Operation of Ultrasonic Flow Meters Under Non-calibration Conditions

1 Abstract

Currently, the calibration of ultrasonic flowmeters used for natural gas metering is performed as much as possible on flow calibration devices. Since almost all of these devices use natural gas flowing through pipelines, it is usually impossible to change the parameters that affect the speed of sound, such as temperature, pressure, and gas composition. If these parameters differ from the values ​​in the calibration when the ultrasonic flowmeter is in use, will the calibration still be effective?

In order to quantitatively characterize the effect of changes in these parameters on the calibration of ultrasonic flowmeters, a series of carefully controlled calibration experiments were performed. The first experiment involved calibrating a 200 mm (8 inch) and a 300 mm (12 inch) ultrasonic flowmeter in a high-pressure circuit at the Southwest Research Institute (SwRI) using natural gas at a pressure of 2.8 MPa (400 psi). As additional reference, 200 mm and 300 mm turbine flowmeters were also used in the circuit. Then, the flow medium was changed to nitrogen, which changed the speed of sound by 16%, which is numerically equivalent to a natural gas pressure of 4.6 MPa (677 psi).

To further test the effect of pressure on the calibration of ultrasonic flowmeters, a series of statistical sound velocity measurements were made on a 300mm flowmeter using nitrogen at pressures ranging from 1.4MPa (200psi) to 7MPa (1000psi). The measurements showed that the change in sound velocity over this pressure range was within 0.03% of the calculated value.

In addition, further experiments were conducted to investigate the change in sound velocity caused by changes in temperature and fluid medium. Calibration experiments were performed with natural gas at 21℃ (70℉) and 10℃ (50℉), and with nitrogen at 21℃ (70℉) and 32℃ (90℉). For each series of calibrations, the average calibration curve was compared to determine the effect of the change on the calibration. Under conditions that met the expected device and flowmeter reproducibility, the calibration of the ultrasonic flowmeter did not respond to changes in sound velocity, temperature, and pressure. The small changes observed when the fluid medium used for calibration was changed from natural gas to nitrogen were due to the different equations of state used for the two gases.

These test results prove that if the calibration procedure of ultrasonic flowmeter is feasible under one set of conditions, it can also be used under other conditions, including with different gas media.

2 Introduction

The principle of ultrasonic flowmeter for natural gas measurement in related transactions is to measure the propagation time of ultrasonic waves in gas. When the ultrasonic wave is in line with the flow direction of the fluid, the propagation time is shorter than that in the counterflow. The difference in propagation time between the two states is used to calculate the average velocity of the gas flow. The actual volume flow rate can be expressed as follows:

Here K = meter factor, ∆T = time difference, T1 = time of propagation in downstream, T2 = time of propagation in upstream

Since the flow equation only includes the physical dimensions of the flow meter and the propagation time, it is independent of the speed of sound (SOS) in the flowing gas. Therefore, it can be assumed that the determination of gas velocity is independent of factors that affect the speed of sound in the gas, such as temperature, pressure and gas composition. If this assumption is not correct, the validity of the calibration of ultrasonic flowmeters under conditions different from those in the field operation should be considered.

First, the determination of gas velocity for ultrasonic flowmeters is independent of the speed of sound, but there may be some secondary effects due to the following reasons.

Acoustic impedance changes the coupling of the signal to the gas;
Changes in the Reynolds number. The Reynolds number is proportional to the ratio of the specific gravity (SG) to the viscosity;
The wavelength (WL) of the signal changes with the gas composition.

It is interesting to note these parameters for different media. The following table is for standard conditions, note that for a given pipe size and flow rate, the Reynolds number is almost constant.

Table 1 Gas properties

When changing from natural gas to air or nitrogen, many gas properties change, such as sonic velocity, specific gravity, and viscosity. However, since they also vary with temperature and pressure, there is a conceivable overlap in gas properties for ultrasonic flowmeters over the range of operating conditions, indicating that deviations from standard conditions are not that important.

3 Research Objectives

The research objectives described in this paper were to determine the effects of temperature, pressure, and fluid media changes on gas ultrasonic flowmeters. In addition to verifying ultrasonic flowmeter technology, the procedure also has the effect of supporting the calibration of these natural gas flowmeters with nitrogen or air.

Currently, there are only two facilities in North America that can calibrate ultrasonic flowmeters larger than 200 mm over a wide range of flow rates. The installation of these flowmeters is increasing at a rate of more than 10% per year. In the future, the calibration facilities will become very limited. These calibration facilities may need to be recalibrated after only a few years of use.

If the calibration of ultrasonic flowmeters is limited to natural gas installations, the possibility of building new installations will be limited due to location and cost. However, if it can be demonstrated that the calibration is equivalent with other media, the possibility of building new installations is greatly improved. The calibration of natural gas flowmeters with air is not unique to ultrasonic flowmeters. Almost all turbine flowmeters used for natural gas measurement and residential gas meters can be calibrated with air.

4 Flow Loop Calibration

To achieve the objectives of this procedure, experiments were performed at zero flow and other flow conditions. Zero flow was achieved to determine the possible effects of pressure on calibration.

4.1 Flow Loop Experiments

Since there are no pressurized flow calibration devices that can be calibrated with both natural gas and air in the same test loop, the best choice is to use inert nitrogen, which has properties close to those of air (air is 78% nitrogen). Southwest Research Institute has a circulation system (not part of the gas pipeline) that is the only facility in North America that can be used for both nitrogen and natural gas testing in the same loop with the same instrumentation. Although the sonic nozzle device is a calibration device that uses a weighing system to determine mass flow rate, the sonic nozzle flow rate calculation requires gas composition and an equation of state to determine gas properties. It was also decided to use a reference turbine flowmeter in the loop to compare the two volumetric flowmeters (i.e., turbine and ultrasonic flowmeters). This reference meter method is less dependent on gas composition than the flowmeter-to-sonic nozzle method.

A series of standard calibrations were performed in the high pressure loop at the Southwest Research Institute using nitrogen and natural gas as the test fluids. In addition, the temperature was changed to change the velocity of sound. The test setup, including instrumentation, piping layout, and data acquisition system, remained unchanged during these calibration experiments.

Two Daniel 300mm multi-channel ultrasonic flowmeters were already included in the high pressure loop, and a Daniel 300mm gas turbine flowmeter was installed in the reference section. A Daniel 200mm multi-channel flowmeter was installed in the test section of the loop immediately following a Daniel 200mm turbine flowmeter. The 200mm flowmeter was installed in the test section of the high pressure loop, protected from direct sunlight. A flow conditioner (Daniel Profile) was installed 5D downstream of the change in diameter between the 300mm and 200mm pipes. There was a minimum of 5D between the two flowmeters, with up to 24D between the flow conditioner and the ultrasonic flowmeter. The 200mm turbine flowmeter is installed in the 200mm diameter section and is at least 5D long from the change in diameter from 200mm to 300mm. [page]

The full calibration includes 7 flow points, repeated 6 times at each point. The flow points on the 200mm flowmeter are 1.68, 3.35, 6.71, 10.1, 13.4, 16.8 and 20m/s (5.5, 11, 22, 33, 44, 55 and 66ft/sec) with natural gas, and the corresponding small flow rate is displayed on the 300 flowmeter. These flow rates are measured with a sonic nozzle and tested with natural gas and nitrogen respectively. The circuit distribution diagram of these calibrations is shown in Figure 1.

Figure 1. High-voltage calibration circuit at Southwest Research Institute

The calibration sequence is as follows:

(1) Calibrate with natural gas at 2.8 MPa and 21 °C;
(2) Change the temperature to 10 °C and recalibrate. The change in temperature reduces the sound velocity in natural gas, which makes it very close to the sound velocity in nitrogen;
(3) Change the medium from natural gas to nitrogen. Calibrate in nitrogen at 2.8 MPa and 21 °C. Note that in order to use the same sonic nozzle, the flow rate value in the two sonic velocity ratios is reduced by about 0.84;
(4) Change the temperature to 32 °C. The change in temperature increases the sound velocity in nitrogen. This makes it very close to the sound velocity in natural gas. The

following data from the above 5 tables were collected at each flow point:

Chord sound velocity and average sound velocity of the ultrasonic flowmeter;
average gas flow rate;
calibration flow rate;
calibration sound velocity (calculated by Southwest Research Institute);
temperature and pressure of Southwest Research Institute.

4.2 Data Analysis

The curves of the natural gas test results and the nitrogen test results were compared. Calibration data were analyzed day-to-day and temperature-to-temperature for the following items:

flow calibration data (flowmeter to sonic nozzle);
flow calibration data (ultrasonic flowmeter to turbine flowmeter);
Chord velocity data (calculated velocity based on Chord velocity pairs from AGA Report No. 8 and gas composition analysis).

Southwest Research Institute proposes a total uncertainty of about 0.25% for calibrating a flowmeter at a 95% confidence level. Comparing the two calibrations gives a total uncertainty of 0.35%. However, in this case, the only difference between the two calibrations being compared was the test fluid. The sonic nozzle, turbine flowmeter, pipeline layout, data acquisition, and ultrasonic flowmeter were all identical. By comparing the differences between different calibrations of the same flowmeter, much of the bias against the system can be eliminated. The uncertainty in the equation of state for both nitrogen and natural gas was calculated to be 0.1%. The random uncertainty of the system operating on different days and under different environmental conditions was calculated to be 0.14%. The expected total uncertainty can be achieved by calibrating with natural gas and nitrogen for the same flowmeter, the same sonic nozzle, and the same pipeline layout.

4.3 Results

Each of the five flowmeters (two turbine flowmeters and three ultrasonic flowmeters) was calibrated eight times.

Four calibrations were performed over two days at two temperatures, 21°C and 10°C, using natural gas; and
four calibrations were performed over two days at two temperatures, 21°C and 32°C, using nitrogen.

The initial calibration with natural gas at 21°C was used as a reference for each flowmeter. Another numbered polynomial was added to the data analysis to generate calibration coefficients, which were used in subsequent calibrations. The notation for the calibration curves is as follows:

NG 10.14 = test at 10°C on August 14, 2001 with natural gas;
N2 21.17 = test at 21°C on August 17, 2001 with nitrogen.

Figure 2 200mm (8-inch) ultrasonic flowmeter calibration curve using natural gas and nitrogen

Figure 2 shows the results of eight calibrations of the 200 mm ultrasonic flowmeter in the loop test section. The following observations can be made from the curves of the calibration runs. The

day-to-day calibration data for both gases are very reproducible, averaging about 0.1%.
The difference between the two calibrations at 10 °C and 21 °C is even smaller than the day-to-day calibration data for both gases, averaging less than 0.1%.
The difference between the two calibration curves for natural gas and nitrogen is averaging less than 0.2%, as expected in Section 4.3. The nitrogen calibration curve lies flat below the natural gas calibration curve. It

is also interesting to compare the calibrations of the 200 mm turbine flowmeter with the two gases. These are shown in Figure 3. The deviation in the calibration result at 32 °C with nitrogen at the flow rate of 11.3 m/s is believed to be due to instrument error. For the given gas, the calibration repeatability is very good. Again, the curve for the calibration with nitrogen lies below the natural gas calibration curve. At these pressure conditions, gas composition effects are the most likely explanation for the perceived differences in the two gas calibration curves, since the turbine flowmeter showed no density effects in many previous tests.

Figure 3 200mm (8-inch) turbine flowmeter calibration curve using natural gas and nitrogen [page]

If the turbine flowmeter is used as a reference meter, the calibration curve shown in Figure 2 now becomes that shown in Figure 4. In this case, the calibration curves for the two gas runs overlap. For the 200 mm flowmeter, the maximum flow rate that can be achieved with natural gas in the high pressure circuit is 20 m/s. In the calibration experiment with nitrogen, this flow rate was reduced to 16.8 m/s in order to use the same sonic nozzle.

Figure 4 200mm (8-inch) ultrasonic flowmeter calibration curve using natural gas and nitrogen
(using turbine flowmeter as reference)

The calibration data from the 300 mm flowmeter gave similar results. However, the calibration data was slightly more scattered at low flows because the test flow points were operated below 33% of the full scale of the flowmeter and the calibration process was performed under sunlight. The calibration data for the 300 mm ultrasonic flowmeter and the 300 mm turbine flowmeter are shown in Figures 5 and 6. Figure 7 shows the ultrasonic flowmeter calibration curve with the turbine flowmeter as the reference, and the calibration curves for natural gas and nitrogen overlap. The same is true for the 200 mm flowmeter.

Figure 5 300mm (12 inch) ultrasonic flowmeter calibration curve using natural gas and nitrogen

Figure 6 300mm (12 inch) turbine flowmeter calibration curve using natural gas and nitrogen

Figure 7 300mm (12 inch) ultrasonic flowmeter calibration curve using natural gas and nitrogen
(using turbine flowmeter as reference)

During the calibration of all ultrasonic flowmeters, the velocity of sound was recorded. Southwest Research Institute used an on-line Daniel Danalyzer gas chromatograph to obtain gas composition data and used this data together with temperature, pressure and the equation of state presented in the AGA NO 8 report to theoretically calculate the velocity of sound with an average difference of less than 0.04%.

5 Pressure Measurements

In a 1998 paper, Grimley and Bowles [1] presented calibration data for four different configurations of 200 mm ultrasonic flowmeters. The experiments were designed to determine the effect of each piping arrangement and flow condition setting on the calibration results. Baseline measurements were made for each flowmeter at 2.8 MPa and 6.2 MPa. Both ultrasonic flowmeters showed a difference of up to 0.5% between the two pressures.

Grimley [2] also made measurements using multi-channel flowmeters from three manufacturers and published the results that year. These measurements were made at 1.4 MPa, 2.8 MPa and 6.9 MPa. The report suggested that the pressure dependence of the transducer behavior could explain some of the flowmeter calibration results. Although Grimley concluded that this effect was minor in the case of the Daniel flowmeter, we decided to look at this effect in more detail. Our experiments are described in the following section.

5.1 Determination of the Velocity of Sound

The delay time of an ultrasonic flowmeter is the time from the time the transmitting transducer sends the signal to the time the sound wave is received by the receiving transducer minus the propagation time of the ultrasound wave in the medium. If the delay time at the transducer varies with pressure, an error will be reflected in the measured flow rate. As pointed out in Grimley's report No. 2 [2], the error in flow rate will be approximately twice the error in the delay time (or velocity of sound). [page]

During the production of the Daniel ultrasonic flowmeter, the delay time of each pair of transducers is measured and the value is stored in the flowmeter electronics. This measurement is made while the flowmeter is filled with pure nitrogen at a pressure of 1.4 MPa. In order to determine the possible effect of pressure on the delay time, the sound velocity in nitrogen was measured at 2.8MPa and 6.9MPa using a 300mm ultrasonic flowmeter.

Figure 8 — Difference between measured and calculated sound velocity

5.2 Results

The results of the measurement of the velocity of sound as a function of pressure are shown in Figure 8, together with the error curve of the velocity determination. This curve was obtained by comparing the velocity of sound measured by the flow meter with the velocity of sound calculated based on the equation of state and the data of pressure, temperature and gas composition in AGA Report No. 8.

As shown in the figure, the error measured over the pressure span of 5.5 MPa is 0.03%, which only accounts for 0.06% of the flow rate error. These statistical results are almost completely consistent with the results of Grimley's flow loop test.

Grimley concluded that for the Daniel flow meter, the changes in the velocity of sound caused by pressure are too small to cause appreciable errors in the measured flow rate. In addition, he pointed out that the changes in the flow rate distribution caused by pressure are not large enough to cause deviations in the Daniel flow meter.

6 Conclusions

The objectives of the research program were achieved, with the following conclusions:

the average error between the measured sound velocity values ​​recorded by SWRI in all experiments and the theoretically calculated values ​​was 0.04%;
the ultrasonic flowmeters showed no variation when calibrated with natural gas from 21 °C to 10 °C or with nitrogen from 21 °C to 32 °C, despite dependence on the temperature of the gas;
the day-to-day variation in the data for the SWRI high-pressure loop calibration results was less than 0.1% for both gases. The reproducibility of the calibration equipment and flowmeters was high;
with the turbine flowmeter as the reference, a reference system based on volumetric measurement, the calibration of the ultrasonic flowmeter ultimately showed no difference between natural gas and nitrogen as the medium;
with the sonic nozzle as the reference, a reference system based on mass measurement, the ultrasonic and turbine flowmeters showed a variation of slightly less than 0.2% when the gas changed from natural gas to nitrogen. This variation is small, but may be significant for the gas composition data associated with the calibration of the sonic nozzle;
the series of calibration analysis data conducted by SWRI proves that the calibration procedure for ultrasonic flowmeters under one set of conditions is equally valid if applied to other conditions, including different gases. This will allow the construction of air calibration facilities in convenient areas. However, the operating conditions at the calibration point must be strictly controlled to match the conditions at the point of use of the ultrasonic flowmeter.
The statistical determination of the sound velocity of a 300mm flowmeter filled with nitrogen in the pressure range of 5.5MPa showed only a 0.03% error with the calculated value. This negates the possibility that pressure has a significant effect on the characteristics (delay time) of the ultrasonic transducer.

7 References
[1] TAGRIMLEY and EBBOWLES "Industrial Researcher Evaluates Ultrasonic Flowmeter Performance" Pipeline and Gas Industry December 1998.
[2] TAGRIMLEY "Effects of Pipe Diameter Mismatch and Line Pressure Variation on Ultrasonic Gas Flowmeter Performance" GRI-02/0031 February 2002. (end)