24508-48
CUSTODY TRANSFER FLOW MEASUREMENT
WITH NEW TECHNOLOGIES
Stephen A. Ifft
McCrometer Inc.
Hemet, California, USA
ABSTRACT
New technologies can often bring advances to the operational processes within many
industries. These advances can improve the overall production of a facility with better
performance, better reliability, and lower costs. Obstacles exist, however, to the
introduction and use of these new technologies. The natural gas industry has such
obstacles, particularly with the use of new technology for custody transfer flow
measurement. Paper standards from international organizations like the International
Organization for Standardization, the American Petroleum Institute and the American
Gas Association are examples of these obstacles. While these paper standards serve to
protect and guide companies in their use of technology, they prevent the introduction of
new and often better technology. A reform is underway in the natural gas industry to
allow companies to take advantage of newer technologies that were not accessible
before. This will hopefully redefine the phrase “approved for custody transfer
measurement.” This phrase has been used incorrectly around the world for decades
since none of the organizations listed above actually approve meters for custody transfer
measurement. If companies are to reap the benefits of newer and better technology, the
industry must continue to reform the existing paper standards that exclude every
technology but those that are decades old. As new technologies become available, the
industry must have procedures ready for evaluating their possible benefits and
detriments. Without these procedures, the advances of the modern world will be
overlooked. McCrometer Inc. is a manufacturer of flow measurement devices, including
the V-Cone differential pressure flowmeter. McCrometer has first-hand knowledge of the
obstacles to bringing a new technology to the natural gas market. This paper will
explain how one new technology has been used successfully in custody transfer flow
measurement applications even without “custody transfer approval”. Also, the author
will review how the industry is transforming (and should transform) to exploit the new
technologies available today.
INTRODUCTION
The natural gas industry is the leader for
many other industries in terms of
measurement
technology
and
knowledge. Standards within the United
States natural gas industry are often used
within unrelated industries, such as
chemical, paper, and power industries.
These industries and others turn to the
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
natural gas leaders for standards of
measurement that can guide the
installation, use, and evaluation of
measurement devices.
Organizations within the United States
natural gas include the American Gas
Association (AGA) and the American
Petroleum Institute (API). Currently the
Page 1
AGA is focusing its efforts towards
natural gas distribution and consumer
use. The API is focusing its efforts
towards
gas
production
and
transmission. Even with their different
focuses, there is substantial overlap
between the organizations and there is
much cooperation between them.
AGA, API, and ISO all have one thing in
common, the term “Custody Transfer”.
This term has many different definitions
and uses. This author will define the
term custody transfer as the flow
measurement of a product between
parties where the measurement will be
used for financial purposes.
AGA and API both have programs that
write, publish, and support paper
standards. These standards cover a wide
range of topics including gas sampling,
gas storage, safety and pollution. This
paper will focus on the paper standards
for flow measurement devices only. By
far the most widely used standards are
those written around the orifice plate
differential pressure flow meter. This is
because the concentric, square-edged
orifice plate is used in more than 50% of
flow measurement applications around
the world.
By using standards written by these
organizations, a flow meter user can be
assured that the flow measurement is the
best possible level available by that
device.
The AGA and API standards concerning
orifice plates are as follows:
AGA Report No. 3, parts 1, 2, 3, 4
API Chapter 14.3, parts 1, 2, 3, 4
The International Organization for
Standardization (ISO) also writes,
publishes and supports paper standards
for measurement, including flow
measurement devices. Their standard
for the orifice plate is as follows:
ISO 5167-1:1991
This standard also covers other
differential pressure meters, such as
venturis and flow nozzles.
CUSTODY
TRANSFER
MEASUREMENT
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
FLOW
For instance, if a user buys, installs and
maintains an orifice plate according to
one of the above standards, that user will
be making a measurement that is as
accurate as can be expected from an
orifice plate. This accuracy is usually in
the range of 0.5 to 1.0% of reading.
Another advantage to using these
standards is the legal support they give
the user. Ideally a custody transfer
measurement is an agreement to buy and
sell a product between two parties. This
is not normally just two people shaking
hands over an agreement.
The
agreement must be in a legal
environment. As a legal issue, the
agreement must be binding and
supportable. By referring to a paper
standard for flow measurement, both the
buyer and seller (through their legal
departments) agree to use a certain type
of meter in a certain way. For instance,
if the agreement states the flow
measurement must be made in
accordance with AGA Report #3, then
an orifice plate is the choice of meters.
If any disagreement occurs between the
parties, the AGA paper standard is used
to determine if the flow measurement
was properly made or not.
Page 2
New technologies
As new technologies for flow
measurement enter the industry, paper
standards are not automatically written
around them. This is understandable for
many reasons. Many new technologies
enter the industry every year. The
demand to write a new paper standard
for each new technology would be
overwhelming. AGA, API, and ISO
make money off the sale of their
standards, but they could not commit the
resources to write a standard for so many
new products. Many of these new
technologies also will not last the test of
time. This has been proven over and
over. A new technology will appear to
solve
many
traditional
flow
measurement problems. As this new
product is tested and used over time,
new, unforeseen problems occur that
make the meter unusable for many
applications.
All the standards
organization would not spend time
writing a paper standard around a soonto-be-obsolete product.
As expected, there is also a legal reason
why these organizations do not write
standards for new technologies. By
writing a paper standard, these
organizations are guaranteeing the
success of a product. If Company X has
a product that has a paper standard
written around it, it would very likely do
better than a product from Company Y
without such a document. For this
reason, these organizations will not
consider writing a paper standard around
a metering device with a proprietary
design.
Design standards
The paper standards that exist today are
considered design standards. Not only
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
do the standards call out how the user
should use the meters, but also how they
should be built. Thus any meter that is
covered under a paper standard could not
be a proprietary design. All the AGA,
API, and ISO paper standards specify
exactly how the meter itself should be
built. If a company with a patented
design wanted to have a design standard
written around the product, it would
have to release the design information
that makes their product unique.
Obviously, most companies with new,
patented technologies will not release
such data.
A recent movement in the natural gas
industry may be changing the very
nature of the paper standards of today.
API is considering making new paper
standards not design standards but
performance standards. Thus, a meter
with the performance required for
certain applications would receive
approval. This movement is due mainly
to the increased popularity of ultrasonic
meters. Many natural gas customers
would like to use ultrasonic meters for
measurement but each manufacturer
makes their meter slightly different.
With so many different designs, API
could not reasonably write a design
standard for each one. A performance
standard was proposed and is now being
considered.
Government involvement
Within the United States, the
government has surprisingly little to do
with the custody transfer flow
measurement of natural gas. While there
exist standards regulating the flow
measuring of gasoline at consumer gas
stations and standards regulating the
flow measurement of pasteurized milk,
the government keeps a laissez-faire
Page 3
approach to the natural gas industry.
This is understandable since the industry
can safely and fairly regulate itself.
While the consumer has little protection
against measurement biases, large
corporations have a vested interest in
receiving and delivering accurate
amounts of product.
This type of self-regulation exists in the
United States and has been a successful
approach for more than a hundred years.
The governments of other countries,
however, do get involved in the
production and transportation of natural
gas. Canada is one such example. the
Canadian government regulates the
custody transfer transportation of natural
gas flow measurement. The branch of
the government responsible for this is
called Industry Canada. Under Industry
Canada is the Measurement Canada
division, which does this regulation.
(http://mc.ic.gc.ca)
Measurement
Canada has a specific approval process
that manufacturers of flow measurement
and other products must follow before
using their instrument for custody
transfer measurement in Canada.
While Measurement Canada is a
completely separate entity, it is closely
associated with the American natural gas
industry. This is because the approval
processes that they follow are linked to
the standards mentioned earlier. To
approve a flow meter, a manufacturer
must meet the design standards given by
API. Therefore, new technologies are
also effectively blocked from acceptance
in Canada.
This pattern repeats itself through North,
Central and South America. Countries
in those continents refer back to paper
standards from the United States. In
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Stephen A. Ifft, McCrometer Inc.
Europe, national standards refer back to
the appropriate ISO paper standards.
For Asia, Africa, and the rest of the
world, the particular standard referenced
in government documents varies.
“APPROVED
FOR
CUSTODY
TRANSFER”
The term “approved for custody
transfer” is used throughout the world.
If a vendor tries to introduce a new
product to an industry, one of the first
questions is “Is the meter approved for
custody transfer measurement?” In the
United States the answer to this question
is “No.” Even if the meter under
question is an orifice plate, the answer is
“No.” This is because there is no
organization that approves meters for
custody transfer measurement.
The
United States government certainly does
not. AGA and API only write standards
around certain meter design. They do
not approve meters in any way.
The question above needs to be
reworded to “Does your meter have an
AGA or API paper standard written
around its design?” The answer to this
question can only be answered positively
if the manufacturer is producing an
orifice plate, venturi, flow nozzle,
turbine, and, some would say, an
ultrasonic meter. Any other type of
device has no paper standard written
around it.
This question also carries a lot of weight
since the answer to it often defines
whether a certain meter will be
considered for an application or not.
This question can also block new
technologies from non-custody transfer
applications. A meter without “custody
transfer approval” is considered not
equal to those that do.
Page 4
McCROMETER V-CONE
The V-Cone differential pressure
flowmeter,
manufactured
by
McCrometer Inc., is an example of new
technology available to industry today.
The V-Cone has many benefits that
could potentially help the natural gas
industry, and other industries, with some
basic flow measurement problems. It is
also an example of how such a
technology can be blocked from
acceptance because of the paper standard
system of the AGA, API, and ISO.
V-Cone
The V-Cone is a differential pressure
flowmeter invented and manufactured by
McCrometer Inc. Patented in 1986 as a
new type of differential pressure flow
meter, the V-Cone is based on the
principles of Bernoulli.
The geometry of the V-Cone is a
radically
different
approach
to
differential pressure flow metering, see
Figure 1. As with other differential
pressure devices, the flow constricts to
create a high velocity area, which creates
a lower pressure just past the
constriction. By measuring the pressure
upstream and downstream of the cone, a
differential pressure can be calculated
and related to the flowrate through the
pipeline. The V-Cone’s constriction,
however, is not a concentric opening
through the center of the pipe like
traditional
differential
pressure
flowmeters. The V-Cone creates an
annular opening, forcing the fluid to
flow around a cone positioned in the
center of the pipe.
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
Figure 1: Illustration of a typical
V-Cone design
Equations for the V-Cone are only
slightly
different
from
standard
differential pressure equations.
The
V-Cone beta ratio follows the same
principle as other differential pressure
devices. Thus a V-Cone and an orifice
plate beta ratio are equivalent to each
other in terms of open area. The basic
equation of flow for the V-Cone is
similar to standard differential pressure
equations.
The V-Cone offers many distinct
advantages because of it geometry and
engineering. A number advantages are
listed below that appeal particularly to
the natural gas industry:
1. Short installation requirements. The
V-Cone can be installed with no or
very little installation runs upstream
or downstream of the meter. This
can provide substantial savings
during new installation planning or
when a pipeline is retrofitted for flow
measurement.
2. Wide turndown.
The V-Cone
discharge
coefficient
remains
constant over a wide range of flows.
This allows for one meter to measure
the span of multiple orifice plate
runs.
3. Low signal noise. The low signal
noise of the V-Cone give the user
Page 5
much faster response time in critical
application, such as anti-surge
measurement.
4. Little or no maintenance or
recalibration required.
The selfcleaning design of the V-Cone
makes it less susceptible to coating
or abrasion over time. This makes
the V-Cone ideal for remote and
unmanned installations.
Selling without “custody transfer
approval”
The V-Cone was introduced over 13
years ago and is now well accepted
through the world for accurate and
dependable flow measurement.
The
design and use of the V-Cone is patented
worldwide and so AGA or API have not
been able to write a paper standard
around its proprietary design. This has
certainly stunted the growth of the
V-Cone.
More importantly to the
natural gas industry, the V-Cone has
been blocked as a new and potentially
money-saving technology in many
applications, even non-custody transfer.
Even with this extra-hurdle to clear, the
V-Cone has been used successfully and
has also measured many custody transfer
applications.
There are two main
reasons for this.
First, the V-Cone is a completely
traceable and accurate means to measure
flowrate. Each V-Cone is calibrated on
a flow measurement standard traceable
to the national standards of the United
States, the National Institute of
Standards and Technology (NIST).
Many V-Cones intended for custody
transfer applications are calibrated
outside
of
McCrometer
at
an
independent facility.
As completely
separate entities from McCrometer, the
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
testing and calibration facilities produce
results from the meter that are reliable
without question. This means the enduser will receive a meter that has
received a full calibration and testing
prior to installation.
Any defects,
inaccuracies, or problems with the
V-Cone would be evident during the
testing. This type of custody transfer
traceability has been used in the natural
gas industry, as well as other industries
such as power and municipal.
Second, McCrometer has successfully
proven the superior performance of the
meter to the government of Canada. In
March of 1998, Industry Canada
approved
the
V-Cone
for
the
measurement of custody transfer natural
gas. This may seem illogical since the
Canadian
government
uses
API
standards to approve or disapprove
meter manufacturers. The remainder of
the paper will discuss the obstacles and
eventual success of McCrometer in this
endeavor.
CANADIAN CUSTODY TRANSFER
APPROVAL
The approval process with the Canadian
government
is
well-defined
in
documents such as the Specifications for
Approval of Type of Gas Meters and
Auxiliary Devices (LMB-EG-08). This
document states, among others, the
requirements for approval of certain
types of flowmeters. These meters are
generally defined as:
1. Diaphragm meters
Section 5
2. Rotary meters
Section 6
3. Turbine meters
Section 7
4. Orifice meters
Section 8
5. Mass flow meters
Section 9
The V-Cone is a differential pressure
type device and McCrometer’s intention
Page 6
was to have the V-Cone certified under
the same principles and requirements as
an orifice plate.
After receiving the application for type
approval for the V-Cone, Measurement
Canada reviewed the product data and
existing performance data regarding the
V-Cone. Even though the V-Cone is
based on the same principles as the
orifice place, the V-Cone could not be
evaluated under the same requirements
as the orifice meter’s section.
Section 8 of the specifications refers
extensively to the American National
Standard, ANSI/API 2530, “Orifice
Metering of Natural Gas and Other
Related Hydrocarbon Fluids.”
This
standard deals exclusively with the
orifice plate design and could not be
correlated to a V-Cone application.
Measurement Canada then needed to
decide how to deal with the V-Cone and
under what section the evaluation should
proceed.
For two apparent reasons, the V-Cone
application would be evaluated under
Section 7 of the specifications regarding
turbine meters. The first reason was the
performance specifications of the
V-Cone. The standard accuracy and
turndown of the V-Cone is stated as
±0.5% of rate over a 10:1 turndown.
The requirements for turbine meters
under this section call for 1% of rate for
the entire measurement system over a
10:1 flow turndown. A system accuracy
of ±1% of rate is easily possible with a
combination of the V-Cone and the
correct measurement and calculation
equipment.
The second reason was the issue of
calibration. Similar to turbine meters,
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
V-Cone meters need initial in-line
calibrations for the best accuracy. Each
custody transfer V-Cone will be flow
calibrated at a laboratory directly
traceable to Canadian or American
national measurement standards. These
laboratories are typically independent
companies whose expertise is in
compressible gas flow and calibration.
Performance Test
A performance test was a necessary part
of the evaluation process. Measurement
Canada required a witnessed test of the
performance of the meter and instrument
system. This test would support the
documented data already produced
during the evaluation process.
A typical turbine meter calibration
would take place in Measurement
Canada’s gas flow facility. This system
operated at atmospheric pressure and
was not suited for the higher-pressure
performance test of the V-Cone. With
consent from both Measurement Canada
and
McCrometer,
the
Colorado
Engineering Experiment Station, Inc.
(CEESI) was selected as the test
laboratory for the performance test.
CEESI is well acquainted with the
V-Cone and well equipped for the type
of calibration required.
McCrometer was to supply the V-Cone
and the necessary instrumentation.
Measurement Canada would witness and
certify the test. An existing four-inch
V-Cone with a beta ratio of 0.45 was
selected. This size meter and cone
would fit easily into the CEESI test lab
and require only moderately high
flowrates to generate a sufficient
differential pressure.
A Rosemount
3095MV
was
the
secondary
Page 7
instrumentation chosen for the flow
measurement system. The 3095MV,
when programmed to work with the
V-Cone, would output a 4-20 mA signal
proportional to the mass flowrate
through the meter. McCrometer chose a
multivariable transmitter to simplify the
verification of the flow calculations.
CEESI’s laboratory is referenced using
critical flow venturi nozzles. These
nozzles and the entire instrumentation
system are completely traceable NIST.
A large volume of high-pressure air
supplies the test system. The system
vents air back to atmosphere a sufficient
distance downstream of the test section.
The results of the test indicate
performance well within the required
specifications for Measurement Canada.
See Appendices A & B for tabular and
graphical results. Absolute pressure
during the test was approximately 200
psia and covered a Reynolds number
range of approximately 1 million to
75,000. Over this flow range of 13:1,
the system accuracy of the V-Cone and
Rosemount 3095MV was +0.30 to 0.54% of rate. By adjusting the flow
coefficient according to the calibration,
the system accuracy could be stated as
±0.42% of rate.
This exceeds the
specifications of the V-Cone primary
element. When considering the added
uncertainty of the instrumentation and
flow calculations, this test shows very
good performance.
Notice of Approval
Following the performance tests, several
drafts of the notice of approval were
reviewed.
After the review and
translation of the document were
complete, the final Notice of Approval
(NOA) was granted March 19, 1998.
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
The notice states “The V-Cone meter is
a differential pressure type flowmeter
approved for custody transfer of natural
gas.”
Following the guidelines of Section 7 of
the specifications, the installation
requirements must be in accordance with
McCrometer’s recommendations. The
markings on any Canadian custody
transfer V-Cone must include certain
information, including the departmental
approval number.
Also following Section 7, the V-Cone
must be verified either in-situ or at “a
high pressure gas meter calibration
facility acceptable to Industry Canada.”
CEESI and other laboratories are
available for this testing if necessary.
The NOA states “This V-Cone meter
uses any approved and compatible flow
transmitter or flow computer that is
approved to perform V-Cone meter
calculations for determining the volume
of gas through the meter at standard
conditions.” This sentence refers to the
method of calculation used to determine
mass flowrate of gas through the meter.
Two methods are currently being used
by the natural gas industry. This author
will label these methods “traditional”
and “multivariable”.
Both methods utilize the same basic
principles. As displayed in Fig. 2, the
measurements take place separately from
the calculations. The measurements are
also split between the primary element
measurement, in this case the V-Cone,
and the secondary measurements of
differential pressure, pressure and
temperature.
Figure 2: Basic differential pressure
flow measurement system
Page 8
Measurements
Primary
V-Cone
Secondary
DP, P, T
Calculations
In traditional calculation methods, the
measurements are done separately from
the calculations. Transmitters would be
used for the measurements of differential
pressure, pressure, and temperature.
Signals from these transmitters would be
sent to a flow computer or a distributed
control system (DCS).
The flow
calculations would be done separately
from the measurement area and
displayed and used in various ways.
A relatively new method of flow
calculation is now being accepted in the
natural gas industry. The multivariable
method uses a single instrument to
measure differential pressure, pressure
and temperature.
This reduces the
instruments and pipeline connections
necessary in the differential pressure
flow meter. The multivariable system
uses these inputs and calculates the flow
in the same instrument. This blurs the
line between the measurement and
calculation areas.
The NOA calls for “approved” devices
to calculate the flow through a V-Cone.
Currently no flow transmitters or flow
computers are approved for use with the
V-Cone.
McCrometer is currently
working with Measurement Canada to
define the approval process for V-Cone
calculation devices. Since the V-Cone is
based on the same principles as
traditional differential pressure devices
and uses virtually the same mass flow
equations as a venturi, this process
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
should
go
rapidly.
Several
manufacturers of flow transmitters and
flow
computers
have
already
incorporated the V-Cone into their
devices.
The Measurement Canada
approvals for these devices will need
only updating to show the current
changes.
The option available to users at time of
printing is the use of a DCS system. A
DCS could be programmed to correctly
calculate mass flow rate through a
V-Cone, similarly to what is done for
orifice plates. These systems must be
individually
approved
through
Measurement Canada.
Conclusions
The McCrometer V-Cone meter has
been approved for custody transfer
measurement of natural gas in Canada.
The V-Cone performed above the
requirements given by Measurement
Canada.
This approval is significant for the
V-Cone and will have impact well
beyond Canada or even North America.
The Measurement Canada approval
process is the only government-based
process in North America. The United
States government does not provide this
service. Independent organizations such
as the American Gas Association (AGA)
and the American Petroleum Institute
(API) are expected to provide such
standards and guidelines. The “approval
process” through these organizations is
not clearly defined, since the standards
deal with meter design rather than
performance. A patented meter design
such as the V-Cone could not be covered
with such a design standard. This may
be changing as ultrasonic technology is
entering the industry. Ultrasonic meters,
Page 9
while all use the same basic principles,
have proprietary designs. Current drafts
of standards within AGA and API deal
with design and performance issues in
different ways.
The impact of this approval has been
noticed in Canada and worldwide.
Canadian users recognize the importance
of this approval and have opened
previously closed doors to the V-Cone
technology. Users in the United States
acknowledge the importance of the only
approval process in North America.
This author has been asked about this
approval in places as far away as
Australia and Norway.
References
1. Specifications for Approval of Type
of Gas Meters and Auxiliary Devices
(LMB-EG-08),
Consumer
and
Corporate Affairs Canada, Legal
Metrology Branch, 1987.
2. Notice of Approval, V-Cone Meter
(AG-0428), Measurement Canada,
March 19, 1998.
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Stephen A. Ifft, McCrometer Inc.
Page 10
Appendix A
COLORADO ENGINEERING
EXPERIMENT STATION, INC.
Calibration of a McCrometer V-Cone
Model: V5104
Serial No. 97042300
For: McCrometer
Order:
Data File: 97MCC022
Disc: 0997-018 Date: 24 September 1997
Inlet diameter: 4.09 inches
Throat diameter: 3.659 inches
Test gas: AIR
Standard density= .074915 lbm/cu-ft
at standard conditions of 529.69 deg R, and 14.696 psia
Mtr Read: Meter reading in volts DC across a 99.995 ohms resistor
Mdot: Mass flowrate in Lbm/sec
Rey No: Inlet (pipe) Reynolds number
Mtr Read2: Meter reading in Lbm/sec
L
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Mtr Read
2.04827
1.96022
1.877705
1.988706
1.83909
1.736693
1.62633
1.75828
1.486764
1.315351
1.473358
1.101089
0.985557
1.089277
0.841574
0.709143
0.62474
0.599846
0.683298
0.61198
0.578701
0.54688
0.528939
0.554899
Mdot
3.107034
2.937754
2.784982
2.992303
2.711715
2.51872
2.304196
2.560127
2.038151
1.717084
2.010799
1.317516
1.100524
1.294442
0.830255
0.581577
0.421559
0.375346
0.531777
0.398872
0.334258
0.27452
0.241366
0.28954
Rey No
979671.9
929007.2
882329.4
949333.8
861650.7
801073.4
733300.8
815130.8
649239.9
546966.2
640427.2
419555.6
350291.8
411758.4
263978.5
184854.3
128848.2
119100.3
164978.3
123801.4
103731.1
85167.09
74870.05
89840.09
Mtr Read 2
3.0903
2.9252
2.7705
2.9786
2.6981
2.5061
2.2992
2.5466
2.0375
1.7162
2.0124
1.3144
1.0978
1.2923
0.8279
0.5796
0.4213
0.3747
0.5311
0.3974
0.3350
0.2753
0.2417
0.2904
Average values for above results:
Press: 204.53 psia
Density: 1. 0919 lbm/cu-ft
Temp: 508.89 Deg R
Viscosity: .00000098726 lbm/inch-sec
Compressibility factor: .99379
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
Page 11
Appendix B
CEESI Calibration for Industry Canada Evaluation
4" V-Cone Beta 0.45 System Accuracy
2.00
1.50
% difference
1.00
0.50
0.00
-0.50
-1.00
-1.50
-2.00
0
200000
400000
600000
800000
1000000
1200000
Reynolds Number
Saudi Aramco 1999
Stephen A. Ifft, McCrometer Inc.
Page 12
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