Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter
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Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter
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1 INTRODUCTION
3 VELOCITY PROFILE
The primary function of the ultrasonic meter is to measure the
The four chordal velocities give an indication of the velocity
actual volume flow rate. The process involves measuring four
profile in the meter, established by the flow through the upstream
velocities on chords located in four different radial positions and
pipe work. Three helpful ratios can be defined as: Asymmetry =
in two different vertical planes. The eight transducers are fired
(VA + VB)/(VC + VD), Cross flow = (VA + VC)/(VB + VD) and Swirl
about 50 times per second and the transit times to traverse each
chord in both directions are measured. This vast array of data
= (VB+ VC)/(VA + VD).
The asymmetry compares the flow in the top half of the pipe with
can be processed to yield useful diagnostic information, which
that in the bottom half; in good condition it should be close to 1.
forms the subject of this paper and shows that the four-path
The cross flow compares the chords in one plane with those in
ultrasonic meter does much more than just measure the flow
the other plane at right angles: in good condition it should be
rate. It has sufficient diagnostic ability to confirm the authenticity
close to 1. The swirl compares the inner chords to the outer
of the measurement, and develop the source for conditional
chords and it is an indicator of swirl due to both the different
based maintenance and re-calibration.
radial locations and planes. In good condition the swirl should
be close to 1.042/0.89 = 1.17 [1].
2 METER GEOMETRY AND FUNCTION
Fig, 1a. End View
Fig. 1b. Top View
There are two equations for the transit time with (t1) and against
(t2) the flow, which can be solved for the chord velocity (Vi)
Where C = speed of sound
L = distance between transducers
X = axial distance in the flow
R = meter radius
The average velocity (V) and actual volume flow rate (Q) are
found from:
W = the weighting factor
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Examples of analytical flow profiles with swirl are shown in Fig.
2, and how the swirl ratio can estimate the magnitude of the
swirl angle in Fig. 3.
Fig. 2 VELOCITY PROFILE WITH SWIRL
Fig. 3 SWIRL RATIO (Vb+Vc)/(Va+Vd)
Actual measured ratios are shown in Fig. 4 for a 20” meter.
Fig. 3 SWIRL RATIO (Vb+Vc)/(Va+Vd)
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Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter
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Because of tolerances in the manufacture of the ultrasonic
is higher on the outer chord, nearer the pipe wall where there is
meter and the difficulty of achieving ideal fully developed flow,
more shear.
the actual ratios are never exactly at their theoretical values,
and give the meter a unique fingerprint. However they are
If flow pulsations or fluctuations are present, this turbulence
usually within ±2%, which is sufficient to say that the flow profile
parameter will increase above the 2% to 5% value associated
is near perfect, which is not surprising since Fig.4 comes from
with good flow.
a lab calibration.
In general, four paths are not sufficient to resolve any arbitrary
3-dimensional flow field containing asymmetry, swirl and cross
flow. However, fiscal flow measurement practice attempts to
establish good flow conditions, which can certainly be verified
by these ratios. Never the less, if the ratios differ significantly
from their ideal value they can give a reasonable indication of
the type of disturbance, especially if only one of the ratios has
4 SPEED OF SOUND
The speed of sound can be evaluated from the same two transit
times for each chord:
The average speed of sound C is just the average of the chords
C = (CA +CB + CC +CD)/4
changed significantly.
The speed of sound can be used as a diagnostic in several
3.1 Turbulence, pulsation and fluctuation
4.1 Compare a measured and calculated value
In discussing the velocity profile we have been considering the
The speed of sound can be calculated from independent
average velocity obtained from a batch of transit times from all
eight transducers. The velocity depends upon the transit time
difference Δt = (t2 – t1). Typically a batch of 20 Δt values is used
to determine an average Δt and hence the average velocity. The
batch of 20 also allows the calculation of a standard deviation
σΔt, and then the ratio σΔt/Δt is a measure of turbulence or
ways:
measurements of gas composition, pressure and temperature,
using methods described in AGA 10 [2]. This is an independent
check on the transit time measurement and is important because
the ultrasonic meter basically measures transit times.
An example is shown in Fig. 6 for a 4” meter. Note that 4” is
velocity fluctuation.
the smallest ultrasonic meter typically used and the small length
Some typical values are given in Fig. 5, for the inner and outer
determine the speed of sound.
chords of a meter during calibration in good flow.
The turbulence varies from 2 to 5% of the velocity. The inner
chord-C has an average turbulence of 3%, while the outer
chord-D has an average turbulence of 4%. This is in keeping
with typical point values in pipe flow of 6% at z/R = 0.309 and
9% at z/R = 0.809, and the general concept that the turbulence
Fig. 5 TURBULENCE % = 100* STD-DEV Dt / Dt
and short transit time make it the most difficult size to accurately
Despite the small size the agreement between measured
and calculate speed of sound is good to within ± 0.02%. This
calibration at SwRI re-circulates the same gas in a closed loop;
hence there is no change in gas composition for the results in
Fig. 6.
Fig. 6 4” METER SOS DEVIATION FROM AGA 10
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Fig 9. SOS LONG - SOS SHORT %
4.2 Compare the 4 chordal values with one
another
At a reasonable gas velocity (say > 5 ft/s), the gas composition
and temperature should be uniform over the pipe cross-section
and all chords should read the same speed of sound. See Fig.
7 for an example from a 12” meter. If all four values agree, it is
more likely that they are all correct than all in error by exactly
the same amount.
Fig. 7 CHORDAL SPEED OF SOUND FT/S
= 2.7R giving a length ratio = 2.7/1.7 = 1.6. If the speed of sound
is the same on chords of different length, this indicates that both
the transit times and delay times (time not spent in the gas) are
correct. The normal way of determining the delay time is with a
gas of known speed of sound, typically nitrogen. Another way is
to use two different lengths in the same, but unknown, speed of
The values of speed of sound on all four chords agree to within
sound. Thus the different chord lengths allow a dynamic method
± 1 ft/s This is not quite as good a test as the one in section 4.1,
of checking the delay times.
but it has the advantage of not requiring any additional external
inputs (pressure, temperature & composition).
4.3 Use the difference between the chordal and
average value
Fig. 9 shows very small variation of 0.002% SOS or about 20 ns
in transit time, which is close to the stability limit of the metering
system.
Because of manufacturing tolerances the four chordal values
Note: three examples have been shown where the SOS
of speed of sound will never be exactly equal. These small
variations are 0.1%, 0.02% and 0.002%. A good value for the
differences can be used as another fingerprint of the meter.
average field application would be 0.05%.
See Fig.8 as an example
Fig. 8 SOS DIFFERENCE FROM AVERAGE %
4.5 Correction for stratification
An example is given for a velocity of 2 ft/s in a 12” pipe with the
gas temperature at 70o F and the ambient temperature at 90o F,
in a long un-insulated pipe, shown in Figs 10 & 11.
Fig 10. TEMPERATURE [SOS] GRADIENT
4.4 Check the agreement between chords of
different length
Fig.9 shows an example for a 12” meter under stable zero flow
conditions.
The 4-path Daniel meter has paths of different length. The outer
chords (A & D) have L = 1.7R and the inner chords (B&C) have L
The 4 chords are horizontal and spaced vertically, so they
see the temperature stratification: low density gas, with high
temperature and higher speed of sound floats on top of the
Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter
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higher density gas, with lower temperature and lower speed of
•
An upstream flow control valve being adjusted
sound. In this case a SOS gradient of 8 ft/s corresponds to the
•
An upstream branching flow of varying proportion to
temperature gradient of 6oF. This temperature difference also
the metered flow
drives a natural convection current: gas heated by the pipe wall
•
A flow conditioner trapping debris
rises to the top of the pipe, while cold gas in the center falls to
•
Erosion, corrosion or deposition changing the
the bottom of the pipe. This convection current, which is normal
to the axial flow, pushes the maximum axial velocity down from
upstream pipe roughness
the center of the pipe, and the effect is seen in the velocity
5.1 Pipe roughness
profile shown in Fig. 11.
The meter can detect an increase in pipe roughness by its effect
on the velocity profile [3]. In general the velocity profile depends
non-
upon both roughness and Reynolds Number, but at the high Re
representative gas temperature measurement. A reasonable
No associated with natural gas transport the roughness effects
approach to the correct gas temperature is a Flow Weighted
dominate. The profile can be described by the ratio (VB+ VC)/(VA
Mean Temperature (FWMT) based on using the same velocity
+ VD), but here we are looking for change from a flatter profile to
flow weighting factors Wi for the chordal temperatures. The result
a more pointed profile (Fig.12) with time, and not swirl.
in this case is FWMT = 73.5o F seen in Fig.10. Unfortunately
The ratio (VB+ VC)/(VA + VD) can be linked to pipe roughness (Fig.
the high pipe temperature and the highest gas temperature
13) in terms of relative roughness k/D, where k = the roughness
influence the thermo-well located on top of the pipe, and reads
height and D = the pipe diameter.
Another
consequence
of
stratification
is
a
poor
a temperature = 77.8o F. This error of 4.3o F in 530 o R will give
a 0.8% error in the corrected volume flow. The SOS gradient can
Again the idea is that fixed piping gives a fixed velocity profile, so
be used to recognize and correct the error; this is unique to the
a changing profile with time is an indication of pipe roughness. If
chordal ultrasonic meter, while non-chordal ultrasonic meters
the velocity profile does not change with time, it is an indication
and other flow meters would suffer from stratification without
that surface roughness has probably remained unchanged.
knowing.
Fig.12 VELOCITY PROFILE - ROUGH
Fig11. VELOCITY PROFILE WITH CONVECTION
5. TRENDING
All the diagnostics discussed above can be trended to see if
anything is changing with time, by recording the data at suitable
intervals. The time interval depends on the specific application,
but it can be extended if nothing is seen to change.
The velocity profile is determined by the pipe and fittings
upstream of the meter. The pipe and fittings are fixed, so one
would normally not expected the velocity profile to change.
However there are some exceptions where the velocity profile
would change, due to:
DANIEL MEASUREMENT AND CONTROL WHITE PAPERS
Fig. 13 VELOCITY RATIO (B + C) / (A + D) - ROUGHNESS
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useful diagnostic.
As part of the signal detection many checks are made:
•
The noise, found upstream of the signal
•
The ratio of signal to noise
•
The standard deviation of the transit times
•
The signal quality, a measure of how quickly the
signal rises
•
A comparison between the transmitted and received
signals
•
A comparison between the upstream and downstream
received signals
5.2 Speed of Sound
The SOS will change with gas composition, temperature and
pressure, and can be a useful check on plant operation. In
particular, if nitrogen purging is required for safety, the SOS can
detect the nitrogen to natural gas change over.
The speed of sound depends only on the distance between the
transducers and the transit time. If it is not changing with time,
either internally between the chords or externally compared to
independent calculations, it is a very good sign that the meter
is functioning correctly, and the other inputs (P, T & gas
composition) needed for the calculation must be correct. If
it does change it could be due to deposits on the transducer
face or transducer damage. Deposits on the transducer would
probably be accompanied by deposit on the pipe wall, which
would also show in the velocity profile.
The SOS and velocity profile can certainly confirm that the
meter is functioning correctly, but if they reveal a problem then a
deeper level of diagnostics is required.
6 DIAGNOSTIC LEVEL
The discussion so far has made use of the four chord velocities
and the four chord values of SOS, which are directly available
from the meter output. There is a deeper level of diagnostic
associated with the digital signal processing.
6.1 Digital Signal Processing
The detection of the received ultrasonic signal must find
a consistent reliable zero crossing to use for the transit time
measurement. The transmitted signal strength is limited by
intrinsic safety considerations, so the received signal amplitude
is a function of the acoustic impedance of the gas, the meter size
and the gas velocity. An automatic gain control (AGC) is applied
to the received signal to always achieve the same amplitude,
to simplify detection. The value of the gain is a measure of the
health of the transducer or attenuation in the path, and is a
•
A check for peak switching
•
The tracking of a consistent zero crossing
If a signal does not pass all these tests it is not used for a
transit time measurement and an alarm is given that is decoded
to explain why the signal was rejected. This is a very useful
diagnostic. The number of signals used in a batch is reported
as Performance. A 100% performance is a sign that the meter
is working well, and is the normally expected performance up to
the full rated capacity of the meter. Anything less than 100% is
another useful diagnostic.
An example of the power of this deeper diagnostics is the ability
to detect wet gas [4]. The presence of liquid drops dispersed in
the gas affect the SOS, gain, standard deviation, signal to noise,
signal quality and performance.
Deposits on the pipe wall change the velocity profile and deposits
on the transducer may change the SOS, but they would also
affect the gain and signal to noise.
6.2 Multiple diagnostic parameters
The velocity profile gives a fingerprint, detects asymmetry, swirl
and cross flow, while the standard deviation of the velocity
indicates turbulence (5 parameters). The SOS gives another
fingerprint. It can be compared with calculations from gas
composition, pressure & temperature, and gives four values
from two different chord lengths, that can detect stratification &
convection currents, and can correct temperature measurements
(6 parameters). The DSP and AGC add a further 9 parameters
for each of the eight transducers. The waveform and spectra
(frequency content) can be displayed, another 2 parameters.
This gives a total of 22 potentially useful diagnostic parameters.
If all 22 parameters are normal, then there is no doubt that the
meter is working correctly. If the meter fails, there is sufficient
information to diagnose and fix the problem. If there are problems
with the flow metering system, and one has sufficient confidence
Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter
page 7
that the meter is working correctly, it is then possible to look
To change this situation, a manufacturer could offer a “health
for other system problems. Typical system problems are swirl,
check” service where say once a month he had remote access
turbulence, pulsations, fluctuations and noise.
to all the diagnostic data to give the meter a clean bill of health, or
raise warning signs. This should be mutually beneficial, leading
If a transducer is short circuited to the body by liquid or debris,
to conditional based maintenance and recalibration instead of
noise through the body will show on all transducers, while
fixed routine maintenance and mandatory recalibration intervals.
external noise will be much more on the transducers facing the
noise source. The meter will indicate where to look for the noise
source, upstream or downstream. The waveform and spectra
will also give information on the noise as well as the signal.
Gain can be useful, but remember it is dependent on the gas
Klaus J. Zanker, Daniel Industries, USA
7 REFERENCES
1. Klaus J. Zanker, INSTALLATION EFFECTS ON SINGLE-
pressure, or more precisely the gas acoustic impedance = SOS
AND MULTI-PATH ULTRASONIC METERS, Flomeko 2000
* density. If gain increase with time (for the same pressure) there
2. AGA Report No 10, SPEED OF SOUND IN NATURAL GAS
can be two causes: transducer damage or obstruction of the
AND OTHER RELATED HYDROCARBON GASES, July
acoustic path. Further diagnostic can follow from a series of
2002
questions:
3.
Klaus J. Zanker, THE EFFECTS OF REYNOLDS NUMBER,
•
Are one or more transducers involved?
WALL ROUGHNESS, AND PROFILE ASYMMETRY ON
•
Are one or more chords involved?
SINGLE- AND MULTI- PATH ULTRASONIC METERS,
•
Is it the bottom D-Chord, most likely to accumulate
NSFMW, Oct 1999
debris and liquid?
4. Klaus J. Zanker & Gregor J. Brown, THE PERFORMANCE
•
Has the velocity profile changed?
OF A MULTI-PATH ULTRASONIC METER WITH WET
•
Has the SOS profile changed?
GAS, NSFMW Oct 2000.
•
Has the signal quality changed?
In general, if any diagnostic parameter is suspect, and one
can postulates a cause, it then becomes possible to find other
parameters to try to confirm or refute the postulate.
7 CONCLUSIONS
A major advantage of the ultrasonic meter is that it produces an
abundance of diagnostic data.
If all the diagnostic parameters are normal, one can have
complete confidence that the meter is working correctly. This
confidence is very important, because one can then look for
problems in other parts of the metering system.
If a meter fails, the diagnostics quickly reveals the problem and
solution.
The range of decline between perfect performance and complete
failure is more difficult to quantify. Trending the diagnostic
parameters will certainly show if changes are occurring, but
knowing how much change is tolerable, before intervention is
necessary, is at present very much a judgment call.
As a meter manufacturer, we basically only see the extremes of
new meter calibrations and field failures. We do not have access
to long-term normal operational data in typical fiscal applications.
Emerson Process Management
Daniel Measurement and Control, Inc.
www.daniel.com
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