Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meterpage 1DANIEL MEASUREMENT AND CONTROL WHITE PAPERS

1 INTRODUCTIONThe primary function of the ultrasonic meter is to measure the actual volume flow rate. The process involves measuring four velocities on chords located in four different radial positions andin two different vertical planes. The eight transducers are fired about 50 times per second and the transit times to traverse each chord in both directions are measured. This vast array of data can be processed to yield useful diagnostic information, which forms the subject of this paper and shows that the four-path ultrasonic meter does much more than just measure the flow rate. It has sufficient diagnostic ability to confirm the authenticity of the measurement, and develop the source for conditional based maintenance and re-calibration.

2 METER GEOMETRY AND FUNCTION

There are two equations for the transit time with (t1) and against (t2) the flow, which can be solved for the chord velocity (Vi)

The average velocity (V) and actual volume flow rate (Q) are found from:

3 VELOCITY PROFILEThe four chordal velocities give an indication of the velocity profile in the meter, established by the flow through the upstream pipe work. Three helpful ratios can be defined as: Asymmetry =(VA + VB)/(VC + VD), Cross flow = (VA + VC)/(VB + VD) and Swirl = (VB+ VC)/(VA + VD).The asymmetry compares the flow in the top half of the pipe with that in the bottom half; in good condition it should be close to 1. The cross flow compares the chords in one plane with those inthe other plane at right angles: in good condition it should be close to 1. The swirl compares the inner chords to the outer chords and it is an indicator of swirl due to both the different radial locations and planes. In good condition the swirl should be close to 1.042/0.89 = 1.17 [1].

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Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meter

Fig, 1a. End View Fig. 1b. Top View

Where C = speed of sound

L = distance between transducers

X = axial distance in the flow

R = meter radius

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.

Actual measured ratios are shown in Fig. 4 for a 20” meter.

Fig. 2 VELOCITY PROFILE WITH SWIRL

Fig. 3 SWIRL RATIO (Vb+Vc)/(Va+Vd)

Fig. 3 SWIRL RATIO (Vb+Vc)/(Va+Vd)

Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meterpage 3

Because of tolerances in the manufacture of the ultrasonic meter and the difficulty of achieving ideal fully developed flow, the actual ratios are never exactly at their theoretical values, and give the meter a unique fingerprint. However they are usually within ±2%, which is sufficient to say that the flow profile is near perfect, which is not surprising since Fig.4 comes from 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 changed significantly.

3.1 Turbulence, pulsation and fluctuationIn discussing the velocity profile we have been considering the 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 deviationσΔt, and then the ratio σΔt/Δt is a measure of turbulence or velocity fluctuation.

Some typical values are given in Fig. 5, for the inner and outer 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

is higher on the outer chord, nearer the pipe wall where there is more shear.

If flow pulsations or fluctuations are present, this turbulence parameter will increase above the 2% to 5% value associated with good flow.

4 SPEED OF SOUNDThe 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)/4The speed of sound can be used as a diagnostic in several ways:

4.1 Compare a measured and calculated valueThe speed of sound can be calculated from independent 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 the smallest ultrasonic meter typically used and the small length and short transit time make it the most difficult size to accuratelydetermine the speed of sound.

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. 5 TURBULENCE % = 100* STD-DEV Dt / Dt

Fig. 6 4” METER SOS DEVIATION FROM AGA 10

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4.2 Compare the 4 chordal values with one anotherAt 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.

The values of speed of sound on all four chords agree to within ± 1 ft/s This is not quite as good a test as the one in section 4.1, 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 valueBecause of manufacturing tolerances the four chordal values of speed of sound will never be exactly equal. These small differences can be used as another fingerprint of the meter. See Fig.8 as an example

4.4 Check the agreement between chords of different lengthFig.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

= 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 sound. Thus the different chord lengths allow a dynamic method of checking the delay times.

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.

Note: three examples have been shown where the SOS variations are 0.1%, 0.02% and 0.002%. A good value for the average field application would be 0.05%.

4.5 Correction for stratificationAn 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.

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

Fig. 7 CHORDAL SPEED OF SOUND FT/S

Fig. 8 SOS DIFFERENCE FROM AVERAGE %

Fig 9. SOS LONG - SOS SHORT %

Fig 10. TEMPERATURE [SOS] GRADIENT

Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meterpage 5

higher density gas, with lower temperature and lower speed of sound. In this case a SOS gradient of 8 ft/s corresponds to the temperature gradient of 6oF. This temperature difference also drives a natural convection current: gas heated by the pipe wall rises to the top of the pipe, while cold gas in the center falls to the bottom of the pipe. This convection current, which is normal to the axial flow, pushes the maximum axial velocity down from the center of the pipe, and the effect is seen in the velocity profile shown in Fig. 11.

Another consequence of stratification is a poor non-representative gas temperature measurement. A reasonable approach to the correct gas temperature is a Flow Weighted Mean Temperature (FWMT) based on using the same velocity flow weighting factors Wi for the chordal temperatures. The result in this case is FWMT = 73.5o F seen in Fig.10. Unfortunately the high pipe temperature and the highest gas temperature influence the thermo-well located on top of the pipe, and reads 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 be used to recognize and correct the error; this is unique to the chordal ultrasonic meter, while non-chordal ultrasonic meters and other flow meters would suffer from stratification without knowing.

5. TRENDINGAll 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:

• An upstream flow control valve being adjusted• An upstream branching flow of varying proportion to

the metered flow• A flow conditioner trapping debris• Erosion, corrosion or deposition changing the

upstream pipe roughness

5.1 Pipe roughnessThe meter can detect an increase in pipe roughness by its effect on the velocity profile [3]. In general the velocity profile depends upon both roughness and Reynolds Number, but at the high Re No associated with natural gas transport the roughness effects dominate. The profile can be described by the ratio (VB+ VC)/(VA + VD), but here we are looking for change from a flatter profile to a more pointed profile (Fig.12) with time, and not swirl.The ratio (VB+ VC)/(VA + VD) can be linked to pipe roughness (Fig. 13) in terms of relative roughness k/D, where k = the roughness height and D = the pipe diameter.

Again the idea is that fixed piping gives a fixed velocity profile, so a changing profile with time is an indication of pipe roughness. If the velocity profile does not change with time, it is an indicationthat surface roughness has probably remained unchanged.

Fig11. VELOCITY PROFILE WITH CONVECTION

Fig.12 VELOCITY PROFILE - ROUGH

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5.2 Speed of SoundThe 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 toindependent 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 LEVELThe 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 ProcessingThe 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

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• 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 parametersThe 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 problemswith the flow metering system, and one has sufficient confidence

Fig. 13 VELOCITY RATIO (B + C) / (A + D) - ROUGHNESS

Diagnostic Ability of the Daniel Four Path Ultrasonic Flow Meterpage 7

that the meter is working correctly, it is then possible to look for other system problems. Typical system problems are swirl, turbulence, pulsations, fluctuations and noise.

If a transducer is short circuited to the body by liquid or debris, noise through the body will show on all transducers, while 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 pressure, or more precisely the gas acoustic impedance = SOS * density. If gain increase with time (for the same pressure) there can be two causes: transducer damage or obstruction of the acoustic path. Further diagnostic can follow from a series of questions:

• Are one or more transducers involved?• Are one or more chords involved?• Is it the bottom D-Chord, most likely to accumulate

debris and liquid?• Has the velocity profile changed?• Has the SOS profile changed?• 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 CONCLUSIONSA 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.

To change this situation, a manufacturer could offer a “health check” service where say once a month he had remote access to all the diagnostic data to give the meter a clean bill of health, or raise warning signs. This should be mutually beneficial, leading to conditional based maintenance and recalibration instead of fixed routine maintenance and mandatory recalibration intervals.

Klaus J. Zanker, Daniel Industries, USA

7 REFERENCES1. Klaus J. Zanker, INSTALLATION EFFECTS ON SINGLE-

AND MULTI-PATH ULTRASONIC METERS, Flomeko 20002. AGA Report No 10, SPEED OF SOUND IN NATURAL GAS

AND OTHER RELATED HYDROCARBON GASES, July 2002

3. Klaus J. Zanker, THE EFFECTS OF REYNOLDS NUMBER, WALL ROUGHNESS, AND PROFILE ASYMMETRY ON SINGLE- AND MULTI- PATH ULTRASONIC METERS, NSFMW, Oct 1999

4. Klaus J. Zanker & Gregor J. Brown, THE PERFORMANCE OF A MULTI-PATH ULTRASONIC METER WITH WET GAS, NSFMW Oct 2000.

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