtesy
Micro Motion).
Flow
Fluid force
Flow
Tube
oscillation
Figure 8.7. Forces acting on the tube
as a result of fluid flow (courtesy Micro
Motion).
Fluid force
Fluid force
Twist
angel
Twist
angel
Fluid force
Tube
oscillation
Figure 8.8. The complete loop
is twisted by an amount that is
directly
and
linearly
proportional to the mass flow
rate of the fluid (courtesy
Micro Motion).
Because of this twisting motion, one of the major design factors of the oscillating tube is to
prevent the pipe fracturing because of stress ageing. Here, computer simulation has given rise
to a geometric design for thick-walled tubes that does not expose them to bending stress but
to torsional strain applied evenly to the cross-section of the tube.
A further factor in reducing stress fractures is to limit the oscillation amplitude to
approximately 1 mm that, in an optimally designed system, would be about 20 % of the
maximum permitted value. Thus, because the distortion caused by the Coriolis forces is
about 100 times smaller (a magnitude of about 10 μm) a measurement resolution of ± 0.1 %
amounts to only a few nanometres. Although the possibility of stress fractures occurring is
small, consideration must be given to the fact that a stress fracture could occur – resulting in
the release of the process medium. As a result, considerable attention has been paid to
secondary containment of the process medium.
It should be noted that secondary containment does not necessarily match the maximum
process pressure specifications. Thus, for example, whilst the measuring tube and flanges
may be suitable for up to 400 bar, or more, the secondary containment may only be rated up
to a pressure of 100 bar.
193
Industrial Flow Measurement
8.4
Mass Flow Measurement
Multiple phase flow
Whilst fundamentally suitable for both gaseous and liquid media, in practice the Coriolis
technique is really only suitable for those gases with mass flow rates typical of liquid
medium. These are generally only obtained with high density gases.
Mixtures having low admixtures of finely injected gas in liquids or fine grain solid
admixtures, react almost like a single phase liquid in that the admixtures merely alter the
density. A Coriolis mass measurement is thus still effective.
At higher levels of non-homogeneity, two problem areas occur. First, a non-homogenous
mixture results in an irregular fluctuating density and, thus, a constantly fluctuating resonant
frequency that can put the system out of phase. A second problem is that the Coriolis method
assumes that all particles of the medium are accelerated on orbits in accordance with the
movement of the pipes. With high proportions of gas, particles in the middle of the pipe will
no longer complete the movement of the pipe. Conversely, the Coriolis forces of the mass
particles in the centre of the pipe will no longer affect the pipe walls. The result is that the
measuring value will be systematically reduced.
Most Coriolis-based systems can still tolerate an air-water gas volume of between 4 and 6%.
However, because the behaviour of liquid-gas mixtures depends on the distribution of
bubbles, and the velocity of sound depends very largely on the materials involved, these
figures cannot simply be transferred to other mixtures. With liquids having a lower surface
tension than water, for example, considerably higher proportions of gas can be tolerated.
The conditions for solids in water are a great deal more favourable and many good systems
can tolerate suspensions of fine grain solids of up to 20% in water without any difficulty.
8.5
Density Measurement
The measurement of mass flow by the Coriolis meter is, fundamentally, independent of the
density of the medium. However, the resonant frequency of the oscillating pipe will vary
with density – falling as the density increases. In many instruments this effect is used to
provide a direct measurement of density by tracking the resonant oscillation frequency.
The temperature of the pipe system changes with the temperature of the measured medium
and alters its modulus of elasticity. This not only alters the oscillation frequency but also the
flexibility of the loop system. Thus, the temperature must be measured as an independent
quantity and used as a compensating variable. The temperature of the medium is, therefore,
also available as a measured output.
194
Industrial Flow Measurement
8.6
Mass Flow Measurement
Loop arrangements
There are many different designs of Coriolis Mass Flowmeter, in the majority of which the
primary sensor involves an arrangement of convoluted tubes through which the measured
fluid flows.
In any arrangement requiring the tube to be bent to form the desired convolutions, the outside
wall is stretched and becomes thinner whilst the inner wall becomes thicker. This distortion
will vary from one tube to another and, when the flowmeter requires two such convoluted
tubes, it becomes difficult to balance them both dimensionally and dynamically. Furthermore,
if the fluid to be measured is abrasive, this already weakened part of the flowmeter is likely to
be most severely stressed. Abrasive material can also cause erosion that will change the
stiffness of the resonant elements and so cause measurement errors.
In the parallel loop arrangement (Figure 8.9) the flow is split at the inlet to follow parallel
paths through the two sections. The advantage of this is that the total cross-sectional area of
the flow path is the sum of the cross-sections of both pipes. At the same time, since each
pipe has a relatively small cross section it may be designed with to have a high flexibility –
thus increasing the sensitivity to the Coriolis effect.
Figure 8.9. Parallel loop arrangement with
flow splitter.
Pick-ups
Exciter
A disadvantage of this arrangement is that the action of
splitting and then re-combining the flow introduces a
significant pressure drop. Furthermore, the flow may
not be divided equally, in which case an unbalance is
generated – especially if solids or gases are entrained in the liquid flow. The same reasoning
applies if the balance of the split is disturbed by partial or complete blockage of one section –
again leading to measurement errors. The balance may also be disturbed by separation of the
components in a two-phase flow, such as air or solids entrained in liquid flow. A similar
problem exists with shear sensitive fluids.
Figure 8.10. Serial loop arrangement.
In the serial arrangement (Figure 8.10) the total
length of the pipe is considerably greater due to the
Exciter
second loop and must therefore have a larger crosssectional area to reduce the pressure loss. This
however leads to increased rigidity that makes it less
sensitive to the Coriolis effect at low flow rates. At
high flow rates however, there is less pressure drop, and the pipe is easier to clean.
Pick-ups
195
Industrial Flow Measurement
8.7
Mass Flow Measurement
Straight through tube
The development of a straight through tube mass flowmeter, without any loops or bends, is
based on the fact that a vibrating tube, fixed at its ends, also has a rotational movement about
the fixed points and thereby generates a Coriolis force.
In the first of such designs (shown in Figure 8.11) two tubes are vibrated at their resonant
frequency. Infrared sensors are placed at two exactly defined locations at the inlet and outlet
of the pipe to detect the phase of the pipe oscillation. At zero flow the oscillation of the
system is in phase (Figure 8.12) . When liquid flows into the system the flowing medium is
accelerated on the inlet (Figure 8.13) and decelerated on the outlet (Figure 8.14) and the
oscillation of the system is out of phase. The measured phase difference is proportional to
mass flow.
Figure 8.11. Two tubes are vibrated at their resonant frequency with
sensors place at two exactly defined locations at the inlet and outlet
of the pipe to detect the phase of the pipe oscillation.
Figure 8.12. At zero flow the oscillation of
the system is in phase (courtesy Endress +
Hauser).
Figure 8.13 . When liquid flows into the
system the flowing medium is accelerated
on the inlet (courtesy Endress + Hauser).
196
Industrial Flow Measurement
Mass Flow Measurement
A
B
Figure 8.14. The flowing medium is
decelerated on the outlet and the
oscillation of the system is out of phase
(courtesy Endress + Hauser).
In comparison with the 'looped' type Coriolis mass flowmeter, the straight through pipe
obviously offers a much lower pressure loss and since it has no bends or loops, it is easier to
clean.
Although this design avoids many of the problems associated with the convoluted tube meter,
the flow splitter still causes a pressure drop and an unbalance can occur due to partial or
complete blockage of one section. Straight dual-tube Coriolis meters are available in pipe
sizes up to 250 mm diameter.
In more recent years several manufacturers have introduced single straight-tube designs with
no bends or splitters. In the single tube system shown in Figure 8.15 a driver sets the
measuring tube (AB) into a uniform fundamental oscillation mode.
Sensor
A
Driver
B
Figure 8.15. In the single tube system a
driver sets the measuring tube (AC) into a
uniform fundamental oscillation mode
(Courtesy Krohne).
Sensor
C
When the flow velocity is zero the Coriolis force Fc is also zero. Under flowing conditions,
with the fluid particles in the product are accelerated between points AC and decelerated
between points CB. As a result, a Coriolis force Fc is generated by the inertia of the fluid
particles accelerated between points AC and of those decelerated between points CB, which
causes an extremely slight distortion of the measuring tube (Figure 8.16).
Coriolis force
Coriolis force
A
B
C
197
Figure 8.16 The Coriolis force Fc generated
by the inertia of the fluid particles
accelerated between points AC and of those
decelerated between points CB, causes an
extremely slight distortion of the measuring
tube (Courtesy Krohne).
Industrial Flow Measurement
Mass Flow Measurement
This distortion is superimposed on the fundamental component and is directly proportional to
the mass flowrate.
Currently, single tube straight Coriolis meters are limited to a maximum pipe diameter of 100
mm.
8.8
Summary of Coriolis mass measurement
Coriolis meters may well supplant the electromagnetic flowmeter as the answer to the
majority of flowmetering applications. For critical control, mass flow rate is the preferred
method of measurement and, because of their accuracy, Coriolis meters are becoming
common for applications requiring very tight control. Apart from custody transfer
applications, they are used for chemical processes and expensive fluid handling.
8.8.1 Advantages
Some of the many benefits include:
¾ direct, in-line and accurate mass flow measurement of both liquids and gases;
¾ accuracies as high as 0.1% for liquids and 0.5% for gases;
¾ mass flow measurement ranges cover from less than 5 g/m to more than 350 tons/hr;
¾ measurement independent of temperature, pressure, viscosity, conductivity and density of
the medium;
¾ direct, in-line and accurate density measurement of both liquids and gases;
¾ mass flow, density and temperature can be accessed from the one sensor; and
¾ can be used for almost any application irrespective of the density of the process;
8.8.2 Drawbacks
On the downside, despite tremendous strides in the technology, some of the drawbacks
include:
¾ expensive
¾ many models are affected by vibration
¾ current technology limits the upper pipeline diameter to 150 mm; and
¾ secondary containment can be an area of concern.
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Industrial Flow Measurement
8.9
Mass Flow Measurement
Thermal mass flowmeters
Thermal mass flow measurement, which dates back to the 1930's, is a quasi-direct method,
suited, above all, for measuring gas flow. Thermal mass flow meters infer their
measurement from the thermal properties of the flowing medium (such as specific heat and
thermal conductivity) and hence are capable of providing measurements which are
proportional to the mass of the medium.
In the ranges normally encountered in the process industry, the specific heat cp of the gas is
essentially independent of pressure and temperature and is proportional to density and
therefore to mass.
The two most commonly used methods of measuring flow using thermal techniques are either
to measure the rate of heat loss from a heated body in the flow stream; or to measure the rise
in temperature of the flowing medium when it is heated.
8.9.1
Heat loss or `hot wire’ method
In its simplest form a hot body (a heated wire, thermistor, or RTD) is placed in the main
stream of the flow (Figure 8.17). According to the first law of thermodynamics, heat may be
converted into work and vice versa. Thus, the electrical power (I2R ) supplied to the sensor is
equal to the heat convected away from it.
Mass flow sensor
Figure 8.17. Basic schematic of `hot wire’
method.
Power supply and
signal processing
Since it is the molecules (and hence mass) of the flowing gas that interact with the heated
boundary layer surrounding the velocity sensor and convect away the heat, the electrical
power supplied to the sensor is a direct measure of the mass flow rate.
X
The rate of heat loss of a small wire is given by:
P = h A (Tw – Tf) ..………..………………………………….…….(8.3)
where:
P
h
A
Tw
Tf
=
=
=
=
=
heat loss in watts
heat transfer coefficient
surface area of the wire
wire temperature
fluid temperature
199
Industrial Flow Measurement
Mass Flow Measurement
The heat transfer coefficiency depends on: the wire geometry, the specific heat; the thermal
conductivity and density of the fluid; as well as the fluid velocity in the following way:
H = C1 + C2 ρ v .……..………………………………….…….(8.4)
where C1 and C2 are constants that depend on the wire geometry and gas properties. The term
√ρv indicates that the output of the hot wire flow meter is related to the product of density
and velocity, which can be shown to be proportional to mass flow rate.W
In practice, this device can be used only if the medium temperature is constant, since the
measured electrical resistance of the hot wire cannot determine whether the change in
resistance is the result of a change in flow speed or of a change in medium temperature. To
solve this problem the temperature of the medium must be used as a reference value and a
second temperature sensor immersed in the flow to monitor the medium temperature and
correct for temperature changes (Figure 8.18).
Temperature
sensor
Figure 8.18. A second
‘temperature sensor’ monitors
the gas temperature and
automatically correct for
temperature changes.
Mass flow
sensor
Power supply and
signal processing
The mass measuring RTD has a much lower resistance than the temperature RTD and is self
heated by the electronics. In a constant temperature system, the instrument measures I2R and
maintains the temperature differential between the two sensors at a constant level.
Complete hot wire mass flowmeters (Figure 8.19) are available for pipes up to 200 mm
diameter (size DN 200). Above this size, insertion probes, which incorporate a complete
system at the end of a rod, are used.
Heated
velocity
sensor
Heat
Temperature
sensor
Figure 8.19. Typical in-line hot wire mass flowmeter
(Courtesy Sierra Instruments Ltd).
Mass
flow
RTD sensor
and heater
combination
RTD sensor
200
Industrial Flow Measurement
Mass Flow Measurement
The main limitation of this method is that by its very ‘point’ measurement it is affected by the
flow profile within the pipe as well as by the media viscosity and pressure. Further, since the
measurement is determined by the thermal characteristics of the media, the system must be
calibrated for each particular gas – with each mass flow/temperature sensor pair individually
calibrated over its entire flow range.
The measured value, itself, is primarily non-linear and thus requires relatively complex
conversion. On the positive side, however, this inherent non-linearity is responsible for the
instrument’s wide rangeability (1000:1) and low speed sensitivity (60 mm/s).
Such instruments also have a fast response to velocity changes (typically 2 s) and provide a
high level signal, ranging from 0.5 to 8 W over the range of 0 to 60 m/s.
One of the limitations of many conventional hot wire systems is that they soon to reach their
performance limits when higher mass flow speeds need to be detected. The thermal current
into the medium depends on the flow speed and thus a constant heat input would mean that
when the flow speed is low there would be a build-up of heat and a corresponding
temperature increase. And at high flow speeds the temperature differential would be around
zero. To overcome this problem, the heat input may be adapted to the flow speed. This is
achieved in the sensor shown in Figure 8.20 which consists of a high thermal-conductive
ceramic substrate upon which are deposited a thick film heating resistor (Rh) and two
temperature-dependent thick film resistors (T1and T2) (Figure 8.21).
Figure 8.20. Sensor consists of a high thermalconductive ceramic substrate upon which are
deposited a thick film heating resistor and two
temperature-dependent thick film resistors
(courtesy Weber Sensors Group).
0C
Ceramic
substrate
Temperature gradient across substrate
Ceramic
substrate
Rh
Heating
resistor
T1
T2
Figure 8.21. As the process medium flows along the
front of the ceramic substrate the thermal current
produced by the heating resistor forms a temperature
gradient.
Temperature
sensors
201
Industrial Flow Measurement
Mass Flow Measurement
As the process medium flows along the front of the ceramic substrate, the thermal current
produced by the heating resistor forms a temperature gradient as illustrated in Figure 8.21.
The temperature differential between the two resistors is then used to regulate the current
controlling the heating resistor.
8.9.2
Temperature rise method
In this method, the gas flows through a thin tube in which the entire gas stream is heated by a
constantly powered source – with the change in temperature being measured by RTDs located
upstream and downstream of the heating element (Figure 8.22). Because of the heat
requirements this method is used for very low gas flows.
Resistance
thermometer
Resistance
thermometer
Figure 8.22. Basic schematic of
‘temperature rise’ method.
Heating
element
Power supply and
signal processing
X
Here, the mass flow rate qm is:
qm =k. qQ/cp.ΔT…………………….……..………………………………….…….(8.5)
where:
k = constant
qQ = the heat input (W)
cp = specific heat capacity of the gas (J/kg.K)
ΔT = temperature difference (°C)
W
The main disadvantages of this method is that it is only suitable for low gas flows; the sensors
are subject to erosion and corrosion; and the multiple tapping points increase chances of
leakage.
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Industrial Flow Measurement
Mass Flow Measurement
8.9.3
External temperature rise method
An alternative arrangement places the heating element and temperature sensors external to the
pipe. In the arrangement shown in Figures 8.23 and 8.24, the heating elements and
temperature sensors are combined so that the RTD coils are used to direct a constant amount
of heat through the thin walls of the sensor tube into the gas. At the same time, the RTD coils
sense changes in temperature through changes in their resistance.
Flow
Figure 8.23. Thermal flowmeter with external
elements and heater.
Film
Upstream
temperature
sensor
Heater
Downstream
temperature
sensor
RTD coils wound
externally on
tube
Thin walled
capillary tube
Figure 8.24. In the capillary tube meter the RTD coils are used to direct a constant amount
of heat through the thin walls of the sensor tube into the gas (courtesy Sierra Instruments).
The main advantage of this method is that it provides non-contact, non-intrusive sensing with
no obstruction to flow.
8.9.4
Capillary-tube meter
In a typical capillary-tube thermal mass flowmeter the medium divides into two paths, one
(m2) through the bypass and the other (m1) through the sensor tube (Figure 8.25).
RTD coils
Capillary tube
m1
T1
T2
P1
m2
P2
m
Shunt bypass
203
Figure 8.25. A
typical capillarytube thermal mass
flowmeter
(courtesy
Sierra
Instruments).
Industrial Flow Measurement
Mass Flow Measurement
As the name implies, the role of the bypass is to bypass a defined portion of the flow so that a
constant ratio of bypass flow to sensor flow (m2/m1) is maintained. This condition will only
apply if the flow in the bypass is laminar so that the pressure drop across the bypass is
linearly proportional to the bypass flow. An orifice bypass, for example, has non-laminar flow
so that the ratio of total flow to sensor flow is non-linear.
One solution lies in the use of multiple disks or sintered filter elements. Another solution is
the bypass element used by Sierra (Figure 8.26) which comprises a single machined element
having small rectangular passages with a high length-to-width ratio. This element provides
pure laminar flow and is easily removed and cleaned.
Figure 8.26. Single machined elements having
small rectangular passages with a high length-towidth ratio provides pure laminar flow and are
easily removed and cleaned (courtesy Sierra
Instruments).
With a linear pressure drop (P1-P2) maintained across the sensor tube, a small fraction of the
mass flow passes through the sensor tube. The sensor tube has a relatively small diameter and
a large length-to-diameter ratio in the range 50:1 to 100:1 – both features being characteristic
of capillary tubes.
These dimensions reduce the Reynolds number to a level less than 2 000 to produce a pure
laminar flow in which the pressure drop (P1 - P2) is linearly proportional to the sensor’s mass
flow rate (m1).
In operation, the long length-to-diameter ratio of the tube ensures that the entire cross-section
of the stream is heated by the coils – with the mass flow carrying heat from the upstream coil
to the downstream coil. This means the first law of thermodynamics can be applied in its
simplest form.
This method is largely independent of the flow profile and the medium viscosity and pressure.
It means that the flow calibration for any gas can be obtained by multiplying the flow
calibration for a convenient reference gas by a constant K-factor. K-factors are now available
for over 300 gases, giving capillary-tube meters almost universal applicability.
Although the output is not intrinsically linear with mass flow, it is nearly linear over the
normal operating range. Accurate linearity is achieved with multiple-breakpoint linearization
(for example at 25, 50, 75 and 100% of full scale).
In addition to its applicability to very low gas flows, the capillary tube method can also be
used for larger flows by changing the bypass to effect a higher or lower value of the bypass
ratio (m2/m1).
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Industrial Flow Measurement
Mass Flow Measurement
8.9.5
Liquid mass flow
Although the main application of the thermal mass flow meter lies with gases, the same
technology can also be applied to the measurement of very low liquid flows, for example,
down to 30 grams/hour. A typical meter is shown in Figure 8.27.
T1
Thermally conductive
‘guidline’
Heater
Tg
Zone 1
Zone 2
T3
T2
T4
T4
Tg
T3
T4
T1
T2
T3
Figure 8.27. A typical liquid thermal mass flow meter (courtesy Brookes - Rosemount).
Here, the inlet and outlet of the sensor tube are maintained at a constant temperature by a heat
sink – with the mid-point of the sensor tube heated to a controlled level e.g. 20°C above the
temperature of the inlet-outlet heat sink. These two locations, together with the flow tube,
are mechanically connected by a thermally conductive path.
In this manner, the flowing fluid is slightly heated and cooled along the sensor zones, 1 and 2
respectively, to create an energy flow perpendicular to the flow tube. Two RTDs (T1 and T2),
located at the mid-point of the sensor tube determine the temperature difference. This
temperature difference is directly proportional to the energy flow and is, therefore, directly
proportional to the mass flow times the specific heat of the fluid.
205
Industrial Flow Measurement
Mass Flow Measurement
206
Industrial Flow Measurement
Open Channel Flow Measurement
Chapter 9. Open Channel Flow
Industrial Flow
Measurement
207
Industrial Flow Measurement
Open Channel Flow Measurement
208
Industrial Flow Measurement
Open Channel Flow Measurement
Chapter 9
Open Channel Flow Measurement
9.1
Introduction
In many applications, liquid media is distributed in open channels. Open channels are found
extensively in water irrigation schemes, sewage processing and effluent control, water
treatment and mining beneficiation.
The most commonly used method of measuring flow in an open channel is through the use of
a hydraulic structure (known as a primary measuring device) that changes the level of the
liquid. By selecting the shape and dimensions of the primary device (a form of restriction)
the rate of flow through or over the restriction will be related to the liquid level in a known
manner. In this manner, a secondary measuring element may be used to measure the
upstream depth and infer the flow rate in the open channel.
In order that the flow rate can be expressed as a function of the head over the restriction, all
such structures are designed so that the liquid level on the upstream side is raised to make the
discharge independent of the downstream level. The two primary devices in general use are
the weir and the flume.
9.2
The weir
A weir (Figure 9.1) is essentially a dam mounted at right angles to the direction of flow, over
which the liquid flows.
Figure 9.1. A basic weir – a dam
mounted at right angles to the
direction of flow.
The dam usually comprises a notched metal plate – with the three most commonly used
being: the rectangular weir; the triangular (or V-notch) weir; and the trapezoidal (or
Cipolletti) weir –each having an associated equation for determining the flow rate over the
weir that is based on the depth of the upstream pool. The crest of the weir, the edge or surface
over which the liquid passes, is usually bevelled – with a sharp upstream corner.
209
Industrial Flow Measurement
Open Channel Flow Measurement
For the associated equation to hold true and accurate flow measurement determined, the
stream of water leaving the crest (the nappe), should have sufficient fall (Figure 9.2). This is
called free or critical flow, with air flowing freely beneath the nappe so that it is aerated.
Should the level of the downstream water rise to a point where the nappe is not ventilated, the
discharge rate may be inaccurate and dependable measurements cannot be expected.
Head
measuring
point
Crest
Nappe
Head (h)
Ventilation
Channel
floor
Figure 9.2. For accurate flow
measurement, the nappe should
have sufficient fall.
Weir plate
9.2.1
Rectangular weir
The rectangular weir was probably the earliest type in use and, due to its simplicity and ease
of construction is still the most popular type.
In its simplest form (Figure 9.3 (a)), the weir extends across the entire width of the channel
with no lateral contraction.
X
The discharge equation (head vs. flow rate), without end contractions, is:
k L h1.5 ……………………………………………...(9.1)
q
=
=
=
=
=
flow rate;
constant;
length of crest; and
the head.
where:
W
q
k
L
h
(a)
(b)
Figure 9.3. Rectangular weir (a) with no contraction; and (b) with lateral contraction.
210
Industrial Flow Measurement
Open Channel Flow Measurement
Generally, this means that for a 1 % change in flow, there will be a 0.7 % change in the level.
A problem with rectangular weirs without contraction is that the air supply can become
restricted and the nappe clings to the crest. In such cases a contracted rectangular weir
(Figure 9.3 (b)) is used where end contractions reduce the width and accelerate the channel
flow as it passes over the weir and provides the needed ventilation.
X
In this case the discharge equation of such a restriction, with end contractions, becomes:
where: q
k
L
h
W
k (L – 0.2 h) h1.5 …………………………………...(9.2)
q
=
=
=
=
=
flow rate;
constant;
length of crest; and
the head.
The rectangular weir can normally handle flow rates in the range of 1:20 from about 0 - 15 ℓ/s
up to 10 000 ℓ/s or more (3 m crest length).
9.2.2
Trapezoidal (Cipolletti) weir
In the trapezoidal type of weir (Figure 9.4) the sides are inclined to produce a trapezoidal
opening. When the sides slope one horizontal to four vertical the weir is known as a
Cipolletti weir and its discharge equation (head vs. flow rate) is similar to that of a rectangular
weir with no end contractions:
q
=
k L h1.5 ……..….…………………………………...(9.3)
The trapezoidal type of weir has the same flow range as a rectangular weir.
Figure 9.4. The trapezoidal or Cipolletti weir.
9.2.3
Triangular or V- notch weir
The V-notch weir (Figure 9.5) comprises an angular v-shaped notch – usually of 90° – and
is particularly suited for low flows.
A major problem with both the rectangular and trapezoidal type weirs is that at low flow rates
the nappe clings to the crest and reduces the accuracy of the measurement. In the V-notch
weir, however, the head required for a small flow is greater than that required for other types
of weirs and freely clears the crest – even at small flow rates.
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Industrial Flow Measurement
X
Open Channel Flow Measurement
The discharge equation of the V-notch weir is given by:
k h2.5 ………………….……………………………...(9.4)
q
=
=
=
=
flow rate;
constant; and
the head.
where:
q
k
h
This equates to a 0.4 % change in height for a 1 % change in flow.
W
V-notch weirs are suitable for flow rates between 2 and 100 ℓ/s and, for good edge conditions,
the flow range is 1: 100. Higher flow rates can be obtained by placing a number of triangular
weirs in parallel.
Figure 9.5. The Triangular or V- notch
weir.
9.2.4
Application Limitations
There is a high unrecoverable pressure loss with weirs, which may not be a problem in most
applications. However with the operation of a weir, it is required that the flow clears the weir
on departure. If the liquid is not free flowing and there is back pressure obstructing the free
flow, then the level over the weir is affected and hence the level and flow measurement.
Advantages
¾ Simple operation.
¾ Good Rangeability (for detecting high and low flow).
Disadvantages
¾ Pressure loss.
¾ Accuracy of about 2%.
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Industrial Flow Measurement
9.3
Open Channel Flow Measurement
The flume
The second class of primary devices in general use is the flume (Figure 9.6). The main
disadvantage of flow metering with weirs is that the water must be dammed, which may cause
changes in the inflow region. Further, weirs suffer from the effects of silt build-up on the
upside stream. In contrast, a flume measures flow in an open channel in which a specially
shaped flow section restricts the channel area and/or changes the channel slope to produce an
increased velocity and a change in the level of the liquid flowing through it.
Figure 9.6. Basic flume in which a
specially shaped flow section produces
an increased velocity and a change in
the liquid level.
Major benefits offered by the flume include: a higher flow rate measurement than for a
comparably sized weir; a much smaller head loss than a weir; and better suitability for flows
containing sediment or solids because the high flow velocity through the flume tends to make
it self-cleaning.
The major disadvantage is that a flume installation is typically more expensive than a weir.
9.3.1
Flume flow considerations
An important consideration in flumes is the state of the flow. When the flow velocity is low
and is due mainly to gravity, it is called tranquil or sub-critical. Under these conditions, it is
necessary to measure the head in both the approach section and in the throat in order to
determine the discharge rate.
As the flow velocity increases and the inertial forces are equal to or greater than the
gravitational force, the flow is termed critical or supercritical. For both critical and
supercritical states of flow, a definitive head/discharge relationship can be established and
measurement can be based on a single head reading.
9.3.2
Venturi flume meter
The most common flume is the Venturi flume ( Figure 9.7) whose interior contour is similar
to that of a Venturi flow tube with the top removed: normally consisting of a converging
section, a throat section, and a diverging section.
The rectangular venturi flume, with constrictions at the side, is the most commonly used since
it is easy to construct. In addition, the throat cross section can also be trapezoidal or Ushaped. Trapezoidal flumes are more difficult to design and construct, but provide a wide
flow range with low pressure loss. A U-shaped section is used where the upstream approach
section is also U-shaped and gives higher sensitivity – especially at low (tranquil) flows.
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Industrial Flow Measurement
Converging
section
Open Channel Flow Measurement
Diverging
section
Throat section
Figure 9.7. Rectangular venturi flume with
constrictions at the side.
Hydraulic
jump
X
Although the theory of operation of flumes is more complicated than that of weirs, it can
be shown that the volume flow rate through a rectangular Venturi flume is given by:
q = k h1.5 …………………………………………………………....(9.5)
where:
W
q = the volume flow;
k = constant determined by the proportions of the flume; and
h = the upstream fluid depth.
9.3.3
Parshall venturi flume
The Parshall Venturi Flume (Figure 9.8) differs from the conventional flat bottomed venturi
flume in that it incorporates a contoured or stepped floor that ensures the transition from subcritical to supercritical flow. This allows it to function over a wide operating range whilst
requiring only a single head measurement. The Parshall Venturi flume also has better selfcleaning properties and relatively low head loss.
Converging
section
Throat
section
Diverging
section
Water surface
214
Figure 9.8. The Parshall Venturi Flume
incorporates a contoured or stepped floor.
Industrial Flow Measurement
Open Channel Flow Measurement
Parshall Venturi flume are manufactured in a variety of fixed sizes and are usually made of
glass fibre reinforced polyester. The user need only install it in the existing channel.
X
Because of its slightly changed shape, the discharge equation of the Parshall Venturi
flume changes slightly to:
q = k hn …………………………………………………………....(9.5)
where:
q
=
h
=
k and n
flow rate;
the head; and
constants determined by the proportions of the flume.
Generally, the exponent n varies between 1.522 and 1.607, determined mainly by the throat
width. W
Application Limitations
Providing excellent self cleaning properties, the venturi flume has replaced the weir in most
applications, and the Parshall flume is, at present, possibly the most accurate open channel
flow measuring system with flow ranges from 0.15 to 4000 ℓ/s.
Advantages include: reliable and repeatable measurements; no erosion; insensitive to dirt and
debris; low head pressure loss; and simple operation and maintenance. However it is more
expensive than the rectangular venturi flume and more difficult to install.
9.3.4
Palmer Bowlus
The Palmer Bowlus flume (Figure 9.9) was also developed in the USA in 1936 for use in
waste water treatment and its name derives from the inventors, Messrs. Palmer and Bowlus.
As shown it comprises a U-sectioned channel having a trapezoidal throat section and a raised
invert. Its main advantage is its ability to match up to circular pipes and it can be fitted inside
existing pipes in special applications. Flow ranges from 0.3 to 3500 ℓ/s.
Figure 9.9. The Palmer Bowlus flume comprises a U-sectioned channel
having a trapezoidal throat section and a raised invert (courtesy Neuplast).
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Industrial Flow Measurement
Open Channel Flow Measurement
9.3.5
Khafagi flume
Similar to the venturi flume the Khafagi flume (Figure 9.10) does not have a parallel throat
section. Instead, the throat section is that point at which the inlet section meets the curve of
the divergent discharge section. The floor is horizontal throughout its length. The flow range
is from 0.25 to 1500 ℓ/s.
Converging
section
9.4
Diverging
section
Throat
Figure 9.10. The Khafagi flume does
not have a parallel throat section.
Level measurement
Whilst a weir or a flume restricts the flow and generates a liquid level which is related to the
flow rate, a secondary device is required to measure this level. Several measuring methods
exist:
9.4.1
Float measurement
Float measurement is a direct measurement method in which the height of the float is
proportional to the water level (Figure 9.11). This height is mechanically transmitted via
either a cable and pulley or a pivoting arm, and converted into an angular position of a shaft
that is proportional to liquid level. Alternatively, the mechanical movement may be
electrically linearised and converted to a standardised output signal.
Scale
Pulley
Cam
Figure 9.11. Float-operated flow meter
(Courtesy Isco Inc.)
Cable
Stilling
well
Counter
weight
Float
Floats are not only affected by changes in ambient air temperature, but are also subject to
build up of grease and other deposits that can alter the immersion depth of the float and thus
affect the measured value. Floats generally require the use of a stilling well and, since this
method has moving parts that are subject to wear, periodic maintenance and repair is required.
216
Industrial Flow Measurement
Open Channel Flow Measurement
9.4.2
Capacitive
The principle of capacitive level measurement is based on the change in capacitance between
an insulated probe immersed in the liquid and a grounding plate or tube which is also in
contact with the liquid (Figure 9.11). The probe forms one plate of a capacitor; the grounding
plate, together with the conductive liquid, form the other plate; and the PVC or Teflon coating
forms the dielectric. As the liquid level changes, it alters the size of the plate and, therefore,
its capacitance. By measuring the capacitance a reading can be obtained that can be directly
related to level and the flow.
Capacity level
probe
Teflon coating
Earthing
plate and
terminal
Figure 9.11. Insulated probe and
grounding plate form a capacitor –
with the liquid acting as the dielectric
(Courtesy Endress + Hauser).
The main advantages of this system are that there are no moving parts; no mains power is
required at the measuring point; and the distance between the probe and the control room can
be up to 3000 m.
The main disadvantage is that accuracy is affected by changes in the characteristics of the
liquid. Further, despite the very smooth surface of the Teflon or PVC coating, waste water
containing grease can still lead to deposits on the measuring probe and affect the measured
value.
9.4.3
Hydrostatic
This method makes use of a submerged sealed pressure transducer to measure the hydrostatic
pressure of the liquid above it (Figure 9.12). The hydrostatic pressure is the force exerted by a
column of water above a reference point and is proportional to the height.
Hydrostatic
pressure
transducer at
lowest level
217
Figure 9.12. Hydrostatic
pressure measurement uses
a submerged sealed pressure
transducer to measure the
hydrostatic pressure of the
liquid above it.
Industrial Flow Measurement
Open Channel Flow Measurement
The transducer comprises a membrane which is firmly attached to the channel wall – with an
oil fill transmitting the pressure on the membrane to a capacitive metering cell.
Submerged pressure transducers are not affected by wind, steam, turbulence, floating foam
and debris, or by deposits or contamination.
However, because they are submerged, the transducers may be difficult to install in large
channels with high flow, and may require periodic maintenance in flow streams with high
concentrations of suspended solids or silt. Further, accuracy may be affected by changes in
the temperature of the process medium.
9.4.4
Bubble injection
Like the submerged pressure transducer, the bubble injection method or ‘bubbler’ measures
the hydrostatic pressure of the liquid (Figure 9.13). The system comprises a pressure
transducer connected to a ‘bubble tube’ which is located in the flow stream and whose outlet
is at the lowest point.
Pressure meter or
converter
Differential pressure
regulator and valve
Bubbler tube
Figure 9.13. Bubble injection system
(Courtesy Bailey-Fischer + Porter).
Air supply
Air or other gas, at a constant pressure, is applied to the tube so that bubbles are released from
the end of the bubble tube at a constant rate. The pressure measured by the transducer, which
is required to maintain the bubble rate, is proportional to the liquid level.
Because the pressure transducer is not in contact with the fluid, it is not subject to chemical or
mechanical attack. Additionally the cost for providing explosion proof protection is minimal.
When used in channels with high concentrations of grease, suspended solids, or silt, bubblers
may require occasional maintenance – although periodic air purges of the bubble tube often
minimise this problem. Additional maintenance is also required to regenerate desiccators that
prevent moisture from being drawn into the air system of a bubbler.
218
Industrial Flow Measurement
Open Channel Flow Measurement
9.4.5
Ultrasonic
Ultrasonic level measurement makes use of a transducer, located above the channel, which
transmits a burst of ultrasonic energy that is reflected from the surface of the water (Figure
9.14). The time delay from the transmitted pulse to the received echo is converted into
distance and hence determines the liquid level. That you are all the are' like history is it to do
the things you exactly how popular
Figure
9.14.
Ultrasonic
level
measurement uses a transducer
mounted above the channel, which
transmits a burst of ultrasonic energy
that is reflected from the liquid
surface (Courtesy Milltronics)
Ultrasonic sensors have no contact with the liquid; are easy to install; require minimal
maintenance; and are not affected by grease, suspended solids, silt, and corrosive chemicals in
the flow stream.
Modern ultrasonic systems are also capable of providing very high level measuring
accuracies (down to ± 0.25%).
9.5
Linearization
Open channel flow measurement does not end with the measurement of level, since it still
remains to convert the measured liquid level into a corresponding flow rate. This conversion
or linearization must be carried out according to the level-flow rate relationship for the
primary measuring device being used and can be accomplished in several ways:
9.5.1
Non-linear scale
The simplest method, where readout on an analog meter is sufficient, is to calibrate the scale
according to the calculated values. Apart from its obvious inaccuracy, this method is not
suitable for applications where the flow signal is required for process purposes.
9.5.2
Mechanical cam
In this method a mechanical cam is rotated by the level measuring device. The profile of the
cam is contoured according to the specific level-flow rate relationship of the primary
measuring device being used and thus the position of the cam follower is then proportional to
flow rate.
219
Industrial Flow Measurement
Open Channel Flow Measurement
9.5.3
Software
In modern level measuring instruments, linearization is usually carried out in software in
which a wide range of different compensating curves are stored in the instrument’s memory.
During commissioning of the system, users may then access the correct curve – dependent
on the type and dimensions of the weir or flume.
220
Chapter 10. Common Installation Practices
Industrial Flow Measurement
Common Installation Practices
Industrial Flow
Measurement
221
Industrial Flow Measurement
Common Installation Practices
222
Industrial Flow Measurement
Common Installation Practices
Chapter 10
Common Installation Practices
10.1 Introduction
In non-fiscal and non-custody transfer applications, flowmeters are rarely calibrated and are
often left in situ for 10 or more years without any thought to their accuracy. Further, in too
many instances, the initial installation is often so poorly undertaken, without any regard to
basic installation practices, that it is highly unlikely that the meter in question ever met the
manufacturer's stated accuracy. The data supplied by most manufacturers is based on steady
flow conditions and installation in long straight pipes both upstream and downstream of the
meter. In practice, most meter installations rarely meet these idealised requirements – with
bends, elbows, valves, T-junctions, pumps and other discontinuities all producing
disturbances that have an adverse effect on meter accuracy.
Both swirl and distortion of the flow profile can occur – either separately or together.
Research has shown that swirl can persist for distances of up to 100 pipe diameters from a
discontinuity whilst in excess of 150 pipe diameters can be required for a fully developed
flow profile to form.
10.2 Environmental influences
The most important feature of a flow meter is that it should be sensitive to flow and as
insensitive to environmental influences as possible. The most important environmental
influences include:
10.2.1 Fluid temperature
The temperature range of the fluid itself will vary considerably depending on the industry in
which it is to be used:
•
food industry 0 to 130 °C to withstand CIP (clean in place);
•
industrial steam, water, gases – 0 to 200 °C;
•
industrial superheated steam – up to 300 °C;
•
industrial outdoor usage – down to -40 °C; and
•
cryogenics – down to -200 °C.
10.2.2 Pressure pulsations
Pressure pulsations can be a problem when measuring liquids since, after they are created,
they travel a long way down the pipeline without being significantly damped. In vortex
meters, for example, such symmetrical pulsations could be detected as a vortex signal. The
insensitivity to such 'common mode' pressure fluctuations should, therefore, be at least 15 Pa.
Differential pressure flow measurement systems can be susceptible to common mode pressure
variations if the connection systems on either side of the differential pressure cell are not
identical and as short as possible.
223
Industrial Flow Measurement
Common Installation Practices
10.2.3 Vibration
Vibration is present on any piece of pipework in industry and is of particular significance in
Coriolis and vortex meters. The vortex frequencies for gas, for example, lie in the range 5 to
500 Hz. Consequently, vibration induced signals in this range cannot be fully filtered out.
Where possible, therefore, the sensor itself should be insensitive to pipe vibration.
10.3
Flow conditioning
While the effect of most flow disturbances can be overcome through the use of sufficient
straight pipe length, upstream of the meter, this is not always practical. In such cases use can
be made of one of a number of flow conditioners or straightening vanes or pipes. (Figure
10.1). Straighteners are effective in eliminating swirl and helping to restore grossly distorted
flow profiles. However they cannot, generally, provide the mixing action of fluid layers
required to normalise a velocity profile and some length of straight piping is still required
downstream of the conditioner to provide the necessary mixing action.
For example, a Vortab Flow Conditioner is 3 diameters long, and requires 4 diameters of
straight pipe between it and the
meter. This reduces the total
upstream pipe run (including the
flow conditioner) to just 7
diameters for any upstream
Tube-type
disturbance.
Folded vane
Zanker-type
Fin-type
Figure 10.1. A number of flow
conditioners or straighteners
Vortab-type are available for use in the
upstream line in order to
minimised the effects of
Disturbance
plate (Sprenkle)
disturbances.
Folded vane and fin type straightening vanes are normally used on gases whilst the tubular
type is normally used on steam or liquids. It is usually recommended that vanes be installed
only in extreme cases after all other alternatives have been exhausted.
There is always a danger of straightening vanes coming loose in the flow line and causing
serious damage to expensive equipment. They should be installed as securely as possible and
should be used only for applications where moderate line velocities, pressures and
temperatures exist.
224
Industrial Flow Measurement
10.4
Common Installation Practices
General installation requirements
One To ensure reliable flowmeter operation, the following check-list will minimise problems:
¾ Install the meter in the recommended position and attitude.
¾ Ensure the measuring tube is completely filled at all times.
¾ When measuring liquids, ensure there is no air or vapour in the liquid.
¾ When measuring gases, ensure there are no liquid droplets in the gas.
¾ To minimise the effects of vibration support the pipeline on both sides of the flowmeter.
¾ If necessary, provide filtration upstream of the meter.
¾ Protect meters from pressure pulsations and flow surges.
¾ Install flow control or flow limiters downstream of the meter.
¾ Avoid strong electromagnetic fields in the vicinity of the flowmeter
¾ Where there is vortex or corkscrew flow, increase inlet and outlet sections or install flow
straighteners.
¾ Install two or more meters in parallel if the flow rate is too great for one meter.
¾ Allow for expansion of the pipework.
¾ Make sure there is sufficient clearance for installation and maintenance work.
¾ Where possible provide proving connections downstream of the meter for regular in-situ
calibrations.
¾ To enable meters to be removed for servicing without station shutdown, provide a by-pass
line.
Figures 10.2 to 10.7 illustrate a number of recommended installation practices laid down
specifically for electromagnetic flowmeters. The same principles also apply to most other
flow metering devices.
Figure 10.2. Preferred
locations. Since air bubbles
collect at the highest point on a
pipe run, installation of the
meter at this point could result
in faulty measurements. The
meter should not be installed in
a downpipe where the pipe may
be drained (courtesy Krohne).
Figure 10.3. In a horizontal
pipe run, the meter should be
installed in a slightly rising pipe
section (courtesy Krohne).
225
Industrial Flow Measurement
Common Installation Practices
Figure 10.4. Where there is an
open discharge, install the
meter in a low section of the
pipe (courtesy Krohne).
Figure 10.5. In long pipes, always install shutoff valves downstream of the flowmeter
(courtesy Krohne).
Figure 10.6. Never install a flowmeter on
the pump suction side (courtesy Krohne).
Air valve
>5 m
Figure 10.7. Where a downpipe is 5 m lower than the main inlet pipe, install an air valve at
the highest point (courtesy Krohne).
226
Industrial Flow Measurement
10.5
Common Installation Practices
Torquing
The role of a gasket is to form a sandwich between the flanges and ensure that the medium
flowing through the meter is safely contained.
If the flange bolts are not tightened enough the gasket will leak. If over-tightened, the gasket
may become deformed – resulting in a leakage. More seriously, many gaskets (for example,
an O-ring) are recessed, as shown in Figure 10.8, and are normally tightened until a metal-tometal contact occurs. In this case over-tightening can cause deformation of the flanges –
leading to damage to the meter itself. Ceramic liners, in particular, have been prone to
damage through over-tightening as their mechanical characteristics are quite different from
metals.
Figure 10.8. Recessed
gaskets are normally
tightened until a metal-tometal contact occurs
(courtesy Endress +
Hauser).
During commissioning or replacement of a meter, the flange bolts should be tightened only
when the maximum process temperature is reached. Conversely, meters should be
disconnected when the temperature is below 40 °C to avoid the risk of damaging the surface
of the gasket.
If a flange connection leaks, despite the fact that the bolts are tight, then they should NOT BE
TIGHTENED ANY FURTHER. Loosen the bolts opposite the leak and tighten the bolts by
the leak. If the leak persists, then the seal should be checked for foreign objects trapped in
between.
The torque values given in Table 10.1 are based on greased bolts and serve as guidelines only
since they depend on the material from which the bolts are manufactured.
227
Industrial Flow Measurement
Common Installation Practices
Table 10.1. Torque values based on greased bolts for various gaskets
(Courtesy Endress + Hauser).
DN
15
20
25
32
40
50
65
80
l00
25
150
200
250
300
350
400
450
500
600
700
800
900
1000
PN
40
16
10/16
Bolts
4xM12
4xM12
4xM12
4xM16
4xM16
4xM16
4xM16
8xM16
8xM16
8xM16
8xM20
12xM20
12xM20
12xM20
16xM20
16xM24
20XM24
20XM24
20XM27
24xM27
24xM30
28XM30
28xM33
Torque values DIN in Nm
Klingeri Soft rubber
PTFE
te
15
25
25
5
33
40
8
53
50
11
67
64
15
84
87
22
114
53
14
70
65
22
85
80
30
103
110
48
140
108
53
137
104/125 29/56
139/166
191/170 39/78
159/227
141/193 39/79
188/258
191/245 59/111
255/326
170/251 58/111
227/335
197/347 70/152
262/463
261/529 107/236
348/706
312/355 122/235
417/471 173/330
399/451 183/349
513/644 245/470
10.6 Grounding and earthing
To ensure measuring accuracy and avoid corrosion damage to the electrodes of
electromagnetic flowmeters, the sensor and the process medium must be at the same electrical
potential. This is achieved by earthing the primary head as well as the pipeline by any one or
more of a number of methods including: earthing straps, ground rings, lining protectors and
earthing electrodes.
Improper earthing is one of the most frequent causes of problems in installations. If the
earthing is not symmetrical, earth loop currents give rise to interference voltages – producing
zero-point shifts.
Figures 10.9 to 10.13 show the most effective earthing configurations.
228
Industrial Flow Measurement
Common Installation Practices
Earth
Figure 10.9. Earthing for conductive unlined pipe and conductive pipe
with earthing electrode (courtesy Emerson).
Lining protector tab
Earth
Lining protector
Figure 10.10. Earthing for conductive unlined and lined pipe with lining
protectors (courtesy Emerson).
Earth
Earthing rings
Figure 10.11. Earthing for non-conductive pipe with earthing rings
(courtesy Emerson).
229
Industrial Flow Measurement
Common Installation Practices
Figure 10.12. Earthing for conductive lined pipe with earthing rings
(courtesy Emerson).
Figure 10.13. Earthing for non-conductive lined pipe with earthing electrodes
(courtesy Emerson).
It is essential in cathodic protection installations to ensure that there is an electrical
connection between the two piping runs using earthing rings or electrodes. It is also essential
that no connection is made to earth.
230
Industrial Flow Measurement
Common Installation Practices
Earth
Earth
GRND rings
Figure 10.14. Cathodic protection installations (courtesy Emerson).
231
Industrial Flow Measurement
Common Installation Practices
232
Industrial Flow Measurement
Selection Charts
Chapter 11. Selection charts
Industrial Flow
Measurement
233
Industrial Flow Measurement
Selection Charts
234
Industrial Flow Measurement
Selection Charts
Chapter 11
n n n {
Electromagnetic
n
Flow nozzles
n
Fluidic
} }
} n
n
n
n n n n
Flumes
n
Orifice plate
n
Pitot
}
}
n n
}
n
n
n
} }
{ }
n }
} }
} n
n }
n
} }
n {
Positive displacement
n n
n n n n
Target
n
Thermal mass
n
Turbine
{
Ultrasonic – Doppler
Ultrasonic – Transit time
n
n
Variable area
Venturi tubes
n
n
n
n
n
n n n n
Vortex shedding
Vortex precession
n
n n n n
Weirs
}
Open channel
Semi-filled pipe
Steam
Gas
Fibrous slurries
Abrasive slurries
} n n n n }
} { n } } n
} } } } } }
} } { n { {
} { n { { }
n n n } } {
} } } } { {
} n n n } {
} } } n } }
} { n } } }
} n } } { {
{ { } } } }
{ } } } { {
n { } } { {
} } } } } }
n n { } { {
} { { } { {
} { n { { }
Applicable under certain conditions
235
Non-newtonian
High viscosity
Low temperature
(cryogenics)
Low velocity
High temperature
Low conductivity
Corrosive liquids
n n n n
Coriolis
n Very suitable
Dirty liquids
Measuring technology
Clean liquids
Selection charts
n n { { {
n {
{
} }
{ n
}
{ {
}
n n { {
}
{
{ n n
{ n n { {
{ n n { {
{ n
}
{ {
{ n n { {
}
n n { {
}
{
{ n n {
}
{ n { {
}
{ n
}
{ { {
}
{ {
n n { {
{ n n { {
{ n n { {
}
{
{ Not suitable
{ n n
Life
Abrasive or
corrosive
Purchase
price
Range of
adjustment
Clean or
dirty
Viscosity
and density
Maintainable
accuracy
Process
conditions
Single or
multi-phase
Performance
Repeatability
236
Flow
conditioning
Installation
requirements
Power
requirements
Installed
cost
RFI-EMI
Ambient
conditions
Ancillary
equipment
Failure
pattern
Failure mode
Signal
integrity
Pressure
rating
Intelligence
Reliability
Temperature
ratings
Line size
Cost of
Maintenance
Reference
accuracy
Properties of
process fluid
Required
Measurement
Compatability
Response
time
Industrial Flow Measurement
Dynamic
range
Safety
Temperature
Corrosion
Humidity
Vibration
Cost of
ownership
Selection Charts
Parameters to consider when choosing a flowmeter (courtesy ABB-Kent)
Industrial Flow Measurement
Measurement of steam
Chapter 12. Measurement of steam
Industrial Flow
Measurement
237
Industrial Flow Measurement
Measurement of steam
238
Industrial Flow Measurement
Measurement of steam
Chapter 12.
Measurement of steam
Water converts from its liquid phase to its vapour phase (steam) at its boiling point of 100 °C
at atmospheric pressure, rising as the system pressure increases.
Steam that is fully vaporised, but has not been heated to a temperature above the boiling point
temperature, is called saturated steam. Steam that is fully vaporised and heated to
temperature above the boiling point is called superheated steam.
Steam that is not fully vaporised is called wet steam. The percentage, by weight, of the water
droplets in wet steam is known as the percentage moisture, and subtracting the percentage
moisture from 100 gives the percentage quality of the steam.
The measurement of 'wet' low quality steam is possible with a vortex meter – depending on
the distribution of the liquid phase within the steam. Ideally, the secondary phase should be
homogeneously dispersed within the primary phase (Figure 12.1). This tends to be the case
with low amounts of secondary phase due to the high velocities and turbulence produced
by the meter.
Homogeneous
mixture
Figure 12.1. Homogeneous distribution of 'wet'
low quality steam (courtesy Krohne).
However, for low quality steam the distribution of the liquid phase, within the steam, may be
stratified. In horizontal pipes the water phase travels continuously along the bottom of the
pipe and the vapour phase travels as a continuous stream along the top. Here, the best
installation for the vortex meter would be in a horizontal line with the shedder positioned in
the horizontal plane (Figure 12.2).
Condensate
Figure 12.2. Recommended installation for ‘wet’
low quality steam with stratified flow in horizontal
pipes (courtesy Krohne).
Bluff body
Bluff body
Recommended Not recommended
239
Industrial Flow Measurement
Measurement of steam
In vertical pipes the trend is towards 'slug' flow in which the water phase travels as
discontinuous slugs down the pipeline, suspended between the vapour phase (Figure 12.3)
Slug
Figure 12.3. 'Slug' flow in vertical pipes (courtesy
Krohne).
Again, however, users should be aware that the meter will, at best, measure the total volume
and performance will not be to standard specifications. Most meters cannot make a
measurement if slug flow exists and many meters will be destroyed by slug flow.
240
Industrial Flow Measurement
Standards organisations
Chapter 13. Standards organisations
Industrial Flow
Measurement
241
Industrial Flow Measurement
Standards organisations
242
Industrial Flow Measurement
Standards organisations
Chapter 13.
Standards organisations
A large number of organisations who are not normally involved in the field of instrumentation
have been involved in the field of flow measurement. Such organisations have been involved
specifically in determining the limits for custody and fiscal management; to cover the
requirements for safety; and to the cover the requirements for environmental protection.
Some of the organisations involved are shown in Table 13.1
Table 13.1. Some of the organisations involved in setting standards for the measurement of
flow in an industrial environment.
Abbreviation
AChI
AGA
ANSI
API
ASME
ASTM
BSI
DIN
EIA
HSE
IEC
IEEE
ISA
ISO
NEMA
OSHA
TIA
Organisation
American Chemical Institute
American Gas Association
American National Standards Institute
American Petroleum Institute
American Society of Mechanical Engineers
American Society for Testing and Materials
British Standards Institute
Deutsches Institit für Normung
Electronic Industries Alliance
Health and Safety Executive
International Electrotechnical Commission
Institute of Electrical & Electronic Engineers
International Society for Automation (formerly Instrument Society of
America)
International Organisation for Standards
National Electrical Manufacturers Association
Occupational Safety and Health Administration
Telecommunications Industry Association
243
Industrial Flow Measurement
Standards organisations
244
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